TSTP Solution File: SWW301+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW301+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:06:53 EDT 2024
% Result : Theorem 157.29s 157.21s
% Output : CNFRefutation 157.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW301+1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 04:56:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.52/0.55 start to proof:theBenchmark
% 156.96/157.03 %-------------------------------------------
% 156.96/157.03 % File :CSE---1.7
% 156.96/157.03 % Problem :theBenchmark
% 156.96/157.03 % Transform :cnf
% 156.96/157.03 % Format :tptp:raw
% 156.96/157.03 % Command :java -jar mcs_scs.jar %d %s
% 156.96/157.03
% 156.96/157.03 % Result :Theorem 142.890000s
% 156.96/157.03 % Output :CNFRefutation 142.890000s
% 156.96/157.03 %-------------------------------------------
% 156.96/157.04 %------------------------------------------------------------------------------
% 156.96/157.04 % File : SWW301+1 : TPTP v8.2.0. Released v5.2.0.
% 156.96/157.04 % Domain : Software Verification
% 156.96/157.04 % Problem : Hoare's Logic with Procedures 434830, 5000 axioms selected
% 156.96/157.04 % Version : Especial.
% 156.96/157.04 % English :
% 156.96/157.04
% 156.96/157.04 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 156.96/157.04 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 156.96/157.04 % Source : [Bla11]
% 156.96/157.04 % Names : hoare_434830.5000.p [Bla11]
% 156.96/157.04
% 156.96/157.04 % Status : ContradictoryAxioms
% 156.96/157.04 % Rating : 0.75 v8.1.0, 0.81 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.83 v7.0.0, 0.87 v6.4.0, 0.85 v6.3.0, 0.75 v6.2.0, 0.84 v6.1.0, 0.87 v6.0.0, 0.83 v5.5.0, 0.89 v5.4.0, 0.96 v5.3.0, 0.93 v5.2.0
% 156.96/157.04 % Syntax : Number of formulae : 5224 (1671 unt; 0 def)
% 156.96/157.04 % Number of atoms : 12725 (4453 equ)
% 156.96/157.04 % Maximal formula atoms : 13 ( 2 avg)
% 156.96/157.04 % Number of connectives : 8519 (1018 ~; 147 |; 733 &)
% 156.96/157.04 % ( 899 <=>;5722 =>; 0 <=; 0 <~>)
% 156.96/157.04 % Maximal formula depth : 22 ( 6 avg)
% 156.96/157.04 % Maximal term depth : 19 ( 2 avg)
% 156.96/157.04 % Number of predicates : 146 ( 145 usr; 0 prp; 1-6 aty)
% 156.96/157.04 % Number of functors : 387 ( 387 usr; 52 con; 0-7 aty)
% 156.96/157.04 % Number of variables : 16582 (16430 !; 152 ?)
% 156.96/157.04 % SPC : FOF_CAX_RFO_SEQ
% 156.96/157.04
% 156.96/157.04 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 156.96/157.04 % 2011-03-01 11:31:32
% 156.96/157.04 %------------------------------------------------------------------------------
% 156.96/157.04 %----Relevant facts (4983)
% 156.96/157.04 fof(fact_ext,axiom,
% 156.96/157.04 ! [V_g_2,V_f_2] :
% 156.96/157.04 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 156.96/157.04 => V_f_2 = V_g_2 ) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_empty,axiom,
% 156.96/157.04 ! [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))) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 156.96/157.04 ! [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))) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_triple_Oinject,axiom,
% 156.96/157.04 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
% 156.96/157.04 ( 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)
% 156.96/157.04 <=> ( V_fun1_2 = V_fun1_H_2
% 156.96/157.04 & V_com_2 = V_com_H_2
% 156.96/157.04 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_cut,axiom,
% 156.96/157.04 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 156.96/157.04 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 156.96/157.04 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 156.96/157.04 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_hoare__derivs_Oinsert,axiom,
% 156.96/157.04 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 156.96/157.04 ( 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))))
% 156.96/157.04 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
% 156.96/157.04 => 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)) ) ) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_triple_Orecs,axiom,
% 156.96/157.04 ! [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) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_triple_Osimps_I2_J,axiom,
% 156.96/157.04 ! [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) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_empty__not__insert,axiom,
% 156.96/157.04 ! [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) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_insert__not__empty,axiom,
% 156.96/157.04 ! [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)) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_doubleton__eq__iff,axiom,
% 156.96/157.04 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 156.96/157.04 ( 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))))
% 156.96/157.04 <=> ( ( V_a_2 = V_ca_2
% 156.96/157.04 & V_b_2 = V_d_2 )
% 156.96/157.04 | ( V_a_2 = V_d_2
% 156.96/157.04 & V_b_2 = V_ca_2 ) ) ) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_singleton__inject,axiom,
% 156.96/157.04 ! [V_b_2,V_a_2,T_b] :
% 156.96/157.04 ( 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)))
% 156.96/157.04 => V_a_2 = V_b_2 ) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_bot__apply,axiom,
% 156.96/157.04 ! [V_x_2,T_c,T_b] :
% 156.96/157.04 ( class_Orderings_Obot(T_b)
% 156.96/157.04 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_hoare__derivs_OSkip,axiom,
% 156.96/157.04 ! [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)))) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 156.96/157.04 ! [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)))) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_conseq1,axiom,
% 156.96/157.04 ! [V_Pa_2,V_Qa_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] :
% 156.96/157.04 ( 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))))
% 156.96/157.04 => ( ! [B_Z,B_s] :
% 156.96/157.04 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 156.96/157.04 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 156.96/157.04 => 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)))) ) ) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_Comp,axiom,
% 156.96/157.04 ! [V_R_2,V_d_2,V_Qa_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
% 156.96/157.04 ( 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))))
% 156.96/157.04 => ( 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))))
% 156.96/157.04 => 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)))) ) ) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_the__elem__eq,axiom,
% 156.96/157.04 ! [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 ).
% 156.96/157.04
% 156.96/157.04 fof(fact_insert__code,axiom,
% 156.96/157.04 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 156.96/157.04 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 156.96/157.04 <=> ( V_y_2 = V_x_2
% 156.96/157.04 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_insert__commute,axiom,
% 156.96/157.04 ! [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)) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_insert__absorb2,axiom,
% 156.96/157.04 ! [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) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_com_Osimps_I12_J,axiom,
% 156.96/157.04 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 156.96/157.04
% 156.96/157.04 fof(fact_com_Osimps_I13_J,axiom,
% 156.96/157.05 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 156.96/157.05
% 156.96/157.05 fof(fact_com_Osimps_I3_J,axiom,
% 156.96/157.05 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 156.96/157.05 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 156.96/157.05 <=> ( V_com1_2 = V_com1_H_2
% 156.96/157.05 & V_com2_2 = V_com2_H_2 ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_conseq12,axiom,
% 156.96/157.05 ! [V_Qa_2,V_Pa_2,V_Q_Ha_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] :
% 156.96/157.05 ( 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_Ha_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 156.96/157.05 => ( ! [B_Z,B_s] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 156.96/157.05 => ! [B_s_H] :
% 156.96/157.05 ( ! [B_Z_H] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s))
% 156.96/157.05 => hBOOL(hAPP(hAPP(V_Q_Ha_2,B_Z_H),B_s_H)) )
% 156.96/157.05 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) )
% 156.96/157.05 => 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)))) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_subset__singletonD,axiom,
% 156.96/157.05 ! [V_x_2,V_A_2,T_b] :
% 156.96/157.05 ( 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)))))
% 156.96/157.05 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 156.96/157.05 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_singletonE,axiom,
% 156.96/157.05 ! [V_a_2,V_b_2,T_b] :
% 156.96/157.05 ( 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)))))
% 156.96/157.05 => V_b_2 = V_a_2 ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_singleton__iff,axiom,
% 156.96/157.05 ! [V_a_2,V_b_2,T_b] :
% 156.96/157.05 ( 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)))))
% 156.96/157.05 <=> V_b_2 = V_a_2 ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_folding__one_Osingleton,axiom,
% 156.96/157.05 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 156.96/157.05 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 156.96/157.05 => 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 ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_fold1Set__sing,axiom,
% 156.96/157.05 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 156.96/157.05 ( 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))
% 156.96/157.05 <=> V_a_2 = V_b_2 ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_insert__is__Un,axiom,
% 156.96/157.05 ! [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) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_insert__Diff__single,axiom,
% 156.96/157.05 ! [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) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Diff__insert2,axiom,
% 156.96/157.05 ! [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) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_order__refl,axiom,
% 156.96/157.05 ! [V_x,T_a] :
% 156.96/157.05 ( class_Orderings_Opreorder(T_a)
% 156.96/157.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_equalityCE,axiom,
% 156.96/157.05 ! [V_ca_2,T_b,V_B_2,V_A_2] :
% 156.96/157.05 ( V_A_2 = V_B_2
% 156.96/157.05 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 156.96/157.05 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) )
% 156.96/157.05 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 156.96/157.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_equalityI,axiom,
% 156.96/157.05 ! [V_B_2,V_A_2,T_b] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 156.96/157.05 => V_A_2 = V_B_2 ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_emptyE,axiom,
% 156.96/157.05 ! [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)))) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_insertE,axiom,
% 156.96/157.05 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 156.96/157.05 => ( V_a_2 != V_b_2
% 156.96/157.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_insertCI,axiom,
% 156.96/157.05 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 156.96/157.05 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 156.96/157.05 => V_a_2 = V_b_2 )
% 156.96/157.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_subsetD,axiom,
% 156.96/157.05 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.05 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 156.96/157.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_UnE,axiom,
% 156.96/157.05 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 156.96/157.05 ( 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)))
% 156.96/157.05 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 156.96/157.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_UnCI,axiom,
% 156.96/157.05 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 156.96/157.05 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 156.96/157.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
% 156.96/157.05 => 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))) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_DiffI,axiom,
% 156.96/157.05 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 156.96/157.05 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 156.96/157.05 => 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))) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_DiffE,axiom,
% 156.96/157.05 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 156.96/157.05 ( 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)))
% 156.96/157.05 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 156.96/157.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_empty__subsetI,axiom,
% 156.96/157.05 ! [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)) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_subset__refl,axiom,
% 156.96/157.05 ! [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)) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Un__upper1,axiom,
% 156.96/157.05 ! [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))) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Un__upper2,axiom,
% 156.96/157.05 ! [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))) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Un__absorb,axiom,
% 156.96/157.05 ! [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 ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Diff__subset,axiom,
% 156.96/157.05 ! [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)) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_le__fun__def,axiom,
% 156.96/157.05 ! [V_g_2,V_f_2,T_b,T_c] :
% 156.96/157.05 ( class_Orderings_Oord(T_c)
% 156.96/157.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 156.96/157.05 <=> ! [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))) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_mem__def,axiom,
% 156.96/157.05 ! [V_A_2,V_x_2,T_b] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.05 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Un__commute,axiom,
% 156.96/157.05 ! [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) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_linorder__linear,axiom,
% 156.96/157.05 ! [V_y,V_x,T_a] :
% 156.96/157.05 ( class_Orderings_Olinorder(T_a)
% 156.96/157.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 156.96/157.05 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_subset__Un__eq,axiom,
% 156.96/157.05 ! [V_B_2,V_A_2,T_b] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.05 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_set__eq__subset,axiom,
% 156.96/157.05 ! [T_b,V_B_2,V_A_2] :
% 156.96/157.05 ( V_A_2 = V_B_2
% 156.96/157.05 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_order__eq__iff,axiom,
% 156.96/157.05 ! [V_y_2,V_x_2,T_b] :
% 156.96/157.05 ( class_Orderings_Oorder(T_b)
% 156.96/157.05 => ( V_x_2 = V_y_2
% 156.96/157.05 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 156.96/157.05 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Un__Diff__cancel,axiom,
% 156.96/157.05 ! [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) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Un__left__absorb,axiom,
% 156.96/157.05 ! [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) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Un__left__commute,axiom,
% 156.96/157.05 ! [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)) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Diff__iff,axiom,
% 156.96/157.05 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 156.96/157.05 ( 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)))
% 156.96/157.05 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 156.96/157.05 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Un__iff,axiom,
% 156.96/157.05 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 156.96/157.05 ( 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)))
% 156.96/157.05 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 156.96/157.05 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Diff__idemp,axiom,
% 156.96/157.05 ! [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) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Un__Diff__cancel2,axiom,
% 156.96/157.05 ! [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) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Diff__subset__conv,axiom,
% 156.96/157.05 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 156.96/157.05 ( 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))
% 156.96/157.05 <=> 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))) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Un__assoc,axiom,
% 156.96/157.05 ! [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)) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_Un__Diff,axiom,
% 156.96/157.05 ! [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)) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_bex__Un,axiom,
% 156.96/157.05 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 156.96/157.05 ( ? [B_x] :
% 156.96/157.05 ( 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)))
% 156.96/157.05 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 156.96/157.05 <=> ( ? [B_x] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 156.96/157.05 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 156.96/157.05 | ? [B_x] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 156.96/157.05 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_ball__Un,axiom,
% 156.96/157.05 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 156.96/157.05 ( ! [B_x] :
% 156.96/157.05 ( 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)))
% 156.96/157.05 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 156.96/157.05 <=> ( ! [B_x] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 156.96/157.05 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 156.96/157.05 & ! [B_x] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 156.96/157.05 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_equalityD1,axiom,
% 156.96/157.05 ! [T_b,V_B_2,V_A_2] :
% 156.96/157.05 ( V_A_2 = V_B_2
% 156.96/157.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_equalityD2,axiom,
% 156.96/157.05 ! [T_b,V_B_2,V_A_2] :
% 156.96/157.05 ( V_A_2 = V_B_2
% 156.96/157.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_order__eq__refl,axiom,
% 156.96/157.05 ! [V_y,V_x,T_a] :
% 156.96/157.05 ( class_Orderings_Opreorder(T_a)
% 156.96/157.05 => ( V_x = V_y
% 156.96/157.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 156.96/157.05
% 156.96/157.05 fof(fact_UnI1,axiom,
% 156.96/157.05 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 156.96/157.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 156.96/157.05 => 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))) ) ).
% 156.96/157.05
% 156.96/157.06 fof(fact_UnI2,axiom,
% 156.96/157.06 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 156.96/157.06 => 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))) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_le__funD,axiom,
% 156.96/157.06 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 156.96/157.06 ( class_Orderings_Oord(T_c)
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 156.96/157.06 => 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))) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Un__absorb1,axiom,
% 156.96/157.06 ! [V_B_2,V_A_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.06 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Un__absorb2,axiom,
% 156.96/157.06 ! [V_A_2,V_B_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 156.96/157.06 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_eqset__imp__iff,axiom,
% 156.96/157.06 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 156.96/157.06 ( V_A_2 = V_B_2
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.06 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_eqelem__imp__iff,axiom,
% 156.96/157.06 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 156.96/157.06 ( V_x_2 = V_y_2
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.06 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_in__mono,axiom,
% 156.96/157.06 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_order__antisym__conv,axiom,
% 156.96/157.06 ! [V_x_2,V_y_2,T_b] :
% 156.96/157.06 ( class_Orderings_Oorder(T_b)
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 156.96/157.06 <=> V_x_2 = V_y_2 ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Diff__partition,axiom,
% 156.96/157.06 ! [V_B_2,V_A_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.06 => 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 ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_eq__mem__trans,axiom,
% 156.96/157.06 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 156.96/157.06 ( V_a_2 = V_b_2
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_ord__eq__le__trans,axiom,
% 156.96/157.06 ! [V_c,V_b,V_a,T_a] :
% 156.96/157.06 ( class_Orderings_Oord(T_a)
% 156.96/157.06 => ( V_a = V_b
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_xt1_I3_J,axiom,
% 156.96/157.06 ! [V_c,V_b,V_a,T_a] :
% 156.96/157.06 ( class_Orderings_Oorder(T_a)
% 156.96/157.06 => ( V_a = V_b
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_set__rev__mp,axiom,
% 156.96/157.06 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_set__mp,axiom,
% 156.96/157.06 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_subset__trans,axiom,
% 156.96/157.06 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_ord__le__eq__trans,axiom,
% 156.96/157.06 ! [V_c,V_b,V_a,T_a] :
% 156.96/157.06 ( class_Orderings_Oord(T_a)
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 156.96/157.06 => ( V_b = V_c
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_xt1_I4_J,axiom,
% 156.96/157.06 ! [V_c,V_a,V_b,T_a] :
% 156.96/157.06 ( class_Orderings_Oorder(T_a)
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 156.96/157.06 => ( V_b = V_c
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_order__antisym,axiom,
% 156.96/157.06 ! [V_y,V_x,T_a] :
% 156.96/157.06 ( class_Orderings_Oorder(T_a)
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 156.96/157.06 => V_x = V_y ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_order__trans,axiom,
% 156.96/157.06 ! [V_z,V_y,V_x,T_a] :
% 156.96/157.06 ( class_Orderings_Opreorder(T_a)
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_xt1_I5_J,axiom,
% 156.96/157.06 ! [V_x,V_y,T_a] :
% 156.96/157.06 ( class_Orderings_Oorder(T_a)
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 156.96/157.06 => V_x = V_y ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_xt1_I6_J,axiom,
% 156.96/157.06 ! [V_z,V_x,V_y,T_a] :
% 156.96/157.06 ( class_Orderings_Oorder(T_a)
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Un__least,axiom,
% 156.96/157.06 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 156.96/157.06 => 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)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Un__mono,axiom,
% 156.96/157.06 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 156.96/157.06 => 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))) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Diff__mono,axiom,
% 156.96/157.06 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 156.96/157.06 => 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))) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_double__diff,axiom,
% 156.96/157.06 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 156.96/157.06 => 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 ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_equalityE,axiom,
% 156.96/157.06 ! [T_b,V_B_2,V_A_2] :
% 156.96/157.06 ( V_A_2 = V_B_2
% 156.96/157.06 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_le__funE,axiom,
% 156.96/157.06 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 156.96/157.06 ( class_Orderings_Oord(T_c)
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 156.96/157.06 => 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))) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_DiffD1,axiom,
% 156.96/157.06 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 156.96/157.06 ( 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)))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_DiffD2,axiom,
% 156.96/157.06 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 156.96/157.06 ( 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)))
% 156.96/157.06 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_linorder__le__cases,axiom,
% 156.96/157.06 ! [V_y,V_x,T_a] :
% 156.96/157.06 ( class_Orderings_Olinorder(T_a)
% 156.96/157.06 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_insert__Diff1,axiom,
% 156.96/157.06 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 156.96/157.06 => 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) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_insert__Diff__if,axiom,
% 156.96/157.06 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 156.96/157.06 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 156.96/157.06 => 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) )
% 156.96/157.06 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 156.96/157.06 => 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)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_subset__insert,axiom,
% 156.96/157.06 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 156.96/157.06 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.06 => ( 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)))
% 156.96/157.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_insert__subset,axiom,
% 156.96/157.06 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 156.96/157.06 ( 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))
% 156.96/157.06 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 156.96/157.06 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_subset__insert__iff,axiom,
% 156.96/157.06 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 156.96/157.06 ( 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)))
% 156.96/157.06 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.06 => 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)) )
% 156.96/157.06 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_diff__single__insert,axiom,
% 156.96/157.06 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 156.96/157.06 ( 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))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.06 => 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))) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_empty__fold1SetE,axiom,
% 156.96/157.06 ! [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)) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_fold1Set__nonempty,axiom,
% 156.96/157.06 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 156.96/157.06 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Diff__insert__absorb,axiom,
% 156.96/157.06 ! [V_A_2,V_x_2,T_b] :
% 156.96/157.06 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.06 => 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 ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_insert__Diff,axiom,
% 156.96/157.06 ! [V_A_2,V_a_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 156.96/157.06 => 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 ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_empty__Diff,axiom,
% 156.96/157.06 ! [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)) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Diff__empty,axiom,
% 156.96/157.06 ! [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 ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Diff__cancel,axiom,
% 156.96/157.06 ! [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)) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Un__empty__left,axiom,
% 156.96/157.06 ! [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 ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Un__empty__right,axiom,
% 156.96/157.06 ! [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 ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Un__empty,axiom,
% 156.96/157.06 ! [V_B_2,V_A_2,T_b] :
% 156.96/157.06 ( 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))
% 156.96/157.06 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 156.96/157.06 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Un__insert__right,axiom,
% 156.96/157.06 ! [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)) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Un__insert__left,axiom,
% 156.96/157.06 ! [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)) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_bot__least,axiom,
% 156.96/157.06 ! [V_x,T_a] :
% 156.96/157.06 ( class_Orderings_Obot(T_a)
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_all__not__in__conv,axiom,
% 156.96/157.06 ! [V_A_2,T_b] :
% 156.96/157.06 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 156.96/157.06 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_ex__in__conv,axiom,
% 156.96/157.06 ! [V_A_2,T_b] :
% 156.96/157.06 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 156.96/157.06 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_empty__iff,axiom,
% 156.96/157.06 ! [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)))) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_equals0D,axiom,
% 156.96/157.06 ! [V_a_2,T_b,V_A_2] :
% 156.96/157.06 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 156.96/157.06 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_subset__empty,axiom,
% 156.96/157.06 ! [V_A_2,T_b] :
% 156.96/157.06 ( 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))))
% 156.96/157.06 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_insertI1,axiom,
% 156.96/157.06 ! [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))) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_insert__iff,axiom,
% 156.96/157.06 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 156.96/157.06 <=> ( V_a_2 = V_b_2
% 156.96/157.06 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_insert__ident,axiom,
% 156.96/157.06 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 156.96/157.06 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.06 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 156.96/157.06 => ( 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)
% 156.96/157.06 <=> V_A_2 = V_B_2 ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_insertI2,axiom,
% 156.96/157.06 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 156.96/157.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_insert__absorb,axiom,
% 156.96/157.06 ! [V_A_2,V_a_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 156.96/157.06 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_subset__insertI,axiom,
% 156.96/157.06 ! [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))) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_subset__insertI2,axiom,
% 156.96/157.06 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.06 => 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))) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_insert__mono,axiom,
% 156.96/157.06 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 156.96/157.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 156.96/157.06 => 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))) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_asm,axiom,
% 156.96/157.06 ! [V_Ga_2,V_ts_2,T_b] :
% 156.96/157.06 ( 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))
% 156.96/157.06 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_weaken,axiom,
% 156.96/157.06 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] :
% 156.96/157.06 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 156.96/157.06 => ( 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))
% 156.96/157.06 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_Diff__insert,axiom,
% 156.96/157.06 ! [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)))) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_sup1CI,axiom,
% 156.96/157.06 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 156.96/157.06 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 156.96/157.06 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 156.96/157.06 => 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)) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_sup1E,axiom,
% 156.96/157.06 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 156.96/157.06 ( 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))
% 156.96/157.06 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 156.96/157.06 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_minus__apply,axiom,
% 156.96/157.06 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 156.96/157.06 ( class_Groups_Ominus(T_b)
% 156.96/157.06 => 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)) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_sup__apply,axiom,
% 156.96/157.06 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 156.96/157.06 ( class_Lattices_Olattice(T_b)
% 156.96/157.06 => 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)) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_sup__bot__left,axiom,
% 156.96/157.06 ! [V_x,T_a] :
% 156.96/157.06 ( class_Lattices_Obounded__lattice__bot(T_a)
% 156.96/157.06 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_sup__bot__right,axiom,
% 156.96/157.06 ! [V_x,T_a] :
% 156.96/157.06 ( class_Lattices_Obounded__lattice__bot(T_a)
% 156.96/157.06 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_sup__eq__bot__iff,axiom,
% 156.96/157.06 ! [V_y_2,V_x_2,T_b] :
% 156.96/157.06 ( class_Lattices_Obounded__lattice__bot(T_b)
% 156.96/157.06 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 156.96/157.06 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 156.96/157.06 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_le__supE,axiom,
% 156.96/157.06 ! [V_x,V_b,V_a,T_a] :
% 156.96/157.06 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.06 => ( 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))
% 156.96/157.06 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 156.96/157.06 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_sup__mono,axiom,
% 156.96/157.06 ! [V_d,V_b,V_c,V_a,T_a] :
% 156.96/157.06 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 156.96/157.06 => 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))) ) ) ) ).
% 156.96/157.06
% 156.96/157.06 fof(fact_sup__least,axiom,
% 156.96/157.06 ! [V_z,V_x,V_y,T_a] :
% 156.96/157.06 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 156.96/157.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 156.96/157.07 => 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)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_le__supI,axiom,
% 156.96/157.07 ! [V_b,V_x,V_a,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 156.96/157.07 => 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)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup__absorb1,axiom,
% 156.96/157.07 ! [V_x,V_y,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 156.96/157.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_eq__mem,axiom,
% 156.96/157.07 ! [V_y_2,V_x_2,T_b] :
% 156.96/157.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 156.96/157.07 <=> V_x_2 = V_y_2 ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup_Oidem,axiom,
% 156.96/157.07 ! [V_a,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup__idem,axiom,
% 156.96/157.07 ! [V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup_Ocommute,axiom,
% 156.96/157.07 ! [V_b,V_a,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => 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) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_inf__sup__aci_I5_J,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Olattice(T_a)
% 156.96/157.07 => 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) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup__commute,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => 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) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup_Oleft__idem,axiom,
% 156.96/157.07 ! [V_b,V_a,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => 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) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_inf__sup__aci_I8_J,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Olattice(T_a)
% 156.96/157.07 => 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) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup__left__idem,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => 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) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup_Oleft__commute,axiom,
% 156.96/157.07 ! [V_c,V_a,V_b,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => 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)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_inf__sup__aci_I7_J,axiom,
% 156.96/157.07 ! [V_z,V_y,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Olattice(T_a)
% 156.96/157.07 => 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)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup__left__commute,axiom,
% 156.96/157.07 ! [V_z,V_y,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => 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)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup_Oassoc,axiom,
% 156.96/157.07 ! [V_c,V_b,V_a,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => 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)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_inf__sup__aci_I6_J,axiom,
% 156.96/157.07 ! [V_z,V_y,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Olattice(T_a)
% 156.96/157.07 => 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)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup__assoc,axiom,
% 156.96/157.07 ! [V_z,V_y,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => 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)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_rev__predicate1D,axiom,
% 156.96/157.07 ! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
% 156.96/157.07 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 156.96/157.07 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_predicate1D,axiom,
% 156.96/157.07 ! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
% 156.96/157.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 156.96/157.07 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 156.96/157.07 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup1I1,axiom,
% 156.96/157.07 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 156.96/157.07 ( hBOOL(hAPP(V_A_2,V_x_2))
% 156.96/157.07 => 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)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup1I2,axiom,
% 156.96/157.07 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 156.96/157.07 ( hBOOL(hAPP(V_B_2,V_x_2))
% 156.96/157.07 => 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)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_inf__sup__ord_I3_J,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Olattice(T_a)
% 156.96/157.07 => 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))) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup__ge1,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => 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))) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_inf__sup__ord_I4_J,axiom,
% 156.96/157.07 ! [V_x,V_y,T_a] :
% 156.96/157.07 ( class_Lattices_Olattice(T_a)
% 156.96/157.07 => 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))) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup__ge2,axiom,
% 156.96/157.07 ! [V_x,V_y,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => 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))) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_le__iff__sup,axiom,
% 156.96/157.07 ! [V_y_2,V_x_2,T_b] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_b)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 156.96/157.07 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_le__sup__iff,axiom,
% 156.96/157.07 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_b)
% 156.96/157.07 => ( 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))
% 156.96/157.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 156.96/157.07 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_le__supI1,axiom,
% 156.96/157.07 ! [V_b,V_a,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 156.96/157.07 => 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))) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_le__supI2,axiom,
% 156.96/157.07 ! [V_a,V_b,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 156.96/157.07 => 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))) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_sup__absorb2,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 156.96/157.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_diff__eq__diff__less__eq,axiom,
% 156.96/157.07 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 156.96/157.07 ( class_Groups_Oordered__ab__group__add(T_b)
% 156.96/157.07 => ( 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)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 156.96/157.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_folding__one_Oremove,axiom,
% 156.96/157.07 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 156.96/157.07 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 156.96/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.07 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 156.96/157.07 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 156.96/157.07 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 156.96/157.07 => 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)))))) ) ) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_fold1Set_Ointros,axiom,
% 156.96/157.07 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 156.96/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 156.96/157.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 156.96/157.07 => 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)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_psubset__insert__iff,axiom,
% 156.96/157.07 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 156.96/157.07 ( 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)))
% 156.96/157.07 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 156.96/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 156.96/157.07 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 156.96/157.07 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.07 => 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)) )
% 156.96/157.07 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 156.96/157.07 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 156.96/157.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.07 => ( 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)
% 156.96/157.07 => 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)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_Diff1__fold__graph,axiom,
% 156.96/157.07 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 156.96/157.07 ( 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))
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.07 => 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))) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_folding__one_Oinsert__remove,axiom,
% 156.96/157.07 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 156.96/157.07 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 156.96/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 156.96/157.07 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 156.96/157.07 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 156.96/157.07 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 156.96/157.07 => 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)))))) ) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_folding__one_Oinsert,axiom,
% 156.96/157.07 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 156.96/157.07 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 156.96/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 156.96/157.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 156.96/157.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 156.96/157.07 => 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)) ) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_nonempty__iff,axiom,
% 156.96/157.07 ! [T_b,V_A_2] :
% 156.96/157.07 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 156.96/157.07 <=> ? [B_x,B_B] :
% 156.96/157.07 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B)
% 156.96/157.07 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_Sup__fin_Oidem,axiom,
% 156.96/157.07 ! [V_x,T_a] :
% 156.96/157.07 ( class_Lattices_Olattice(T_a)
% 156.96/157.07 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_Powp__mono,axiom,
% 156.96/157.07 ! [V_B_2,V_A_2,T_b] :
% 156.96/157.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.07 => 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))) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_finite_OemptyI,axiom,
% 156.96/157.07 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_finite_OinsertI,axiom,
% 156.96/157.07 ! [V_a_2,V_A_2,T_b] :
% 156.96/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 156.96/157.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_finite__Diff,axiom,
% 156.96/157.07 ! [V_B_2,V_A_2,T_b] :
% 156.96/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 156.96/157.07 => 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))) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_order__less__irrefl,axiom,
% 156.96/157.07 ! [V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Opreorder(T_a)
% 156.96/157.07 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_linorder__neq__iff,axiom,
% 156.96/157.07 ! [V_y_2,V_x_2,T_b] :
% 156.96/157.07 ( class_Orderings_Olinorder(T_b)
% 156.96/157.07 => ( V_x_2 != V_y_2
% 156.96/157.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 156.96/157.07 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_not__less__iff__gr__or__eq,axiom,
% 156.96/157.07 ! [V_y_2,V_x_2,T_b] :
% 156.96/157.07 ( class_Orderings_Olinorder(T_b)
% 156.96/157.07 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 156.96/157.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 156.96/157.07 | V_x_2 = V_y_2 ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_linorder__less__linear,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Olinorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 156.96/157.07 | V_x = V_y
% 156.96/157.07 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_linorder__antisym__conv3,axiom,
% 156.96/157.07 ! [V_x_2,V_y_2,T_b] :
% 156.96/157.07 ( class_Orderings_Olinorder(T_b)
% 156.96/157.07 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 156.96/157.07 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 156.96/157.07 <=> V_x_2 = V_y_2 ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_linorder__neqE,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Olinorder(T_a)
% 156.96/157.07 => ( V_x != V_y
% 156.96/157.07 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 156.96/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_less__imp__neq,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Oorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 156.96/157.07 => V_x != V_y ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_order__less__not__sym,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Opreorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 156.96/157.07 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_order__less__imp__not__less,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Opreorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 156.96/157.07 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_order__less__imp__not__eq,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Oorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 156.96/157.07 => V_x != V_y ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_order__less__imp__not__eq2,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Oorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 156.96/157.07 => V_y != V_x ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_order__less__asym_H,axiom,
% 156.96/157.07 ! [V_b,V_a,T_a] :
% 156.96/157.07 ( class_Orderings_Opreorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 156.96/157.07 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_xt1_I9_J,axiom,
% 156.96/157.07 ! [V_a,V_b,T_a] :
% 156.96/157.07 ( class_Orderings_Oorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 156.96/157.07 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_ord__eq__less__trans,axiom,
% 156.96/157.07 ! [V_c,V_b,V_a,T_a] :
% 156.96/157.07 ( class_Orderings_Oord(T_a)
% 156.96/157.07 => ( V_a = V_b
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 156.96/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_xt1_I1_J,axiom,
% 156.96/157.07 ! [V_c,V_b,V_a,T_a] :
% 156.96/157.07 ( class_Orderings_Oorder(T_a)
% 156.96/157.07 => ( V_a = V_b
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 156.96/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_psubset__trans,axiom,
% 156.96/157.07 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 156.96/157.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 156.96/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_ord__less__eq__trans,axiom,
% 156.96/157.07 ! [V_c,V_b,V_a,T_a] :
% 156.96/157.07 ( class_Orderings_Oord(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 156.96/157.07 => ( V_b = V_c
% 156.96/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_xt1_I2_J,axiom,
% 156.96/157.07 ! [V_c,V_a,V_b,T_a] :
% 156.96/157.07 ( class_Orderings_Oorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 156.96/157.07 => ( V_b = V_c
% 156.96/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_order__less__trans,axiom,
% 156.96/157.07 ! [V_z,V_y,V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Opreorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 156.96/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_xt1_I10_J,axiom,
% 156.96/157.07 ! [V_z,V_x,V_y,T_a] :
% 156.96/157.07 ( class_Orderings_Oorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 156.96/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_order__less__asym,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Opreorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 156.96/157.07 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_linorder__cases,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Olinorder(T_a)
% 156.96/157.07 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 156.96/157.07 => ( V_x != V_y
% 156.96/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_finite,axiom,
% 156.96/157.07 ! [V_A_2,T_b] :
% 156.96/157.07 ( class_Finite__Set_Ofinite(T_b)
% 156.96/157.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_finite__code,axiom,
% 156.96/157.07 ! [V_A_2,T_b] :
% 156.96/157.07 ( class_Finite__Set_Ofinite(T_b)
% 156.96/157.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_fold__graph__imp__finite,axiom,
% 156.96/157.07 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 156.96/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 156.96/157.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_diff__eq__diff__less,axiom,
% 156.96/157.07 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 156.96/157.07 ( class_Groups_Oordered__ab__group__add(T_b)
% 156.96/157.07 => ( 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)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 156.96/157.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 156.96/157.07 ! [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) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 156.96/157.07 ! [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) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_less__fun__def,axiom,
% 156.96/157.07 ! [V_g_2,V_f_2,T_b,T_c] :
% 156.96/157.07 ( class_Orderings_Oord(T_c)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 156.96/157.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 156.96/157.07 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_linorder__not__less,axiom,
% 156.96/157.07 ! [V_y_2,V_x_2,T_b] :
% 156.96/157.07 ( class_Orderings_Olinorder(T_b)
% 156.96/157.07 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 156.96/157.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_linorder__not__le,axiom,
% 156.96/157.07 ! [V_y_2,V_x_2,T_b] :
% 156.96/157.07 ( class_Orderings_Olinorder(T_b)
% 156.96/157.07 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 156.96/157.07 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_linorder__le__less__linear,axiom,
% 156.96/157.07 ! [V_y,V_x,T_a] :
% 156.96/157.07 ( class_Orderings_Olinorder(T_a)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 156.96/157.07 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_order__less__le,axiom,
% 156.96/157.07 ! [V_y_2,V_x_2,T_b] :
% 156.96/157.07 ( class_Orderings_Oorder(T_b)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 156.96/157.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 156.96/157.07 & V_x_2 != V_y_2 ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_less__le__not__le,axiom,
% 156.96/157.07 ! [V_y_2,V_x_2,T_b] :
% 156.96/157.07 ( class_Orderings_Opreorder(T_b)
% 156.96/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 156.96/157.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 156.96/157.07 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 156.96/157.07
% 156.96/157.07 fof(fact_order__le__less,axiom,
% 157.09/157.07 ! [V_y_2,V_x_2,T_b] :
% 157.09/157.07 ( class_Orderings_Oorder(T_b)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.09/157.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.09/157.07 | V_x_2 = V_y_2 ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_leI,axiom,
% 157.09/157.07 ! [V_y,V_x,T_a] :
% 157.09/157.07 ( class_Orderings_Olinorder(T_a)
% 157.09/157.07 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_not__leE,axiom,
% 157.09/157.07 ! [V_x,V_y,T_a] :
% 157.09/157.07 ( class_Orderings_Olinorder(T_a)
% 157.09/157.07 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_linorder__antisym__conv1,axiom,
% 157.09/157.07 ! [V_y_2,V_x_2,T_b] :
% 157.09/157.07 ( class_Orderings_Olinorder(T_b)
% 157.09/157.07 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.09/157.07 <=> V_x_2 = V_y_2 ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_order__neq__le__trans,axiom,
% 157.09/157.07 ! [V_b,V_a,T_a] :
% 157.09/157.07 ( class_Orderings_Oorder(T_a)
% 157.09/157.07 => ( V_a != V_b
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_xt1_I12_J,axiom,
% 157.09/157.07 ! [V_b,V_a,T_a] :
% 157.09/157.07 ( class_Orderings_Oorder(T_a)
% 157.09/157.07 => ( V_a != V_b
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_leD,axiom,
% 157.09/157.07 ! [V_x,V_y,T_a] :
% 157.09/157.07 ( class_Orderings_Olinorder(T_a)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.09/157.07 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_order__less__imp__le,axiom,
% 157.09/157.07 ! [V_y,V_x,T_a] :
% 157.09/157.07 ( class_Orderings_Opreorder(T_a)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_linorder__antisym__conv2,axiom,
% 157.09/157.07 ! [V_y_2,V_x_2,T_b] :
% 157.09/157.07 ( class_Orderings_Olinorder(T_b)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.09/157.07 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 157.09/157.07 <=> V_x_2 = V_y_2 ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_order__le__imp__less__or__eq,axiom,
% 157.09/157.07 ! [V_y,V_x,T_a] :
% 157.09/157.07 ( class_Orderings_Oorder(T_a)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.09/157.07 | V_x = V_y ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_order__le__neq__trans,axiom,
% 157.09/157.07 ! [V_b,V_a,T_a] :
% 157.09/157.07 ( class_Orderings_Oorder(T_a)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.09/157.07 => ( V_a != V_b
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_xt1_I11_J,axiom,
% 157.09/157.07 ! [V_a,V_b,T_a] :
% 157.09/157.07 ( class_Orderings_Oorder(T_a)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.09/157.07 => ( V_a != V_b
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_order__less__le__trans,axiom,
% 157.09/157.07 ! [V_z,V_y,V_x,T_a] :
% 157.09/157.07 ( class_Orderings_Opreorder(T_a)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_xt1_I7_J,axiom,
% 157.09/157.07 ! [V_z,V_x,V_y,T_a] :
% 157.09/157.07 ( class_Orderings_Oorder(T_a)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_order__le__less__trans,axiom,
% 157.09/157.07 ! [V_z,V_y,V_x,T_a] :
% 157.09/157.07 ( class_Orderings_Opreorder(T_a)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_xt1_I8_J,axiom,
% 157.09/157.07 ! [V_z,V_x,V_y,T_a] :
% 157.09/157.07 ( class_Orderings_Oorder(T_a)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_psubsetD,axiom,
% 157.09/157.07 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_not__psubset__empty,axiom,
% 157.09/157.07 ! [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)))) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_less__supI2,axiom,
% 157.09/157.07 ! [V_a,V_b,V_x,T_a] :
% 157.09/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 157.09/157.07 => 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))) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_less__supI1,axiom,
% 157.09/157.07 ! [V_b,V_a,V_x,T_a] :
% 157.09/157.07 ( class_Lattices_Osemilattice__sup(T_a)
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 157.09/157.07 => 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))) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_psubset__eq,axiom,
% 157.09/157.07 ! [V_B_2,V_A_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.09/157.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.09/157.07 & V_A_2 != V_B_2 ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_subset__iff__psubset__eq,axiom,
% 157.09/157.07 ! [V_B_2,V_A_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.09/157.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.09/157.07 | V_A_2 = V_B_2 ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_psubset__imp__subset,axiom,
% 157.09/157.07 ! [V_B_2,V_A_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_psubset__subset__trans,axiom,
% 157.09/157.07 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_subset__psubset__trans,axiom,
% 157.09/157.07 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_finite_Oequations_I1_J,axiom,
% 157.09/157.07 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_finite__insert,axiom,
% 157.09/157.07 ! [V_A_2,V_a_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 157.09/157.07 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_finite__subset,axiom,
% 157.09/157.07 ! [V_B_2,V_A_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.09/157.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_rev__finite__subset,axiom,
% 157.09/157.07 ! [V_A_2,V_B_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.09/157.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_finite__UnI,axiom,
% 157.09/157.07 ! [V_Ga_2,V_F_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 157.09/157.07 => 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))) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_finite__Un,axiom,
% 157.09/157.07 ! [V_Ga_2,V_F_2,T_b] :
% 157.09/157.07 ( 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)))
% 157.09/157.07 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.09/157.07 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_finite__Diff2,axiom,
% 157.09/157.07 ! [V_A_2,V_B_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.09/157.07 => ( 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)))
% 157.09/157.07 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 157.09/157.07 ! [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)) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_fold__graph_OemptyI,axiom,
% 157.09/157.07 ! [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)) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_empty__fold__graphE,axiom,
% 157.09/157.07 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 157.09/157.07 ( 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))
% 157.09/157.07 => V_x_2 = V_z_2 ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_finite__Diff__insert,axiom,
% 157.09/157.07 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 157.09/157.07 ( 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))))
% 157.09/157.07 <=> 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))) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_fold__graph_OinsertI,axiom,
% 157.09/157.07 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 157.09/157.07 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 157.09/157.07 => 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))) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_diff__eq__diff__eq,axiom,
% 157.09/157.07 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.09/157.07 ( class_Groups_Oab__group__add(T_b)
% 157.09/157.07 => ( 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)
% 157.09/157.07 => ( V_a_2 = V_b_2
% 157.09/157.07 <=> V_ca_2 = V_d_2 ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_folding__image__simple_Oremove,axiom,
% 157.09/157.07 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.09/157.07 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 157.09/157.07 => 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)))))) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 157.09/157.07 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.09/157.07 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.09/157.07 => 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)))))) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_Sup__fin_Oremove,axiom,
% 157.09/157.07 ! [V_x_2,V_A_2,T_b] :
% 157.09/157.07 ( class_Lattices_Olattice(T_b)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.09/157.07 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.09/157.07 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 157.09/157.07 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.09/157.07 => 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)))))) ) ) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 157.09/157.07 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 157.09/157.07 ( 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))
% 157.09/157.07 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 157.09/157.07 | ? [B_x,B_y] :
% 157.09/157.07 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 157.09/157.07 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 157.09/157.07 & 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) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_folding__one_Oclosed,axiom,
% 157.09/157.07 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 157.09/157.07 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 => ( ! [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))))))
% 157.09/157.07 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_finite__empty__induct,axiom,
% 157.09/157.07 ! [V_Pa_2,V_A_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( hBOOL(hAPP(V_Pa_2,V_A_2))
% 157.09/157.07 => ( ! [B_a,B_A] :
% 157.09/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 157.09/157.07 => ( hBOOL(hAPP(V_Pa_2,B_A))
% 157.09/157.07 => 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)))))) ) ) )
% 157.09/157.07 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 157.09/157.07 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.09/157.07 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.09/157.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 => 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)) ) ) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_finite__subset__induct,axiom,
% 157.09/157.07 ! [V_Pa_2,V_A_2,V_F_2,T_b] :
% 157.09/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 157.09/157.07 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.09/157.07 => ( ! [B_a,B_F] :
% 157.09/157.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 157.09/157.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 157.09/157.07 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 157.09/157.07 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 157.09/157.07 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 157.09/157.07 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.09/157.07 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.09/157.07 => 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) ) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 157.09/157.07 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.09/157.07 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 => 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)) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 157.09/157.07 ! [V_x_2,V_A_2,T_b] :
% 157.09/157.07 ( class_Lattices_Olattice(T_b)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.09/157.07 => 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 )
% 157.09/157.07 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.09/157.07 => 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)))))) ) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_folding__one__idem_Oidem,axiom,
% 157.09/157.07 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 157.09/157.07 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.09/157.07 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_folding__image__simple_Oempty,axiom,
% 157.09/157.07 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.09/157.07 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.09/157.07 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_Sup__fin_Osingleton,axiom,
% 157.09/157.07 ! [V_x_2,T_b] :
% 157.09/157.07 ( class_Lattices_Olattice(T_b)
% 157.09/157.07 => 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 ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_Sup__fin_Oin__idem,axiom,
% 157.09/157.07 ! [V_x_2,V_A_2,T_b] :
% 157.09/157.07 ( class_Lattices_Olattice(T_b)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.09/157.07 => 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) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_folding__one__idem_Oin__idem,axiom,
% 157.09/157.07 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.09/157.07 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.09/157.07 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 157.09/157.07 ! [V_x_2,V_A_2,T_b] :
% 157.09/157.07 ( class_Lattices_Olattice(T_b)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 => 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)) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_Sup__fin_Osubset__idem,axiom,
% 157.09/157.07 ! [V_B_2,V_A_2,T_b] :
% 157.09/157.07 ( class_Lattices_Olattice(T_b)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.09/157.07 => 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) ) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_Sup__fin_Ounion__idem,axiom,
% 157.09/157.07 ! [V_B_2,V_A_2,T_b] :
% 157.09/157.07 ( class_Lattices_Olattice(T_b)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.09/157.07 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 => 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)) ) ) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_folding__image__simple_Oinsert,axiom,
% 157.09/157.07 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.09/157.07 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.09/157.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 157.09/157.07 => 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)) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_Sup__fin_Oinsert,axiom,
% 157.09/157.07 ! [V_x_2,V_A_2,T_b] :
% 157.09/157.07 ( class_Lattices_Olattice(T_b)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.09/157.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 => 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)) ) ) ) ) ).
% 157.09/157.07
% 157.09/157.07 fof(fact_Sup__fin_Oclosed,axiom,
% 157.09/157.07 ! [V_A_2,T_b] :
% 157.09/157.07 ( class_Lattices_Olattice(T_b)
% 157.09/157.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.07 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.07 => ( ! [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))))))
% 157.09/157.08 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_insert__fold1SetE,axiom,
% 157.09/157.08 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 157.09/157.08 ( 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))
% 157.09/157.08 => ~ ! [B_a,B_A] :
% 157.09/157.08 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 157.09/157.08 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_fold1Set_Oequations,axiom,
% 157.09/157.08 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 157.09/157.08 ( 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))
% 157.09/157.08 <=> ? [B_a,B_A] :
% 157.09/157.08 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 157.09/157.08 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 157.09/157.08 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_setsum__diff1__ring,axiom,
% 157.09/157.08 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 157.09/157.08 ( class_Rings_Oring(T_c)
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.09/157.08 => 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)) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_setsum__diff1,axiom,
% 157.09/157.08 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 157.09/157.08 ( class_Groups_Oab__group__add(T_c)
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.08 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.09/157.08 => 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)) )
% 157.09/157.08 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.09/157.08 => 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) ) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_fold__graph__permute__diff,axiom,
% 157.09/157.08 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 157.09/157.08 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.09/157.08 => ( 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))
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.09/157.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 157.09/157.08 => 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)) ) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,T_b] :
% 157.09/157.08 ( class_Lattices_Olattice(T_b)
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.09/157.08 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.09/157.08 => ( 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))
% 157.09/157.08 => 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)) ) ) ) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Sup__fin_Ounion__inter,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,T_b] :
% 157.09/157.08 ( class_Lattices_Olattice(T_b)
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.09/157.08 => ( 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))
% 157.09/157.08 => 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)) ) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.09/157.08 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.09/157.08 => 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)) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.09/157.08 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.09/157.08 => 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) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 157.09/157.08 ! [V_x_2,V_A_2,T_b] :
% 157.09/157.08 ( class_Lattices_Olattice(T_b)
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.09/157.08 => 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) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf1I,axiom,
% 157.09/157.08 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 157.09/157.08 ( hBOOL(hAPP(V_A_2,V_x_2))
% 157.09/157.08 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 157.09/157.08 => 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)) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf1E,axiom,
% 157.09/157.08 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 157.09/157.08 ( 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))
% 157.09/157.08 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 157.09/157.08 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_IntI,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.09/157.08 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 157.09/157.08 => 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))) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_IntE,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.09/157.08 ( 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)))
% 157.09/157.08 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.09/157.08 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_finite__Int,axiom,
% 157.09/157.08 ! [V_Ga_2,V_F_2,T_b] :
% 157.09/157.08 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.09/157.08 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 157.09/157.08 => 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))) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_times_Oidem,axiom,
% 157.09/157.08 ! [V_a,T_a] :
% 157.09/157.08 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 157.09/157.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_mult__idem,axiom,
% 157.09/157.08 ! [V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 157.09/157.08 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf_Oidem,axiom,
% 157.09/157.08 ! [V_a,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__idem,axiom,
% 157.09/157.08 ! [V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf_Ocommute,axiom,
% 157.09/157.08 ! [V_b,V_a,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => 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) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__sup__aci_I1_J,axiom,
% 157.09/157.08 ! [V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Olattice(T_a)
% 157.09/157.08 => 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) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__commute,axiom,
% 157.09/157.08 ! [V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => 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) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_mult__left__idem,axiom,
% 157.09/157.08 ! [V_b,V_a,T_a] :
% 157.09/157.08 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 157.09/157.08 => 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) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf_Oleft__idem,axiom,
% 157.09/157.08 ! [V_b,V_a,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => 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) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__sup__aci_I4_J,axiom,
% 157.09/157.08 ! [V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Olattice(T_a)
% 157.09/157.08 => 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) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__left__idem,axiom,
% 157.09/157.08 ! [V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => 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) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf_Oleft__commute,axiom,
% 157.09/157.08 ! [V_c,V_a,V_b,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__sup__aci_I3_J,axiom,
% 157.09/157.08 ! [V_z,V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Olattice(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__left__commute,axiom,
% 157.09/157.08 ! [V_z,V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf_Oassoc,axiom,
% 157.09/157.08 ! [V_c,V_b,V_a,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__sup__aci_I2_J,axiom,
% 157.09/157.08 ! [V_z,V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Olattice(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__assoc,axiom,
% 157.09/157.08 ! [V_z,V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__apply,axiom,
% 157.09/157.08 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 157.09/157.08 ( class_Lattices_Olattice(T_b)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf1D1,axiom,
% 157.09/157.08 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 157.09/157.08 ( 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))
% 157.09/157.08 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf1D2,axiom,
% 157.09/157.08 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 157.09/157.08 ( 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))
% 157.09/157.08 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__absorb,axiom,
% 157.09/157.08 ! [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 ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__commute,axiom,
% 157.09/157.08 ! [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) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__left__absorb,axiom,
% 157.09/157.08 ! [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) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__left__commute,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__assoc,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Inf__fin_Oidem,axiom,
% 157.09/157.08 ! [V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Olattice(T_a)
% 157.09/157.08 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 157.09/157.08 ! [V_c,V_b,V_a,T_a] :
% 157.09/157.08 ( class_Groups_Oab__semigroup__mult(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 157.09/157.08 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.09/157.08 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.09/157.08 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_fold__inf__insert,axiom,
% 157.09/157.08 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_b)
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.08 => 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)) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_le__infE,axiom,
% 157.09/157.08 ! [V_b,V_a,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => ( 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)))
% 157.09/157.08 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.09/157.08 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__mono,axiom,
% 157.09/157.08 ! [V_d,V_b,V_c,V_a,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 157.09/157.08 => 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))) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__greatest,axiom,
% 157.09/157.08 ! [V_z,V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 157.09/157.08 => 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))) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_le__infI,axiom,
% 157.09/157.08 ! [V_b,V_a,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 157.09/157.08 => 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))) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__absorb2,axiom,
% 157.09/157.08 ! [V_x,V_y,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.09/157.08 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__absorb1,axiom,
% 157.09/157.08 ! [V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.09/157.08 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_le__infI2,axiom,
% 157.09/157.08 ! [V_a,V_x,V_b,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 157.09/157.08 => 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)) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_le__infI1,axiom,
% 157.09/157.08 ! [V_b,V_x,V_a,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 157.09/157.08 => 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)) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_le__inf__iff,axiom,
% 157.09/157.08 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_b)
% 157.09/157.08 => ( 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)))
% 157.09/157.08 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.09/157.08 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_le__iff__inf,axiom,
% 157.09/157.08 ! [V_y_2,V_x_2,T_b] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_b)
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.09/157.08 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__le2,axiom,
% 157.09/157.08 ! [V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__sup__ord_I2_J,axiom,
% 157.09/157.08 ! [V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Olattice(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__le1,axiom,
% 157.09/157.08 ! [V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__sup__ord_I1_J,axiom,
% 157.09/157.08 ! [V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Olattice(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_less__infI1,axiom,
% 157.09/157.08 ! [V_b,V_x,V_a,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 157.09/157.08 => 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)) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_less__infI2,axiom,
% 157.09/157.08 ! [V_a,V_x,V_b,T_a] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_a)
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 157.09/157.08 => 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)) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__bot__left,axiom,
% 157.09/157.08 ! [V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Obounded__lattice__bot(T_a)
% 157.09/157.08 => 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) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__bot__right,axiom,
% 157.09/157.08 ! [V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Obounded__lattice__bot(T_a)
% 157.09/157.08 => 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) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_sup__inf__distrib2,axiom,
% 157.09/157.08 ! [V_x,V_z,V_y,T_a] :
% 157.09/157.08 ( class_Lattices_Odistrib__lattice(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__sup__distrib2,axiom,
% 157.09/157.08 ! [V_x,V_z,V_y,T_a] :
% 157.09/157.08 ( class_Lattices_Odistrib__lattice(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_sup__inf__distrib1,axiom,
% 157.09/157.08 ! [V_z,V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Odistrib__lattice(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__sup__distrib1,axiom,
% 157.09/157.08 ! [V_z,V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Odistrib__lattice(T_a)
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_sup__inf__absorb,axiom,
% 157.09/157.08 ! [V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Olattice(T_a)
% 157.09/157.08 => 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 ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_inf__sup__absorb,axiom,
% 157.09/157.08 ! [V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Olattice(T_a)
% 157.09/157.08 => 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 ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__iff,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.09/157.08 ( 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)))
% 157.09/157.08 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.09/157.08 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_IntD1,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.09/157.08 ( 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)))
% 157.09/157.08 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_IntD2,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 157.09/157.08 ( 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)))
% 157.09/157.08 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_fold__empty,axiom,
% 157.09/157.08 ! [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 ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__empty__left,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__empty__right,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_disjoint__iff__not__equal,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,T_b] :
% 157.09/157.08 ( 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))
% 157.09/157.08 <=> ! [B_x] :
% 157.09/157.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.09/157.08 => ! [B_xa] :
% 157.09/157.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 157.09/157.08 => B_x != B_xa ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_insert__inter__insert,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__lower1,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__lower2,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__absorb2,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,T_b] :
% 157.09/157.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.09/157.08 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__absorb1,axiom,
% 157.09/157.08 ! [V_A_2,V_B_2,T_b] :
% 157.09/157.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.09/157.08 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__greatest,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 157.09/157.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 157.09/157.08 => 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))) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__mono,axiom,
% 157.09/157.08 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 157.09/157.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 157.09/157.08 => 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))) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__Un__distrib,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Un__Int__distrib,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__Un__distrib2,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Un__Int__distrib2,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Un__Int__crazy,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Diff__Int__distrib,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__Diff,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Diff__Int__distrib2,axiom,
% 157.09/157.08 ! [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)) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Diff__Int2,axiom,
% 157.09/157.08 ! [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) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_fold__inf__le__inf,axiom,
% 157.09/157.08 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 157.09/157.08 ( class_Lattices_Osemilattice__inf(T_b)
% 157.09/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.09/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.09/157.08 => 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))) ) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_distrib__inf__le,axiom,
% 157.09/157.08 ! [V_z,V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Olattice(T_a)
% 157.09/157.08 => 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)))) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_distrib__sup__le,axiom,
% 157.09/157.08 ! [V_z,V_y,V_x,T_a] :
% 157.09/157.08 ( class_Lattices_Olattice(T_a)
% 157.09/157.08 => 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)))) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__insert__left__if1,axiom,
% 157.09/157.08 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 157.09/157.08 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__insert__right__if1,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 157.09/157.08 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.09/157.08 => 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)) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__insert__left__if0,axiom,
% 157.09/157.08 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 157.09/157.08 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 157.09/157.08 => 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) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__insert__right__if0,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 157.09/157.08 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.09/157.08 => 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) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__insert__left,axiom,
% 157.09/157.08 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 157.09/157.08 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 157.09/157.08 => 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)) )
% 157.09/157.08 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 157.09/157.08 => 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) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Int__insert__right,axiom,
% 157.09/157.08 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 157.09/157.08 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.09/157.08 => 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)) )
% 157.09/157.08 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.09/157.08 => 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) ) ) ).
% 157.09/157.08
% 157.09/157.08 fof(fact_Diff__triv,axiom,
% 157.13/157.08 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.08 ( 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))
% 157.13/157.08 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Diff__disjoint,axiom,
% 157.13/157.08 ! [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)) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Un__Int__assoc__eq,axiom,
% 157.13/157.08 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.13/157.08 ( 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))
% 157.13/157.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Diff__Int,axiom,
% 157.13/157.08 ! [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)) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Diff__Un,axiom,
% 157.13/157.08 ! [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)) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Un__Diff__Int,axiom,
% 157.13/157.08 ! [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 ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum__diff__nat,axiom,
% 157.13/157.08 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 157.13/157.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.13/157.08 => 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)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_union__fold__insert,axiom,
% 157.13/157.08 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => 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) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fold__sup__insert,axiom,
% 157.13/157.08 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Osemilattice__sup(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => 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)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_inf__Sup__absorb,axiom,
% 157.13/157.08 ! [V_a_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.08 => 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 ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fold__graph__insert__swap,axiom,
% 157.13/157.08 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 157.13/157.08 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.13/157.08 => ( 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))
% 157.13/157.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 157.13/157.08 => 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))) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 157.13/157.08 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => 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) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 157.13/157.08 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.13/157.08 => 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)) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum__diff1__nat,axiom,
% 157.13/157.08 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 157.13/157.08 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.08 => 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)) )
% 157.13/157.08 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.08 => 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) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum__diff,axiom,
% 157.13/157.08 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.08 ( class_Groups_Oab__group__add(T_c)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.13/157.08 => 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)) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_sup__le__fold__sup,axiom,
% 157.13/157.08 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Osemilattice__sup(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.08 => 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))) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 157.13/157.08 ! [V_a_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => 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) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_folding__one_Oeq__fold_H,axiom,
% 157.13/157.08 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.08 => 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) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_folding__one_Ounion__inter,axiom,
% 157.13/157.08 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.08 => ( 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))
% 157.13/157.08 => 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)) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_folding__one_Ounion__disjoint,axiom,
% 157.13/157.08 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.08 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => ( 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))
% 157.13/157.08 => 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)) ) ) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 157.13/157.08 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.13/157.08 => ( 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))
% 157.13/157.08 => 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)) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 157.13/157.08 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 157.13/157.08 => 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) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 157.13/157.08 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.13/157.08 => 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)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 157.13/157.08 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.08 => 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)))))) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 157.13/157.08 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => 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)))))) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Oremove,axiom,
% 157.13/157.08 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.08 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.13/157.08 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 157.13/157.08 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.13/157.08 => 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)))))) ) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 157.13/157.08 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.08 => 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)) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 157.13/157.08 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.08 => 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) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum__strict__mono,axiom,
% 157.13/157.08 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 157.13/157.08 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.08 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => ( ! [B_x] :
% 157.13/157.08 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.13/157.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 157.13/157.08 => 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))) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum__diff1_H,axiom,
% 157.13/157.08 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 157.13/157.08 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.08 => 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)))))) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum_Oremove,axiom,
% 157.13/157.08 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 157.13/157.08 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.08 => 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)))))) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 157.13/157.08 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.08 => 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) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Ounion__inter,axiom,
% 157.13/157.08 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.08 => ( 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))
% 157.13/157.08 => 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)) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__right__imp__eq,axiom,
% 157.13/157.08 ! [V_c,V_a,V_b,T_a] :
% 157.13/157.08 ( class_Groups_Ocancel__semigroup__add(T_a)
% 157.13/157.08 => ( 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)
% 157.13/157.08 => V_b = V_c ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__imp__eq,axiom,
% 157.13/157.08 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 157.13/157.08 => ( 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)
% 157.13/157.08 => V_b = V_c ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__left__imp__eq,axiom,
% 157.13/157.08 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Ocancel__semigroup__add(T_a)
% 157.13/157.08 => ( 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)
% 157.13/157.08 => V_b = V_c ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__right__cancel,axiom,
% 157.13/157.08 ! [V_ca_2,V_a_2,V_b_2,T_b] :
% 157.13/157.08 ( class_Groups_Ocancel__semigroup__add(T_b)
% 157.13/157.08 => ( 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)
% 157.13/157.08 <=> V_b_2 = V_ca_2 ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__left__cancel,axiom,
% 157.13/157.08 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.13/157.08 ( class_Groups_Ocancel__semigroup__add(T_b)
% 157.13/157.08 => ( 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)
% 157.13/157.08 <=> V_b_2 = V_ca_2 ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 157.13/157.08 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Oab__semigroup__add(T_a)
% 157.13/157.08 => 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)) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 157.13/157.08 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.13/157.08 => 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)) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__le__cancel__right,axiom,
% 157.13/157.08 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 157.13/157.08 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__le__cancel__left,axiom,
% 157.13/157.08 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.13/157.08 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__right__mono,axiom,
% 157.13/157.08 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.08 => 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))) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__left__mono,axiom,
% 157.13/157.08 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.08 => 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))) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__mono,axiom,
% 157.13/157.08 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 157.13/157.08 => 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))) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__le__imp__le__right,axiom,
% 157.13/157.08 ! [V_b,V_c,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__le__imp__le__left,axiom,
% 157.13/157.08 ! [V_b,V_a,V_c,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__less__cancel__right,axiom,
% 157.13/157.08 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 157.13/157.08 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__less__cancel__left,axiom,
% 157.13/157.08 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.13/157.08 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__strict__right__mono,axiom,
% 157.13/157.08 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.13/157.08 => 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))) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__strict__left__mono,axiom,
% 157.13/157.08 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.13/157.08 => 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))) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__strict__mono,axiom,
% 157.13/157.08 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 157.13/157.08 => 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))) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__less__imp__less__right,axiom,
% 157.13/157.08 ! [V_b,V_c,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__less__imp__less__left,axiom,
% 157.13/157.08 ! [V_b,V_a,V_c,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_diff__add__cancel,axiom,
% 157.13/157.08 ! [V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Ogroup__add(T_a)
% 157.13/157.08 => 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 ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__diff__cancel,axiom,
% 157.13/157.08 ! [V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Ogroup__add(T_a)
% 157.13/157.08 => 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 ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fun__left__comm,axiom,
% 157.13/157.08 ! [T_b] :
% 157.13/157.08 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.13/157.08 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__less__le__mono,axiom,
% 157.13/157.08 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 157.13/157.08 => 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))) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_add__le__less__mono,axiom,
% 157.13/157.08 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.13/157.08 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 157.13/157.08 => 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))) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 157.13/157.08 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 157.13/157.08 => V_y_2 = V_x_2 ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Osingleton,axiom,
% 157.13/157.08 ! [V_x_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => 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 ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum__Un__nat,axiom,
% 157.13/157.08 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 157.13/157.08 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.08 => 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))) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 157.13/157.08 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => 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) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_sup__Inf__absorb,axiom,
% 157.13/157.08 ! [V_a_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.08 => 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 ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Oin__idem,axiom,
% 157.13/157.08 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.08 => 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) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 157.13/157.08 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 157.13/157.08 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum_Oinsert,axiom,
% 157.13/157.08 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 157.13/157.08 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.08 => 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)) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum__insert,axiom,
% 157.13/157.08 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 157.13/157.08 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.13/157.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 157.13/157.08 => 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)) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum__Un__Int,axiom,
% 157.13/157.08 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.08 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.08 => 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)) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 157.13/157.08 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => 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)) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Osubset__idem,axiom,
% 157.13/157.08 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.13/157.08 => 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) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Ounion__idem,axiom,
% 157.13/157.08 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.08 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => 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)) ) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__le__Sup,axiom,
% 157.13/157.08 ! [V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => 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))) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 157.13/157.08 ! [V_a_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => 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) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum_Oinsert__remove,axiom,
% 157.13/157.08 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 157.13/157.08 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => 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)))))) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum__Un__disjoint,axiom,
% 157.13/157.08 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.08 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.08 => ( 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))
% 157.13/157.08 => 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)) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_setsum__Un,axiom,
% 157.13/157.08 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.08 ( class_Groups_Oab__group__add(T_c)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.08 => 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))) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 157.13/157.08 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => 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))) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Oinsert,axiom,
% 157.13/157.08 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => 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)) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 157.13/157.08 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.13/157.08 => 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 )
% 157.13/157.08 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.13/157.08 => 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)))))) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 157.13/157.08 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.08 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => ( 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))
% 157.13/157.08 => 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)) ) ) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_less__add__iff2,axiom,
% 157.13/157.08 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.13/157.08 ( class_Rings_Oordered__ring(T_b)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 <=> 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))) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_less__add__iff1,axiom,
% 157.13/157.08 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.13/157.08 ( class_Rings_Oordered__ring(T_b)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 <=> 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)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_le__add__iff2,axiom,
% 157.13/157.08 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.13/157.08 ( class_Rings_Oordered__ring(T_b)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 <=> 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))) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_le__add__iff1,axiom,
% 157.13/157.08 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.13/157.08 ( class_Rings_Oordered__ring(T_b)
% 157.13/157.08 => ( 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)))
% 157.13/157.08 <=> 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)) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_eq__add__iff2,axiom,
% 157.13/157.08 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.13/157.08 ( class_Rings_Oring(T_b)
% 157.13/157.08 => ( 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)
% 157.13/157.08 <=> 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) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_eq__add__iff1,axiom,
% 157.13/157.08 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 157.13/157.08 ( class_Rings_Oring(T_b)
% 157.13/157.08 => ( 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)
% 157.13/157.08 <=> 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 ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 157.13/157.08 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.08 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 157.13/157.08 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.08 => ? [B_y_H] :
% 157.13/157.08 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 157.13/157.08 & 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)) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_Inf__fin_Oclosed,axiom,
% 157.13/157.08 ! [V_A_2,T_b] :
% 157.13/157.08 ( class_Lattices_Olattice(T_b)
% 157.13/157.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.08 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.08 => ( ! [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))))))
% 157.13/157.08 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 157.13/157.08 ! [V_z,V_y,V_x,T_a] :
% 157.13/157.08 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.08 => 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)) ) ).
% 157.13/157.08
% 157.13/157.08 fof(fact_crossproduct__noteq,axiom,
% 157.13/157.08 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.13/157.08 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 157.13/157.08 => ( ( V_a_2 != V_b_2
% 157.13/157.09 & V_ca_2 != V_d_2 )
% 157.13/157.09 <=> 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_linorder__neqE__linordered__idom,axiom,
% 157.13/157.09 ! [V_y,V_x,T_a] :
% 157.13/157.09 ( class_Rings_Olinordered__idom(T_a)
% 157.13/157.09 => ( V_x != V_y
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 157.13/157.09 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 157.13/157.09 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 157.13/157.09 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 157.13/157.09 ! [V_d,V_c,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 157.13/157.09 ! [V_d,V_c,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 157.13/157.09 ! [V_c,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 157.13/157.09 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 157.13/157.09 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 157.13/157.09 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 157.13/157.09 ! [V_rx,V_ly,V_lx,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 157.13/157.09 ! [V_rx,V_ly,V_lx,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 157.13/157.09 ! [V_ry,V_rx,V_lx,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 157.13/157.09 ! [V_ry,V_rx,V_lx,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 157.13/157.09 ! [V_b,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_crossproduct__eq,axiom,
% 157.13/157.09 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 157.13/157.09 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 157.13/157.09 => ( 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))
% 157.13/157.09 <=> ( V_w_2 = V_x_2
% 157.13/157.09 | V_y_2 = V_z_2 ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_combine__common__factor,axiom,
% 157.13/157.09 ! [V_c,V_b,V_e,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Osemiring(T_a)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 157.13/157.09 ! [V_b,V_m,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 157.13/157.09 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__class_Odistrib,axiom,
% 157.13/157.09 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring(T_a)
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__diff__inverse,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => 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 ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__diff__conv,axiom,
% 157.13/157.09 ! [V_k_2,V_j_2,V_i_2] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 <=> 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__cancel2,axiom,
% 157.13/157.09 ! [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) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__cancel,axiom,
% 157.13/157.09 ! [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) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__diff__left,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__add__inverse,axiom,
% 157.13/157.09 ! [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 ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__add__inverse2,axiom,
% 157.13/157.09 ! [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 ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__diff__right,axiom,
% 157.13/157.09 ! [V_i,V_j,V_k] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__diff__conv,axiom,
% 157.13/157.09 ! [V_i_2,V_k_2,V_j_2] :
% 157.13/157.09 ( 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))
% 157.13/157.09 <=> 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__add__diff,axiom,
% 157.13/157.09 ! [V_m,V_n,V_k] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__square,axiom,
% 157.13/157.09 ! [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))) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__cube,axiom,
% 157.13/157.09 ! [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)))) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_mult__le__mono1,axiom,
% 157.13/157.09 ! [V_k,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_mult__le__mono2,axiom,
% 157.13/157.09 ! [V_k,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_mult__le__mono,axiom,
% 157.13/157.09 ! [V_l,V_k,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 157.13/157.09 => 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__antisym,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.13/157.09 => V_m = V_n ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__trans,axiom,
% 157.13/157.09 ! [V_k,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_eq__imp__le,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( V_m = V_n
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__le__linear,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__refl,axiom,
% 157.13/157.09 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__not__refl,axiom,
% 157.13/157.09 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__neq__iff,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( V_m_2 != V_n_2
% 157.13/157.09 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_linorder__neqE__nat,axiom,
% 157.13/157.09 ! [V_y,V_x] :
% 157.13/157.09 ( V_x != V_y
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__irrefl__nat,axiom,
% 157.13/157.09 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__not__refl2,axiom,
% 157.13/157.09 ! [V_m,V_n] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 157.13/157.09 => V_m != V_n ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__not__refl3,axiom,
% 157.13/157.09 ! [V_t,V_s] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 157.13/157.09 => V_s != V_t ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__less__cases,axiom,
% 157.13/157.09 ! [V_Pa_2,V_n_2,V_m_2] :
% 157.13/157.09 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 157.13/157.09 => ( ( V_m_2 = V_n_2
% 157.13/157.09 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 157.13/157.09 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 157.13/157.09 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 157.13/157.09 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__less__le,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 & V_m_2 != V_n_2 ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__eq__less__or__eq,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 | V_m_2 = V_n_2 ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__imp__le__nat,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__neq__implies__less,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => ( V_m != V_n
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__or__eq__imp__le,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 | V_m = V_n )
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__lessD1,axiom,
% 157.13/157.09 ! [V_k,V_j,V_i] :
% 157.13/157.09 ( 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))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__add__eq__less,axiom,
% 157.13/157.09 ! [V_n,V_m,V_l,V_k] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 157.13/157.09 => ( 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)
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__less__mono,axiom,
% 157.13/157.09 ! [V_l,V_k,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 157.13/157.09 => 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__less__mono1,axiom,
% 157.13/157.09 ! [V_k,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_trans__less__add2,axiom,
% 157.13/157.09 ! [V_m,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_trans__less__add1,axiom,
% 157.13/157.09 ! [V_m,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__add__left__cancel__less,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_not__add__less2,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_not__add__less1,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__add__right__cancel,axiom,
% 157.13/157.09 ! [V_n_2,V_k_2,V_m_2] :
% 157.13/157.09 ( 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)
% 157.13/157.09 <=> V_m_2 = V_n_2 ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__add__left__cancel,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.09 ( 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)
% 157.13/157.09 <=> V_m_2 = V_n_2 ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__add__assoc,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__add__left__commute,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__add__commute,axiom,
% 157.13/157.09 ! [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) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__add2,axiom,
% 157.13/157.09 ! [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))) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__add1,axiom,
% 157.13/157.09 ! [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))) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__iff__add,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__add__left__cancel__le,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_trans__le__add1,axiom,
% 157.13/157.09 ! [V_m,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_trans__le__add2,axiom,
% 157.13/157.09 ! [V_m,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__le__mono1,axiom,
% 157.13/157.09 ! [V_k,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__le__mono,axiom,
% 157.13/157.09 ! [V_l,V_k,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 157.13/157.09 => 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__leD2,axiom,
% 157.13/157.09 ! [V_n,V_k,V_m] :
% 157.13/157.09 ( 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))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__leD1,axiom,
% 157.13/157.09 ! [V_n,V_k,V_m] :
% 157.13/157.09 ( 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))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__leE,axiom,
% 157.13/157.09 ! [V_n,V_k,V_m] :
% 157.13/157.09 ( 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))
% 157.13/157.09 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__mult__distrib2,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__mult__distrib,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__mult__distrib,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__mult__distrib2,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__diff__iff,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 157.13/157.09 => ( 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)))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Nat_Odiff__diff__eq,axiom,
% 157.13/157.09 ! [V_n,V_m,V_k] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 157.13/157.09 => 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) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_eq__diff__iff,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 157.13/157.09 => ( 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)
% 157.13/157.09 <=> V_m_2 = V_n_2 ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__diff__cancel,axiom,
% 157.13/157.09 ! [V_n,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 157.13/157.09 => 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 ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__le__mono,axiom,
% 157.13/157.09 ! [V_l,V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__le__mono2,axiom,
% 157.13/157.09 ! [V_l,V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__le__self,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__commute,axiom,
% 157.13/157.09 ! [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) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__imp__diff__less,axiom,
% 157.13/157.09 ! [V_n,V_k,V_j] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__less__mono,axiom,
% 157.13/157.09 ! [V_c,V_b,V_a] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 157.13/157.09 => 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__less__mono2,axiom,
% 157.13/157.09 ! [V_l,V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 157.13/157.09 => 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__diff__iff,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 157.13/157.09 => ( 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)))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__add__assoc2,axiom,
% 157.13/157.09 ! [V_i,V_j,V_k] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__diff__assoc2,axiom,
% 157.13/157.09 ! [V_i,V_j,V_k] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__add__assoc,axiom,
% 157.13/157.09 ! [V_i,V_j,V_k] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__imp__diff__is__add,axiom,
% 157.13/157.09 ! [V_k_2,V_j_2,V_i_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 157.13/157.09 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 157.13/157.09 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__add__diff__inverse2,axiom,
% 157.13/157.09 ! [V_m,V_n] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.13/157.09 => 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 ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__diff__conv2,axiom,
% 157.13/157.09 ! [V_i_2,V_j_2,V_k_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 157.13/157.09 => ( 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)))
% 157.13/157.09 <=> 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__diff__assoc,axiom,
% 157.13/157.09 ! [V_i,V_j,V_k] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__add__diff__inverse,axiom,
% 157.13/157.09 ! [V_m,V_n] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.13/157.09 => 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 ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__less__add__iff1,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 157.13/157.09 => ( 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)))
% 157.13/157.09 <=> 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__less__add__iff2,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 157.13/157.09 => ( 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)))
% 157.13/157.09 <=> 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__eq__add__iff2,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 157.13/157.09 => ( 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)
% 157.13/157.09 <=> 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) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__diff__add__eq2,axiom,
% 157.13/157.09 ! [V_n,V_m,V_u,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__le__add__iff2,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 157.13/157.09 => ( 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)))
% 157.13/157.09 <=> 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__eq__add__iff1,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 157.13/157.09 => ( 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)
% 157.13/157.09 <=> 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 ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__diff__add__eq1,axiom,
% 157.13/157.09 ! [V_n,V_m,V_u,V_i,V_j] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__le__add__iff1,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 157.13/157.09 => ( 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)))
% 157.13/157.09 <=> 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_termination__basic__simps_I3_J,axiom,
% 157.13/157.09 ! [V_z,V_y,V_x] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__mult__assoc,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__mult__commute,axiom,
% 157.13/157.09 ! [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) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_left__add__mult__distrib,axiom,
% 157.13/157.09 ! [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) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_termination__basic__simps_I1_J,axiom,
% 157.13/157.09 ! [V_z,V_y,V_x] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_termination__basic__simps_I2_J,axiom,
% 157.13/157.09 ! [V_y,V_z,V_x] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_termination__basic__simps_I5_J,axiom,
% 157.13/157.09 ! [V_y,V_x] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_termination__basic__simps_I4_J,axiom,
% 157.13/157.09 ! [V_y,V_z,V_x] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Sup__fold__sup,axiom,
% 157.13/157.09 ! [V_A_2,T_b] :
% 157.13/157.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fold1__eq__fold,axiom,
% 157.13/157.09 ! [V_a_2,V_A_2,T_b] :
% 157.13/157.09 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.09 => 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) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fold1__Un,axiom,
% 157.13/157.09 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.09 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.09 => ( 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))
% 157.13/157.09 => 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)) ) ) ) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__Diff1__less,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__Diff2__less,axiom,
% 157.13/157.09 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.13/157.09 => 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))) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 157.13/157.09 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.09 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.13/157.09 => ( ! [B_x] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 => hAPP(V_g_2,B_x) = V_z_2 )
% 157.13/157.09 => 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)) ) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fold1__insert,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.13/157.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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)) ) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 157.13/157.09 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.09 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.13/157.09 => ( 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))
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => ~ ! [B_y] :
% 157.13/157.09 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 157.13/157.09 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 157.13/157.09 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 157.13/157.09 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 157.13/157.09 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 157.13/157.09 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_finite__UnionD,axiom,
% 157.13/157.09 ! [V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 157.13/157.09 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fun__left__comm__idem__insert,axiom,
% 157.13/157.09 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fun__left__comm__idem,axiom,
% 157.13/157.09 ! [T_b] :
% 157.13/157.09 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.13/157.09 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fun__left__comm__idem__sup,axiom,
% 157.13/157.09 ! [T_b] :
% 157.13/157.09 ( class_Lattices_Osemilattice__sup(T_b)
% 157.13/157.09 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fun__left__comm__idem__inf,axiom,
% 157.13/157.09 ! [T_b] :
% 157.13/157.09 ( class_Lattices_Osemilattice__inf(T_b)
% 157.13/157.09 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fold1__singleton__def,axiom,
% 157.13/157.09 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 157.13/157.09 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 157.13/157.09 => 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 ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fold1__singleton,axiom,
% 157.13/157.09 ! [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 ).
% 157.13/157.09
% 157.13/157.09 fof(fact_folding__one_Oeq__fold,axiom,
% 157.13/157.09 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 157.13/157.09 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__insert__le,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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)))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__seteq,axiom,
% 157.13/157.09 ! [V_A_2,V_B_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.13/157.09 => ( 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)))
% 157.13/157.09 => V_A_2 = V_B_2 ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__mono,axiom,
% 157.13/157.09 ! [V_A_2,V_B_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.13/157.09 => 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_psubset__card__mono,axiom,
% 157.13/157.09 ! [V_A_2,V_B_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.13/157.09 => 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Sup__fin_OF__eq,axiom,
% 157.13/157.09 ! [V_A_2,T_b] :
% 157.13/157.09 ( class_Lattices_Olattice(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Inf__fin_OF__eq,axiom,
% 157.13/157.09 ! [V_A_2,T_b] :
% 157.13/157.09 ( class_Lattices_Olattice(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__Un__Int,axiom,
% 157.13/157.09 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card_Ounion__inter,axiom,
% 157.13/157.09 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__Diff__subset,axiom,
% 157.13/157.09 ! [V_A_2,V_B_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.13/157.09 => 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__Diff__subset__Int,axiom,
% 157.13/157.09 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__card__le__card__Diff,axiom,
% 157.13/157.09 ! [V_A_2,V_B_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => 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)))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__psubset,axiom,
% 157.13/157.09 ! [V_A_2,V_B_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.13/157.09 => ( 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)))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_sup__Sup__fold__sup,axiom,
% 157.13/157.09 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fold1__belowI,axiom,
% 157.13/157.09 ! [V_a_2,V_A_2,T_b] :
% 157.13/157.09 ( class_Lattices_Osemilattice__inf(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.09 => 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)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_below__fold1__iff,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( class_Lattices_Osemilattice__inf(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.09 => ( 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)))
% 157.13/157.09 <=> ! [B_x] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Sup__fin__Sup,axiom,
% 157.13/157.09 ! [V_A_2,T_b] :
% 157.13/157.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.09 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fold1__insert__idem,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.13/157.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fold1__Un2,axiom,
% 157.13/157.09 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.09 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.09 => 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)) ) ) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fold1__eq__fold__idem,axiom,
% 157.13/157.09 ! [V_a_2,V_A_2,T_b] :
% 157.13/157.09 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__Un__disjoint,axiom,
% 157.13/157.09 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => ( 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))
% 157.13/157.09 => 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)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__Diff1__le,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 157.13/157.09 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 157.13/157.09 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Sup__binary,axiom,
% 157.13/157.09 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_semilattice__big_OF__eq,axiom,
% 157.13/157.09 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 157.13/157.09 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Sup__insert,axiom,
% 157.13/157.09 ! [V_A_2,V_a_2,T_b] :
% 157.13/157.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Sup__singleton,axiom,
% 157.13/157.09 ! [V_a_2,T_b] :
% 157.13/157.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.13/157.09 => 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 ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Sup__empty,axiom,
% 157.13/157.09 ! [T_b] :
% 157.13/157.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Sup__upper,axiom,
% 157.13/157.09 ! [V_A_2,V_x_2,T_b] :
% 157.13/157.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_UnionI,axiom,
% 157.13/157.09 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 157.13/157.09 => 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))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Union__mono,axiom,
% 157.13/157.09 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.09 ( 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))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fold1__in,axiom,
% 157.13/157.09 ! [V_A_2,T_b] :
% 157.13/157.09 ( class_Groups_Oab__semigroup__mult(T_b)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.09 => ( ! [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))))))
% 157.13/157.09 => 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)) ) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Union__empty,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Union__upper,axiom,
% 157.13/157.09 ! [V_A_2,V_B_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.13/157.09 => 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))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Union__insert,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Un__eq__Union,axiom,
% 157.13/157.09 ! [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))))) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Union__Un__distrib,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Union__disjoint,axiom,
% 157.13/157.09 ! [V_A_2,V_C_2,T_b] :
% 157.13/157.09 ( 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))
% 157.13/157.09 <=> ! [B_x] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 157.13/157.09 => 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Union__Int__subset,axiom,
% 157.13/157.09 ! [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)))) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Sup__le__iff,axiom,
% 157.13/157.09 ! [V_b_2,V_A_2,T_b] :
% 157.13/157.09 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.13/157.09 => ( 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))
% 157.13/157.09 <=> ! [B_x] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__Sup__iff,axiom,
% 157.13/157.09 ! [V_S_2,V_a_2,T_b] :
% 157.13/157.09 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.13/157.09 & class_Orderings_Olinorder(T_b) )
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 157.13/157.09 <=> ? [B_x] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.13/157.09 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__Diff__singleton__if,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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)) )
% 157.13/157.09 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__Diff__singleton,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card_Oremove,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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)))))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_finite__Union,axiom,
% 157.13/157.09 ! [V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 157.13/157.09 => ( ! [B_M] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 157.13/157.09 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 157.13/157.09 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card_Oinsert__remove,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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)))))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__Diff__insert,axiom,
% 157.13/157.09 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 157.13/157.09 => 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)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__Suc__Diff1,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod_Oremove,axiom,
% 157.13/157.09 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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)))))) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_insert__partition,axiom,
% 157.13/157.09 ! [V_F_2,V_x_2,T_b] :
% 157.13/157.09 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 157.13/157.09 => ( ! [B_x] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 => ! [B_xa] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 => ( B_x != B_xa
% 157.13/157.09 => 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)) ) ) )
% 157.13/157.09 => 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_lessI,axiom,
% 157.13/157.09 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__mono,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod__infinite,axiom,
% 157.13/157.09 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod_Oinfinite,axiom,
% 157.13/157.09 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod__eq__1__iff,axiom,
% 157.13/157.09 ! [V_f_2,V_F_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.13/157.09 => ( 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)
% 157.13/157.09 <=> ! [B_x] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 157.13/157.09 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_one__reorient,axiom,
% 157.13/157.09 ! [V_x_2,T_b] :
% 157.13/157.09 ( class_Groups_Oone(T_b)
% 157.13/157.09 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 157.13/157.09 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod__empty,axiom,
% 157.13/157.09 ! [V_f_2,T_c,T_b] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod_Oempty,axiom,
% 157.13/157.09 ! [V_g_2,T_c,T_b] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__Suc__1,axiom,
% 157.13/157.09 ! [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 ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__inject,axiom,
% 157.13/157.09 ! [V_y,V_x] :
% 157.13/157.09 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 157.13/157.09 => V_x = V_y ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat_Oinject,axiom,
% 157.13/157.09 ! [V_nat_H_2,V_nat_2] :
% 157.13/157.09 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 157.13/157.09 <=> V_nat_2 = V_nat_H_2 ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__n__not__n,axiom,
% 157.13/157.09 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 157.13/157.09
% 157.13/157.09 fof(fact_n__not__Suc__n,axiom,
% 157.13/157.09 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_mult_Ocomm__neutral,axiom,
% 157.13/157.09 ! [V_a,T_a] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_a)
% 157.13/157.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_mult__1__right,axiom,
% 157.13/157.09 ! [V_a,T_a] :
% 157.13/157.09 ( class_Groups_Omonoid__mult(T_a)
% 157.13/157.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_mult__1,axiom,
% 157.13/157.09 ! [V_a,T_a] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_a)
% 157.13/157.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_mult__1__left,axiom,
% 157.13/157.09 ! [V_a,T_a] :
% 157.13/157.09 ( class_Groups_Omonoid__mult(T_a)
% 157.13/157.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 157.13/157.09 ! [V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 157.13/157.09 ! [V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_not__less__eq,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__Suc__eq,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 157.13/157.09 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 | V_m_2 = V_n_2 ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__less__eq,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_not__less__less__Suc__eq,axiom,
% 157.13/157.09 ! [V_m_2,V_n_2] :
% 157.13/157.09 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 157.13/157.09 <=> V_n_2 = V_m_2 ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__antisym,axiom,
% 157.13/157.09 ! [V_m,V_n] :
% 157.13/157.09 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 157.13/157.09 => V_m = V_n ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__SucI,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__lessI,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__trans__Suc,axiom,
% 157.13/157.09 ! [V_k,V_j,V_i] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__SucE,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => V_m = V_n ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__lessD,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__less__SucD,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__Suc__shift,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__Suc,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_add__Suc__right,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__leD,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__SucE,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__SucI,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__le__mono,axiom,
% 157.13/157.09 ! [V_m_2,V_n_2] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__Suc__eq,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 157.13/157.09 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_not__less__eq__eq,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__n__not__le__n,axiom,
% 157.13/157.09 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__Suc__Suc,axiom,
% 157.13/157.09 ! [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) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__diff__diff,axiom,
% 157.13/157.09 ! [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) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__mult__cancel1,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.09 ( 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)
% 157.13/157.09 <=> V_m_2 = V_n_2 ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__mult__1,axiom,
% 157.13/157.09 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__1__eq__mult__iff,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 157.13/157.09 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.13/157.09 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__mult__1__right,axiom,
% 157.13/157.09 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 157.13/157.09
% 157.13/157.09 fof(fact_nat__mult__eq__1__iff,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.13/157.09 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.13/157.09 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__add__one,axiom,
% 157.13/157.09 ! [V_a,T_a] :
% 157.13/157.09 ( class_Rings_Olinordered__semidom(T_a)
% 157.13/157.09 => 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)))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__1__mult,axiom,
% 157.13/157.09 ! [V_n,V_m,T_a] :
% 157.13/157.09 ( class_Rings_Olinordered__semidom(T_a)
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 157.13/157.09 => 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))) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 157.13/157.09 ! [V_m,V_a,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 157.13/157.09 ! [V_a,V_m,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 157.13/157.09 ! [V_m,T_a] :
% 157.13/157.09 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.09 => 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) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__iff__Suc__add,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__add__Suc2,axiom,
% 157.13/157.09 ! [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)))) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__add__Suc1,axiom,
% 157.13/157.09 ! [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)))) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__eq__Suc__le,axiom,
% 157.13/157.09 ! [V_m_2,V_n_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_less__Suc__eq__le,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__le__eq,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__imp__less__Suc,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__leI,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_le__less__Suc__eq,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.13/157.09 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 157.13/157.09 <=> V_n_2 = V_m_2 ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__le__lessD,axiom,
% 157.13/157.09 ! [V_n,V_m] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 157.13/157.09 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__less__Suc,axiom,
% 157.13/157.09 ! [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))) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__mult__less__cancel1,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_mult__Suc__right,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_mult__Suc,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__diff__le,axiom,
% 157.13/157.09 ! [V_m,V_n] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__mult__le__cancel1,axiom,
% 157.13/157.09 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__Suc__diff__eq2,axiom,
% 157.13/157.09 ! [V_m,V_j,V_k] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__Suc__diff__eq1,axiom,
% 157.13/157.09 ! [V_m,V_j,V_k] :
% 157.13/157.09 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 157.13/157.09 => 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)) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod__insert,axiom,
% 157.13/157.09 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.09 => 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)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod_Oinsert,axiom,
% 157.13/157.09 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod__Un__Int,axiom,
% 157.13/157.09 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => 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)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod_Ounion__inter,axiom,
% 157.13/157.09 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => 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)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__insert__disjoint,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__insert__if,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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) )
% 157.13/157.09 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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)) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod_Oinsert__remove,axiom,
% 157.13/157.09 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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)))))) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod_Ounion__disjoint,axiom,
% 157.13/157.09 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => ( 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))
% 157.13/157.09 => 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)) ) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod__Un__disjoint,axiom,
% 157.13/157.09 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => ( 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))
% 157.13/157.09 => 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)) ) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card__insert,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => 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)))))) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_card_Oinsert,axiom,
% 157.13/157.09 ! [V_x_2,V_A_2,T_b] :
% 157.13/157.09 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.13/157.09 => 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)) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 157.13/157.09 ! [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) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__eq__plus1__left,axiom,
% 157.13/157.09 ! [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) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_Suc__eq__plus1,axiom,
% 157.13/157.09 ! [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)) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod__Un__one,axiom,
% 157.13/157.09 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.13/157.09 => ( ! [B_x] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.13/157.09 => 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)) ) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 157.13/157.09 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.09 => ( ! [B_x] :
% 157.13/157.09 ( 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)))
% 157.13/157.09 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.13/157.09 => 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)) ) ) ) ) ).
% 157.13/157.09
% 157.13/157.09 fof(fact_fold__Un__disjoint,axiom,
% 157.13/157.09 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.09 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.09 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.10 => ( 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))
% 157.13/157.10 => 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)) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setprod__mono__one__left,axiom,
% 157.13/157.10 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 157.13/157.10 => ( ! [B_x] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.13/157.10 => 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) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setprod__mono__one__right,axiom,
% 157.13/157.10 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 157.13/157.10 => ( ! [B_x] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.13/157.10 => 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) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_fold__image__empty,axiom,
% 157.13/157.10 ! [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 ).
% 157.13/157.10
% 157.13/157.10 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 157.13/157.10 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.10 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.13/157.10 => 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) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_fold__image__insert,axiom,
% 157.13/157.10 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Oab__semigroup__mult(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.10 => 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)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setprod_OF__eq,axiom,
% 157.13/157.10 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.10 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => 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) )
% 157.13/157.10 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => 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) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setprod_Oeq__fold,axiom,
% 157.13/157.10 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => 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) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_fold__image__Un__Int,axiom,
% 157.13/157.10 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_comm__monoid__big_OF__eq,axiom,
% 157.13/157.10 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.10 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.13/157.10 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.13/157.10 => 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) )
% 157.13/157.10 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.13/157.10 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_fold__image__Un__one,axiom,
% 157.13/157.10 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.13/157.10 => ( ! [B_x] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.13/157.10 => 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)) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_convex__bound__lt,axiom,
% 157.13/157.10 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 157.13/157.10 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 157.13/157.10 => 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)) ) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_card__partition,axiom,
% 157.13/157.10 ! [V_k_2,V_C_2,T_b] :
% 157.13/157.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 157.13/157.10 => ( ! [B_c] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 157.13/157.10 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 157.13/157.10 => ( ! [B_c1] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 157.13/157.10 => ! [B_c2] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 157.13/157.10 => ( B_c1 != B_c2
% 157.13/157.10 => 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)) ) ) )
% 157.13/157.10 => 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)) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_fold__image__1,axiom,
% 157.13/157.10 ! [V_f_2,V_S_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.13/157.10 => ( ! [B_x] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.13/157.10 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 157.13/157.10 => 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) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_card__Plus,axiom,
% 157.13/157.10 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.13/157.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.13/157.10 => 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)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_fold__image__cong,axiom,
% 157.13/157.10 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Oab__semigroup__mult(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( ! [B_x] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.13/157.10 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 157.13/157.10 => 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) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_inf__le__fold__inf,axiom,
% 157.13/157.10 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 157.13/157.10 ( class_Lattices_Osemilattice__inf(T_b)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( ! [B_x] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_less__zeroE,axiom,
% 157.13/157.10 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_le0,axiom,
% 157.13/157.10 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__less__Suc,axiom,
% 157.13/157.10 ! [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))) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__reorient,axiom,
% 157.13/157.10 ! [V_x_2,T_b] :
% 157.13/157.10 ( class_Groups_Ozero(T_b)
% 157.13/157.10 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 157.13/157.10 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add_Ocomm__neutral,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__add(T_a)
% 157.13/157.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__0__right,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Groups_Omonoid__add(T_a)
% 157.13/157.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_double__zero__sym,axiom,
% 157.13/157.10 ! [V_a_2,T_b] :
% 157.13/157.10 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.13/157.10 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 157.13/157.10 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__0,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__add(T_a)
% 157.13/157.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__0__left,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Groups_Omonoid__add(T_a)
% 157.13/157.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__0__iff,axiom,
% 157.13/157.10 ! [V_a_2,V_b_2,T_b] :
% 157.13/157.10 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 157.13/157.10 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 157.13/157.10 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__zero__left,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Rings_Omult__zero(T_a)
% 157.13/157.10 => 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) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.10 => 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) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__zero__right,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Rings_Omult__zero(T_a)
% 157.13/157.10 => 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) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.13/157.10 => 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) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__eq__0__iff,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.10 ( class_Rings_Oring__no__zero__divisors(T_b)
% 157.13/157.10 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.10 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.10 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_no__zero__divisors,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Ono__zero__divisors(T_a)
% 157.13/157.10 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.13/157.10 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.13/157.10 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_divisors__zero,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Ono__zero__divisors(T_a)
% 157.13/157.10 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 157.13/157.10 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 157.13/157.10 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_diff__0__right,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Groups_Ogroup__add(T_a)
% 157.13/157.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_diff__self,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Groups_Ogroup__add(T_a)
% 157.13/157.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_eq__iff__diff__eq__0,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.10 ( class_Groups_Oab__group__add(T_b)
% 157.13/157.10 => ( V_a_2 = V_b_2
% 157.13/157.10 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_right__minus__eq,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.10 ( class_Groups_Ogroup__add(T_b)
% 157.13/157.10 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.10 <=> V_a_2 = V_b_2 ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__neq__one,axiom,
% 157.13/157.10 ! [T_a] :
% 157.13/157.10 ( class_Rings_Ozero__neq__one(T_a)
% 157.13/157.10 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_one__neq__zero,axiom,
% 157.13/157.10 ! [T_a] :
% 157.13/157.10 ( class_Rings_Ozero__neq__one(T_a)
% 157.13/157.10 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_Suc__neq__Zero,axiom,
% 157.13/157.10 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_Zero__neq__Suc,axiom,
% 157.13/157.10 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_nat_Osimps_I3_J,axiom,
% 157.13/157.10 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_Suc__not__Zero,axiom,
% 157.13/157.10 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_nat_Osimps_I2_J,axiom,
% 157.13/157.10 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_Zero__not__Suc,axiom,
% 157.13/157.10 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_not__less0,axiom,
% 157.13/157.10 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_neq0__conv,axiom,
% 157.13/157.10 ! [V_n_2] :
% 157.13/157.10 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_less__nat__zero__code,axiom,
% 157.13/157.10 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_gr__implies__not0,axiom,
% 157.13/157.10 ! [V_n,V_m] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.13/157.10 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_gr0I,axiom,
% 157.13/157.10 ! [V_n] :
% 157.13/157.10 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__eq__self__zero,axiom,
% 157.13/157.10 ! [V_n,V_m] :
% 157.13/157.10 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 157.13/157.10 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__is__0,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2] :
% 157.13/157.10 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_Nat_Oadd__0__right,axiom,
% 157.13/157.10 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 157.13/157.10
% 157.13/157.10 fof(fact_plus__nat_Oadd__0,axiom,
% 157.13/157.10 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 157.13/157.10
% 157.13/157.10 fof(fact_le__0__eq,axiom,
% 157.13/157.10 ! [V_n_2] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 157.13/157.10 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 157.13/157.10 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_diff__0__eq__0,axiom,
% 157.13/157.10 ! [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) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_minus__nat_Odiff__0,axiom,
% 157.13/157.10 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 157.13/157.10
% 157.13/157.10 fof(fact_diff__self__eq__0,axiom,
% 157.13/157.10 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_diffs0__imp__equal,axiom,
% 157.13/157.10 ! [V_n,V_m] :
% 157.13/157.10 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 => V_m = V_n ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.10 ( 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)
% 157.13/157.10 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 | V_m_2 = V_n_2 ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__0,axiom,
% 157.13/157.10 ! [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) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__0__right,axiom,
% 157.13/157.10 ! [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) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__is__0,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2] :
% 157.13/157.10 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__cancel1,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.10 ( 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)
% 157.13/157.10 <=> ( V_m_2 = V_n_2
% 157.13/157.10 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__cancel2,axiom,
% 157.13/157.10 ! [V_n_2,V_k_2,V_m_2] :
% 157.13/157.10 ( 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)
% 157.13/157.10 <=> ( V_m_2 = V_n_2
% 157.13/157.10 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_finite__PlusD_I2_J,axiom,
% 157.13/157.10 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_finite__PlusD_I1_J,axiom,
% 157.13/157.10 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_finite__Plus,axiom,
% 157.13/157.10 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.13/157.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.13/157.10 => 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))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_finite__Plus__iff,axiom,
% 157.13/157.10 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_card__Plus__conv__if,axiom,
% 157.13/157.10 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.13/157.10 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 157.13/157.10 => 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)) )
% 157.13/157.10 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 157.13/157.10 => 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) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 157.13/157.10 ! [V_a_2,T_b] :
% 157.13/157.10 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 157.13/157.10 ! [V_a_2,T_b] :
% 157.13/157.10 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__nonneg__nonneg,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__nonneg__eq__0__iff,axiom,
% 157.13/157.10 ! [V_y_2,V_x_2,T_b] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 157.13/157.10 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.10 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.10 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__increasing,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__increasing2,axiom,
% 157.13/157.10 ! [V_a,V_b,V_c,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__nonpos__nonpos,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_split__mult__neg__le,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__cancel__semiring(T_a)
% 157.13/157.10 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 157.13/157.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 157.13/157.10 => 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))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_split__mult__pos__le,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__ring(T_a)
% 157.13/157.10 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 157.13/157.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 157.13/157.10 => 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))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__mono,axiom,
% 157.13/157.10 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__semiring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__mono_H,axiom,
% 157.13/157.10 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__semiring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__left__mono__neg,axiom,
% 157.13/157.10 ! [V_c,V_a,V_b,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__ring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__right__mono__neg,axiom,
% 157.13/157.10 ! [V_c,V_a,V_b,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__ring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_comm__mult__left__mono,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__comm__semiring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__left__mono,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__semiring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__right__mono,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__semiring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__nonpos__nonpos,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__ring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__nonpos__nonneg,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__cancel__semiring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__nonneg__nonpos2,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__cancel__semiring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__nonneg__nonpos,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__cancel__semiring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__nonneg__nonneg,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Oordered__cancel__semiring(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__le__0__iff,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 157.13/157.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__le__mult__iff,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 157.13/157.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__le__square,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__ring(T_a)
% 157.13/157.10 => 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))) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 157.13/157.10 ! [V_a_2,T_b] :
% 157.13/157.10 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 157.13/157.10 ! [V_a_2,T_b] :
% 157.13/157.10 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__pos__pos,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__neg__neg,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_pos__add__strict,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semidom(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_not__square__less__zero,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__ring(T_a)
% 157.13/157.10 => ~ 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))) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__less__cancel__right__disj,axiom,
% 157.13/157.10 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 157.13/157.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__less__cancel__left__disj,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 157.13/157.10 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__less__cancel__left__pos,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__pos__pos,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__pos__neg,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__pos__neg2,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__less__mult__pos,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__less__mult__pos2,axiom,
% 157.13/157.10 ! [V_a,V_b,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__less__cancel__left__neg,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__neg__pos,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__neg__neg,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__strict__right__mono,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__strict__left__mono,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_comm__mult__strict__left__mono,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__strict__right__mono__neg,axiom,
% 157.13/157.10 ! [V_c,V_a,V_b,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__strict__left__mono__neg,axiom,
% 157.13/157.10 ! [V_c,V_a,V_b,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_le__iff__diff__le__0,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.10 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 157.13/157.10 <=> 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))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_less__iff__diff__less__0,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.10 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 157.13/157.10 <=> 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))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__scale__eq__noteq,axiom,
% 157.13/157.10 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 157.13/157.10 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 157.13/157.10 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 157.13/157.10 => ( ( V_a = V_b
% 157.13/157.10 & V_c != V_d )
% 157.13/157.10 => 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)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_sum__squares__eq__zero__iff,axiom,
% 157.13/157.10 ! [V_y_2,V_x_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.13/157.10 => ( 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)
% 157.13/157.10 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.10 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__le__one,axiom,
% 157.13/157.10 ! [T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semidom(T_a)
% 157.13/157.10 => 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))) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_not__one__le__zero,axiom,
% 157.13/157.10 ! [T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semidom(T_a)
% 157.13/157.10 => ~ 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))) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_not__one__less__zero,axiom,
% 157.13/157.10 ! [T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semidom(T_a)
% 157.13/157.10 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__less__one,axiom,
% 157.13/157.10 ! [T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semidom(T_a)
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum_Oempty,axiom,
% 157.13/157.10 ! [V_g_2,T_c,T_b] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.13/157.10 => 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) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum__empty,axiom,
% 157.13/157.10 ! [V_f_2,T_c,T_b] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.13/157.10 => 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) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum__infinite,axiom,
% 157.13/157.10 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.10 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => 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) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum_Oinfinite,axiom,
% 157.13/157.10 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.10 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => 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) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setprod__zero__iff,axiom,
% 157.13/157.10 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 157.13/157.10 & class_Rings_Ono__zero__divisors(T_c) )
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( 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)
% 157.13/157.10 <=> ? [B_x] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.13/157.10 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setprod__zero,axiom,
% 157.13/157.10 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Rings_Ocomm__semiring__1(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( ? [B_x] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.13/157.10 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 157.13/157.10 => 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) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_less__Suc__eq__0__disj,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 157.13/157.10 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 | ? [B_j] :
% 157.13/157.10 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_less__Suc0,axiom,
% 157.13/157.10 ! [V_n_2] :
% 157.13/157.10 ( 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))))
% 157.13/157.10 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_gr0__conv__Suc,axiom,
% 157.13/157.10 ! [V_n_2] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 157.13/157.10 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__is__1,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2] :
% 157.13/157.10 ( 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))
% 157.13/157.10 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.13/157.10 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.13/157.10 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_one__is__add,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2] :
% 157.13/157.10 ( 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)
% 157.13/157.10 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.13/157.10 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.13/157.10 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__gr__0,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 157.13/157.10 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_card_Oempty,axiom,
% 157.13/157.10 ! [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) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_card__infinite,axiom,
% 157.13/157.10 ! [V_A_2,T_b] :
% 157.13/157.10 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__eq__1__iff,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2] :
% 157.13/157.10 ( 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))
% 157.13/157.10 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.13/157.10 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__less__diff,axiom,
% 157.13/157.10 ! [V_m_2,V_n_2] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_diff__less,axiom,
% 157.13/157.10 ! [V_m,V_n] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 157.13/157.10 => 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)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__less__mono2,axiom,
% 157.13/157.10 ! [V_k,V_j,V_i] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 157.13/157.10 => 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))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__less__mono1,axiom,
% 157.13/157.10 ! [V_k,V_j,V_i] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 157.13/157.10 => 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))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__less__cancel2,axiom,
% 157.13/157.10 ! [V_n_2,V_k_2,V_m_2] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__less__cancel1,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_nat__0__less__mult__iff,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 157.13/157.10 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_nat__mult__less__cancel1,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_nat__mult__eq__cancel1,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.13/157.10 => ( 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)
% 157.13/157.10 <=> V_m_2 = V_n_2 ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_diff__add__0,axiom,
% 157.13/157.10 ! [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) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_diff__is__0__eq_H,axiom,
% 157.13/157.10 ! [V_n,V_m] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.13/157.10 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_diff__is__0__eq,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2] :
% 157.13/157.10 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_One__nat__def,axiom,
% 157.13/157.10 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__eq__self__implies__10,axiom,
% 157.13/157.10 ! [V_n,V_m] :
% 157.13/157.10 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 157.13/157.10 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.13/157.10 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum__eq__0__iff,axiom,
% 157.13/157.10 ! [V_f_2,V_F_2,T_b] :
% 157.13/157.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.13/157.10 => ( 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)
% 157.13/157.10 <=> ! [B_x] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 157.13/157.10 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__pos__nonneg,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__nonneg__pos,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__strict__increasing,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__strict__increasing2,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__neg__nonpos,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__nonpos__neg,axiom,
% 157.13/157.10 ! [V_b,V_a,T_a] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__le__cancel__left__pos,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__le__cancel__left__neg,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__strict__mono,axiom,
% 157.13/157.10 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__strict__mono_H,axiom,
% 157.13/157.10 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__less__le__imp__less,axiom,
% 157.13/157.10 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__le__less__imp__less,axiom,
% 157.13/157.10 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => 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))) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__right__less__imp__less,axiom,
% 157.13/157.10 ! [V_b,V_c,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring(T_a)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__less__imp__less__right,axiom,
% 157.13/157.10 ! [V_b,V_c,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__left__less__imp__less,axiom,
% 157.13/157.10 ! [V_b,V_a,V_c,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring(T_a)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__less__imp__less__left,axiom,
% 157.13/157.10 ! [V_b,V_a,V_c,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__right__le__imp__le,axiom,
% 157.13/157.10 ! [V_b,V_c,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__left__le__imp__le,axiom,
% 157.13/157.10 ! [V_b,V_a,V_c,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__strict(T_a)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_sum__squares__le__zero__iff,axiom,
% 157.13/157.10 ! [V_y_2,V_x_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.10 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_sum__squares__ge__zero,axiom,
% 157.13/157.10 ! [V_y,V_x,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__ring(T_a)
% 157.13/157.10 => 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)))) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_not__sum__squares__lt__zero,axiom,
% 157.13/157.10 ! [V_y,V_x,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__ring(T_a)
% 157.13/157.10 => ~ 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))) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_sum__squares__gt__zero__iff,axiom,
% 157.13/157.10 ! [V_y_2,V_x_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__ring__strict(T_b)
% 157.13/157.10 => ( 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))))
% 157.13/157.10 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.10 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__left__le__one__le,axiom,
% 157.13/157.10 ! [V_y,V_x,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__idom(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 157.13/157.10 => 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)) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__right__le__one__le,axiom,
% 157.13/157.10 ! [V_y,V_x,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__idom(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 157.13/157.10 => 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)) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_zero__less__two,axiom,
% 157.13/157.10 ! [T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semidom(T_a)
% 157.13/157.10 => 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)))) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_card__eq__0__iff,axiom,
% 157.13/157.10 ! [V_A_2,T_b] :
% 157.13/157.10 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.10 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_card__ge__0__finite,axiom,
% 157.13/157.10 ! [V_A_2,T_b] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_diff__Suc__less,axiom,
% 157.13/157.10 ! [V_i,V_n] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.13/157.10 => 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)) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_Suc__pred,axiom,
% 157.13/157.10 ! [V_n] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.13/157.10 => 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 ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_n__less__m__mult__n,axiom,
% 157.13/157.10 ! [V_m,V_n] :
% 157.13/157.10 ( 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))
% 157.13/157.10 => ( 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))
% 157.13/157.10 => 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))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_n__less__n__mult__m,axiom,
% 157.13/157.10 ! [V_m,V_n] :
% 157.13/157.10 ( 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))
% 157.13/157.10 => ( 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))
% 157.13/157.10 => 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))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_one__less__mult,axiom,
% 157.13/157.10 ! [V_m,V_n] :
% 157.13/157.10 ( 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))
% 157.13/157.10 => ( 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))
% 157.13/157.10 => 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))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_nat__diff__split__asm,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,V_Pa_2] :
% 157.13/157.10 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 157.13/157.10 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 157.13/157.10 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 157.13/157.10 | ? [B_d] :
% 157.13/157.10 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 157.13/157.10 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_nat__diff__split,axiom,
% 157.13/157.10 ! [V_b_2,V_a_2,V_Pa_2] :
% 157.13/157.10 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 157.13/157.10 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 157.13/157.10 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 157.13/157.10 & ! [B_d] :
% 157.13/157.10 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 157.13/157.10 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_one__le__mult__iff,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 <=> ( 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))
% 157.13/157.10 & 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)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__le__cancel2,axiom,
% 157.13/157.10 ! [V_n_2,V_k_2,V_m_2] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__le__cancel1,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_nat__mult__le__cancel1,axiom,
% 157.13/157.10 ! [V_n_2,V_m_2,V_k_2] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum__eq__Suc0__iff,axiom,
% 157.13/157.10 ! [V_f_2,V_A_2,T_b] :
% 157.13/157.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( 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))
% 157.13/157.10 <=> ? [B_x] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.13/157.10 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.13/157.10 & ! [B_xa] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 157.13/157.10 => ( B_x != B_xa
% 157.13/157.10 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum__eq__1__iff,axiom,
% 157.13/157.10 ! [V_f_2,V_A_2,T_b] :
% 157.13/157.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( 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)
% 157.13/157.10 <=> ? [B_x] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.13/157.10 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 157.13/157.10 & ! [B_xa] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 157.13/157.10 => ( B_x != B_xa
% 157.13/157.10 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setprod__pos__nat__iff,axiom,
% 157.13/157.10 ! [V_f_2,V_S_2,T_b] :
% 157.13/157.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> ! [B_x] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.13/157.10 => 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))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_convex__bound__le,axiom,
% 157.13/157.10 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 157.13/157.10 ( class_Rings_Olinordered__semiring__1(T_a)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 157.13/157.10 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 157.13/157.10 => 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)) ) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_card__gt__0__iff,axiom,
% 157.13/157.10 ! [V_A_2,T_b] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.10 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum_Oeq__fold,axiom,
% 157.13/157.10 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => 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) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum_OF__eq,axiom,
% 157.13/157.10 ! [V_g_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.10 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => 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) )
% 157.13/157.10 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => 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) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_Suc__diff__1,axiom,
% 157.13/157.10 ! [V_n] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.13/157.10 => 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 ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_Suc__pred_H,axiom,
% 157.13/157.10 ! [V_n] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.13/157.10 => 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))) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__eq__if,axiom,
% 157.13/157.10 ! [V_n,V_m] :
% 157.13/157.10 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 157.13/157.10 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 => 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)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_mult__eq__if,axiom,
% 157.13/157.10 ! [V_n,V_m] :
% 157.13/157.10 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.13/157.10 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 => 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)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 157.13/157.10 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.13/157.10 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.13/157.10 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.13/157.10 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_even__less__0__iff,axiom,
% 157.13/157.10 ! [V_a_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__idom(T_b)
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_triple_Osize_I1_J,axiom,
% 157.13/157.10 ! [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) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum__mono2,axiom,
% 157.13/157.10 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.13/157.10 => ( ! [B_b] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 157.13/157.10 => 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))) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_Plus__eq__empty__conv,axiom,
% 157.13/157.10 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.13/157.10 ( 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))
% 157.13/157.10 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.13/157.10 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_card_Ounion__inter__neutral,axiom,
% 157.13/157.10 ! [V_B_2,V_A_2,T_b] :
% 157.13/157.10 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.10 => ( ( ? [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)))
% 157.13/157.10 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.13/157.10 => 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)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum__Un__zero,axiom,
% 157.13/157.10 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.13/157.10 => ( ! [B_x] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 157.13/157.10 => 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)) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 157.13/157.10 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.10 => ( ! [B_x] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 157.13/157.10 => 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)) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum__mono3,axiom,
% 157.13/157.10 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 157.13/157.10 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.10 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.13/157.10 => ( ! [B_x] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 157.13/157.10 => 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))) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_bot__nat__def,axiom,
% 157.13/157.10 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_double__eq__0__iff,axiom,
% 157.13/157.10 ! [V_a_2,T_b] :
% 157.13/157.10 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.13/157.10 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.10 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_triple_Osize_I2_J,axiom,
% 157.13/157.10 ! [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) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_card__Suc__eq,axiom,
% 157.13/157.10 ! [V_k_2,V_A_2,T_b] :
% 157.13/157.10 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 157.13/157.10 <=> ? [B_b,B_B] :
% 157.13/157.10 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 157.13/157.10 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 157.13/157.10 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 157.13/157.10 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.13/157.10 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_Ints__odd__less__0,axiom,
% 157.13/157.10 ! [V_a_2,T_b] :
% 157.13/157.10 ( class_Rings_Olinordered__idom(T_b)
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.13/157.10 => ( 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)))
% 157.13/157.10 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_com_Osize_I4_J,axiom,
% 157.13/157.10 ! [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))) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_com_Osize_I12_J,axiom,
% 157.13/157.10 ! [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))) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setprod__diff1,axiom,
% 157.13/157.10 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 157.13/157.10 ( class_Fields_Ofield(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.13/157.10 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 157.13/157.10 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.10 => 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)) )
% 157.13/157.10 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.13/157.10 => 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) ) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_ex__least__nat__less,axiom,
% 157.13/157.10 ! [V_n_2,V_Pa_2] :
% 157.13/157.10 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 157.13/157.10 => ( hBOOL(hAPP(V_Pa_2,V_n_2))
% 157.13/157.10 => ? [B_k] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 157.13/157.10 & ! [B_i] :
% 157.13/157.10 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 157.13/157.10 => ~ hBOOL(hAPP(V_Pa_2,B_i)) )
% 157.13/157.10 & 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)))) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_setsum__mono__zero__right,axiom,
% 157.13/157.10 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 157.13/157.10 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.13/157.10 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.13/157.10 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 157.13/157.10 => ( ! [B_x] :
% 157.13/157.10 ( 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)))
% 157.13/157.10 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 157.13/157.10 => 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) ) ) ) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_divide__zero,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 157.13/157.10 => 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) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_divide__zero__left,axiom,
% 157.13/157.10 ! [V_a,T_a] :
% 157.13/157.10 ( class_Rings_Odivision__ring(T_a)
% 157.13/157.10 => 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) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_add__divide__distrib,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Odivision__ring(T_a)
% 157.13/157.10 => 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)) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_times__divide__eq__right,axiom,
% 157.13/157.10 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.10 ( class_Rings_Odivision__ring(T_a)
% 157.13/157.10 => 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) ) ).
% 157.13/157.10
% 157.13/157.10 fof(fact_diff__divide__distrib,axiom,
% 157.13/157.11 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.11 ( class_Rings_Odivision__ring(T_a)
% 157.13/157.11 => 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)) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_divide__1,axiom,
% 157.13/157.11 ! [V_a,T_a] :
% 157.13/157.11 ( class_Rings_Odivision__ring(T_a)
% 157.13/157.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_eq__divide__imp,axiom,
% 157.13/157.11 ! [V_b,V_a,V_c,T_a] :
% 157.13/157.11 ( class_Rings_Odivision__ring(T_a)
% 157.13/157.11 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.13/157.11 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 157.13/157.11 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_divide__eq__imp,axiom,
% 157.13/157.11 ! [V_a,V_b,V_c,T_a] :
% 157.13/157.11 ( class_Rings_Odivision__ring(T_a)
% 157.13/157.11 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.13/157.11 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 157.13/157.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_nonzero__divide__eq__eq,axiom,
% 157.13/157.11 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 157.13/157.11 ( class_Rings_Odivision__ring(T_b)
% 157.13/157.11 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.11 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 157.13/157.11 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_nonzero__eq__divide__eq,axiom,
% 157.13/157.11 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.13/157.11 ( class_Rings_Odivision__ring(T_b)
% 157.13/157.11 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.11 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 157.13/157.11 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_right__inverse__eq,axiom,
% 157.13/157.11 ! [V_a_2,V_b_2,T_b] :
% 157.13/157.11 ( class_Rings_Odivision__ring(T_b)
% 157.13/157.11 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.11 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 157.13/157.11 <=> V_a_2 = V_b_2 ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_divide__self,axiom,
% 157.13/157.11 ! [V_a,T_a] :
% 157.13/157.11 ( class_Rings_Odivision__ring(T_a)
% 157.13/157.11 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.13/157.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_divide__self__if,axiom,
% 157.13/157.11 ! [V_a,T_a] :
% 157.13/157.11 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 157.13/157.11 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 157.13/157.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 157.13/157.11 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.13/157.11 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_Ints__0,axiom,
% 157.13/157.11 ! [T_b] :
% 157.13/157.11 ( class_Rings_Oring__1(T_b)
% 157.13/157.11 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_Ints__add,axiom,
% 157.13/157.11 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.11 ( class_Rings_Oring__1(T_b)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.13/157.11 => 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))) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_Ints__mult,axiom,
% 157.13/157.11 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.11 ( class_Rings_Oring__1(T_b)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.13/157.11 => 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))) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_Ints__diff,axiom,
% 157.13/157.11 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.11 ( class_Rings_Oring__1(T_b)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.13/157.11 => 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))) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_Ints__1,axiom,
% 157.13/157.11 ! [T_b] :
% 157.13/157.11 ( class_Rings_Oring__1(T_b)
% 157.13/157.11 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_com_Osize_I9_J,axiom,
% 157.13/157.11 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_com_Osize_I1_J,axiom,
% 157.13/157.11 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_Ints__double__eq__0__iff,axiom,
% 157.13/157.11 ! [V_a_2,T_b] :
% 157.13/157.11 ( class_Int_Oring__char__0(T_b)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.13/157.11 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.13/157.11 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_Ints__odd__nonzero,axiom,
% 157.13/157.11 ! [V_a_2,T_b] :
% 157.13/157.11 ( class_Int_Oring__char__0(T_b)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.13/157.11 => 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) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_le__divide__eq,axiom,
% 157.13/157.11 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.13/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.13/157.11 => ( 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)))
% 157.13/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.13/157.11 => 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)) )
% 157.13/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.13/157.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.11 => 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))) )
% 157.13/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_divide__le__eq,axiom,
% 157.13/157.11 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 157.13/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.13/157.11 => ( 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))
% 157.13/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.13/157.11 => 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))) )
% 157.13/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.13/157.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.11 => 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)) )
% 157.13/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_pos__le__divide__eq,axiom,
% 157.13/157.11 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.13/157.11 ( class_Fields_Olinordered__field(T_b)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.13/157.11 => ( 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)))
% 157.13/157.11 <=> 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)) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_pos__divide__le__eq,axiom,
% 157.13/157.11 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 157.13/157.11 ( class_Fields_Olinordered__field(T_b)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.13/157.11 => ( 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))
% 157.13/157.11 <=> 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))) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_mult__imp__div__pos__le,axiom,
% 157.13/157.11 ! [V_z,V_x,V_y,T_a] :
% 157.13/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.13/157.11 => ( 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)))
% 157.13/157.11 => 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)) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_mult__imp__le__div__pos,axiom,
% 157.13/157.11 ! [V_x,V_z,V_y,T_a] :
% 157.13/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.13/157.11 => ( 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))
% 157.13/157.11 => 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))) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_neg__le__divide__eq,axiom,
% 157.13/157.11 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.13/157.11 ( class_Fields_Olinordered__field(T_b)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.11 => ( 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)))
% 157.13/157.11 <=> 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))) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_neg__divide__le__eq,axiom,
% 157.13/157.11 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 157.13/157.11 ( class_Fields_Olinordered__field(T_b)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.11 => ( 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))
% 157.13/157.11 <=> 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)) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_times__divide__times__eq,axiom,
% 157.13/157.11 ! [V_w,V_z,V_y,V_x,T_a] :
% 157.13/157.11 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.13/157.11 => 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)) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_divide__right__mono__neg,axiom,
% 157.13/157.11 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.13/157.11 => 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))) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_divide__right__mono,axiom,
% 157.13/157.11 ! [V_c,V_b,V_a,T_a] :
% 157.13/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.13/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.13/157.11 => 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))) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_divide__le__0__iff,axiom,
% 157.13/157.11 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.13/157.11 => ( 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)))
% 157.13/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.13/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 157.13/157.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_zero__le__divide__iff,axiom,
% 157.13/157.11 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.13/157.11 => ( 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)))
% 157.13/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.13/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 157.13/157.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 157.13/157.11
% 157.13/157.11 fof(fact_zero__less__divide__iff,axiom,
% 157.13/157.11 ! [V_b_2,V_a_2,T_b] :
% 157.13/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.13/157.11 => ( 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)))
% 157.13/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.13/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 157.13/157.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.13/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__less__0__iff,axiom,
% 157.23/157.11 ! [V_b_2,V_a_2,T_b] :
% 157.23/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 157.23/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 157.23/157.11 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__pos__pos,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__pos__neg,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__neg__pos,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__neg__neg,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__strict__right__mono,axiom,
% 157.23/157.11 ! [V_c,V_b,V_a,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__strict__right__mono__neg,axiom,
% 157.23/157.11 ! [V_c,V_a,V_b,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_frac__eq__eq,axiom,
% 157.23/157.11 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 157.23/157.11 ( class_Fields_Ofield(T_b)
% 157.23/157.11 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => ( 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)
% 157.23/157.11 <=> 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) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_mult__divide__mult__cancel__left,axiom,
% 157.23/157.11 ! [V_b,V_a,V_c,T_a] :
% 157.23/157.11 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.23/157.11 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => 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) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_mult__divide__mult__cancel__right,axiom,
% 157.23/157.11 ! [V_b,V_a,V_c,T_a] :
% 157.23/157.11 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.23/157.11 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => 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) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__eq__eq,axiom,
% 157.23/157.11 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 157.23/157.11 ( class_Fields_Ofield__inverse__zero(T_b)
% 157.23/157.11 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 157.23/157.11 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) )
% 157.23/157.11 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_eq__divide__eq,axiom,
% 157.23/157.11 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.23/157.11 ( class_Fields_Ofield__inverse__zero(T_b)
% 157.23/157.11 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 157.23/157.11 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 )
% 157.23/157.11 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__nonpos__neg,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__nonpos__pos,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_frac__le,axiom,
% 157.23/157.11 ! [V_z,V_w,V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 157.23/157.11 => 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))) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_frac__less,axiom,
% 157.23/157.11 ! [V_z,V_w,V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 157.23/157.11 => 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))) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_frac__less2,axiom,
% 157.23/157.11 ! [V_z,V_w,V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 157.23/157.11 => 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))) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__nonneg__neg,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__nonneg__pos,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__strict__left__mono__neg,axiom,
% 157.23/157.11 ! [V_c,V_b,V_a,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.23/157.11 => ( 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)))
% 157.23/157.11 => 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))) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__strict__left__mono,axiom,
% 157.23/157.11 ! [V_c,V_a,V_b,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.23/157.11 => ( 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)))
% 157.23/157.11 => 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))) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_neg__divide__less__eq,axiom,
% 157.23/157.11 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => ( 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))
% 157.23/157.11 <=> 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)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_neg__less__divide__eq,axiom,
% 157.23/157.11 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_mult__imp__less__div__pos,axiom,
% 157.23/157.11 ! [V_x,V_z,V_y,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.23/157.11 => ( 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))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_mult__imp__div__pos__less,axiom,
% 157.23/157.11 ! [V_z,V_x,V_y,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.23/157.11 => ( 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)))
% 157.23/157.11 => 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)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_pos__divide__less__eq,axiom,
% 157.23/157.11 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => ( 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))
% 157.23/157.11 <=> 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_pos__less__divide__eq,axiom,
% 157.23/157.11 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> 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)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__less__eq,axiom,
% 157.23/157.11 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 157.23/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.23/157.11 => ( 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))
% 157.23/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => 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))) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => 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)) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_less__divide__eq,axiom,
% 157.23/157.11 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.23/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => 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)) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => 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))) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_add__num__frac,axiom,
% 157.23/157.11 ! [V_x,V_z,V_y,T_a] :
% 157.23/157.11 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.23/157.11 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => 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) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_add__divide__eq__iff,axiom,
% 157.23/157.11 ! [V_y,V_x,V_z,T_a] :
% 157.23/157.11 ( class_Fields_Ofield(T_a)
% 157.23/157.11 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => 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) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_add__frac__num,axiom,
% 157.23/157.11 ! [V_z,V_x,V_y,T_a] :
% 157.23/157.11 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.23/157.11 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => 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) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__add__eq__iff,axiom,
% 157.23/157.11 ! [V_y,V_x,V_z,T_a] :
% 157.23/157.11 ( class_Fields_Ofield(T_a)
% 157.23/157.11 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => 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) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_add__frac__eq,axiom,
% 157.23/157.11 ! [V_w,V_x,V_z,V_y,T_a] :
% 157.23/157.11 ( class_Fields_Ofield(T_a)
% 157.23/157.11 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => 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)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_diff__frac__eq,axiom,
% 157.23/157.11 ! [V_w,V_x,V_z,V_y,T_a] :
% 157.23/157.11 ( class_Fields_Ofield(T_a)
% 157.23/157.11 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => 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)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__diff__eq__iff,axiom,
% 157.23/157.11 ! [V_y,V_x,V_z,T_a] :
% 157.23/157.11 ( class_Fields_Ofield(T_a)
% 157.23/157.11 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => 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) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_diff__divide__eq__iff,axiom,
% 157.23/157.11 ! [V_y,V_x,V_z,T_a] :
% 157.23/157.11 ( class_Fields_Ofield(T_a)
% 157.23/157.11 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.11 => 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) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_gt__half__sum,axiom,
% 157.23/157.11 ! [V_b,V_a,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.23/157.11 => 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)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_less__half__sum,axiom,
% 157.23/157.11 ! [V_b,V_a,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.23/157.11 => 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))))) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__left__mono__neg,axiom,
% 157.23/157.11 ! [V_c,V_b,V_a,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 157.23/157.11 => ( 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)))
% 157.23/157.11 => 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))) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__left__mono,axiom,
% 157.23/157.11 ! [V_c,V_a,V_b,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 157.23/157.11 => ( 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)))
% 157.23/157.11 => 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))) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_setprod__Un,axiom,
% 157.23/157.11 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.23/157.11 ( class_Fields_Ofield(T_c)
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.23/157.11 => ( ! [B_x] :
% 157.23/157.11 ( 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)))
% 157.23/157.11 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 157.23/157.11 => 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))) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_setsum__mono__zero__left,axiom,
% 157.23/157.11 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 157.23/157.11 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 157.23/157.11 => ( ! [B_x] :
% 157.23/157.11 ( 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)))
% 157.23/157.11 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 157.23/157.11 => 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) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_field__le__mult__one__interval,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.23/157.11 => ( ! [B_z] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 157.23/157.11 => 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)) ) )
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_setprod__pos__nat,axiom,
% 157.23/157.11 ! [V_f_2,V_S_2,T_b] :
% 157.23/157.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.23/157.11 => ( ! [B_x] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.23/157.11 => 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))) )
% 157.23/157.11 => 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))) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_setsum__SucD,axiom,
% 157.23/157.11 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 157.23/157.11 ( 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)
% 157.23/157.11 => ? [B_x] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.23/157.11 & 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))) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osize_I5_J,axiom,
% 157.23/157.11 ! [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))) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osize_I13_J,axiom,
% 157.23/157.11 ! [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))) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_card_Oneutral,axiom,
% 157.23/157.11 ! [V_A_2,T_b] :
% 157.23/157.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.11 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.23/157.11 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.23/157.11 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I4_J,axiom,
% 157.23/157.11 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 157.23/157.11 ( 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)
% 157.23/157.11 <=> ( V_fun_2 = V_fun_H_2
% 157.23/157.11 & V_com1_2 = V_com1_H_2
% 157.23/157.11 & V_com2_2 = V_com2_H_2 ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I44_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I45_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I14_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I15_J,axiom,
% 157.23/157.11 ! [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 ).
% 157.23/157.11
% 157.23/157.11 fof(fact_fold__sup__le__sup,axiom,
% 157.23/157.11 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 157.23/157.11 ( class_Lattices_Osemilattice__sup(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.11 => ( ! [B_x] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_expand__Suc,axiom,
% 157.23/157.11 ! [V_v] :
% 157.23/157.11 ( 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)))
% 157.23/157.11 => 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))) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osize_I11_J,axiom,
% 157.23/157.11 ! [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))) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osize_I3_J,axiom,
% 157.23/157.11 ! [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))) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_UnionE,axiom,
% 157.23/157.11 ! [V_C_2,V_A_2,T_b] :
% 157.23/157.11 ( 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)))
% 157.23/157.11 => ~ ! [B_X] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 157.23/157.11 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_setprod__pos,axiom,
% 157.23/157.11 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.23/157.11 ( class_Rings_Olinordered__semidom(T_c)
% 157.23/157.11 => ( ! [B_x] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 157.23/157.11 => 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))) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_setprod__nonneg,axiom,
% 157.23/157.11 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.23/157.11 ( class_Rings_Olinordered__semidom(T_c)
% 157.23/157.11 => ( ! [B_x] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 157.23/157.11 => 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))) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I2_J,axiom,
% 157.23/157.11 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 157.23/157.11 ( 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)
% 157.23/157.11 <=> ( V_loc_2 = V_loc_H_2
% 157.23/157.11 & V_fun_2 = V_fun_H_2
% 157.23/157.11 & V_com_2 = V_com_H_2 ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_number__of__reorient,axiom,
% 157.23/157.11 ! [V_x_2,V_w_2,T_b] :
% 157.23/157.11 ( class_Int_Onumber(T_b)
% 157.23/157.11 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 157.23/157.11 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_eq__number__of,axiom,
% 157.23/157.11 ! [V_y_2,V_x_2,T_b] :
% 157.23/157.11 ( ( class_Int_Onumber__ring(T_b)
% 157.23/157.11 & class_Int_Oring__char__0(T_b) )
% 157.23/157.11 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 157.23/157.11 <=> V_x_2 = V_y_2 ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_le__number__of,axiom,
% 157.23/157.11 ! [V_y_2,V_x_2,T_b] :
% 157.23/157.11 ( ( class_Int_Onumber__ring(T_b)
% 157.23/157.11 & class_Rings_Olinordered__idom(T_b) )
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_less__number__of,axiom,
% 157.23/157.11 ! [V_y_2,V_x_2,T_b] :
% 157.23/157.11 ( ( class_Int_Onumber__ring(T_b)
% 157.23/157.11 & class_Rings_Olinordered__idom(T_b) )
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_number__of__add,axiom,
% 157.23/157.11 ! [V_w,V_v,T_a] :
% 157.23/157.11 ( class_Int_Onumber__ring(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_add__number__of__eq,axiom,
% 157.23/157.11 ! [V_w,V_v,T_a] :
% 157.23/157.11 ( class_Int_Onumber__ring(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_add__number__of__left,axiom,
% 157.23/157.11 ! [V_z,V_w,V_v,T_a] :
% 157.23/157.11 ( class_Int_Onumber__ring(T_a)
% 157.23/157.11 => 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) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_mult__number__of__left,axiom,
% 157.23/157.11 ! [V_z,V_w,V_v,T_a] :
% 157.23/157.11 ( class_Int_Onumber__ring(T_a)
% 157.23/157.11 => 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) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_arith__simps_I32_J,axiom,
% 157.23/157.11 ! [V_w,V_v,T_a] :
% 157.23/157.11 ( class_Int_Onumber__ring(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_number__of__mult,axiom,
% 157.23/157.11 ! [V_w,V_v,T_a] :
% 157.23/157.11 ( class_Int_Onumber__ring(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_number__of__diff,axiom,
% 157.23/157.11 ! [V_w,V_v,T_a] :
% 157.23/157.11 ( class_Int_Onumber__ring(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I37_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I36_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I34_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I35_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I11_J,axiom,
% 157.23/157.11 ! [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 ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I10_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_le__number__of__eq__not__less,axiom,
% 157.23/157.11 ! [V_w_2,V_v_2,T_b] :
% 157.23/157.11 ( ( class_Int_Onumber(T_b)
% 157.23/157.11 & class_Orderings_Olinorder(T_b) )
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> ~ 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))) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_right__distrib__number__of,axiom,
% 157.23/157.11 ! [V_c,V_b,V_v,T_b] :
% 157.23/157.11 ( ( class_Int_Onumber(T_b)
% 157.23/157.11 & class_Rings_Osemiring(T_b) )
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_left__distrib__number__of,axiom,
% 157.23/157.11 ! [V_v,V_b,V_a,T_b] :
% 157.23/157.11 ( ( class_Int_Onumber(T_b)
% 157.23/157.11 & class_Rings_Osemiring(T_b) )
% 157.23/157.11 => 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))) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_add__number__of__diff1,axiom,
% 157.23/157.11 ! [V_c,V_w,V_v,T_a] :
% 157.23/157.11 ( class_Int_Onumber__ring(T_a)
% 157.23/157.11 => 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) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_left__diff__distrib__number__of,axiom,
% 157.23/157.11 ! [V_v,V_b,V_a,T_b] :
% 157.23/157.11 ( ( class_Int_Onumber(T_b)
% 157.23/157.11 & class_Rings_Oring(T_b) )
% 157.23/157.11 => 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))) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_right__diff__distrib__number__of,axiom,
% 157.23/157.11 ! [V_c,V_b,V_v,T_b] :
% 157.23/157.11 ( ( class_Int_Onumber(T_b)
% 157.23/157.11 & class_Rings_Oring(T_b) )
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_Ints__number__of,axiom,
% 157.23/157.11 ! [V_w_2,T_b] :
% 157.23/157.11 ( class_Int_Onumber__ring(T_b)
% 157.23/157.11 => 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))) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_eq__divide__eq__number__of1,axiom,
% 157.23/157.11 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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))
% 157.23/157.11 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => 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 )
% 157.23/157.11 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_eq__divide__eq__number__of,axiom,
% 157.23/157.11 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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)
% 157.23/157.11 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => 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 )
% 157.23/157.11 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__eq__eq__number__of,axiom,
% 157.23/157.11 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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)
% 157.23/157.11 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => 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) )
% 157.23/157.11 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__eq__eq__number__of1,axiom,
% 157.23/157.11 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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
% 157.23/157.11 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => 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)) )
% 157.23/157.11 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.11 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_less__divide__eq__number__of1,axiom,
% 157.23/157.11 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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))))
% 157.23/157.11 <=> ( ( 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)))
% 157.23/157.11 => 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)) )
% 157.23/157.11 & ( ~ 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)))
% 157.23/157.11 => ( ( 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)))
% 157.23/157.11 => 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)))) )
% 157.23/157.11 & ( ~ 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)))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_less__divide__eq__number__of,axiom,
% 157.23/157.11 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => 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)) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => 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))) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => 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))) ) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__less__eq__number__of,axiom,
% 157.23/157.11 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => 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))) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => 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)) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => 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))) ) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__less__eq__number__of1,axiom,
% 157.23/157.11 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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))
% 157.23/157.11 <=> ( ( 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)))
% 157.23/157.11 => 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)))) )
% 157.23/157.11 & ( ~ 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)))
% 157.23/157.11 => ( ( 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)))
% 157.23/157.11 => 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)) )
% 157.23/157.11 & ( ~ 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)))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__le__eq__number__of1,axiom,
% 157.23/157.11 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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))
% 157.23/157.11 <=> ( ( 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)))
% 157.23/157.11 => 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)))) )
% 157.23/157.11 & ( ~ 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)))
% 157.23/157.11 => ( ( 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)))
% 157.23/157.11 => 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)) )
% 157.23/157.11 & ( ~ 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)))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_divide__le__eq__number__of,axiom,
% 157.23/157.11 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => 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))) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => 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)) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => 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))) ) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_le__divide__eq__number__of,axiom,
% 157.23/157.11 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => 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)) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 157.23/157.11 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => 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))) )
% 157.23/157.11 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 157.23/157.11 => 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))) ) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_le__divide__eq__number__of1,axiom,
% 157.23/157.11 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 157.23/157.11 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.23/157.11 & class_Int_Onumber(T_b) )
% 157.23/157.11 => ( 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))))
% 157.23/157.11 <=> ( ( 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)))
% 157.23/157.11 => 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)) )
% 157.23/157.11 & ( ~ 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)))
% 157.23/157.11 => ( ( 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)))
% 157.23/157.11 => 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)))) )
% 157.23/157.11 & ( ~ 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)))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_finite__induct,axiom,
% 157.23/157.11 ! [V_Pa_2,V_F_2,T_b] :
% 157.23/157.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.23/157.11 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.23/157.11 => ( ! [B_x,B_F] :
% 157.23/157.11 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 157.23/157.11 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 157.23/157.11 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 157.23/157.11 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 157.23/157.11 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_fold1__antimono,axiom,
% 157.23/157.11 ! [V_B_2,V_A_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.23/157.11 => 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))) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osize_I6_J,axiom,
% 157.23/157.11 ! [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))) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osize_I14_J,axiom,
% 157.23/157.11 ! [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))) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_number__of__succ,axiom,
% 157.23/157.11 ! [V_k,T_a] :
% 157.23/157.11 ( class_Int_Onumber__ring(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_field__le__epsilon,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.11 => ( ! [B_e] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 157.23/157.11 => 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))) )
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_pair__box_Osize_I1_J,axiom,
% 157.23/157.11 ! [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))) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_times__numeral__code_I5_J,axiom,
% 157.23/157.11 ! [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)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_plus__numeral__code_I9_J,axiom,
% 157.23/157.11 ! [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)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_less__number__of__int__code,axiom,
% 157.23/157.11 ! [V_l_2,V_k_2] :
% 157.23/157.11 ( 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)))
% 157.23/157.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_less__eq__number__of__int__code,axiom,
% 157.23/157.11 ! [V_l_2,V_k_2] :
% 157.23/157.11 ( 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)))
% 157.23/157.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_pos__zmult__eq__1__iff,axiom,
% 157.23/157.11 ! [V_n_2,V_m_2] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 157.23/157.11 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.23/157.11 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.23/157.11 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_odd__nonzero,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_int__one__le__iff__zero__less,axiom,
% 157.23/157.11 ! [V_z_2] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 157.23/157.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_int__0__less__1,axiom,
% 157.23/157.11 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))) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_le__imp__0__less,axiom,
% 157.23/157.11 ! [V_z] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.23/157.11 => 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))) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_odd__less__0,axiom,
% 157.23/157.11 ! [V_z_2] :
% 157.23/157.11 ( 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)))
% 157.23/157.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zmult__zless__mono2,axiom,
% 157.23/157.11 ! [V_k,V_j,V_i] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 157.23/157.11 => 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))) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zadd__0,axiom,
% 157.23/157.11 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zadd__0__right,axiom,
% 157.23/157.11 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 157.23/157.11
% 157.23/157.11 fof(fact_less__bin__lemma,axiom,
% 157.23/157.11 ! [V_l_2,V_k_2] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 157.23/157.11 <=> 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))) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zadd__left__mono,axiom,
% 157.23/157.11 ! [V_k,V_j,V_i] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 157.23/157.11 => 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))) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zadd__strict__right__mono,axiom,
% 157.23/157.11 ! [V_k,V_j,V_i] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 157.23/157.11 => 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))) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zadd__zless__mono,axiom,
% 157.23/157.11 ! [V_z,V_z_H,V_w,V_w_H] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 157.23/157.11 => 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))) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zle__antisym,axiom,
% 157.23/157.11 ! [V_w,V_z] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 157.23/157.11 => V_z = V_w ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zle__trans,axiom,
% 157.23/157.11 ! [V_k,V_j,V_i] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zle__linear,axiom,
% 157.23/157.11 ! [V_w,V_z] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 157.23/157.11 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zle__refl,axiom,
% 157.23/157.11 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zless__linear,axiom,
% 157.23/157.11 ! [V_y,V_x] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 157.23/157.11 | V_x = V_y
% 157.23/157.11 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zless__le,axiom,
% 157.23/157.11 ! [V_w_2,V_z_2] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 157.23/157.11 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 157.23/157.11 & V_z_2 != V_w_2 ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zadd__assoc,axiom,
% 157.23/157.11 ! [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)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zadd__left__commute,axiom,
% 157.23/157.11 ! [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)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zadd__commute,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zadd__zmult__distrib,axiom,
% 157.23/157.11 ! [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)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zadd__zmult__distrib2,axiom,
% 157.23/157.11 ! [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)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zmult__assoc,axiom,
% 157.23/157.11 ! [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)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zmult__commute,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zdiff__zmult__distrib2,axiom,
% 157.23/157.11 ! [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)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zdiff__zmult__distrib,axiom,
% 157.23/157.11 ! [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)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zless__add1__eq,axiom,
% 157.23/157.11 ! [V_z_2,V_w_2] :
% 157.23/157.11 ( 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))))
% 157.23/157.11 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 157.23/157.11 | V_w_2 = V_z_2 ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zle__add1__eq__le,axiom,
% 157.23/157.11 ! [V_z_2,V_w_2] :
% 157.23/157.11 ( 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))))
% 157.23/157.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_add1__zle__eq,axiom,
% 157.23/157.11 ! [V_z_2,V_w_2] :
% 157.23/157.11 ( 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))
% 157.23/157.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zless__imp__add1__zle,axiom,
% 157.23/157.11 ! [V_z,V_w] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zle__diff1__eq,axiom,
% 157.23/157.11 ! [V_z_2,V_w_2] :
% 157.23/157.11 ( 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))))
% 157.23/157.11 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_succ__def,axiom,
% 157.23/157.11 ! [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)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zmult__1__right,axiom,
% 157.23/157.11 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 157.23/157.11
% 157.23/157.11 fof(fact_zmult__1,axiom,
% 157.23/157.11 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 157.23/157.11
% 157.23/157.11 fof(fact_pair__box_Oinject,axiom,
% 157.23/157.11 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 157.23/157.11 ( 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)
% 157.23/157.11 <=> ( V_a_2 = V_a_H_2
% 157.23/157.11 & V_b_2 = V_b_H_2 ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_Min_Oidem,axiom,
% 157.23/157.11 ! [V_x,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I5_J,axiom,
% 157.23/157.11 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 157.23/157.11 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 157.23/157.11 <=> ( V_fun_2 = V_fun_H_2
% 157.23/157.11 & V_com_2 = V_com_H_2 ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf__assoc,axiom,
% 157.23/157.11 ! [V_z,V_y,V_x,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf_Oassoc,axiom,
% 157.23/157.11 ! [V_c,V_b,V_a,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf__left__commute,axiom,
% 157.23/157.11 ! [V_z,V_y,V_x,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 157.23/157.11 ! [V_c,V_a,V_b,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf__left__idem,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => 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) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 157.23/157.11 ! [V_b,V_a,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => 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) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf__commute,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => 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) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf_Ocommute,axiom,
% 157.23/157.11 ! [V_b,V_a,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => 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) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf_Oidem,axiom,
% 157.23/157.11 ! [V_a,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf__le1,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf__le2,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Ole__iff__inf,axiom,
% 157.23/157.11 ! [V_y_2,V_x_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.23/157.11 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Ole__inf__iff,axiom,
% 157.23/157.11 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.23/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Ole__infI1,axiom,
% 157.23/157.11 ! [V_b,V_x,V_a,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 157.23/157.11 => 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)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Ole__infI2,axiom,
% 157.23/157.11 ! [V_a,V_x,V_b,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 157.23/157.11 => 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)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf__absorb1,axiom,
% 157.23/157.11 ! [V_y,V_x,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.23/157.11 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf__absorb2,axiom,
% 157.23/157.11 ! [V_x,V_y,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.23/157.11 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Ole__infI,axiom,
% 157.23/157.11 ! [V_b,V_a,V_x,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf__greatest,axiom,
% 157.23/157.11 ! [V_z,V_y,V_x,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oinf__mono,axiom,
% 157.23/157.11 ! [V_d,V_b,V_c,V_a,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Ole__infE,axiom,
% 157.23/157.11 ! [V_b,V_a,V_x,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => ( 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)))
% 157.23/157.11 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.23/157.11 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__le__iff__disj,axiom,
% 157.23/157.11 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( 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))
% 157.23/157.11 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 157.23/157.11 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__less__iff__disj,axiom,
% 157.23/157.11 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( 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))
% 157.23/157.11 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 157.23/157.11 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__less__iff__conj,axiom,
% 157.23/157.11 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 157.23/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oless__infI2,axiom,
% 157.23/157.11 ! [V_a,V_x,V_b,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 157.23/157.11 => 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)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Oless__infI1,axiom,
% 157.23/157.11 ! [V_b,V_x,V_a,T_a] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_a)
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 157.23/157.11 => 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)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__add__distrib__left,axiom,
% 157.23/157.11 ! [V_z,V_y,V_x,T_a] :
% 157.23/157.11 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__diff__distrib__left,axiom,
% 157.23/157.11 ! [V_z,V_y,V_x,T_a] :
% 157.23/157.11 ( class_Groups_Oordered__ab__group__add(T_a)
% 157.23/157.11 => 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)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_inf__min,axiom,
% 157.23/157.11 ! [T_b] :
% 157.23/157.11 ( ( class_Lattices_Osemilattice__inf(T_b)
% 157.23/157.11 & class_Orderings_Olinorder(T_b) )
% 157.23/157.11 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__0L,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__0R,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__Suc__Suc,axiom,
% 157.23/157.11 ! [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)) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__diff,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 157.23/157.11 ! [T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I52_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I53_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I46_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I47_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I38_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I39_J,axiom,
% 157.23/157.11 ! [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) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I16_J,axiom,
% 157.23/157.11 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_com_Osimps_I17_J,axiom,
% 157.23/157.11 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__number__of,axiom,
% 157.23/157.11 ! [V_v,V_u,T_b] :
% 157.23/157.11 ( ( class_Int_Onumber(T_b)
% 157.23/157.11 & class_Orderings_Oord(T_b) )
% 157.23/157.11 => ( ( 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)))
% 157.23/157.11 => 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) )
% 157.23/157.11 & ( ~ 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)))
% 157.23/157.11 => 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) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Ofold__inf__insert,axiom,
% 157.23/157.11 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.11 => 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)) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 157.23/157.11 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.23/157.11 => 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))) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Ofold1__belowI,axiom,
% 157.23/157.11 ! [V_a_2,V_A_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.23/157.11 => 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)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 157.23/157.11 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.11 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> ! [B_x] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_fold1__below__iff,axiom,
% 157.23/157.11 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.11 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.11 => ( 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))
% 157.23/157.11 <=> ? [B_x] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.23/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_fold1__strict__below__iff,axiom,
% 157.23/157.11 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.11 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.11 => ( 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))
% 157.23/157.11 <=> ? [B_x] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.23/157.11 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_strict__below__fold1__iff,axiom,
% 157.23/157.11 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.11 ( class_Orderings_Olinorder(T_b)
% 157.23/157.11 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.11 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.11 => ( 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)))
% 157.23/157.11 <=> ! [B_x] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_self__quotient__aux1,axiom,
% 157.23/157.11 ! [V_q,V_r,V_a] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.23/157.11 => ( 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))
% 157.23/157.11 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 157.23/157.11 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 157.23/157.11
% 157.23/157.11 fof(fact_self__quotient__aux2,axiom,
% 157.23/157.11 ! [V_q,V_r,V_a] :
% 157.23/157.11 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.23/157.12 => ( 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))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 157.23/157.12 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 157.23/157.12 ( 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)
% 157.23/157.12 => ( 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)))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_unique__quotient__lemma__neg,axiom,
% 157.23/157.12 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zdiv__mono2__lemma,axiom,
% 157.23/157.12 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 157.23/157.12 ( 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)
% 157.23/157.12 => ( 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)))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_unique__quotient__lemma,axiom,
% 157.23/157.12 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_q__neg__lemma,axiom,
% 157.23/157.12 ! [V_r_H,V_q_H,V_b_H] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_number__of__is__id,axiom,
% 157.23/157.12 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 157.23/157.12
% 157.23/157.12 fof(fact_inf__nat__def,axiom,
% 157.23/157.12 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__0__neq__1,axiom,
% 157.23/157.12 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_q__pos__lemma,axiom,
% 157.23/157.12 ! [V_r_H,V_q_H,V_b_H] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 157.23/157.12 ! [V_y,V_x] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.23/157.12 => 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))) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 157.23/157.12 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))) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 157.23/157.12 ! [V_y,V_x] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.23/157.12 => 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))) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_pair__box_Osize_I2_J,axiom,
% 157.23/157.12 ! [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) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_pair__box_Orecs,axiom,
% 157.23/157.12 ! [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) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_pair__box_Osimps_I2_J,axiom,
% 157.23/157.12 ! [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) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__ord__min,axiom,
% 157.23/157.12 ! [T_b] :
% 157.23/157.12 ( class_Orderings_Oord(T_b)
% 157.23/157.12 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 157.23/157.12 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))) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Suc__nat__number__of__add,axiom,
% 157.23/157.12 ! [V_n,V_v] :
% 157.23/157.12 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.23/157.12 => 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) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_tsub__def,axiom,
% 157.23/157.12 ! [V_x,V_y] :
% 157.23/157.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 157.23/157.12 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 157.23/157.12 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_Oremove,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.23/157.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.23/157.12 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 157.23/157.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.23/157.12 => 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)))))) ) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.23/157.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.23/157.12 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 157.23/157.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.23/157.12 => 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)))))) ) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Suc__nat__number__of,axiom,
% 157.23/157.12 ! [V_v] :
% 157.23/157.12 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.23/157.12 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.23/157.12 => 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)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__number__of__lemma,axiom,
% 157.23/157.12 ! [V_v,T_a] :
% 157.23/157.12 ( class_Int_Onumber__ring(T_a)
% 157.23/157.12 => ( ( 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)))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ 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)))
% 157.23/157.12 => 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) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_Oeq__fold_H,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.23/157.12 => 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) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 157.23/157.12 ! [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)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__eq__iff,axiom,
% 157.23/157.12 ! [V_n_2,V_m_2,T_b] :
% 157.23/157.12 ( class_Nat_Osemiring__char__0(T_b)
% 157.23/157.12 => ( 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)
% 157.23/157.12 <=> V_m_2 = V_n_2 ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_not__neg__int,axiom,
% 157.23/157.12 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_not__neg__0,axiom,
% 157.23/157.12 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_not__neg__1,axiom,
% 157.23/157.12 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__nat__number__of,axiom,
% 157.23/157.12 ! [V_v] :
% 157.23/157.12 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.23/157.12 => 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) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__0,axiom,
% 157.23/157.12 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) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__eq__0__conv,axiom,
% 157.23/157.12 ! [V_n_2] :
% 157.23/157.12 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.23/157.12 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 157.23/157.12 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)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zero__zle__int,axiom,
% 157.23/157.12 ! [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))) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 157.23/157.12 ! [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))) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 157.23/157.12 ! [V_Pa_2] :
% 157.23/157.12 ( ? [B_x] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.23/157.12 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.23/157.12 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 157.23/157.12 ! [V_Pa_2] :
% 157.23/157.12 ( ! [B_x] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.23/157.12 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.23/157.12 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__less__0__conv,axiom,
% 157.23/157.12 ! [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))) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zless__int,axiom,
% 157.23/157.12 ! [V_n_2,V_m_2] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 157.23/157.12 ! [V_y_2,V_x_2] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zle__int,axiom,
% 157.23/157.12 ! [V_n_2,V_m_2] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 157.23/157.12 ! [V_y_2,V_x_2] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zadd__int__left,axiom,
% 157.23/157.12 ! [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) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zadd__int,axiom,
% 157.23/157.12 ! [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)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 157.23/157.12 ! [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)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zle__iff__zadd,axiom,
% 157.23/157.12 ! [V_z_2,V_w_2] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 157.23/157.12 <=> ? [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)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__0__le__iff,axiom,
% 157.23/157.12 ! [V_n,T_a] :
% 157.23/157.12 ( class_Rings_Olinordered__semidom(T_a)
% 157.23/157.12 => 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))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zero__le__imp__of__nat,axiom,
% 157.23/157.12 ! [V_m,T_a] :
% 157.23/157.12 ( class_Rings_Olinordered__semidom(T_a)
% 157.23/157.12 => 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))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__less__0__iff,axiom,
% 157.23/157.12 ! [V_m,T_a] :
% 157.23/157.12 ( class_Rings_Olinordered__semidom(T_a)
% 157.23/157.12 => ~ 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))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__number__of__eq,axiom,
% 157.23/157.12 ! [V_v,T_a] :
% 157.23/157.12 ( class_Int_Onumber__ring(T_a)
% 157.23/157.12 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.23/157.12 => 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) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zmult__int,axiom,
% 157.23/157.12 ! [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)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__mult,axiom,
% 157.23/157.12 ! [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)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 157.23/157.12 ! [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)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__0,axiom,
% 157.23/157.12 ! [T_a] :
% 157.23/157.12 ( class_Rings_Osemiring__1(T_a)
% 157.23/157.12 => 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) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__less__imp__less,axiom,
% 157.23/157.12 ! [V_n,V_m,T_a] :
% 157.23/157.12 ( class_Rings_Olinordered__semidom(T_a)
% 157.23/157.12 => ( 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)))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_less__imp__of__nat__less,axiom,
% 157.23/157.12 ! [V_n,V_m,T_a] :
% 157.23/157.12 ( class_Rings_Olinordered__semidom(T_a)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.23/157.12 => 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))) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__less__iff,axiom,
% 157.23/157.12 ! [V_n_2,V_m_2,T_b] :
% 157.23/157.12 ( class_Rings_Olinordered__semidom(T_b)
% 157.23/157.12 => ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__1,axiom,
% 157.23/157.12 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) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 157.23/157.12 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)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__le__iff,axiom,
% 157.23/157.12 ! [V_n_2,V_m_2,T_b] :
% 157.23/157.12 ( class_Rings_Olinordered__semidom(T_b)
% 157.23/157.12 => ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__add,axiom,
% 157.23/157.12 ! [V_n,V_m,T_a] :
% 157.23/157.12 ( class_Rings_Osemiring__1(T_a)
% 157.23/157.12 => 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)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__mult,axiom,
% 157.23/157.12 ! [V_n,V_m,T_a] :
% 157.23/157.12 ( class_Rings_Osemiring__1(T_a)
% 157.23/157.12 => 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)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__1,axiom,
% 157.23/157.12 ! [T_a] :
% 157.23/157.12 ( class_Rings_Osemiring__1(T_a)
% 157.23/157.12 => 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) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Ints__of__nat,axiom,
% 157.23/157.12 ! [V_n_2,T_b] :
% 157.23/157.12 ( class_Rings_Oring__1(T_b)
% 157.23/157.12 => 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))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_Osingleton,axiom,
% 157.23/157.12 ! [V_x_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => 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 ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_not__neg__eq__ge__0,axiom,
% 157.23/157.12 ! [V_x_2] :
% 157.23/157.12 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_neg__def,axiom,
% 157.23/157.12 ! [V_Z_2] :
% 157.23/157.12 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__le__0__conv,axiom,
% 157.23/157.12 ! [V_n_2] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__Suc0__eq__1,axiom,
% 157.23/157.12 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) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zless__iff__Suc__zadd,axiom,
% 157.23/157.12 ! [V_z_2,V_w_2] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 157.23/157.12 <=> ? [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))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__Suc,axiom,
% 157.23/157.12 ! [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)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zdiff__int,axiom,
% 157.23/157.12 ! [V_m,V_n] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.23/157.12 => 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)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__Suc,axiom,
% 157.23/157.12 ! [V_m,T_a] :
% 157.23/157.12 ( class_Rings_Osemiring__1(T_a)
% 157.23/157.12 => 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)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__diff,axiom,
% 157.23/157.12 ! [V_m,V_n,T_a] :
% 157.23/157.12 ( class_Rings_Oring__1(T_a)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.23/157.12 => 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)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.23/157.12 => 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) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min__le,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.23/157.12 => 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)) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 157.23/157.12 ! [V_x_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => 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 ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min__in,axiom,
% 157.23/157.12 ! [V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_Oin__idem,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.23/157.12 => 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) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_neg__imp__number__of__eq__0,axiom,
% 157.23/157.12 ! [V_v] :
% 157.23/157.12 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.23/157.12 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 157.23/157.12 ! [V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => 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) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_OF__eq,axiom,
% 157.23/157.12 ! [V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => 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) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zero__less__int__conv,axiom,
% 157.23/157.12 ! [V_n_2] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zmult__zless__mono2__lemma,axiom,
% 157.23/157.12 ! [V_k,V_j,V_i] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 157.23/157.12 => 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))) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__0__less__iff,axiom,
% 157.23/157.12 ! [V_n_2,T_b] :
% 157.23/157.12 ( class_Rings_Olinordered__semidom(T_b)
% 157.23/157.12 => ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => 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)) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 157.23/157.12 ! [V_B_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.23/157.12 => 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) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 157.23/157.12 ! [V_B_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.23/157.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => 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)) ) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min__antimono,axiom,
% 157.23/157.12 ! [V_N_2,V_M_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 157.23/157.12 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.23/157.12 => 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))) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 157.23/157.12 ! [V_a_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => 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) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min__insert,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => 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)) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_Osubset__idem,axiom,
% 157.23/157.12 ! [V_B_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.23/157.12 => 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) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min__Un,axiom,
% 157.23/157.12 ! [V_B_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.23/157.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => 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)) ) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_eq__nat__number__of,axiom,
% 157.23/157.12 ! [V_v_H_2,V_v_2] :
% 157.23/157.12 ( 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)
% 157.23/157.12 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 157.23/157.12 => 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))) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 157.23/157.12 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 157.23/157.12 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 157.23/157.12 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_nat__number__of__add__left,axiom,
% 157.23/157.12 ! [V_k,V_v_H,V_v] :
% 157.23/157.12 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.23/157.12 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.23/157.12 => 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) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 157.23/157.12 ! [V_a_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => 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) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 157.23/157.12 ! [V_y,V_x] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.23/157.12 => 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))) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_tsub__eq,axiom,
% 157.23/157.12 ! [V_x,V_y] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 157.23/157.12 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.23/157.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => 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)) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.23/157.12 => 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 )
% 157.23/157.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.23/157.12 => 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)))))) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 157.23/157.12 ! [V_B_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.23/157.12 => ( 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))
% 157.23/157.12 => 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)) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 157.23/157.12 ! [V_B_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.23/157.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => ( 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))
% 157.23/157.12 => 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)) ) ) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.23/157.12 => 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) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_Oinsert,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.23/157.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => 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)) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_Oinsert__remove,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.23/157.12 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 157.23/157.12 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.23/157.12 => 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)))))) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_Ounion__inter,axiom,
% 157.23/157.12 ! [V_B_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.23/157.12 => ( 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))
% 157.23/157.12 => 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)) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_Ounion__disjoint,axiom,
% 157.23/157.12 ! [V_B_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.23/157.12 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => ( 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))
% 157.23/157.12 => 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)) ) ) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zdiff__int__split,axiom,
% 157.23/157.12 ! [V_y_2,V_x_2,V_Pa_2] :
% 157.23/157.12 ( 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))))
% 157.23/157.12 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 157.23/157.12 => 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)))) )
% 157.23/157.12 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 157.23/157.12 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 157.23/157.12 ! [V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => ( ! [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))))))
% 157.23/157.12 => 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)) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min_Oclosed,axiom,
% 157.23/157.12 ! [V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.23/157.12 => ( ! [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))))))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_setsum__bounded,axiom,
% 157.23/157.12 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 157.23/157.12 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 157.23/157.12 & class_Rings_Osemiring__1(T_c) )
% 157.23/157.12 => ( ! [B_i] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 157.23/157.12 => 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))) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_nat__1__add__number__of,axiom,
% 157.23/157.12 ! [V_v] :
% 157.23/157.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => 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)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_nat__number__of__add__1,axiom,
% 157.23/157.12 ! [V_v] :
% 157.23/157.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => 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)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_neg__number__of__pred__iff__0,axiom,
% 157.23/157.12 ! [V_v_2] :
% 157.23/157.12 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 157.23/157.12 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 157.23/157.12 ! [V_y_2,V_x_2] :
% 157.23/157.12 ( 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)
% 157.23/157.12 <=> V_x_2 = V_y_2 ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__int__eq,axiom,
% 157.23/157.12 ! [V_n_2,V_m_2] :
% 157.23/157.12 ( 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)
% 157.23/157.12 <=> V_m_2 = V_n_2 ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Pls__def,axiom,
% 157.23/157.12 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_rel__simps_I19_J,axiom,
% 157.23/157.12 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_rel__simps_I2_J,axiom,
% 157.23/157.12 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_add__Pls__right,axiom,
% 157.23/157.12 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 157.23/157.12
% 157.23/157.12 fof(fact_add__Pls,axiom,
% 157.23/157.12 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 157.23/157.12
% 157.23/157.12 fof(fact_mult__Pls,axiom,
% 157.23/157.12 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 157.23/157.12
% 157.23/157.12 fof(fact_diff__bin__simps_I1_J,axiom,
% 157.23/157.12 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 157.23/157.12
% 157.23/157.12 fof(fact_succ__pred,axiom,
% 157.23/157.12 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 157.23/157.12
% 157.23/157.12 fof(fact_semiring__norm_I112_J,axiom,
% 157.23/157.12 ! [T_a] :
% 157.23/157.12 ( class_Int_Onumber__ring(T_a)
% 157.23/157.12 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_number__of__Pls,axiom,
% 157.23/157.12 ! [T_a] :
% 157.23/157.12 ( class_Int_Onumber__ring(T_a)
% 157.23/157.12 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_add__numeral__0,axiom,
% 157.23/157.12 ! [V_a,T_a] :
% 157.23/157.12 ( class_Int_Onumber__ring(T_a)
% 157.23/157.12 => 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 ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_add__numeral__0__right,axiom,
% 157.23/157.12 ! [V_a,T_a] :
% 157.23/157.12 ( class_Int_Onumber__ring(T_a)
% 157.23/157.12 => 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 ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_number__of2,axiom,
% 157.23/157.12 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))) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_bin__less__0__simps_I1_J,axiom,
% 157.23/157.12 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_nat__number__of__Pls,axiom,
% 157.23/157.12 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_semiring__norm_I113_J,axiom,
% 157.23/157.12 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zero__is__num__zero,axiom,
% 157.23/157.12 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Suc__diff__number__of,axiom,
% 157.23/157.12 ! [V_m,V_v] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 157.23/157.12 => 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))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_not__neg__number__of__Pls,axiom,
% 157.23/157.12 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_le__iff__pred__less,axiom,
% 157.23/157.12 ! [V_l_2,V_k_2] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_pred__def,axiom,
% 157.23/157.12 ! [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)) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_nat__number__of__diff__1,axiom,
% 157.23/157.12 ! [V_v] :
% 157.23/157.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => 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)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_divide__Numeral0,axiom,
% 157.23/157.12 ! [V_x,T_a] :
% 157.23/157.12 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 157.23/157.12 & class_Int_Onumber__ring(T_a) )
% 157.23/157.12 => 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) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_eq__number__of__0,axiom,
% 157.23/157.12 ! [V_v_2] :
% 157.23/157.12 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_eq__0__number__of,axiom,
% 157.23/157.12 ! [V_v_2] :
% 157.23/157.12 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_less__nat__number__of,axiom,
% 157.23/157.12 ! [V_v_H_2,V_v_2] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 157.23/157.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_le__nat__number__of,axiom,
% 157.23/157.12 ! [V_v_H_2,V_v_2] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_le__special_I3_J,axiom,
% 157.23/157.12 ! [V_x_2,T_b] :
% 157.23/157.12 ( ( class_Int_Onumber__ring(T_b)
% 157.23/157.12 & class_Rings_Olinordered__idom(T_b) )
% 157.23/157.12 => ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_le__special_I1_J,axiom,
% 157.23/157.12 ! [V_y_2,T_b] :
% 157.23/157.12 ( ( class_Int_Onumber__ring(T_b)
% 157.23/157.12 & class_Rings_Olinordered__idom(T_b) )
% 157.23/157.12 => ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_less__special_I1_J,axiom,
% 157.23/157.12 ! [V_y_2,T_b] :
% 157.23/157.12 ( ( class_Int_Onumber__ring(T_b)
% 157.23/157.12 & class_Rings_Olinordered__idom(T_b) )
% 157.23/157.12 => ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_less__special_I3_J,axiom,
% 157.23/157.12 ! [V_x_2,T_b] :
% 157.23/157.12 ( ( class_Int_Onumber__ring(T_b)
% 157.23/157.12 & class_Rings_Olinordered__idom(T_b) )
% 157.23/157.12 => ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_less__0__number__of,axiom,
% 157.23/157.12 ! [V_v_2] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_add__nat__number__of,axiom,
% 157.23/157.12 ! [V_v_H,V_v] :
% 157.23/157.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 157.23/157.12 => 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)) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_nat__number__of__mult__left,axiom,
% 157.23/157.12 ! [V_k,V_v_H,V_v] :
% 157.23/157.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => 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) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_mult__nat__number__of,axiom,
% 157.23/157.12 ! [V_v_H,V_v] :
% 157.23/157.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => 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) )
% 157.23/157.12 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 157.23/157.12 => 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)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nats__number__of,axiom,
% 157.23/157.12 ! [V_w_2,T_b] :
% 157.23/157.12 ( class_Int_Onumber__ring(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 157.23/157.12 => 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))) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_decr__mult__lemma,axiom,
% 157.23/157.12 ! [V_k_2,V_Pa_2,V_d_2] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 157.23/157.12 => ( ! [B_x] :
% 157.23/157.12 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.23/157.12 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.23/157.12 => ! [B_x] :
% 157.23/157.12 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.23/157.12 => 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)))) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_incr__mult__lemma,axiom,
% 157.23/157.12 ! [V_k_2,V_Pa_2,V_d_2] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 157.23/157.12 => ( ! [B_x] :
% 157.23/157.12 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.23/157.12 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.23/157.12 => ! [B_x] :
% 157.23/157.12 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.23/157.12 => 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)))) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zero__less__imp__eq__int,axiom,
% 157.23/157.12 ! [V_k] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 157.23/157.12 => ? [B_n] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 157.23/157.12 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_decr__lemma,axiom,
% 157.23/157.12 ! [V_z,V_x,V_d] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 157.23/157.12 => 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)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_incr__lemma,axiom,
% 157.23/157.12 ! [V_x,V_z,V_d] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 157.23/157.12 => 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)))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__idempotent,axiom,
% 157.23/157.12 ! [V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => 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) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__le__D1,axiom,
% 157.23/157.12 ! [V_b,V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__ge__self,axiom,
% 157.23/157.12 ! [V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__zero,axiom,
% 157.23/157.12 ! [T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__eq__0,axiom,
% 157.23/157.12 ! [V_a_2,T_b] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.23/157.12 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.23/157.12 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__add__abs,axiom,
% 157.23/157.12 ! [V_b,V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => 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)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__mult__self,axiom,
% 157.23/157.12 ! [V_a,T_a] :
% 157.23/157.12 ( class_Rings_Olinordered__idom(T_a)
% 157.23/157.12 => 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) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__mult,axiom,
% 157.23/157.12 ! [V_b,V_a,T_a] :
% 157.23/157.12 ( class_Rings_Olinordered__idom(T_a)
% 157.23/157.12 => 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)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__minus__commute,axiom,
% 157.23/157.12 ! [V_b,V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => 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)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__one,axiom,
% 157.23/157.12 ! [T_a] :
% 157.23/157.12 ( class_Rings_Olinordered__idom(T_a)
% 157.23/157.12 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__of__nat,axiom,
% 157.23/157.12 ! [V_n,T_a] :
% 157.23/157.12 ( class_Rings_Olinordered__idom(T_a)
% 157.23/157.12 => 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) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__divide,axiom,
% 157.23/157.12 ! [V_b,V_a,T_a] :
% 157.23/157.12 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.23/157.12 => 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)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__int__eq,axiom,
% 157.23/157.12 ! [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) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__of__nonneg,axiom,
% 157.23/157.12 ! [V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.23/157.12 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__le__zero__iff,axiom,
% 157.23/157.12 ! [V_a_2,T_b] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.23/157.12 => ( 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)))
% 157.23/157.12 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__ge__zero,axiom,
% 157.23/157.12 ! [V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => 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))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__of__pos,axiom,
% 157.23/157.12 ! [V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.23/157.12 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zero__less__abs__iff,axiom,
% 157.23/157.12 ! [V_a_2,T_b] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.23/157.12 => ( 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)))
% 157.23/157.12 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__not__less__zero,axiom,
% 157.23/157.12 ! [V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => ~ 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))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__triangle__ineq,axiom,
% 157.23/157.12 ! [V_b,V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => 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)))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__mult__less,axiom,
% 157.23/157.12 ! [V_d,V_b,V_c,V_a,T_a] :
% 157.23/157.12 ( class_Rings_Olinordered__idom(T_a)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 157.23/157.12 => 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))) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__triangle__ineq2__sym,axiom,
% 157.23/157.12 ! [V_b,V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => 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)))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__triangle__ineq2,axiom,
% 157.23/157.12 ! [V_b,V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => 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)))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__triangle__ineq3,axiom,
% 157.23/157.12 ! [V_b,V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => 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)))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_nonzero__abs__divide,axiom,
% 157.23/157.12 ! [V_a,V_b,T_a] :
% 157.23/157.12 ( class_Fields_Olinordered__field(T_a)
% 157.23/157.12 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.23/157.12 => 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)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__zmult__eq__1,axiom,
% 157.23/157.12 ! [V_n,V_m] :
% 157.23/157.12 ( 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)
% 157.23/157.12 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__mult__pos,axiom,
% 157.23/157.12 ! [V_y,V_x,T_a] :
% 157.23/157.12 ( class_Rings_Olinordered__idom(T_a)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.23/157.12 => 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)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__eq__mult,axiom,
% 157.23/157.12 ! [V_b,V_a,T_a] :
% 157.23/157.12 ( class_Rings_Oordered__ring__abs(T_a)
% 157.23/157.12 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.23/157.12 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 157.23/157.12 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.23/157.12 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 157.23/157.12 => 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)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__diff__triangle__ineq,axiom,
% 157.23/157.12 ! [V_d,V_c,V_b,V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => 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))))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__triangle__ineq4,axiom,
% 157.23/157.12 ! [V_b,V_a,T_a] :
% 157.23/157.12 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.23/157.12 => 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)))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_abs__div__pos,axiom,
% 157.23/157.12 ! [V_x,V_y,T_a] :
% 157.23/157.12 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.23/157.12 => 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)) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_zabs__less__one__iff,axiom,
% 157.23/157.12 ! [V_z_2] :
% 157.23/157.12 ( 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)))
% 157.23/157.12 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nats__0,axiom,
% 157.23/157.12 ! [T_b] :
% 157.23/157.12 ( class_Rings_Osemiring__1(T_b)
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nats__add,axiom,
% 157.23/157.12 ! [V_b_2,V_a_2,T_b] :
% 157.23/157.12 ( class_Rings_Osemiring__1(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 157.23/157.12 => 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))) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nats__mult,axiom,
% 157.23/157.12 ! [V_b_2,V_a_2,T_b] :
% 157.23/157.12 ( class_Rings_Osemiring__1(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 157.23/157.12 => 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))) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Nats__1,axiom,
% 157.23/157.12 ! [T_b] :
% 157.23/157.12 ( class_Rings_Osemiring__1(T_b)
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_of__nat__in__Nats,axiom,
% 157.23/157.12 ! [V_n_2,T_b] :
% 157.23/157.12 ( class_Rings_Osemiring__1(T_b)
% 157.23/157.12 => 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))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_int__val__lemma,axiom,
% 157.23/157.12 ! [V_k_2,V_f_2,V_n_2] :
% 157.23/157.12 ( ! [B_i] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 157.23/157.12 => 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))) )
% 157.23/157.12 => ( 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))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 157.23/157.12 => ? [B_i] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 157.23/157.12 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_nat0__intermed__int__val,axiom,
% 157.23/157.12 ! [V_k_2,V_f_2,V_n_2] :
% 157.23/157.12 ( ! [B_i] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 157.23/157.12 => 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))) )
% 157.23/157.12 => ( 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))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 157.23/157.12 => ? [B_i] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 157.23/157.12 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 157.23/157.12 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( ! [B_x] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 157.23/157.12 => 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))) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Min__eqI,axiom,
% 157.23/157.12 ! [V_x_2,V_A_2,T_b] :
% 157.23/157.12 ( class_Orderings_Olinorder(T_b)
% 157.23/157.12 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.23/157.12 => ( ! [B_y] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 157.23/157.12 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.23/157.12 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_nat__intermed__int__val,axiom,
% 157.23/157.12 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 157.23/157.12 ( ! [B_i] :
% 157.23/157.12 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 157.23/157.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 157.23/157.12 => 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))) )
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 157.23/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 157.23/157.12 => ? [B_i] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 157.23/157.12 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 157.23/157.12 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 157.23/157.12 ! [V_m,V_n] :
% 157.23/157.12 ( 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))
% 157.23/157.12 => 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)))) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_rel__simps_I51_J,axiom,
% 157.23/157.12 ! [V_l_2,V_k_2] :
% 157.23/157.12 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 157.23/157.12 <=> V_k_2 = V_l_2 ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_less__eq__int__code_I16_J,axiom,
% 157.23/157.12 ! [V_k2_2,V_k1_2] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_rel__simps_I34_J,axiom,
% 157.23/157.12 ! [V_l_2,V_k_2] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.23/157.12
% 157.23/157.12 fof(fact_rel__simps_I17_J,axiom,
% 157.23/157.12 ! [V_l_2,V_k_2] :
% 157.23/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 157.23/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_less__int__code_I16_J,axiom,
% 157.29/157.12 ! [V_k2_2,V_k1_2] :
% 157.29/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_rel__simps_I46_J,axiom,
% 157.29/157.12 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 157.29/157.12
% 157.29/157.12 fof(fact_rel__simps_I39_J,axiom,
% 157.29/157.12 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_bin__less__0__simps_I4_J,axiom,
% 157.29/157.12 ! [V_w_2] :
% 157.29/157.12 ( 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)))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_rel__simps_I22_J,axiom,
% 157.29/157.12 ! [V_k_2] :
% 157.29/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_rel__simps_I12_J,axiom,
% 157.29/157.12 ! [V_k_2] :
% 157.29/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_Bit1__def,axiom,
% 157.29/157.12 ! [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) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_neg__number__of__Bit1,axiom,
% 157.29/157.12 ! [V_w_2] :
% 157.29/157.12 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 157.29/157.12 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_succ__Pls,axiom,
% 157.29/157.12 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_number__of__Bit1,axiom,
% 157.29/157.12 ! [V_w,T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => 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)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_mult__numeral__1,axiom,
% 157.29/157.12 ! [V_a,T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => 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 ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_mult__numeral__1__right,axiom,
% 157.29/157.12 ! [V_a,T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => 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 ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_numeral__1__eq__1,axiom,
% 157.29/157.12 ! [T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_semiring__norm_I110_J,axiom,
% 157.29/157.12 ! [T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_rel__simps_I5_J,axiom,
% 157.29/157.12 ! [V_k_2] :
% 157.29/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_rel__simps_I29_J,axiom,
% 157.29/157.12 ! [V_k_2] :
% 157.29/157.12 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_divide__numeral__1,axiom,
% 157.29/157.12 ! [V_a,T_a] :
% 157.29/157.12 ( ( class_Fields_Ofield(T_a)
% 157.29/157.12 & class_Int_Onumber__ring(T_a) )
% 157.29/157.12 => 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 ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_divide__Numeral1,axiom,
% 157.29/157.12 ! [V_x,T_a] :
% 157.29/157.12 ( ( class_Fields_Ofield(T_a)
% 157.29/157.12 & class_Int_Onumber__ring(T_a) )
% 157.29/157.12 => 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 ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_one__is__num__one,axiom,
% 157.29/157.12 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_Numeral1__eq1__nat,axiom,
% 157.29/157.12 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_nat__numeral__1__eq__1,axiom,
% 157.29/157.12 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_numeral__1__eq__Suc__0,axiom,
% 157.29/157.12 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)) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_numeral__3__eq__3,axiom,
% 157.29/157.12 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)))) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 157.29/157.12 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))))) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_Suc3__eq__add__3,axiom,
% 157.29/157.12 ! [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) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 157.29/157.12 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)))) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_le__special_I4_J,axiom,
% 157.29/157.12 ! [V_x_2,T_b] :
% 157.29/157.12 ( ( class_Int_Onumber__ring(T_b)
% 157.29/157.12 & class_Rings_Olinordered__idom(T_b) )
% 157.29/157.12 => ( 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)))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_le__special_I2_J,axiom,
% 157.29/157.12 ! [V_y_2,T_b] :
% 157.29/157.12 ( ( class_Int_Onumber__ring(T_b)
% 157.29/157.12 & class_Rings_Olinordered__idom(T_b) )
% 157.29/157.12 => ( 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)))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_less__special_I2_J,axiom,
% 157.29/157.12 ! [V_y_2,T_b] :
% 157.29/157.12 ( ( class_Int_Onumber__ring(T_b)
% 157.29/157.12 & class_Rings_Olinordered__idom(T_b) )
% 157.29/157.12 => ( 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)))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_less__special_I4_J,axiom,
% 157.29/157.12 ! [V_x_2,T_b] :
% 157.29/157.12 ( ( class_Int_Onumber__ring(T_b)
% 157.29/157.12 & class_Rings_Olinordered__idom(T_b) )
% 157.29/157.12 => ( 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)))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_add__special_I3_J,axiom,
% 157.29/157.12 ! [V_v,T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => 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))) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_add__special_I2_J,axiom,
% 157.29/157.12 ! [V_w,T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => 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)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_one__code__numeral__code,axiom,
% 157.29/157.12 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)) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_diff__special_I2_J,axiom,
% 157.29/157.12 ! [V_v,T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => 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)))) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_diff__special_I1_J,axiom,
% 157.29/157.12 ! [V_w,T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => 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))) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_less__2__cases,axiom,
% 157.29/157.12 ! [V_n] :
% 157.29/157.12 ( 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)))))
% 157.29/157.12 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.12 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_half__gt__zero__iff,axiom,
% 157.29/157.12 ! [V_r_2,T_b] :
% 157.29/157.12 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 157.29/157.12 & class_Int_Onumber__ring(T_b) )
% 157.29/157.12 => ( 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))))))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_half__gt__zero,axiom,
% 157.29/157.12 ! [V_r,T_a] :
% 157.29/157.12 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 157.29/157.12 & class_Int_Onumber__ring(T_a) )
% 157.29/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 157.29/157.12 => 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)))))) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_negative__zle,axiom,
% 157.29/157.12 ! [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))) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_negative__zless,axiom,
% 157.29/157.12 ! [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))) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_minus__number__of__mult,axiom,
% 157.29/157.12 ! [V_z,V_w,T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => 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) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_double__compl,axiom,
% 157.29/157.12 ! [V_x,T_a] :
% 157.29/157.12 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.12 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_uminus__apply,axiom,
% 157.29/157.12 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.29/157.12 ( class_Groups_Ouminus(T_b)
% 157.29/157.12 => 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)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_compl__eq__compl__iff,axiom,
% 157.29/157.12 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.12 ( class_Lattices_Oboolean__algebra(T_b)
% 157.29/157.12 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 157.29/157.12 <=> V_x_2 = V_y_2 ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_minus__minus,axiom,
% 157.29/157.12 ! [V_a,T_a] :
% 157.29/157.12 ( class_Groups_Ogroup__add(T_a)
% 157.29/157.12 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_equation__minus__iff,axiom,
% 157.29/157.12 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.12 ( class_Groups_Ogroup__add(T_b)
% 157.29/157.12 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 157.29/157.12 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_minus__equation__iff,axiom,
% 157.29/157.12 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.12 ( class_Groups_Ogroup__add(T_b)
% 157.29/157.12 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 157.29/157.12 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_neg__equal__iff__equal,axiom,
% 157.29/157.12 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.12 ( class_Groups_Ogroup__add(T_b)
% 157.29/157.12 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 157.29/157.12 <=> V_a_2 = V_b_2 ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_zminus__zminus,axiom,
% 157.29/157.12 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 157.29/157.12
% 157.29/157.12 fof(fact_minus__Bit0,axiom,
% 157.29/157.12 ! [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)) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_rel__simps_I48_J,axiom,
% 157.29/157.12 ! [V_l_2,V_k_2] :
% 157.29/157.12 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 157.29/157.12 <=> V_k_2 = V_l_2 ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_code__numeral__zero__minus__one,axiom,
% 157.29/157.12 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) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_number__of__minus,axiom,
% 157.29/157.12 ! [V_w,T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => 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)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_arith__simps_I30_J,axiom,
% 157.29/157.12 ! [V_w,T_a] :
% 157.29/157.12 ( class_Int_Onumber__ring(T_a)
% 157.29/157.12 => 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)) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_le__imp__neg__le,axiom,
% 157.29/157.12 ! [V_b,V_a,T_a] :
% 157.29/157.12 ( class_Groups_Oordered__ab__group__add(T_a)
% 157.29/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.29/157.12 => 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))) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_neg__le__iff__le,axiom,
% 157.29/157.12 ! [V_a_2,V_b_2,T_b] :
% 157.29/157.12 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.12 => ( 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)))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_minus__le__iff,axiom,
% 157.29/157.12 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.12 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.12 => ( 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))
% 157.29/157.12 <=> 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)) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_le__minus__iff,axiom,
% 157.29/157.12 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.12 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.12 => ( 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)))
% 157.29/157.12 <=> 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))) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_compl__mono,axiom,
% 157.29/157.12 ! [V_y,V_x,T_a] :
% 157.29/157.12 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.12 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.29/157.12 => 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))) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_compl__le__compl__iff,axiom,
% 157.29/157.12 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.12 ( class_Lattices_Oboolean__algebra(T_b)
% 157.29/157.12 => ( 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)))
% 157.29/157.12 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_minus__zero,axiom,
% 157.29/157.12 ! [T_a] :
% 157.29/157.12 ( class_Groups_Ogroup__add(T_a)
% 157.29/157.12 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.29/157.12
% 157.29/157.12 fof(fact_neg__0__equal__iff__equal,axiom,
% 157.29/157.12 ! [V_a_2,T_b] :
% 157.29/157.12 ( class_Groups_Ogroup__add(T_b)
% 157.29/157.12 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 157.29/157.13 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_equal__neg__zero,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.29/157.13 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 157.29/157.13 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__equal__0__iff__equal,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Ogroup__add(T_b)
% 157.29/157.13 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.29/157.13 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__equal__zero,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.29/157.13 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 157.29/157.13 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__less__iff__less,axiom,
% 157.29/157.13 ! [V_a_2,V_b_2,T_b] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__less__iff,axiom,
% 157.29/157.13 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_less__minus__iff,axiom,
% 157.29/157.13 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__add__distrib,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oab__group__add(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__add,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Groups_Ogroup__add(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_add__minus__cancel,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Groups_Ogroup__add(T_a)
% 157.29/157.13 => 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 ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__add__cancel,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Groups_Ogroup__add(T_a)
% 157.29/157.13 => 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 ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_square__eq__iff,axiom,
% 157.29/157.13 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.13 ( class_Rings_Oidom(T_b)
% 157.29/157.13 => ( 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)
% 157.29/157.13 <=> ( V_a_2 = V_b_2
% 157.29/157.13 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__mult__minus,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Rings_Oring(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__mult__commute,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Rings_Oring(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__mult__left,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Rings_Oring(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__mult__right,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Rings_Oring(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__diff__eq,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oab__group__add(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I31_J,axiom,
% 157.29/157.13 ! [V_l_2,V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_less__eq__int__code_I13_J,axiom,
% 157.29/157.13 ! [V_k2_2,V_k1_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_less__int__code_I13_J,axiom,
% 157.29/157.13 ! [V_k2_2,V_k1_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I14_J,axiom,
% 157.29/157.13 ! [V_l_2,V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zminus__0,axiom,
% 157.29/157.13 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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Bit0__Pls,axiom,
% 157.29/157.13 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I38_J,axiom,
% 157.29/157.13 ! [V_l_2] :
% 157.29/157.13 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 157.29/157.13 <=> c_Int_OPls = V_l_2 ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I44_J,axiom,
% 157.29/157.13 ! [V_k_2] :
% 157.29/157.13 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 157.29/157.13 <=> V_k_2 = c_Int_OPls ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I49_J,axiom,
% 157.29/157.13 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I50_J,axiom,
% 157.29/157.13 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Bit0__def,axiom,
% 157.29/157.13 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_add__Bit0__Bit0,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__divide__right,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__divide__divide,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__divide__left,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Rings_Odivision__ring(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mult__Bit0,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_abs__minus__cancel,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__Pls,axiom,
% 157.29/157.13 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zminus__zadd__distrib,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__numeral__code_I5_J,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__bin__simps_I7_J,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmult__zminus,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__le__self__iff,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.29/157.13 => ( 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))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__le__0__iff__le,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_le__minus__self__iff,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__0__le__iff__le,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_less__minus__self__iff,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__less__nonneg,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__less__0__iff__less,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__0__less__iff__less,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_right__minus,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Groups_Ogroup__add(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 157.29/157.13 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Ogroup__add(T_b)
% 157.29/157.13 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 157.29/157.13 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_left__minus,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Groups_Ogroup__add(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_ab__left__minus,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oab__group__add(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__unique,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Groups_Ogroup__add(T_a)
% 157.29/157.13 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__0,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Groups_Ogroup__add(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 157.29/157.13 ! [V_y,V_x,T_a] :
% 157.29/157.13 ( class_Rings_Ocomm__ring__1(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__def,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Groups_Ogroup__add(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_ab__diff__minus,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oab__group__add(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__minus__eq__add,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Groups_Ogroup__add(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 157.29/157.13 ! [V_x,T_a] :
% 157.29/157.13 ( class_Rings_Ocomm__ring__1(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_square__eq__1__iff,axiom,
% 157.29/157.13 ! [V_x_2,T_b] :
% 157.29/157.13 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 157.29/157.13 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 157.29/157.13 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 157.29/157.13 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_compl__inf__bot,axiom,
% 157.29/157.13 ! [V_x,T_a] :
% 157.29/157.13 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_inf__compl__bot,axiom,
% 157.29/157.13 ! [V_x,T_a] :
% 157.29/157.13 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__eq,axiom,
% 157.29/157.13 ! [V_y,V_x,T_a] :
% 157.29/157.13 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_compl__sup,axiom,
% 157.29/157.13 ! [V_y,V_x,T_a] :
% 157.29/157.13 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_compl__inf,axiom,
% 157.29/157.13 ! [V_y,V_x,T_a] :
% 157.29/157.13 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_nonzero__minus__divide__right,axiom,
% 157.29/157.13 ! [V_a,V_b,T_a] :
% 157.29/157.13 ( class_Rings_Odivision__ring(T_a)
% 157.29/157.13 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_nonzero__minus__divide__divide,axiom,
% 157.29/157.13 ! [V_a,V_b,T_a] :
% 157.29/157.13 ( class_Rings_Odivision__ring(T_a)
% 157.29/157.13 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_abs__ge__minus__self,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.29/157.13 => 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))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_abs__le__iff,axiom,
% 157.29/157.13 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.29/157.13 => ( 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))
% 157.29/157.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 157.29/157.13 & 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)) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_abs__leI,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 157.29/157.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_abs__le__D2,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 157.29/157.13 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_abs__less__iff,axiom,
% 157.29/157.13 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.13 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 157.29/157.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_bin__less__0__simps_I3_J,axiom,
% 157.29/157.13 ! [V_w_2] :
% 157.29/157.13 ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I27_J,axiom,
% 157.29/157.13 ! [V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I21_J,axiom,
% 157.29/157.13 ! [V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_less__eq__int__code_I14_J,axiom,
% 157.29/157.13 ! [V_k2_2,V_k1_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I32_J,axiom,
% 157.29/157.13 ! [V_l_2,V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I4_J,axiom,
% 157.29/157.13 ! [V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I10_J,axiom,
% 157.29/157.13 ! [V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I16_J,axiom,
% 157.29/157.13 ! [V_l_2,V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_less__int__code_I15_J,axiom,
% 157.29/157.13 ! [V_k2_2,V_k1_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_add__Bit1__Bit0,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_add__Bit0__Bit1,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zadd__zminus__inverse2,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_negative__eq__positive,axiom,
% 157.29/157.13 ! [V_m_2,V_n_2] :
% 157.29/157.13 ( 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)
% 157.29/157.13 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.13 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__bin__simps_I3_J,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__bin__simps_I9_J,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__bin__simps_I10_J,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_not__int__zless__negative,axiom,
% 157.29/157.13 ! [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)))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__int__def,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__int__def__symmetric,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Ints__minus,axiom,
% 157.29/157.13 ! [V_a_2,T_b] :
% 157.29/157.13 ( class_Rings_Oring__1(T_b)
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.29/157.13 => 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))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__number__of__Bit0,axiom,
% 157.29/157.13 ! [V_w_2] :
% 157.29/157.13 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 157.29/157.13 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_pred__Bit0,axiom,
% 157.29/157.13 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_pred__Bit1,axiom,
% 157.29/157.13 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__Bit1,axiom,
% 157.29/157.13 ! [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))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_succ__Bit1,axiom,
% 157.29/157.13 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_succ__Bit0,axiom,
% 157.29/157.13 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_number__of__Bit0,axiom,
% 157.29/157.13 ! [V_w,T_a] :
% 157.29/157.13 ( class_Int_Onumber__ring(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_abs__minus__le__zero,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.29/157.13 => 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))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_abs__of__nonpos,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.29/157.13 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_abs__of__neg,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.29/157.13 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_abs__if,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Groups_Oabs__if(T_a)
% 157.29/157.13 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.29/157.13 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 157.29/157.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.29/157.13 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_less__eq__int__code_I15_J,axiom,
% 157.29/157.13 ! [V_k2_2,V_k1_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I33_J,axiom,
% 157.29/157.13 ! [V_l_2,V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_less__int__code_I14_J,axiom,
% 157.29/157.13 ! [V_k2_2,V_k1_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_rel__simps_I15_J,axiom,
% 157.29/157.13 ! [V_l_2,V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__number__of__eq,axiom,
% 157.29/157.13 ! [V_w,V_v,T_a] :
% 157.29/157.13 ( class_Int_Onumber__ring(T_a)
% 157.29/157.13 => 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))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mult__Bit1,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_int__zle__neg,axiom,
% 157.29/157.13 ! [V_m_2,V_n_2] :
% 157.29/157.13 ( 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))))
% 157.29/157.13 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.13 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_negative__zle__0,axiom,
% 157.29/157.13 ! [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))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_minus__numeral__code_I6_J,axiom,
% 157.29/157.13 ! [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))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zabs__def,axiom,
% 157.29/157.13 ! [V_i] :
% 157.29/157.13 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 157.29/157.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__zminus__int,axiom,
% 157.29/157.13 ! [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))))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_diff__bin__simps_I8_J,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_add__Bit1__Bit1,axiom,
% 157.29/157.13 ! [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))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zero__code__numeral__code,axiom,
% 157.29/157.13 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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_double__number__of__Bit0,axiom,
% 157.29/157.13 ! [V_w,T_a] :
% 157.29/157.13 ( class_Int_Onumber__ring(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_abs__number__of,axiom,
% 157.29/157.13 ! [V_x,T_a] :
% 157.29/157.13 ( ( class_Int_Onumber__ring(T_a)
% 157.29/157.13 & class_Rings_Olinordered__idom(T_a) )
% 157.29/157.13 => ( ( 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)))
% 157.29/157.13 => 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)) )
% 157.29/157.13 & ( ~ 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)))
% 157.29/157.13 => 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) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_add__number__of__diff2,axiom,
% 157.29/157.13 ! [V_w,V_c,V_v,T_a] :
% 157.29/157.13 ( class_Int_Onumber__ring(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_number__of1,axiom,
% 157.29/157.13 ! [V_n] :
% 157.29/157.13 ( 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)))
% 157.29/157.13 => ( 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))))
% 157.29/157.13 & 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)))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_number__of__pred,axiom,
% 157.29/157.13 ! [V_w,T_a] :
% 157.29/157.13 ( class_Int_Onumber__ring(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_not__zle__0__negative,axiom,
% 157.29/157.13 ! [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))))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_negative__zless__0,axiom,
% 157.29/157.13 ! [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))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mult__2__right,axiom,
% 157.29/157.13 ! [V_z,T_a] :
% 157.29/157.13 ( class_Int_Onumber__ring(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mult__2,axiom,
% 157.29/157.13 ! [V_z,T_a] :
% 157.29/157.13 ( class_Int_Onumber__ring(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_one__add__one__is__two,axiom,
% 157.29/157.13 ! [T_a] :
% 157.29/157.13 ( class_Int_Onumber__ring(T_a)
% 157.29/157.13 => 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))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_numeral__2__eq__2,axiom,
% 157.29/157.13 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))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_semiring__norm_I115_J,axiom,
% 157.29/157.13 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))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 157.29/157.13 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))))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_add__2__eq__Suc,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_add__2__eq__Suc_H,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_nat__mult__2__right,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_nat__mult__2,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 157.29/157.13 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)))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_nat__1__add__1,axiom,
% 157.29/157.13 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))) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_eq__special_I4_J,axiom,
% 157.29/157.13 ! [V_x_2,T_b] :
% 157.29/157.13 ( class_Int_Onumber__ring(T_b)
% 157.29/157.13 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 157.29/157.13 <=> 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))))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_eq__special_I2_J,axiom,
% 157.29/157.13 ! [V_y_2,T_b] :
% 157.29/157.13 ( class_Int_Onumber__ring(T_b)
% 157.29/157.13 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 157.29/157.13 <=> 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)))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__zmod__mult__2,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__number__of__Bit1,axiom,
% 157.29/157.13 ! [V_v,V_w] :
% 157.29/157.13 ( ( 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)))
% 157.29/157.13 => 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)) )
% 157.29/157.13 & ( ~ 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)))
% 157.29/157.13 => 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)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_pos__zmod__mult__2,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.13 => 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))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__zdiv__mult__2,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_ComplI,axiom,
% 157.29/157.13 ! [V_A_2,V_ca_2,T_b] :
% 157.29/157.13 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.29/157.13 => 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))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__zadd1__eq,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__mod__trivial,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zdiv__trivial,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__div__trivial,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_DIVISION__BY__ZERO,axiom,
% 157.29/157.13 ! [V_a] :
% 157.29/157.13 ( 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)
% 157.29/157.13 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__mod__equality,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__mod__equality2,axiom,
% 157.29/157.13 ! [V_c,V_a,V_b,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__div__equality,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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 ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__div__equality2,axiom,
% 157.29/157.13 ! [V_a,V_b,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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 ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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 ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__zmod__equality2,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__zmod__equality,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__zmult1__eq,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zdiv__equality,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zdiv__equality_H,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmult__div__cancel,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__0,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__by__0,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__self,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__add__self2,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__add__self1,axiom,
% 157.29/157.13 ! [V_a,V_b,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__add__right__eq,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__add__left__eq,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__add__eq,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__simps_I2_J,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__simps_I1_J,axiom,
% 157.29/157.13 ! [V_b,V_c,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__add__cong,axiom,
% 157.29/157.13 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 157.29/157.13 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 157.29/157.13 => 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) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__mult__cong,axiom,
% 157.29/157.13 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 157.29/157.13 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 157.29/157.13 => 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) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__simps_I4_J,axiom,
% 157.29/157.13 ! [V_b,V_c,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__mult__mult2,axiom,
% 157.29/157.13 ! [V_b,V_c,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__mult__mult1,axiom,
% 157.29/157.13 ! [V_b,V_a,V_c,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__mult__eq,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__mult__left__eq,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__mult__right__eq,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__diff__right__eq,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Oring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__diff__left__eq,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Oring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__diff__eq,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Oring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__diff__cong,axiom,
% 157.29/157.13 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Oring__div(T_a)
% 157.29/157.13 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 157.29/157.13 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 157.29/157.13 => 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) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__minus__cong,axiom,
% 157.29/157.13 ! [V_a_H,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Oring__div(T_a)
% 157.29/157.13 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 157.29/157.13 => 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) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__minus__eq,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Oring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_ComplE,axiom,
% 157.29/157.13 ! [V_A_2,V_ca_2,T_b] :
% 157.29/157.13 ( 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)))
% 157.29/157.13 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_ComplD,axiom,
% 157.29/157.13 ! [V_A_2,V_ca_2,T_b] :
% 157.29/157.13 ( 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)))
% 157.29/157.13 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Compl__iff,axiom,
% 157.29/157.13 ! [V_A_2,V_ca_2,T_b] :
% 157.29/157.13 ( 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)))
% 157.29/157.13 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__zero,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zero,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__self,axiom,
% 157.29/157.13 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Compl__anti__mono,axiom,
% 157.29/157.13 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.13 => 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))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Compl__subset__Compl__iff,axiom,
% 157.29/157.13 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.13 ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__zminus__zminus,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__zminus2,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__simps_I3_J,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zmult1__eq,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiff__zmod__right,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiff__zmod__left,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zminus__zmod,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zminus__zminus,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zminus2,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__0,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__by__0,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__by__1,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__mult__self2__is__0,axiom,
% 157.29/157.13 ! [V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__mult__self1__is__0,axiom,
% 157.29/157.13 ! [V_a,V_b,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zmult2__eq,axiom,
% 157.29/157.13 ! [V_b,V_a,V_c] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__mult__self1,axiom,
% 157.29/157.13 ! [V_b,V_c,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__mult__self2,axiom,
% 157.29/157.13 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__by__1,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__zminus1__eq__if,axiom,
% 157.29/157.13 ! [V_a,V_b] :
% 157.29/157.13 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => 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)) )
% 157.29/157.13 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => 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)) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__zminus2__eq__if,axiom,
% 157.29/157.13 ! [V_a,V_b] :
% 157.29/157.13 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => 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)) )
% 157.29/157.13 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => 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)) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_iszero__0,axiom,
% 157.29/157.13 ! [T_a] :
% 157.29/157.13 ( class_Rings_Osemiring__1(T_a)
% 157.29/157.13 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_iszero__def,axiom,
% 157.29/157.13 ! [V_z_2,T_b] :
% 157.29/157.13 ( class_Rings_Osemiring__1(T_b)
% 157.29/157.13 => ( c_Int_Oiszero(T_b,V_z_2)
% 157.29/157.13 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 157.29/157.13 ! [V_y,V_x] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.29/157.13 => 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))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_not__iszero__1,axiom,
% 157.29/157.13 ! [T_a] :
% 157.29/157.13 ( class_Rings_Osemiring__1(T_a)
% 157.29/157.13 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 157.29/157.13 ! [V_a_2,V_b_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 157.29/157.13 ! [V_a_2,V_b_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__neg__pos__less0,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.13 => 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))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__self,axiom,
% 157.29/157.13 ! [V_a] :
% 157.29/157.13 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_subset__Compl__self__eq,axiom,
% 157.29/157.13 ! [V_A_2,T_b] :
% 157.29/157.13 ( 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)))
% 157.29/157.13 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 157.29/157.13 ! [V_y,V_x] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.29/157.13 => 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))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__le__nonneg__dividend,axiom,
% 157.29/157.13 ! [V_k,V_m] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_pos__mod__bound,axiom,
% 157.29/157.13 ! [V_a,V_b] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.13 => 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)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__mod__bound,axiom,
% 157.29/157.13 ! [V_a,V_b] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => 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))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Compl__disjoint,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Compl__disjoint2,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__number__of__Bit0,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__eq__0__iff,axiom,
% 157.29/157.13 ! [V_d_2,V_m_2] :
% 157.29/157.13 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Compl__Un,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Compl__Int,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zminus1__not__zero,axiom,
% 157.29/157.13 ! [V_l,V_k] :
% 157.29/157.13 ( 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)
% 157.29/157.13 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zminus2__not__zero,axiom,
% 157.29/157.13 ! [V_l,V_k] :
% 157.29/157.13 ( 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)
% 157.29/157.13 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Compl__Diff__eq,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Diff__Compl,axiom,
% 157.29/157.13 ! [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) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_Diff__eq,axiom,
% 157.29/157.13 ! [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)) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__mult__mult1__if,axiom,
% 157.29/157.13 ! [V_b,V_a,V_c,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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) )
% 157.29/157.13 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__mult__self2__is__id,axiom,
% 157.29/157.13 ! [V_a,V_b,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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 ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__mult__self1__is__id,axiom,
% 157.29/157.13 ! [V_a,V_b,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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 ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__mult__mult2,axiom,
% 157.29/157.13 ! [V_b,V_a,V_c,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__mult__mult1,axiom,
% 157.29/157.13 ! [V_b,V_a,V_c,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__self,axiom,
% 157.29/157.13 ! [V_a,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_split__neg__lemma,axiom,
% 157.29/157.13 ! [V_n_2,V_Pa_2,V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> ! [B_i,B_j] :
% 157.29/157.13 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 & 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) )
% 157.29/157.13 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_split__pos__lemma,axiom,
% 157.29/157.13 ! [V_n_2,V_Pa_2,V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> ! [B_i,B_j] :
% 157.29/157.13 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 157.29/157.13 & 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) )
% 157.29/157.13 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__mono1__neg,axiom,
% 157.29/157.13 ! [V_b,V_a_H,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => 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))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__mono1,axiom,
% 157.29/157.13 ! [V_b,V_a_H,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.13 => 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))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__neg__neg__trivial,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 157.29/157.13 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__mono2__neg,axiom,
% 157.29/157.13 ! [V_b,V_b_H,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 157.29/157.13 => 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))) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__nonpos__pos__le0,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.13 => 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))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 157.29/157.13 ! [V_a_2,V_b_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__pos__pos__trivial,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.29/157.13 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__nonneg__neg__le0,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => 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))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__mono2,axiom,
% 157.29/157.13 ! [V_b,V_b_H,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 157.29/157.13 => 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))) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 157.29/157.13 ! [V_b_2,V_a_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 157.29/157.13 ! [V_i_2,V_k_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 157.29/157.13 ! [V_a_2,V_b_2] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 157.29/157.13 => ( 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)))
% 157.29/157.13 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__eq__0__iff,axiom,
% 157.29/157.13 ! [V_k_2,V_i_2] :
% 157.29/157.13 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 157.29/157.13 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_int__div__less__self,axiom,
% 157.29/157.13 ! [V_k,V_x] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 157.29/157.13 => 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)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zdiv__zmult2__eq,axiom,
% 157.29/157.13 ! [V_b,V_a,V_c] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.29/157.13 => 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) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__neg__neg__trivial,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 157.29/157.13 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__mod__conj,axiom,
% 157.29/157.13 ! [V_a,V_b] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => ( 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)))
% 157.29/157.13 & 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))) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_neg__mod__sign,axiom,
% 157.29/157.13 ! [V_a,V_b] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => 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))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__pos__pos__trivial,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.29/157.13 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_pos__mod__conj,axiom,
% 157.29/157.13 ! [V_a,V_b] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.13 => ( 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)))
% 157.29/157.13 & 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)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_pos__mod__sign,axiom,
% 157.29/157.13 ! [V_a,V_b] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.13 => 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))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_disjoint__eq__subset__Compl,axiom,
% 157.29/157.13 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.13 ( 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))
% 157.29/157.13 <=> 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))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zminus2__eq__if,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => 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) )
% 157.29/157.13 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => 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) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmod__zminus1__eq__if,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => 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) )
% 157.29/157.13 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => 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)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__mult__self1,axiom,
% 157.29/157.13 ! [V_c,V_a,V_b,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__mult__self2,axiom,
% 157.29/157.13 ! [V_c,V_a,V_b,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__add__self2,axiom,
% 157.29/157.13 ! [V_a,V_b,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_div__add__self1,axiom,
% 157.29/157.13 ! [V_a,V_b,T_a] :
% 157.29/157.13 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.13 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.13 => 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)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_iszero__Numeral0,axiom,
% 157.29/157.13 ! [T_a] :
% 157.29/157.13 ( class_Int_Onumber__ring(T_a)
% 157.29/157.13 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_iszero__number__of__Bit1,axiom,
% 157.29/157.13 ! [V_w,T_a] :
% 157.29/157.13 ( ( class_Int_Onumber__ring(T_a)
% 157.29/157.13 & class_Int_Oring__char__0(T_a) )
% 157.29/157.13 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_iszero__number__of__Bit0,axiom,
% 157.29/157.13 ! [V_w_2,T_b] :
% 157.29/157.13 ( ( class_Int_Onumber__ring(T_b)
% 157.29/157.13 & class_Int_Oring__char__0(T_b) )
% 157.29/157.13 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 157.29/157.13 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_mod__pos__neg__trivial,axiom,
% 157.29/157.13 ! [V_b,V_a] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.13 => ( 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)))
% 157.29/157.13 => 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) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_divmod__int__rel__div__eq,axiom,
% 157.29/157.13 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 157.29/157.13 ( 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)
% 157.29/157.13 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 157.29/157.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 157.29/157.13 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_split__zdiv,axiom,
% 157.29/157.13 ! [V_k_2,V_n_2,V_Pa_2] :
% 157.29/157.13 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 157.29/157.13 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.29/157.13 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.29/157.13 => ! [B_i] :
% 157.29/157.13 ( ? [B_j] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 157.29/157.13 & 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) )
% 157.29/157.13 => hBOOL(hAPP(V_Pa_2,B_i)) ) )
% 157.29/157.13 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 => ! [B_i] :
% 157.29/157.13 ( ? [B_j] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.13 & 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) )
% 157.29/157.13 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_divmod__int__rel__mod__eq,axiom,
% 157.29/157.13 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 157.29/157.13 ( 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)
% 157.29/157.13 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 157.29/157.13 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 157.29/157.13 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 157.29/157.13 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.13 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 157.29/157.13
% 157.29/157.13 fof(fact_zmult2__lemma__aux2,axiom,
% 157.29/157.13 ! [V_q,V_r,V_b,V_c] :
% 157.29/157.13 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.29/157.13 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.14 => 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))) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zmult2__lemma__aux1,axiom,
% 157.29/157.14 ! [V_q,V_r,V_b,V_c] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.14 => 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))) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zmult2__lemma__aux4,axiom,
% 157.29/157.14 ! [V_q,V_b,V_r,V_c] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 157.29/157.14 => 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))) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zmult2__lemma__aux3,axiom,
% 157.29/157.14 ! [V_q,V_b,V_r,V_c] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 157.29/157.14 => 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))) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_split__zmod,axiom,
% 157.29/157.14 ! [V_k_2,V_n_2,V_Pa_2] :
% 157.29/157.14 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 157.29/157.14 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.14 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 157.29/157.14 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 157.29/157.14 => ! [B_i,B_j] :
% 157.29/157.14 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 157.29/157.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 157.29/157.14 & 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) )
% 157.29/157.14 => hBOOL(hAPP(V_Pa_2,B_j)) ) )
% 157.29/157.14 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.14 => ! [B_i,B_j] :
% 157.29/157.14 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 157.29/157.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.14 & 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) )
% 157.29/157.14 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zmod__number__of__Bit0,axiom,
% 157.29/157.14 ! [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))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_not__iszero__Numeral1,axiom,
% 157.29/157.14 ! [T_a] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_eq__number__of__eq,axiom,
% 157.29/157.14 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_b)
% 157.29/157.14 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 157.29/157.14 <=> 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)))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zdiv__number__of__Bit1,axiom,
% 157.29/157.14 ! [V_v,V_w] :
% 157.29/157.14 ( ( 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)))
% 157.29/157.14 => 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)) )
% 157.29/157.14 & ( ~ 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)))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_eq__special_I3_J,axiom,
% 157.29/157.14 ! [V_x_2,T_b] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_b)
% 157.29/157.14 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.29/157.14 <=> 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)))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_eq__special_I1_J,axiom,
% 157.29/157.14 ! [V_y_2,T_b] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_b)
% 157.29/157.14 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 157.29/157.14 <=> 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)))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_pos__zdiv__mult__2,axiom,
% 157.29/157.14 ! [V_b,V_a] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__of__aux__code,axiom,
% 157.29/157.14 ! [V_n,V_i] :
% 157.29/157.14 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.14 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 157.29/157.14 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_z3div__def,axiom,
% 157.29/157.14 ! [V_k,V_l] :
% 157.29/157.14 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.29/157.14 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_z3mod__def,axiom,
% 157.29/157.14 ! [V_k,V_l] :
% 157.29/157.14 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.29/157.14 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_of__nat__double,axiom,
% 157.29/157.14 ! [V_x,T_a] :
% 157.29/157.14 ( class_Rings_Osemiring__1(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__minus1__odd,axiom,
% 157.29/157.14 ! [V_n,T_a] :
% 157.29/157.14 ( class_Rings_Oring__1(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_odd__power__less__zero,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_double__complement,axiom,
% 157.29/157.14 ! [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 ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Compl__eq__Compl__iff,axiom,
% 157.29/157.14 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.14 ( 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)
% 157.29/157.14 <=> V_A_2 = V_B_2 ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__mult2__eq,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__mult1__eq,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__power__eq,axiom,
% 157.29/157.14 ! [V_n,V_z] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__add1__eq,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 157.29/157.14 ! [V_n,V_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Divides_Omod__div__equality_H,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mult__div__cancel,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__mod__equality_H,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_int__power,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zpower__int,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 157.29/157.14 ! [V_q,V_y,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__le__dividend,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__le__mono,axiom,
% 157.29/157.14 ! [V_k,V_n,V_m] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.29/157.14 => 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))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__mult2__eq,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__less,axiom,
% 157.29/157.14 ! [V_n,V_m] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.29/157.14 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__less__eq__dividend,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__mult__distrib2,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__mult__distrib,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__int,axiom,
% 157.29/157.14 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 157.29/157.14
% 157.29/157.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 157.29/157.14 ! [V_q,V_p,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zpower__zpower,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 157.29/157.14 ! [V_x,T_a] :
% 157.29/157.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.14 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zpower__zmod,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__nat__number__of__number__of,axiom,
% 157.29/157.14 ! [V_w,V_v] :
% 157.29/157.14 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.29/157.14 => 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)) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__nat__number__of,axiom,
% 157.29/157.14 ! [V_n,V_v] :
% 157.29/157.14 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.29/157.14 => 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) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 157.29/157.14 ! [V_y,V_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__div__distrib,axiom,
% 157.29/157.14 ! [V_y,V_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 157.29/157.14 ! [V_y,V_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__mod__distrib,axiom,
% 157.29/157.14 ! [V_y,V_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__1,axiom,
% 157.29/157.14 ! [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 ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__less,axiom,
% 157.29/157.14 ! [V_n,V_m] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.29/157.14 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__mult__div__cancel__disj,axiom,
% 157.29/157.14 ! [V_n,V_m,V_k] :
% 157.29/157.14 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 => 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) )
% 157.29/157.14 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 => 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) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 157.29/157.14 ! [V_q,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 157.29/157.14 ! [V_q,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 157.29/157.14 ! [V_q,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__0,axiom,
% 157.29/157.14 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 157.29/157.14 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__Suc,axiom,
% 157.29/157.14 ! [V_n,V_m] :
% 157.29/157.14 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 157.29/157.14 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.29/157.14 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__1,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__less__divisor,axiom,
% 157.29/157.14 ! [V_m,V_n] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 157.29/157.14 ! [V_x,T_a] :
% 157.29/157.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 157.29/157.14 ! [V_q,V_p,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_eq__nat__nat__iff,axiom,
% 157.29/157.14 ! [V_z_H_2,V_z_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 157.29/157.14 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 157.29/157.14 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_ex__nat,axiom,
% 157.29/157.14 ! [V_Pa_2] :
% 157.29/157.14 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.29/157.14 <=> ? [B_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.29/157.14 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_all__nat,axiom,
% 157.29/157.14 ! [V_Pa_2] :
% 157.29/157.14 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.29/157.14 <=> ! [B_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.29/157.14 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 157.29/157.14 ! [V_y_2,V_x_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 157.29/157.14 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 157.29/157.14 <=> V_x_2 = V_y_2 ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__eq__0__iff,axiom,
% 157.29/157.14 ! [V_d_2,V_m_2] :
% 157.29/157.14 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 157.29/157.14 ! [V_n,V_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.14 => 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))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__geq,axiom,
% 157.29/157.14 ! [V_n,V_m] :
% 157.29/157.14 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__if,axiom,
% 157.29/157.14 ! [V_n,V_m] :
% 157.29/157.14 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.29/157.14 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 157.29/157.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.29/157.14 => 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) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__mult__self3,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_le__mod__geq,axiom,
% 157.29/157.14 ! [V_m,V_n] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zdiv__int,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__number__of,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__number__of__def,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zpower__zadd__distrib,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 157.29/157.14 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zmod__int,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_neg__nat,axiom,
% 157.29/157.14 ! [V_z] :
% 157.29/157.14 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 157.29/157.14 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_not__neg__nat,axiom,
% 157.29/157.14 ! [V_z] :
% 157.29/157.14 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 157.29/157.14 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Ints__power,axiom,
% 157.29/157.14 ! [V_n_2,V_a_2,T_b] :
% 157.29/157.14 ( class_Rings_Oring__1(T_b)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__nat__number__of,axiom,
% 157.29/157.14 ! [V_v_H,V_v] :
% 157.29/157.14 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.29/157.14 => 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) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__nat__number__of,axiom,
% 157.29/157.14 ! [V_v_H,V_v] :
% 157.29/157.14 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.29/157.14 => 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) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 157.29/157.14 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.29/157.14 => 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) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.29/157.14 => 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))) ) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_one__div__nat__number__of,axiom,
% 157.29/157.14 ! [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))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__le__mono2,axiom,
% 157.29/157.14 ! [V_k,V_n,V_m] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__mult__self1__is__m,axiom,
% 157.29/157.14 ! [V_m,V_n] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.14 => 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 ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__mult__self__is__m,axiom,
% 157.29/157.14 ! [V_m,V_n] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.14 => 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 ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__mult__div__cancel1,axiom,
% 157.29/157.14 ! [V_n,V_m,V_k] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__less__dividend,axiom,
% 157.29/157.14 ! [V_m,V_n] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__0__iff,axiom,
% 157.29/157.14 ! [V_i_2] :
% 157.29/157.14 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__le__0,axiom,
% 157.29/157.14 ! [V_z] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.14 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__mono__iff,axiom,
% 157.29/157.14 ! [V_w_2,V_z_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 157.29/157.14 => ( 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)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zless__nat__conj,axiom,
% 157.29/157.14 ! [V_z_2,V_w_2] :
% 157.29/157.14 ( 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)))
% 157.29/157.14 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 157.29/157.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__le__divisor,axiom,
% 157.29/157.14 ! [V_m,V_n] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 157.29/157.14 ! [V_y_2,V_x_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 157.29/157.14 => ( 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)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__1,axiom,
% 157.29/157.14 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__mult__self4,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_int__nat__eq,axiom,
% 157.29/157.14 ! [V_z] :
% 157.29/157.14 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.29/157.14 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 157.29/157.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.29/157.14 => 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) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_int__eq__iff,axiom,
% 157.29/157.14 ! [V_z_2,V_m_2] :
% 157.29/157.14 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 157.29/157.14 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 157.29/157.14 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__0__le,axiom,
% 157.29/157.14 ! [V_z] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.29/157.14 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zless__nat__eq__int__zless,axiom,
% 157.29/157.14 ! [V_z_2,V_m_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 157.29/157.14 <=> 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__zminus__int,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zero__le__zpower__abs,axiom,
% 157.29/157.14 ! [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))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__abs__mult__distrib,axiom,
% 157.29/157.14 ! [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))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_one__mod__nat__number__of,axiom,
% 157.29/157.14 ! [V_v_H] :
% 157.29/157.14 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.29/157.14 => 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)) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__geq,axiom,
% 157.29/157.14 ! [V_m,V_n] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.14 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__if,axiom,
% 157.29/157.14 ! [V_m,V_n] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.14 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.29/157.14 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.29/157.14 => 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)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_split__div,axiom,
% 157.29/157.14 ! [V_k_2,V_n_2,V_Pa_2] :
% 157.29/157.14 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 157.29/157.14 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 157.29/157.14 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 => ! [B_i,B_j] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 157.29/157.14 => ( 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)
% 157.29/157.14 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zero__less__nat__eq,axiom,
% 157.29/157.14 ! [V_z_2] :
% 157.29/157.14 ( 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)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__less__eq__zless,axiom,
% 157.29/157.14 ! [V_z_2,V_w_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.29/157.14 => ( 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)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 157.29/157.14 ! [V_y_2,V_x_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 157.29/157.14 => ( 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)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__eq__iff,axiom,
% 157.29/157.14 ! [V_m_2,V_w_2] :
% 157.29/157.14 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 157.29/157.14 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.29/157.14 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.29/157.14 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__eq__iff2,axiom,
% 157.29/157.14 ! [V_w_2,V_m_2] :
% 157.29/157.14 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 157.29/157.14 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.29/157.14 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.29/157.14 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__le__eq__zle,axiom,
% 157.29/157.14 ! [V_z_2,V_w_2] :
% 157.29/157.14 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.29/157.14 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 157.29/157.14 => ( 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)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_split__nat,axiom,
% 157.29/157.14 ! [V_i_2,V_Pa_2] :
% 157.29/157.14 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
% 157.29/157.14 <=> ( ! [B_n] :
% 157.29/157.14 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 157.29/157.14 => hBOOL(hAPP(V_Pa_2,B_n)) )
% 157.29/157.14 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.14 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_split__mod,axiom,
% 157.29/157.14 ! [V_k_2,V_n_2,V_Pa_2] :
% 157.29/157.14 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 157.29/157.14 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 157.29/157.14 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 => ! [B_i,B_j] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 157.29/157.14 => ( 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)
% 157.29/157.14 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__lemma,axiom,
% 157.29/157.14 ! [V_q,V_b,V_r,V_c] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__add__distrib,axiom,
% 157.29/157.14 ! [V_z_H,V_z] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 157.29/157.14 ! [V_y,V_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power3__eq__cube,axiom,
% 157.29/157.14 ! [V_a,T_a] :
% 157.29/157.14 ( class_Groups_Omonoid__mult(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_int__eq__iff__number__of,axiom,
% 157.29/157.14 ! [V_v_2,V_m_2] :
% 157.29/157.14 ( 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)
% 157.29/157.14 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 157.29/157.14 & 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__mult__distrib,axiom,
% 157.29/157.14 ! [V_z_H,V_z] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 157.29/157.14 ! [V_y,V_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__diff__distrib,axiom,
% 157.29/157.14 ! [V_z,V_z_H] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Suc__times__mod__eq,axiom,
% 157.29/157.14 ! [V_m,V_k] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 157.29/157.14 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)))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__eq__if,axiom,
% 157.29/157.14 ! [V_p,V_m] :
% 157.29/157.14 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 157.29/157.14 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 => 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)))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zero__less__zpower__abs__iff,axiom,
% 157.29/157.14 ! [V_n_2,V_x_2] :
% 157.29/157.14 ( 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)))
% 157.29/157.14 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.14 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 157.29/157.14 ! [V_y,V_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_le__div__geq,axiom,
% 157.29/157.14 ! [V_m,V_n] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_split__div__lemma,axiom,
% 157.29/157.14 ! [V_m_2,V_q_2,V_n_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 157.29/157.14 => ( ( 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))
% 157.29/157.14 & 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)))) )
% 157.29/157.14 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_split__div_H,axiom,
% 157.29/157.14 ! [V_n_2,V_m_2,V_Pa_2] :
% 157.29/157.14 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 157.29/157.14 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 157.29/157.14 | ? [B_q] :
% 157.29/157.14 ( 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))
% 157.29/157.14 & 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))))
% 157.29/157.14 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__Suc__eq__div__add3,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Suc__div__eq__add3__div,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div2__Suc__Suc,axiom,
% 157.29/157.14 ! [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))))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_add__self__div__2,axiom,
% 157.29/157.14 ! [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 ).
% 157.29/157.14
% 157.29/157.14 fof(fact_one__less__nat__eq,axiom,
% 157.29/157.14 ! [V_z_2] :
% 157.29/157.14 ( 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)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__less__iff,axiom,
% 157.29/157.14 ! [V_m_2,V_w_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 157.29/157.14 <=> 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 157.29/157.14 ! [V_z] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zero__power2,axiom,
% 157.29/157.14 ! [T_a] :
% 157.29/157.14 ( class_Rings_Osemiring__1(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zero__eq__power2,axiom,
% 157.29/157.14 ! [V_a_2,T_b] :
% 157.29/157.14 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 157.29/157.14 => ( 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)
% 157.29/157.14 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 157.29/157.14 ! [V_x,T_a] :
% 157.29/157.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.14 => 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)))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power2__eq__square,axiom,
% 157.29/157.14 ! [V_a,T_a] :
% 157.29/157.14 ( class_Groups_Omonoid__mult(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod2__Suc__Suc,axiom,
% 157.29/157.14 ! [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)))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_one__power2,axiom,
% 157.29/157.14 ! [T_a] :
% 157.29/157.14 ( class_Rings_Osemiring__1(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 157.29/157.14 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)))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power2__minus,axiom,
% 157.29/157.14 ! [V_a,T_a] :
% 157.29/157.14 ( class_Rings_Oring__1(T_a)
% 157.29/157.14 => 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)))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__mult__distrib__neg,axiom,
% 157.29/157.14 ! [V_z_H,V_z] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.14 => 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))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__even__eq,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Groups_Omonoid__mult(T_a)
% 157.29/157.14 => 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)))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_abs__power2,axiom,
% 157.29/157.14 ! [V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => 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)))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power2__abs,axiom,
% 157.29/157.14 ! [V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => 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)))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power2__eq__imp__eq,axiom,
% 157.29/157.14 ! [V_y,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( 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))))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.29/157.14 => V_x = V_y ) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power2__le__imp__le,axiom,
% 157.29/157.14 ! [V_y,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( 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))))))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.29/157.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zero__le__power2,axiom,
% 157.29/157.14 ! [V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => 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)))))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power2__less__0,axiom,
% 157.29/157.14 ! [V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => ~ 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))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zero__less__power2,axiom,
% 157.29/157.14 ! [V_a_2,T_b] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.14 => ( 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))))))
% 157.29/157.14 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_sum__power2__eq__zero__iff,axiom,
% 157.29/157.14 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.14 => ( 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)
% 157.29/157.14 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.29/157.14 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__2,axiom,
% 157.29/157.14 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))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power2__eq__square__number__of,axiom,
% 157.29/157.14 ! [V_w,T_b] :
% 157.29/157.14 ( ( class_Groups_Omonoid__mult(T_b)
% 157.29/157.14 & class_Int_Onumber(T_b) )
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power2__eq__1__iff,axiom,
% 157.29/157.14 ! [V_a_2,T_b] :
% 157.29/157.14 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 157.29/157.14 => ( 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)
% 157.29/157.14 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 157.29/157.14 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 157.29/157.14 ! [V_n,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__minus__even,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Oring__1(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__2__gt__zero,axiom,
% 157.29/157.14 ! [V_n] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 157.29/157.14 => 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)))))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power2__less__imp__less,axiom,
% 157.29/157.14 ! [V_y,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( 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))))))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 157.29/157.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_sum__power2__le__zero__iff,axiom,
% 157.29/157.14 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.14 => ( 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)))
% 157.29/157.14 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.29/157.14 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_sum__power2__ge__zero,axiom,
% 157.29/157.14 ! [V_y,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => 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))))))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_sum__power2__gt__zero__iff,axiom,
% 157.29/157.14 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.14 => ( 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)))))))
% 157.29/157.14 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 157.29/157.14 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_not__sum__power2__lt__zero,axiom,
% 157.29/157.14 ! [V_y,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => ~ 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))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power2__sum,axiom,
% 157.29/157.14 ! [V_y,V_x,T_a] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zero__le__even__power_H,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => 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)))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 157.29/157.14 ! [V_n,V_x,T_a] :
% 157.29/157.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.14 => 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))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__odd__eq,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Groups_Omonoid__mult(T_a)
% 157.29/157.14 => 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))))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mod2__gr__0,axiom,
% 157.29/157.14 ! [V_m_2] :
% 157.29/157.14 ( 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))))))
% 157.29/157.14 <=> 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__minus1__even,axiom,
% 157.29/157.14 ! [V_n,T_a] :
% 157.29/157.14 ( class_Rings_Oring__1(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_int__power__div__base,axiom,
% 157.29/157.14 ! [V_k,V_m] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 157.29/157.14 => 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)))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 157.29/157.14 ! [V_n] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.14 => 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)))))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power2__diff,axiom,
% 157.29/157.14 ! [V_y,V_x,T_a] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => ( 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)))))
% 157.29/157.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_int__of__code,axiom,
% 157.29/157.14 ! [V_k] :
% 157.29/157.14 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.14 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.29/157.14 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.14 => ( ( 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)
% 157.29/157.14 => 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)))))) )
% 157.29/157.14 & ( 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)
% 157.29/157.14 => 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)) ) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__strict__mono,axiom,
% 157.29/157.14 ! [V_n,V_b,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.14 => 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))) ) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__diff,axiom,
% 157.29/157.14 ! [V_m,V_n,V_a,T_a] :
% 157.29/157.14 ( class_Fields_Ofield(T_a)
% 157.29/157.14 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.29/157.14 => 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)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_one__less__power,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.14 => 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))) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__le__imp__le__exp,axiom,
% 157.29/157.14 ! [V_n,V_m,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.29/157.14 => ( 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)))
% 157.29/157.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_field__power__not__zero,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 157.29/157.14 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.14 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__Suc__0,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 157.29/157.14 ! [V_m_2,V_x_2] :
% 157.29/157.14 ( 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))
% 157.29/157.14 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__zero__less__power__iff,axiom,
% 157.29/157.14 ! [V_n_2,V_x_2] :
% 157.29/157.14 ( 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)))
% 157.29/157.14 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 157.29/157.14 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__power__less__imp__less,axiom,
% 157.29/157.14 ! [V_n,V_m,V_i] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 157.29/157.14 => ( 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)))
% 157.29/157.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__mult__distrib,axiom,
% 157.29/157.14 ! [V_n,V_b,V_a,T_a] :
% 157.29/157.14 ( class_Groups_Ocomm__monoid__mult(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__commutes,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Groups_Omonoid__mult(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__one,axiom,
% 157.29/157.14 ! [V_n,T_a] :
% 157.29/157.14 ( class_Groups_Omonoid__mult(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_of__nat__power,axiom,
% 157.29/157.14 ! [V_n,V_m,T_a] :
% 157.29/157.14 ( class_Rings_Osemiring__1(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__mult,axiom,
% 157.29/157.14 ! [V_n,V_m,V_a,T_a] :
% 157.29/157.14 ( class_Groups_Omonoid__mult(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__divide,axiom,
% 157.29/157.14 ! [V_n,V_b,V_a,T_a] :
% 157.29/157.14 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__abs,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__one__right,axiom,
% 157.29/157.14 ! [V_a,T_a] :
% 157.29/157.14 ( class_Groups_Omonoid__mult(T_a)
% 157.29/157.14 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zero__le__power,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__mono,axiom,
% 157.29/157.14 ! [V_n,V_b,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.14 => 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))) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zero__less__power,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__eq__0__iff,axiom,
% 157.29/157.14 ! [V_n_2,V_a_2,T_b] :
% 157.29/157.14 ( ( class_Power_Opower(T_b)
% 157.29/157.14 & class_Rings_Omult__zero(T_b)
% 157.29/157.14 & class_Rings_Ono__zero__divisors(T_b)
% 157.29/157.14 & class_Rings_Ozero__neq__one(T_b) )
% 157.29/157.14 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.29/157.14 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 157.29/157.14 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_one__le__power,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.29/157.14 => 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))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__0__Suc,axiom,
% 157.29/157.14 ! [V_n,T_a] :
% 157.29/157.14 ( ( class_Power_Opower(T_a)
% 157.29/157.14 & class_Rings_Osemiring__0(T_a) )
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__inject__exp,axiom,
% 157.29/157.14 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_b)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 157.29/157.14 => ( 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)
% 157.29/157.14 <=> V_m_2 = V_n_2 ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__Suc,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Power_Opower(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__Suc2,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Groups_Omonoid__mult(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__one__le__power,axiom,
% 157.29/157.14 ! [V_n,V_i] :
% 157.29/157.14 ( 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))
% 157.29/157.14 => 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))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__0,axiom,
% 157.29/157.14 ! [V_a,T_a] :
% 157.29/157.14 ( class_Power_Opower(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__add,axiom,
% 157.29/157.14 ! [V_n,V_m,V_a,T_a] :
% 157.29/157.14 ( class_Groups_Omonoid__mult(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nonzero__power__divide,axiom,
% 157.29/157.14 ! [V_n,V_a,V_b,T_a] :
% 157.29/157.14 ( class_Fields_Ofield(T_a)
% 157.29/157.14 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.14 => 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)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__one__over,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Fields_Ofield__inverse__zero(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_abs__power__minus,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__less__imp__less__base,axiom,
% 157.29/157.14 ! [V_b,V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( 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)))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.29/157.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__le__imp__le__base,axiom,
% 157.29/157.14 ! [V_b,V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( 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))))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.29/157.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__inject__base,axiom,
% 157.29/157.14 ! [V_b,V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( 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))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.29/157.14 => V_a = V_b ) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__gt1__lemma,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.29/157.14 => 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)))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__less__power__Suc,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.29/157.14 => 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)))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__0__left,axiom,
% 157.29/157.14 ! [V_n,T_a] :
% 157.29/157.14 ( ( class_Power_Opower(T_a)
% 157.29/157.14 & class_Rings_Osemiring__0(T_a) )
% 157.29/157.14 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 => 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) )
% 157.29/157.14 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.14 => 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) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__gt1,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.29/157.14 => 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)))) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__strict__increasing__iff,axiom,
% 157.29/157.14 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_b)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 157.29/157.14 => ( 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)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__less__imp__less__exp,axiom,
% 157.29/157.14 ! [V_n,V_m,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.29/157.14 => ( 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)))
% 157.29/157.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__strict__increasing,axiom,
% 157.29/157.14 ! [V_a,V_N,V_n,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.29/157.14 => 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))) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zero__le__power__abs,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.14 => 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))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__increasing,axiom,
% 157.29/157.14 ! [V_a,V_N,V_n,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 157.29/157.14 => 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))) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__minus,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Oring__1(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__Suc__less,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 157.29/157.14 => 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))) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__eq__imp__eq__base,axiom,
% 157.29/157.14 ! [V_b,V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( 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)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.14 => V_a = V_b ) ) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__Suc__less__one,axiom,
% 157.29/157.14 ! [V_n,V_a,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 157.29/157.14 => 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))) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__strict__decreasing,axiom,
% 157.29/157.14 ! [V_a,V_N,V_n,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 157.29/157.14 => 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))) ) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__decreasing,axiom,
% 157.29/157.14 ! [V_a,V_N,V_n,T_a] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_a)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 157.29/157.14 => 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))) ) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__increasing__iff,axiom,
% 157.29/157.14 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 157.29/157.14 ( class_Rings_Olinordered__semidom(T_b)
% 157.29/157.14 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 157.29/157.14 => ( 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)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nat__aux__def,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_transfer__morphism__nat__int,axiom,
% 157.29/157.14 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))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_card__Pow,axiom,
% 157.29/157.14 ! [V_A_2,T_b] :
% 157.29/157.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__power__power,axiom,
% 157.29/157.14 ! [T_b] :
% 157.29/157.14 ( class_Power_Opower(T_b)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__m1__odd,axiom,
% 157.29/157.14 ! [V_n,T_a] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_PowI,axiom,
% 157.29/157.14 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.14 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I24_J,axiom,
% 157.29/157.14 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I7_J,axiom,
% 157.29/157.14 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I37_J,axiom,
% 157.29/157.14 c_Int_OPls != c_Int_OMin ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I40_J,axiom,
% 157.29/157.14 c_Int_OMin != c_Int_OPls ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I47_J,axiom,
% 157.29/157.14 ! [V_k_2] :
% 157.29/157.14 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 157.29/157.14 <=> V_k_2 = c_Int_OMin ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I43_J,axiom,
% 157.29/157.14 ! [V_l_2] :
% 157.29/157.14 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 157.29/157.14 <=> c_Int_OMin = V_l_2 ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Bit1__Min,axiom,
% 157.29/157.14 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I45_J,axiom,
% 157.29/157.14 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I42_J,axiom,
% 157.29/157.14 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Pow__top,axiom,
% 157.29/157.14 ! [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))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Union__Pow__eq,axiom,
% 157.29/157.14 ! [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 ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Pow__not__empty,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_bin__less__0__simps_I2_J,axiom,
% 157.29/157.14 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I20_J,axiom,
% 157.29/157.14 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I23_J,axiom,
% 157.29/157.14 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I30_J,axiom,
% 157.29/157.14 ! [V_k_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I26_J,axiom,
% 157.29/157.14 ! [V_k_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I6_J,axiom,
% 157.29/157.14 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I3_J,axiom,
% 157.29/157.14 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I9_J,axiom,
% 157.29/157.14 ! [V_k_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I13_J,axiom,
% 157.29/157.14 ! [V_k_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I28_J,axiom,
% 157.29/157.14 ! [V_k_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I8_J,axiom,
% 157.29/157.14 ! [V_k_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_eq__number__of__Pls__Min,axiom,
% 157.29/157.14 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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Int_OMin__def,axiom,
% 157.29/157.14 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mult__Min,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_neg__number__of__Min,axiom,
% 157.29/157.14 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_pred__Pls,axiom,
% 157.29/157.14 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 157.29/157.14
% 157.29/157.14 fof(fact_add__Min__right,axiom,
% 157.29/157.14 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_add__Min,axiom,
% 157.29/157.14 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_pred__Min,axiom,
% 157.29/157.14 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_nonzero__number__of__Min,axiom,
% 157.29/157.14 ! [T_a] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_succ__Min,axiom,
% 157.29/157.14 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 157.29/157.14
% 157.29/157.14 fof(fact_diff__bin__simps_I2_J,axiom,
% 157.29/157.14 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Pow__bottom,axiom,
% 157.29/157.14 ! [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))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Pow__iff,axiom,
% 157.29/157.14 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_PowD,axiom,
% 157.29/157.14 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 157.29/157.14 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Pow__mono,axiom,
% 157.29/157.14 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.14 => 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))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_finite__Pow__iff,axiom,
% 157.29/157.14 ! [V_A_2,T_b] :
% 157.29/157.14 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 157.29/157.14 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mult__minus1,axiom,
% 157.29/157.14 ! [V_z,T_a] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_mult__minus1__right,axiom,
% 157.29/157.14 ! [V_z,T_a] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_subset__Pow__Union,axiom,
% 157.29/157.14 ! [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)))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_arith__simps_I31_J,axiom,
% 157.29/157.14 ! [T_a] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_number__of__Min,axiom,
% 157.29/157.14 ! [T_a] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_abs__minus__one,axiom,
% 157.29/157.14 ! [T_a] :
% 157.29/157.14 ( ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 & class_Rings_Olinordered__idom(T_a) )
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_divide__minus1,axiom,
% 157.29/157.14 ! [V_x,T_a] :
% 157.29/157.14 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 157.29/157.14 & class_Int_Onumber__ring(T_a) )
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I11_J,axiom,
% 157.29/157.14 ! [V_k_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_rel__simps_I25_J,axiom,
% 157.29/157.14 ! [V_k_2] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zmod__minus1__right,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_diff__bin__simps_I4_J,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_minus__Min,axiom,
% 157.29/157.14 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 157.29/157.14 ! [V_n,V_m] :
% 157.29/157.14 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.29/157.14 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.29/157.14 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zmult__eq__1__iff,axiom,
% 157.29/157.14 ! [V_n_2,V_m_2] :
% 157.29/157.14 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.29/157.14 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 157.29/157.14 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 157.29/157.14 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 157.29/157.14 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_diff__bin__simps_I5_J,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_diff__bin__simps_I6_J,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power_Opower_Opower__0,axiom,
% 157.29/157.14 ! [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 ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power_Opower_Opower__Suc,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zdiv__minus1__right,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Pow__Int__eq,axiom,
% 157.29/157.14 ! [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)) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_minus1__divide,axiom,
% 157.29/157.14 ! [V_x,T_a] :
% 157.29/157.14 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 157.29/157.14 & class_Int_Onumber__ring(T_a) )
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_abs__power__minus__one,axiom,
% 157.29/157.14 ! [V_n,T_a] :
% 157.29/157.14 ( ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 & class_Rings_Olinordered__idom(T_a) )
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__eq__minus1,axiom,
% 157.29/157.14 ! [V_b] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Pow__empty,axiom,
% 157.29/157.14 ! [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))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Un__Pow__subset,axiom,
% 157.29/157.14 ! [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)))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_div__pos__neg__trivial,axiom,
% 157.29/157.14 ! [V_b,V_a] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.14 => ( 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)))
% 157.29/157.14 => 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) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_zmod__minus1,axiom,
% 157.29/157.14 ! [V_b] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.14 => 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)) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_power__m1__even,axiom,
% 157.29/157.14 ! [V_n,T_a] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_code__numeral_Osize_I1_J,axiom,
% 157.29/157.14 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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_of__int__of__nat,axiom,
% 157.29/157.14 ! [V_k,T_a] :
% 157.29/157.14 ( class_Rings_Oring__1(T_a)
% 157.29/157.14 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.14 => 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)))) )
% 157.29/157.14 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.14 => 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)) ) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 157.29/157.14 ! [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)))) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_negD,axiom,
% 157.29/157.14 ! [V_x] :
% 157.29/157.14 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.14 => ? [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))) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_code__numeral_Osize_I3_J,axiom,
% 157.29/157.14 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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_of__int__eq__iff,axiom,
% 157.29/157.14 ! [V_z_2,V_w_2,T_b] :
% 157.29/157.14 ( class_Int_Oring__char__0(T_b)
% 157.29/157.14 => ( 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)
% 157.29/157.14 <=> V_w_2 = V_z_2 ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_number__of__eq,axiom,
% 157.29/157.14 ! [V_k,T_a] :
% 157.29/157.14 ( class_Int_Onumber__ring(T_a)
% 157.29/157.14 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_int__number__of__def,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_of__int__int__eq,axiom,
% 157.29/157.14 ! [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) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_of__int__eq__0__iff,axiom,
% 157.29/157.14 ! [V_z_2,T_b] :
% 157.29/157.14 ( class_Int_Oring__char__0(T_b)
% 157.29/157.14 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.29/157.14 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_of__int__0__eq__iff,axiom,
% 157.29/157.14 ! [V_z_2,T_b] :
% 157.29/157.14 ( class_Int_Oring__char__0(T_b)
% 157.29/157.14 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 157.29/157.14 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_of__int__0,axiom,
% 157.29/157.14 ! [T_a] :
% 157.29/157.14 ( class_Rings_Oring__1(T_a)
% 157.29/157.14 => 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) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_of__int__le__iff,axiom,
% 157.29/157.14 ! [V_z_2,V_w_2,T_b] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.14 => ( 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)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_of__int__less__iff,axiom,
% 157.29/157.14 ! [V_z_2,V_w_2,T_b] :
% 157.29/157.14 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.14 => ( 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)))
% 157.29/157.14 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 157.29/157.14
% 157.29/157.14 fof(fact_of__int__add,axiom,
% 157.29/157.15 ! [V_z,V_w,T_a] :
% 157.29/157.15 ( class_Rings_Oring__1(T_a)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__number__of__eq,axiom,
% 157.29/157.15 ! [V_v,T_a] :
% 157.29/157.15 ( class_Int_Onumber__ring(T_a)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__mult,axiom,
% 157.29/157.15 ! [V_z,V_w,T_a] :
% 157.29/157.15 ( class_Rings_Oring__1(T_a)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__1,axiom,
% 157.29/157.15 ! [T_a] :
% 157.29/157.15 ( class_Rings_Oring__1(T_a)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__diff,axiom,
% 157.29/157.15 ! [V_z,V_w,T_a] :
% 157.29/157.15 ( class_Rings_Oring__1(T_a)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__of__nat__eq,axiom,
% 157.29/157.15 ! [V_n,T_a] :
% 157.29/157.15 ( class_Rings_Oring__1(T_a)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__minus,axiom,
% 157.29/157.15 ! [V_z,T_a] :
% 157.29/157.15 ( class_Rings_Oring__1(T_a)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Ints__of__int,axiom,
% 157.29/157.15 ! [V_z_2,T_b] :
% 157.29/157.15 ( class_Rings_Oring__1(T_b)
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__power,axiom,
% 157.29/157.15 ! [V_n,V_z,T_a] :
% 157.29/157.15 ( class_Rings_Oring__1(T_a)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__m1,axiom,
% 157.29/157.15 ! [T_a] :
% 157.29/157.15 ( class_Int_Onumber__ring(T_a)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__0__le__iff,axiom,
% 157.29/157.15 ! [V_z_2,T_b] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.15 => ( 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)))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__le__0__iff,axiom,
% 157.29/157.15 ! [V_z_2,T_b] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.15 => ( 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)))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__less__0__iff,axiom,
% 157.29/157.15 ! [V_z_2,T_b] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.15 => ( 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)))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__0__less__iff,axiom,
% 157.29/157.15 ! [V_z_2,T_b] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.15 => ( 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)))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__nat__nat,axiom,
% 157.29/157.15 ! [V_z,T_a] :
% 157.29/157.15 ( class_Rings_Oring__1(T_a)
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 157.29/157.15 => 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) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_code__numeral_Osize_I4_J,axiom,
% 157.29/157.15 ! [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))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_code__numeral_Osize_I2_J,axiom,
% 157.29/157.15 ! [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))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sgn__if,axiom,
% 157.29/157.15 ! [V_x,T_a] :
% 157.29/157.15 ( class_Groups_Osgn__if(T_a)
% 157.29/157.15 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.15 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 157.29/157.15 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.29/157.15 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 157.29/157.15 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sgn__1__neg,axiom,
% 157.29/157.15 ! [V_a_2,T_b] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.15 => ( 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))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sgn__sgn,axiom,
% 157.29/157.15 ! [V_a,T_a] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_code__numeral_Oinject,axiom,
% 157.29/157.15 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 157.29/157.15 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 157.29/157.15 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sgn0,axiom,
% 157.29/157.15 ! [T_a] :
% 157.29/157.15 ( class_Groups_Osgn__if(T_a)
% 157.29/157.15 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sgn__0__0,axiom,
% 157.29/157.15 ! [V_a_2,T_b] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.15 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 157.29/157.15 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sgn__times,axiom,
% 157.29/157.15 ! [V_b,V_a,T_a] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 157.29/157.15 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sgn__greater,axiom,
% 157.29/157.15 ! [V_a_2,T_b] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.15 => ( 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)))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sgn__less,axiom,
% 157.29/157.15 ! [V_a_2,T_b] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.15 => ( 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)))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_abs__sgn,axiom,
% 157.29/157.15 ! [V_k,T_a] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mult__sgn__abs,axiom,
% 157.29/157.15 ! [V_x,T_a] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.15 => 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 ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Suc__code__numeral__minus__one,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sgn__pos,axiom,
% 157.29/157.15 ! [V_a,T_a] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.15 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sgn__1__pos,axiom,
% 157.29/157.15 ! [V_a_2,T_b] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.15 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__gcd_Osimps,axiom,
% 157.29/157.15 ! [V_x,V_y] :
% 157.29/157.15 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.15 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 157.29/157.15 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_zsgn__def,axiom,
% 157.29/157.15 ! [V_i] :
% 157.29/157.15 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.29/157.15 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 157.29/157.15 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 157.29/157.15 => 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)) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sgn__neg,axiom,
% 157.29/157.15 ! [V_a,T_a] :
% 157.29/157.15 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 157.29/157.15 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 157.29/157.15 ! [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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_compl__unique,axiom,
% 157.29/157.15 ! [V_y,V_x,T_a] :
% 157.29/157.15 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.15 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 157.29/157.15 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 157.29/157.15 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 157.29/157.15 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_UNIV__I,axiom,
% 157.29/157.15 ! [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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Pow__UNIV,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_finite__UNIV,axiom,
% 157.29/157.15 ! [T_b] :
% 157.29/157.15 ( class_Finite__Set_Ofinite(T_b)
% 157.29/157.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_subset__UNIV,axiom,
% 157.29/157.15 ! [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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_UNIV__Plus__UNIV,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_finite__Prod__UNIV,axiom,
% 157.29/157.15 ! [T_c,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 157.29/157.15 => 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)))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_finite__option__UNIV,axiom,
% 157.29/157.15 ! [T_b] :
% 157.29/157.15 ( 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))))
% 157.29/157.15 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Sup__UNIV,axiom,
% 157.29/157.15 ! [T_b] :
% 157.29/157.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Union__UNIV,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_top__apply,axiom,
% 157.29/157.15 ! [V_x_2,T_c,T_b] :
% 157.29/157.15 ( class_Orderings_Otop(T_b)
% 157.29/157.15 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_UNIV__not__empty,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_finite__fun__UNIVD2,axiom,
% 157.29/157.15 ! [T_c,T_b] :
% 157.29/157.15 ( 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))))
% 157.29/157.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Int__UNIV__left,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Int__UNIV__right,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Un__UNIV__left,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Un__UNIV__right,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_card__UNIV__unit,axiom,
% 157.29/157.15 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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_finite__Plus__UNIV__iff,axiom,
% 157.29/157.15 ! [T_c,T_b] :
% 157.29/157.15 ( 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))))
% 157.29/157.15 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.29/157.15 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 157.29/157.15 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 157.29/157.15 ! [V_y,V_x] :
% 157.29/157.15 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.29/157.15 => ( c_Nat__Transfer_Ois__nat(V_y)
% 157.29/157.15 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 157.29/157.15 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 157.29/157.15 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 157.29/157.15 ! [V_y,V_x] :
% 157.29/157.15 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.29/157.15 => ( c_Nat__Transfer_Ois__nat(V_y)
% 157.29/157.15 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 157.29/157.15 ! [V_y,V_x] :
% 157.29/157.15 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.29/157.15 => ( c_Nat__Transfer_Ois__nat(V_y)
% 157.29/157.15 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 157.29/157.15 ! [V_y,V_x] :
% 157.29/157.15 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.29/157.15 => ( c_Nat__Transfer_Ois__nat(V_y)
% 157.29/157.15 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_top__greatest,axiom,
% 157.29/157.15 ! [V_x,T_a] :
% 157.29/157.15 ( class_Orderings_Otop(T_a)
% 157.29/157.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sup__top__left,axiom,
% 157.29/157.15 ! [V_x,T_a] :
% 157.29/157.15 ( class_Lattices_Obounded__lattice__top(T_a)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sup__top__right,axiom,
% 157.29/157.15 ! [V_x,T_a] :
% 157.29/157.15 ( class_Lattices_Obounded__lattice__top(T_a)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inf__eq__top__iff,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.15 ( class_Lattices_Obounded__lattice__top(T_b)
% 157.29/157.15 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 157.29/157.15 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 157.29/157.15 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inf__top__right,axiom,
% 157.29/157.15 ! [V_x,T_a] :
% 157.29/157.15 ( class_Lattices_Obounded__lattice__top(T_a)
% 157.29/157.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inf__top__left,axiom,
% 157.29/157.15 ! [V_x,T_a] :
% 157.29/157.15 ( class_Lattices_Obounded__lattice__top(T_a)
% 157.29/157.15 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 157.29/157.15 ! [V_n,V_x] :
% 157.29/157.15 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.29/157.15 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Diff__UNIV,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 157.29/157.15 ! [V_y,V_x] :
% 157.29/157.15 ( c_Nat__Transfer_Ois__nat(V_x)
% 157.29/157.15 => ( c_Nat__Transfer_Ois__nat(V_y)
% 157.29/157.15 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 157.29/157.15 ! [V_A_2,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.29/157.15 => ( 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)))
% 157.29/157.15 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Compl__UNIV__eq,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Compl__empty__eq,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_finite__compl,axiom,
% 157.29/157.15 ! [V_A_2,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 157.29/157.15 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Compl__partition,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Compl__partition2,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_is__nat__def,axiom,
% 157.29/157.15 ! [V_x_2] :
% 157.29/157.15 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_compl__top__eq,axiom,
% 157.29/157.15 ! [T_a] :
% 157.29/157.15 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.15 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_compl__bot__eq,axiom,
% 157.29/157.15 ! [T_a] :
% 157.29/157.15 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.15 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_compl__sup__top,axiom,
% 157.29/157.15 ! [V_x,T_a] :
% 157.29/157.15 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sup__compl__top,axiom,
% 157.29/157.15 ! [V_x,T_a] :
% 157.29/157.15 ( class_Lattices_Oboolean__algebra(T_a)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 157.29/157.15 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_finite__UNIV__card__ge__0,axiom,
% 157.29/157.15 ! [T_b] :
% 157.29/157.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.29/157.15 => 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))))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_card__UNIV__bool,axiom,
% 157.29/157.15 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))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_finite__fun__UNIVD1,axiom,
% 157.29/157.15 ! [T_c,T_b] :
% 157.29/157.15 ( 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))))
% 157.29/157.15 => ( 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))
% 157.29/157.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inf__fold__inf,axiom,
% 157.29/157.15 ! [V_A_2,T_b] :
% 157.29/157.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => 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) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__mod__eq__lemma,axiom,
% 157.29/157.15 ! [V_y,V_n,V_x] :
% 157.29/157.15 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 157.29/157.15 => ? [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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mod__induct__0,axiom,
% 157.29/157.15 ! [V_i_2,V_Pa_2,V_p_2] :
% 157.29/157.15 ( ! [B_i] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 157.29/157.15 => ( hBOOL(hAPP(V_Pa_2,B_i))
% 157.29/157.15 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 157.29/157.15 => ( hBOOL(hAPP(V_Pa_2,V_i_2))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 157.29/157.15 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_log_Osimps,axiom,
% 157.29/157.15 ! [V_i,V_b] :
% 157.29/157.15 ( ( ( 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)))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 157.29/157.15 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 157.29/157.15 & ( ~ ( 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)))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 157.29/157.15 => 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))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_finite__Inter,axiom,
% 157.29/157.15 ! [V_M_2,T_b] :
% 157.29/157.15 ( ? [B_x] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 157.29/157.15 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 157.29/157.15 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_top1I,axiom,
% 157.29/157.15 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_InterE,axiom,
% 157.29/157.15 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 157.29/157.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_InterD,axiom,
% 157.29/157.15 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 157.29/157.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inter__UNIV,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inter__empty,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_le__Inf__iff,axiom,
% 157.29/157.15 ! [V_A_2,V_b_2,T_b] :
% 157.29/157.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 => ( 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)))
% 157.29/157.15 <=> ! [B_x] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inf__less__iff,axiom,
% 157.29/157.15 ! [V_a_2,V_S_2,T_b] :
% 157.29/157.15 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 & class_Orderings_Olinorder(T_b) )
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 157.29/157.15 <=> ? [B_x] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.29/157.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inf__UNIV,axiom,
% 157.29/157.15 ! [T_b] :
% 157.29/157.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inter__lower,axiom,
% 157.29/157.15 ! [V_A_2,V_B_2,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inter__anti__mono,axiom,
% 157.29/157.15 ! [V_A_2,V_B_2,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inter__insert,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inf__lower,axiom,
% 157.29/157.15 ! [V_A_2,V_x_2,T_b] :
% 157.29/157.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inter__Un__distrib,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inf__singleton,axiom,
% 157.29/157.15 ! [V_a_2,T_b] :
% 157.29/157.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 => 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 ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inf__empty,axiom,
% 157.29/157.15 ! [T_b] :
% 157.29/157.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inf__insert,axiom,
% 157.29/157.15 ! [V_A_2,V_a_2,T_b] :
% 157.29/157.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Int__eq__Inter,axiom,
% 157.29/157.15 ! [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))))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inter__Un__subset,axiom,
% 157.29/157.15 ! [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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inf__binary,axiom,
% 157.29/157.15 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inf__Inf__fold__inf,axiom,
% 157.29/157.15 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => 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) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inf__fin__Inf,axiom,
% 157.29/157.15 ! [V_A_2,T_b] :
% 157.29/157.15 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.15 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_minus__shift__def,axiom,
% 157.29/157.15 ! [V_r,V_l,V_k] :
% 157.29/157.15 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 157.29/157.15 => 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) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inc__shift__def,axiom,
% 157.29/157.15 ! [V_k,V_v] :
% 157.29/157.15 ( ( V_v = V_k
% 157.29/157.15 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 157.29/157.15 & ( V_v != V_k
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_iso__tuple__UNIV__I,axiom,
% 157.29/157.15 ! [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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mod__div__decomp,axiom,
% 157.29/157.15 ! [V_b,V_a,T_a] :
% 157.29/157.15 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Inter__subset,axiom,
% 157.29/157.15 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.15 ( ! [B_X] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 157.29/157.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 157.29/157.15 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_InterI,axiom,
% 157.29/157.15 ! [V_A_2,V_C_2,T_b] :
% 157.29/157.15 ( ! [B_X] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 157.29/157.15 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_subtract__code__numeral__def,axiom,
% 157.29/157.15 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_minus__code__numeral__code,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 157.29/157.15 ! [V_w] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( 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))))
% 157.29/157.15 => 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))) )
% 157.29/157.15 & ( ~ 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))))
% 157.29/157.15 => 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)))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat_Osize_I2_J,axiom,
% 157.29/157.15 ! [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))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_diff__nat__number__of,axiom,
% 157.29/157.15 ! [V_v_2,V_v_H_2] :
% 157.29/157.15 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__abs,axiom,
% 157.29/157.15 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__abs__ge__zero,axiom,
% 157.29/157.15 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum_Odistrib,axiom,
% 157.29/157.15 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_pred__subset__eq,axiom,
% 157.29/157.15 ! [V_S_2,V_R_2,T_b] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_pred__subset__eq2,axiom,
% 157.29/157.15 ! [V_S_2,V_R_2,T_c,T_b] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 <=> 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__addf,axiom,
% 157.29/157.15 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__setsum,axiom,
% 157.29/157.15 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Rings_Oring__1(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__setprod,axiom,
% 157.29/157.15 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.29/157.15 & class_Rings_Oring__1(T_b) )
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__negf,axiom,
% 157.29/157.15 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Oab__group__add(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_fun__Compl__def,axiom,
% 157.29/157.15 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Ouminus(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setprod__1,axiom,
% 157.29/157.15 ! [V_A_2,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_abs__setsum__abs,axiom,
% 157.29/157.15 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_abs__setprod,axiom,
% 157.29/157.15 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Fields_Olinordered__field(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__right__distrib,axiom,
% 157.29/157.15 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 157.29/157.15 ( class_Rings_Osemiring__0(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__left__distrib,axiom,
% 157.29/157.15 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Rings_Osemiring__0(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__product,axiom,
% 157.29/157.15 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Rings_Osemiring__0(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sup__fun__def,axiom,
% 157.29/157.15 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Lattices_Olattice(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inf__fun__def,axiom,
% 157.29/157.15 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Lattices_Olattice(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setprod__timesf,axiom,
% 157.29/157.15 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 157.29/157.15 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.29/157.15 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_pred__equals__eq,axiom,
% 157.29/157.15 ! [V_S_2,V_R_2,T_b] :
% 157.29/157.15 ( 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)
% 157.29/157.15 <=> V_R_2 = V_S_2 ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_pred__equals__eq2,axiom,
% 157.29/157.15 ! [V_S_2,V_R_2,T_c,T_b] :
% 157.29/157.15 ( 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)
% 157.29/157.15 <=> V_R_2 = V_S_2 ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 157.29/157.15 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.29/157.15 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__commute,axiom,
% 157.29/157.15 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sup__Un__eq2,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 <=> 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_bot__empty__eq2,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,T_c,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 <=> 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)))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inf__Int__eq2,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 <=> 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inf__Int__eq,axiom,
% 157.29/157.15 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 <=> 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sup__Un__eq,axiom,
% 157.29/157.15 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 <=> 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_bot__fun__def,axiom,
% 157.29/157.15 ! [V_x_2,T_c,T_b] :
% 157.29/157.15 ( class_Orderings_Obot(T_b)
% 157.29/157.15 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_bot__empty__eq,axiom,
% 157.29/157.15 ! [V_x_2,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__divide__distrib,axiom,
% 157.29/157.15 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Fields_Ofield(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_fold__image__def,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_int__setsum,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__0,axiom,
% 157.29/157.15 ! [V_A_2,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_fun__diff__def,axiom,
% 157.29/157.15 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Ominus(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__subtractf,axiom,
% 157.29/157.15 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Groups_Oab__group__add(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_int__setprod,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setprod_Odistrib,axiom,
% 157.29/157.15 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_less__eq__Suc__le__raw,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__number__of__Bit0,axiom,
% 157.29/157.15 ! [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))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setprod__dividef,axiom,
% 157.29/157.15 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 157.29/157.15 ( class_Fields_Ofield__inverse__zero(T_c)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat_Osize_I1_J,axiom,
% 157.29/157.15 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__nat__setsum,axiom,
% 157.29/157.15 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( class_Rings_Osemiring__1(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_card__eq__setsum,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__nat__setprod,axiom,
% 157.29/157.15 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.29/157.15 & class_Rings_Osemiring__1(T_b) )
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__delta_H,axiom,
% 157.29/157.15 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.29/157.15 => 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) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__delta,axiom,
% 157.29/157.15 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.29/157.15 => 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) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setprod__delta,axiom,
% 157.29/157.15 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.29/157.15 => 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) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setprod__delta_H,axiom,
% 157.29/157.15 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.29/157.15 => 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) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__constant,axiom,
% 157.29/157.15 ! [V_A_2,V_y_2,T_c,T_b] :
% 157.29/157.15 ( class_Rings_Osemiring__1(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_power__number__of__even,axiom,
% 157.29/157.15 ! [V_w_2,V_z_2,T_b] :
% 157.29/157.15 ( class_Int_Onumber__ring(T_b)
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_fold__image__distrib,axiom,
% 157.29/157.15 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setprod__constant,axiom,
% 157.29/157.15 ! [V_y_2,V_A_2,T_b,T_c] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_zpower__number__of__even,axiom,
% 157.29/157.15 ! [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))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Powp__Pow__eq,axiom,
% 157.29/157.15 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__restrict__set,axiom,
% 157.29/157.15 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => 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) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_power__number__of__even__number__of,axiom,
% 157.29/157.15 ! [V_w_2,V_v_2,T_b] :
% 157.29/157.15 ( class_Int_Onumber__ring(T_b)
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_card__def,axiom,
% 157.29/157.15 ! [V_A_2,T_b] :
% 157.29/157.15 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_card_Oeq__fold__g,axiom,
% 157.29/157.15 ! [V_A_2,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_fun__left__comm__idem__remove,axiom,
% 157.29/157.15 ! [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))))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_diff__nat__eq__if,axiom,
% 157.29/157.15 ! [V_z_2,V_z_H_2] :
% 157.29/157.15 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_negDivAlg__div__mod,axiom,
% 157.29/157.15 ! [V_l,V_k] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_negDivAlg__minus1,axiom,
% 157.29/157.15 ! [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))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_adjust__eq,axiom,
% 157.29/157.15 ! [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))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_minus__fold__remove,axiom,
% 157.29/157.15 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_eq__number__of__Suc,axiom,
% 157.29/157.15 ! [V_n_2,V_v_2] :
% 157.29/157.15 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 157.29/157.15 <=> 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))))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Suc__eq__number__of,axiom,
% 157.29/157.15 ! [V_v_2,V_n_2] :
% 157.29/157.15 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 157.29/157.15 <=> 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))))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__number__of__Bit1,axiom,
% 157.29/157.15 ! [V_w_2] :
% 157.29/157.15 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 157.29/157.15 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 157.29/157.15 => 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)))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_less__Suc__number__of,axiom,
% 157.29/157.15 ! [V_v_2,V_n_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 <=> 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))))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_less__number__of__Suc,axiom,
% 157.29/157.15 ! [V_n_2,V_v_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 <=> 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)))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_le__number__of__Suc,axiom,
% 157.29/157.15 ! [V_n_2,V_v_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 <=> 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)))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_le__Suc__number__of,axiom,
% 157.29/157.15 ! [V_v_2,V_n_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 <=> 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))))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_power__number__of__odd,axiom,
% 157.29/157.15 ! [V_z_2,V_w_2,T_b] :
% 157.29/157.15 ( class_Int_Onumber__ring(T_b)
% 157.29/157.15 => ( ( 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)))
% 157.29/157.15 => 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))) )
% 157.29/157.15 & ( ~ 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)))
% 157.29/157.15 => 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) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setprod__gen__delta,axiom,
% 157.29/157.15 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.29/157.15 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.29/157.15 => 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)))) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 157.29/157.15 => 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)) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_zpower__number__of__odd,axiom,
% 157.29/157.15 ! [V_z_2,V_w_2] :
% 157.29/157.15 ( ( 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)))
% 157.29/157.15 => 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))) )
% 157.29/157.15 & ( ~ 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)))
% 157.29/157.15 => 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) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_negDivAlg_Osimps,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( ( ( 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)))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( ~ ( 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)))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.29/157.15 => 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))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_min__number__of__Suc,axiom,
% 157.29/157.15 ! [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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_min__Suc__number__of,axiom,
% 157.29/157.15 ! [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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_power__number__of__odd__number__of,axiom,
% 157.29/157.15 ! [V_v_2,V_w_2,T_b] :
% 157.29/157.15 ( class_Int_Onumber__ring(T_b)
% 157.29/157.15 => ( ( 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)))
% 157.29/157.15 => 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))) )
% 157.29/157.15 & ( ~ 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)))
% 157.29/157.15 => 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) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_negDivAlg__eqn,axiom,
% 157.29/157.15 ! [V_a,V_b] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => ( ( 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)))
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( ~ 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)))
% 157.29/157.15 => 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))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_negDivAlg__eqn__number__of,axiom,
% 157.29/157.15 ! [V_w,V_v] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( 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))))
% 157.29/157.15 => 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))) )
% 157.29/157.15 & ( ~ 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))))
% 157.29/157.15 => 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)))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_norm__frac_Osimps,axiom,
% 157.29/157.15 ! [V_a_2,V_b_2] :
% 157.29/157.15 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.29/157.15 => 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))) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__case__add__eq__if,axiom,
% 157.29/157.15 ! [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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 157.29/157.15 ! [V_w] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( 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)))
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( ~ 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)))
% 157.29/157.15 => 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)))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_posDivAlg_Osimps,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.29/157.15 => 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))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sup2E,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sup2CI,axiom,
% 157.29/157.15 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 157.29/157.15 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inf2I,axiom,
% 157.29/157.15 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inf2E,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 157.29/157.15 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_bot2E,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inf2D1,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_inf2D2,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sup2I1,axiom,
% 157.29/157.15 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_sup2I2,axiom,
% 157.29/157.15 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_less__by__empty,axiom,
% 157.29/157.15 ! [V_B_2,T_b,V_A_2] :
% 157.29/157.15 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_rev__predicate2D,axiom,
% 157.29/157.15 ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 157.29/157.15 => ( 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))
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_predicate2D,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__case__0,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__case__Suc,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_posDivAlg__0,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 157.29/157.15 ! [V_n_2,V_m_2] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 157.29/157.15 <=> 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_diff__Suc,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_min__Suc1,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_min__Suc2,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_posDivAlg__div__mod,axiom,
% 157.29/157.15 ! [V_l,V_k] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__case__number__of,axiom,
% 157.29/157.15 ! [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))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_posDivAlg__eqn__number__of,axiom,
% 157.29/157.15 ! [V_w,V_v] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( 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)))
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( ~ 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)))
% 157.29/157.15 => 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)))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_posDivAlg__eqn,axiom,
% 157.29/157.15 ! [V_a,V_b] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 157.29/157.15 => 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))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_in__rel__def,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 157.29/157.15 <=> 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_div__mod__code__numeral__def,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nitpick_Orefl_H__def,axiom,
% 157.29/157.15 ! [V_r_2,T_b] :
% 157.29/157.15 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 157.29/157.15 <=> ! [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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_adjust__def,axiom,
% 157.29/157.15 ! [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))))))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__int__num,axiom,
% 157.29/157.15 ! [V_k_2,T_b] :
% 157.29/157.15 ( class_Rings_Oring__1(T_b)
% 157.29/157.15 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 157.29/157.15 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => 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))) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => 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))))) ) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__step,axiom,
% 157.29/157.15 ! [V_m,V_n] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__rec__add__eq__if,axiom,
% 157.29/157.15 ! [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))))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 157.29/157.15 ! [V_n_2,T_b] :
% 157.29/157.15 ( class_Rings_Osemiring__1(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__rec__0,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__rec__Suc,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__zero,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 157.29/157.15 ! [V_i_2,V_inc_2,T_b] :
% 157.29/157.15 ( class_Rings_Osemiring__1(T_b)
% 157.29/157.15 => 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 ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 157.29/157.15 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 157.29/157.15 ( class_Rings_Osemiring__1(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__base,axiom,
% 157.29/157.15 ! [V_n,V_m] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__div__mod,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__mod__div,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__rec__number__of,axiom,
% 157.29/157.15 ! [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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Nitpick_OFrac__def,axiom,
% 157.29/157.15 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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__def,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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))) ) ) ) ) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => 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))) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__pdivmod,axiom,
% 157.29/157.15 ! [V_l_2,V_k_2] :
% 157.29/157.15 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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)))) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 157.29/157.15 ! [V_c,V_r,V_q,V_b,V_a] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 157.29/157.15 => 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)))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_negateSnd__def,axiom,
% 157.29/157.15 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__rel__unique,axiom,
% 157.29/157.15 ! [V_qr_H,V_qr,V_n,V_m] :
% 157.29/157.15 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 157.29/157.15 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 157.29/157.15 => V_qr = V_qr_H ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__eq,axiom,
% 157.29/157.15 ! [V_qr,V_n,V_m] :
% 157.29/157.15 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 157.29/157.15 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 157.29/157.15 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mod__eq,axiom,
% 157.29/157.15 ! [V_r,V_q,V_n,V_m] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_div__eq,axiom,
% 157.29/157.15 ! [V_r,V_q,V_n,V_m] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_negateSnd__eq,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__rel,axiom,
% 157.29/157.15 ! [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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 157.29/157.15 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( 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)))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 157.29/157.15 => 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)))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_pdivmod__def,axiom,
% 157.29/157.15 ! [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))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_pdivmod__posDivAlg,axiom,
% 157.29/157.15 ! [V_k,V_l] :
% 157.29/157.15 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__code,axiom,
% 157.29/157.15 ! [V_l_2,V_k_2] :
% 157.29/157.15 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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)))) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 157.29/157.15 ! [V_a,V_r,V_q,V_c,V_b] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 157.29/157.15 => 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)))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_splitI,axiom,
% 157.29/157.15 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_prod__caseI,axiom,
% 157.29/157.15 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_negDivAlg_Opsimps,axiom,
% 157.29/157.15 ! [V_b_2,V_a_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( ( 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)))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( ~ ( 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)))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.29/157.15 => 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))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_dual__max,axiom,
% 157.29/157.15 ! [T_b] :
% 157.29/157.15 ( class_Orderings_Olinorder(T_b)
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_accp_Osimps,axiom,
% 157.29/157.15 ! [V_a_2,V_r_2,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 157.29/157.15 <=> ! [B_x] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 157.29/157.15 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_accp_Oequations,axiom,
% 157.29/157.15 ! [V_a_2,V_r_2,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 157.29/157.15 <=> ! [B_x] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 157.29/157.15 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_accp__downward,axiom,
% 157.29/157.15 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 157.29/157.15 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_accp__subset,axiom,
% 157.29/157.15 ! [V_R2_2,V_R1_2,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Pair__inject,axiom,
% 157.29/157.15 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 157.29/157.15 ( 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)
% 157.29/157.15 => ~ ( V_a = V_a_H
% 157.29/157.15 => V_b != V_b_H ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Pair__eq,axiom,
% 157.29/157.15 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.15 ( 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)
% 157.29/157.15 <=> ( V_a_2 = V_a_H_2
% 157.29/157.15 & V_b_2 = V_b_H_2 ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_split__paired__All,axiom,
% 157.29/157.15 ! [T_c,T_b,V_Pa_2] :
% 157.29/157.15 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.29/157.15 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_split__weak__cong,axiom,
% 157.29/157.15 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 157.29/157.15 ( V_p_2 = V_q_2
% 157.29/157.15 => 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) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_prod_Osimps_I2_J,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_split__conv,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_splitD,axiom,
% 157.29/157.15 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_apsnd__conv,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_split__eta,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_split__twice,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_posDivAlg_Opsimps,axiom,
% 157.29/157.15 ! [V_b_2,V_a_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.29/157.15 => 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))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_norm__frac_Opsimps,axiom,
% 157.29/157.15 ! [V_b_2,V_a_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.29/157.15 => 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)) )
% 157.29/157.15 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 157.29/157.15 => 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))) ) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_negDivAlg_Opinduct,axiom,
% 157.29/157.15 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ! [B_a,B_b] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( ~ ( 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)))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.29/157.15 => 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))) )
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_zmult2__lemma,axiom,
% 157.29/157.15 ! [V_c,V_r,V_q,V_b,V_a] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 157.29/157.15 => 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)))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mem__splitI,axiom,
% 157.29/157.15 ! [T_d,T_c,V_b_2,V_a_2,V_ca_2,V_z_2,T_b] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2)))
% 157.29/157.15 => 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)))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_splitD_H,axiom,
% 157.29/157.15 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 157.29/157.15 ( 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))
% 157.29/157.15 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__rel__0,axiom,
% 157.29/157.15 ! [V_b] :
% 157.29/157.15 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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)))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_self__remainder,axiom,
% 157.29/157.15 ! [V_r,V_q,V_a] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_unique__quotient,axiom,
% 157.29/157.15 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( 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)))
% 157.29/157.15 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => V_q = V_q_H ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_unique__remainder,axiom,
% 157.29/157.15 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( 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)))
% 157.29/157.15 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => V_r = V_r_H ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__rel__neg,axiom,
% 157.29/157.15 ! [V_qr,V_b,V_a] :
% 157.29/157.15 ( 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))
% 157.29/157.15 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__correct,axiom,
% 157.29/157.15 ! [V_a,V_b] :
% 157.29/157.15 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_self__quotient,axiom,
% 157.29/157.15 ! [V_r,V_q,V_a] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__rel__mod,axiom,
% 157.29/157.15 ! [V_r,V_q,V_b,V_a] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__rel__div,axiom,
% 157.29/157.15 ! [V_r,V_q,V_b,V_a] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_negDivAlg__correct,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__rel__div__mod,axiom,
% 157.29/157.15 ! [V_a,V_b] :
% 157.29/157.15 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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)))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_posDivAlg__correct,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_zadd1__lemma,axiom,
% 157.29/157.15 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( 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)))
% 157.29/157.15 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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)))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_zminus1__lemma,axiom,
% 157.29/157.15 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => 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))))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__if,axiom,
% 157.29/157.15 ! [V_m_2,V_n_2] :
% 157.29/157.15 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 157.29/157.15 => 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) )
% 157.29/157.15 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__relI,axiom,
% 157.29/157.15 ! [V_r,V_q,V_b,V_a] :
% 157.29/157.15 ( 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)
% 157.29/157.15 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 157.29/157.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 157.29/157.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 157.29/157.15 => 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))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_zmult1__lemma,axiom,
% 157.29/157.15 ! [V_a,V_r,V_q,V_c,V_b] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 157.29/157.15 => 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)))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__int__rel__def,axiom,
% 157.29/157.15 ! [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))))))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_posDivAlg_Opinduct,axiom,
% 157.29/157.15 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ! [B_a,B_b] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 157.29/157.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 157.29/157.15 => 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))) )
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__gcd_Opsimps,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.15 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 157.29/157.15 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.15 => 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)) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 157.29/157.15 ! [V_f_2,V_A_2,T_b] :
% 157.29/157.15 ( ! [B_x] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.15 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mod__pos__neg__1__number__of,axiom,
% 157.29/157.15 ! [V_w] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => 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))))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_snd__conv,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_snd__eqD,axiom,
% 157.29/157.15 ! [V_a,V_y,V_x,T_a,T_b] :
% 157.29/157.15 ( 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
% 157.29/157.15 => V_y = V_a ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_snd__apsnd,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_apsnd__eq__conv,axiom,
% 157.29/157.15 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 157.29/157.15 ( 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)
% 157.29/157.15 <=> 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_snd__def,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mod__int__def,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mod__neg__pos,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mod__pos__pos,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mod__pos__pos__1__number__of,axiom,
% 157.29/157.15 ! [V_w] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mod__pos__neg,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => 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)))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mod__neg__neg,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => 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)))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_in__measure,axiom,
% 157.29/157.15 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 <=> 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 157.29/157.15 ! [V_f_2,V_A_2,T_b] :
% 157.29/157.15 ( ! [B_x] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.15 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_norm__frac_Opinduct,axiom,
% 157.29/157.15 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ! [B_a,B_b] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => 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))) )
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_div__pos__neg__1__number__of,axiom,
% 157.29/157.15 ! [V_w] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => 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))))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_Pair__fst__snd__eq,axiom,
% 157.29/157.15 ! [T_c,T_b,V_t_2,V_s_2] :
% 157.29/157.15 ( V_s_2 = V_t_2
% 157.29/157.15 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 157.29/157.15 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_prod__eqI,axiom,
% 157.29/157.15 ! [V_q,V_p,T_b,T_a] :
% 157.29/157.15 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 157.29/157.15 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 157.29/157.15 => V_p = V_q ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_fst__eqD,axiom,
% 157.29/157.15 ! [V_a,V_y,V_x,T_b,T_a] :
% 157.29/157.15 ( 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
% 157.29/157.15 => V_x = V_a ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_fst__conv,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_fst__apsnd,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_fst__def,axiom,
% 157.29/157.15 ! [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) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_pair__collapse,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_surjective__pairing,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_prod__case__beta,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_div__int__def,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mod__nat__def,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_split__comp__eq,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_split__beta,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_split__def,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_div__neg__pos,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_div__pos__pos,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 157.29/157.15 => 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)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_div__pos__pos__1__number__of,axiom,
% 157.29/157.15 ! [V_w] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_div__pos__neg,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => 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)))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_div__neg__neg,axiom,
% 157.29/157.15 ! [V_b,V_a] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 157.29/157.15 => 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)))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_prod__size__simp,axiom,
% 157.29/157.15 ! [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))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_conjI__realizer,axiom,
% 157.29/157.15 ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] :
% 157.29/157.15 ( hBOOL(hAPP(V_Pa_2,V_p_2))
% 157.29/157.15 => ( hBOOL(hAPP(V_Qa_2,V_q_2))
% 157.29/157.15 => ( 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))))
% 157.29/157.15 & 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)))) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_exI__realizer,axiom,
% 157.29/157.15 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
% 157.29/157.15 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
% 157.29/157.15 => 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)))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_nat__gcd_Opinduct,axiom,
% 157.29/157.15 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ! [B_x,B_y] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
% 157.29/157.15 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_div__nat__def,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_divmod__nat__rel__def,axiom,
% 157.29/157.15 ! [V_qr_2,V_n_2,V_m_2] :
% 157.29/157.15 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 157.29/157.15 <=> ( 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))
% 157.29/157.15 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.15 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.29/157.15 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.15 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 157.29/157.15 => ( 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)))
% 157.29/157.15 & 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)) ) )
% 157.29/157.15 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 157.29/157.15 => ( 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)))
% 157.29/157.15 & 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))) ) ) ) ) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_range,axiom,
% 157.29/157.15 ! [V_s,V_k] :
% 157.29/157.15 ( 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))
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_arith__series__int,axiom,
% 157.29/157.15 ! [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)))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mlex__leq,axiom,
% 157.29/157.15 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => ( 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))
% 157.29/157.15 => 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))) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_mlex__less,axiom,
% 157.29/157.15 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 157.29/157.15 ( 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)))
% 157.29/157.15 => 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))) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_finite__lessThan,axiom,
% 157.29/157.15 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_lessThan__0,axiom,
% 157.29/157.15 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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_card__lessThan,axiom,
% 157.29/157.15 ! [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 ).
% 157.29/157.15
% 157.29/157.15 fof(fact_lessThan__Suc,axiom,
% 157.29/157.15 ! [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)) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_lessThan__eq__iff,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.15 ( class_Orderings_Olinorder(T_b)
% 157.29/157.15 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 157.29/157.15 <=> V_x_2 = V_y_2 ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_lessThan__iff,axiom,
% 157.29/157.15 ! [V_k_2,V_i_2,T_b] :
% 157.29/157.15 ( class_Orderings_Oord(T_b)
% 157.29/157.15 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_lessThan__subset__iff,axiom,
% 157.29/157.15 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.15 ( class_Orderings_Olinorder(T_b)
% 157.29/157.15 => ( 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)))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_setsum__lessThan__Suc,axiom,
% 157.29/157.15 ! [V_n_2,V_f_2,T_b] :
% 157.29/157.15 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.15 => 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)) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_lessThan__strict__subset__iff,axiom,
% 157.29/157.15 ! [V_n_2,V_m_2,T_b] :
% 157.29/157.15 ( class_Orderings_Olinorder(T_b)
% 157.29/157.15 => ( 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)))
% 157.29/157.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 157.29/157.15
% 157.29/157.15 fof(fact_single__Diff__lessThan,axiom,
% 157.29/157.15 ! [V_k_2,T_b] :
% 157.29/157.15 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__nat__set__iff__bounded,axiom,
% 157.29/157.16 ! [V_N_2] :
% 157.29/157.16 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 157.29/157.16 <=> ? [B_m] :
% 157.29/157.16 ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 157.29/157.16 ! [V_N_2] :
% 157.29/157.16 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 157.29/157.16 <=> ? [B_m] :
% 157.29/157.16 ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_arith__series__general,axiom,
% 157.29/157.16 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Rings_Ocomm__semiring__1(T_b)
% 157.29/157.16 => 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)))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_arith__series__nat,axiom,
% 157.29/157.16 ! [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)))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_nat_Osize_I4_J,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_prod_Orecs,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ord_OatMost__iff,axiom,
% 157.29/157.16 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 157.29/157.16 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ord_OatLeast__iff,axiom,
% 157.29/157.16 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 157.29/157.16 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_nat__size,axiom,
% 157.29/157.16 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 157.29/157.16
% 157.29/157.16 fof(fact_infinite__UNIV__nat,axiom,
% 157.29/157.16 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_nat_Osize_I3_J,axiom,
% 157.29/157.16 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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ord_OlessThan__iff,axiom,
% 157.29/157.16 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 157.29/157.16 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ord_OgreaterThan__iff,axiom,
% 157.29/157.16 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 157.29/157.16 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_in__lex__prod,axiom,
% 157.29/157.16 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 <=> ( 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))
% 157.29/157.16 | ( V_a_2 = V_a_H_2
% 157.29/157.16 & 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)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_in__finite__psubset,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.16 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_same__fstI,axiom,
% 157.29/157.16 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
% 157.29/157.16 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.16 => ( 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)))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_setsum__nonneg__0,axiom,
% 157.29/157.16 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 157.29/157.16 ( class_Groups_Oordered__ab__group__add(T_c)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 157.29/157.16 => ( ! [B_i] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 157.29/157.16 => ( 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)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 157.29/157.16 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_setsum__nonneg__leq__bound,axiom,
% 157.29/157.16 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 157.29/157.16 ( class_Groups_Oordered__ab__group__add(T_c)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 157.29/157.16 => ( ! [B_i] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 157.29/157.16 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__Suc__number__of,axiom,
% 157.29/157.16 ! [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)))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_sup__max,axiom,
% 157.29/157.16 ! [T_b] :
% 157.29/157.16 ( ( class_Lattices_Osemilattice__sup(T_b)
% 157.29/157.16 & class_Orderings_Olinorder(T_b) )
% 157.29/157.16 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_sup__nat__def,axiom,
% 157.29/157.16 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_le__max__iff__disj,axiom,
% 157.29/157.16 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( 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)))
% 157.29/157.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 157.29/157.16 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Ole__supE,axiom,
% 157.29/157.16 ! [V_x,V_b,V_a,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => ( 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))
% 157.29/157.16 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 157.29/157.16 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__mono,axiom,
% 157.29/157.16 ! [V_d,V_b,V_c,V_a,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 157.29/157.16 => 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))) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__least,axiom,
% 157.29/157.16 ! [V_z,V_x,V_y,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 157.29/157.16 => 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)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Ole__supI,axiom,
% 157.29/157.16 ! [V_b,V_x,V_a,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 157.29/157.16 => 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)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__absorb1,axiom,
% 157.29/157.16 ! [V_x,V_y,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 157.29/157.16 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__absorb2,axiom,
% 157.29/157.16 ! [V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.29/157.16 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Ole__supI2,axiom,
% 157.29/157.16 ! [V_a,V_b,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Ole__supI1,axiom,
% 157.29/157.16 ! [V_b,V_a,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Ole__sup__iff,axiom,
% 157.29/157.16 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( 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))
% 157.29/157.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Ole__iff__sup,axiom,
% 157.29/157.16 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.29/157.16 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_le__maxI2,axiom,
% 157.29/157.16 ! [V_x,V_y,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_le__maxI1,axiom,
% 157.29/157.16 ! [V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__add__distrib__left,axiom,
% 157.29/157.16 ! [V_z,V_y,V_x,T_a] :
% 157.29/157.16 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__less__iff__conj,axiom,
% 157.29/157.16 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( 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))
% 157.29/157.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_less__max__iff__disj,axiom,
% 157.29/157.16 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( 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)))
% 157.29/157.16 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 157.29/157.16 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Oless__supI2,axiom,
% 157.29/157.16 ! [V_a,V_b,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Oless__supI1,axiom,
% 157.29/157.16 ! [V_b,V_a,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__diff__distrib__left,axiom,
% 157.29/157.16 ! [V_z,V_y,V_x,T_a] :
% 157.29/157.16 ( class_Groups_Oordered__ab__group__add(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Oidem,axiom,
% 157.29/157.16 ! [V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__assoc,axiom,
% 157.29/157.16 ! [V_z,V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup_Oassoc,axiom,
% 157.29/157.16 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__left__commute,axiom,
% 157.29/157.16 ! [V_z,V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 157.29/157.16 ! [V_c,V_a,V_b,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__left__idem,axiom,
% 157.29/157.16 ! [V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 157.29/157.16 ! [V_b,V_a,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__commute,axiom,
% 157.29/157.16 ! [V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup_Ocommute,axiom,
% 157.29/157.16 ! [V_b,V_a,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup_Oidem,axiom,
% 157.29/157.16 ! [V_a,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__inf__absorb,axiom,
% 157.29/157.16 ! [V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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 ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 157.29/157.16 ! [V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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 ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 157.29/157.16 ! [V_z,V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 157.29/157.16 ! [V_z,V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 157.29/157.16 ! [V_x,V_z,V_y,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 157.29/157.16 ! [V_x,V_z,V_y,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__Suc__Suc,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__0R,axiom,
% 157.29/157.16 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__0L,axiom,
% 157.29/157.16 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 157.29/157.16 ! [T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__number__of,axiom,
% 157.29/157.16 ! [V_v,V_u,T_b] :
% 157.29/157.16 ( ( class_Int_Onumber(T_b)
% 157.29/157.16 & class_Orderings_Oord(T_b) )
% 157.29/157.16 => ( ( 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)))
% 157.29/157.16 => 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) )
% 157.29/157.16 & ( ~ 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)))
% 157.29/157.16 => 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) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Odistrib__inf__le,axiom,
% 157.29/157.16 ! [V_z,V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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)))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Odistrib__sup__le,axiom,
% 157.29/157.16 ! [V_z,V_y,V_x,T_a] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_a)
% 157.29/157.16 => 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)))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_minus__min__eq__max,axiom,
% 157.29/157.16 ! [V_y,V_x,T_a] :
% 157.29/157.16 ( class_Groups_Olinordered__ab__group__add(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_minus__max__eq__min,axiom,
% 157.29/157.16 ! [V_y,V_x,T_a] :
% 157.29/157.16 ( class_Groups_Olinordered__ab__group__add(T_a)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_nat__minus__add__max,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__Suc1,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__Suc2,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__ord__max,axiom,
% 157.29/157.16 ! [T_b] :
% 157.29/157.16 ( class_Orderings_Oord(T_b)
% 157.29/157.16 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Ofold__sup__insert,axiom,
% 157.29/157.16 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_dual__min,axiom,
% 157.29/157.16 ! [T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => 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) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 157.29/157.16 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.16 => 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))) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 157.29/157.16 ! [V_a_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.16 => 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 ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__number__of__Suc,axiom,
% 157.29/157.16 ! [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)))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Oremove,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.16 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.29/157.16 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 157.29/157.16 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.29/157.16 => 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)))))) ) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OInf__le__Sup,axiom,
% 157.29/157.16 ! [V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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))) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.16 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.29/157.16 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 157.29/157.16 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.29/157.16 => 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)))))) ) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_sum__diff__distrib,axiom,
% 157.29/157.16 ! [V_n_2,V_Pa_2,V_Qa_2] :
% 157.29/157.16 ( ! [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)))
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Osingleton,axiom,
% 157.29/157.16 ! [V_x_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => 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 ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.16 => 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) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max__ge,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.16 => 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))) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 157.29/157.16 ! [V_x_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => 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 ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max__in,axiom,
% 157.29/157.16 ! [V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Oin__idem,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.16 => 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) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 157.29/157.16 ! [V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_OF__eq,axiom,
% 157.29/157.16 ! [V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.29/157.16 => 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) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 157.29/157.16 ! [V_a_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.16 => 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 ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.16 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max__mono,axiom,
% 157.29/157.16 ! [V_N_2,V_M_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 157.29/157.16 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.29/157.16 => 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))) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 157.29/157.16 ! [V_a_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max__insert,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Osubset__idem,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.29/157.16 => 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) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max__Un,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.16 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 157.29/157.16 ! [V_a_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.29/157.16 => 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 )
% 157.29/157.16 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.29/157.16 => 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)))))) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => 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)) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.16 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => 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)) ) ) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.16 => 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) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Oinsert,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Oinsert__remove,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.29/157.16 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 157.29/157.16 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 157.29/157.16 => 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)))))) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Ounion__inter,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => 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)) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Ounion__disjoint,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.16 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => 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)) ) ) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Oeq__fold_H,axiom,
% 157.29/157.16 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.16 => 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) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 157.29/157.16 ! [V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => ( ! [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))))))
% 157.29/157.16 => 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)) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Max_Oclosed,axiom,
% 157.29/157.16 ! [V_A_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => ( ! [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))))))
% 157.29/157.16 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_apfst__apsnd,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_apsnd__apfst,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_apfst__conv,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_apfst__eq__conv,axiom,
% 157.29/157.16 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 157.29/157.16 ( 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)
% 157.29/157.16 <=> 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_fst__apfst,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_snd__apfst,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_apsnd__apfst__commute,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_pair__lessI2,axiom,
% 157.29/157.16 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_setsum__natinterval__difff,axiom,
% 157.29/157.16 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 157.29/157.16 ( class_Groups_Oab__group__add(T_b)
% 157.29/157.16 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.29/157.16 => 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)))) )
% 157.29/157.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.29/157.16 => 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) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_gauss__sum,axiom,
% 157.29/157.16 ! [V_n_2,T_b] :
% 157.29/157.16 ( class_Rings_Ocomm__semiring__1(T_b)
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INFI__fold__inf,axiom,
% 157.29/157.16 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__E,axiom,
% 157.29/157.16 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 157.29/157.16 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__D,axiom,
% 157.29/157.16 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF1__D,axiom,
% 157.29/157.16 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF1__E,axiom,
% 157.29/157.16 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 157.29/157.16 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF2__D,axiom,
% 157.29/157.16 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF2__E,axiom,
% 157.29/157.16 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 157.29/157.16 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__INT,axiom,
% 157.29/157.16 ! [V_A_2,T_c,V_I_2,T_b] :
% 157.29/157.16 ( ? [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 157.29/157.16 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__atLeastAtMost,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_b,T_c] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.16 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.16 ( 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)
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.16 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__subset__iff,axiom,
% 157.29/157.16 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__Int__distrib,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF__commute,axiom,
% 157.29/157.16 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INFI__apply,axiom,
% 157.29/157.16 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__simps_I8_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__extend__simps_I8_J,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Pow__INT__eq,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__extend__simps_I5_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__simps_I5_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__iff,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Inter__def,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__simps_I7_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__simps_I6_J,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__extend__simps_I7_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Un__INT__distrib,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__extend__simps_I6_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Un__INT__distrib2,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF__INT__eq2,axiom,
% 157.29/157.16 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_le__INF__iff,axiom,
% 157.29/157.16 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.16 => ( 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)))
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF__less__iff,axiom,
% 157.29/157.16 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 157.29/157.16 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.16 & class_Orderings_Olinorder(T_b) )
% 157.29/157.16 => ( 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))
% 157.29/157.16 <=> ? [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__insert__distrib,axiom,
% 157.29/157.16 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__lower,axiom,
% 157.29/157.16 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF__INT__eq,axiom,
% 157.29/157.16 ! [V_x_2,V_r_2,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__absorb,axiom,
% 157.29/157.16 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 157.29/157.16 => 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) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF__const,axiom,
% 157.29/157.16 ! [V_M_2,T_b,V_A_2,T_c] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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 ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__empty,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__constant,axiom,
% 157.29/157.16 ! [V_ca_2,T_c,T_b,V_A_2] :
% 157.29/157.16 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) )
% 157.29/157.16 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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 ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__extend__simps_I1_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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 )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__extend__simps_I2_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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 )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__insert,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__Un,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Un__Inter,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastatMost__empty__iff2,axiom,
% 157.29/157.16 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( 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)
% 157.29/157.16 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastatMost__empty__iff,axiom,
% 157.29/157.16 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( 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))
% 157.29/157.16 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastatMost__empty,axiom,
% 157.29/157.16 ! [V_a_2,V_b_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastatMost__subset__iff,axiom,
% 157.29/157.16 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( 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)))
% 157.29/157.16 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 157.29/157.16 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastAtMost__singleton,axiom,
% 157.29/157.16 ! [V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 157.29/157.16 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( 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)))
% 157.29/157.16 <=> ( V_a_2 = V_b_2
% 157.29/157.16 & V_b_2 = V_ca_2 ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastAtMost__singleton_H,axiom,
% 157.29/157.16 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( V_a_2 = V_b_2
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 157.29/157.16 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 157.29/157.16 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 157.29/157.16 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 157.29/157.16 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF__subset,axiom,
% 157.29/157.16 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__simps_I1_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__simps_I2_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__extend__simps_I3_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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) )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__simps_I3_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_card__atLeastAtMost,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastAtMostSuc__conv,axiom,
% 157.29/157.16 ! [V_n_2,V_m_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF__leI,axiom,
% 157.29/157.16 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 157.29/157.16 ! [V_k_2,V_f_2] :
% 157.29/157.16 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Int__atLeastAtMost,axiom,
% 157.29/157.16 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastatMost__psubset__iff,axiom,
% 157.29/157.16 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( 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)))
% 157.29/157.16 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 157.29/157.16 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 157.29/157.16 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2))
% 157.29/157.16 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 157.29/157.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__int_I4_J,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_setsum__head__Suc,axiom,
% 157.29/157.16 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 157.29/157.16 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_pair__lessI1,axiom,
% 157.29/157.16 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_setsum__cl__ivl__Suc,axiom,
% 157.29/157.16 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 157.29/157.16 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.16 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 157.29/157.16 => 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) )
% 157.29/157.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 157.29/157.16 => 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))) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_inf__INFI__fold__inf,axiom,
% 157.29/157.16 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_setsum__ub__add__nat,axiom,
% 157.29/157.16 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 157.29/157.16 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.16 => ( 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))))
% 157.29/157.16 => 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)))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_all__nat__less,axiom,
% 157.29/157.16 ! [V_Pa_2,V_n_2] :
% 157.29/157.16 ( ! [B_m] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 157.29/157.16 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ex__nat__less,axiom,
% 157.29/157.16 ! [V_Pa_2,V_n_2] :
% 157.29/157.16 ( ? [B_m] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 157.29/157.16 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 157.29/157.16 <=> ? [B_x] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_pair__leqI2,axiom,
% 157.29/157.16 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_smin__insertI,axiom,
% 157.29/157.16 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => 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)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF1__iff,axiom,
% 157.29/157.16 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INF2__iff,axiom,
% 157.29/157.16 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_smin__emptyI,axiom,
% 157.29/157.16 ! [V_X_2] :
% 157.29/157.16 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_simp__from__to,axiom,
% 157.29/157.16 ! [V_i_2,V_j_2] :
% 157.29/157.16 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 157.29/157.16 => 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)) )
% 157.29/157.16 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_card__atLeastAtMost__int,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_pair__leqI1,axiom,
% 157.29/157.16 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_wmax__insertI,axiom,
% 157.29/157.16 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => 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)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_wmin__insertI,axiom,
% 157.29/157.16 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => 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)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_smax__insertI,axiom,
% 157.29/157.16 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => 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)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_bset_I8_J,axiom,
% 157.29/157.16 ! [V_B_2,V_t_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => ! [B_x] :
% 157.29/157.16 ( ! [B_xa] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xb] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 157.29/157.16 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 157.29/157.16 => 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))) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__atLeastAtMost__int,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_smax__emptyI,axiom,
% 157.29/157.16 ! [V_Y_2] :
% 157.29/157.16 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 157.29/157.16 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_wmax__emptyI,axiom,
% 157.29/157.16 ! [V_X_2] :
% 157.29/157.16 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_wmin__emptyI,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__weak__def,axiom,
% 157.29/157.16 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)))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_aset_I6_J,axiom,
% 157.29/157.16 ! [V_A_2,V_t_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => ! [B_x] :
% 157.29/157.16 ( ! [B_xa] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xb] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 157.29/157.16 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 157.29/157.16 => 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)) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__weak__def,axiom,
% 157.29/157.16 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)))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_bset_I3_J,axiom,
% 157.29/157.16 ! [V_B_2,V_t_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => ( ! [B_x] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xa] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 157.29/157.16 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 157.29/157.16 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_infinite__UNIV__int,axiom,
% 157.29/157.16 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__strict__def,axiom,
% 157.29/157.16 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__ext__additive,axiom,
% 157.29/157.16 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ( 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)))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__strict__def,axiom,
% 157.29/157.16 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__extp__max__ext__eq,axiom,
% 157.29/157.16 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 157.29/157.16 ( 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)
% 157.29/157.16 <=> 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_aset_I4_J,axiom,
% 157.29/157.16 ! [V_A_2,V_t_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 157.29/157.16 => ! [B_x] :
% 157.29/157.16 ( ! [B_xa] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xb] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 157.29/157.16 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.29/157.16 => ( B_x != V_t_2
% 157.29/157.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_bset_I4_J,axiom,
% 157.29/157.16 ! [V_B_2,V_t_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 157.29/157.16 => ! [B_x] :
% 157.29/157.16 ( ! [B_xa] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xb] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 157.29/157.16 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.29/157.16 => ( B_x != V_t_2
% 157.29/157.16 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_bset_I7_J,axiom,
% 157.29/157.16 ! [V_B_2,V_t_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 157.29/157.16 => ! [B_x] :
% 157.29/157.16 ( ! [B_xa] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xb] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 157.29/157.16 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 157.29/157.16 => 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))) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_aset_I3_J,axiom,
% 157.29/157.16 ! [V_A_2,V_t_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ( 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))
% 157.29/157.16 => ( ! [B_x] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xa] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 157.29/157.16 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 157.29/157.16 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_aset_I5_J,axiom,
% 157.29/157.16 ! [V_A_2,V_t_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 157.29/157.16 => ! [B_x] :
% 157.29/157.16 ( ! [B_xa] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xb] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 157.29/157.16 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 157.29/157.16 => 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)) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_aset_I8_J,axiom,
% 157.29/157.16 ! [V_t_2,V_A_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ! [B_x] :
% 157.29/157.16 ( ! [B_xa] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xb] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 157.29/157.16 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 157.29/157.16 => 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))) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_bset_I6_J,axiom,
% 157.29/157.16 ! [V_t_2,V_B_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ! [B_x] :
% 157.29/157.16 ( ! [B_xa] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xb] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 157.29/157.16 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 157.29/157.16 => 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)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_periodic__finite__ex,axiom,
% 157.29/157.16 ! [V_Pa_2,V_d_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 157.29/157.16 => ( ! [B_x,B_k] :
% 157.29/157.16 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.29/157.16 <=> 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)))) )
% 157.29/157.16 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.29/157.16 <=> ? [B_x] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_bset_I5_J,axiom,
% 157.29/157.16 ! [V_t_2,V_B_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ! [B_x] :
% 157.29/157.16 ( ! [B_xa] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xb] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 157.29/157.16 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 157.29/157.16 => 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)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_aset_I7_J,axiom,
% 157.29/157.16 ! [V_t_2,V_A_2,V_D_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 157.29/157.16 => ! [B_x] :
% 157.29/157.16 ( ! [B_xa] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => ! [B_xb] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 157.29/157.16 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 157.29/157.16 => 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))) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_card__greaterThanLessThan__int,axiom,
% 157.29/157.16 ! [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)))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__greaterThanLessThan__int,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_greaterThanLessThan__empty,axiom,
% 157.29/157.16 ! [V_k_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__int_I12_J,axiom,
% 157.29/157.16 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__int_I13_J,axiom,
% 157.29/157.16 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Int__greaterThanLessThan,axiom,
% 157.29/157.16 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_max__rpair__set,axiom,
% 157.29/157.16 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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_min__rpair__set,axiom,
% 157.29/157.16 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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__un_I19_J,axiom,
% 157.29/157.16 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.29/157.16 => 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) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__un_I4_J,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__greaterThanAtMost,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__greaterThanLessThan,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__greaterThanAtMost__int,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_greaterThanAtMost__empty,axiom,
% 157.29/157.16 ! [V_k_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 157.29/157.16 ! [V_l_2,V_k_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( 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))
% 157.29/157.16 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 157.29/157.16 ! [V_l_2,V_k_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( 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)
% 157.29/157.16 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__un_I20_J,axiom,
% 157.29/157.16 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.29/157.16 => 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) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__int_I14_J,axiom,
% 157.29/157.16 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_card__greaterThanAtMost,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__un_I22_J,axiom,
% 157.29/157.16 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.29/157.16 => 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) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__int_I16_J,axiom,
% 157.29/157.16 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Int__greaterThanAtMost,axiom,
% 157.29/157.16 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__int_I10_J,axiom,
% 157.29/157.16 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_card__greaterThanLessThan,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_card__greaterThanAtMost__int,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__un_I16_J,axiom,
% 157.29/157.16 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 157.29/157.16 => 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) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_setsum__head,axiom,
% 157.29/157.16 ! [V_Pa_2,V_n_2,V_m_2,T_b] :
% 157.29/157.16 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__un_I5_J,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_less__than__iff,axiom,
% 157.29/157.16 ! [V_y_2,V_x_2] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_intrel__iff,axiom,
% 157.29/157.16 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> 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) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_rp__inv__image__rp,axiom,
% 157.29/157.16 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 157.29/157.16 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 157.29/157.16 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUPR__fold__sup,axiom,
% 157.29/157.16 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__I,axiom,
% 157.29/157.16 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUP1__I,axiom,
% 157.29/157.16 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUP2__I,axiom,
% 157.29/157.16 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UNION__empty__conv_I2_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_b,T_c] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.16 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__constant,axiom,
% 157.29/157.16 ! [V_ca_2,T_c,T_b,V_A_2] :
% 157.29/157.16 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) )
% 157.29/157.16 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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 ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__empty2,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UNION__empty__conv_I1_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.16 ( 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)
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.16 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__Un,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__Un__distrib,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__UN,axiom,
% 157.29/157.16 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => ( 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)))
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.16 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__extend__simps_I9_J,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__simps_I9_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__Pow__subset,axiom,
% 157.29/157.16 ! [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)))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__subset__iff,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__simps_I5_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__simps_I4_J,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__extend__simps_I5_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Int__UN__distrib,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__extend__simps_I4_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Int__UN__distrib2,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUP__commute,axiom,
% 157.29/157.16 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUPR__apply,axiom,
% 157.29/157.16 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__simps_I8_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__extend__simps_I8_J,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__extend__simps_I6_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__simps_I6_J,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Union__def,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__iff,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 <=> ? [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUP__UN__eq2,axiom,
% 157.29/157.16 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUP__le__iff,axiom,
% 157.29/157.16 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.16 => ( 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))
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_less__SUP__iff,axiom,
% 157.29/157.16 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 157.29/157.16 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.16 & class_Orderings_Olinorder(T_b) )
% 157.29/157.16 => ( 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)))
% 157.29/157.16 <=> ? [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUP__const,axiom,
% 157.29/157.16 ! [V_M_2,T_b,V_A_2,T_c] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.29/157.16 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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 ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__insert__distrib,axiom,
% 157.29/157.16 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__upper,axiom,
% 157.29/157.16 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUP__UN__eq,axiom,
% 157.29/157.16 ! [V_x_2,V_r_2,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__absorb,axiom,
% 157.29/157.16 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 157.29/157.16 => 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) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__simps_I1_J,axiom,
% 157.29/157.16 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__singleton,axiom,
% 157.29/157.16 ! [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 ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__extend__simps_I1_J,axiom,
% 157.29/157.16 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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))) )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__simps_I3_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__simps_I2_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__extend__simps_I3_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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 )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__extend__simps_I2_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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 )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__insert,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__simps_I7_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__extend__simps_I7_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Int__Union2,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Int__Union,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Compl__INT,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Compl__UN,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__lessThan__UNIV,axiom,
% 157.29/157.16 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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUP__subset,axiom,
% 157.29/157.16 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_pair__less__def,axiom,
% 157.29/157.16 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__extend__simps_I4_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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 )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_le__SUPI,axiom,
% 157.29/157.16 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_INT__simps_I4_J,axiom,
% 157.29/157.16 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 157.29/157.16 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) )
% 157.29/157.16 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.16 => 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)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_sup__SUPR__fold__sup,axiom,
% 157.29/157.16 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 157.29/157.16 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 157.29/157.16 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_nat__def,axiom,
% 157.29/157.16 ! [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)))))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_mlex__prod__def,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_rp__inv__image__def,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__un_I7_J,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__atMost,axiom,
% 157.29/157.16 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ball__UN,axiom,
% 157.29/157.16 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.16 ( ! [B_x] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.16 => ! [B_xa] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 157.29/157.16 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUP1__iff,axiom,
% 157.29/157.16 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> ? [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_SUP2__iff,axiom,
% 157.29/157.16 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 157.29/157.16 ( 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))
% 157.29/157.16 <=> ? [B_x] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.16 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__extend__simps_I9_J,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__simps_I9_J,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__UN__flatten,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Rep__Integ__inject,axiom,
% 157.29/157.16 ! [V_y_2,V_x_2] :
% 157.29/157.16 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 157.29/157.16 <=> V_x_2 = V_y_2 ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atMost__eq__iff,axiom,
% 157.29/157.16 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 157.29/157.16 <=> V_x_2 = V_y_2 ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__atMost__UNIV,axiom,
% 157.29/157.16 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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeast0AtMost,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_lessThan__Suc__atMost,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_card__atMost,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atMost__Suc,axiom,
% 157.29/157.16 ! [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)) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atMost__iff,axiom,
% 157.29/157.16 ! [V_k_2,V_i_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oord(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 157.29/157.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atMost__subset__iff,axiom,
% 157.29/157.16 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => ( 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)))
% 157.29/157.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__le__add__shift,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_setsum__atMost__Suc,axiom,
% 157.29/157.16 ! [V_n_2,V_f_2,T_b] :
% 157.29/157.16 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atMost__0,axiom,
% 157.29/157.16 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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Int__atLeastAtMostR1,axiom,
% 157.29/157.16 ! [V_d_2,V_ca_2,V_b_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_Int__atLeastAtMostL1,axiom,
% 157.29/157.16 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__un_I9_J,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__int_I3_J,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__int_I1_J,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Oorder(T_b)
% 157.29/157.16 => 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_UN__le__eq__Un0,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_measure__def,axiom,
% 157.29/157.16 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__un_I2_J,axiom,
% 157.29/157.16 ! [V_u_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => 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) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__un_I10_J,axiom,
% 157.29/157.16 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.29/157.16 => 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) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_in__inv__image,axiom,
% 157.29/157.16 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 <=> 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)) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_geometric__sum,axiom,
% 157.29/157.16 ! [V_n_2,V_x_2,T_b] :
% 157.29/157.16 ( class_Fields_Ofield(T_b)
% 157.29/157.16 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 157.29/157.16 => 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))) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ivl__disj__un_I18_J,axiom,
% 157.29/157.16 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 157.29/157.16 => 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) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__atLeastLessThan__int,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_finite__atLeastLessThan,axiom,
% 157.29/157.16 ! [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))) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 157.29/157.16 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( 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)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 157.29/157.16 => V_b_2 = V_d_2 ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 157.29/157.16 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( 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)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 157.29/157.16 => V_a_2 = V_ca_2 ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastLessThan__eq__iff,axiom,
% 157.29/157.16 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.16 ( class_Orderings_Olinorder(T_b)
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 157.29/157.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 157.29/157.16 => ( 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)
% 157.29/157.16 <=> ( V_a_2 = V_ca_2
% 157.29/157.16 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_all__nat__less__eq,axiom,
% 157.29/157.16 ! [V_Pa_2,V_n_2] :
% 157.29/157.16 ( ! [B_m] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 157.29/157.16 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 157.29/157.16 <=> ! [B_x] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_ex__nat__less__eq,axiom,
% 157.29/157.16 ! [V_Pa_2,V_n_2] :
% 157.29/157.16 ( ? [B_m] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 157.29/157.16 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 157.29/157.16 <=> ? [B_x] :
% 157.29/157.16 ( 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)))
% 157.29/157.16 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastLessThan__add__Un,axiom,
% 157.29/157.16 ! [V_k_2,V_j_2,V_i_2] :
% 157.29/157.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 157.29/157.16 => 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))) ) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 157.29/157.16 ! [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) ).
% 157.29/157.16
% 157.29/157.16 fof(fact_atLeastLessThan0,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeast0LessThan,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_subset__card__intvl__is__intvl,axiom,
% 157.29/157.17 ! [V_k_2,V_A_2] :
% 157.29/157.17 ( 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)))))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_card__atLeastLessThan,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeastLessThan__empty,axiom,
% 157.29/157.17 ! [V_a_2,V_b_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 157.29/157.17 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => ( 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)
% 157.29/157.17 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeastLessThan__empty__iff,axiom,
% 157.29/157.17 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => ( 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))
% 157.29/157.17 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeastLessThan__subset__iff,axiom,
% 157.29/157.17 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 157.29/157.17 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 157.29/157.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 157.29/157.17 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 157.29/157.17 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__un_I17_J,axiom,
% 157.29/157.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.29/157.17 => 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) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 157.29/157.17 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 157.29/157.17 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__diff,axiom,
% 157.29/157.17 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__int_I11_J,axiom,
% 157.29/157.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_setsum__add__nat__ivl,axiom,
% 157.29/157.17 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 157.29/157.17 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_setsum__diff__nat__ivl,axiom,
% 157.29/157.17 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 157.29/157.17 ( class_Groups_Oab__group__add(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeastLessThan__singleton,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__UN__finite__eq,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__un_I21_J,axiom,
% 157.29/157.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.29/157.17 => 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) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__int_I15_J,axiom,
% 157.29/157.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Int__atLeastLessThan,axiom,
% 157.29/157.17 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__un_I8_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__int_I2_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__int_I9_J,axiom,
% 157.29/157.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 157.29/157.17 ! [V_k_2,V_f_2,T_b] :
% 157.29/157.17 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_setsum__head__upt__Suc,axiom,
% 157.29/157.17 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 157.29/157.17 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_card__atLeastLessThan__int,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeastLessThanSuc,axiom,
% 157.29/157.17 ! [V_n_2,V_m_2] :
% 157.29/157.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.29/157.17 => 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)) )
% 157.29/157.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_setsum__op__ivl__Suc,axiom,
% 157.29/157.17 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 157.29/157.17 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 157.29/157.17 => 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) )
% 157.29/157.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__un_I15_J,axiom,
% 157.29/157.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 157.29/157.17 => 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) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__un_I6_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__un_I3_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_irrefl__def,axiom,
% 157.29/157.17 ! [V_r_2,T_b] :
% 157.29/157.17 ( c_Relation_Oirrefl(T_b,V_r_2)
% 157.29/157.17 <=> ! [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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__finite2__subset,axiom,
% 157.29/157.17 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 157.29/157.17 ( ! [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)))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Field__insert,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Field__empty,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_mono__Field,axiom,
% 157.29/157.17 ! [V_s_2,V_r_2,T_b] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Field__Un,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__Field,axiom,
% 157.29/157.17 ! [V_r_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__finite2__eq,axiom,
% 157.29/157.17 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 157.29/157.17 ( ! [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)
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__finite__subset,axiom,
% 157.29/157.17 ! [V_C_2,V_A_2,T_b] :
% 157.29/157.17 ( ! [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))
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Id__on__def,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Id__on__def_H,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Id__on__empty,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Id__on__eqI,axiom,
% 157.29/157.17 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 157.29/157.17 ( V_a_2 = V_b_2
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Id__on__iff,axiom,
% 157.29/157.17 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 157.29/157.17 ( 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)))
% 157.29/157.17 <=> ( V_x_2 = V_y_2
% 157.29/157.17 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Id__onE,axiom,
% 157.29/157.17 ! [V_A_2,V_ca_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2)))
% 157.29/157.17 => ~ ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.17 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 157.29/157.17 ! [V_x_2,V_y_2,V_ca_2] :
% 157.29/157.17 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 157.29/157.17 => 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)) )
% 157.29/157.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 157.29/157.17 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 157.29/157.17 => 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))) )
% 157.29/157.17 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 157.29/157.17 ! [V_u_2] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__eqI,axiom,
% 157.29/157.17 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 157.29/157.17 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__imageI,axiom,
% 157.29/157.17 ! [V_h_2,T_c,V_F_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__extend__simps_I10_J,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__UN,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__simps_I10_J,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_range__composition,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_rev__image__eqI,axiom,
% 157.29/157.17 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_imageI,axiom,
% 157.29/157.17 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__iff,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 157.29/157.17 <=> ? [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.17 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__image,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.17 <=> 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__Pow__surj,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 157.29/157.17 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2] :
% 157.29/157.17 ( V_A_2 = V_B_2
% 157.29/157.17 <=> 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_INT__simps_I10_J,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_INT__extend__simps_I10_J,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_empty__is__image,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( 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)
% 157.29/157.17 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__empty,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__is__empty,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_b,T_c] :
% 157.29/157.17 ( 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))
% 157.29/157.17 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__insert,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__Un,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__Pow__mono,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__mono,axiom,
% 157.29/157.17 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_subset__image__iff,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 157.29/157.17 ( 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)))
% 157.29/157.17 <=> ? [B_AA] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 157.29/157.17 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_insert__image,axiom,
% 157.29/157.17 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_rangeI,axiom,
% 157.29/157.17 ! [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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_range__eqI,axiom,
% 157.29/157.17 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 157.29/157.17 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 157.29/157.17 => 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))))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__surj,axiom,
% 157.29/157.17 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__Int__subset,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__diff__subset,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__uminus__atLeastAtMost,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.17 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__Suc__atLeastLessThan,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__Suc__atLeastAtMost,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.17 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__constant__conv,axiom,
% 157.29/157.17 ! [V_ca_2,T_c,T_b,V_A_2] :
% 157.29/157.17 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) )
% 157.29/157.17 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__range__imageI,axiom,
% 157.29/157.17 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 157.29/157.17 ( 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)))))
% 157.29/157.17 => 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))))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 157.29/157.17 ! [V_A_2,V_x_2] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 157.29/157.17 <=> 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_b] :
% 157.29/157.17 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__add__atLeastLessThan,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__add__atLeastAtMost,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.17 <=> 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__Union,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_card__image__le,axiom,
% 157.29/157.17 ! [V_f_2,T_c,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__uminus__atLeastLessThan,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.17 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.17 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__constant,axiom,
% 157.29/157.17 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__eq__UN,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_b] :
% 157.29/157.17 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 157.29/157.17 ! [V_A_2] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 157.29/157.17 <=> 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 157.29/157.17 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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__eq__fold__image,axiom,
% 157.29/157.17 ! [V_f_2,T_c,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_minus__Max__eq__Min,axiom,
% 157.29/157.17 ! [V_S_2,T_b] :
% 157.29/157.17 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.29/157.17 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_minus__Min__eq__Max,axiom,
% 157.29/157.17 ! [V_S_2,T_b] :
% 157.29/157.17 ( class_Groups_Olinordered__ab__group__add(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.29/157.17 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 157.29/157.17 ! [V_n_2,V_m_2] :
% 157.29/157.17 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 157.29/157.17 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_surj__Compl__image__subset,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_b,T_c] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => 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)))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_greaterThan__0,axiom,
% 157.29/157.17 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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 157.29/157.17 ! [V_N_2,V_h_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( ! [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))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.29/157.17 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_pair__imageI,axiom,
% 157.29/157.17 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Cantors__paradox,axiom,
% 157.29/157.17 ! [V_A_2,T_b] :
% 157.29/157.17 ~ ? [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_greaterThan__eq__iff,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 157.29/157.17 <=> V_x_2 = V_y_2 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Field__Union,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Union__image__eq,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UNION__eq__Union__image,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Inter__image__eq,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_INTER__eq__Inter__image,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 157.29/157.17 ! [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 ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_greaterThan__iff,axiom,
% 157.29/157.17 ! [V_k_2,V_i_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oord(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 157.29/157.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_greaterThan__subset__iff,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( 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)))
% 157.29/157.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Un__Union__image,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Int__Inter__image,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Pow__insert,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Compl__greaterThan,axiom,
% 157.29/157.17 ! [V_k_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Compl__atMost,axiom,
% 157.29/157.17 ! [V_k_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 157.29/157.17 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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_INT__greaterThan__UNIV,axiom,
% 157.29/157.17 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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__add__int__atLeastLessThan,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__ident,axiom,
% 157.29/157.17 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__int_I7_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__un_I11_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__uminus__lessThan,axiom,
% 157.29/157.17 ! [V_x_2,T_b] :
% 157.29/157.17 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__uminus__greaterThan,axiom,
% 157.29/157.17 ! [V_x_2,T_b] :
% 157.29/157.17 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__int_I5_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_greaterThan__Suc,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 157.29/157.17 ! [V_f_2,V_A_2,T_b] :
% 157.29/157.17 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fun__upd__image,axiom,
% 157.29/157.17 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 157.29/157.17 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => 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)))))) )
% 157.29/157.17 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fun__upd__triv,axiom,
% 157.29/157.17 ! [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 ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.29/157.17 => ( V_A_2 = V_B_2
% 157.29/157.17 <=> 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) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fun__upd__idem,axiom,
% 157.29/157.17 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 157.29/157.17 ( hAPP(V_f_2,V_x_2) = V_y_2
% 157.29/157.17 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fun__upd__other,axiom,
% 157.29/157.17 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 157.29/157.17 ( V_z_2 != V_x_2
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fun__upd__twist,axiom,
% 157.29/157.17 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] :
% 157.29/157.17 ( V_a_2 != V_ca_2
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fun__upd__apply,axiom,
% 157.29/157.17 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 157.29/157.17 ( ( V_z_2 = V_x_2
% 157.29/157.17 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 )
% 157.29/157.17 & ( V_z_2 != V_x_2
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fun__upd__same,axiom,
% 157.29/157.17 ! [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 ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fun__upd__upd,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fun__upd__idem__iff,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
% 157.29/157.17 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fun__upd__def,axiom,
% 157.29/157.17 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 157.29/157.17 ( ( V_x_2 = V_a_2
% 157.29/157.17 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 )
% 157.29/157.17 & ( V_x_2 != V_a_2
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 157.29/157.17 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_nat__set__def,axiom,
% 157.29/157.17 ! [V_S_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_S_2)
% 157.29/157.17 <=> ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2] :
% 157.29/157.17 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 157.29/157.17 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 157.29/157.17 ! [V_x_2,V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 157.29/157.17 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 157.29/157.17 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 157.29/157.17 ! [V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => 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 ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 157.29/157.17 ! [V_x_2,V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 157.29/157.17 ! [V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 157.29/157.17 <=> 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 157.29/157.17 ! [V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 157.29/157.17 ! [V_A_2,V_x_2] :
% 157.29/157.17 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 157.29/157.17 <=> 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))) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.17 <=> 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))) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2] :
% 157.29/157.17 ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.17 <=> 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))) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 157.29/157.17 ! [V_f_2,V_A_2,T_b] :
% 157.29/157.17 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeast__Suc,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 157.29/157.17 ! [V_N_2,V_h_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( ! [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))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.29/157.17 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Max_Ohom__commute,axiom,
% 157.29/157.17 ! [V_N_2,V_h_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( ! [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))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.29/157.17 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeast__eq__iff,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 157.29/157.17 <=> V_x_2 = V_y_2 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeast__iff,axiom,
% 157.29/157.17 ! [V_k_2,V_i_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oord(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 157.29/157.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeast__subset__iff,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => ( 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)))
% 157.29/157.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeast__0,axiom,
% 157.29/157.17 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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Compl__atLeast,axiom,
% 157.29/157.17 ! [V_k_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Compl__lessThan,axiom,
% 157.29/157.17 ! [V_k_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atLeast__Suc__greaterThan,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__un_I14_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__int_I8_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Int__atLeastAtMostL2,axiom,
% 157.29/157.17 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Int__atLeastAtMostR2,axiom,
% 157.29/157.17 ! [V_d_2,V_ca_2,V_a_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__atLeast__UNIV,axiom,
% 157.29/157.17 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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__int_I6_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__uminus__atLeast,axiom,
% 157.29/157.17 ! [V_x_2,T_b] :
% 157.29/157.17 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__uminus__atMost,axiom,
% 157.29/157.17 ! [V_x_2,T_b] :
% 157.29/157.17 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_atMost__Int__atLeast,axiom,
% 157.29/157.17 ! [V_n_2,T_b] :
% 157.29/157.17 ( class_Orderings_Oorder(T_b)
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__un_I1_J,axiom,
% 157.29/157.17 ! [V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__un_I13_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ivl__disj__un_I12_J,axiom,
% 157.29/157.17 ! [V_u_2,V_l_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Min_Ohom__commute,axiom,
% 157.29/157.17 ! [V_N_2,V_h_2,T_b] :
% 157.29/157.17 ( class_Orderings_Olinorder(T_b)
% 157.29/157.17 => ( ! [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))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.29/157.17 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Inf__fin_Ohom__commute,axiom,
% 157.29/157.17 ! [V_N_2,V_h_2,T_b] :
% 157.29/157.17 ( class_Lattices_Olattice(T_b)
% 157.29/157.17 => ( ! [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))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.29/157.17 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Sup__fin_Ohom__commute,axiom,
% 157.29/157.17 ! [V_N_2,V_h_2,T_b] :
% 157.29/157.17 ( class_Lattices_Olattice(T_b)
% 157.29/157.17 => ( ! [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))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.29/157.17 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_hom__fold1__commute,axiom,
% 157.29/157.17 ! [V_N_2,V_h_2,T_b] :
% 157.29/157.17 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.29/157.17 => ( ! [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))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.29/157.17 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equiv__intrel__iff,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2] :
% 157.29/157.17 ( 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))))
% 157.29/157.17 <=> 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 157.29/157.17 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 157.29/157.17 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.29/157.17 => ( V_A_2 = V_B_2
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.29/157.17 => ( ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.29/157.17 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 157.29/157.17 => 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) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Image__Un,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Image__empty,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Image__UN,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Image__Int__subset,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Image__mono,axiom,
% 157.29/157.17 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Un__Image,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Image__Id__on,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Image__INT__subset,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Image__iff,axiom,
% 157.29/157.17 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 157.29/157.17 <=> ? [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.17 & 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_rev__ImageI,axiom,
% 157.29/157.17 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.17 => ( 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))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Image__eq__UN,axiom,
% 157.29/157.17 ! [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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Image__singleton__iff,axiom,
% 157.29/157.17 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 157.29/157.17 ( 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))))))
% 157.29/157.17 <=> 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_of__int,axiom,
% 157.29/157.17 ! [V_j_2,V_i_2,T_b] :
% 157.29/157.17 ( class_Rings_Oring__1(T_b)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_One__int__def,axiom,
% 157.29/157.17 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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_mult,axiom,
% 157.29/157.17 ! [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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Rep__Integ__inverse,axiom,
% 157.29/157.17 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 157.29/157.17
% 157.29/157.17 fof(fact_minus,axiom,
% 157.29/157.17 ! [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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Zero__int__def,axiom,
% 157.29/157.17 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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_int__def,axiom,
% 157.29/157.17 ! [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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_add,axiom,
% 157.29/157.17 ! [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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_nat,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_minus__int__def,axiom,
% 157.29/157.17 ! [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))))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_less,axiom,
% 157.29/157.17 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 157.29/157.17 ( 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)))))))
% 157.29/157.17 <=> 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_le,axiom,
% 157.29/157.17 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 157.29/157.17 ( 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)))))))
% 157.29/157.17 <=> 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_eq__Abs__Integ,axiom,
% 157.29/157.17 ! [V_z_2] :
% 157.29/157.17 ~ ! [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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_quotient__def,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_ImageE,axiom,
% 157.29/157.17 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 157.29/157.17 => ~ ! [B_x] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_quotient__empty,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_quotient__is__empty2,axiom,
% 157.29/157.17 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( 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)
% 157.29/157.17 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_quotient__is__empty,axiom,
% 157.29/157.17 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( 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))
% 157.29/157.17 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_quotientI,axiom,
% 157.29/157.17 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_singleton__quotient,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equiv__class__nondisjoint,axiom,
% 157.29/157.17 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( 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)))))))
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_subset__equiv__class,axiom,
% 157.29/157.17 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( 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))))))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_quotientE,axiom,
% 157.29/157.17 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 157.29/157.17 ( 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)))
% 157.29/157.17 => ~ ! [B_x] :
% 157.29/157.17 ( 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))))
% 157.29/157.17 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equiv__intrel,axiom,
% 157.29/157.17 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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Union__quotient,axiom,
% 157.29/157.17 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => 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 ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equiv__class__self,axiom,
% 157.29/157.17 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.17 => 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)))))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_quotient__disj,axiom,
% 157.29/157.17 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( V_X_2 = V_Y_2
% 157.29/157.17 | 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equiv__class__eq,axiom,
% 157.29/157.17 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( 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))
% 157.29/157.17 => 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)))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_quotient__eq__iff,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 157.29/157.17 => ( V_X_2 = V_Y_2
% 157.29/157.17 <=> 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)) ) ) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_quotient__eqI,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 157.29/157.17 => ( 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))
% 157.29/157.17 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equiv__class__eq__iff,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( 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))
% 157.29/157.17 <=> ( 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))))
% 157.29/157.17 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_eq__equiv__class__iff,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.29/157.17 => ( 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))))
% 157.29/157.17 <=> 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_eq__equiv__class,axiom,
% 157.29/157.17 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 157.29/157.17 ( 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))))
% 157.29/157.17 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equiv__class__subset,axiom,
% 157.29/157.17 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( 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))
% 157.29/157.17 => 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)))))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_eq__equiv__class__iff2,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.29/157.17 => ( 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)
% 157.29/157.17 <=> 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__equiv__class,axiom,
% 157.29/157.17 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.17 => 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) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__equiv__class2,axiom,
% 157.29/157.17 ! [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] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 157.29/157.17 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 157.29/157.17 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 157.29/157.17 => 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) ) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equivp__equiv,axiom,
% 157.29/157.17 ! [V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 157.29/157.17 <=> 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_identity__equivp,axiom,
% 157.29/157.17 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equivp__def,axiom,
% 157.29/157.17 ! [V_R_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.29/157.17 <=> ! [B_x,B_y] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 157.29/157.17 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equivp__reflp,axiom,
% 157.29/157.17 ! [V_x_2,V_R_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.29/157.17 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equivp__symp,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 157.29/157.17 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equivp__transp,axiom,
% 157.29/157.17 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 157.29/157.17 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_congruent2__implies__congruent,axiom,
% 157.29/157.17 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 157.29/157.17 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.17 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_congruent2D,axiom,
% 157.29/157.17 ! [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] :
% 157.29/157.17 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 157.29/157.17 => ( 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))
% 157.29/157.17 => ( 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))
% 157.29/157.17 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_congruentD,axiom,
% 157.29/157.17 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 157.29/157.17 => ( 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))
% 157.29/157.17 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_congruent2__implies__congruent__UN,axiom,
% 157.29/157.17 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 157.29/157.17 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 157.29/157.17 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__equiv__class__inject,axiom,
% 157.29/157.17 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 157.29/157.17 => ( 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)
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.17 => ! [B_y] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 157.29/157.17 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 157.29/157.17 => 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)) ) ) )
% 157.29/157.17 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__equiv__class__type2,axiom,
% 157.29/157.17 ! [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] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 157.29/157.17 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 157.29/157.17 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( ! [B_x1] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 157.29/157.17 => ! [B_x2] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 157.29/157.17 => 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)) ) ) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__equiv__class__type,axiom,
% 157.29/157.17 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => ( ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Integ__def,axiom,
% 157.29/157.17 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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_card__quotient__disjoint,axiom,
% 157.29/157.17 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( 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)
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 157.29/157.17 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 157.29/157.17 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 & class_Groups_Ocomm__monoid__mult(T_b) )
% 157.29/157.17 => ( V_A_2 = V_B_2
% 157.29/157.17 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 157.29/157.17 => ( ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.29/157.17 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 157.29/157.17 => 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) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__empty,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__uminus,axiom,
% 157.29/157.17 ! [V_A_2,T_b] :
% 157.29/157.17 ( class_Groups_Oordered__ab__group__add(T_b)
% 157.29/157.17 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__diff,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__Int,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__onD,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.29/157.17 => V_x_2 = V_y_2 ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__iff,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.29/157.17 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 157.29/157.17 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__contraD,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( V_x_2 != V_y_2
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 157.29/157.17 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__id2,axiom,
% 157.29/157.17 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__def,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 <=> ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.17 => ! [B_xa] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 157.29/157.17 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 157.29/157.17 => B_x = B_xa ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_subset__inj__on,axiom,
% 157.29/157.17 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.17 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_injD,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 157.29/157.17 => V_x_2 = V_y_2 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__eq,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 157.29/157.17 <=> V_x_2 = V_y_2 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__fun,axiom,
% 157.29/157.17 ! [T_d,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__imageD,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 157.29/157.17 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__image__eq__iff,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => ( 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)
% 157.29/157.17 <=> V_A_2 = V_B_2 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => ( 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)
% 157.29/157.17 <=> V_A_2 = V_B_2 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_card__image,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => 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) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__strict__subset,axiom,
% 157.29/157.17 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_range__ex1__eq,axiom,
% 157.29/157.17 ! [V_b_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => ( 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)))))
% 157.29/157.17 <=> ? [B_x] :
% 157.29/157.17 ( V_b_2 = hAPP(V_f_2,B_x)
% 157.29/157.17 & ! [B_y] :
% 157.29/157.17 ( V_b_2 = hAPP(V_f_2,B_y)
% 157.29/157.17 => B_y = B_x ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__image__mem__iff,axiom,
% 157.29/157.17 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => ( 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)))
% 157.29/157.17 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__iff__surj,axiom,
% 157.29/157.17 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 157.29/157.17 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => ( ? [B_f] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 157.29/157.17 & 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)) )
% 157.29/157.17 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_endo__inj__surj,axiom,
% 157.29/157.17 ! [V_f_2,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( 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))
% 157.29/157.17 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 157.29/157.17 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__surj__inj,axiom,
% 157.29/157.17 ! [V_f_2,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__UNIV__surj__inj,axiom,
% 157.29/157.17 ! [V_f_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.29/157.17 => ( 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))
% 157.29/157.17 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__UNIV__inj__surj,axiom,
% 157.29/157.17 ! [V_f_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.29/157.17 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__image__subset__iff,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => ( 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)))
% 157.29/157.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__image__Int,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__Int,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__iff__eq__card,axiom,
% 157.29/157.17 ! [V_f_2,T_c,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 <=> 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_eq__card__imp__inj__on,axiom,
% 157.29/157.17 ! [V_f_2,T_c,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( 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)
% 157.29/157.17 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__image__set__diff,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__set__diff,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_pigeonhole,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( 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)))
% 157.29/157.17 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__fun__updI,axiom,
% 157.29/157.17 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__singleton,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Rep__Integ,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_card__bij__eq,axiom,
% 157.29/157.17 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( 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))
% 157.29/157.17 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 157.29/157.17 => ( 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))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.29/157.17 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__image__Compl__subset,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => 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)))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__insert,axiom,
% 157.29/157.17 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 157.29/157.17 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 & ~ 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))))))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__Un,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( 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))
% 157.29/157.17 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.29/157.17 & 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_card__inj__on__le,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( 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))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.29/157.17 => 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))) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__iff__card__le,axiom,
% 157.29/157.17 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.29/157.17 => ( ? [B_f] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 157.29/157.17 & 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)) )
% 157.29/157.17 <=> 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))) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_quotient__diff1,axiom,
% 157.29/157.17 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 157.29/157.17 ( 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)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__INT,axiom,
% 157.29/157.17 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 157.29/157.17 => ( ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 157.29/157.17 => 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)) )
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_type__definition__Integ,axiom,
% 157.29/157.17 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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_the__inv__into__into,axiom,
% 157.29/157.17 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__Suc,axiom,
% 157.29/157.17 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__add__nat,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__of__nat,axiom,
% 157.29/157.17 ! [T_b] :
% 157.29/157.17 ( class_Nat_Osemiring__char__0(T_b)
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__int,axiom,
% 157.29/157.17 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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_swap__inj__on,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_the__inv__into__f__f,axiom,
% 157.29/157.17 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => 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 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_the__inv__into__f__eq,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.17 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_the__inv__f__f,axiom,
% 157.29/157.17 ! [V_x_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => 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 ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_the__inv__into__onto,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => 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 ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__the__inv__into,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_f__the__inv__into__f,axiom,
% 157.29/157.17 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.29/157.17 => 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 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_type__definition_ORep__range,axiom,
% 157.29/157.17 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.29/157.17 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.29/157.17 => 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 ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_type__definition_OAbs__image,axiom,
% 157.29/157.17 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.29/157.17 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_type__definition_OAbs__inject,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.29/157.17 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 157.29/157.17 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 157.29/157.17 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_type__definition_ORep__inject,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.29/157.17 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.29/157.17 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 157.29/157.17 <=> V_x_2 = V_y_2 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_type__definition_ORep__inverse,axiom,
% 157.29/157.17 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.29/157.17 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.29/157.17 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_type__definition_ORep,axiom,
% 157.29/157.17 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.29/157.17 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_type__definition_OAbs__inverse,axiom,
% 157.29/157.17 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 157.29/157.17 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 157.29/157.17 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_accp__acc__eq,axiom,
% 157.29/157.17 ! [V_x_2,V_r_2,T_b] :
% 157.29/157.17 ( 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))
% 157.29/157.17 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_max__extp_Oequations,axiom,
% 157.29/157.17 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 157.29/157.17 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 157.29/157.17 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 157.29/157.17 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 157.29/157.17 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 & ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 157.29/157.17 => ? [B_xa] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 157.29/157.17 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_max__ext_Ointros,axiom,
% 157.29/157.17 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 157.29/157.17 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => ( ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 157.29/157.17 => ? [B_xa] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 157.29/157.17 & 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)) ) )
% 157.29/157.17 => 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))) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_acc__subset,axiom,
% 157.29/157.17 ! [V_R2_2,V_R1_2,T_b] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_acc_Osimps,axiom,
% 157.29/157.17 ! [V_r_2,V_a_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 157.29/157.17 <=> ! [B_x] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_acc__downward,axiom,
% 157.29/157.17 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 157.29/157.17 => ( 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))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__Inter,axiom,
% 157.29/157.17 ! [V_f_2,T_c,T_b,V_S_2] :
% 157.29/157.17 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 157.29/157.17 => ( ! [B_A] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 157.29/157.17 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_the__elem__def,axiom,
% 157.29/157.17 ! [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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_The__split__eq,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_split__paired__The,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_the__inv__into__def,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fold__def,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_divmod__nat__def,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fold1__def,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_The__split,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nitpick_Oone__frac__def,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Nitpick_Ofrac__def,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_flat__lub__def,axiom,
% 157.29/157.17 ! [V_b_2,V_A_2,T_b] :
% 157.29/157.17 ( ( 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)))))
% 157.29/157.17 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 157.29/157.17 & ( ~ 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)))))
% 157.29/157.17 => 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)))))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__vimage__singleton,axiom,
% 157.29/157.17 ! [V_a_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => 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))))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 157.29/157.17 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 157.29/157.17 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 157.29/157.17 => ( ! [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))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.29/157.17 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimageI,axiom,
% 157.29/157.17 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 157.29/157.17 ( hAPP(V_f_2,V_a_2) = V_b_2
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__eq,axiom,
% 157.29/157.17 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 157.29/157.17 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimageD,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimageI2,axiom,
% 157.29/157.17 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__Diff,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__Int,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__INT,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__Un,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__empty,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__Compl,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__code,axiom,
% 157.29/157.17 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 157.29/157.17 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__ident,axiom,
% 157.29/157.17 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__mono,axiom,
% 157.29/157.17 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__UN,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__UNIV,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__vimage__subset,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_surj__image__vimage__eq,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_b,T_c] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => 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 ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__Union,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__singleton__eq,axiom,
% 157.29/157.17 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 157.29/157.17 ( 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))))))
% 157.29/157.17 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__insert,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__vimageD,axiom,
% 157.29/157.17 ! [V_F_2,V_h_2,T_c,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 157.29/157.17 => ( 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))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__subsetD,axiom,
% 157.29/157.17 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => ( 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))
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__vimage__eq,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__vimageI,axiom,
% 157.29/157.17 ! [V_h_2,T_c,V_F_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 157.29/157.17 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__vimage__image__eq,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => 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 ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__const,axiom,
% 157.29/157.17 ! [T_c,V_A_2,V_ca_2,T_b] :
% 157.29/157.17 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.29/157.17 => 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)) )
% 157.29/157.17 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__eq__UN,axiom,
% 157.29/157.17 ! [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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__subsetI,axiom,
% 157.29/157.17 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_vimage__if,axiom,
% 157.29/157.17 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] :
% 157.29/157.17 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.29/157.17 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 157.29/157.17 => 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)) )
% 157.29/157.17 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 157.29/157.17 => 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 ) ) )
% 157.29/157.17 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 157.29/157.17 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 157.29/157.17 => 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) )
% 157.29/157.17 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 157.29/157.17 => 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)) ) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_image__split__eq__Sigma,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Rep__Integ__cases,axiom,
% 157.29/157.17 ! [V_y_2] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 157.29/157.17 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Rep__Integ__induct,axiom,
% 157.29/157.17 ! [V_Pa_2,V_y_2] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 157.29/157.17 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
% 157.29/157.17 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_SigmaI,axiom,
% 157.29/157.17 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Sigma__empty1,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Sigma__Union,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Sigma__Diff__distrib2,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Times__Diff__distrib1,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Sigma__Diff__distrib1,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Times__eq__cancel2,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 157.29/157.17 => ( 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))
% 157.29/157.17 <=> V_A_2 = V_B_2 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_card__cartesian__product,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_setsum__cartesian__product,axiom,
% 157.29/157.17 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 157.29/157.17 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Times__empty,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.17 ( 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))
% 157.29/157.17 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Sigma__empty2,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Compl__Times__UNIV2,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Compl__Times__UNIV1,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_setprod__cartesian__product,axiom,
% 157.29/157.17 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 157.29/157.17 ( class_Groups_Ocomm__monoid__mult(T_b)
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Sigma__Un__distrib2,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Times__Un__distrib1,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Sigma__Un__distrib1,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_swap__product,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__cartesian__product,axiom,
% 157.29/157.17 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.29/157.17 => 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)))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_equiv__type,axiom,
% 157.29/157.17 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.17 => 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)))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Sigma__Int__distrib1,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Times__Int__distrib1,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Sigma__Int__distrib2,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Id__on__subset__Times,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UNIV__Times__UNIV,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_SigmaE2,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.17 ( 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)))
% 157.29/157.17 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.17 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_SigmaD2,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.17 ( 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)))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_SigmaD1,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.17 ( 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)))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_mem__Sigma__iff,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.17 ( 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)))
% 157.29/157.17 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.17 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_card__cartesian__product__singleton,axiom,
% 157.29/157.17 ! [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) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Times__subset__cancel2,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 157.29/157.17 => ( 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))))
% 157.29/157.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Image__subset,axiom,
% 157.29/157.17 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 157.29/157.17 ( 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))))
% 157.29/157.17 => 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)) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__cartesian__productD2,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.17 ( 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))))
% 157.29/157.17 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__cartesian__productD1,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,T_c,T_b] :
% 157.29/157.17 ( 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))))
% 157.29/157.17 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fst__image__times,axiom,
% 157.29/157.17 ! [V_A_2,T_c,T_b,V_B_2] :
% 157.29/157.17 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) )
% 157.29/157.17 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_snd__image__times,axiom,
% 157.29/157.17 ! [V_B_2,T_c,T_b,V_A_2] :
% 157.29/157.17 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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)) )
% 157.29/157.17 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => 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 ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_insert__times__insert,axiom,
% 157.29/157.17 ! [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)))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__equiv__class,axiom,
% 157.29/157.17 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( 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))))
% 157.29/157.17 => ( 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)))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_UN__Times__distrib,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Sigma__def,axiom,
% 157.29/157.17 ! [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))))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__quotient,axiom,
% 157.29/157.17 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( 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))))
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 157.29/157.17 ! [V_A_2,V_I_2,T_c,T_b] :
% 157.29/157.17 ? [B_f] :
% 157.29/157.17 ( 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))
% 157.29/157.17 & 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fold__image__Sigma,axiom,
% 157.29/157.17 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 157.29/157.17 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_finite__SigmaI,axiom,
% 157.29/157.17 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( ! [B_a] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_setprod__Sigma,axiom,
% 157.29/157.17 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 157.29/157.17 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_setsum__Sigma,axiom,
% 157.29/157.17 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 157.29/157.17 ( class_Groups_Ocomm__monoid__add(T_d)
% 157.29/157.17 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_card__SigmaI,axiom,
% 157.29/157.17 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.29/157.17 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.17 => ( ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.17 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 157.29/157.17 => 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) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_SigmaE,axiom,
% 157.29/157.17 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] :
% 157.29/157.17 ( 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)))
% 157.29/157.17 => ~ ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.17 => ! [B_y] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 157.29/157.17 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_map__pair__surj,axiom,
% 157.29/157.17 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => ( 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))
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_map__pair__inj__on,axiom,
% 157.29/157.17 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.17 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.17 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 157.29/157.17 => 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))) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_map__pair__imageI,axiom,
% 157.29/157.17 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => 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))) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_map__pair__simp,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_fst__map__pair,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_snd__prod__fun,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_map__pair__ident,axiom,
% 157.29/157.17 ! [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 ).
% 157.29/157.17
% 157.29/157.17 fof(fact_map__pair__def,axiom,
% 157.29/157.17 ! [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)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_map__pair__surj__on,axiom,
% 157.29/157.17 ! [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] :
% 157.29/157.17 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 157.29/157.17 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_prod__fun__imageE,axiom,
% 157.29/157.17 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] :
% 157.29/157.17 ( 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)))
% 157.29/157.17 => ~ ! [B_x,B_y] :
% 157.29/157.17 ( 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))
% 157.29/157.17 => ~ 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_refl__on__def,axiom,
% 157.29/157.17 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.17 <=> ( 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))))
% 157.29/157.17 & ! [B_x] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.17 => 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)) ) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_inj__on__INTER,axiom,
% 157.29/157.17 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 157.29/157.17 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.17 => ( ! [B_i] :
% 157.29/157.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 157.29/157.17 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_refl__on__Id__on,axiom,
% 157.29/157.17 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_refl__on__empty,axiom,
% 157.29/157.17 ! [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))) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_refl__on__Un,axiom,
% 157.29/157.17 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_refl__on__Int,axiom,
% 157.29/157.17 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_refl__onD,axiom,
% 157.29/157.17 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.17 => 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)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_refl__onD1,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.17 => ( 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))
% 157.29/157.17 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 157.29/157.17
% 157.29/157.17 fof(fact_refl__onD2,axiom,
% 157.29/157.17 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 157.29/157.17 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_refl__onI,axiom,
% 157.29/157.18 ! [V_A_2,V_r_2,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 => ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.18 => 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)) )
% 157.29/157.18 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_card__less__Suc,axiom,
% 157.29/157.18 ! [V_i_2,V_M_2] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 157.29/157.18 => 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))))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_card__less,axiom,
% 157.29/157.18 ! [V_i_2,V_M_2] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 157.29/157.18 => 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) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_CollectI,axiom,
% 157.29/157.18 ! [T_b,V_a_2,V_Pa_2] :
% 157.29/157.18 ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__Collect__conjI,axiom,
% 157.29/157.18 ! [V_Qa_2,V_Pa_2,T_b] :
% 157.29/157.18 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.29/157.18 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) )
% 157.29/157.18 => 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__Collect__less__nat,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__Collect__le__nat,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Collect__mem__eq,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_mem__Collect__eq,axiom,
% 157.29/157.18 ! [V_Pa_2,V_a_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.29/157.18 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_CollectD,axiom,
% 157.29/157.18 ! [V_Pa_2,V_a_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.29/157.18 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_CollectE,axiom,
% 157.29/157.18 ! [V_Pa_2,V_a_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.29/157.18 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Collect__conj__eq,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Collect__disj__eq,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_insert__Collect,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_empty__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Collect__empty__eq,axiom,
% 157.29/157.18 ! [V_Pa_2,T_b] :
% 157.29/157.18 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_empty__Collect__eq,axiom,
% 157.29/157.18 ! [V_Pa_2,T_b] :
% 157.29/157.18 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
% 157.29/157.18 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__Collect__disjI,axiom,
% 157.29/157.18 ! [V_Qa_2,V_Pa_2,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.29/157.18 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Collect__def,axiom,
% 157.29/157.18 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_UNIV__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_vimage__Collect__eq,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Collect__neg__eq,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_SetCompr__Sigma__eq,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Collect__split,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_insert__compr__raw,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_insert__compr,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Un__def,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Int__Collect,axiom,
% 157.29/157.18 ! [V_Pa_2,V_A_2,V_x_2,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.18 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Int__def,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Collect__conv__if,axiom,
% 157.29/157.18 ! [T_b,V_a_2,V_Pa_2] :
% 157.29/157.18 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.29/157.18 => 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))) )
% 157.29/157.18 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Collect__conv__if2,axiom,
% 157.29/157.18 ! [T_b,V_a_2,V_Pa_2] :
% 157.29/157.18 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.29/157.18 => 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))) )
% 157.29/157.18 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_singleton__conv,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_singleton__conv2,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_set__diff__eq,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__Collect__not,axiom,
% 157.29/157.18 ! [V_Pa_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.29/157.18 => ( 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))))
% 157.29/157.18 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_insert__def,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Compl__eq,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_vimage__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Collect__imp__eq,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__M__bounded__by__nat,axiom,
% 157.29/157.18 ! [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))))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__setsum__restrict,axiom,
% 157.29/157.18 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__add(T_d)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 157.29/157.18 => 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) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_if__image__distrib,axiom,
% 157.29/157.18 ! [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))))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_nat__seg__image__imp__finite,axiom,
% 157.29/157.18 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__restrict__set_H,axiom,
% 157.29/157.18 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => 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) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__image__gen,axiom,
% 157.29/157.18 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Image__singleton,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__cases,axiom,
% 157.29/157.18 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => 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))))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_card__less__Suc2,axiom,
% 157.29/157.18 ! [V_i_2,V_M_2] :
% 157.29/157.18 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 157.29/157.18 => 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))))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__multicount,axiom,
% 157.29/157.18 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 157.29/157.18 => ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 157.29/157.18 => 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 )
% 157.29/157.18 => 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)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.18 ( class_Orderings_Olinorder(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => 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))))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.18 ( class_Orderings_Olinorder(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => 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))))))) ) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__Collect__subsets,axiom,
% 157.29/157.18 ! [V_A_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Pow__Compl,axiom,
% 157.29/157.18 ! [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))))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Pow__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__Collect__bounded__ex,axiom,
% 157.29/157.18 ! [V_Qa_2,T_c,V_Pa_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.29/157.18 => ( 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)))))
% 157.29/157.18 <=> ! [B_y] :
% 157.29/157.18 ( hBOOL(hAPP(V_Pa_2,B_y))
% 157.29/157.18 => 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)))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__image__set,axiom,
% 157.29/157.18 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 157.29/157.18 => 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))))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_inj__graph,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__psubset__def,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_inv__image__def,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_add__Min__commute,axiom,
% 157.29/157.18 ! [V_k_2,V_N_2,T_b] :
% 157.29/157.18 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.29/157.18 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => 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))))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_add__Max__commute,axiom,
% 157.29/157.18 ! [V_k_2,V_N_2,T_b] :
% 157.29/157.18 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 157.29/157.18 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => 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))))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_sup__Inf2__distrib,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.18 ( class_Lattices_Odistrib__lattice(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => 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))))))) ) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_sup__Inf1__distrib,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.18 ( class_Lattices_Odistrib__lattice(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => 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))))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_inf__Sup2__distrib,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.18 ( class_Lattices_Odistrib__lattice(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => 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))))))) ) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_inf__Sup1__distrib,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.18 ( class_Lattices_Odistrib__lattice(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => 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))))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.18 ( class_Orderings_Olinorder(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.18 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => 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))))))) ) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.18 ( class_Orderings_Olinorder(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 => 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))))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nitpick_Oprod__def,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_int__ge__less__than2__def,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_int__ge__less__than__def,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_reflp__def,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Predicate_Oreflp(T_b,V_r_2)
% 157.29/157.18 <=> 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 157.29/157.18 ( class_Rings_Osemiring__0(T_d)
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => 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))))))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__multicount__gen,axiom,
% 157.29/157.18 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 157.29/157.18 => ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 157.29/157.18 => 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) )
% 157.29/157.18 => 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) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_inj__on__id,axiom,
% 157.29/157.18 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_map__pair_Oid,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_map__pair_Oidentity,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_vimage__id,axiom,
% 157.29/157.18 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_id__apply,axiom,
% 157.29/157.18 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 157.29/157.18
% 157.29/157.18 fof(fact_id__def,axiom,
% 157.29/157.18 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_reflpE,axiom,
% 157.29/157.18 ! [V_x_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Predicate_Oreflp(T_b,V_r_2)
% 157.29/157.18 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_apsnd__id,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_apfst__id,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_image__id,axiom,
% 157.29/157.18 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_of__int__eq__id,axiom,
% 157.29/157.18 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_surj__id,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_apsnd__def,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_apfst__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_split__Pair,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__reindex__id,axiom,
% 157.29/157.18 ! [V_B_2,V_f_2,T_b,T_c] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.18 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setprod__reindex__id,axiom,
% 157.29/157.18 ! [V_B_2,V_f_2,T_b,T_c] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.29/157.18 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__conv__nat__seg__image,axiom,
% 157.29/157.18 ! [V_A_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 <=> ? [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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__comp__def,axiom,
% 157.29/157.18 ! [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))))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__Collect__split,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__compI,axiom,
% 157.29/157.18 ! [V_s_2,V_ca_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_RangeI,axiom,
% 157.29/157.18 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__comp__distrib,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__comp__distrib2,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__Id__on,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_O__assoc,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__comp__empty1,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__comp__empty2,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__comp__mono,axiom,
% 157.29/157.18 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__comp__UNION__distrib,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__comp__UNION__distrib2,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_union__comp__emptyR,axiom,
% 157.29/157.18 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_union__comp__emptyL,axiom,
% 157.29/157.18 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__Union,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__empty__iff,axiom,
% 157.29/157.18 ! [V_r_2,T_b,T_c] :
% 157.29/157.18 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__empty,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__comp__subset__Sigma,axiom,
% 157.29/157.18 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 => ( 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))))
% 157.29/157.18 => 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)))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__Un__eq,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__Range,axiom,
% 157.29/157.18 ! [V_r_2,T_c,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 157.29/157.18 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_snd__eq__Range,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__iff,axiom,
% 157.29/157.18 ! [V_r_2,T_c,V_a_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 157.29/157.18 <=> ? [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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__insert,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__Int__subset,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__Diff__subset,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_max__ext__compat,axiom,
% 157.29/157.18 ! [V_S_2,V_R_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_min__ext__compat,axiom,
% 157.29/157.18 ! [V_S_2,V_R_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_RangeP__Range__eq,axiom,
% 157.29/157.18 ! [V_x_2,V_r_2,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_RangeE,axiom,
% 157.29/157.18 ! [V_r_2,T_c,V_b_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 157.29/157.18 => ~ ! [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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_pred__comp__rel__comp__eq,axiom,
% 157.29/157.18 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 <=> 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_pred__comp_Ointros,axiom,
% 157.29/157.18 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 157.29/157.18 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_RangeP_Ointros,axiom,
% 157.29/157.18 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 157.29/157.18 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_pred__comp_Oequations,axiom,
% 157.29/157.18 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 <=> ? [B_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 157.29/157.18 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_RangeP_Oequations,axiom,
% 157.29/157.18 ! [V_a2_2,V_r_2,T_c,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 157.29/157.18 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_reduction__pairI,axiom,
% 157.29/157.18 ! [V_S_2,V_R_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__Collect__split,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_the__sym__eq__trivial,axiom,
% 157.29/157.18 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__less__than,axiom,
% 157.29/157.18 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__empty,axiom,
% 157.29/157.18 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__inv__image,axiom,
% 157.29/157.18 ! [V_f_2,T_c,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__lex__prod,axiom,
% 157.29/157.18 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 157.29/157.18 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 157.29/157.18 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__measure,axiom,
% 157.29/157.18 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_DomainI,axiom,
% 157.29/157.18 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__comp__self,axiom,
% 157.29/157.18 ! [V_R_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.29/157.18 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__subset,axiom,
% 157.29/157.18 ! [V_p_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_min__ext__wf,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__mlex,axiom,
% 157.29/157.18 ! [V_f_2,V_R_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.29/157.18 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__Int1,axiom,
% 157.29/157.18 ! [V_r_H_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__Int2,axiom,
% 157.29/157.18 ! [V_r_H_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__pair__less,axiom,
% 157.29/157.18 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_max__ext__wf,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__Id__on,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__finite__psubset,axiom,
% 157.29/157.18 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__less,axiom,
% 157.29/157.18 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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__irrefl,axiom,
% 157.29/157.18 ! [V_a_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => ~ 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__asym,axiom,
% 157.29/157.18 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => ~ 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__not__sym,axiom,
% 157.29/157.18 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => ~ 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__not__refl,axiom,
% 157.29/157.18 ! [V_a_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => ~ 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__int__ge__less__than,axiom,
% 157.29/157.18 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__int__ge__less__than2,axiom,
% 157.29/157.18 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__Un,axiom,
% 157.29/157.18 ! [V_s_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_acc__wfD,axiom,
% 157.29/157.18 ! [V_x_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__acc__iff,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__no__loop,axiom,
% 157.29/157.18 ! [V_R_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__union__merge,axiom,
% 157.29/157.18 ! [V_S_2,V_R_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 <=> 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__empty__iff,axiom,
% 157.29/157.18 ! [V_r_2,T_c,T_b] :
% 157.29/157.18 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__empty,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__mono,axiom,
% 157.29/157.18 ! [V_s_2,V_r_2,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__Un__eq,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__Domain,axiom,
% 157.29/157.18 ! [V_r_2,T_c,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 157.29/157.18 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_fst__eq__Domain,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 <=> ~ ? [B_f] :
% 157.29/157.18 ! [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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wfE__pf,axiom,
% 157.29/157.18 ! [V_A_2,V_R_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__union__compatible,axiom,
% 157.29/157.18 ! [V_S_2,V_R_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.29/157.18 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__iff,axiom,
% 157.29/157.18 ! [V_r_2,T_c,V_a_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 157.29/157.18 <=> ? [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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf,axiom,
% 157.29/157.18 ! [T_b] :
% 157.29/157.18 ( class_Orderings_Owellorder(T_b)
% 157.29/157.18 => 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__insert,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_reduction__pair__def,axiom,
% 157.29/157.18 ! [V_Pa_2,T_b] :
% 157.29/157.18 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 157.29/157.18 <=> ( 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))
% 157.29/157.18 & 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_reduction__pair__lemma,axiom,
% 157.29/157.18 ! [V_S_2,V_R_2,V_Pa_2,T_b] :
% 157.29/157.18 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 157.29/157.18 => 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)) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__Int__subset,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__Diff__subset,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Field__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__map__pair__image,axiom,
% 157.29/157.18 ! [V_f_2,T_c,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__Union,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_the__eq__trivial,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_DomainP__Domain__eq,axiom,
% 157.29/157.18 ! [V_x_2,V_r_2,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__lenlex,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_DomainE,axiom,
% 157.29/157.18 ! [V_r_2,T_c,V_a_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 157.29/157.18 => ~ ! [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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_DomainP_Ointros,axiom,
% 157.29/157.18 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 157.29/157.18 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_DomainP_Oequations,axiom,
% 157.29/157.18 ! [V_a1_2,V_r_2,T_c,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 157.29/157.18 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_pred__nat__def,axiom,
% 157.29/157.18 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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__lex,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__lexn,axiom,
% 157.29/157.18 ! [V_n_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_lex__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_lexn_Osimps_I1_J,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__pred__nat,axiom,
% 157.29/157.18 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__same__fst,axiom,
% 157.29/157.18 ! [T_b,V_R_2,T_c,V_Pa_2] :
% 157.29/157.18 ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.29/157.18 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 157.29/157.18 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__if__measure,axiom,
% 157.29/157.18 ! [T_b,V_g_2,V_f_2,V_Pa_2] :
% 157.29/157.18 ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.29/157.18 => 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))) )
% 157.29/157.18 => 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))))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wfP__def,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 157.29/157.18 <=> 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wfP__empty,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wfP__accp__iff,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 157.29/157.18 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_accp__wfPD,axiom,
% 157.29/157.18 ! [V_x_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 157.29/157.18 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wfP__subset,axiom,
% 157.29/157.18 ! [V_p_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__in__rel,axiom,
% 157.29/157.18 ! [V_R_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_R_2)
% 157.29/157.18 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wfP__wf__eq,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wfP__acyclicP,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_pigeonhole__infinite,axiom,
% 157.29/157.18 ! [V_f_2,T_c,V_A_2,T_b] :
% 157.29/157.18 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.29/157.18 => ? [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.18 & ~ 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)))))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_refl__on__def_H,axiom,
% 157.29/157.18 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.18 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.18 <=> ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 157.29/157.18 => 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)) )
% 157.29/157.18 & ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.18 => 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)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_ball__empty,axiom,
% 157.29/157.18 ! [V_Pa_2,T_b,B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.29/157.18 => hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__acyclic,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_acyclic__subset,axiom,
% 157.29/157.18 ! [V_r_2,V_s_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Powp__def,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 157.29/157.18 <=> ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 157.29/157.18 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_INFI__bool__eq,axiom,
% 157.29/157.18 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Collect__ball__eq,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_congruent__def,axiom,
% 157.29/157.18 ! [V_f_2,V_r_2,T_c,T_b] :
% 157.29/157.18 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 157.29/157.18 <=> ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_INTER__def,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 157.29/157.18 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__acyclic__wf,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 157.29/157.18 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.29/157.18 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Inf__Sup,axiom,
% 157.29/157.18 ! [V_A_2,T_b] :
% 157.29/157.18 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.18 => 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))))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Sup__Inf,axiom,
% 157.29/157.18 ! [V_A_2,T_b] :
% 157.29/157.18 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.18 => 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)))))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nitpick_Owf_H__def,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 157.29/157.18 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.29/157.18 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 157.29/157.18 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Abs__Integ__induct,axiom,
% 157.29/157.18 ! [V_x_2,V_Pa_2] :
% 157.29/157.18 ( ! [B_y] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 157.29/157.18 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 157.29/157.18 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Abs__Integ__cases,axiom,
% 157.29/157.18 ! [V_x_2] :
% 157.29/157.18 ~ ! [B_y] :
% 157.29/157.18 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 157.29/157.18 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Inter__eq,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__UN__I,axiom,
% 157.29/157.18 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( ! [B_a] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 157.29/157.18 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_inj__on__diff__nat,axiom,
% 157.29/157.18 ! [V_k_2,V_N_2] :
% 157.29/157.18 ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 157.29/157.18 => 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) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wfP__SUP,axiom,
% 157.29/157.18 ! [T_b,V_r_2,T_c] :
% 157.29/157.18 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 157.29/157.18 => ( ! [B_i,B_j] :
% 157.29/157.18 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 157.29/157.18 => 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)) )
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_mem__splitE,axiom,
% 157.29/157.18 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ~ ! [B_x,B_y] :
% 157.29/157.18 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 157.29/157.18 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_mem__splitI2,axiom,
% 157.29/157.18 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 157.29/157.18 ( ! [B_a,B_b] :
% 157.29/157.18 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_vimage__Times,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_o__id,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_id__o,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_o__eq__id__dest,axiom,
% 157.29/157.18 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 157.29/157.18 ( 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)
% 157.29/157.18 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_map__pair_Ocomp,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_map__pair__compose,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_map__pair_Ocompositionality,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_vimage__compose,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_o__eq__elim,axiom,
% 157.29/157.18 ! [V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 157.29/157.18 ( 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)
% 157.29/157.18 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_o__eq__dest,axiom,
% 157.29/157.18 ! [V_v_2,V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 157.29/157.18 ( 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)
% 157.29/157.18 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_o__apply,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_o__assoc,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_o__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_K__record__comp,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 157.29/157.18 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.29/157.18 => 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_comp__cong,axiom,
% 157.29/157.18 ! [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] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => 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) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 157.29/157.18 ! [V_x_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.29/157.18 => 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) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_o__eq__dest__lhs,axiom,
% 157.29/157.18 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 157.29/157.18 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_ca_2
% 157.29/157.18 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_apsnd__compose,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_apfst__compose,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_fun__upd__comp,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_image__compose,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_comp__surj,axiom,
% 157.29/157.18 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_inj__comp,axiom,
% 157.29/157.18 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.18 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_inj__on__imageI2,axiom,
% 157.29/157.18 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 157.29/157.18 ( 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)
% 157.29/157.18 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_comp__inj__on__iff,axiom,
% 157.29/157.18 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 <=> 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) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_comp__inj__on,axiom,
% 157.29/157.18 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_inj__on__imageI,axiom,
% 157.29/157.18 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 157.29/157.18 ( 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)
% 157.29/157.18 => 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__reindex,axiom,
% 157.29/157.18 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__add(T_d)
% 157.29/157.18 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.29/157.18 => 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) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setprod__reindex__cong,axiom,
% 157.29/157.18 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.29/157.18 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.18 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 157.29/157.18 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 157.29/157.18 => 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) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setprod__reindex,axiom,
% 157.29/157.18 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.29/157.18 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 157.29/157.18 => 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) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum_Oreindex,axiom,
% 157.29/157.18 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 157.29/157.18 => 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) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setprod_Oreindex,axiom,
% 157.29/157.18 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__mult(T_c)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 157.29/157.18 => 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) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_the__inv__into__comp,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 157.29/157.18 => ( 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))))
% 157.29/157.18 => 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) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_fold__image__reindex,axiom,
% 157.29/157.18 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 157.29/157.18 ( class_Groups_Oab__semigroup__mult(T_d)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 157.29/157.18 => 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) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Oremove,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.18 => 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)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding__image_Oreindex,axiom,
% 157.29/157.18 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.29/157.18 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 157.29/157.18 => 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) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Ounion,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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)) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Ocommute__left__comp,axiom,
% 157.29/157.18 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Ocommute__comp,axiom,
% 157.29/157.18 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 157.29/157.18 ! [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] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 157.29/157.18 => 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) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_fst__comp__map__pair,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_UN__o,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_snd__comp__map__pair,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding__image_Odistrib,axiom,
% 157.29/157.18 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_split__comp,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Ocommute__comp_H,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 157.29/157.18 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.18 => 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)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 157.29/157.18 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.18 => 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)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Oempty,axiom,
% 157.29/157.18 ! [V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Oeq__fold,axiom,
% 157.29/157.18 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => 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) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding__image_Oeq__fold,axiom,
% 157.29/157.18 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.29/157.18 => 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) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Oinsert,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.18 => 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)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Ounion__inter,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.18 => 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)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding_Oinsert__remove,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_hoare__derivs_OIf,axiom,
% 157.29/157.18 ! [V_d_2,V_Qa_2,V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 => ( 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))))
% 157.29/157.18 => 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)))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Loop,axiom,
% 157.29/157.18 ! [V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 => 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__reindex__nonzero,axiom,
% 157.29/157.18 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__add(T_d)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 157.29/157.18 => ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.29/157.18 => ! [B_y] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 157.29/157.18 => ( B_x != B_y
% 157.29/157.18 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 157.29/157.18 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 157.29/157.18 => 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) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_peek__and__def,axiom,
% 157.29/157.18 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2))
% 157.29/157.18 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2))
% 157.29/157.18 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding__idem_Ounion__idem,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 157.29/157.18 => 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)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.29/157.18 => 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) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding__idem_Oinsert__idem,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding__idem_Oidem__comp,axiom,
% 157.29/157.18 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => 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) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 157.29/157.18 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => 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) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 157.29/157.18 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.18 => 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) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_strong__setprod__reindex__cong,axiom,
% 157.29/157.18 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.29/157.18 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.18 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 157.29/157.18 => ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.18 => 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) )
% 157.29/157.18 => 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) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Eps__split,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wfI__pf,axiom,
% 157.29/157.18 ! [V_R_2,T_b] :
% 157.29/157.18 ( ! [B_A] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 157.29/157.18 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_exE__some,axiom,
% 157.29/157.18 ! [T_b,V_ca_2,V_Pa_2] :
% 157.29/157.18 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.29/157.18 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
% 157.29/157.18 => hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_someI__ex,axiom,
% 157.29/157.18 ! [T_b,V_Pa_2] :
% 157.29/157.18 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.29/157.18 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_some__eq__ex,axiom,
% 157.29/157.18 ! [T_b,V_Pa_2] :
% 157.29/157.18 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
% 157.29/157.18 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_some__eq__trivial,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_some__sym__eq__trivial,axiom,
% 157.29/157.18 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_someI,axiom,
% 157.29/157.18 ! [T_b,V_x_2,V_Pa_2] :
% 157.29/157.18 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.18 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_tfl__some,axiom,
% 157.29/157.18 ! [T_b,B_P] :
% 157.29/157.18 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 157.29/157.18 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Eps__split__eq,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_split__paired__Eps,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Sigma__mono,axiom,
% 157.29/157.18 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 157.29/157.18 => ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.18 => 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))) )
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_not__acc__down,axiom,
% 157.29/157.18 ! [V_R_2,V_x_2,T_b] :
% 157.29/157.18 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 157.29/157.18 => ~ ! [B_z] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_acc_OaccI,axiom,
% 157.29/157.18 ! [V_r_2,V_x_2,T_b] :
% 157.29/157.18 ( ! [B_y] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_max__ext_Osimps,axiom,
% 157.29/157.18 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 157.29/157.18 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 157.29/157.18 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.18 & ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 157.29/157.18 => ? [B_xa] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 157.29/157.18 & 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)) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 157.29/157.18 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 157.29/157.18 ( class_Orderings_Olinorder(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 157.29/157.18 => 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))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Max__eqI,axiom,
% 157.29/157.18 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.18 ( class_Orderings_Olinorder(T_b)
% 157.29/157.18 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.18 => ( ! [B_y] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 157.29/157.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.18 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__no__infinite__down__chainE,axiom,
% 157.29/157.18 ! [V_f_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => ~ ! [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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_iterate_Osimps,axiom,
% 157.29/157.18 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 157.29/157.18 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.18 => 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) )
% 157.29/157.18 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__reindex__cong,axiom,
% 157.29/157.18 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 157.29/157.18 ( class_Groups_Ocomm__monoid__add(T_d)
% 157.29/157.18 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.18 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 157.29/157.18 => ( ! [B_a] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 157.29/157.18 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 157.29/157.18 => 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) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Pair__scomp,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_scomp__Pair,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_scomp__scomp,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_scomp__apply,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_scomp__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_scomp__unfold,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_setsum__ivl__cong,axiom,
% 157.29/157.18 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_b,T_c] :
% 157.29/157.18 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.18 & class_Orderings_Oord(T_b) )
% 157.29/157.18 => ( V_a_2 = V_ca_2
% 157.29/157.18 => ( V_b_2 = V_d_2
% 157.29/157.18 => ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x))
% 157.29/157.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 157.29/157.18 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 157.29/157.18 => 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)) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_less__eq,axiom,
% 157.29/157.18 ! [V_n_2,V_m_2] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__trancl,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_less__than__def,axiom,
% 157.29/157.18 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_acyclic__def,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.29/157.18 <=> ! [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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl_Or__into__trancl,axiom,
% 157.29/157.18 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__subset__Field2,axiom,
% 157.29/157.18 ! [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))))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_r__into__trancl_H,axiom,
% 157.29/157.18 ! [V_r_2,V_p_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__empty,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__domain,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__range,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__trancl,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.29/157.18 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_r__r__into__trancl,axiom,
% 157.29/157.18 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__into__trancl2,axiom,
% 157.29/157.18 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 157.29/157.18 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__trans,axiom,
% 157.29/157.18 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__mono,axiom,
% 157.29/157.18 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__unfold,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__subset__Sigma,axiom,
% 157.29/157.18 ! [V_A_2,V_r_2,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 => 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__Int__subset,axiom,
% 157.29/157.18 ! [V_s_2,V_r_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__insert,axiom,
% 157.29/157.18 ! [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)))))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_reflcl__set__eq,axiom,
% 157.29/157.18 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 <=> 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_r__into__rtrancl,axiom,
% 157.29/157.18 ! [V_r_2,V_p_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_IdI,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__into__rtrancl,axiom,
% 157.29/157.18 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__unfold__right,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__unfold__left,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__reflcl,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_reflcl__trancl,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__rtrancl__absorb,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__trancl__absorb,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__rtrancl,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__rtrancl,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__r__diff__Id,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__idemp,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 157.29/157.18 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 157.29/157.18 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__trans,axiom,
% 157.29/157.18 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_refl__rtrancl,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_in__rtrancl__UnI,axiom,
% 157.29/157.18 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 157.29/157.18 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 157.29/157.18 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 157.29/157.18 => 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Image__closed__trancl,axiom,
% 157.29/157.18 ! [V_X_2,V_r_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__Un__subset,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__reflcl__absorb,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__Un__rtrancl,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__reflcl,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__mono,axiom,
% 157.29/157.18 ! [V_s_2,V_r_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__subset,axiom,
% 157.29/157.18 ! [V_S_2,V_R_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__subset__rtrancl,axiom,
% 157.29/157.18 ! [V_s_2,V_r_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_r__comp__rtrancl__eq,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__idemp__self__comp,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__unfold,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__Int__subset,axiom,
% 157.29/157.18 ! [V_r_2,V_s_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__empty,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Id__O__R,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_R__O__Id,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Image__Id,axiom,
% 157.29/157.18 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_pair__in__Id__conv,axiom,
% 157.29/157.18 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 <=> V_a_2 = V_b_2 ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__eq__or__trancl,axiom,
% 157.29/157.18 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 <=> ( V_x_2 = V_y_2
% 157.29/157.18 | ( V_x_2 != V_y_2
% 157.29/157.18 & 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))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__into__trancl2,axiom,
% 157.29/157.18 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtranclD,axiom,
% 157.29/157.18 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( V_a_2 = V_b_2
% 157.29/157.18 | ( V_a_2 != V_b_2
% 157.29/157.18 & 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))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__into__trancl1,axiom,
% 157.29/157.18 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__rtrancl__trancl,axiom,
% 157.29/157.18 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__trancl__trancl,axiom,
% 157.29/157.18 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__Id,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__Id,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_refl__Id,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_pair__leq__def,axiom,
% 157.29/157.18 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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Not__Domain__rtrancl,axiom,
% 157.29/157.18 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 157.29/157.18 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 <=> V_x_2 = V_y_2 ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_acc__downwards,axiom,
% 157.29/157.18 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_acc__downwards__aux,axiom,
% 157.29/157.18 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__insert,axiom,
% 157.29/157.18 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 & ~ 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_acyclic__insert,axiom,
% 157.29/157.18 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.29/157.18 & ~ 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_refl__reflcl,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Id__def,axiom,
% 157.29/157.18 ! [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))))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_irrefl__diff__Id,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_pred__nat__trancl__eq__le,axiom,
% 157.29/157.18 ! [V_n_2,V_m_2] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__subset__Sigma__aux,axiom,
% 157.29/157.18 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( 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))))
% 157.29/157.18 => ( V_a_2 = V_b_2
% 157.29/157.18 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_irrefl__tranclI,axiom,
% 157.29/157.18 ! [V_x_2,V_r_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ~ 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_sequence__trans,axiom,
% 157.29/157.18 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 157.29/157.18 ( ! [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)))
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__converse,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__Id,axiom,
% 157.29/157.18 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_acyclic__converse,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.29/157.18 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__Id__on,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__inv__image,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__converse,axiom,
% 157.29/157.18 ! [V_r_2,T_c,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 157.29/157.18 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__converse,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Field__converse,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__Int,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_refl__on__converse,axiom,
% 157.29/157.18 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.18 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.29/157.18 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__Un,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__rel__comp,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converseD,axiom,
% 157.29/157.18 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converseI,axiom,
% 157.29/157.18 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__iff,axiom,
% 157.29/157.18 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 <=> 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__UNION,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__INTER,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__converse,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__converse__trancl,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.29/157.18 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_equiv__comp__eq,axiom,
% 157.29/157.18 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.18 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.18 => 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 ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__converse,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Domain__converse,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Range__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__converseD,axiom,
% 157.29/157.18 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__converseI,axiom,
% 157.29/157.18 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__converseD,axiom,
% 157.29/157.18 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 => 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__converseI,axiom,
% 157.29/157.18 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 => 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Image__subset__eq,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 <=> 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))))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_refl__on__comp__subset,axiom,
% 157.29/157.18 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.18 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_comp__equivI,axiom,
% 157.29/157.18 ! [V_A_2,V_r_2,T_b] :
% 157.29/157.18 ( 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
% 157.29/157.18 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 157.29/157.18 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__acyclic__wf__converse,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 157.29/157.18 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.29/157.18 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converse__def,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Image__INT__eq,axiom,
% 157.29/157.18 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 157.29/157.18 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 157.29/157.18 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_total__on__diff__Id,axiom,
% 157.29/157.18 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_single__valued__Id,axiom,
% 157.29/157.18 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_single__valued__rel__comp,axiom,
% 157.29/157.18 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 157.29/157.18 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 157.29/157.18 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 157.29/157.18 => 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_single__valued__subset,axiom,
% 157.29/157.18 ! [V_s_2,V_r_2,T_c,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 157.29/157.18 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_single__valued__Id__on,axiom,
% 157.29/157.18 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_total__on__empty,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_total__on__converse,axiom,
% 157.29/157.18 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.18 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.29/157.18 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_single__valued__def,axiom,
% 157.29/157.18 ! [V_r_2,T_c,T_b] :
% 157.29/157.18 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 157.29/157.18 <=> ! [B_x,B_y] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ! [B_z] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => B_y = B_z ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_single__valuedD,axiom,
% 157.29/157.18 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 157.29/157.18 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => V_y_2 = V_z_2 ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_total__on__def,axiom,
% 157.29/157.18 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.18 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 157.29/157.18 <=> ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.18 => ! [B_xa] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 157.29/157.18 => ( B_x != B_xa
% 157.29/157.18 => ( 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))
% 157.29/157.18 | 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)) ) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_single__valued__confluent,axiom,
% 157.29/157.18 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 157.29/157.18 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 | 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))) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Image__Int__eq,axiom,
% 157.29/157.18 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 157.29/157.18 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 157.29/157.18 => 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 157.29/157.18 ! [V_R_2,V_p_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 157.29/157.18 => 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_acyclicI,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( ! [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)))
% 157.29/157.18 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_single__valued__rel__pow,axiom,
% 157.29/157.18 ! [V_n_2,V_R_2,T_b] :
% 157.29/157.18 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 157.29/157.18 => 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_funpow__mult,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_funpow__swap1,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__exp,axiom,
% 157.29/157.18 ! [V_R_2,V_n_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_comp__funpow,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__commute,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__1,axiom,
% 157.29/157.18 ! [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 ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__power,axiom,
% 157.29/157.18 ! [V_R_2,V_p_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 157.29/157.18 <=> ? [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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__imp__rtrancl,axiom,
% 157.29/157.18 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_relpow_Osimps_I2_J,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__add,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_relpow_Osimps_I1_J,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__0__E,axiom,
% 157.29/157.18 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => V_x_2 = V_y_2 ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__0__I,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__Suc__I2,axiom,
% 157.29/157.18 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__Suc__I,axiom,
% 157.29/157.18 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( 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))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_funpow_Osimps_I2_J,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_funpow__add,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_funpow_Osimps_I1_J,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_trancl__power,axiom,
% 157.29/157.18 ! [V_R_2,V_p_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 157.29/157.18 <=> ? [B_n] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 157.29/157.18 & 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_funpow__code__def,axiom,
% 157.29/157.18 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__E2,axiom,
% 157.29/157.18 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.18 => V_x_2 != V_z_2 )
% 157.29/157.18 => ~ ! [B_y,B_m] :
% 157.29/157.18 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => ~ 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))) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__E,axiom,
% 157.29/157.18 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.18 => V_x_2 != V_z_2 )
% 157.29/157.18 => ~ ! [B_y,B_m] :
% 157.29/157.18 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 157.29/157.18 => ( 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)))
% 157.29/157.18 => ~ 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)) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 157.29/157.18 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 => ( ! [B_x] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ! [B_y] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => B_y = B_x ) )
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__Un__separatorE,axiom,
% 157.29/157.18 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 157.29/157.18 ( 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))))
% 157.29/157.18 => ( ! [B_x] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ! [B_y] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => B_x = B_y ) )
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__Suc__D2,axiom,
% 157.29/157.18 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ? [B_y] :
% 157.29/157.18 ( 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))
% 157.29/157.18 & 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__Suc__E,axiom,
% 157.29/157.18 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ~ ! [B_y] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ~ 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__pow__Suc__E2,axiom,
% 157.29/157.18 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ~ ! [B_y] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ~ 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_tranclD,axiom,
% 157.29/157.18 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ? [B_z] :
% 157.29/157.18 ( 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))
% 157.29/157.18 & 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_tranclD2,axiom,
% 157.29/157.18 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ? [B_z] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 & 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_IdE,axiom,
% 157.29/157.18 ! [V_p_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 157.29/157.18 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_wf__eq__minimal,axiom,
% 157.29/157.18 ! [V_r_2,T_b] :
% 157.29/157.18 ( c_Wellfounded_Owf(T_b,V_r_2)
% 157.29/157.18 <=> ! [B_Q] :
% 157.29/157.18 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 157.29/157.18 => ? [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 157.29/157.18 & ! [B_y] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_transfer__nat__int__set__cong,axiom,
% 157.29/157.18 ! [V_P_H_2,V_Pa_2] :
% 157.29/157.18 ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 157.29/157.18 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.29/157.18 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 157.29/157.18 => 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)) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Int__Collect__mono,axiom,
% 157.29/157.18 ! [V_Qa_2,V_Pa_2,V_B_2,V_A_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.18 => ( ! [B_x] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.18 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.29/157.18 => hBOOL(hAPP(V_Qa_2,B_x)) ) )
% 157.29/157.18 => 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)))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rel__compE,axiom,
% 157.29/157.18 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ~ ! [B_x,B_y,B_z] :
% 157.29/157.18 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 157.29/157.18 => ( 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))
% 157.29/157.18 => ~ 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)) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_converseE,axiom,
% 157.29/157.18 ! [V_r_2,V_yx_2,T_c,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ~ ! [B_x,B_y] :
% 157.29/157.18 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 157.29/157.18 => ~ 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)) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_internal__split__def,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_internal__split__conv,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nitpick_Oof__frac__def,axiom,
% 157.29/157.18 ! [V_q,T_a,T_b] :
% 157.29/157.18 ( ( class_Rings_Oinverse(T_b)
% 157.29/157.18 & class_Rings_Oring__1(T_b) )
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nitpick_Oless__frac__def,axiom,
% 157.29/157.18 ! [V_r_2,V_q_2,T_b] :
% 157.29/157.18 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 157.29/157.18 <=> 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 157.29/157.18 ! [V_r_2,V_q_2,T_b] :
% 157.29/157.18 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 157.29/157.18 <=> 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nitpick_Odenom__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Nitpick_Onum__def,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_bool_Osize_I1_J,axiom,
% 157.29/157.18 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_bool_Osize_I2_J,axiom,
% 157.29/157.18 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_finite__less__ub,axiom,
% 157.29/157.18 ! [V_u_2,V_f_2] :
% 157.29/157.18 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 157.29/157.18 => 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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_lenlex__def,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_neq__if__length__neq,axiom,
% 157.29/157.18 ! [V_ys,V_xs,T_a] :
% 157.29/157.18 ( 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)
% 157.29/157.18 => V_xs != V_ys ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_lexn__length,axiom,
% 157.29/157.18 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.18 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 157.29/157.18 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_lenlex__conv,axiom,
% 157.29/157.18 ! [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)))))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_length__sublist,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_lexn_Osimps_I2_J,axiom,
% 157.29/157.18 ! [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)))))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_impossible__Cons,axiom,
% 157.29/157.18 ! [V_x,V_ys,V_xs,T_a] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_list_Oinject,axiom,
% 157.29/157.18 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 157.29/157.18 ( 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)
% 157.29/157.18 <=> ( V_a_2 = V_a_H_2
% 157.29/157.18 & V_list_2 = V_list_H_2 ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_not__Cons__self2,axiom,
% 157.29/157.18 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 157.29/157.18
% 157.29/157.18 fof(fact_not__Cons__self,axiom,
% 157.29/157.18 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_list_Osize_I4_J,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Cons__in__lex,axiom,
% 157.29/157.18 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.18 <=> ( ( 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))
% 157.29/157.18 & 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) )
% 157.29/157.18 | ( V_x_2 = V_y_2
% 157.29/157.18 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_set__Cons__def,axiom,
% 157.29/157.18 ! [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)))))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_pick_Osimps,axiom,
% 157.29/157.18 ! [V_xs,V_x,T_a,V_i] :
% 157.29/157.18 ( ( 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)))
% 157.29/157.18 => 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) )
% 157.29/157.18 & ( ~ 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)))
% 157.29/157.18 => 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))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_select__weight__cons__zero,axiom,
% 157.29/157.18 ! [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) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_lexord__cons__cons,axiom,
% 157.29/157.18 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.18 <=> ( 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))
% 157.29/157.18 | ( V_a_2 = V_b_2
% 157.29/157.18 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_lexord__lex,axiom,
% 157.29/157.18 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.18 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.18 & 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) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 157.29/157.18 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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)))
% 157.29/157.18 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_list_Osize_I2_J,axiom,
% 157.29/157.18 ! [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))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Cons__acc__listrel1I,axiom,
% 157.29/157.18 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 157.29/157.18 => ( 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))))
% 157.29/157.18 => 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)))) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 157.29/157.18 ! [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)))) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_listrel1__converse,axiom,
% 157.29/157.18 ! [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)) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_listrel1__mono,axiom,
% 157.29/157.18 ! [V_s_2,V_r_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => 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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_listrel1I2,axiom,
% 157.29/157.18 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 157.29/157.18 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_listrel1__eq__len,axiom,
% 157.29/157.18 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.18 => 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) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 157.29/157.18 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 157.29/157.18 => 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) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_in__listrel1__converse,axiom,
% 157.29/157.18 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 157.29/157.18 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_Cons__listrel1__Cons,axiom,
% 157.29/157.18 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.18 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.18 <=> ( ( 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))
% 157.29/157.18 & V_xs_2 = V_ys_2 )
% 157.29/157.18 | ( V_x_2 = V_y_2
% 157.29/157.18 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_listrel1I1,axiom,
% 157.29/157.18 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.18 ( 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))
% 157.29/157.18 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 157.29/157.18
% 157.29/157.18 fof(fact_listrel__Cons,axiom,
% 157.29/157.18 ! [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))))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lexord__linear,axiom,
% 157.29/157.19 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 157.29/157.19 ( ! [B_a,B_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 | B_a = B_b
% 157.29/157.19 | 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)) )
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 | V_x_2 = V_y_2
% 157.29/157.19 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__rtrancl__refl,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__mono,axiom,
% 157.29/157.19 ! [V_s_2,V_r_2,T_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__eq__len,axiom,
% 157.29/157.19 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__rtrancl__trans,axiom,
% 157.29/157.19 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 157.29/157.19 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel1__subset__listrel,axiom,
% 157.29/157.19 ! [V_r_H_2,V_r_2,T_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 157.29/157.19 => 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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 157.29/157.19 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel_OCons,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrelp__listrel__eq,axiom,
% 157.29/157.19 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__Cons1,axiom,
% 157.29/157.19 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 => ~ ! [B_y,B_ys] :
% 157.29/157.19 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 157.29/157.19 => ( 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))
% 157.29/157.19 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrelp_Oequations_I2_J,axiom,
% 157.29/157.19 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 157.29/157.19 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrelp_OCons,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 157.29/157.19 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__Cons2,axiom,
% 157.29/157.19 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 => ~ ! [B_x,B_xs] :
% 157.29/157.19 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 157.29/157.19 => ( 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))
% 157.29/157.19 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__subset,axiom,
% 157.29/157.19 ! [V_A_2,V_r_2,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => 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))))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lists__UNIV,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lists__mono,axiom,
% 157.29/157.19 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_equiv__listrel,axiom,
% 157.29/157.19 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.19 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__refl__on,axiom,
% 157.29/157.19 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.19 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Cons__in__lists__iff,axiom,
% 157.29/157.19 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.19 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lists__accD,axiom,
% 157.29/157.19 ! [V_r_2,V_xs_2,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lists__accI,axiom,
% 157.29/157.19 ! [V_r_2,V_xs_2,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__iff__nth,axiom,
% 157.29/157.19 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 <=> ( 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)
% 157.29/157.19 & ! [B_n] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lexord__irreflexive,axiom,
% 157.29/157.19 ! [V_y_2,V_r_2,T_b] :
% 157.29/157.19 ( ! [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))
% 157.29/157.19 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_infinite__UNIV__listI,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__eq__iff__nth__eq,axiom,
% 157.29/157.19 ! [T_b,V_ys_2,V_xs_2] :
% 157.29/157.19 ( V_xs_2 = V_ys_2
% 157.29/157.19 <=> ( 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)
% 157.29/157.19 & ! [B_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__Cons__Suc,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__Cons__0,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth_Osimps,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__Cons_H,axiom,
% 157.29/157.19 ! [V_xs,V_x,T_a,V_n] :
% 157.29/157.19 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 157.29/157.19 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__Cons__number__of,axiom,
% 157.29/157.19 ! [V_xs,V_x,T_a,V_v] :
% 157.29/157.19 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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 )
% 157.29/157.19 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lexord__take__index__conv,axiom,
% 157.29/157.19 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 <=> ( ( 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)))
% 157.29/157.19 & 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 )
% 157.29/157.19 | ? [B_i] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 157.29/157.19 & 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)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__sublist,axiom,
% 157.29/157.19 ! [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))))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_finite__set,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__subset__Cons,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__all,axiom,
% 157.29/157.19 ! [V_n,V_xs,T_a] :
% 157.29/157.19 ( 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))
% 157.29/157.19 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__take__subset,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__take__subset__set__take,axiom,
% 157.29/157.19 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.29/157.19 => 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__sublist__subset,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__take,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_n,V_i] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__Suc__Cons,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__ConsD,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => ( V_y_2 = V_x_2
% 157.29/157.19 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_in__set__sublistD,axiom,
% 157.29/157.19 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_in__set__takeD,axiom,
% 157.29/157.19 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_notin__set__sublistI,axiom,
% 157.29/157.19 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => ~ 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__take,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__take,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sublist__upt__eq__take,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_card__length,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_all__set__conv__all__nth,axiom,
% 157.29/157.19 ! [V_Pa_2,V_xs_2,T_b] :
% 157.29/157.19 ( ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.19 <=> ! [B_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__size__estimation,axiom,
% 157.29/157.19 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 157.29/157.19 => 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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__size__estimation_H,axiom,
% 157.29/157.19 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 157.29/157.19 => 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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_in__lists__conv__set,axiom,
% 157.29/157.19 ! [V_A_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 157.29/157.19 <=> ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__pos__if__in__set,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__mem,axiom,
% 157.29/157.19 ! [V_xs_2,T_b,V_n_2] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_in__set__conv__nth,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 <=> ? [B_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lists__eq__set,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__conv__nth,axiom,
% 157.29/157.19 ! [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))))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_finite__lists__length__eq,axiom,
% 157.29/157.19 ! [V_n_2,V_A_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.19 => 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))))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_finite__lists__length__le,axiom,
% 157.29/157.19 ! [V_n_2,V_A_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.19 => 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))))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__iff__zip,axiom,
% 157.29/157.19 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 <=> ( 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)
% 157.29/157.19 & ! [B_x] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => 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)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__zip,axiom,
% 157.29/157.19 ! [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)))))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__zip,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__zip,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__Cons__Cons,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__eq__iff__zip__eq,axiom,
% 157.29/157.19 ! [T_b,V_ys_2,V_xs_2] :
% 157.29/157.19 ( V_xs_2 = V_ys_2
% 157.29/157.19 <=> ( 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)
% 157.29/157.19 & ! [B_x] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_in__set__zipE,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__zip__rightD,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__zip__leftD,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__same,axiom,
% 157.29/157.19 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 & V_a_2 = V_b_2 ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__zip,axiom,
% 157.29/157.19 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => ( 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)))
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_greaterThanLessThan__upto,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__setsum__nth,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_atLeastAtMost__upto,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__upto,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 157.29/157.19 ! [V_ns_2] :
% 157.29/157.19 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 <=> ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 157.29/157.19 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_elem__le__listsum__nat,axiom,
% 157.29/157.19 ! [V_ns,V_k] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__simps_I2_J,axiom,
% 157.29/157.19 ! [V_xs,V_x,T_a] :
% 157.29/157.19 ( class_Groups_Omonoid__add(T_a)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_atLeastLessThan__upto,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_greaterThanAtMost__upto,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nat__list__def,axiom,
% 157.29/157.19 ! [V_l_2] :
% 157.29/157.19 ( c_List_Onat__list(V_l_2)
% 157.29/157.19 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__size__pointwise,axiom,
% 157.29/157.19 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 157.29/157.19 ( ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__update__nat,axiom,
% 157.29/157.19 ! [V_n,V_ns,V_k] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_butlast__take,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_n] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__beyond,axiom,
% 157.29/157.19 ! [V_x,V_i,V_xs,T_a] :
% 157.29/157.19 ( 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))
% 157.29/157.19 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__id,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__list__update__neq,axiom,
% 157.29/157.19 ! [V_x,V_xs,T_a,V_j,V_i] :
% 157.29/157.19 ( V_i != V_j
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__list__update,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_butlast__list__update,axiom,
% 157.29/157.19 ! [V_x,V_xs,T_a,V_k] :
% 157.29/157.19 ( ( 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))
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( 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))
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__update,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_update__zip,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__swap,axiom,
% 157.29/157.19 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 157.29/157.19 ( V_i != V_i_H
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__overwrite,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__code_I3_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__code_I2_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_in__set__butlastD,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__update__subsetI,axiom,
% 157.29/157.19 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__update__subset__insert,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__list__update__eq,axiom,
% 157.29/157.19 ! [V_x,V_xs,T_a,V_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__same__conv,axiom,
% 157.29/157.19 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 157.29/157.19 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__list__update,axiom,
% 157.29/157.19 ! [V_x,V_j,V_xs,T_a,V_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => ( ( V_i = V_j
% 157.29/157.19 => 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 )
% 157.29/157.19 & ( V_i != V_j
% 157.29/157.19 => 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) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__butlast,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_n] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__butlast,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__update__memI,axiom,
% 157.29/157.19 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_butlast__conv__take,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel1__iff__update,axiom,
% 157.29/157.19 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 <=> ? [B_y,B_n] :
% 157.29/157.19 ( 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))
% 157.29/157.19 & 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)))
% 157.29/157.19 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__list__update,axiom,
% 157.29/157.19 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 => ( ~ 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))))))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__upto,axiom,
% 157.29/157.19 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__take,axiom,
% 157.29/157.19 ! [V_i,V_xs,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__sublistI,axiom,
% 157.29/157.19 ! [V_I_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__zipI2,axiom,
% 157.29/157.19 ! [V_xs,T_b,V_ys,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__zipI1,axiom,
% 157.29/157.19 ! [V_ys,T_b,V_xs,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct_Osimps_I2_J,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 157.29/157.19 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__card,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_card__distinct,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__eq__iff__index__eq,axiom,
% 157.29/157.19 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 => ( 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)))
% 157.29/157.19 => ( 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)))
% 157.29/157.19 => ( 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)
% 157.29/157.19 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__conv__nth,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 <=> ! [B_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => ! [B_j] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => ( B_i != B_j
% 157.29/157.19 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.19 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Nitpick_Ocard_H__def,axiom,
% 157.29/157.19 ! [V_A_2,T_b] :
% 157.29/157.19 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.19 => 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)))) )
% 157.29/157.19 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.19 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__take__lemma,axiom,
% 157.29/157.19 ! [V_ys,V_xs,T_a,V_k] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => ( 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)))
% 157.29/157.19 => ( ! [B_i] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 157.29/157.19 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 157.29/157.19 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__remove1__eq,axiom,
% 157.29/157.19 ! [V_x_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 => 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__Cons__number__of,axiom,
% 157.29/157.19 ! [V_xs,V_x,T_a,V_v] :
% 157.29/157.19 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lists_ONil,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__Nil2,axiom,
% 157.29/157.19 ! [V_r_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__Nil1,axiom,
% 157.29/157.19 ! [V_r_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__butlast,axiom,
% 157.29/157.19 ! [T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct_Osimps_I1_J,axiom,
% 157.29/157.19 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__remove1,axiom,
% 157.29/157.19 ! [V_x,V_xs,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_butlast_Osimps_I1_J,axiom,
% 157.29/157.19 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_butlast_Osimps_I2_J,axiom,
% 157.29/157.19 ! [V_x,T_a,V_xs] :
% 157.29/157.19 ( ( V_xs = c_List_Olist_ONil(T_a)
% 157.29/157.19 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 157.29/157.19 & ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list_Osize_I1_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remove1_Osimps_I2_J,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_y,V_x] :
% 157.29/157.19 ( ( V_x = V_y
% 157.29/157.19 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 157.29/157.19 & ( V_x != V_y
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list_Osimps_I3_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_upto__empty,axiom,
% 157.29/157.19 ! [V_i,V_j] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 157.29/157.19 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__Nil,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__0,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__eq__Nil,axiom,
% 157.29/157.19 ! [V_xs_2,V_n_2,T_b] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.29/157.19 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sublist__nil,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remove1_Osimps_I1_J,axiom,
% 157.29/157.19 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remove1__commute,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrelp_ONil,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrelp_Oequations_I1_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__Nil,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__simps_I1_J,axiom,
% 157.29/157.19 ! [T_a] :
% 157.29/157.19 ( class_Groups_Omonoid__add(T_a)
% 157.29/157.19 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__0__conv,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list_Osize_I3_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__empty,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.19 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__empty2,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 157.29/157.19 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__nonempty,axiom,
% 157.29/157.19 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 157.29/157.19 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__code_I1_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_in__set__remove1,axiom,
% 157.29/157.19 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 157.29/157.19 ( V_a_2 != V_b_2
% 157.29/157.19 => ( 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))))
% 157.29/157.19 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_notin__set__remove1,axiom,
% 157.29/157.19 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => ~ 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remove1__idem,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sublist__empty,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__remove1__subset,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__greater__0__conv,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__1__Cons,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_not__listrel1__Nil,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_not__Nil__listrel1,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel_ONil,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lexord__Nil__right,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Nil2__notin__lex,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Nil__notin__lex,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__Cons,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_upto_Osimps,axiom,
% 157.29/157.19 ! [V_j,V_i] :
% 157.29/157.19 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 157.29/157.19 => 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)) )
% 157.29/157.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 157.29/157.19 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sublist__singleton,axiom,
% 157.29/157.19 ! [V_x_2,T_b,V_A_2] :
% 157.29/157.19 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 157.29/157.19 => 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)) )
% 157.29/157.19 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lists__empty,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__Cons_H,axiom,
% 157.29/157.19 ! [V_xs,V_x,T_a,V_n] :
% 157.29/157.19 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_upto__rec__number__of,axiom,
% 157.29/157.19 ! [V_n,V_m] :
% 157.29/157.19 ( ( 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)))
% 157.29/157.19 => 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))) )
% 157.29/157.19 & ( ~ 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)))
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel__Nil,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__Cons__sing__Nil,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__remove1,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => 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)) )
% 157.29/157.19 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_upto_Opsimps,axiom,
% 157.29/157.19 ! [V_j_2,V_i_2] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 157.29/157.19 => 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)) )
% 157.29/157.19 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 157.29/157.19 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_select,axiom,
% 157.29/157.19 ! [V_s_2,T_b,V_xs_2] :
% 157.29/157.19 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listset_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__Cons,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list_Osimps_I5_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list_Osimps_I4_J,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listset_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__Cons1,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sorted__list__of__set__remove,axiom,
% 157.29/157.19 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_upto_Opinduct,axiom,
% 157.29/157.19 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => ( ! [B_i,B_j] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 157.29/157.19 => 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)) )
% 157.29/157.19 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) )
% 157.29/157.19 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sorted__list__of__set__empty,axiom,
% 157.29/157.19 ! [T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_anamorph_Osimps,axiom,
% 157.29/157.19 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 157.29/157.19 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sublist__Cons,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append1__eq__conv,axiom,
% 157.29/157.19 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 <=> ( V_xs_2 = V_ys_2
% 157.29/157.19 & V_x_2 = V_y_2 ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Cons__eq__append__conv,axiom,
% 157.29/157.19 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 157.29/157.19 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 157.29/157.19 | ? [B_ys_H] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 157.29/157.19 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__eq__Cons__conv,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 157.29/157.19 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 157.29/157.19 | ? [B_ys_H] :
% 157.29/157.19 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 157.29/157.19 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Cons__eq__appendI,axiom,
% 157.29/157.19 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 157.29/157.19 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 157.29/157.19 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__Cons,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__in__lists__conv,axiom,
% 157.29/157.19 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 157.29/157.19 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__assoc,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__eq__append__conv2,axiom,
% 157.29/157.19 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 <=> ? [B_us] :
% 157.29/157.19 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 157.29/157.19 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 )
% 157.29/157.19 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 157.29/157.19 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_same__append__eq,axiom,
% 157.29/157.19 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 <=> V_ys_2 = V_zs_2 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__same__eq,axiom,
% 157.29/157.19 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 <=> V_ys_2 = V_zs_2 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__eq__appendI,axiom,
% 157.29/157.19 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 157.29/157.19 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 157.29/157.19 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__append,axiom,
% 157.29/157.19 ! [V_ys,V_xs,T_a] :
% 157.29/157.19 ( class_Groups_Omonoid__add(T_a)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__append,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__append,axiom,
% 157.29/157.19 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => ( 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)
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__append,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_eq__Nil__appendI,axiom,
% 157.29/157.19 ! [T_a,V_ys,V_xs] :
% 157.29/157.19 ( V_xs = V_ys
% 157.29/157.19 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__self__conv2,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 157.29/157.19 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__self__conv,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 157.29/157.19 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__is__Nil__conv,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 157.29/157.19 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 157.29/157.19 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_self__append__conv2,axiom,
% 157.29/157.19 ! [V_xs_2,T_b,V_ys_2] :
% 157.29/157.19 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 157.29/157.19 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_self__append__conv,axiom,
% 157.29/157.19 ! [V_ys_2,T_b,V_xs_2] :
% 157.29/157.19 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 157.29/157.19 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__Nil2,axiom,
% 157.29/157.19 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Nil__is__append__conv,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 157.29/157.19 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 157.29/157.19 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__Nil,axiom,
% 157.29/157.19 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 157.29/157.19
% 157.29/157.19 fof(fact_butlast__append,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_ys] :
% 157.29/157.19 ( ( V_ys = c_List_Olist_ONil(T_a)
% 157.29/157.19 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 157.29/157.19 & ( V_ys != c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__append__length,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__append__length__plus,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__append,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__append1,axiom,
% 157.29/157.19 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__length,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remove1__append,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_in__set__butlast__appendI,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 157.29/157.19 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 157.29/157.19 => 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))))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_butlast__snoc,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__listrel1I,axiom,
% 157.29/157.19 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 & V_us_2 = V_vs_2 )
% 157.29/157.19 | ( V_xs_2 = V_ys_2
% 157.29/157.19 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) )
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lexord__append__leftI,axiom,
% 157.29/157.19 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__append,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 157.29/157.19 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 157.29/157.19 & 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__append,axiom,
% 157.29/157.19 ! [V_ys,V_xs,T_a,V_n] :
% 157.29/157.19 ( ( 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)))
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( ~ 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)))
% 157.29/157.19 => 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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__update__append,axiom,
% 157.29/157.19 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 157.29/157.19 ( ( 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)))
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( ~ 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)))
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sublist__append,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel1I,axiom,
% 157.29/157.19 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 => ( 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))
% 157.29/157.19 => ( 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))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lexord__append__left__rightI,axiom,
% 157.29/157.19 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__Suc__conv__app__nth,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 157.29/157.19 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 & V_x_2 = V_y_2 )
% 157.29/157.19 | ( V_xs_2 = V_ys_2
% 157.29/157.19 & 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)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listrel1E,axiom,
% 157.29/157.19 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 => ~ ! [B_x,B_y] :
% 157.29/157.19 ( 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))
% 157.29/157.19 => ! [B_us,B_vs] :
% 157.29/157.19 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 157.29/157.19 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lexord__append__leftD,axiom,
% 157.29/157.19 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 => ( ! [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))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate1__def,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_upd__conv__take__nth__drop,axiom,
% 157.29/157.19 ! [V_a,V_xs,T_a,V_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__take__drop__id,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__Suc__Cons,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__1__Cons,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__via__drop,axiom,
% 157.29/157.19 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 157.29/157.19 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct1__rotate,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 157.29/157.19 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__drop,axiom,
% 157.29/157.19 ! [V_i,V_xs,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__butlast,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_butlast__drop,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__drop,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__take,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__drop,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__0,axiom,
% 157.29/157.19 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__zip,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__drop,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__rotate1,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__rotate1,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_in__set__dropD,axiom,
% 157.29/157.19 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__drop__subset,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate1__is__Nil__conv,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.29/157.19 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__Nil,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__drop__subset__set__drop,axiom,
% 157.29/157.19 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 157.29/157.19 => 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__all,axiom,
% 157.29/157.19 ! [V_n,V_xs,T_a] :
% 157.29/157.19 ( 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))
% 157.29/157.19 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__eq__Nil,axiom,
% 157.29/157.19 ! [V_xs_2,V_n_2,T_b] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.29/157.19 <=> 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__append,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__eq__conv__conj,axiom,
% 157.29/157.19 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 157.29/157.19 <=> ( 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)
% 157.29/157.19 & 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__Cons,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__Cons_H,axiom,
% 157.29/157.19 ! [V_xs,V_x,T_a,V_n] :
% 157.29/157.19 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__drop,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_i,V_n] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__eq__append__conv__if,axiom,
% 157.29/157.19 ! [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] :
% 157.29/157.19 ( 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)
% 157.29/157.19 <=> ( ( 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)))
% 157.29/157.19 => ( 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)
% 157.29/157.19 & 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) ) )
% 157.29/157.19 & ( ~ 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)))
% 157.29/157.19 => ( 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
% 157.29/157.19 & 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 ) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__drop_H,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate__simps,axiom,
% 157.29/157.19 ! [V_xs,V_x,T_b,T_a] :
% 157.29/157.19 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 157.29/157.19 & 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__Cons__number__of,axiom,
% 157.29/157.19 ! [V_xs,V_x,T_a,V_v] :
% 157.29/157.19 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__add,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_j,V_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate1__length01,axiom,
% 157.29/157.19 ! [V_xs,T_a] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__append1,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__append2,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_id__take__nth__drop,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__hd__drop,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_n] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_hd__drop__conv__nth,axiom,
% 157.29/157.19 ! [V_n,T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => ( 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)))
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_hd_Osimps,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_hd__append,axiom,
% 157.29/157.19 ! [V_ys,T_a,V_xs] :
% 157.29/157.19 ( ( V_xs = c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_hd__append2,axiom,
% 157.29/157.19 ! [V_ys,T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_hd__in__set,axiom,
% 157.29/157.19 ! [T_b,V_xs_2] :
% 157.29/157.19 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_hd__conv__nth,axiom,
% 157.29/157.19 ! [T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate1__hd__tl,axiom,
% 157.29/157.19 ! [T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_hd__rotate__conv__nth,axiom,
% 157.29/157.19 ! [V_n,T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_tl__drop,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__tl,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_tl_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__rotate,axiom,
% 157.29/157.19 ! [V_xs_2,V_n_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 157.29/157.19 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__tl,axiom,
% 157.29/157.19 ! [V_xs,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate__rotate,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate0,axiom,
% 157.29/157.19 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate__add,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__rotate,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__rotate,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate__is__Nil__conv,axiom,
% 157.29/157.19 ! [V_xs_2,V_n_2,T_b] :
% 157.29/157.19 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.29/157.19 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_tl_Osimps_I1_J,axiom,
% 157.29/157.19 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate__def,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate1__rotate__swap,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_tl__append2,axiom,
% 157.29/157.19 ! [V_ys,T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__tl,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate__conv__mod,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__Suc,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate__Suc,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_tl__append,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate__id,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_n] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate__length01,axiom,
% 157.29/157.19 ! [V_n,V_xs,T_a] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__tl,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_tl__take,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__Suc,axiom,
% 157.29/157.19 ! [V_n,T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate__drop__take,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_fold1__set,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 157.29/157.19 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sorted__list__of__set__insert,axiom,
% 157.29/157.19 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.19 => 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)))))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_insort__not__Nil,axiom,
% 157.29/157.19 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldl__Nil,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remove1__insort,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => 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 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_start__le__sum,axiom,
% 157.29/157.19 ! [V_ns_2,V_n_2,V_m_2] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_insort__key__left__comm,axiom,
% 157.29/157.19 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldl__assoc,axiom,
% 157.29/157.19 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Groups_Osemigroup__add(T_b)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_fun__left__comm__insort,axiom,
% 157.29/157.19 ! [T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_insort__left__comm,axiom,
% 157.29/157.19 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldl__absorb0,axiom,
% 157.29/157.19 ! [V_zs_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Groups_Omonoid__add(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__insort,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__insort,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldl__Cons,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_insort__key_Osimps_I2_J,axiom,
% 157.29/157.19 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => ( ( 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)))
% 157.29/157.19 => 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)) )
% 157.29/157.19 & ( ~ 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)))
% 157.29/157.19 => 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)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_insort__key_Osimps_I1_J,axiom,
% 157.29/157.19 ! [V_x_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldl__append,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__foldl,axiom,
% 157.29/157.19 ! [T_b] :
% 157.29/157.19 ( class_Groups_Omonoid__add(T_b)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sum__eq__0__conv,axiom,
% 157.29/157.19 ! [V_ns_2,V_m_2] :
% 157.29/157.19 ( 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)
% 157.29/157.19 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 & ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 157.29/157.19 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__insort,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => ( 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)))
% 157.29/157.19 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 157.29/157.19 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Sup__set__fold,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Inf__set__fold,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Sup__fin__set__fold,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Lattices_Olattice(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Inf__fin__set__fold,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Lattices_Olattice(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Min__fin__set__fold,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Max__fin__set__fold,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_SUPR__set__fold,axiom,
% 157.29/157.19 ! [V_f_2,V_xs_2,T_c,T_b] :
% 157.29/157.19 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_INFI__set__fold,axiom,
% 157.29/157.19 ! [V_f_2,V_xs_2,T_c,T_b] :
% 157.29/157.19 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_elem__le__sum,axiom,
% 157.29/157.19 ! [V_ns_2,V_n_2] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_insort__insert__insort__key,axiom,
% 157.29/157.19 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => ( ~ 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))))
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lexord__append__rightI,axiom,
% 157.29/157.19 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 157.29/157.19 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__insort__insert,axiom,
% 157.29/157.19 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 => 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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_insort__insert__triv,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__insort__insert,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_insort__insert__key__triv,axiom,
% 157.29/157.19 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => ( 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))))
% 157.29/157.19 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_insort__insert__insort,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lexord__Nil__left,axiom,
% 157.29/157.19 ! [V_r_2,V_y_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.19 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last__list__update,axiom,
% 157.29/157.19 ! [V_x,V_k,T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => ( ( 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))
% 157.29/157.19 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 157.29/157.19 & ( 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))
% 157.29/157.19 => 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) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last_Osimps,axiom,
% 157.29/157.19 ! [V_x,T_a,V_xs] :
% 157.29/157.19 ( ( V_xs = c_List_Olist_ONil(T_a)
% 157.29/157.19 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 157.29/157.19 & ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last__ConsR,axiom,
% 157.29/157.19 ! [V_x,T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last__ConsL,axiom,
% 157.29/157.19 ! [V_x,T_a,V_xs] :
% 157.29/157.19 ( V_xs = c_List_Olist_ONil(T_a)
% 157.29/157.19 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last__append,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_ys] :
% 157.29/157.19 ( ( V_ys = c_List_Olist_ONil(T_a)
% 157.29/157.19 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 157.29/157.19 & ( V_ys != c_List_Olist_ONil(T_a)
% 157.29/157.19 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last__appendR,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_ys] :
% 157.29/157.19 ( V_ys != c_List_Olist_ONil(T_a)
% 157.29/157.19 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last__appendL,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_ys] :
% 157.29/157.19 ( V_ys = c_List_Olist_ONil(T_a)
% 157.29/157.19 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last__in__set,axiom,
% 157.29/157.19 ! [T_b,V_as_2] :
% 157.29/157.19 ( V_as_2 != c_List_Olist_ONil(T_b)
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last__snoc,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last__drop,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_n] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__butlast__last__id,axiom,
% 157.29/157.19 ! [T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_snoc__eq__iff__butlast,axiom,
% 157.29/157.19 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 157.29/157.19 ( 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
% 157.29/157.19 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 157.29/157.19 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 157.29/157.19 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last__conv__nth,axiom,
% 157.29/157.19 ! [T_a,V_xs] :
% 157.29/157.19 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lists_Osimps,axiom,
% 157.29/157.19 ! [V_A_2,V_a_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 157.29/157.19 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 157.29/157.19 | ? [B_a,B_l] :
% 157.29/157.19 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 157.29/157.19 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 157.29/157.19 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_select__weigth__select,axiom,
% 157.29/157.19 ! [T_b,V_xs_2] :
% 157.29/157.19 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_inj__mapI,axiom,
% 157.29/157.19 ! [V_f_2,T_c,T_b] :
% 157.29/157.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_last__map,axiom,
% 157.29/157.19 ! [V_f_2,T_c,T_b,V_xs_2] :
% 157.29/157.19 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__size__map,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_List_Omap_Ocomp,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__comp__map,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_List_Omap_Ocompositionality,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__map,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_List_Omap_Oid,axiom,
% 157.29/157.19 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_List_Omap_Oidentity,axiom,
% 157.29/157.19 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_drop__map,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_hd__map,axiom,
% 157.29/157.19 ! [V_f_2,T_c,T_b,V_xs_2] :
% 157.29/157.19 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__append,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__map,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__butlast,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_take__map,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__ident,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_inj__map__eq__map,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.19 => ( 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)
% 157.29/157.19 <=> V_xs_2 = V_ys_2 ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__injective,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 157.29/157.19 => V_xs_2 = V_ys_2 ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__addf,axiom,
% 157.29/157.19 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__mult__const,axiom,
% 157.29/157.19 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( class_Rings_Osemiring__0(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__const__mult,axiom,
% 157.29/157.19 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] :
% 157.29/157.19 ( class_Rings_Osemiring__0(T_b)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__0,axiom,
% 157.29/157.19 ! [V_xs_2,T_c,T_b] :
% 157.29/157.19 ( class_Groups_Omonoid__add(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__subtractf,axiom,
% 157.29/157.19 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( class_Groups_Oab__group__add(T_b)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__eq__imp__length__eq,axiom,
% 157.29/157.19 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__map,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__eq__conv,axiom,
% 157.29/157.19 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( 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)
% 157.29/157.19 <=> ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 157.29/157.19 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__update,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__is__Nil__conv,axiom,
% 157.29/157.19 ! [V_xs_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.29/157.19 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Nil__is__map__conv,axiom,
% 157.29/157.19 ! [V_xs_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 157.29/157.19 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__same__conv__map,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__map2,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__zip__map2,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__zip__map,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__map1,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__map__map,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_rotate__map,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__tl,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldl__map,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_inj__on__map__eq__map,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => ( 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)
% 157.29/157.19 <=> V_xs_2 = V_ys_2 ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__inj__on,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => ( 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)))
% 157.29/157.19 => V_xs_2 = V_ys_2 ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__map,axiom,
% 157.29/157.19 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__fun__upd,axiom,
% 157.29/157.19 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 157.29/157.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__map,axiom,
% 157.29/157.19 ! [V_xs_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 157.29/157.19 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 157.29/157.19 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__abs,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 157.29/157.19 => 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_uminus__listsum__map,axiom,
% 157.29/157.19 ! [V_xs_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( class_Groups_Oab__group__add(T_b)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_inj__on__mapI,axiom,
% 157.29/157.19 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_inj__mapD,axiom,
% 157.29/157.19 ! [V_f_2,T_c,T_b] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_inj__map,axiom,
% 157.29/157.19 ! [V_f_2,T_c,T_b] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 157.29/157.19 ! [V_f_2,V_xs_2,T_b,T_c] :
% 157.29/157.19 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.19 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__triv,axiom,
% 157.29/157.19 ! [V_xs_2,V_r_2,T_c,T_b] :
% 157.29/157.19 ( class_Rings_Osemiring__1(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__map__remove1,axiom,
% 157.29/157.19 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 157.29/157.19 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => 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)))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 157.29/157.19 ! [V_f_2,V_A_2,T_b,T_c] :
% 157.29/157.19 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.19 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.19 => 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))))) )
% 157.29/157.19 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.19 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_pick__same,axiom,
% 157.29/157.19 ! [V_xs_2,T_b,V_l_2] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 157.29/157.19 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 157.29/157.19 ! [V_m_2,V_n_2] :
% 157.29/157.19 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 157.29/157.19 <=> V_n_2 = V_m_2 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_times__code__numeral__code,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zero__code__numeral__def,axiom,
% 157.29/157.19 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_one__code__numeral__def,axiom,
% 157.29/157.19 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_less__code__numeral__code,axiom,
% 157.29/157.19 ! [V_m_2,V_n_2] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 157.29/157.19 ! [V_y_2,V_x_2] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.29/157.19 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 157.29/157.19 <=> V_x_2 = V_y_2 ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__fst__zip,axiom,
% 157.29/157.19 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => 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 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__snd__zip,axiom,
% 157.29/157.19 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => 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 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_number__of__code__numeral__def,axiom,
% 157.29/157.19 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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__map__fst__snd,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_plus__code__numeral__code,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_less__eq__code__numeral__code,axiom,
% 157.29/157.19 ! [V_m_2,V_n_2] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_subtract__code__numeral__code,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_pick__member,axiom,
% 157.29/157.19 ! [V_xs_2,T_b,V_i_2] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_zip__eq__conv,axiom,
% 157.29/157.19 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 157.29/157.19 <=> ( 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
% 157.29/157.19 & 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 ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__size__conv__listsum,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_code__numeral__not__eq__zero,axiom,
% 157.29/157.19 ! [V_i_2] :
% 157.29/157.19 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.29/157.19 <=> 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 157.29/157.19 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 157.29/157.19 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 157.29/157.19 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 157.29/157.19 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_select__weight__member,axiom,
% 157.29/157.19 ! [V_s_2,V_xs_2,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_select__weight__def,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_select__def,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsum__mono,axiom,
% 157.29/157.19 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 157.29/157.19 ( ( class_Groups_Omonoid__add(T_c)
% 157.29/157.19 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 157.29/157.19 => ( ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 157.29/157.19 => 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)))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_times__code__numeral__def,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nat__of__inverse,axiom,
% 157.29/157.19 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 157.29/157.19
% 157.29/157.19 fof(fact_of__nat__nat__of,axiom,
% 157.29/157.19 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nat__of__of__nat,axiom,
% 157.29/157.19 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 157.29/157.19 ! [V_l_2,V_k_2] :
% 157.29/157.19 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 157.29/157.19 <=> V_k_2 = V_l_2 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_code__numeral_Onat__of__inject,axiom,
% 157.29/157.19 ! [V_y_2,V_x_2] :
% 157.29/157.19 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 157.29/157.19 <=> V_x_2 = V_y_2 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_type__definition__code__numeral,axiom,
% 157.29/157.19 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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_less__code__numeral__def,axiom,
% 157.29/157.19 ! [V_m_2,V_n_2] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 157.29/157.19 <=> 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nat__of,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nat__of__number,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_int__of__def,axiom,
% 157.29/157.19 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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_less__eq__code__numeral__def,axiom,
% 157.29/157.19 ! [V_m_2,V_n_2] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 157.29/157.19 <=> 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nat__of__code,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nat__of__aux__def,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Suc__code__numeral__def,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_minus__code__numeral__def,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_of__nat__inverse,axiom,
% 157.29/157.19 ! [V_y_2] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.29/157.19 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_plus__code__numeral__def,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_div__code__numeral__def,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_mod__code__numeral__def,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_code__numeral__decr,axiom,
% 157.29/157.19 ! [V_k] :
% 157.29/157.19 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_partition__set,axiom,
% 157.29/157.19 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_partition__P,axiom,
% 157.29/157.19 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => ( ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 157.29/157.19 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.19 & ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 157.29/157.19 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_partition_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_partition_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lists__Int__eq,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_lists__IntI,axiom,
% 157.29/157.19 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsp_ONil,axiom,
% 157.29/157.19 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_append__in__listsp__conv,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 157.29/157.19 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 157.29/157.19 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsp_Oequations_I2_J,axiom,
% 157.29/157.19 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 157.29/157.19 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 157.29/157.19 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsp__infI,axiom,
% 157.29/157.19 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 157.29/157.19 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsp__inf__eq,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsp__conj__eq,axiom,
% 157.29/157.19 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 157.29/157.19 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_in__listsp__conv__set,axiom,
% 157.29/157.19 ! [V_xs_2,V_A_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 157.29/157.19 <=> ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsp_Oequations_I1_J,axiom,
% 157.29/157.19 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsp__mono,axiom,
% 157.29/157.19 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_listsp__lists__eq,axiom,
% 157.29/157.19 ! [V_x_2,V_A_2,T_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_product_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__def,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.29/157.19 <=> ( 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)
% 157.29/157.19 & ! [B_x] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__map2,axiom,
% 157.29/157.19 ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 <=> 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__map1,axiom,
% 157.29/157.19 ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 <=> 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__Nil,axiom,
% 157.29/157.19 ! [V_ys_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2)
% 157.29/157.19 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__Nil2,axiom,
% 157.29/157.19 ! [V_xs_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c))
% 157.29/157.19 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__lengthD,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__eq,axiom,
% 157.29/157.19 ! [T_b,V_ys_2,V_xs_2] :
% 157.29/157.19 ( V_xs_2 = V_ys_2
% 157.29/157.19 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__takeI,axiom,
% 157.29/157.19 ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__Cons,axiom,
% 157.29/157.19 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( 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))
% 157.29/157.19 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 157.29/157.19 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__append,axiom,
% 157.29/157.19 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 => ( 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))
% 157.29/157.19 <=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.29/157.19 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__appendI,axiom,
% 157.29/157.19 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2)
% 157.29/157.19 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2)
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__dropI,axiom,
% 157.29/157.19 ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_product_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__conv__all__nth,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.29/157.19 <=> ( 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)
% 157.29/157.19 & ! [B_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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))) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__nthD,axiom,
% 157.29/157.19 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.29/157.19 => ( 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)))
% 157.29/157.19 => 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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__nthD2,axiom,
% 157.29/157.19 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.29/157.19 => ( 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)))
% 157.29/157.19 => 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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__update__cong,axiom,
% 157.29/157.19 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 157.29/157.19 => 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)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2__update__cong2,axiom,
% 157.29/157.19 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.29/157.19 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 157.29/157.19 => ( 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)))
% 157.29/157.19 => 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)) ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__product,axiom,
% 157.29/157.19 ! [V_ys,T_b,V_xs,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_product__list__set,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sublists__powset,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__sublists,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sublists_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sublists_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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))))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__set__sublists,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 => 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)))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__n__lists,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_enum__the__def,axiom,
% 157.29/157.19 ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__n__lists,axiom,
% 157.29/157.19 ! [V_n,V_xs,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_n__lists__Nil,axiom,
% 157.29/157.19 ! [T_a,V_n] :
% 157.29/157.19 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => 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))) )
% 157.29/157.19 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.19 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_n__lists_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__n__lists,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__n__lists__elem,axiom,
% 157.29/157.19 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_list__all2I,axiom,
% 157.29/157.19 ! [V_Pa_2,V_b_2,V_a_2,T_c,T_b] :
% 157.29/157.19 ( ! [B_x] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) )
% 157.29/157.19 => ( 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)
% 157.29/157.19 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_all__nth__imp__all__set,axiom,
% 157.29/157.19 ! [V_x_2,V_Pa_2,V_xs_2,T_b] :
% 157.29/157.19 ( ! [B_i] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 157.29/157.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 157.29/157.19 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__removeAll__inj__on,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__remdups,axiom,
% 157.29/157.19 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__remdups__leq,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__remdups__id,axiom,
% 157.29/157.19 ! [V_xs,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__removeAll,axiom,
% 157.29/157.19 ! [V_x,V_xs,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remdups__id__iff__distinct,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 157.29/157.19 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__remdups__eq,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( 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)
% 157.29/157.19 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__remdups,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remdups__remdups,axiom,
% 157.29/157.19 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_removeAll__append,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_removeAll_Osimps_I2_J,axiom,
% 157.29/157.19 ! [V_xs,T_a,V_y,V_x] :
% 157.29/157.19 ( ( V_x = V_y
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( V_x != V_y
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remdups__eq__nil__iff,axiom,
% 157.29/157.19 ! [V_x_2,T_b] :
% 157.29/157.19 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 157.29/157.19 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_removeAll_Osimps_I1_J,axiom,
% 157.29/157.19 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remdups__eq__nil__right__iff,axiom,
% 157.29/157.19 ! [V_x_2,T_b] :
% 157.29/157.19 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 157.29/157.19 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remdups_Osimps_I1_J,axiom,
% 157.29/157.19 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remdups__map__remdups,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remove1__remdups,axiom,
% 157.29/157.19 ! [V_x,V_xs,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_removeAll__id,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__remove1__removeAll,axiom,
% 157.29/157.19 ! [V_x,V_xs,T_a] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.19 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remdups_Osimps_I2_J,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => 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) )
% 157.29/157.19 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => 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)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__remdups__card__conv,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__removeAll__inj,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 157.29/157.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__removeAll,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__remdups__concat,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_concat__conv__foldl,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldl__conv__concat,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sort__key__simps_I1_J,axiom,
% 157.29/157.19 ! [V_f_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__sort,axiom,
% 157.29/157.19 ! [V_xs_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__sort,axiom,
% 157.29/157.19 ! [V_xs_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__sort,axiom,
% 157.29/157.19 ! [V_xs_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 157.29/157.19 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_concat_Osimps_I1_J,axiom,
% 157.29/157.19 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_concat_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_concat__eq__Nil__conv,axiom,
% 157.29/157.19 ! [V_xss_2,T_b] :
% 157.29/157.19 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 157.29/157.19 <=> ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 157.29/157.19 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_Nil__eq__concat__conv,axiom,
% 157.29/157.19 ! [V_xss_2,T_b] :
% 157.29/157.19 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 157.29/157.19 <=> ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 157.29/157.19 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_map__concat,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__concat,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__concat,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sort__key__simps_I2_J,axiom,
% 157.29/157.19 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_concat__append,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sort__foldl__insort,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_concat__eq__concat__iff,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( ! [B_x] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => 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)) )
% 157.29/157.19 => ( 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)
% 157.29/157.19 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 157.29/157.19 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_concat__injective,axiom,
% 157.29/157.19 ! [V_ys_2,V_xs_2,T_b] :
% 157.29/157.19 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 157.29/157.19 => ( 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)
% 157.29/157.19 => ( ! [B_x] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => 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)) )
% 157.29/157.19 => V_xs_2 = V_ys_2 ) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_concat__map__singleton,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_n__lists_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose_Osimps_I3_J,axiom,
% 157.29/157.19 ! [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))))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose__aux__filter__head,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter__concat,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter__sort,axiom,
% 157.29/157.19 ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_distinct__filter,axiom,
% 157.29/157.19 ! [V_Pa_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__filter__le,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sum__length__filter__compl,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter__id__conv,axiom,
% 157.29/157.19 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.19 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
% 157.29/157.19 <=> ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter__is__subset,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter__remove1,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remove1__filter__not,axiom,
% 157.29/157.19 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.29/157.19 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter__filter,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter__insort__triv,axiom,
% 157.29/157.19 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
% 157.29/157.19 ( class_Orderings_Olinorder(T_c)
% 157.29/157.19 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_partition__filter1,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter__map,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter__append,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter_Osimps_I2_J,axiom,
% 157.29/157.19 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.29/157.19 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.19 => 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)) )
% 157.29/157.19 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.19 => 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) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter__empty__conv,axiom,
% 157.29/157.19 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.19 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.29/157.19 <=> ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_removeAll__filter__not__eq,axiom,
% 157.29/157.19 ! [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))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_remdups__filter,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_removeAll__filter__not,axiom,
% 157.29/157.19 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.29/157.19 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_partition__filter2,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_nth__transpose,axiom,
% 157.29/157.19 ! [V_xs_2,T_b,V_i_2] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose__map__map,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__filter,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__filter__map,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__filter__less,axiom,
% 157.29/157.19 ! [V_Pa_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.19 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.19 => 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))) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_partition__filter__conv,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_set__minus__filter__out,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_filter__in__sublist,axiom,
% 157.29/157.19 ! [V_s_2,V_xs_2,T_b] :
% 157.29/157.19 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose__empty,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 157.29/157.19 <=> ! [B_x] :
% 157.29/157.19 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 157.29/157.19 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__filter__conv__card,axiom,
% 157.29/157.19 ! [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))))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose__aux__filter__tail,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose_Opsimps_I3_J,axiom,
% 157.29/157.19 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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))))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose_Opsimps_I2_J,axiom,
% 157.29/157.19 ! [V_xss_2,T_b] :
% 157.29/157.19 ( 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)))
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sublist__shift__lemma__Suc,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_pick__drop__zero,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_select__weigth__drop__zero,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose_Opsimps_I1_J,axiom,
% 157.29/157.19 ! [T_b] :
% 157.29/157.19 ( 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))))
% 157.29/157.19 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose__max__length,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_transpose__aux__max,axiom,
% 157.29/157.19 ! [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)))) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldr__append,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldr_Osimps_I2_J,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldr_Osimps_I1_J,axiom,
% 157.29/157.19 ! [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 ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldr__conv__foldl,axiom,
% 157.29/157.19 ! [V_a_2,V_xs_2,T_b] :
% 157.29/157.19 ( class_Groups_Oab__semigroup__add(T_b)
% 157.29/157.19 => 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) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldr__map,axiom,
% 157.29/157.19 ! [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) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldl__foldr1,axiom,
% 157.29/157.19 ! [V_xs_2,T_b] :
% 157.29/157.19 ( class_Groups_Omonoid__add(T_b)
% 157.29/157.19 => 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)) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_foldl__foldr1__lemma,axiom,
% 157.29/157.19 ! [V_xs_2,V_a_2,T_b] :
% 157.29/157.19 ( class_Groups_Omonoid__add(T_b)
% 157.29/157.19 => 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))) ) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_length__transpose,axiom,
% 157.29/157.19 ! [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)) ).
% 157.29/157.19
% 157.29/157.19 fof(fact_sublist__def,axiom,
% 157.29/157.19 ! [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))))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sublist__shift__lemma,axiom,
% 157.29/157.20 ! [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))))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_set__upt,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_atLeastLessThan__upt,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_upt__0,axiom,
% 157.29/157.20 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_upt__eq__Nil__conv,axiom,
% 157.29/157.20 ! [V_j_2,V_i_2] :
% 157.29/157.20 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 157.29/157.20 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.20 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_upt__conv__Nil,axiom,
% 157.29/157.20 ! [V_i,V_j] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 157.29/157.20 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_upt__conv__Cons,axiom,
% 157.29/157.20 ! [V_j,V_i] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_upt__rec,axiom,
% 157.29/157.20 ! [V_j,V_i] :
% 157.29/157.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.29/157.20 => 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)) )
% 157.29/157.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.29/157.20 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_upt__add__eq__append,axiom,
% 157.29/157.20 ! [V_k,V_j,V_i] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_upt__Suc__append,axiom,
% 157.29/157.20 ! [V_j,V_i] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_upt__Suc,axiom,
% 157.29/157.20 ! [V_j,V_i] :
% 157.29/157.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.29/157.20 => 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))) )
% 157.29/157.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.29/157.20 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_drop__upt,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_hd__upt,axiom,
% 157.29/157.20 ! [V_j,V_i] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.29/157.20 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__list__of__set__range,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_take__upt,axiom,
% 157.29/157.20 ! [V_n,V_m,V_i] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_distinct__upt,axiom,
% 157.29/157.20 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_length__upt,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_upt__rec__number__of,axiom,
% 157.29/157.20 ! [V_n,V_m] :
% 157.29/157.20 ( ( 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)))
% 157.29/157.20 => 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))) )
% 157.29/157.20 & ( ~ 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)))
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_upt__eq__Cons__conv,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 157.29/157.20 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 157.29/157.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 157.29/157.20 & V_i_2 = V_x_2
% 157.29/157.20 & 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 ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_last__upt,axiom,
% 157.29/157.20 ! [V_j,V_i] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_map__Suc__upt,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_atLeastAtMost__upt,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_atLeast__upt,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_nth__upt,axiom,
% 157.29/157.20 ! [V_j,V_k,V_i] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_greaterThanAtMost__upt,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_greaterThanLessThan__upt,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_atMost__upto,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_map__nth,axiom,
% 157.29/157.20 ! [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 ).
% 157.29/157.20
% 157.29/157.20 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 157.29/157.20 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 157.29/157.20 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 157.29/157.20 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 157.29/157.20 ( class_Groups_Ocomm__monoid__add(T_b)
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_nth__map__upt,axiom,
% 157.29/157.20 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_transpose__rectangle,axiom,
% 157.29/157.20 ! [V_n_2,T_b,V_xs_2] :
% 157.29/157.20 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 157.29/157.20 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 157.29/157.20 => ( ! [B_i] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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 )
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_insort__key__remove1,axiom,
% 157.29/157.20 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_c)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 157.29/157.20 => ( 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
% 157.29/157.20 => 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 ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted_ONil,axiom,
% 157.29/157.20 ! [T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__single,axiom,
% 157.29/157.20 ! [V_x,T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__upt,axiom,
% 157.29/157.20 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__sort,axiom,
% 157.29/157.20 ! [V_xs_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__insort__insert,axiom,
% 157.29/157.20 ! [V_x_2,V_xs_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__tl,axiom,
% 157.29/157.20 ! [V_xs,T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__remove1,axiom,
% 157.29/157.20 ! [V_a,V_xs,T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__take,axiom,
% 157.29/157.20 ! [V_n,V_xs,T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__upto,axiom,
% 157.29/157.20 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__drop,axiom,
% 157.29/157.20 ! [V_n,V_xs,T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__insort,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( 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))
% 157.29/157.20 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__many,axiom,
% 157.29/157.20 ! [V_zs,V_y,V_x,T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 157.29/157.20 => 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))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__many__eq,axiom,
% 157.29/157.20 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( 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)))
% 157.29/157.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 157.29/157.20 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted_Oequations_I1_J,axiom,
% 157.29/157.20 ! [T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__butlast,axiom,
% 157.29/157.20 ! [V_xs,T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__remdups,axiom,
% 157.29/157.20 ! [V_l,T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__distinct__set__unique,axiom,
% 157.29/157.20 ! [V_ys_2,V_xs_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.29/157.20 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 157.29/157.20 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 157.29/157.20 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 157.29/157.20 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__sort__key,axiom,
% 157.29/157.20 ! [V_xs_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__insort__insert__key,axiom,
% 157.29/157.20 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 157.29/157.20 => 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__map__remove1,axiom,
% 157.29/157.20 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 157.29/157.20 => 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__insort__key,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( 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)))
% 157.29/157.20 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__map__same,axiom,
% 157.29/157.20 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__filter,axiom,
% 157.29/157.20 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 157.29/157.20 => 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__same,axiom,
% 157.29/157.20 ! [V_xs_2,V_g_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__Cons,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 157.29/157.20 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.29/157.20 & ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__append,axiom,
% 157.29/157.20 ! [V_ys_2,V_xs_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 157.29/157.20 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.29/157.20 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 157.29/157.20 & ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => ! [B_xa] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_filter__insort,axiom,
% 157.29/157.20 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 157.29/157.20 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => 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)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted_Oequations_I2_J,axiom,
% 157.29/157.20 ! [V_a1_2,V_a2_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 157.29/157.20 <=> ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 157.29/157.20 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__list__of__set,axiom,
% 157.29/157.20 ! [V_A_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.20 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 157.29/157.20 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 157.29/157.20 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_insort__remove1,axiom,
% 157.29/157.20 ! [V_xs_2,V_a_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.29/157.20 => 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 ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__equals__nth__mono,axiom,
% 157.29/157.20 ! [V_xs_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.29/157.20 <=> ! [B_j] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ! [B_i] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 157.29/157.20 => 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))) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__nth__mono,axiom,
% 157.29/157.20 ! [V_j,V_i,V_xs,T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => 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))) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_map__sorted__distinct__set__unique,axiom,
% 157.29/157.20 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_c)
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 157.29/157.20 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 157.29/157.20 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 157.29/157.20 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 157.29/157.20 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_transpose__column,axiom,
% 157.29/157.20 ! [V_i_2,V_xs_2,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_nth__nth__transpose__sorted,axiom,
% 157.29/157.20 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( 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))))
% 157.29/157.20 => ( 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))))
% 157.29/157.20 => 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) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inj__on__rev,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_distinct__rev,axiom,
% 157.29/157.20 ! [V_xs_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 157.29/157.20 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__append,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_singleton__rev__conv,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( 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)
% 157.29/157.20 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__singleton__conv,axiom,
% 157.29/157.20 ! [V_x_2,V_xs_2,T_b] :
% 157.29/157.20 ( 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))
% 157.29/157.20 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__is__Nil__conv,axiom,
% 157.29/157.20 ! [V_xs_2,T_b] :
% 157.29/157.20 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 157.29/157.20 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Nil__is__rev__conv,axiom,
% 157.29/157.20 ! [V_xs_2,T_b] :
% 157.29/157.20 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 157.29/157.20 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev_Osimps_I1_J,axiom,
% 157.29/157.20 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__concat,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__map,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__filter,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_zip__rev,axiom,
% 157.29/157.20 ! [V_ys,T_b,V_xs,T_a] :
% 157.29/157.20 ( 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)
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_set__rev,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all2__rev,axiom,
% 157.29/157.20 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.29/157.20 ( 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))
% 157.29/157.20 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all2__rev1,axiom,
% 157.29/157.20 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 157.29/157.20 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 157.29/157.20 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__rev__ident,axiom,
% 157.29/157.20 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__swap,axiom,
% 157.29/157.20 ! [V_ys_2,V_xs_2,T_b] :
% 157.29/157.20 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 157.29/157.20 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__is__rev__conv,axiom,
% 157.29/157.20 ! [V_ys_2,V_xs_2,T_b] :
% 157.29/157.20 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 157.29/157.20 <=> V_xs_2 = V_ys_2 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_listsum__rev,axiom,
% 157.29/157.20 ! [V_xs,T_a] :
% 157.29/157.20 ( class_Groups_Ocomm__monoid__add(T_a)
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_length__rev,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_foldl__foldr,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_foldr__foldl,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__eq__Cons__iff,axiom,
% 157.29/157.20 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 157.29/157.20 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 157.29/157.20 <=> 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev_Osimps_I2_J,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_hd__rev,axiom,
% 157.29/157.20 ! [T_a,V_xs] :
% 157.29/157.20 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.20 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_last__rev,axiom,
% 157.29/157.20 ! [T_a,V_xs] :
% 157.29/157.20 ( V_xs != c_List_Olist_ONil(T_a)
% 157.29/157.20 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__transpose,axiom,
% 157.29/157.20 ! [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)))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__foldl__cons,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__drop,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__take,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rotate__rev,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__nth,axiom,
% 157.29/157.20 ! [V_xs,T_a,V_n] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__update,axiom,
% 157.29/157.20 ! [V_y,V_xs,T_a,V_k] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__rev__nth__mono,axiom,
% 157.29/157.20 ! [V_j,V_i,V_xs,T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => 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))) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_foldr__max__sorted,axiom,
% 157.29/157.20 ! [V_y_2,V_xs_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 157.29/157.20 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 157.29/157.20 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 157.29/157.20 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.29/157.20 => 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) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_length__transpose__sorted,axiom,
% 157.29/157.20 ! [V_xs_2,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 157.29/157.20 => 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) )
% 157.29/157.20 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 157.29/157.20 => 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))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_transpose__column__length,axiom,
% 157.29/157.20 ! [V_i_2,V_xs_2,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_transpose__transpose,axiom,
% 157.29/157.20 ! [V_xs_2,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 157.29/157.20 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__takeWhile,axiom,
% 157.29/157.20 ! [V_Pa_2,V_xs_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_length__takeWhile__le,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__eq__all__conv,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2
% 157.29/157.20 <=> ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_set__takeWhileD,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,V_x_2,T_b] :
% 157.29/157.20 ( 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))))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_zip__takeWhile__fst,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_zip__takeWhile__snd,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__map,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 157.29/157.20 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.29/157.20 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => 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)) )
% 157.29/157.20 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__tail,axiom,
% 157.29/157.20 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.29/157.20 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__eq__take,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_distinct__takeWhile,axiom,
% 157.29/157.20 ! [V_Pa_2,V_xs_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.20 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_return__list__def,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__append1,axiom,
% 157.29/157.20 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__nth,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 157.29/157.20 ( 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))))
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_nth__length__takeWhile,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ~ 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))))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__not__last,axiom,
% 157.29/157.20 ! [T_b,V_xs_2] :
% 157.29/157.20 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 157.29/157.20 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 157.29/157.20 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 157.29/157.20 ! [V_l] :
% 157.29/157.20 ( c_List_Onat__list(V_l)
% 157.29/157.20 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_embed__list__def,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__neq__rev,axiom,
% 157.29/157.20 ! [V_x_2,V_xs_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dropWhile__neq__rev,axiom,
% 157.29/157.20 ! [V_x_2,V_xs_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__dropWhile__id,axiom,
% 157.29/157.20 ! [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 ).
% 157.29/157.20
% 157.29/157.20 fof(fact_hd__dropWhile,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 157.29/157.20 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__dropWhile,axiom,
% 157.29/157.20 ! [V_Pa_2,V_xs_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_length__dropWhile__le,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 157.29/157.20 <=> ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 157.29/157.20 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 157.29/157.20 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => 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) )
% 157.29/157.20 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_distinct__dropWhile,axiom,
% 157.29/157.20 ! [V_Pa_2,V_xs_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 157.29/157.20 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dropWhile__map,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dropWhile__append1,axiom,
% 157.29/157.20 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 157.29/157.20 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( 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)
% 157.29/157.20 <=> ( 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))
% 157.29/157.20 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dropWhile__eq__drop,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dropWhile__nth,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 157.29/157.20 ( 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))))
% 157.29/157.20 => 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)))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_listsum__map__filter,axiom,
% 157.29/157.20 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] :
% 157.29/157.20 ( class_Groups_Omonoid__add(T_c)
% 157.29/157.20 => ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => ( ~ hBOOL(hAPP(V_Pa_2,B_x))
% 157.29/157.20 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted__nth__monoI,axiom,
% 157.29/157.20 ! [V_xs,T_a] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_a)
% 157.29/157.20 => ( ! [B_i,B_j] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => 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))) ) )
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__eq__filter,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( ! [B_x] :
% 157.29/157.20 ( 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))))
% 157.29/157.20 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 157.29/157.20 ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
% 157.29/157.20 ( ! [B_i] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 157.29/157.20 => ( ( 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)))
% 157.29/157.20 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 157.29/157.20 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_length__takeWhile__less__P__nth,axiom,
% 157.29/157.20 ! [V_xs_2,T_b,V_Pa_2,V_j_2] :
% 157.29/157.20 ( ! [B_i] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => 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)))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted_Osimps,axiom,
% 157.29/157.20 ! [V_a_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 157.29/157.20 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 157.29/157.20 | ? [B_xs,B_x] :
% 157.29/157.20 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 157.29/157.20 & ! [B_xa] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 157.29/157.20 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_List_Oinsert__def,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 157.29/157.20 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_not__in__set__insert,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_insert__remdups,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_distinct__insert,axiom,
% 157.29/157.20 ! [V_x,V_xs,T_a] :
% 157.29/157.20 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 157.29/157.20 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_in__set__insert,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_List_Oset__insert,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_insert__Nil,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_maps__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_concat__map__maps,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_maps__simps_I2_J,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_maps__simps_I1_J,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_distinct__concat,axiom,
% 157.29/157.20 ! [V_xs_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 157.29/157.20 => ( ! [B_ys] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 157.29/157.20 => ( ! [B_ys] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 157.29/157.20 => ! [B_zs] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 157.29/157.20 => ( B_ys != B_zs
% 157.29/157.20 => 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)) ) ) )
% 157.29/157.20 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_measures__lesseq,axiom,
% 157.29/157.20 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => 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)))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_wf__measures,axiom,
% 157.29/157.20 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_in__measures_I1_J,axiom,
% 157.29/157.20 ! [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))))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_measures__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_in__measures_I2_J,axiom,
% 157.29/157.20 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 157.29/157.20 ( 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))))
% 157.29/157.20 <=> ( 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)))
% 157.29/157.20 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 157.29/157.20 & 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))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_measures__less,axiom,
% 157.29/157.20 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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)))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_foldl__apply,axiom,
% 157.29/157.20 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 157.29/157.20 ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => 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)) )
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_order__fun_I2_J,axiom,
% 157.29/157.20 ! [V_g_2,V_f_2,T_b,T_c] :
% 157.29/157.20 ( ( class_Orderings_Oorder(T_c)
% 157.29/157.20 & class_Enum_Oenum(T_b) )
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 157.29/157.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 157.29/157.20 & 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)))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_enum__ex__prod__def,axiom,
% 157.29/157.20 ! [V_Pa_2,T_b,T_c] :
% 157.29/157.20 ( ( class_Enum_Oenum(T_c)
% 157.29/157.20 & class_Enum_Oenum(T_b) )
% 157.29/157.20 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2))
% 157.29/157.20 <=> 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))))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_enum__ex,axiom,
% 157.29/157.20 ! [V_Pa_2,T_b] :
% 157.29/157.20 ( class_Enum_Oenum(T_b)
% 157.29/157.20 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2))
% 157.29/157.20 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_exists__code,axiom,
% 157.29/157.20 ! [V_Pa_2,T_b] :
% 157.29/157.20 ( class_Enum_Oenum(T_b)
% 157.29/157.20 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.29/157.20 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_zip__obtain__same__length,axiom,
% 157.29/157.20 ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 157.29/157.20 ( ( 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))
% 157.29/157.20 => 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)))) )
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_pos__not__random__dseq__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dropWhile__append2,axiom,
% 157.29/157.20 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 157.29/157.20 ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all2__all__nthI,axiom,
% 157.29/157.20 ! [V_Pa_2,V_b_2,T_c,V_a_2,T_b] :
% 157.29/157.20 ( 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)
% 157.29/157.20 => ( ! [B_n] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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))) )
% 157.29/157.20 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_finite__sorted__distinct__unique,axiom,
% 157.29/157.20 ! [V_A_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.20 => ? [B_x] :
% 157.29/157.20 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 157.29/157.20 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 157.29/157.20 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 157.29/157.20 & ! [B_y] :
% 157.29/157.20 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 157.29/157.20 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 157.29/157.20 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 157.29/157.20 => B_y = B_x ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_takeWhile__append2,axiom,
% 157.29/157.20 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 157.29/157.20 ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_insort__is__Cons,axiom,
% 157.29/157.20 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_c)
% 157.29/157.20 => ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Cons__eq__filter__iff,axiom,
% 157.29/157.20 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( 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)
% 157.29/157.20 <=> ? [B_us,B_vs] :
% 157.29/157.20 ( 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))
% 157.29/157.20 & ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 157.29/157.20 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_filter__eq__Cons__iff,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] :
% 157.29/157.20 ( 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)
% 157.29/157.20 <=> ? [B_us,B_vs] :
% 157.29/157.20 ( 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))
% 157.29/157.20 & ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 157.29/157.20 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_order__fun_I1_J,axiom,
% 157.29/157.20 ! [V_g_2,V_f_2,T_b,T_c] :
% 157.29/157.20 ( ( class_Orderings_Oorder(T_c)
% 157.29/157.20 & class_Enum_Oenum(T_b) )
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 157.29/157.20 <=> 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_all__code,axiom,
% 157.29/157.20 ! [V_Pa_2,T_b] :
% 157.29/157.20 ( class_Enum_Oenum(T_b)
% 157.29/157.20 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 157.29/157.20 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_enum__all,axiom,
% 157.29/157.20 ! [V_Pa_2,T_b] :
% 157.29/157.20 ( class_Enum_Oenum(T_b)
% 157.29/157.20 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2))
% 157.29/157.20 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_enum__all__prod__def,axiom,
% 157.29/157.20 ! [V_Pa_2,T_b,T_c] :
% 157.29/157.20 ( ( class_Enum_Oenum(T_c)
% 157.29/157.20 & class_Enum_Oenum(T_b) )
% 157.29/157.20 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2))
% 157.29/157.20 <=> 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))))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ball__nth,axiom,
% 157.29/157.20 ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sorted_OCons,axiom,
% 157.29/157.20 ! [V_x_2,V_xs_2,T_b] :
% 157.29/157.20 ( class_Orderings_Olinorder(T_b)
% 157.29/157.20 => ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 157.29/157.20 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 157.29/157.20 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex__length,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 157.29/157.20 <=> ? [B_n] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_in__set__conv__decomp,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 <=> ? [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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex__simps_I2_J,axiom,
% 157.29/157.20 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex__append,axiom,
% 157.29/157.20 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 157.29/157.20 <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 157.29/157.20 | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex__iff,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 157.29/157.20 <=> ? [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex__rev,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 157.29/157.20 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex__simps_I1_J,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 157.29/157.20 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_in__set__conv__decomp__first,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 <=> ? [B_ys] :
% 157.29/157.20 ( ? [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))
% 157.29/157.20 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_in__set__conv__decomp__last,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 <=> ? [B_ys,B_zs] :
% 157.29/157.20 ( 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))
% 157.29/157.20 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all__length,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 157.29/157.20 <=> ! [B_n] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_measure__function__int,axiom,
% 157.29/157.20 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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all__simps_I2_J,axiom,
% 157.29/157.20 ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all__append,axiom,
% 157.29/157.20 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 157.29/157.20 <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 157.29/157.20 & c_List_Olist__all(T_b,V_Pa_2,V_ys_2) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_measure__size,axiom,
% 157.29/157.20 ! [T_b] :
% 157.29/157.20 ( class_Nat_Osize(T_b)
% 157.29/157.20 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_is__measure_Osimps,axiom,
% 157.29/157.20 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_is__measure_Oequations,axiom,
% 157.29/157.20 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_is__measure_Ointros,axiom,
% 157.29/157.20 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all__iff,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 157.29/157.20 <=> ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_measure__snd,axiom,
% 157.29/157.20 ! [T_c,V_f_2,T_b] :
% 157.29/157.20 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_measure__fst,axiom,
% 157.29/157.20 ! [T_c,V_f_2,T_b] :
% 157.29/157.20 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all__rev,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 157.29/157.20 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all__simps_I1_J,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 157.29/157.20 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Ball__set__list__all,axiom,
% 157.29/157.20 ! [V_Pa_2,V_xs_2,T_b] :
% 157.29/157.20 ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all__iff__raw,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 157.29/157.20 <=> ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex1__simps_I2_J,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 157.29/157.20 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => 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) )
% 157.29/157.20 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_transfer__morphism__int__nat,axiom,
% 157.29/157.20 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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex1__simps_I1_J,axiom,
% 157.29/157.20 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bool_Osize_I3_J,axiom,
% 157.29/157.20 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bool_Osize_I4_J,axiom,
% 157.29/157.20 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex1__iff,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
% 157.29/157.20 <=> ? [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_x))
% 157.29/157.20 & ! [B_y] :
% 157.29/157.20 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_y)) )
% 157.29/157.20 => B_y = B_x ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 157.29/157.20 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 157.29/157.20 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.20 => 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) )
% 157.29/157.20 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 157.29/157.20 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 157.29/157.20 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.20 => 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) )
% 157.29/157.20 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 157.29/157.20 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_pos__empty__def,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_neg__bind__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_neg__map__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_neg__single__def,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_pos__bind__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_pos__map__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_pos__single__def,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_length__splice,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_splice_Osimps_I3_J,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_splice_Osimps_I1_J,axiom,
% 157.29/157.20 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 157.29/157.20
% 157.29/157.20 fof(fact_splice__Nil2,axiom,
% 157.29/157.20 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 157.29/157.20
% 157.29/157.20 fof(fact_splice_Osimps_I2_J,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_New__DSequence_Opos__single__def,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_acyclicP__converse,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( 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))))
% 157.29/157.20 <=> 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_converse__meet,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_conversep__noteq,axiom,
% 157.29/157.20 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.20 ( 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))
% 157.29/157.20 <=> V_x_2 != V_y_2 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_conversepD,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 157.29/157.20 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_conversep_Ointros,axiom,
% 157.29/157.20 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_conversep_Oequations,axiom,
% 157.29/157.20 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 157.29/157.20 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_conversep__iff,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 157.29/157.20 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_conversep__conversep,axiom,
% 157.29/157.20 ! [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 ).
% 157.29/157.20
% 157.29/157.20 fof(fact_conversep__eq,axiom,
% 157.29/157.20 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 157.29/157.20
% 157.29/157.20 fof(fact_converse__pred__comp,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_converse__join,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_conversep__converse__eq,axiom,
% 157.29/157.20 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 157.29/157.20 ( 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))
% 157.29/157.20 <=> 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_,axiom,
% 157.29/157.20 ! [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)))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_tl__replicate,axiom,
% 157.29/157.20 ! [V_x,T_a,V_n] :
% 157.29/157.20 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_replicate__length__filter,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_length__replicate,axiom,
% 157.29/157.20 ! [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 ).
% 157.29/157.20
% 157.29/157.20 fof(fact_map__replicate__const,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_replicate__app__Cons__same,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_replicate__Suc,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rev__replicate,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_take__replicate,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_hd__replicate,axiom,
% 157.29/157.20 ! [V_x,T_a,V_n] :
% 157.29/157.20 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.20 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_drop__replicate,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_last__replicate,axiom,
% 157.29/157.20 ! [V_x,T_a,V_n] :
% 157.29/157.20 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.20 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_zip__replicate,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Bex__set__replicate,axiom,
% 157.29/157.20 ! [V_Pa_2,V_a_2,V_n_2,T_b] :
% 157.29/157.20 ( ? [B_x] :
% 157.29/157.20 ( 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))))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.29/157.20 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Ball__set__replicate,axiom,
% 157.29/157.20 ! [V_Pa_2,V_a_2,V_n_2,T_b] :
% 157.29/157.20 ( ! [B_x] :
% 157.29/157.20 ( 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))))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 157.29/157.20 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_replicate__eq__replicate,axiom,
% 157.29/157.20 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 157.29/157.20 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 157.29/157.20 <=> ( V_m_2 = V_n_2
% 157.29/157.20 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.20 => V_x_2 = V_y_2 ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_nth__replicate,axiom,
% 157.29/157.20 ! [V_x,T_a,V_n,V_i] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 157.29/157.20 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_append__replicate__commute,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_replicate__add,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_filter__replicate,axiom,
% 157.29/157.20 ! [V_n_2,T_b,V_x_2,V_Pa_2] :
% 157.29/157.20 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => 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) )
% 157.29/157.20 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_concat__replicate__trivial,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_replicate__0,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_empty__replicate,axiom,
% 157.29/157.20 ! [V_x_2,V_n_2,T_b] :
% 157.29/157.20 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 157.29/157.20 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_replicate__empty,axiom,
% 157.29/157.20 ! [V_x_2,V_n_2,T_b] :
% 157.29/157.20 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 157.29/157.20 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_map__replicate,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_in__set__replicate,axiom,
% 157.29/157.20 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 157.29/157.20 ( 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))))
% 157.29/157.20 <=> ( V_x_2 = V_y_2
% 157.29/157.20 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_replicate__append__same,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_map__replicate__trivial,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_set__replicate__conv__if,axiom,
% 157.29/157.20 ! [V_x_2,T_b,V_n_2] :
% 157.29/157.20 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.20 => 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)) )
% 157.29/157.20 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.20 => 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_set__replicate,axiom,
% 157.29/157.20 ! [V_x_2,T_b,V_n_2] :
% 157.29/157.20 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_set__replicate__Suc,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_small__lazy__list_Osimps,axiom,
% 157.29/157.20 ! [V_d_2,T_b] :
% 157.29/157.20 ( class_Lazy__Sequence_Osmall__lazy(T_b)
% 157.29/157.20 => 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)))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_eq__comp__r,axiom,
% 157.29/157.20 ! [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 ).
% 157.29/157.20
% 157.29/157.20 fof(fact_small__lazy__prod__def,axiom,
% 157.29/157.20 ! [V_d,T_b,T_a] :
% 157.29/157.20 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 157.29/157.20 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_New__DSequence_Opos__union__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact__01,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence_Oinject,axiom,
% 157.29/157.20 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 157.29/157.20 ( 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)
% 157.29/157.20 <=> ( V_a_2 = V_a_H_2
% 157.29/157.20 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_pos__union__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_small__lazy_H_Osimps,axiom,
% 157.29/157.20 ! [V_i,V_d] :
% 157.29/157.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 157.29/157.20 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 157.29/157.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 157.29/157.20 => 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)))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_small__lazy_H_Opsimps,axiom,
% 157.29/157.20 ! [V_i_2,V_d_2] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 157.29/157.20 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 157.29/157.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 157.29/157.20 => 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)))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_small__lazy__int__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_small__lazy_H_Opinduct,axiom,
% 157.29/157.20 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( ! [B_d,B_i] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 157.29/157.20 => 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)))) )
% 157.29/157.20 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i)) ) )
% 157.29/157.20 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_size__code,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence__size__code,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_seq__case,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_yieldn__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_refl__on__INTER,axiom,
% 157.29/157.20 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 157.29/157.20 ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.29/157.20 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_List_Omember__def,axiom,
% 157.29/157.20 ! [V_x_2,V_xs_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
% 157.29/157.20 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_member__rec_I2_J,axiom,
% 157.29/157.20 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_member__set,axiom,
% 157.29/157.20 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_member__rec_I1_J,axiom,
% 157.29/157.20 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( 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))
% 157.29/157.20 <=> ( V_x_2 = V_y_2
% 157.29/157.20 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_in__set__member,axiom,
% 157.29/157.20 ! [V_xs_2,V_x_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex1__iff__raw,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
% 157.29/157.20 <=> ? [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_x))
% 157.29/157.20 & ! [B_y] :
% 157.29/157.20 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_y)) )
% 157.29/157.20 => B_y = B_x ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_setsum__UNION__zero,axiom,
% 157.29/157.20 ! [V_f_2,V_S_2,T_b,T_c] :
% 157.29/157.20 ( class_Groups_Ocomm__monoid__add(T_c)
% 157.29/157.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
% 157.29/157.20 => ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
% 157.29/157.20 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 157.29/157.20 => ( ! [B_T1] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
% 157.29/157.20 => ! [B_T2] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
% 157.29/157.20 => ( B_T1 != B_T2
% 157.29/157.20 => ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
% 157.29/157.20 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
% 157.29/157.20 => 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) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_THE__default__def,axiom,
% 157.29/157.20 ! [V_d_2,T_b,V_Pa_2] :
% 157.29/157.20 ( ( ? [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.29/157.20 & ! [B_y] :
% 157.29/157.20 ( hBOOL(hAPP(V_Pa_2,B_y))
% 157.29/157.20 => B_y = B_x ) )
% 157.29/157.20 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) )
% 157.29/157.20 & ( ~ ? [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(V_Pa_2,B_x))
% 157.29/157.20 & ! [B_y] :
% 157.29/157.20 ( hBOOL(hAPP(V_Pa_2,B_y))
% 157.29/157.20 => B_y = B_x ) )
% 157.29/157.20 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2 ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_INF2__I,axiom,
% 157.29/157.20 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,T_b] :
% 157.29/157.20 ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.20 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) )
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_SUP2__E,axiom,
% 157.29/157.20 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => ~ ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.20 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_finite__maxlen,axiom,
% 157.29/157.20 ! [V_M_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
% 157.29/157.20 => ? [B_n] :
% 157.29/157.20 ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence_Osize_I3_J,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence_Osize_I1_J,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact__02,axiom,
% 157.29/157.20 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence_Osimps_I2_J,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence_Osimps_I3_J,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence_Osimps_I4_J,axiom,
% 157.29/157.20 ! [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 ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all__iff__all__interval__int,axiom,
% 157.29/157.20 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.29/157.20 ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
% 157.29/157.20 <=> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex__iff__not__all__inverval__int,axiom,
% 157.29/157.20 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.29/157.20 ( c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
% 157.29/157.20 <=> ~ 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_all__interval__int__def,axiom,
% 157.29/157.20 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.29/157.20 ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2)
% 157.29/157.20 <=> ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Random_Osimps,axiom,
% 157.29/157.20 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 157.29/157.20 ( ( 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)))
% 157.29/157.20 => 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)) )
% 157.29/157.20 & ( ~ 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)))
% 157.29/157.20 => 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))))))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_exE__realizer,axiom,
% 157.29/157.20 ! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( ! [B_x,B_y] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x))
% 157.29/157.20 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 157.29/157.20 => 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Random__Sequence_Oempty__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Random__Sequence_Osingle__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Random__Sequence_Omap__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Image__Collect__split,axiom,
% 157.29/157.20 ! [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)))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Bex__set__list__ex,axiom,
% 157.29/157.20 ! [V_Pa_2,V_xs_2,T_b] :
% 157.29/157.20 ( ? [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex__iff__raw,axiom,
% 157.29/157.20 ! [V_xs_2,V_Pa_2,T_b] :
% 157.29/157.20 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 157.29/157.20 <=> ? [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_SUPR__bool__eq,axiom,
% 157.29/157.20 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bex__empty,axiom,
% 157.29/157.20 ! [V_Pa_2,T_b] :
% 157.29/157.20 ~ ? [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_finite__Collect__bex,axiom,
% 157.29/157.20 ! [V_Qa_2,T_c,V_A_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.20 => ( 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)))))
% 157.29/157.20 <=> ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.20 => 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)))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bex__UNIV,axiom,
% 157.29/157.20 ! [V_Pa_2,T_b] :
% 157.29/157.20 ( ? [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Union__eq,axiom,
% 157.29/157.20 ! [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)))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_UN__eq,axiom,
% 157.29/157.20 ! [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))))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_INT__eq,axiom,
% 157.29/157.20 ! [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))))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Sup__apply,axiom,
% 157.29/157.20 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.29/157.20 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.20 => 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)))))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Sup__fun__def,axiom,
% 157.29/157.20 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.29/157.20 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.20 => 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)))))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Inf__apply,axiom,
% 157.29/157.20 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.29/157.20 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.20 => 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)))))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Inf__fun__def,axiom,
% 157.29/157.20 ! [V_x_2,V_A_2,T_c,T_b] :
% 157.29/157.20 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 157.29/157.20 => 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)))))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_max__extp_Ointros,axiom,
% 157.29/157.20 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 157.29/157.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 157.29/157.20 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.20 => ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 157.29/157.20 => ? [B_xa] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 157.29/157.20 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) )
% 157.29/157.20 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_max__extp_Osimps,axiom,
% 157.29/157.20 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 157.29/157.20 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 157.29/157.20 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 157.29/157.20 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 157.29/157.20 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 157.29/157.20 & ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 157.29/157.20 => ? [B_xa] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 157.29/157.20 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_fun__lub__def,axiom,
% 157.29/157.20 ! [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)))))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lexord__trans,axiom,
% 157.29/157.20 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 157.29/157.20 => ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__less__than,axiom,
% 157.29/157.20 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__lex__prod,axiom,
% 157.29/157.20 ! [V_R2_2,T_c,V_R1_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,V_R1_2)
% 157.29/157.20 => ( c_Relation_Otrans(T_c,V_R2_2)
% 157.29/157.20 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__inv__image,axiom,
% 157.29/157.20 ! [V_f_2,T_c,V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__reflclI,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__Int,axiom,
% 157.29/157.20 ! [V_s_2,V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => ( c_Relation_Otrans(T_b,V_s_2)
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__rtrancl,axiom,
% 157.29/157.20 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__finite__psubset,axiom,
% 157.29/157.20 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__Id__on,axiom,
% 157.29/157.20 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__trancl,axiom,
% 157.29/157.20 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trancl__id,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__Id,axiom,
% 157.29/157.20 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lexord__transI,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__converse,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.29/157.20 <=> c_Relation_Otrans(T_b,V_r_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_listrel__trans,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__O__subset,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__def,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 <=> ! [B_x,B_y] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => ! [B_z] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => 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)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_transD,axiom,
% 157.29/157.20 ! [V_ca_2,V_b_2,V_a_2,V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => ( 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))
% 157.29/157.20 => ( 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))
% 157.29/157.20 => 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)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_transp__def,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Predicate_Otransp(T_b,V_r_2)
% 157.29/157.20 <=> 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_trans__diff__Id,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => ( c_Relation_Oantisym(T_b,V_r_2)
% 157.29/157.20 => 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_antisym__empty,axiom,
% 157.29/157.20 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_antisym__converse,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.29/157.20 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_antisym__Id,axiom,
% 157.29/157.20 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_transpE,axiom,
% 157.29/157.20 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 157.29/157.20 ( c_Predicate_Otransp(T_b,V_r_2)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
% 157.29/157.20 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_antisym__Id__on,axiom,
% 157.29/157.20 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_antisym__subset,axiom,
% 157.29/157.20 ! [V_s_2,V_r_2,T_b] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => ( c_Relation_Oantisym(T_b,V_s_2)
% 157.29/157.20 => c_Relation_Oantisym(T_b,V_r_2) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_antisym__def,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Oantisym(T_b,V_r_2)
% 157.29/157.20 <=> ! [B_x,B_y] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => ( 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))
% 157.29/157.20 => B_x = B_y ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_antisymD,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Oantisym(T_b,V_r_2)
% 157.29/157.20 => ( 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))
% 157.29/157.20 => ( 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))
% 157.29/157.20 => V_a_2 = V_b_2 ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_antisym__reflcl,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_acyclic__impl__antisym__rtrancl,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 157.29/157.20 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_equivp__reflp__symp__transp,axiom,
% 157.29/157.20 ! [V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.29/157.20 <=> ( c_Predicate_Oreflp(T_b,V_R_2)
% 157.29/157.20 & c_Predicate_Osymp(T_b,V_R_2)
% 157.29/157.20 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_equivpI,axiom,
% 157.29/157.20 ! [V_R_2,T_b] :
% 157.29/157.20 ( c_Predicate_Oreflp(T_b,V_R_2)
% 157.29/157.20 => ( c_Predicate_Osymp(T_b,V_R_2)
% 157.29/157.20 => ( c_Predicate_Otransp(T_b,V_R_2)
% 157.29/157.20 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sympE,axiom,
% 157.29/157.20 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 157.29/157.20 ( c_Predicate_Osymp(T_b,V_r_2)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 157.29/157.20 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_equivpE,axiom,
% 157.29/157.20 ! [V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.29/157.20 => ~ ( c_Predicate_Oreflp(T_b,V_R_2)
% 157.29/157.20 => ( c_Predicate_Osymp(T_b,V_R_2)
% 157.29/157.20 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__trans__comp__subset,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 => ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_part__equivp__refl__symp__transp,axiom,
% 157.29/157.20 ! [V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.29/157.20 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 157.29/157.20 & c_Predicate_Osymp(T_b,V_R_2)
% 157.29/157.20 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_symD,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 => ( 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))
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__def,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 <=> ! [B_x,B_y] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_listrel__sym,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__conv__converse__eq,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__converse,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 157.29/157.20 <=> c_Relation_Osym(T_b,V_r_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__Id,axiom,
% 157.29/157.20 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__Un,axiom,
% 157.29/157.20 ! [V_s_2,V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 => ( c_Relation_Osym(T_b,V_s_2)
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__trancl,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_part__equivp__def,axiom,
% 157.29/157.20 ! [V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.29/157.20 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 157.29/157.20 & ! [B_x,B_y] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 157.29/157.20 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 157.29/157.20 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
% 157.29/157.20 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_part__equivp__symp,axiom,
% 157.29/157.20 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 157.29/157.20 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_part__equivp__transp,axiom,
% 157.29/157.20 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 157.29/157.20 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__Id__on,axiom,
% 157.29/157.20 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__rtrancl,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_equivp__implies__part__equivp,axiom,
% 157.29/157.20 ! [V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.29/157.20 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__Int,axiom,
% 157.29/157.20 ! [V_s_2,V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 => ( c_Relation_Osym(T_b,V_s_2)
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__Un__converse,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__inv__image,axiom,
% 157.29/157.20 ! [V_f_2,T_c,V_r_2,T_b] :
% 157.29/157.20 ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_sym__Int__converse,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_equiv__def,axiom,
% 157.29/157.20 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.20 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.20 & c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 & c_Relation_Otrans(T_b,V_r_2) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_equivI,axiom,
% 157.29/157.20 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.20 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.20 => ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 => ( c_Relation_Otrans(T_b,V_r_2)
% 157.29/157.20 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_equivE,axiom,
% 157.29/157.20 ! [V_r_2,V_A_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 157.29/157.20 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 157.29/157.20 => ( c_Relation_Osym(T_b,V_r_2)
% 157.29/157.20 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_symp__def,axiom,
% 157.29/157.20 ! [V_r_2,T_b] :
% 157.29/157.20 ( c_Predicate_Osymp(T_b,V_r_2)
% 157.29/157.20 <=> 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_part__equivpI,axiom,
% 157.29/157.20 ! [T_b,V_R_2] :
% 157.29/157.20 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 157.29/157.20 => ( c_Predicate_Osymp(T_b,V_R_2)
% 157.29/157.20 => ( c_Predicate_Otransp(T_b,V_R_2)
% 157.29/157.20 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_part__equivpE,axiom,
% 157.29/157.20 ! [V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.29/157.20 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 157.29/157.20 => ( c_Predicate_Osymp(T_b,V_R_2)
% 157.29/157.20 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_part__equivp__typedef,axiom,
% 157.29/157.20 ! [V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 157.29/157.20 => ? [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))))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inj__iff,axiom,
% 157.29/157.20 ! [V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.20 <=> 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__o__cancel,axiom,
% 157.29/157.20 ! [V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__into__def,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__f__eq,axiom,
% 157.29/157.20 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.20 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 157.29/157.20 => 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 ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__f__f,axiom,
% 157.29/157.20 ! [V_x_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.20 => 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 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__into__f__f,axiom,
% 157.29/157.20 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.20 => 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 ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__into__f__eq,axiom,
% 157.29/157.20 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 157.29/157.20 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 157.29/157.20 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_f__inv__into__f,axiom,
% 157.29/157.20 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 157.29/157.20 => 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 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__into__into,axiom,
% 157.29/157.20 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__into__injective,axiom,
% 157.29/157.20 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 157.29/157.20 ( 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)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 157.29/157.20 => V_x_2 = V_y_2 ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_surj__iff__all,axiom,
% 157.29/157.20 ! [V_f_2,T_b,T_c] :
% 157.29/157.20 ( 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))
% 157.29/157.20 <=> ! [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 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_surj__f__inv__f,axiom,
% 157.29/157.20 ! [V_y_2,V_f_2,T_b,T_c] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => 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 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_image__surj__f__inv__f,axiom,
% 157.29/157.20 ! [V_A_2,V_f_2,T_b,T_c] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => 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 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_image__inv__into__cancel,axiom,
% 157.29/157.20 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 157.29/157.20 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 157.29/157.20 => 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 ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__id,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_o__inv__o__cancel,axiom,
% 157.29/157.20 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.20 => 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 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inj__imp__surj__inv,axiom,
% 157.29/157.20 ! [V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_image__inv__f__f,axiom,
% 157.29/157.20 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.20 => 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 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__image__comp,axiom,
% 157.29/157.20 ! [V_X_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.20 => 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 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_surj__imp__inj__inv,axiom,
% 157.29/157.20 ! [V_f_2,T_b,T_c] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inj__on__inv__into,axiom,
% 157.29/157.20 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__into__image__cancel,axiom,
% 157.29/157.20 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 157.29/157.20 => 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 ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__into__comp,axiom,
% 157.29/157.20 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 157.29/157.20 => ( 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))))
% 157.29/157.20 => 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) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_surj__iff,axiom,
% 157.29/157.20 ! [V_f_2,T_b,T_c] :
% 157.29/157.20 ( 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))
% 157.29/157.20 <=> 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inj__transfer,axiom,
% 157.29/157.20 ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.20 => ( ! [B_y] :
% 157.29/157.20 ( 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)))))
% 157.29/157.20 => 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))) )
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_fold__image__UN__disjoint,axiom,
% 157.29/157.20 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
% 157.29/157.20 ( class_Groups_Ocomm__monoid__mult(T_d)
% 157.29/157.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
% 157.29/157.20 => ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 157.29/157.20 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 157.29/157.20 => ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 157.29/157.20 => ! [B_xa] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
% 157.29/157.20 => ( B_x != B_xa
% 157.29/157.20 => 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)) ) ) )
% 157.29/157.20 => 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) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_nat__of__induct,axiom,
% 157.29/157.20 ! [V_Pa_2,V_y_2] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.29/157.20 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_nat__of__cases,axiom,
% 157.29/157.20 ! [V_y_2] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.29/157.20 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_of__nat__induct,axiom,
% 157.29/157.20 ! [V_x_2,V_Pa_2] :
% 157.29/157.20 ( ! [B_y] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_of__nat__cases,axiom,
% 157.29/157.20 ! [V_x_2] :
% 157.29/157.20 ~ ! [B_y] :
% 157.29/157.20 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
% 157.29/157.20 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence_Orecs_I1_J,axiom,
% 157.29/157.20 ! [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 ).
% 157.29/157.20
% 157.29/157.20 fof(fact_beyond__def,axiom,
% 157.29/157.20 ! [V_l,V_k] :
% 157.29/157.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 157.29/157.20 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 157.29/157.20 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 157.29/157.20 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_beyond__zero,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_lazy__sequence_Orecs_I2_J,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__image__Collect__eq,axiom,
% 157.29/157.20 ! [V_Pa_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_curry__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_curryI,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 157.29/157.20 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__id,axiom,
% 157.29/157.20 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_o__inv__distrib,axiom,
% 157.29/157.20 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__inv__into,axiom,
% 157.29/157.20 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__into__inv__into__eq,axiom,
% 157.29/157.20 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__imp__bij__inv,axiom,
% 157.29/157.20 ! [V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inv__inv__eq,axiom,
% 157.29/157.20 ! [V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_curry__split,axiom,
% 157.29/157.20 ! [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 ).
% 157.29/157.20
% 157.29/157.20 fof(fact_split__curry,axiom,
% 157.29/157.20 ! [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 ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bijI,axiom,
% 157.29/157.20 ! [V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.20 => ( 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))
% 157.29/157.20 => 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__def,axiom,
% 157.29/157.20 ! [V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 157.29/157.20 & 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)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__Disj__Un,axiom,
% 157.29/157.20 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => ( 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))
% 157.29/157.20 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 157.29/157.20 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 157.29/157.20 => 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)) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__combine,axiom,
% 157.29/157.20 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.29/157.20 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 157.29/157.20 => ( 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))
% 157.29/157.20 => 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)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__same__card,axiom,
% 157.29/157.20 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.29/157.20 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__the__inv__into,axiom,
% 157.29/157.20 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__empty2,axiom,
% 157.29/157.20 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__empty1,axiom,
% 157.29/157.20 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)
% 157.29/157.20 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__finite,axiom,
% 157.29/157.20 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.29/157.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.20 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_BIJ,axiom,
% 157.29/157.20 ! [V_B_2,T_c,V_A_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 157.29/157.20 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 157.29/157.20 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__id__iff,axiom,
% 157.29/157.20 ! [V_B_2,V_A_2,T_b] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 157.29/157.20 <=> V_A_2 = V_B_2 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__id,axiom,
% 157.29/157.20 ! [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))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__subset,axiom,
% 157.29/157.20 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.29/157.20 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 157.29/157.20 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__is__surj,axiom,
% 157.29/157.20 ! [V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__imp__surj,axiom,
% 157.29/157.20 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_inj__on__imp__bij__betw,axiom,
% 157.29/157.20 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__def,axiom,
% 157.29/157.20 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.29/157.20 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.20 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__imp__inj__on,axiom,
% 157.29/157.20 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.29/157.20 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__is__inj,axiom,
% 157.29/157.20 ! [V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__image__Compl__eq,axiom,
% 157.29/157.20 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_finite__vimage__iff,axiom,
% 157.29/157.20 ! [V_F_2,V_h_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 157.29/157.20 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_curry__conv,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_curryE,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 157.29/157.20 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_curryD,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 157.29/157.20 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__comp__iff,axiom,
% 157.29/157.20 ! [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] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 157.29/157.20 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 157.29/157.20 <=> 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__trans,axiom,
% 157.29/157.20 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 157.29/157.20 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 157.29/157.20 => 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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__comp,axiom,
% 157.29/157.20 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__betw__comp__iff2,axiom,
% 157.29/157.20 ! [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] :
% 157.29/157.20 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 157.29/157.20 => ( 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))
% 157.29/157.20 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 157.29/157.20 <=> 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) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__image__INT,axiom,
% 157.29/157.20 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_vimage__subset__eq,axiom,
% 157.29/157.20 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( 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))
% 157.29/157.20 <=> 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bij__vimage__eq__inv__image,axiom,
% 157.29/157.20 ! [V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 157.29/157.20 ! [V_M_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 157.29/157.20 => ? [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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Cantor__Bernstein,axiom,
% 157.29/157.20 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 157.29/157.20 => ( 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))
% 157.29/157.20 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 157.29/157.20 => ( 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))
% 157.29/157.20 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_ex__bij__betw__nat__finite,axiom,
% 157.29/157.20 ! [V_M_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 157.29/157.20 => ? [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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_ex__bij__betw__finite__nat,axiom,
% 157.29/157.20 ! [V_M_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 157.29/157.20 => ? [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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_refl__on__UNION,axiom,
% 157.29/157.20 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 157.29/157.20 ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 157.29/157.20 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 157.29/157.20 => 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)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bex__reg__eqv,axiom,
% 157.29/157.20 ! [V_Pa_2,V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.29/157.20 => ( ? [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_in__respects,axiom,
% 157.29/157.20 ! [V_R_2,V_x_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
% 157.29/157.20 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Respects__def,axiom,
% 157.29/157.20 ! [V_x_2,V_R_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
% 157.29/157.20 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_bex__reg__right,axiom,
% 157.29/157.20 ! [V_Pa_2,V_Qa_2,V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.29/157.20 => ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(V_Qa_2,B_x))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 157.29/157.20 => ( ? [B_x1] : hBOOL(hAPP(V_Qa_2,B_x1))
% 157.29/157.20 => ? [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 157.29/157.20 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_babs__reg__eqv,axiom,
% 157.29/157.20 ! [V_Pa_2,T_c,V_R_2,T_b] :
% 157.29/157.20 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 157.29/157.20 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2 ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_Babs__def,axiom,
% 157.29/157.20 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
% 157.29/157.20 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_wf__weak__decr__stable,axiom,
% 157.29/157.20 ! [V_r_2,V_f_2,T_b] :
% 157.29/157.20 ( ! [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)))
% 157.29/157.20 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
% 157.29/157.20 => ? [B_i] :
% 157.29/157.20 ! [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) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_INT__anti__mono,axiom,
% 157.29/157.20 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 157.29/157.20 => ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.20 => 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))) )
% 157.29/157.20 => 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))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_INT__greatest,axiom,
% 157.29/157.20 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
% 157.29/157.20 ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 157.29/157.20 => 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))) )
% 157.29/157.20 => 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))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_rtrancl__induct2,axiom,
% 157.29/157.20 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2))
% 157.29/157.20 => ( ! [B_a,B_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ! [B_aa,B_ba] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
% 157.29/157.20 => hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) )
% 157.29/157.20 => hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_converse__rtranclE2,axiom,
% 157.29/157.20 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( 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)
% 157.29/157.20 => ~ ! [B_a,B_b] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => ~ 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))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_converse__rtrancl__induct2,axiom,
% 157.29/157.20 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2))
% 157.29/157.20 => ( ! [B_a,B_b,B_aa,B_ba] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => ( 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)))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))
% 157.29/157.20 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) )
% 157.29/157.20 => hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_congruentI,axiom,
% 157.29/157.20 ! [T_c,V_f_2,V_r_2,T_b] :
% 157.29/157.20 ( ! [B_y,B_z] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
% 157.29/157.20 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_congruent2I_H,axiom,
% 157.29/157.20 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
% 157.29/157.20 ( ! [B_y1,B_z1] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => ! [B_y2,B_z2] :
% 157.29/157.20 ( 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))
% 157.29/157.20 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
% 157.29/157.20 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact__03,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__all__iff__all__interval__nat,axiom,
% 157.29/157.20 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.29/157.20 ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
% 157.29/157.20 <=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact__04,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_all__interval__nat__def,axiom,
% 157.29/157.20 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.29/157.20 ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2)
% 157.29/157.20 <=> ! [B_x] :
% 157.29/157.20 ( 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)))
% 157.29/157.20 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
% 157.29/157.20 ! [V_j_2,V_i_2,V_Pa_2] :
% 157.29/157.20 ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
% 157.29/157.20 <=> ~ 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) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact__05,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_folding__image_Ocong,axiom,
% 157.29/157.20 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 157.29/157.20 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 157.29/157.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 157.29/157.20 => ( ! [B_x] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 157.29/157.20 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 157.29/157.20 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact__06,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact__07,axiom,
% 157.29/157.20 ! [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) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_New__DSequence_Opos__map__def,axiom,
% 157.29/157.20 ! [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)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_power__dvd__imp__le,axiom,
% 157.29/157.20 ! [V_n,V_m,V_i] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_Oorder__refl,axiom,
% 157.29/157.20 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__0__right,axiom,
% 157.29/157.20 ! [V_a,T_a] :
% 157.29/157.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__1__left,axiom,
% 157.29/157.20 ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__setprod,axiom,
% 157.29/157.20 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
% 157.29/157.20 ( class_Rings_Ocomm__semiring__1(T_c)
% 157.29/157.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
% 157.29/157.20 ! [V_y_2,V_x_2,T_b] :
% 157.29/157.20 ( ( class_Divides_Osemiring__div(T_b)
% 157.29/157.20 & class_Int_Onumber(T_b) )
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 157.29/157.20 <=> c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 157.29/157.20 ! [V_ca_2,V_b_2,V_a_2] :
% 157.29/157.20 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
% 157.29/157.20 <=> ( V_a_2 = V_b_2
% 157.29/157.20 & V_b_2 = V_ca_2 ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 157.29/157.20 ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2] :
% 157.29/157.20 ( V_a_2 = V_b_2
% 157.29/157.20 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2] :
% 157.29/157.20 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
% 157.29/157.20 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 157.29/157.20 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 157.29/157.20 ! [V_l_2,V_k_2] :
% 157.29/157.20 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
% 157.29/157.20 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 157.29/157.20 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2] :
% 157.29/157.20 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 157.29/157.20 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 157.29/157.20 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 157.29/157.20 ! [V_l_2,V_k_2] :
% 157.29/157.20 ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 157.29/157.20 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 157.29/157.20 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 157.29/157.20 ! [V_k_2,V_l_2] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 157.29/157.20 => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 157.29/157.20 ! [V_a_2,V_b_2] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 157.29/157.20 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 157.29/157.20 ! [V_k_2,V_l_2] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 157.29/157.20 => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2] :
% 157.29/157.20 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)
% 157.29/157.20 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2] :
% 157.29/157.20 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 157.29/157.20 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd_OatLeastatMost__empty,axiom,
% 157.29/157.20 ! [V_a_2,V_b_2] :
% 157.29/157.20 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 157.29/157.20 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
% 157.29/157.20 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__1__iff__1,axiom,
% 157.29/157.20 ! [V_m_2] :
% 157.29/157.20 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 157.29/157.20 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_div__power,axiom,
% 157.29/157.20 ! [V_n,V_x,V_y,T_a] :
% 157.29/157.20 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 157.29/157.20 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_div__add,axiom,
% 157.29/157.20 ! [V_y,V_x,V_z,T_a] :
% 157.29/157.20 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
% 157.29/157.20 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__imp__mod__0,axiom,
% 157.29/157.20 ! [V_b,V_a,T_a] :
% 157.29/157.20 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 157.29/157.20 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__eq__mod__eq__0,axiom,
% 157.29/157.20 ! [V_b_2,V_a_2,T_b] :
% 157.29/157.20 ( class_Divides_Osemiring__div(T_b)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 157.29/157.20 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__power__same,axiom,
% 157.29/157.20 ! [V_n,V_y,V_x,T_a] :
% 157.29/157.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__mod__iff,axiom,
% 157.29/157.20 ! [V_m_2,V_n_2,V_k_2,T_b] :
% 157.29/157.20 ( class_Divides_Osemiring__div(T_b)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))
% 157.29/157.20 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_mod__mod__cancel,axiom,
% 157.29/157.20 ! [V_a,V_b,V_c,T_a] :
% 157.29/157.20 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 157.29/157.20 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__mod,axiom,
% 157.29/157.20 ! [V_n,V_m,V_k,T_a] :
% 157.29/157.20 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__mod__imp__dvd,axiom,
% 157.29/157.20 ! [V_n,V_m,V_k,T_a] :
% 157.29/157.20 ( class_Divides_Osemiring__div(T_a)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_div__dvd__div,axiom,
% 157.29/157.20 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 157.29/157.20 ( class_Divides_Osemiring__div(T_b)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2))
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ca_2),V_a_2)))
% 157.29/157.20 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)) ) ) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__if__abs__eq,axiom,
% 157.29/157.20 ! [V_k,V_l,T_a] :
% 157.29/157.20 ( class_Rings_Olinordered__idom(T_a)
% 157.29/157.20 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
% 157.29/157.20 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_abs__dvd__iff,axiom,
% 157.29/157.20 ! [V_k_2,V_m_2,T_b] :
% 157.29/157.20 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
% 157.29/157.20 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__abs__iff,axiom,
% 157.29/157.20 ! [V_k_2,V_m_2,T_b] :
% 157.29/157.20 ( class_Rings_Olinordered__idom(T_b)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
% 157.29/157.20 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 157.29/157.20
% 157.29/157.20 fof(fact_dvd__0__left,axiom,
% 157.29/157.20 ! [V_a,T_a] :
% 157.29/157.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.20 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 157.29/157.20 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oeq__iff,axiom,
% 157.29/157.21 ! [V_y_2,V_x_2] :
% 157.29/157.21 ( V_x_2 = V_y_2
% 157.29/157.21 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 157.29/157.21 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Ole__less,axiom,
% 157.29/157.21 ! [V_y_2,V_x_2] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 157.29/157.21 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 157.29/157.21 | V_x_2 = V_y_2 ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oless__le,axiom,
% 157.29/157.21 ! [V_y_2,V_x_2] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 157.29/157.21 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 157.29/157.21 & V_x_2 != V_y_2 ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oneq__le__trans,axiom,
% 157.29/157.21 ! [V_b,V_a] :
% 157.29/157.21 ( V_a != V_b
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oeq__refl,axiom,
% 157.29/157.21 ! [V_y,V_x] :
% 157.29/157.21 ( V_x = V_y
% 157.29/157.21 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oantisym__conv,axiom,
% 157.29/157.21 ! [V_x_2,V_y_2] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 157.29/157.21 <=> V_x_2 = V_y_2 ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 157.29/157.21 ! [V_y,V_x] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 157.29/157.21 | V_x = V_y ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Ole__neq__trans,axiom,
% 157.29/157.21 ! [V_b,V_a] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 157.29/157.21 => ( V_a != V_b
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 157.29/157.21 ! [V_c,V_b,V_a] :
% 157.29/157.21 ( V_a = V_b
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 157.29/157.21 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 157.29/157.21 ! [V_c,V_b,V_a] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 157.29/157.21 => ( V_b = V_c
% 157.29/157.21 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd__antisym,axiom,
% 157.29/157.21 ! [V_n,V_m] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 157.29/157.21 => V_m = V_n ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oantisym,axiom,
% 157.29/157.21 ! [V_y,V_x] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 157.29/157.21 => V_x = V_y ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oorder__trans,axiom,
% 157.29/157.21 ! [V_z,V_y,V_x] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 157.29/157.21 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 157.29/157.21 ! [V_c,V_b,V_a] :
% 157.29/157.21 ( V_a = V_b
% 157.29/157.21 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) )
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Ole__less__trans,axiom,
% 157.29/157.21 ! [V_z,V_y,V_x] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oless__imp__neq,axiom,
% 157.29/157.21 ! [V_y,V_x] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 157.29/157.21 => V_x != V_y ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oless__not__sym,axiom,
% 157.29/157.21 ! [V_y,V_x] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 157.29/157.21 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oless__imp__le,axiom,
% 157.29/157.21 ! [V_y,V_x] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 157.29/157.21 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oless__imp__not__less,axiom,
% 157.29/157.21 ! [V_y,V_x] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 157.29/157.21 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 157.29/157.21 ! [V_y,V_x] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 157.29/157.21 => V_x != V_y ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 157.29/157.21 ! [V_y,V_x] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 157.29/157.21 => V_y != V_x ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 157.29/157.21 ! [V_c,V_b,V_a] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 157.29/157.21 => ( V_b = V_c
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oless__le__trans,axiom,
% 157.29/157.21 ! [V_z,V_y,V_x] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oless__asym_H,axiom,
% 157.29/157.21 ! [V_b,V_a] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 157.29/157.21 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oless__trans,axiom,
% 157.29/157.21 ! [V_z,V_y,V_x] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 157.29/157.21 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd_Oless__asym,axiom,
% 157.29/157.21 ! [V_y,V_x] :
% 157.29/157.21 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 157.29/157.21 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 157.29/157.21 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd__refl,axiom,
% 157.29/157.21 ! [V_a,T_a] :
% 157.29/157.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.21 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd__trans,axiom,
% 157.29/157.21 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 157.29/157.21 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_one__dvd,axiom,
% 157.29/157.21 ! [V_a,T_a] :
% 157.29/157.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.21 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_nat__dvd__1__iff__1,axiom,
% 157.29/157.21 ! [V_m_2] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 157.29/157.21 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd__add,axiom,
% 157.29/157.21 ! [V_c,V_b,V_a,T_a] :
% 157.29/157.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 157.29/157.21 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 157.29/157.21 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ) ).
% 157.29/157.21
% 157.29/157.21 fof(fact_dvd__reduce,axiom,
% 157.29/157.21 ! [V_n_2,V_k_2] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))
% 157.29/157.21 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ) ).
% 157.29/157.21
% 157.29/157.21 %----Arity declarations (218)
% 157.29/157.21 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 157.29/157.21 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Lattices_Obounded__lattice(T_1)
% 157.29/157.21 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 157.29/157.21 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Lattices_Obounded__lattice(T_1)
% 157.29/157.21 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Lattices_Obounded__lattice(T_1)
% 157.29/157.21 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Lattices_Olattice(T_1)
% 157.29/157.21 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Lattices_Olattice(T_1)
% 157.29/157.21 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Lattices_Odistrib__lattice(T_1)
% 157.29/157.21 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Lattices_Oboolean__algebra(T_1)
% 157.29/157.21 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Orderings_Opreorder,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Orderings_Opreorder(T_1)
% 157.29/157.21 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 157.29/157.21 ! [T_1,T_2] :
% 157.29/157.21 ( ( class_Finite__Set_Ofinite(T_2)
% 157.29/157.21 & class_Finite__Set_Ofinite(T_1) )
% 157.29/157.21 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Lattices_Olattice,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Lattices_Olattice(T_1)
% 157.29/157.21 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Orderings_Oorder,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Orderings_Oorder(T_1)
% 157.29/157.21 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Orderings_Otop,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Orderings_Otop(T_1)
% 157.29/157.21 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Orderings_Oord,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Orderings_Oord(T_1)
% 157.29/157.21 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Orderings_Obot,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Orderings_Obot(T_1)
% 157.29/157.21 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Groups_Ouminus,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Groups_Ouminus(T_1)
% 157.29/157.21 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Groups_Ominus,axiom,
% 157.29/157.21 ! [T_2,T_1] :
% 157.29/157.21 ( class_Groups_Ominus(T_1)
% 157.29/157.21 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_fun__Enum_Oenum,axiom,
% 157.29/157.21 ! [T_1,T_2] :
% 157.29/157.21 ( ( class_Enum_Oenum(T_2)
% 157.29/157.21 & class_Enum_Oenum(T_1) )
% 157.29/157.21 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Com__Ocom__Nat_Osize,axiom,
% 157.29/157.21 class_Nat_Osize(tc_Com_Ocom) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 157.29/157.21 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 157.29/157.21 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 157.29/157.21 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 157.29/157.21 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 157.29/157.21 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 157.29/157.21 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 157.29/157.21 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 157.29/157.21 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 157.29/157.21 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 157.29/157.21 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 157.29/157.21 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 157.29/157.21 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 157.29/157.21 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 157.29/157.21 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 157.29/157.21 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 157.29/157.21 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 157.29/157.21 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 157.29/157.21 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 157.29/157.21 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 157.29/157.21 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 157.29/157.21 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 157.29/157.21 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 157.29/157.21 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 157.29/157.21 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 157.29/157.21 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 157.29/157.21 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 157.29/157.21 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 157.29/157.21 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 157.29/157.21 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 157.29/157.21 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 157.29/157.21 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 157.29/157.21 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 157.29/157.21 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 157.29/157.21 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 157.29/157.21 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 157.29/157.21 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 157.29/157.21 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 157.29/157.21 class_Orderings_Opreorder(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 157.29/157.21 class_Orderings_Olinorder(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 157.29/157.21 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 157.29/157.21 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 157.29/157.21 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 157.29/157.21 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 157.29/157.21 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 157.29/157.21 class_Lattices_Olattice(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 157.29/157.21 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 157.29/157.21 class_Divides_Oring__div(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 157.29/157.21 class_Rings_Omult__zero(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 157.29/157.21 class_Orderings_Oorder(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 157.29/157.21 class_Int_Oring__char__0(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 157.29/157.21 class_Int_Onumber__ring(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 157.29/157.21 class_Rings_Osemiring(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 157.29/157.21 class_Orderings_Oord(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 157.29/157.21 class_Groups_Ouminus(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 157.29/157.21 class_Groups_Osgn__if(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 157.29/157.21 class_Groups_Oabs__if(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 157.29/157.21 class_Rings_Oring__1(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 157.29/157.21 class_Groups_Ominus(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Power_Opower,axiom,
% 157.29/157.21 class_Power_Opower(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 157.29/157.21 class_Groups_Ozero(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Oring,axiom,
% 157.29/157.21 class_Rings_Oring(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 157.29/157.21 class_Rings_Oidom(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Int_Onumber,axiom,
% 157.29/157.21 class_Int_Onumber(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Int__Oint__Groups_Oone,axiom,
% 157.29/157.21 class_Groups_Oone(tc_Int_Oint) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 157.29/157.21 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 157.29/157.21 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 157.29/157.21 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 157.29/157.21 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 157.29/157.21 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 157.29/157.21 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 157.29/157.21 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 157.29/157.21 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 157.29/157.21 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 157.29/157.21 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 157.29/157.21 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 157.29/157.21 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 157.29/157.21 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 157.29/157.21 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 157.29/157.21 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 157.29/157.21 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 157.29/157.21 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 157.29/157.21 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 157.29/157.21 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 157.29/157.21 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 157.29/157.21 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 157.29/157.21 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 157.29/157.21 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 157.29/157.21 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 157.29/157.21 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 157.29/157.21 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 157.29/157.21 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 157.29/157.21 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 157.29/157.21 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 157.29/157.21 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 157.29/157.21 class_Lattices_Olattice(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 157.29/157.21 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 157.29/157.21 class_Orderings_Oorder(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 157.29/157.21 class_Rings_Osemiring(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 157.29/157.21 class_Orderings_Oord(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 157.29/157.21 class_Orderings_Obot(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 157.29/157.21 class_Groups_Ominus(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Power_Opower,axiom,
% 157.29/157.21 class_Power_Opower(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 157.29/157.21 class_Groups_Ozero(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 157.29/157.21 class_Int_Onumber(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 157.29/157.21 class_Groups_Oone(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 157.29/157.21 class_Nat_Osize(tc_Nat_Onat) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 157.29/157.21 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 157.29/157.21 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 157.29/157.21 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 157.29/157.21 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 157.29/157.21 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 157.29/157.21 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 157.29/157.21 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 157.29/157.21 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 157.29/157.21 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 157.29/157.21 class_Lattices_Olattice(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 157.29/157.21 class_Orderings_Oorder(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 157.29/157.21 class_Orderings_Otop(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 157.29/157.21 class_Orderings_Oord(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 157.29/157.21 class_Orderings_Obot(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 157.29/157.21 class_Groups_Ouminus(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 157.29/157.21 class_Groups_Ominus(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 157.29/157.21 class_Enum_Oenum(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 157.29/157.21 class_Nat_Osize(tc_HOL_Obool) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Com__Ostate__Nat_Osize,axiom,
% 157.29/157.21 class_Nat_Osize(tc_Com_Ostate) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 157.29/157.21 ! [T_1] :
% 157.29/157.21 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 157.29/157.21 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_List__Olist__Nat_Osize,axiom,
% 157.29/157.21 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 157.29/157.21 ! [T_1,T_2] :
% 157.29/157.21 ( ( class_Finite__Set_Ofinite(T_2)
% 157.29/157.21 & class_Finite__Set_Ofinite(T_1) )
% 157.29/157.21 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_sum__Enum_Oenum,axiom,
% 157.29/157.21 ! [T_1,T_2] :
% 157.29/157.21 ( ( class_Enum_Oenum(T_2)
% 157.29/157.21 & class_Enum_Oenum(T_1) )
% 157.29/157.21 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_sum__Nat_Osize,axiom,
% 157.29/157.21 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 157.29/157.21 ! [T_1] :
% 157.29/157.21 ( class_Finite__Set_Ofinite(T_1)
% 157.29/157.21 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 157.29/157.21 ! [T_1] :
% 157.29/157.21 ( class_Enum_Oenum(T_1)
% 157.29/157.21 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 157.29/157.21 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
% 157.29/157.21 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 157.29/157.21 ! [T_1,T_2] :
% 157.29/157.21 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 157.29/157.21 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 157.29/157.21 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 157.29/157.21 ! [T_1,T_2] :
% 157.29/157.21 ( ( class_Finite__Set_Ofinite(T_2)
% 157.29/157.21 & class_Finite__Set_Ofinite(T_1) )
% 157.29/157.21 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_prod__Enum_Oenum,axiom,
% 157.29/157.21 ! [T_1,T_2] :
% 157.29/157.21 ( ( class_Enum_Oenum(T_2)
% 157.29/157.21 & class_Enum_Oenum(T_1) )
% 157.29/157.21 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_prod__Nat_Osize,axiom,
% 157.29/157.21 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 157.29/157.21 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 157.29/157.21 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 157.29/157.21 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 157.29/157.21 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 157.29/157.21 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 157.29/157.21 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 157.29/157.21 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 157.29/157.21 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 157.29/157.21 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 157.29/157.21 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 157.29/157.21 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 157.29/157.21 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 157.29/157.21 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 157.29/157.21 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 157.29/157.21 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 157.29/157.21 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 157.29/157.21 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 157.29/157.21 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 157.29/157.21 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 157.29/157.21 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 157.29/157.21 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 157.29/157.21 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 157.29/157.21 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 157.29/157.21 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 157.29/157.21 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 157.29/157.21 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 157.29/157.21 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 157.29/157.21 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 157.29/157.21 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 157.29/157.21 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 157.29/157.21 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 157.29/157.21 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 157.29/157.21 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 157.29/157.21 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 157.29/157.21 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 157.29/157.21 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 157.29/157.21 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 157.29/157.21 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 157.29/157.21 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 157.29/157.21 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 157.29/157.21 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 157.29/157.21 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 157.29/157.21
% 157.29/157.21 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 157.29/157.21 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 157.29/157.21
% 157.29/157.21 %----Helper facts (20)
% 157.29/157.21 fof(help_c__COMBI__1,axiom,
% 157.29/157.21 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__COMBK__1,axiom,
% 157.29/157.21 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__COMBB__1,axiom,
% 157.29/157.21 ! [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)) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__COMBC__1,axiom,
% 157.29/157.21 ! [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) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__COMBS__1,axiom,
% 157.29/157.21 ! [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)) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fequal__1,axiom,
% 157.29/157.21 ! [V_y_2,V_x_2] :
% 157.29/157.21 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 157.29/157.21 | V_x_2 = V_y_2 ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fequal__2,axiom,
% 157.29/157.21 ! [V_y_2,V_x_2] :
% 157.29/157.21 ( V_x_2 != V_y_2
% 157.29/157.21 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fFalse__1,axiom,
% 157.29/157.21 ~ hBOOL(c_fFalse) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fTrue__1,axiom,
% 157.29/157.21 hBOOL(c_fTrue) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fNot__1,axiom,
% 157.29/157.21 ! [V_Pa_2] :
% 157.29/157.21 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2))
% 157.29/157.21 | ~ hBOOL(V_Pa_2) ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fNot__2,axiom,
% 157.29/157.21 ! [V_Pa_2] :
% 157.29/157.21 ( ~ ~ hBOOL(V_Pa_2)
% 157.29/157.21 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fconj__1,axiom,
% 157.29/157.21 ! [V_Qa_2,V_Pa_2] :
% 157.29/157.21 ( ~ hBOOL(V_Pa_2)
% 157.29/157.21 | ~ hBOOL(V_Qa_2)
% 157.29/157.21 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fconj__2,axiom,
% 157.29/157.21 ! [V_Qa_2,V_Pa_2] :
% 157.29/157.21 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 157.29/157.21 | hBOOL(V_Pa_2) ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fconj__3,axiom,
% 157.29/157.21 ! [V_Qa_2,V_Pa_2] :
% 157.29/157.21 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 157.29/157.21 | hBOOL(V_Qa_2) ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fdisj__1,axiom,
% 157.29/157.21 ! [V_Qa_2,V_Pa_2] :
% 157.29/157.21 ( ~ hBOOL(V_Pa_2)
% 157.29/157.21 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fdisj__2,axiom,
% 157.29/157.21 ! [V_Pa_2,V_Qa_2] :
% 157.29/157.21 ( ~ hBOOL(V_Qa_2)
% 157.29/157.21 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fdisj__3,axiom,
% 157.29/157.21 ! [V_Qa_2,V_Pa_2] :
% 157.29/157.21 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
% 157.29/157.21 | hBOOL(V_Pa_2)
% 157.29/157.21 | hBOOL(V_Qa_2) ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fimplies__1,axiom,
% 157.29/157.21 ! [V_Qa_2,V_Pa_2] :
% 157.29/157.21 ( hBOOL(V_Pa_2)
% 157.29/157.21 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fimplies__2,axiom,
% 157.29/157.21 ! [V_Pa_2,V_Qa_2] :
% 157.29/157.21 ( ~ hBOOL(V_Qa_2)
% 157.29/157.21 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(help_c__fimplies__3,axiom,
% 157.29/157.21 ! [V_Qa_2,V_Pa_2] :
% 157.29/157.21 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
% 157.29/157.21 | ~ hBOOL(V_Pa_2)
% 157.29/157.21 | hBOOL(V_Qa_2) ) ).
% 157.29/157.21
% 157.29/157.21 %----Conjectures (3)
% 157.29/157.21 fof(conj_0,hypothesis,
% 157.29/157.21 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,v_P,v_c,v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ).
% 157.29/157.21
% 157.29/157.21 fof(conj_1,hypothesis,
% 157.29/157.21 ! [B_Z,B_s] :
% 157.29/157.21 ( hBOOL(hAPP(hAPP(v_Q_H,B_Z),B_s))
% 157.29/157.21 => hBOOL(hAPP(hAPP(v_Q,B_Z),B_s)) ) ).
% 157.29/157.21
% 157.29/157.21 fof(conj_2,conjecture,
% 157.29/157.21 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,v_P,v_c,v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ).
% 157.29/157.21
% 157.29/157.21 %------------------------------------------------------------------------------
% 157.29/157.21 %-------------------------------------------
% 157.29/157.21 % Proof found
% 157.29/157.21 % SZS status Theorem for theBenchmark
% 157.29/157.21 % SZS output start Proof
% 157.29/157.21 %ClaNum:10408(EqnAxiom:3077)
% 157.29/157.21 %VarNum:70551(SingletonVarNum:20396)
% 157.29/157.21 %MaxLitNum:8
% 157.29/157.21 %MaxfuncDepth:13
% 157.29/157.21 %SharedTerms:996
% 157.29/157.21 %goalClause: 4713
% 157.29/157.21 %singleGoalClaCount:1
% 157.29/157.21 [3081]P1(a905)
% 157.29/157.21 [3082]P1(a909)
% 157.29/157.21 [3083]P105(a187)
% 157.29/157.21 [3084]P106(a905)
% 157.29/157.21 [3085]P106(a909)
% 157.29/157.21 [3086]P106(a1)
% 157.29/157.21 [3087]P106(a99)
% 157.29/157.21 [3088]P107(a905)
% 157.29/157.21 [3089]P107(a909)
% 157.29/157.21 [3090]P107(a1)
% 157.29/157.21 [3091]P107(a99)
% 157.29/157.21 [3092]P108(a909)
% 157.29/157.21 [3093]P108(a1)
% 157.29/157.21 [3094]P108(a99)
% 157.29/157.21 [3095]P109(a905)
% 157.29/157.21 [3096]P109(a909)
% 157.29/157.21 [3097]P109(a1)
% 157.29/157.21 [3098]P109(a99)
% 157.29/157.21 [3099]P2(a905)
% 157.29/157.21 [3100]P2(a909)
% 157.29/157.21 [3101]P2(a1)
% 157.29/157.21 [3102]P2(a99)
% 157.29/157.21 [3103]P77(a905)
% 157.29/157.21 [3104]P77(a909)
% 157.29/157.21 [3105]P77(a1)
% 157.29/157.21 [3106]P78(a905)
% 157.29/157.21 [3107]P100(a905)
% 157.29/157.21 [3108]P100(a909)
% 157.29/157.21 [3109]P100(a1)
% 157.29/157.21 [3110]P79(a1)
% 157.29/157.21 [3111]P3(a905)
% 157.29/157.21 [3112]P3(a912)
% 157.29/157.21 [3113]P66(a1)
% 157.29/157.21 [3114]P110(a1)
% 157.29/157.21 [3115]P67(a909)
% 157.29/157.21 [3116]P67(a1)
% 157.29/157.21 [3117]P67(a99)
% 157.29/157.21 [3118]P101(a905)
% 157.29/157.21 [3119]P101(a909)
% 157.29/157.21 [3120]P101(a1)
% 157.29/157.21 [3121]P98(a905)
% 157.29/157.21 [3122]P98(a909)
% 157.29/157.21 [3123]P98(a1)
% 157.29/157.21 [3124]P69(a909)
% 157.29/157.21 [3125]P69(a1)
% 157.29/157.21 [3126]P69(a99)
% 157.29/157.21 [3127]P83(a909)
% 157.29/157.21 [3128]P83(a1)
% 157.29/157.21 [3129]P83(a99)
% 157.29/157.21 [3130]P70(a909)
% 157.29/157.21 [3131]P70(a1)
% 157.29/157.21 [3132]P70(a99)
% 157.29/157.21 [3133]P71(a909)
% 157.29/157.21 [3134]P71(a1)
% 157.29/157.21 [3135]P71(a99)
% 157.29/157.21 [3136]P68(a909)
% 157.29/157.21 [3137]P68(a1)
% 157.29/157.21 [3138]P68(a99)
% 157.29/157.21 [3139]P84(a909)
% 157.29/157.21 [3140]P84(a1)
% 157.29/157.21 [3141]P84(a99)
% 157.29/157.21 [3142]P85(a909)
% 157.29/157.21 [3143]P85(a1)
% 157.29/157.21 [3144]P85(a99)
% 157.29/157.21 [3145]P73(a1)
% 157.29/157.21 [3146]P111(a1)
% 157.29/157.21 [3147]P112(a909)
% 157.29/157.21 [3148]P112(a1)
% 157.29/157.21 [3149]P112(a99)
% 157.29/157.21 [3150]P137(a909)
% 157.29/157.21 [3151]P137(a1)
% 157.29/157.21 [3152]P118(a1)
% 157.29/157.21 [3153]P138(a909)
% 157.29/157.21 [3154]P138(a1)
% 157.29/157.21 [3155]P138(a99)
% 157.29/157.21 [3156]P113(a909)
% 157.29/157.21 [3157]P113(a1)
% 157.29/157.21 [3158]P113(a99)
% 157.29/157.21 [3159]P4(a905)
% 157.29/157.21 [3160]P74(a909)
% 157.29/157.21 [3161]P74(a1)
% 157.29/157.21 [3162]P74(a99)
% 157.29/157.21 [3163]P80(a909)
% 157.29/157.21 [3164]P80(a1)
% 157.29/157.21 [3165]P80(a99)
% 157.29/157.21 [3166]P81(a909)
% 157.29/157.21 [3167]P81(a1)
% 157.29/157.21 [3168]P81(a99)
% 157.29/157.21 [3169]P124(a909)
% 157.29/157.21 [3170]P124(a1)
% 157.29/157.21 [3171]P124(a99)
% 157.29/157.21 [3172]P127(a1)
% 157.29/157.21 [3173]P87(a909)
% 157.29/157.21 [3174]P87(a1)
% 157.29/157.21 [3175]P87(a99)
% 157.29/157.21 [3176]P82(a909)
% 157.29/157.21 [3177]P82(a1)
% 157.29/157.21 [3178]P82(a99)
% 157.29/157.21 [3179]P75(a1)
% 157.29/157.21 [3180]P130(a909)
% 157.29/157.21 [3181]P130(a1)
% 157.29/157.21 [3182]P130(a99)
% 157.29/157.21 [3183]P139(a1)
% 157.29/157.21 [3184]P132(a909)
% 157.29/157.21 [3185]P132(a1)
% 157.29/157.21 [3186]P132(a99)
% 157.29/157.21 [3187]P142(a909)
% 157.29/157.21 [3188]P142(a1)
% 157.29/157.21 [3189]P142(a99)
% 157.29/157.21 [3190]P88(a909)
% 157.29/157.21 [3191]P88(a1)
% 157.29/157.21 [3192]P88(a99)
% 157.29/157.21 [3193]P133(a909)
% 157.29/157.21 [3194]P133(a1)
% 157.29/157.21 [3195]P133(a99)
% 157.29/157.21 [3196]P135(a909)
% 157.29/157.21 [3197]P135(a1)
% 157.29/157.21 [3198]P135(a99)
% 157.29/157.21 [3199]P134(a909)
% 157.29/157.21 [3200]P134(a1)
% 157.29/157.21 [3201]P134(a99)
% 157.29/157.21 [3202]P125(a1)
% 157.29/157.21 [3203]P126(a1)
% 157.29/157.21 [3204]P131(a909)
% 157.29/157.21 [3205]P131(a1)
% 157.29/157.21 [3206]P131(a99)
% 157.29/157.21 [3207]P119(a909)
% 157.29/157.21 [3208]P119(a1)
% 157.29/157.21 [3209]P119(a99)
% 157.29/157.21 [3210]P128(a909)
% 157.29/157.21 [3211]P128(a1)
% 157.29/157.21 [3212]P128(a99)
% 157.29/157.21 [3213]P129(a1)
% 157.29/157.21 [3214]P140(a1)
% 157.29/157.21 [3215]P92(a1)
% 157.29/157.21 [3216]P93(a909)
% 157.29/157.21 [3217]P93(a1)
% 157.29/157.21 [3218]P93(a99)
% 157.29/157.21 [3219]P94(a1)
% 157.29/157.21 [3220]P102(a909)
% 157.29/157.21 [3221]P102(a1)
% 157.29/157.21 [3222]P102(a99)
% 157.29/157.21 [3223]P143(a909)
% 157.29/157.21 [3224]P143(a1)
% 157.29/157.21 [3225]P143(a99)
% 157.29/157.21 [3226]P86(a1)
% 157.29/157.21 [3227]P136(a1)
% 157.29/157.21 [3228]P95(a905)
% 157.29/157.21 [3229]P89(a905)
% 157.29/157.21 [3230]P89(a1)
% 157.29/157.21 [3231]P120(a1)
% 157.29/157.21 [3232]P114(a1)
% 157.29/157.21 [3233]P141(a1)
% 157.29/157.21 [3234]P72(a1)
% 157.29/157.21 [3235]P59(a909)
% 157.29/157.21 [3236]P59(a1)
% 157.29/157.21 [3237]P59(a99)
% 157.29/157.21 [3238]P60(a1)
% 157.29/157.21 [3239]P115(a909)
% 157.29/157.21 [3240]P115(a1)
% 157.29/157.21 [3241]P115(a99)
% 157.29/157.21 [3242]P144(a909)
% 157.29/157.21 [3243]P144(a1)
% 157.29/157.21 [3244]P144(a99)
% 157.29/157.21 [3245]P90(a1)
% 157.29/157.21 [3246]P116(a905)
% 157.29/157.21 [3247]P99(a905)
% 157.29/157.21 [3248]P76(a909)
% 157.29/157.21 [3249]P76(a1)
% 157.29/157.21 [3250]P76(a99)
% 157.29/157.21 [3251]P117(a909)
% 157.29/157.21 [3252]P91(a909)
% 157.29/157.21 [3253]P91(a1)
% 157.29/157.21 [3254]P91(a99)
% 157.29/157.21 [3255]P61(a905)
% 157.29/157.21 [3256]P61(a912)
% 157.29/157.21 [3257]P104(a905)
% 157.29/157.21 [3258]P104(a909)
% 157.29/157.21 [3259]P104(a906)
% 157.29/157.21 [3260]P104(a99)
% 157.29/157.21 [3261]P104(a912)
% 157.29/157.21 [3262]P104(a907)
% 157.29/157.21 [3263]P104(a322)
% 157.29/157.21 [3264]P103(a1)
% 157.29/157.21 [3265]P103(a912)
% 157.29/157.21 [3266]P97(a905)
% 157.29/157.21 [3282]P36(a909,a239)
% 157.29/157.21 [3283]P36(a909,a316)
% 157.29/157.21 [3284]P37(a909,a239)
% 157.29/157.21 [4624]~E(a97,a82)
% 157.29/157.21 [4625]~P105(a238)
% 157.29/157.21 [3078]E(f2(a1),a82)
% 157.29/157.21 [3079]E(f3(a99),a4)
% 157.29/157.21 [3080]E(f100(a99),a5)
% 157.29/157.21 [3267]E(f188(a909),f2(a909))
% 157.29/157.21 [3268]E(f28(a25),f2(a909))
% 157.29/157.21 [3269]E(f101(a909),f232(a909))
% 157.29/157.21 [3270]E(f110(a909),f233(a909))
% 157.29/157.21 [3271]E(f102(a1),f31(a1))
% 157.29/157.21 [3272]E(f83(a238),f2(a909))
% 157.29/157.21 [3273]E(f83(a187),f2(a909))
% 157.29/157.21 [3274]P5(f77(a1))
% 157.29/157.21 [3275]P5(f2(a1))
% 157.29/157.21 [3331]P36(f916(a909,a909),a32)
% 157.29/157.21 [3676]E(f319(a909,a909,a239,a239),a32)
% 157.29/157.21 [4626]~E(f77(a1),f2(a1))
% 157.29/157.21 [3276]E(f6(f2(a99)),f2(a909))
% 157.29/157.21 [3277]E(f111(f2(a909)),f2(a909))
% 157.29/157.21 [3286]E(f326(f78(a1),a82),a82)
% 157.29/157.21 [3289]E(f326(a112,f2(a909)),f77(a909))
% 157.29/157.21 [3290]E(f326(a104,f77(a1)),f77(a909))
% 157.29/157.21 [3291]E(f326(a5,f77(a909)),f77(a99))
% 157.29/157.21 [3293]E(f326(a5,f2(a909)),f2(a99))
% 157.29/157.21 [3295]E(f326(f103(a1),a82),f2(a1))
% 157.29/157.21 [3296]E(f326(f103(a99),a82),f2(a99))
% 157.29/157.21 [3297]E(f326(a104,f2(a1)),f2(a909))
% 157.29/157.21 [3298]E(f326(f189(a905),a238),f2(a909))
% 157.29/157.21 [3299]E(f326(f189(a905),a187),f2(a909))
% 157.29/157.21 [3300]E(f326(f189(a906),a25),f2(a909))
% 157.29/157.21 [3301]E(f326(f103(a909),a82),f2(a909))
% 157.29/157.21 [3307]E(f326(f78(a1),f77(a1)),a97)
% 157.29/157.21 [3315]E(f326(f189(a99),f2(a99)),f2(a909))
% 157.29/157.21 [3316]E(f326(f100(a1),f77(a909)),f77(a1))
% 157.29/157.21 [3317]E(f326(f100(a1),f2(a909)),f2(a1))
% 157.29/157.21 [3318]E(f326(f78(a1),f2(a1)),f2(a1))
% 157.29/157.21 [3328]E(f326(a104,f77(a1)),f326(a112,f2(a909)))
% 157.29/157.21 [3329]E(f317(f916(a909,a909),a32),a33)
% 157.29/157.21 [3330]E(f318(f916(a909,a909),a32),a34)
% 157.29/157.21 [3357]E(f326(f281(a909),f2(a909)),f188(f917(a909,a905)))
% 157.29/157.21 [3358]E(f326(f282(a909),f2(a909)),f241(f917(a909,a905)))
% 157.29/157.21 [3366]P39(f188(f917(a1,a905)))
% 157.29/157.21 [3400]E(f326(f326(f3(a99),f2(a99)),f77(a99)),f2(a99))
% 157.29/157.21 [3475]P105(f326(f326(f235(a1),a97),f2(a1)))
% 157.29/157.21 [3499]P105(f326(f326(f234(a1),f2(a1)),f77(a1)))
% 157.29/157.21 [3501]P105(f326(f326(f235(a1),f2(a1)),f77(a1)))
% 157.29/157.21 [3707]E(f326(f326(f288(a909,a909,a909),a316),f306(a909,a316)),a239)
% 157.29/157.21 [3745]P40(a1,a909,a104,f326(f234(a1),f2(a1)))
% 157.29/157.21 [3749]E(f326(f326(f39(a909,f917(a909,a905)),f241(f917(a909,a905))),f303(a909)),f188(f917(a909,a905)))
% 157.29/157.21 [3750]E(f326(f326(f40(a909,f917(a909,a905)),f241(f917(a909,a905))),f281(a909)),f241(f917(a909,a905)))
% 157.29/157.21 [3751]E(f326(f326(f40(a909,f917(a909,a905)),f241(f917(a909,a905))),f300(a909)),f241(f917(a909,a905)))
% 157.29/157.21 [3752]E(f326(f326(f40(a909,f917(a909,a905)),f241(f917(a909,a905))),f282(a909)),f241(f917(a909,a905)))
% 157.29/157.21 [3767]P24(a909,a1,f100(a1),f241(f917(a909,a905)))
% 157.29/157.21 [3781]P40(a909,a1,f100(a1),f326(f18(a905,a909),a187))
% 157.29/157.21 [3918]E(f326(f72(a909,a99,a1,a5),a104),f103(a99))
% 157.29/157.21 [4143]P55(a99,a909,a22,a5,f241(f917(a909,a905)))
% 157.29/157.21 [4147]P55(a1,f917(f916(a909,a909),a905),a107,a88,a98)
% 157.29/157.21 [4404]E(f257(a1,a1,a1,a1,f31(a1),f78(a1)),a51)
% 157.29/157.21 [4641]~E(f326(f103(a1),a97),f326(f103(a1),a82))
% 157.29/157.21 [4642]~P105(f326(a193,f77(a1)))
% 157.29/157.21 [4643]~P105(f326(a193,f2(a1)))
% 157.29/157.21 [4680]~P105(f326(f326(f235(a1),a82),f2(a1)))
% 157.29/157.21 [3349]E(f326(f326(f3(a1),a97),a97),a82)
% 157.29/157.21 [3364]E(f326(f100(a1),f326(a112,f2(a909))),f77(a1))
% 157.29/157.21 [3429]E(f326(f35(a912),f241(f917(a912,a905))),f77(a909))
% 157.29/157.21 [3449]P105(f326(a193,f326(f103(a1),a97)))
% 157.29/157.21 [3451]P105(f326(f326(f234(a1),a97),a82))
% 157.29/157.21 [3453]P105(f326(f326(f235(a1),a97),a82))
% 157.29/157.21 [3510]E(f326(f326(f308(a909),f2(a909)),f188(f917(a909,a905))),f326(f300(a909),f2(a909)))
% 157.29/157.21 [3565]P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),a82)))
% 157.29/157.21 [3577]E(f326(f309(a909,a909,a112),f241(f917(a909,a905))),f326(f303(a909),f2(a909)))
% 157.29/157.21 [3614]P7(f916(a909,a909),f241(f917(f916(a909,a909),a905)),a108)
% 157.29/157.21 [3925]E(f326(f72(a909,a1,a99,f100(a1)),a22),a24)
% 157.29/157.21 [3986]P36(a909,f326(f261(f916(a909,a909)),f326(f256(a909,a909,a905),f235(a909))))
% 157.29/157.21 [4671]~P105(f326(a193,f326(f103(a1),a82)))
% 157.29/157.21 [4672]~P105(f326(f326(f234(a1),a82),a97))
% 157.29/157.21 [4673]~P105(f326(f326(f235(a1),a82),a82))
% 157.29/157.21 [4674]~P105(f326(f326(f235(a1),a82),a97))
% 157.29/157.21 [4675]~P105(f326(f326(f235(a1),a97),a97))
% 157.29/157.21 [4686]~P105(f326(f61(a909),f241(f917(a909,a905))))
% 157.29/157.21 [4687]~P105(f326(f61(a1),f241(f917(a1,a905))))
% 157.29/157.21 [4292]P23(a904,a918,f326(f326(f308(f908(a904)),f91(a904,a919,a920,a921)),f188(f917(f908(a904),a905))))
% 157.29/157.21 [4570]E(f326(f256(a1,a1,a905),f326(f326(f10(f917(a1,a905),f917(a1,a905),a1),f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f235(a1),f2(a1))))),f326(f326(f9(a1,a1,f917(a1,a905)),f326(f326(f10(f917(a1,f917(a1,a905)),f917(a1,f917(a1,a905)),a1),f9(a1,a1,a905)),f326(f326(f10(f917(a1,a1),f917(a1,f917(a1,a905)),a1),f326(f10(a1,f917(a1,a905),a1),a323)),a217))),f77(a1)))),a213)
% 157.29/157.21 [4713]~P23(a904,a918,f326(f326(f308(f908(a904)),f91(a904,a919,a920,a922)),f188(f917(f908(a904),a905))))
% 157.29/157.21 [3651]E(f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97),f326(f78(a1),a97))
% 157.29/157.21 [3689]E(f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97),f326(f326(f3(a1),a82),a97))
% 157.29/157.21 [3851]E(f326(f326(f60(f916(a909,a909)),f241(f917(f916(a909,a909),a905))),a108),a98)
% 157.29/157.21 [3880]E(f326(f103(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f77(a1))
% 157.29/157.21 [3881]E(f326(f103(a99),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f77(a99))
% 157.29/157.21 [3882]E(f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f77(a909))
% 157.29/157.21 [3886]E(f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(a112,f2(a909)))
% 157.29/157.21 [4269]E(f326(f326(f110(f917(f916(f916(a909,a909),f916(a909,a909)),a905)),a32),f306(f916(a909,a909),f188(f917(f916(f916(a909,a909),f916(a909,a909)),a905)))),a70)
% 157.29/157.21 [4338]E(f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),f77(a909)),f2(a909))),f188(f917(f916(a909,a909),a905))))),f77(a1))
% 157.29/157.21 [4339]E(f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),f2(a909)),f2(a909))),f188(f917(f916(a909,a909),a905))))),f2(a1))
% 157.29/157.21 [4352]E(f326(f261(f916(a909,a909)),f326(f256(a909,a909,a905),f326(f326(f10(a909,f917(a909,a905),a909),f326(f9(a909,a909,a905),a323)),a112))),a316)
% 157.29/157.21 [4324]E(f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),f326(a112,f326(a112,f2(a909))))
% 157.29/157.21 [4327]E(f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),f326(f326(f79(a909),f77(a909)),f77(a909)))
% 157.29/157.21 [4328]E(f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),f326(f35(a905),f241(f917(a905,a905))))
% 157.29/157.21 [4391]P5(f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))
% 157.29/157.21 [4460]P26(f917(f916(a909,a909),a905),f326(f326(f251(f917(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),a905),f917(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),a905)),a33),a71))
% 157.29/157.21 [4461]P26(f917(f916(a909,a909),a905),f326(f326(f251(f917(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),a905),f917(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),a905)),a34),a69))
% 157.29/157.21 [4501]E(f326(f326(f110(f917(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),a905)),f318(f916(a909,a909),a70)),f326(f326(f308(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),f188(f917(f916(a909,a909),a905))),f188(f917(f916(a909,a909),a905)))),f188(f917(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),a905)))),a69)
% 157.29/157.21 [4502]E(f326(f326(f110(f917(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),a905)),f317(f916(a909,a909),a70)),f326(f326(f308(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),f188(f917(f916(a909,a909),a905))),f188(f917(f916(a909,a909),a905)))),f188(f917(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),a905)))),a71)
% 157.29/157.21 [4393]E(f326(a104,f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(a112,f326(a112,f2(a909))))
% 157.29/157.21 [4438]E(f326(f100(a1),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))
% 157.29/157.21 [4471]P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.29/157.21 [4472]E(f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97)),f326(a112,f326(a112,f326(a112,f2(a909)))))
% 157.29/157.21 [4516]P5(f326(f103(a1),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97)))
% 157.29/157.21 [4542]E(f326(f100(a1),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97))),f326(f103(a1),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97)))
% 157.29/157.21 [4555]P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97))))
% 157.29/157.21 [3285]P6(x32851,a323)
% 157.29/157.21 [3677]P24(a909,a909,a112,x36771)
% 157.29/157.21 [3278]P104(f908(x32781))
% 157.29/157.21 [3279]P104(f913(x32791))
% 157.29/157.21 [3280]P104(f910(x32801))
% 157.29/157.21 [3281]P104(f911(x32811))
% 157.29/157.21 [3302]P36(a1,f105(x33021))
% 157.29/157.21 [3303]P36(a1,f106(x33031))
% 157.29/157.21 [3353]P36(f917(x33531,a905),f313(x33531))
% 157.29/157.21 [3354]P37(f917(x33541,a905),f313(x33541))
% 157.29/157.21 [3378]E(f242(x33781,x33781,a323),a323)
% 157.29/157.21 [3393]E(f45(a1,x33931,x33931),f2(a1))
% 157.29/157.21 [3446]P13(x34461,f917(x34461,a905),f308(x34461))
% 157.29/157.21 [4628]~E(f326(a112,x46281),x46281)
% 157.29/157.21 [4638]~E(f326(a112,x46381),f2(a909))
% 157.29/157.21 [3287]E(f326(f189(a909),x32871),x32871)
% 157.29/157.21 [3288]E(f326(f103(a1),x32881),x32881)
% 157.29/157.21 [3304]E(f326(a88,f327(x33041)),x33041)
% 157.29/157.21 [3305]E(f326(a5,f574(x33051)),x33051)
% 157.29/157.21 [3306]E(f240(x33061,f2(a99)),f2(a99))
% 157.29/157.21 [3319]E(f114(x33191,f113(x33191)),f113(x33191))
% 157.29/157.21 [3320]E(f152(x33201,f113(x33201)),f113(x33201))
% 157.29/157.21 [3325]E(f326(f167(x33251),f113(x33251)),f113(x33251))
% 157.29/157.21 [3326]E(f326(f171(x33261),f113(x33261)),f113(x33261))
% 157.29/157.21 [3327]E(f326(f168(x33271),f113(x33271)),f113(x33271))
% 157.29/157.21 [3332]E(f326(f103(a1),x33321),f326(f102(a1),x33321))
% 157.29/157.21 [3333]E(f326(a88,f326(a107,x33331)),x33331)
% 157.29/157.21 [3335]E(f326(a5,f326(a22,x33351)),x33351)
% 157.29/157.21 [3336]E(f326(a22,f326(a5,x33361)),x33361)
% 157.29/157.21 [3338]P5(f326(f100(a1),x33381))
% 157.29/157.21 [3347]E(f326(f189(f910(x33471)),f113(x33471)),f2(a909))
% 157.29/157.21 [3348]E(f326(f189(f911(x33481)),f119(x33481)),f2(a909))
% 157.29/157.21 [3369]E(f326(f326(f3(a909),x33691),f2(a909)),x33691)
% 157.29/157.21 [3370]E(f326(f326(f80(a909),x33701),f77(a909)),x33701)
% 157.29/157.21 [3371]E(f326(f326(f80(a1),x33711),f77(a1)),x33711)
% 157.29/157.21 [3372]E(f326(f326(f79(a909),x33721),f2(a909)),x33721)
% 157.29/157.21 [3373]E(f326(f326(f79(a1),x33731),f2(a1)),x33731)
% 157.29/157.21 [3374]E(f326(f326(f233(a909),x33741),f2(a909)),x33741)
% 157.29/157.21 [3375]E(f326(f326(f80(a909),x33751),f2(a909)),f2(a909))
% 157.29/157.21 [3376]E(f326(f326(f232(a909),x33761),f2(a909)),f2(a909))
% 157.29/157.21 [3377]E(f326(f326(f36(a1),x33771),f2(a1)),f2(a1))
% 157.29/157.21 [3384]E(f326(f172(x33841),f113(x33841)),f188(f917(x33841,a905)))
% 157.29/157.21 [3388]P105(f326(f137(x33881),f113(x33881)))
% 157.29/157.21 [3394]E(f326(f154(x33941,x33941),f7(x33941)),f31(f910(x33941)))
% 157.29/157.21 [3395]E(f326(f154(x33951,x33951),f31(x33951)),f31(f910(x33951)))
% 157.29/157.21 [3396]E(f45(a1,x33961,f2(a1)),x33961)
% 157.29/157.21 [3397]E(f326(f234(a909),f326(a112,x33971)),f326(f235(a909),x33971))
% 157.29/157.21 [3398]E(f326(f281(a909),f326(a112,x33981)),f326(f300(a909),x33981))
% 157.29/157.21 [3399]E(f326(f282(a909),f326(a112,x33991)),f326(f303(a909),x33991))
% 157.29/157.21 [3401]E(f45(a1,f2(a1),x34011),f2(a1))
% 157.29/157.21 [3414]E(f326(f326(f79(a909),x34141),f77(a909)),f326(a112,x34141))
% 157.29/157.21 [3423]E(f326(f301(a909,x34231),f2(a909)),f188(f917(a909,a905)))
% 157.29/157.21 [3435]E(f302(a909,f2(a909),x34351),f326(f300(a909),x34351))
% 157.29/157.21 [3478]E(f326(f326(f3(a909),f326(a112,x34781)),f77(a909)),x34781)
% 157.29/157.21 [3490]E(f47(f2(a1),x34901),f326(f326(f251(a1,a1),f2(a1)),f2(a1)))
% 157.29/157.21 [3540]P105(f326(f326(f235(a909),x35401),f326(a112,x35401)))
% 157.29/157.21 [3552]P105(f326(f326(f235(a909),f2(a909)),f326(a112,x35521)))
% 157.29/157.21 [3780]E(f90(x37801,x37801,f241(f917(x37801,a905)),f31(x37801)),f31(x37801))
% 157.29/157.21 [3838]E(f326(f326(f3(a99),f326(a5,f326(a112,f326(a22,x38381)))),f77(a99)),x38381)
% 157.29/157.21 [3909]P105(f326(f326(f234(a1),f326(f78(a1),f326(f100(a1),x39091))),f2(a1)))
% 157.29/157.21 [4058]P105(f326(f326(f235(a1),f326(f78(a1),f326(f100(a1),f326(a112,x40581)))),f2(a1)))
% 157.29/157.21 [4648]~E(f241(f917(x46481,a905)),f188(f917(x46481,a905)))
% 157.29/157.21 [4683]~P105(f326(f326(f235(a909),x46831),f2(a909)))
% 157.29/157.21 [4696]~P105(f326(f326(f235(a1),f326(f100(a1),x46961)),f2(a1)))
% 157.29/157.21 [3337]E(f120(x33371,f119(f911(x33371))),f119(x33371))
% 157.29/157.21 [3352]E(f179(x33521,f113(f910(x33521))),f113(f910(x33521)))
% 157.29/157.21 [3355]E(f326(f326(f80(a1),a82),x33551),a82)
% 157.29/157.21 [3356]E(f326(f326(f79(a1),a82),x33561),x33561)
% 157.29/157.21 [3359]E(f326(a104,f326(f100(a1),x33591)),x33591)
% 157.29/157.21 [3360]E(f326(f326(f3(a1),x33601),a82),x33601)
% 157.29/157.21 [3361]E(f326(f326(f79(a1),x33611),a82),x33611)
% 157.29/157.21 [3363]E(f326(f326(f3(a909),x33631),x33631),f2(a909))
% 157.29/157.21 [3367]E(f326(f35(a909),f326(f281(a909),x33671)),x33671)
% 157.29/157.21 [3368]E(f326(f78(a1),f326(f78(a1),x33681)),x33681)
% 157.29/157.21 [3379]E(f326(f326(f80(a909),f77(a909)),x33791),x33791)
% 157.29/157.21 [3380]E(f326(f326(f80(a1),f77(a1)),x33801),x33801)
% 157.29/157.21 [3381]E(f326(f326(f79(a909),f2(a909)),x33811),x33811)
% 157.29/157.21 [3382]E(f326(f326(f79(a1),f2(a1)),x33821),x33821)
% 157.29/157.21 [3383]E(f326(f326(f233(a909),f2(a909)),x33831),x33831)
% 157.29/157.21 [3389]E(f326(f326(f3(a909),f2(a909)),x33891),f2(a909))
% 157.29/157.21 [3390]E(f326(f326(f80(a909),f2(a909)),x33901),f2(a909))
% 157.29/157.21 [3391]E(f326(f326(f232(a909),f2(a909)),x33911),f2(a909))
% 157.29/157.21 [3392]E(f326(f326(f36(a1),f2(a1)),x33921),f2(a1))
% 157.29/157.21 [3402]E(f128(x34021,f326(f78(a1),x34021)),f132(a1,x34021))
% 157.29/157.21 [3407]E(f326(f301(a909,f2(a909)),x34071),f326(f281(a909),x34071))
% 157.29/157.21 [3408]E(f326(f326(f80(a1),a97),x34081),f326(f78(a1),x34081))
% 157.29/157.21 [3416]E(f326(a104,f326(f103(a1),x34161)),f326(f103(a909),x34161))
% 157.29/157.21 [3417]E(f326(a22,f326(f103(a99),x34171)),f326(f103(a909),x34171))
% 157.29/157.21 [3418]E(f326(f35(a909),f326(f300(a909),x34181)),f326(a112,x34181))
% 157.29/157.21 [3427]E(f326(f326(f79(a909),f77(a909)),x34271),f326(a112,x34271))
% 157.29/157.21 [3431]E(f326(f75(a1),f326(f100(a1),x34311)),f326(f100(a1),x34311))
% 157.29/157.21 [3432]E(f326(f102(a1),f326(f100(a1),x34321)),f326(f100(a1),x34321))
% 157.29/157.21 [3436]E(f326(f35(x34361),f188(f917(x34361,a905))),f2(a909))
% 157.29/157.21 [3438]E(f326(f326(f36(a909),x34381),f326(a112,f2(a909))),x34381)
% 157.29/157.21 [3447]E(f45(a909,x34471,f326(a112,f2(a909))),f2(a909))
% 157.29/157.21 [3448]E(f45(a1,x34481,f326(f103(a1),a97)),f2(a1))
% 157.29/157.21 [3462]E(f326(f326(f36(a1),x34621),f326(f103(a1),a97)),f326(f78(a1),x34621))
% 157.29/157.21 [3466]E(f139(a909,f326(f301(a909,x34661),f2(a909))),f113(a909))
% 157.29/157.21 [3467]E(f326(f326(f79(a1),x34671),f77(a1)),f326(f326(f3(a1),x34671),a97))
% 157.29/157.21 [3468]E(f326(f326(f3(a1),x34681),f77(a1)),f326(f326(f79(a1),x34681),a97))
% 157.29/157.21 [3472]P105(f326(f326(f234(a909),x34721),x34721))
% 157.29/157.21 [3473]P105(f326(f326(f234(a1),x34731),x34731))
% 157.29/157.21 [3474]P105(f326(f326(f286(a909),x34741),x34741))
% 157.29/157.21 [3479]E(f326(f78(a1),f326(f103(a1),x34791)),f326(f103(a1),f326(f78(a1),x34791)))
% 157.29/157.21 [3480]P105(f326(f61(a909),f326(f281(a909),x34801)))
% 157.29/157.21 [3481]P105(f326(f61(a909),f326(f300(a909),x34811)))
% 157.29/157.21 [3488]E(f161(x34881,f241(f917(x34881,a905))),f241(f917(f910(x34881),a905)))
% 157.29/157.21 [3493]P105(f326(f326(f234(a909),f2(a909)),x34931))
% 157.29/157.21 [3503]E(f326(f326(f79(a909),f111(x35031)),f326(a112,f2(a909))),f111(f326(a112,x35031)))
% 157.29/157.21 [3504]E(f326(f261(x35041),f326(f18(a905,x35041),a238)),f188(f917(x35041,a905)))
% 157.29/157.21 [3505]E(f326(f261(x35051),f326(f18(a905,x35051),a187)),f241(f917(x35051,a905)))
% 157.29/157.21 [3509]E(f326(f326(f308(a909),x35091),f326(f281(a909),x35091)),f326(f281(a909),f326(a112,x35091)))
% 157.29/157.21 [3521]E(f326(f326(f79(a1),f77(a1)),f326(f100(a1),x35211)),f326(f100(a1),f326(a112,x35211)))
% 157.29/157.21 [3523]E(f326(f326(f151(f910(x35231)),f113(x35231)),f113(f910(x35231))),f54(x35231,f113(x35231)))
% 157.29/157.21 [3543]E(f188(f917(f916(x35431,x35431),a905)),f262(x35431,f188(f917(x35431,a905))))
% 157.29/157.21 [3544]E(f326(f307(x35441),f241(f917(x35441,a905))),f241(f917(f917(x35441,a905),a905)))
% 157.29/157.21 [3545]E(f326(f78(f917(x35451,a905)),f188(f917(x35451,a905))),f241(f917(x35451,a905)))
% 157.29/157.21 [3546]E(f326(f78(f917(x35461,a905)),f241(f917(x35461,a905))),f188(f917(x35461,a905)))
% 157.29/157.21 [3548]P105(f326(f61(x35481),f188(f917(x35481,a905))))
% 157.29/157.21 [3550]E(f326(f301(a909,x35501),f326(a112,x35501)),f326(f326(f308(a909),x35501),f188(f917(a909,a905))))
% 157.29/157.21 [3551]E(f84(f916(a909,a909),f48(x35511,f2(a909))),f326(f326(f251(a909,a909),f2(a909)),x35511))
% 157.29/157.21 [3564]E(f326(f326(f308(a909),f326(a112,x35641)),f326(f300(a909),x35641)),f326(f300(a909),f326(a112,x35641)))
% 157.29/157.21 [3568]P36(x35681,f188(f917(f916(x35681,x35681),a905)))
% 157.29/157.21 [3569]P38(x35691,f188(f917(f916(x35691,x35691),a905)))
% 157.29/157.21 [3572]P105(f326(f326(f234(a1),f2(a1)),f326(f100(a1),x35721)))
% 157.29/157.21 [3579]E(f326(f326(f79(a909),f326(f189(a909),x35791)),f326(a112,f2(a909))),f326(f189(a909),f326(a112,x35791)))
% 157.29/157.21 [3684]P39(f326(f309(a909,a1,f100(a1)),x36841))
% 157.29/157.21 [3722]P51(x37221,f188(f917(x37221,a905)),f188(f917(f916(x37221,x37221),a905)))
% 157.29/157.21 [3741]E(f326(f326(f251(a1,a1),f326(f103(a1),a97)),f326(f326(f3(a1),x37411),f77(a1))),f50(f326(f103(a1),a97),x37411))
% 157.29/157.21 [3793]P58(x37931,f326(f18(f917(x37931,a905),x37931),f326(f18(a905,x37931),a238)))
% 157.29/157.21 [3805]E(f289(a909,f286(a909),x38051,x38051),f326(f326(f308(a909),x38051),f188(f917(a909,a905))))
% 157.29/157.21 [3998]P105(f326(f326(f328(f917(f916(a909,a909),a905)),f327(x39981)),a98))
% 157.29/157.21 [4024]P105(f326(f326(f328(f917(f916(a909,a909),a905)),f326(a107,x40241)),a98))
% 157.29/157.21 [4156]P24(x41561,f917(x41561,a905),f326(f326(f9(x41561,f917(x41561,a905),f917(x41561,a905)),f308(x41561)),f188(f917(x41561,a905))),f241(f917(x41561,a905)))
% 157.29/157.21 [4645]~E(f326(f326(f79(a1),x46451),x46451),a97)
% 157.29/157.21 [4670]~E(f326(a5,f326(a112,f326(a22,x46701))),f2(a99))
% 157.29/157.21 [4676]~P105(f326(a193,f326(f100(a1),x46761)))
% 157.29/157.21 [4679]~P105(f326(f326(f235(a909),x46791),x46791))
% 157.29/157.21 [4689]~P105(f326(f326(f234(a909),f326(a112,x46891)),x46891))
% 157.29/157.21 [3495]E(f326(a104,f326(f78(a1),f326(f100(a1),x34951))),f2(a909))
% 157.29/157.21 [3498]E(f326(f326(f79(a1),f326(f78(a1),x34981)),x34981),f2(a1))
% 157.29/157.21 [3502]E(f326(f35(a1),f326(f301(a1,f2(a1)),x35021)),f326(a104,x35021))
% 157.29/157.21 [3514]E(f326(f326(f243(a909),f326(a112,f2(a909))),x35141),f326(a112,f2(a909)))
% 157.29/157.21 [3611]E(f326(f280(x36111),f188(f917(f916(x36111,x36111),a905))),f188(f917(x36111,a905)))
% 157.29/157.21 [3619]E(f37(f917(x36191,a905),f188(f917(f917(x36191,a905),a905))),f188(f917(x36191,a905)))
% 157.29/157.21 [3620]E(f37(f917(x36201,a905),f241(f917(f917(x36201,a905),a905))),f241(f917(x36201,a905)))
% 157.29/157.21 [3621]E(f38(f917(x36211,a905),f188(f917(f917(x36211,a905),a905))),f241(f917(x36211,a905)))
% 157.29/157.21 [3622]E(f38(f917(x36221,a905),f241(f917(f917(x36221,a905),a905))),f188(f917(x36221,a905)))
% 157.29/157.21 [3626]P105(f326(f326(f286(a909),f326(a112,f2(a909))),x36261))
% 157.29/157.21 [3667]E(f326(f326(f308(f910(x36671)),f113(x36671)),f188(f917(f910(x36671),a905))),f161(x36671,f188(f917(x36671,a905))))
% 157.29/157.21 [3668]E(f326(f326(f308(f910(x36681)),f113(x36681)),f188(f917(f910(x36681),a905))),f162(x36681,f113(f917(x36681,a905))))
% 157.29/157.21 [3706]E(f326(f326(f79(a909),f6(x37061)),f326(a112,f2(a909))),f6(f326(a5,f326(a112,f326(a22,x37061)))))
% 157.29/157.21 [3732]E(f326(f35(a1),f326(f309(a909,a1,f100(a1)),x37321)),f326(f35(a909),x37321))
% 157.29/157.21 [3733]P105(f326(f326(f234(a909),x37331),f326(f326(f80(a909),x37331),x37331)))
% 157.29/157.21 [3771]E(f326(f309(a1,a909,a104),f302(a1,f2(a1),f326(f100(a1),x37711))),f326(f300(a909),x37711))
% 157.29/157.21 [3788]E(f326(f326(f36(a909),f326(a112,f2(a909))),f326(f103(a909),x37881)),f326(a104,f326(f326(f36(a1),f77(a1)),f326(f103(a1),x37881))))
% 157.29/157.21 [3790]E(f326(f172(a909),f139(a909,f326(f301(a909,f2(a909)),f326(a112,x37901)))),f326(f300(a909),x37901))
% 157.29/157.21 [3791]E(f326(f326(f79(a909),f326(f189(a99),x37911)),f326(a112,f2(a909))),f326(f189(a99),f326(a5,f326(a112,f326(a22,x37911)))))
% 157.29/157.21 [3811]P38(x38111,f306(x38111,f188(f917(f916(x38111,x38111),a905))))
% 157.29/157.21 [3812]P50(x38121,f306(x38121,f188(f917(f916(x38121,x38121),a905))))
% 157.29/157.21 [3813]E(f326(f309(a1,a909,a104),f326(f309(a909,a1,f100(a1)),x38131)),x38131)
% 157.29/157.21 [3844]E(f326(f326(f308(a909),f2(a909)),f326(f309(a909,a909,a112),f326(f281(a909),x38441))),f326(f281(a909),f326(a112,x38441)))
% 157.29/157.21 [3850]P53(x38501,x38501,f306(x38501,f188(f917(f916(x38501,x38501),a905))))
% 157.29/157.21 [3856]P105(f326(a193,f326(f78(a1),f326(f100(a1),f326(a112,x38561)))))
% 157.29/157.21 [3866]E(f326(f326(f3(f917(a909,a905)),f326(f282(a909),x38661)),f326(f326(f308(a909),x38661),f188(f917(a909,a905)))),f326(f282(a909),f326(a112,x38661)))
% 157.29/157.21 [3883]E(f326(f326(f79(a1),f326(f326(f3(a1),a82),x38831)),f326(f326(f3(a1),a82),x38831)),f326(f326(f3(a1),a82),f326(f326(f79(a1),x38831),x38831)))
% 157.29/157.21 [3898]E(f326(f326(f308(f917(x38981,a905)),f188(f917(x38981,a905))),f188(f917(f917(x38981,a905),a905))),f326(f307(x38981),f188(f917(x38981,a905))))
% 157.29/157.21 [3926]E(f326(f326(f3(f917(a909,a905)),f326(f303(a909),x39261)),f326(f326(f308(a909),f326(a112,x39261)),f188(f917(a909,a905)))),f326(f303(a909),f326(a112,x39261)))
% 157.29/157.21 [4036]E(f326(f103(a909),f326(f326(f79(a1),x40361),x40361)),f326(f326(f85(a909,a909),f326(f103(a909),x40361)),f326(f326(f20(a909,a909,a909),f79(a909)),f7(a909))))
% 157.29/157.21 [4413]P13(x44131,f917(x44131,a905),f326(f326(f10(f917(x44131,a905),f917(f917(x44131,a905),f917(x44131,a905)),x44131),f326(f9(f917(x44131,a905),f917(x44131,a905),f917(x44131,a905)),f3(f917(x44131,a905)))),f326(f326(f9(x44131,f917(x44131,a905),f917(x44131,a905)),f308(x44131)),f188(f917(x44131,a905)))))
% 157.29/157.21 [4500]E(f326(f261(f916(a1,a1)),f326(f256(a1,a1,a905),f326(f326(f10(f917(a1,a905),f917(a1,a905),a1),f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),x45001)))),f235(a1)))),f105(x45001))
% 157.29/157.21 [4533]E(f326(f261(f916(a1,a1)),f326(f256(a1,a1,a905),f326(f326(f20(a1,f917(a1,a905),f917(a1,a905)),f326(f326(f10(f917(a905,a905),f917(f917(a1,a905),f917(a1,a905)),a1),f10(a905,a905,a1)),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),x45331)))),f235(a1)))),f106(x45331))
% 157.29/157.21 [4586]E(f326(f261(f916(f917(x45861,a905),f917(x45861,a905))),f326(f256(f917(x45861,a905),f917(x45861,a905),a905),f326(f326(f9(f917(x45861,a905),f917(f917(x45861,a905),a905),f917(f917(x45861,a905),a905)),f326(f326(f10(f917(f917(x45861,a905),f917(a905,a905)),f917(f917(f917(x45861,a905),a905),f917(f917(x45861,a905),a905)),f917(x45861,a905)),f20(f917(x45861,a905),a905,a905)),f326(f326(f10(f917(f917(x45861,a905),a905),f917(f917(x45861,a905),f917(a905,a905)),f917(x45861,a905)),f326(f10(a905,f917(a905,a905),f917(x45861,a905)),a324)),f235(f917(x45861,a905))))),f61(x45861)))),f313(x45861))
% 157.29/157.21 [4693]~P105(f326(f61(f910(x46931)),f241(f917(f910(x46931),a905))))
% 157.29/157.21 [4705]~P105(f326(f326(f234(a1),f2(a1)),f326(f78(a1),f326(f100(a1),f326(a112,x47051)))))
% 157.29/157.21 [3646]E(f326(f326(f3(a1),f326(f326(f79(a1),x36461),a97)),a97),x36461)
% 157.29/157.21 [3660]E(f326(f172(a909),f139(a909,f326(f301(a909,f2(a909)),x36601))),f326(f281(a909),x36601))
% 157.29/157.21 [3905]E(f326(f326(f79(a1),f326(f326(f79(a1),f77(a1)),x39051)),x39051),f326(f326(f3(a1),f326(f326(f79(a1),x39051),x39051)),a97))
% 157.29/157.21 [3954]E(f326(f285(x39541,x39541),f306(x39541,f188(f917(f916(x39541,x39541),a905)))),f306(x39541,f188(f917(f916(x39541,x39541),a905))))
% 157.29/157.21 [4001]P105(f326(f326(f234(a909),x40011),f326(f326(f80(a909),x40011),f326(f326(f80(a909),x40011),x40011))))
% 157.29/157.21 [4273]P105(f326(f61(a909),f326(f261(a909),f326(f326(f9(a909,a909,a905),f234(a909)),x42731))))
% 157.29/157.21 [4274]P105(f326(f61(a909),f326(f261(a909),f326(f326(f9(a909,a909,a905),f235(a909)),x42741))))
% 157.29/157.21 [4549]E(f326(f261(f916(x45491,x45491)),f326(f326(f10(f917(x45491,a905),a905,f916(x45491,x45491)),f86(x45491)),f326(f326(f9(f916(x45491,x45491),f917(x45491,f916(x45491,x45491)),f917(x45491,a905)),f326(f326(f10(f917(f916(x45491,x45491),a905),f917(f917(x45491,f916(x45491,x45491)),f917(x45491,a905)),f916(x45491,x45491)),f10(f916(x45491,x45491),a905,x45491)),a323)),f326(f326(f20(x45491,x45491,f916(x45491,x45491)),f251(x45491,x45491)),f7(x45491))))),f306(x45491,f188(f917(f916(x45491,x45491),a905))))
% 157.29/157.21 [4695]~E(f326(f326(f3(a1),f326(f326(f79(a1),x46951),x46951)),a97),a82)
% 157.29/157.21 [4697]~E(f326(f326(f79(a1),f326(f326(f79(a1),f77(a1)),x46971)),x46971),f2(a1))
% 157.29/157.21 [4047]E(f326(f326(f79(a1),f326(f326(f3(a1),a97),x40471)),f326(f326(f3(a1),a97),x40471)),f326(f326(f3(a1),a97),f326(f326(f3(a1),f326(f326(f79(a1),x40471),x40471)),a97)))
% 157.29/157.21 [4164]E(f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),a97),x41641)),f326(f326(f3(a1),a97),x41641))),a97),f326(f326(f3(a1),a97),f326(f326(f79(a1),x41641),x41641)))
% 157.29/157.21 [4196]E(f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f79(a1),x41961),a97)),f326(f326(f79(a1),x41961),a97))),a97),f326(f326(f79(a1),f326(f326(f79(a1),x41961),x41961)),a97))
% 157.29/157.21 [4234]E(f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),a97),x42341)),f326(f326(f3(a1),a97),x42341))),a97),f326(f326(f3(a1),a82),f326(f326(f3(a1),f326(f326(f79(a1),x42341),x42341)),a97)))
% 157.29/157.21 [4334]E(f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x43341),f2(a909))),f188(f917(f916(a909,a909),a905))))),f326(f100(a1),x43341))
% 157.29/157.21 [4344]E(f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),f331(x43441)),f500(x43441))),f188(f917(f916(a909,a909),a905))))),x43441)
% 157.29/157.21 [4377]E(f326(f261(a1),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),f2(a1)))),x43771)),f326(f309(a909,a1,f100(a1)),f326(f261(a909),f326(f326(f10(a1,a905,a909),x43771),f100(a1)))))
% 157.29/157.21 [4421]P39(f326(f261(a1),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),f2(a1)))),x44211)))
% 157.29/157.21 [4441]P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),x44411),f188(f917(f916(a909,a909),a905)))),a71))
% 157.29/157.21 [4446]E(f326(f309(a1,a909,a104),f326(f261(a1),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),f2(a1)))),f326(f326(f10(a909,a905,a1),x44461),a104)))),f326(f261(a909),x44461))
% 157.29/157.21 [4601]E(f311(a909,f326(f326(f40(f916(a909,a909),f917(a909,a905)),f326(a107,x46011)),f326(f256(a909,a909,f917(a909,a905)),f326(f326(f9(a909,f917(a909,a905),f917(a909,f917(a909,a905))),f326(f326(f10(f917(a909,f917(f917(a909,a905),f917(a909,a905))),f917(f917(a909,a905),f917(a909,f917(a909,a905))),a909),f9(a909,f917(a909,a905),f917(a909,a905))),f326(f326(f10(f917(a909,a909),f917(a909,f917(f917(a909,a905),f917(a909,a905))),a909),f326(f10(a909,f917(f917(a909,a905),f917(a909,a905)),a909),f308(a909))),f3(a909)))),f188(f917(a909,a905)))))),f326(a104,x46011))
% 157.29/157.21 [4094]E(f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),x40941),x40941)),a97)),a97),f326(f326(f79(a1),x40941),x40941))
% 157.29/157.21 [4144]E(f326(f326(f3(a1),f326(f326(f3(a1),f326(f326(f79(a1),x41441),x41441)),a97)),a97),f326(f326(f79(a1),f326(f326(f3(a1),x41441),a97)),f326(f326(f3(a1),x41441),a97)))
% 157.29/157.21 [4350]E(f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f79(a1),f326(f78(a1),x43501)),a97)),f326(f326(f79(a1),f326(f78(a1),x43501)),a97))),a97),f326(f78(a1),f326(f326(f3(a1),f326(f326(f79(a1),x43501),x43501)),a97)))
% 157.29/157.21 [4394]E(f326(f326(f79(a909),x43941),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(a112,f326(a112,x43941)))
% 157.29/157.21 [4395]E(f326(f326(f80(a909),x43951),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(f326(f79(a909),x43951),x43951))
% 157.29/157.21 [4396]E(f326(f326(f36(a909),f326(f326(f79(a909),x43961),x43961)),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x43961)
% 157.29/157.21 [4474]E(f45(a909,f326(a112,f326(a112,x44741)),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f45(a909,x44741,f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.29/157.21 [4615]E(f326(a88,f326(f326(f40(f916(a909,a909),f917(f916(a909,a909),a905)),f326(a107,x46151)),f326(f256(a909,a909,f917(f916(a909,a909),a905)),f326(f326(f10(f917(a909,f917(f916(a909,a909),a905)),f917(a909,f917(f916(a909,a909),a905)),a909),f326(f10(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905),a909),f284(f916(a909,a909),f916(a909,a909),a108))),f326(f326(f9(a909,f917(f916(a909,a909),a905),f917(a909,f917(f916(a909,a909),a905))),f326(f326(f10(f917(a909,f917(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f917(f917(f916(a909,a909),a905),f917(a909,f917(f916(a909,a909),a905))),a909),f9(a909,f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f10(f917(a909,f916(a909,a909)),f917(a909,f917(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),a909),f326(f10(f916(a909,a909),f917(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),a909),f308(f916(a909,a909)))),f326(f9(a909,a909,f916(a909,a909)),f251(a909,a909))))),f188(f917(f916(a909,a909),a905))))))),f326(f78(a1),x46151))
% 157.29/157.21 [4469]E(f326(f326(f79(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x44691),f326(a112,f326(a112,x44691)))
% 157.29/157.21 [4470]E(f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x44701),f326(f326(f79(a909),x44701),x44701))
% 157.29/157.21 [4506]E(f326(f326(f36(a909),f326(a112,f326(a112,x45061))),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(a112,f326(f326(f36(a909),x45061),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))
% 157.29/157.21 [4556]E(f326(f326(f79(a909),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97))),x45561),f326(a112,f326(a112,f326(a112,x45561))))
% 157.29/157.21 [4622]E(f326(f256(a1,a1,f916(a1,a1)),f326(f326(f20(a1,f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),f326(f326(f10(f917(a1,f917(f916(a1,a1),f916(a1,a1))),f917(f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),a1),f20(a1,f916(a1,a1),f916(a1,a1))),f326(f326(f10(f917(a1,f916(a1,a1)),f917(a1,f917(f916(a1,a1),f916(a1,a1))),a1),f326(f20(a1,f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),f326(f326(f10(a905,f917(f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),a1),f96(f916(a1,a1))),f326(f326(f10(a1,a905,a1),f326(f234(a1),f2(a1))),f326(f326(f9(a1,a1,a1),f3(a1)),x46221))))),f326(f326(f9(a1,f917(a1,a1),f917(a1,f916(a1,a1))),f326(f326(f10(f917(a1,f916(a1,a1)),f917(f917(a1,a1),f917(a1,f916(a1,a1))),a1),f10(a1,f916(a1,a1),a1)),f326(f326(f10(a1,f917(a1,f916(a1,a1)),a1),f251(a1,a1)),f326(f326(f9(a1,a1,a1),f326(f326(f10(a1,f917(a1,a1),a1),f79(a1)),f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))),f77(a1))))),f326(f326(f9(a1,a1,a1),f3(a1)),x46221))))),f326(f326(f10(a1,f917(a1,f916(a1,a1)),a1),f251(a1,a1)),f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))),f43(x46221))
% 157.29/157.21 [3322]P104(f915(x33221,x33222))
% 157.29/157.21 [3323]P104(f914(x33231,x33232))
% 157.29/157.21 [3324]P104(f916(x33241,x33242))
% 157.29/157.21 [3341]P12(a1,f178(x33411,x33412))
% 157.29/157.21 [3342]P36(x33421,f153(x33421,x33422))
% 157.29/157.21 [3343]P37(x33431,f262(x33431,x33432))
% 157.29/157.21 [3344]P37(x33441,f306(x33441,x33442))
% 157.29/157.21 [3345]P38(x33451,f262(x33451,x33452))
% 157.29/157.21 [3346]P50(x33461,f262(x33461,x33462))
% 157.29/157.21 [3409]P30(x34091,x34092,f113(x34091))
% 157.29/157.21 [3442]P51(x34421,x34422,f262(x34421,x34422))
% 157.29/157.21 [3443]P53(x34431,x34431,f262(x34431,x34432))
% 157.29/157.21 [3709]P24(x37091,x37091,f7(x37091),x37092)
% 157.29/157.21 [3710]P24(x37101,x37101,f31(x37101),x37102)
% 157.29/157.21 [3718]P31(x37181,x37182,f113(x37181),f113(x37181))
% 157.29/157.21 [3726]P24(f910(x37261),f910(x37261),f168(x37261),x37262)
% 157.29/157.21 [4134]P25(x41341,x41341,f31(x41341),x41342,x41342)
% 157.29/157.21 [4631]~E(f30(x46311,x46312),a25)
% 157.29/157.21 [4632]~E(f29(x46321,x46322),a25)
% 157.29/157.21 [4657]~P32(x46571,x46572,f113(x46571))
% 157.29/157.21 [4658]~P34(x46581,x46582,f113(x46581))
% 157.29/157.21 [3308]E(f326(f7(x33081),x33082),x33082)
% 157.29/157.21 [3309]E(f326(f261(x33091),x33092),x33092)
% 157.29/157.21 [3311]E(f326(f31(x33111),x33112),x33112)
% 157.29/157.21 [3321]E(f326(f191(x33211),x33212),f115(x33211))
% 157.29/157.21 [3339]E(f84(x33391,f326(a323,x33392)),x33392)
% 157.29/157.21 [3340]E(f89(x33401,f326(a323,x33402)),x33402)
% 157.29/157.21 [3362]E(f326(f125(x33621,x33622),f119(x33621)),f2(a909))
% 157.29/157.21 [3365]E(f326(f136(x33651,x33652),f113(x33651)),f113(x33651))
% 157.29/157.21 [3385]E(f306(x33851,f306(x33851,x33852)),f306(x33851,x33852))
% 157.29/157.21 [3386]E(f152(x33861,f152(x33861,x33862)),f152(x33861,x33862))
% 157.29/157.21 [3404]E(f326(f326(f134(x34041),x34042),f113(x34041)),x34042)
% 157.29/157.21 [3410]E(f173(x34101,x34102,f113(x34101)),x34102)
% 157.29/157.21 [3411]E(f173(x34111,f113(x34111),x34112),x34112)
% 157.29/157.21 [3412]E(f116(x34121,f119(x34121),x34122),x34122)
% 157.29/157.21 [3413]E(f169(x34131,f2(a909),x34132),f113(x34131))
% 157.29/157.21 [3419]E(f326(f326(f175(x34191),x34192),f113(x34191)),f113(x34191))
% 157.29/157.21 [3420]E(f326(f326(f138(x34201),x34202),f113(x34201)),f113(x34201))
% 157.29/157.21 [3422]E(f155(x34221,x34222,f113(x34221)),f2(a909))
% 157.29/157.21 [3424]E(f170(x34241,x34242,f113(x34241)),f113(x34241))
% 157.29/157.21 [3425]E(f177(x34251,x34252,f113(x34251)),f113(x34251))
% 157.29/157.21 [3426]E(f176(x34261,f113(x34261),x34262),f113(x34261))
% 157.29/157.21 [3430]E(f326(f172(x34301),f152(x34301,x34302)),f326(f172(x34301),x34302))
% 157.29/157.21 [3433]E(f326(f283(x34331,x34331),f262(x34331,x34332)),x34332)
% 157.29/157.21 [3434]E(f326(f263(x34341,x34341),f262(x34341,x34342)),x34342)
% 157.29/157.21 [3441]E(f326(f285(x34411,x34411),f262(x34411,x34412)),f262(x34411,x34412))
% 157.29/157.21 [3454]E(f306(f910(x34541),f157(x34541,x34542)),f158(x34541,f306(x34541,x34542)))
% 157.29/157.21 [3456]P105(f326(f137(a1),f178(x34561,x34562)))
% 157.29/157.21 [3464]E(f326(f283(x34641,x34641),f306(x34641,x34642)),f241(f917(x34641,a905)))
% 157.29/157.21 [3465]E(f326(f263(x34651,x34651),f306(x34651,x34652)),f241(f917(x34651,a905)))
% 157.29/157.21 [3469]P105(f326(f137(x34691),f152(x34691,x34692)))
% 157.29/157.21 [3471]P105(f326(f160(x34711,x34712),f113(x34711)))
% 157.29/157.21 [3477]E(f326(f172(a1),f178(x34771,x34772)),f302(a1,x34771,x34772))
% 157.29/157.21 [3491]P54(x34911,f188(f917(x34911,a905)),x34912)
% 157.29/157.21 [3496]E(f326(f255(a1,a1),f46(x34961,x34962)),f45(a1,x34961,x34962))
% 157.29/157.21 [3497]E(f326(f301(a909,x34971),f326(a112,x34972)),f302(a909,x34971,x34972))
% 157.29/157.21 [3513]E(f326(f326(f151(x35131),x35132),f113(x35131)),f140(x35131,x35132,f113(x35131)))
% 157.29/157.21 [3525]E(f302(a909,f326(a112,x35251),x35252),f304(a909,x35251,x35252))
% 157.29/157.21 [3528]P51(x35281,f241(f917(x35281,a905)),f306(x35281,x35282))
% 157.29/157.21 [3591]E(f326(f326(f3(a909),x35911),f326(a112,x35912)),f326(f35(a909),f305(a909,x35912,x35911)))
% 157.29/157.21 [3647]E(f166(x36471,x36472,f113(x36471)),f326(f326(f251(f910(x36471),f910(x36471)),f113(x36471)),f113(x36471)))
% 157.29/157.21 [3665]E(f326(f256(x36651,x36652,f916(x36651,x36652)),f251(x36651,x36652)),f31(f916(x36651,x36652)))
% 157.29/157.21 [3669]P105(f326(f326(f328(f910(x36691)),f113(x36691)),f161(x36691,x36692)))
% 157.29/157.21 [3670]E(f326(f189(f910(x36701)),f114(x36701,x36702)),f326(f326(f3(a909),f326(f189(f910(x36701)),x36702)),f77(a909)))
% 157.29/157.21 [3678]P105(f326(f61(a909),f302(a909,x36781,x36782)))
% 157.29/157.21 [3679]P105(f326(f61(a909),f305(a909,x36791,x36792)))
% 157.29/157.21 [3680]P105(f326(f61(a909),f304(a909,x36801,x36802)))
% 157.29/157.21 [3681]P105(f326(f61(a1),f302(a1,x36811,x36812)))
% 157.29/157.21 [3682]P105(f326(f61(a1),f305(a1,x36821,x36822)))
% 157.29/157.21 [3683]P105(f326(f61(a1),f304(a1,x36831,x36832)))
% 157.29/157.21 [3787]E(f326(f309(a909,a909,a112),f302(a909,x37871,x37872)),f302(a909,f326(a112,x37871),f326(a112,x37872)))
% 157.29/157.21 [3807]E(f326(f326(f288(x38071,x38071,x38071),f306(x38071,x38072)),f306(x38071,x38072)),f306(x38071,x38072))
% 157.29/157.21 [3842]E(f326(f326(f251(a99,a99),f326(f326(f36(a99),x38421),x38422)),f45(a99,x38421,x38422)),f23(x38421,x38422))
% 157.29/157.21 [3843]E(f326(f326(f251(a1,a1),f326(f326(f36(a1),x38431),x38432)),f45(a1,x38431,x38432)),f46(x38431,x38432))
% 157.29/157.21 [3870]E(f326(f326(f251(a909,a909),f326(f326(f36(a909),x38701),x38702)),f45(a909,x38701,x38702)),f84(f916(a909,a909),f48(x38701,x38702)))
% 157.29/157.21 [3922]P105(f326(f326(f235(a909),f326(f326(f3(a909),x39221),x39222)),f326(a112,x39221)))
% 157.29/157.21 [3972]P37(x39721,f326(f326(f288(x39721,x39721,x39721),x39722),f306(x39721,x39722)))
% 157.29/157.21 [4023]E(f326(f326(f79(a1),f326(f326(f80(a1),x40231),f326(f326(f36(a1),x40232),x40231))),f45(a1,x40232,x40231)),x40232)
% 157.29/157.21 [4027]E(f326(f326(f40(a909,f917(f916(f910(x40271),f910(x40271)),a905)),f241(f917(a909,a905))),f143(x40271,x40272)),f145(x40271,x40272))
% 157.29/157.21 [4250]P105(f326(f326(f328(f916(f910(x42501),f910(x42501))),f326(f326(f251(f910(x42501),f910(x42501)),f113(x42501)),f113(x42501))),f158(x42501,x42502)))
% 157.29/157.21 [4362]E(f252(x43621,x43621,x43621,a323,f252(x43621,x43621,x43621,x43622,a323)),x43622)
% 157.29/157.21 [4406]E(f257(x44061,x44061,x44062,x44062,f7(x44061),f7(x44062)),f31(f916(x44061,x44062)))
% 157.29/157.21 [4408]E(f257(x44081,x44081,x44082,x44082,f31(x44081),f31(x44082)),f31(f916(x44081,x44082)))
% 157.29/157.21 [3403]E(f326(f168(x34031),f326(f168(x34031),x34032)),x34032)
% 157.29/157.21 [3405]E(f326(f326(f138(x34051),f2(a909)),x34052),x34052)
% 157.29/157.21 [3421]E(f326(f326(f175(x34211),f2(a909)),x34212),f113(x34211))
% 157.29/157.21 [3428]E(f326(f326(f134(x34281),f113(x34281)),x34282),x34282)
% 157.29/157.21 [3437]E(f37(f917(x34371,a905),f326(f307(x34371),x34372)),x34372)
% 157.29/157.21 [3439]E(f326(f172(x34391),f326(f167(x34391),x34392)),f326(f172(x34391),x34392))
% 157.29/157.21 [3440]E(f326(f172(x34401),f326(f168(x34401),x34402)),f326(f172(x34401),x34402))
% 157.29/157.21 [3445]E(f326(f326(f3(a99),x34451),x34452),f326(f326(a4,x34451),x34452))
% 157.29/157.21 [3458]E(f326(f326(f80(a909),x34581),x34582),f326(f326(f80(a909),x34582),x34581))
% 157.29/157.21 [3459]E(f326(f326(f80(a1),x34591),x34592),f326(f326(f80(a1),x34592),x34591))
% 157.29/157.21 [3460]E(f326(f326(f79(a909),x34601),x34602),f326(f326(f79(a909),x34602),x34601))
% 157.29/157.21 [3461]E(f326(f326(f79(a1),x34611),x34612),f326(f326(f79(a1),x34612),x34611))
% 157.29/157.21 [3483]E(f326(f326(f183(x34831,x34831),f2(a909)),x34832),f31(x34831))
% 157.29/157.21 [3484]E(f326(f189(f910(x34841)),f326(f167(x34841),x34842)),f326(f189(f910(x34841)),x34842))
% 157.29/157.21 [3485]E(f326(f189(f910(x34851)),f326(f168(x34851),x34852)),f326(f189(f910(x34851)),x34852))
% 157.29/157.21 [3486]E(f176(x34861,x34862,f188(f917(a909,a905))),f113(x34861))
% 157.29/157.21 [3487]E(f326(f326(f154(x34871,x34871),f7(x34871)),x34872),x34872)
% 157.29/157.21 [3489]E(f326(f250(a1,a1),f46(x34891,x34892)),f326(f326(f36(a1),x34891),x34892))
% 157.29/157.21 [3506]E(f326(f189(f910(x35061)),f152(x35061,x35062)),f326(f35(x35061),f326(f172(x35061),x35062)))
% 157.29/157.21 [3507]E(f28(f29(x35071,x35072)),f326(f326(f79(a909),f28(x35072)),f326(a112,f2(a909))))
% 157.29/157.21 [3508]E(f326(f280(x35081),f326(f285(x35081,x35081),x35082)),f326(f280(x35081),x35082))
% 157.29/157.21 [3512]P105(f326(f61(x35121),f326(f172(x35121),x35122)))
% 157.29/157.21 [3520]E(f326(f326(f79(a1),x35201),f326(f78(a1),x35202)),f326(f326(f3(a1),x35201),x35202))
% 157.29/157.21 [3527]P23(x35271,x35272,f188(f917(f908(x35271),a905)))
% 157.29/157.21 [3529]E(f326(f309(x35291,x35291,f7(x35291)),x35292),x35292)
% 157.29/157.21 [3530]E(f326(f309(x35301,x35301,f31(x35301)),x35302),x35302)
% 157.29/157.21 [3531]E(f326(f310(x35311,x35311,f7(x35311)),x35312),x35312)
% 157.29/157.21 [3532]E(f326(f310(x35321,x35321,f31(x35321)),x35322),x35322)
% 157.29/157.21 [3533]P105(f326(f241(f917(x35331,a905)),x35332))
% 157.29/157.21 [3535]E(f326(f35(a909),f326(f301(a909,x35351),x35352)),f326(f326(f3(a909),x35352),x35351))
% 157.29/157.21 [3536]E(f326(f301(a909,f326(a112,x35361)),x35362),f305(a909,x35361,x35362))
% 157.29/157.21 [3549]E(f326(f326(f308(x35491),x35492),f188(f917(x35491,a905))),f326(f261(x35491),f326(a323,x35492)))
% 157.29/157.21 [3554]E(f306(x35541,f326(f285(x35541,x35541),x35542)),f326(f285(x35541,x35541),f306(x35541,x35542)))
% 157.29/157.21 [3559]E(f326(f326(f79(a909),f326(a112,x35591)),x35592),f326(f326(f79(a909),x35591),f326(a112,x35592)))
% 157.29/157.21 [3560]E(f326(f326(f3(a909),f326(a112,x35601)),f326(a112,x35602)),f326(f326(f3(a909),x35601),x35602))
% 157.29/157.21 [3566]E(f55(x35661,f2(a909),x35662),f326(f326(f151(f910(x35661)),f113(x35661)),f113(f910(x35661))))
% 157.29/157.21 [3567]E(f326(f35(a909),f304(a909,x35671,x35672)),f326(f326(f3(a909),x35672),x35671))
% 157.29/157.21 [3576]P36(x35761,f326(f326(f287(a909,x35761),a239),x35762))
% 157.29/157.21 [3578]P12(a909,f139(a909,f326(f301(a909,x35781),x35782)))
% 157.29/157.21 [3580]P105(f326(f61(a909),f326(f301(a909,x35801),x35802)))
% 157.29/157.21 [3581]P105(f326(f61(a1),f326(f301(a1,x35811),x35812)))
% 157.29/157.21 [3584]E(f326(f285(f910(x35841),f910(x35841)),f157(x35841,x35842)),f157(x35841,f326(f285(x35841,x35841),x35842)))
% 157.29/157.21 [3585]E(f326(f189(a906),f29(x35851,x35852)),f326(f326(f79(a909),f326(f189(a906),x35852)),f326(a112,f2(a909))))
% 157.29/157.21 [3587]E(f326(f301(a1,x35871),f326(f326(f79(a1),x35872),f77(a1))),f302(a1,x35871,x35872))
% 157.29/157.21 [3590]E(f326(f326(f36(a1),f326(f78(a1),x35901)),f326(f78(a1),x35902)),f326(f326(f36(a1),x35901),x35902))
% 157.29/157.21 [3598]E(f326(f326(f183(f916(x35981,x35981),a905),f77(a909)),x35982),x35982)
% 157.29/157.21 [3600]E(f326(f326(f110(f917(x36001,a905)),x36002),f188(f917(x36001,a905))),x36002)
% 157.29/157.21 [3601]E(f326(f326(f3(f917(x36011,a905)),x36012),f188(f917(x36011,a905))),x36012)
% 157.29/157.21 [3602]E(f326(f326(f101(f917(x36021,a905)),x36022),f241(f917(x36021,a905))),x36022)
% 157.29/157.21 [3603]E(f326(f250(a909,a909),f84(f916(a909,a909),f48(x36031,x36032))),f326(f326(f36(a909),x36031),x36032))
% 157.29/157.21 [3610]E(f302(a1,f326(f326(f79(a1),x36101),f77(a1)),x36102),f304(a1,x36101,x36102))
% 157.29/157.21 [3615]E(f326(f255(a909,a909),f84(f916(a909,a909),f48(x36151,x36152))),f45(a909,x36151,x36152))
% 157.29/157.21 [3625]P105(f326(f326(f328(x36251),x36252),f241(f917(x36251,a905))))
% 157.29/157.21 [3630]E(f326(f326(f3(a909),f326(a112,x36301)),x36302),f326(f35(a909),f302(a909,x36302,x36301)))
% 157.29/157.21 [3656]E(f326(f326(f110(f917(x36561,a905)),x36562),f241(f917(x36561,a905))),f241(f917(x36561,a905)))
% 157.29/157.21 [3657]E(f326(f326(f3(f917(x36571,a905)),x36572),f241(f917(x36571,a905))),f188(f917(x36571,a905)))
% 157.29/157.21 [3658]E(f326(f326(f101(f917(x36581,a905)),x36582),f188(f917(x36581,a905))),f188(f917(x36581,a905)))
% 157.29/157.21 [3673]E(f45(a1,f326(f100(a1),x36731),f326(f100(a1),x36732)),f326(f100(a1),f45(a909,x36731,x36732)))
% 157.29/157.21 [3674]E(f45(a1,f326(f78(a1),x36741),f326(f78(a1),x36742)),f326(f78(a1),f45(a1,x36741,x36742)))
% 157.29/157.21 [3685]E(f326(f189(f910(x36851)),f326(f171(x36851),x36852)),f326(f326(f3(a909),f326(f189(f910(x36851)),x36852)),f77(a909)))
% 157.29/157.21 [3711]E(f326(f326(f36(a1),f45(a1,x37111,x37112)),x37112),f2(a1))
% 157.29/157.21 [3720]E(f326(a5,f45(a909,f326(a22,x37201),f326(a22,x37202))),f45(a99,x37201,x37202))
% 157.29/157.21 [3754]E(f326(a5,f326(f326(f3(a909),f326(a22,x37541)),f326(a22,x37542))),f326(f326(f3(a99),x37541),x37542))
% 157.29/157.21 [3755]E(f326(a5,f326(f326(f80(a909),f326(a22,x37551)),f326(a22,x37552))),f326(f326(f80(a99),x37551),x37552))
% 157.29/157.21 [3756]E(f326(a5,f326(f326(f79(a909),f326(a22,x37561)),f326(a22,x37562))),f326(f326(f79(a99),x37561),x37562))
% 157.29/157.21 [3757]E(f326(a5,f326(f326(f36(a909),f326(a22,x37571)),f326(a22,x37572))),f326(f326(f36(a99),x37571),x37572))
% 157.29/157.21 [3765]E(f326(f309(a909,a909,a112),f326(f301(a909,x37651),x37652)),f326(f301(a909,f326(a112,x37651)),f326(a112,x37652)))
% 157.29/157.21 [3792]P105(f326(f48(x37921,x37922),f84(f916(a909,a909),f48(x37921,x37922))))
% 157.29/157.21 [3816]E(f326(f326(f79(a909),f326(f326(f79(a909),f28(x38161)),f28(x38162))),f326(a112,f2(a909))),f28(f30(x38161,x38162)))
% 157.29/157.21 [3817]E(f45(a909,f326(a112,f45(a909,x38171,x38172)),x38172),f45(a909,f326(a112,x38171),x38172))
% 157.29/157.21 [3829]E(f326(f326(f40(f917(x38291,a905),f917(x38291,a905)),x38292),f7(f917(x38291,a905))),f37(f917(x38291,a905),x38292))
% 157.29/157.21 [3830]E(f326(f326(f39(f917(x38301,a905),f917(x38301,a905)),x38302),f7(f917(x38301,a905))),f38(f917(x38301,a905),x38302))
% 157.29/157.21 [3831]E(f326(f309(f910(x38311),f917(x38311,a905),f172(x38311)),f326(f172(f910(x38311)),f54(x38311,x38312))),f326(f307(x38311),f326(f172(x38311),x38312)))
% 157.29/157.21 [3835]P105(f326(f326(f328(f917(x38351,a905)),x38352),f326(f307(x38351),x38352)))
% 157.29/157.21 [3841]E(f45(a1,f326(f78(a1),f45(a1,x38411,x38412)),x38412),f45(a1,f326(f78(a1),x38411),x38412))
% 157.29/157.21 [3852]P105(f326(f326(f234(f917(x38521,a905)),x38522),f241(f917(x38521,a905))))
% 157.29/157.21 [3854]E(f326(f326(f288(x38541,x38541,x38541),f306(x38541,x38542)),f306(x38541,f306(x38541,x38542))),f306(x38541,x38542))
% 157.29/157.21 [3855]E(f326(f326(f110(f917(x38551,a905)),f326(f263(x38551,x38551),x38552)),f326(f283(x38551,x38551),x38552)),f326(f280(x38551),x38552))
% 157.29/157.21 [3876]E(f312(x38761,x38762,f241(f917(x38761,a905)),f241(f917(x38762,a905))),f241(f917(f915(x38761,x38762),a905)))
% 157.29/157.21 [3927]P105(f326(f326(f234(a909),f45(a909,x39271,x39272)),x39271))
% 157.29/157.21 [3952]P105(f326(f326(f234(a1),f326(f78(a1),f326(f100(a1),x39521))),f326(f100(a1),x39522)))
% 157.29/157.21 [3977]P105(f326(f326(f328(f917(x39771,a905)),f188(f917(x39771,a905))),f326(f307(x39771),x39772)))
% 157.29/157.21 [3982]E(f306(x39821,f326(f326(f288(x39821,x39821,x39821),x39822),f306(x39821,x39822))),f306(x39821,x39822))
% 157.29/157.21 [3985]E(f326(f326(f288(x39851,x39851,x39851),f306(x39851,x39852)),x39852),f326(f326(f288(x39851,x39851,x39851),x39852),f306(x39851,x39852)))
% 157.29/157.21 [3987]E(f326(a104,f326(f326(f79(a1),f326(f326(f3(a1),x39871),x39872)),f77(a1))),f326(f35(a1),f302(a1,x39872,x39871)))
% 157.29/157.21 [4002]E(f326(f283(x40021,x40021),f326(f326(f288(x40021,x40021,x40021),x40022),f306(x40021,x40022))),f326(f283(x40021,x40021),x40022))
% 157.29/157.21 [4003]E(f326(f263(x40031,x40031),f326(f326(f288(x40031,x40031,x40031),x40032),f306(x40031,x40032))),f326(f263(x40031,x40031),x40032))
% 157.29/157.21 [4019]E(f326(f326(f79(a909),f326(f326(f79(a909),f326(f189(a906),x40191)),f326(f189(a906),x40192))),f326(a112,f2(a909))),f326(f189(a906),f30(x40191,x40192)))
% 157.29/157.21 [4022]E(f326(f142(f910(x40221),f910(x40221),f134(x40221),f113(x40221)),f169(f910(x40221),x40222,f113(x40221))),f113(x40221))
% 157.29/157.21 [4031]P24(a909,a909,f326(f326(f9(a909,a909,a909),f79(a909)),x40311),x40312)
% 157.29/157.21 [4033]P12(a909,f326(f168(a909),f326(f326(f154(f910(x40331),a909),f189(f910(x40331))),f179(x40331,x40332))))
% 157.29/157.21 [4066]P50(x40661,f326(f326(f110(f917(f916(x40661,x40661),a905)),x40662),f326(f285(x40661,x40661),x40662)))
% 157.29/157.21 [4067]P50(x40671,f326(f326(f101(f917(f916(x40671,x40671),a905)),x40672),f326(f285(x40671,x40671),x40672)))
% 157.29/157.21 [4078]P105(f326(f326(f235(a1),f326(f78(a1),f326(f100(a1),f326(a112,x40781)))),f326(f100(a1),x40782)))
% 157.29/157.21 [4123]E(f326(f142(f910(x41231),x41231,f326(f9(x41231,f910(x41231),f910(x41231)),f151(x41231)),f113(x41231)),x41232),f326(f168(x41231),x41232))
% 157.29/157.21 [4171]P105(f326(f326(f234(f917(f916(f910(x41711),f910(x41711)),a905)),f158(x41711,x41712)),f306(f910(x41711),f157(x41711,x41712))))
% 157.29/157.21 [4200]P105(f326(f48(x42001,x42002),f326(f326(f251(a909,a909),f326(f326(f36(a909),x42001),x42002)),f45(a909,x42001,x42002))))
% 157.29/157.21 [4212]P105(f326(f326(f234(f917(f916(f910(x42121),f910(x42121)),a905)),f157(x42121,f306(x42121,x42122))),f306(f910(x42121),f157(x42121,x42122))))
% 157.29/157.21 [4431]E(f326(f326(f258(f916(a99,a99),a99,f916(a99,a99),f916(x44311,f916(a99,a99))),f266(f326(f165(a99),f326(f326(f154(f916(a99,x44311),a99),f250(a99,x44311)),x44312)))),f326(f326(f10(x44311,f917(f916(a99,a99),f916(x44311,f916(a99,a99))),a99),f251(x44311,f916(a99,a99))),f267(x44311,x44312))),f265(x44311,x44312))
% 157.29/157.21 [4508]E(f223(a909,f916(x45081,f911(x45081)),f2(a909),f326(f256(x45081,f911(x45081),a909),f326(f18(f917(f911(x45081),a909),x45081),f326(f326(f9(f911(x45081),a909,a909),f326(f326(f10(a909,f917(a909,a909),f911(x45081)),f79(a909)),f189(f911(x45081)))),f77(a909)))),f326(f135(x45081),x45082)),f326(f189(f911(x45081)),x45082))
% 157.29/157.21 [4614]E(f326(f256(f917(f916(x46141,x46141),a905),f917(f916(x46141,x46141),a905),f917(f917(x46142,x46141),f916(f917(f916(x46142,x46142),a905),f917(f916(x46142,x46142),a905)))),f326(f326(f9(f917(f916(x46141,x46141),a905),f917(f917(f916(x46141,x46141),a905),f917(f917(x46142,x46141),f917(f916(x46142,x46142),a905))),f917(f917(f916(x46141,x46141),a905),f917(f917(x46142,x46141),f916(f917(f916(x46142,x46142),a905),f917(f916(x46142,x46142),a905))))),f326(f326(f10(f917(f917(f917(x46142,x46141),f917(f916(x46142,x46142),a905)),f917(f917(x46142,x46141),f916(f917(f916(x46142,x46142),a905),f917(f916(x46142,x46142),a905)))),f917(f917(f917(f916(x46141,x46141),a905),f917(f917(x46142,x46141),f917(f916(x46142,x46142),a905))),f917(f917(f916(x46141,x46141),a905),f917(f917(x46142,x46141),f916(f917(f916(x46142,x46142),a905),f917(f916(x46142,x46142),a905))))),f917(f916(x46141,x46141),a905)),f10(f917(f917(x46142,x46141),f917(f916(x46142,x46142),a905)),f917(f917(x46142,x46141),f916(f917(f916(x46142,x46142),a905),f917(f916(x46142,x46142),a905))),f917(f916(x46141,x46141),a905))),f326(f326(f10(f917(f917(x46142,x46141),f917(f917(f916(x46142,x46142),a905),f916(f917(f916(x46142,x46142),a905),f917(f916(x46142,x46142),a905)))),f917(f917(f917(x46142,x46141),f917(f916(x46142,x46142),a905)),f917(f917(x46142,x46141),f916(f917(f916(x46142,x46142),a905),f917(f916(x46142,x46142),a905)))),f917(f916(x46141,x46141),a905)),f20(f917(x46142,x46141),f917(f916(x46142,x46142),a905),f916(f917(f916(x46142,x46142),a905),f917(f916(x46142,x46142),a905)))),f326(f326(f10(f917(f917(x46142,x46141),f917(f916(x46142,x46142),a905)),f917(f917(x46142,x46141),f917(f917(f916(x46142,x46142),a905),f916(f917(f916(x46142,x46142),a905),f917(f916(x46142,x46142),a905)))),f917(f916(x46141,x46141),a905)),f326(f10(f917(f916(x46142,x46142),a905),f917(f917(f916(x46142,x46142),a905),f916(f917(f916(x46142,x46142),a905),f917(f916(x46142,x46142),a905))),f917(x46142,x46141)),f251(f917(f916(x46142,x46142),a905),f917(f916(x46142,x46142),a905)))),f287(x46141,x46142))))),f287(x46141,x46142))),f73(x46141,x46142))
% 157.29/157.21 [4677]~E(f326(f307(x46771),x46772),f188(f917(f917(x46771,a905),a905)))
% 157.29/157.21 [4688]~P105(f326(f326(f172(x46881),f113(x46881)),x46882))
% 157.29/157.21 [4692]~P105(f326(f326(f328(x46921),x46922),f188(f917(x46921,a905))))
% 157.29/157.21 [4700]~P105(f326(f326(f235(f917(x47001,a905)),x47002),f188(f917(x47001,a905))))
% 157.29/157.21 [3538]E(f326(f326(f3(a909),x35381),f326(f326(f79(a909),x35381),x35382)),f2(a909))
% 157.29/157.21 [3541]E(f326(f326(f110(f917(x35411,a905)),x35412),x35412),x35412)
% 157.29/157.21 [3542]E(f326(f326(f101(f917(x35421,a905)),x35422),x35422),x35422)
% 157.29/157.21 [3570]E(f326(f326(f3(f917(x35701,a905)),x35702),x35702),f188(f917(x35701,a905)))
% 157.29/157.21 [3573]E(f326(f143(x35731,x35732),f2(a909)),f188(f917(f916(f910(x35731),f910(x35731)),a905)))
% 157.29/157.21 [3574]E(f326(f326(f79(a909),x35741),f326(a112,x35742)),f326(a112,f326(f326(f79(a909),x35741),x35742)))
% 157.29/157.21 [3586]E(f194(f326(f100(a1),x35861),f326(f100(a1),x35862)),f326(f100(a1),f326(f326(f3(a909),x35861),x35862)))
% 157.29/157.21 [3589]E(f326(f326(f36(a1),f326(f78(a1),x35891)),x35892),f326(f326(f36(a1),x35891),f326(f78(a1),x35892)))
% 157.29/157.21 [3593]E(f326(f35(a1),f326(f301(a1,x35931),x35932)),f326(a104,f326(f326(f3(a1),x35932),x35931)))
% 157.29/157.21 [3596]E(f326(f326(f79(a909),f326(a112,x35961)),x35962),f326(a112,f326(f326(f79(a909),x35961),x35962)))
% 157.29/157.21 [3599]E(f326(f78(f917(x35991,a905)),f326(f78(f917(x35991,a905)),x35992)),x35992)
% 157.29/157.21 [3612]E(f179(x36121,f326(f326(f151(f910(x36121)),f113(x36121)),x36122)),f179(x36121,x36122))
% 157.29/157.21 [3616]E(f326(f326(f79(a909),x36161),f326(f326(f80(a909),x36161),x36162)),f326(f326(f80(a909),x36161),f326(a112,x36162)))
% 157.29/157.21 [3623]E(f326(f326(a4,f326(a5,x36231)),f326(a5,x36232)),f326(a5,f326(f326(f3(a909),x36231),x36232)))
% 157.29/157.21 [3638]E(f326(f326(f80(a1),f326(f78(a1),x36381)),x36382),f326(f78(a1),f326(f326(f80(a1),x36381),x36382)))
% 157.29/157.21 [3640]E(f326(f326(f243(a1),f326(f100(a1),x36401)),x36402),f326(f100(a1),f326(f326(f243(a909),x36401),x36402)))
% 157.29/157.21 [3641]E(f326(f326(f80(a99),f326(a5,x36411)),f326(a5,x36412)),f326(a5,f326(f326(f80(a909),x36411),x36412)))
% 157.29/157.21 [3642]E(f326(f326(f79(a99),f326(a5,x36421)),f326(a5,x36422)),f326(a5,f326(f326(f79(a909),x36421),x36422)))
% 157.29/157.21 [3643]E(f326(f326(f232(a909),f326(a112,x36431)),f326(a112,x36432)),f326(a112,f326(f326(f232(a909),x36431),x36432)))
% 157.29/157.21 [3644]E(f326(f326(f233(a909),f326(a112,x36441)),f326(a112,x36442)),f326(a112,f326(f326(f233(a909),x36441),x36442)))
% 157.29/157.21 [3649]E(f326(f172(a909),f139(a909,f326(f301(a909,x36491),x36492))),f326(f301(a909,x36491),x36492))
% 157.29/157.21 [3650]E(f311(x36501,f326(f326(f308(x36501),x36502),f188(f917(x36501,a905)))),x36502)
% 157.29/157.21 [3654]E(f326(f283(x36541,x36542),f188(f917(f916(x36541,x36542),a905))),f188(f917(x36542,a905)))
% 157.29/157.21 [3655]E(f326(f263(x36551,x36552),f188(f917(f916(x36551,x36552),a905))),f188(f917(x36551,a905)))
% 157.29/157.21 [3659]E(f326(a104,f326(f326(f3(a1),x36591),x36592)),f326(f35(a1),f304(a1,x36592,x36591)))
% 157.29/157.21 [3664]E(f326(f326(f79(a909),x36641),f326(f326(f80(a909),x36642),x36641)),f326(f326(f80(a909),f326(a112,x36642)),x36641))
% 157.29/157.21 [3666]E(f326(f326(f60(x36661),f188(f917(x36661,a905))),x36662),f188(f917(f917(x36661,a905),a905)))
% 157.29/157.21 [3675]E(f326(f189(f910(a909)),f139(a909,f326(f301(a909,x36751),x36752))),f326(f326(f3(a909),x36752),x36751))
% 157.29/157.21 [3690]E(f326(f326(f110(f917(x36901,a905)),f188(f917(x36901,a905))),x36902),x36902)
% 157.29/157.21 [3691]E(f326(f326(f101(f917(x36911,a905)),f241(f917(x36911,a905))),x36912),x36912)
% 157.29/157.21 [3694]E(f326(f326(f79(a1),f326(f78(a1),x36941)),f326(f78(a1),x36942)),f326(f78(a1),f326(f326(f79(a1),x36941),x36942)))
% 157.29/157.21 [3696]E(f326(f326(f80(a1),f326(f103(a1),x36961)),f326(f103(a1),x36962)),f326(f103(a1),f326(f326(f80(a1),x36961),x36962)))
% 157.29/157.21 [3698]E(f326(f326(f80(a1),f326(f100(a1),x36981)),f326(f100(a1),x36982)),f326(f100(a1),f326(f326(f80(a909),x36981),x36982)))
% 157.29/157.21 [3699]E(f326(f326(f79(a1),f326(f103(a1),x36991)),f326(f103(a1),x36992)),f326(f103(a1),f326(f326(f79(a1),x36991),x36992)))
% 157.29/157.21 [3701]E(f326(f326(f79(a1),f326(f100(a1),x37011)),f326(f100(a1),x37012)),f326(f100(a1),f326(f326(f79(a909),x37011),x37012)))
% 157.29/157.21 [3702]E(f326(f326(f36(a1),f326(f100(a1),x37021)),f326(f100(a1),x37022)),f326(f100(a1),f326(f326(f36(a909),x37021),x37022)))
% 157.29/157.21 [3721]E(f326(f326(f8(x37211,a909),f326(f18(a909,x37211),f77(a909))),x37212),f326(f35(x37211),x37212))
% 157.29/157.21 [3727]E(f326(f78(a1),f45(a1,f326(f78(a1),x37271),x37272)),f45(a1,x37271,f326(f78(a1),x37272)))
% 157.29/157.21 [3729]E(f326(f172(a1),f178(x37291,f326(f326(f3(a1),x37292),f77(a1)))),f326(f301(a1,x37291),x37292))
% 157.29/157.21 [3734]P105(f326(f326(f234(a909),x37341),f326(f326(f79(a909),x37342),x37341)))
% 157.29/157.21 [3735]P105(f326(f326(f234(a909),x37351),f326(f326(f79(a909),x37351),x37352)))
% 157.29/157.21 [3737]E(f326(f326(f110(f917(x37371,a905)),f241(f917(x37371,a905))),x37372),f241(f917(x37371,a905)))
% 157.29/157.21 [3738]E(f326(f326(f3(f917(x37381,a905)),f188(f917(x37381,a905))),x37382),f188(f917(x37381,a905)))
% 157.29/157.21 [3739]E(f326(f326(f101(f917(x37391,a905)),f188(f917(x37391,a905))),x37392),f188(f917(x37391,a905)))
% 157.29/157.21 [3746]E(f326(f326(f251(a1,a1),x37461),f326(f78(a1),x37462)),f326(a51,f326(f326(f251(a1,a1),x37461),x37462)))
% 157.29/157.21 [3747]E(f326(f301(a1,f326(f326(f79(a1),x37471),f77(a1))),x37472),f305(a1,x37471,x37472))
% 157.29/157.21 [3758]E(f326(f326(f80(a909),x37581),f326(f326(f36(a909),x37582),x37581)),f326(f326(f3(a909),x37582),f45(a909,x37582,x37581)))
% 157.29/157.21 [3759]E(f326(f326(f80(a1),x37591),f326(f326(f36(a1),x37592),x37591)),f326(f326(f3(a1),x37592),f45(a1,x37592,x37591)))
% 157.29/157.21 [3762]E(f326(f172(a1),f178(f326(f326(f79(a1),x37621),f77(a1)),x37622)),f304(a1,x37621,x37622))
% 157.29/157.21 [3766]P105(f326(f326(f234(f917(x37661,a905)),x37662),x37662))
% 157.29/157.21 [3769]E(f326(f326(f110(f917(x37691,a905)),x37692),f326(f78(f917(x37691,a905)),x37692)),f241(f917(x37691,a905)))
% 157.29/157.21 [3770]E(f326(f326(f101(f917(x37701,a905)),x37702),f326(f78(f917(x37701,a905)),x37702)),f188(f917(x37701,a905)))
% 157.29/157.21 [3778]E(f326(f326(f3(a909),f326(f326(f3(a909),x37781),f77(a909))),x37782),f326(f326(f3(a909),x37781),f326(a112,x37782)))
% 157.29/157.21 [3784]E(f326(f326(f3(f917(x37841,a905)),f241(f917(x37841,a905))),x37842),f326(f78(f917(x37841,a905)),x37842))
% 157.29/157.21 [3785]E(f326(f326(f3(a1),f326(f103(a1),x37851)),f326(f103(a1),x37852)),f326(f103(a1),f326(f326(f79(a1),x37851),f326(f78(a1),x37852))))
% 157.29/157.21 [3798]E(f326(f172(a909),f139(a909,f326(f301(a909,x37981),f326(a112,x37982)))),f302(a909,x37981,x37982))
% 157.29/157.21 [3814]E(f326(f189(f910(f910(x38141))),f54(x38141,x38142)),f326(f326(f243(a909),f326(a112,f326(a112,f2(a909)))),f326(f189(f910(x38141)),x38142)))
% 157.29/157.21 [3833]E(f326(f326(f183(f916(x38331,x38331),a905),f2(a909)),x38332),f306(x38331,f188(f917(f916(x38331,x38331),a905))))
% 157.29/157.21 [3837]P105(f326(f137(a909),f139(a909,f326(f301(a909,x38371),x38372))))
% 157.29/157.21 [3853]E(f326(f309(a1,a909,a104),f302(a1,f326(f100(a1),x38531),f326(f100(a1),x38532))),f302(a909,x38531,x38532))
% 157.29/157.21 [3862]E(f185(a909,f2(a909),f7(a909),f326(f326(f3(a909),x38621),x38622)),f326(f326(f3(a909),x38621),f326(a112,x38622)))
% 157.29/157.21 [3863]E(f326(a104,f326(f326(f3(a1),x38631),f326(f326(f79(a1),x38632),f77(a1)))),f326(f35(a1),f305(a1,x38632,x38631)))
% 157.29/157.21 [3899]E(f326(f326(f154(a909,a909),a112),f139(a909,f326(f301(a909,x38991),x38992))),f139(a909,f326(f301(a909,f326(a112,x38991)),f326(a112,x38992))))
% 157.29/157.21 [3907]E(f326(f172(a1),f178(f326(f326(f79(a1),x39071),f77(a1)),f326(f326(f3(a1),x39072),f77(a1)))),f305(a1,x39071,x39072))
% 157.29/157.21 [3919]P105(f326(f326(f234(f917(x39191,a905)),f188(f917(x39191,a905))),x39192))
% 157.29/157.21 [3923]E(f84(x39231,f326(f326(f9(x39231,x39231,a905),a323),x39232)),x39232)
% 157.29/157.21 [3924]E(f89(x39241,f326(f326(f9(x39241,x39241,a905),a323),x39242)),x39242)
% 157.29/157.21 [3928]E(f326(f172(a909),f139(a909,f326(f301(a909,f326(a112,x39281)),f326(a112,x39282)))),f304(a909,x39281,x39282))
% 157.29/157.21 [3955]E(f326(f326(f253(x39551,x39552),f241(f917(x39551,a905))),f326(f18(f917(x39552,a905),x39551),f241(f917(x39552,a905)))),f241(f917(f916(x39551,x39552),a905)))
% 157.29/157.21 [3989]E(f326(f261(x39891),f326(f326(f10(a905,a905,x39891),a321),x39892)),f326(f78(f917(x39891,a905)),f326(f261(x39891),x39892)))
% 157.29/157.21 [3992]E(f326(f261(x39921),f326(f326(f9(x39921,x39921,a905),a323),x39922)),f326(f326(f308(x39921),x39922),f188(f917(x39921,a905))))
% 157.29/157.21 [3999]E(f326(f326(f79(a1),f326(f326(f3(a1),x39991),x39992)),f326(f326(f3(a1),x39991),x39992)),f326(f326(f3(a1),f326(f326(f79(a1),x39991),x39991)),f326(f326(f79(a1),x39992),x39992)))
% 157.29/157.21 [4000]E(f326(f326(f79(a1),f326(f326(f79(a1),x40001),x40001)),f326(f326(f79(a1),x40002),x40002)),f326(f326(f79(a1),f326(f326(f79(a1),x40001),x40002)),f326(f326(f79(a1),x40001),x40002)))
% 157.29/157.21 [4016]P105(f326(f326(f234(a909),f326(f35(x40161),f326(f172(x40161),x40162))),f326(f189(f910(x40161)),x40162)))
% 157.29/157.21 [4017]P105(f326(f326(f234(a909),f326(f189(f910(x40171)),f152(x40171,x40172))),f326(f189(f910(x40171)),x40172)))
% 157.29/157.21 [4028]E(f326(f261(x40281),f326(f326(f9(x40281,f917(x40281,a905),a905),f328(x40281)),x40282)),x40282)
% 157.29/157.21 [4042]E(f326(f326(f175(x40421),f326(f326(f3(a909),f326(f189(f910(x40421)),x40422)),f77(a909))),x40422),f114(x40421,x40422))
% 157.29/157.21 [4065]E(f185(a909,f2(a909),f326(f326(f10(a909,a909,a909),a112),f326(f232(a909),x40651)),x40652),f326(f326(f232(a909),f326(a112,x40651)),x40652))
% 157.29/157.21 [4070]E(f37(f917(x40701,a905),f326(f309(f917(f916(x40701,x40701),a905),f917(x40701,a905),f280(x40701)),x40702)),f326(f280(x40701),f37(f917(f916(x40701,x40701),a905),x40702)))
% 157.29/157.21 [4071]E(f185(a909,f326(a112,x40711),f326(f326(f10(a909,a909,a909),a112),f326(f233(a909),x40711)),x40712),f326(f326(f233(a909),f326(a112,x40711)),x40712))
% 157.29/157.21 [4073]E(f326(f326(f251(a1,a1),f326(f326(f36(a1),f326(f75(a1),x40731)),f326(f75(a1),x40732))),f45(a1,f326(f75(a1),x40731),f326(f75(a1),x40732))),f53(x40731,x40732))
% 157.29/157.21 [4096]P105(f326(f326(f234(f917(f917(x40961,a905),a905)),x40962),f326(f307(x40961),f37(f917(x40961,a905),x40962))))
% 157.29/157.21 [4128]E(f326(f326(f40(x41281,f917(x41281,a905)),x41282),f326(f326(f9(x41281,f917(x41281,a905),f917(x41281,a905)),f308(x41281)),f188(f917(x41281,a905)))),x41282)
% 157.29/157.21 [4129]E(f326(f326(f288(x41291,x41291,x41291),f326(f285(x41291,x41291),x41292)),f306(x41291,f326(f285(x41291,x41291),x41292))),f326(f285(x41291,x41291),f326(f326(f288(x41291,x41291,x41291),x41292),f306(x41291,x41292))))
% 157.29/157.21 [4192]E(f326(f172(x41921),f326(f142(f910(x41921),f910(x41921),f134(x41921),f113(x41921)),x41922)),f326(f326(f40(f910(x41921),f917(x41921,a905)),f326(f172(f910(x41921)),x41922)),f172(x41921)))
% 157.29/157.21 [4223]E(f326(f326(f110(f917(f916(x42231,x42231),a905)),f306(x42231,f188(f917(f916(x42231,x42231),a905)))),f326(f326(f288(x42231,x42231,x42231),f306(x42231,x42232)),x42232)),f306(x42231,x42232))
% 157.29/157.21 [4259]E(f326(f326(f181(x42591,x42591),x42592),x42592),f326(f326(f154(x42591,f916(x42591,x42591)),f326(f326(f20(x42591,x42591,f916(x42591,x42591)),f251(x42591,x42591)),f7(x42591))),x42592))
% 157.29/157.21 [4373]E(f326(f142(a909,f910(x43731),f326(f9(f910(x43731),a909,a909),f326(f326(f10(a909,f917(a909,a909),f910(x43731)),f233(a909)),f189(f910(x43731)))),f2(a909)),f326(f168(f910(x43731)),x43732)),f326(f189(f910(f910(x43731))),f179(x43731,x43732)))
% 157.29/157.21 [4445]E(f326(f326(f287(f916(a909,f910(x44451)),f910(x44451)),f319(a909,f910(x44451),a239,f145(x44451,x44452))),f326(f326(f20(f910(x44451),f910(x44451),f916(a909,f910(x44451))),f326(f326(f10(a909,f917(f910(x44451),f916(a909,f910(x44451))),f910(x44451)),f251(a909,f910(x44451))),f189(f910(x44451)))),f7(f910(x44451)))),f146(x44451,x44452))
% 157.29/157.21 [4572]E(f326(f261(x45721),f326(f326(f10(f917(f917(x45721,a905),a905),a905,x45721),f86(f917(x45721,a905))),f326(f326(f10(f917(f917(x45721,a905),a905),f917(f917(x45721,a905),a905),x45721),f326(f20(f917(x45721,a905),a905,a905),f326(f326(f10(a905,f917(a905,a905),f917(x45721,a905)),a324),f326(f326(f9(f917(x45721,a905),f917(f917(x45721,a905),a905),a905),f328(f917(x45721,a905))),x45722)))),f328(x45721)))),f37(f917(x45721,a905),x45722))
% 157.29/157.21 [4573]E(f326(f261(x45731),f326(f326(f10(f917(f917(x45731,a905),a905),a905,x45731),f87(f917(x45731,a905))),f326(f326(f10(f917(f917(x45731,a905),a905),f917(f917(x45731,a905),a905),x45731),f326(f20(f917(x45731,a905),a905,a905),f326(f326(f10(a905,f917(a905,a905),f917(x45731,a905)),a329),f326(f326(f9(f917(x45731,a905),f917(f917(x45731,a905),a905),a905),f328(f917(x45731,a905))),x45732)))),f328(x45731)))),f38(f917(x45731,a905),x45732))
% 157.29/157.21 [4701]~P105(f326(f326(f235(a1),f326(f100(a1),x47011)),f326(f78(a1),f326(f100(a1),x47012))))
% 157.29/157.21 [3662]E(f326(f326(f3(a909),f326(f326(f79(a909),x36621),x36622)),x36622),x36621)
% 157.29/157.21 [3663]E(f326(f326(f3(a909),f326(f326(f79(a909),x36631),x36632)),x36631),x36632)
% 157.29/157.21 [3728]E(f326(f326(f79(a909),f326(f326(f3(a909),x37281),x37282)),x37282),f326(f326(f233(a909),x37281),x37282))
% 157.29/157.21 [3840]E(f326(f326(f80(a909),f326(f326(f36(a909),x38401),x38402)),x38402),f326(f326(f3(a909),x38401),f45(a909,x38401,x38402)))
% 157.29/157.21 [3867]E(f326(f172(a909),f139(a909,f326(f301(a909,f326(a112,x38671)),x38672))),f305(a909,x38671,x38672))
% 157.29/157.21 [3875]E(f326(f100(a1),f216(f326(a104,f326(f75(a1),x38751)),f326(a104,f326(f75(a1),x38752)))),f326(f326(a217,x38751),x38752))
% 157.29/157.21 [3877]E(f326(f326(f110(f917(x38771,a905)),f326(f78(f917(x38771,a905)),x38772)),x38772),f241(f917(x38771,a905)))
% 157.29/157.21 [3878]E(f326(f326(f101(f917(x38781,a905)),f326(f78(f917(x38781,a905)),x38782)),x38782),f188(f917(x38781,a905)))
% 157.29/157.21 [3895]P105(f326(f326(f234(a909),f326(f326(f3(a909),x38951),x38952)),x38951))
% 157.29/157.21 [3896]P105(f326(f326(f234(a909),f326(f326(f36(a909),x38961),x38962)),x38961))
% 157.29/157.21 [3920]P105(f326(f326(f235(a909),x39201),f326(a112,f326(f326(f79(a909),x39202),x39201))))
% 157.29/157.21 [3921]P105(f326(f326(f235(a909),x39211),f326(a112,f326(f326(f79(a909),x39211),x39212))))
% 157.29/157.21 [3939]E(f326(f326(f80(a909),f326(a104,f326(f75(a1),x39391))),f326(a104,f326(f75(a1),x39392))),f326(a104,f326(f75(a1),f326(f326(f80(a1),x39391),x39392))))
% 157.29/157.21 [3951]P105(f326(f326(f234(a1),f2(a1)),f326(f326(f243(a1),f326(f75(a1),x39511)),x39512)))
% 157.29/157.21 [4021]E(f326(f284(f910(x40211),f910(x40211),f158(x40211,x40212)),f326(f326(f308(f910(x40211)),f113(x40211)),f188(f917(f910(x40211),a905)))),f326(f326(f308(f910(x40211)),f113(x40211)),f188(f917(f910(x40211),a905))))
% 157.29/157.21 [4040]E(f326(f326(f110(f917(f916(x40401,x40401),a905)),f306(x40401,x40402)),f306(x40401,f188(f917(f916(x40401,x40401),a905)))),f306(x40401,x40402))
% 157.29/157.21 [4053]E(f326(f326(f36(a1),f326(f103(a1),f326(f326(f79(a1),x40531),x40531))),f326(f103(a1),f326(f326(f79(a1),x40532),x40532))),f326(f326(f36(a1),f326(f103(a1),x40531)),f326(f103(a1),x40532)))
% 157.29/157.21 [4118]E(f326(f326(f243(a1),x41181),f326(f103(a909),f326(f326(f79(a1),x41182),x41182))),f326(f326(f85(a1,a1),f326(f326(f243(a1),x41181),f326(f103(a909),x41182))),f326(f326(f20(a1,a1,a1),f80(a1)),f7(a1))))
% 157.29/157.21 [4124]E(f326(f261(f917(x41241,a905)),f326(f326(f9(f917(x41241,a905),f917(x41241,a905),a905),f234(f917(x41241,a905))),x41242)),f326(f307(x41241),x41242))
% 157.29/157.21 [4140]E(f326(f326(f154(a1,a909),a104),f326(f326(f134(a1),f326(f326(f154(a909,a1),f100(a1)),x41401)),f326(f326(f154(a909,a1),f100(a1)),x41402))),f326(f326(f134(a909),x41401),x41402))
% 157.29/157.21 [4170]E(f326(f309(a1,a1,f326(f326(f9(a1,a1,a1),f79(a1)),x41701)),f326(f301(a1,f2(a1)),f326(f326(f3(a1),x41702),x41701))),f326(f301(a1,x41701),x41702))
% 157.29/157.21 [4172]P52(x41721,f326(f326(f3(f917(f916(x41721,x41721),a905)),x41722),f306(x41721,f188(f917(f916(x41721,x41721),a905)))))
% 157.29/157.21 [4190]E(f326(f189(f910(x41901)),f326(f142(f910(x41901),f910(x41901),f134(x41901),f113(x41901)),x41902)),f326(f165(a909),f326(f326(f154(f910(x41901),a909),f189(f910(x41901))),x41902)))
% 157.29/157.21 [4194]P51(x41941,f241(f917(x41941,a905)),f326(f326(f110(f917(f916(x41941,x41941),a905)),x41942),f306(x41941,f188(f917(f916(x41941,x41941),a905)))))
% 157.29/157.21 [4239]E(f185(a909,f2(a909),f326(f326(f10(a909,a909,a909),a112),f326(f326(f9(a909,a909,a909),f232(a909)),x42391)),x42392),f326(f326(f232(a909),x42392),f326(a112,x42391)))
% 157.29/157.21 [4242]E(f185(a909,f326(a112,x42421),f326(f326(f10(a909,a909,a909),a112),f326(f326(f9(a909,a909,a909),f233(a909)),x42421)),x42422),f326(f326(f233(a909),x42422),f326(a112,x42421)))
% 157.29/157.21 [4245]E(f326(f309(x42451,f910(x42451),f326(f326(f9(x42451,f910(x42451),f910(x42451)),f151(x42451)),f113(x42451))),x42452),f174(x42451,x42452,f326(f326(f308(f910(x42451)),f113(x42451)),f188(f917(f910(x42451),a905)))))
% 157.29/157.21 [4247]E(f326(f326(f110(f917(f916(x42471,x42471),a905)),f326(f326(f288(x42471,x42471,x42471),x42472),f306(x42471,x42472))),f306(x42471,f188(f917(f916(x42471,x42471),a905)))),f306(x42471,x42472))
% 157.29/157.21 [4254]P105(f326(f326(f234(f917(f916(x42541,x42541),a905)),f262(x42541,x42542)),f326(f326(f253(x42541,x42541),x42542),f326(f18(f917(x42541,a905),x42541),x42542))))
% 157.29/157.21 [4257]E(f326(f309(a1,a909,a104),f326(f326(f110(f917(a1,a905)),f326(f309(a909,a1,f100(a1)),x42571)),f326(f309(a909,a1,f100(a1)),x42572))),f326(f326(f110(f917(a909,a905)),x42571),x42572))
% 157.29/157.21 [4258]E(f326(f309(a1,a909,a104),f326(f326(f101(f917(a1,a905)),f326(f309(a909,a1,f100(a1)),x42581)),f326(f309(a909,a1,f100(a1)),x42582))),f326(f326(f101(f917(a909,a905)),x42581),x42582))
% 157.29/157.21 [4261]E(f326(f261(x42611),f326(f326(f10(a905,a905,x42611),a321),f326(f326(f9(x42611,f917(x42611,a905),a905),f328(x42611)),x42612))),f326(f78(f917(x42611,a905)),x42612))
% 157.29/157.21 [4288]E(f326(f142(f910(x42881),f910(x42881),f134(x42881),f113(x42881)),f326(f326(f154(f910(x42881),f910(x42881)),f168(x42881)),f326(f168(f910(x42881)),x42882))),f326(f168(x42881),f326(f142(f910(x42881),f910(x42881),f134(x42881),f113(x42881)),x42882)))
% 157.29/157.21 [4317]E(f326(f326(f40(a909,f917(f916(x43171,x43171),a905)),f241(f917(a909,a905))),f326(f326(f9(a909,f917(f916(x43171,x43171),a905),f917(f916(x43171,x43171),a905)),f183(f916(x43171,x43171),a905)),x43172)),f306(x43171,x43172))
% 157.29/157.21 [4335]E(f84(x43351,f326(f326(f10(f917(x43351,a905),a905,x43351),f326(a323,x43352)),f326(f326(f9(x43351,f917(x43351,a905),f917(x43351,a905)),f308(x43351)),f188(f917(x43351,a905))))),f311(x43351,x43352))
% 157.29/157.21 [4343]E(f326(f189(f910(x43431)),f152(x43431,f326(f142(f910(x43431),f910(x43431),f134(x43431),f113(x43431)),x43432))),f326(f35(x43431),f326(f326(f40(f910(x43431),f917(x43431,a905)),f326(f172(f910(x43431)),x43432)),f172(x43431))))
% 157.29/157.21 [4357]E(f326(f326(f110(f917(f916(x43571,x43571),a905)),x43572),f326(f326(f288(x43571,x43571,x43571),f326(f326(f288(x43571,x43571,x43571),x43572),f306(x43571,x43572))),x43572)),f326(f326(f288(x43571,x43571,x43571),x43572),f306(x43571,x43572)))
% 157.29/157.21 [4381]P105(f326(f326(f234(f917(f916(x43811,x43811),a905)),f326(f326(f288(x43811,x43811,x43811),x43812),f306(x43811,x43812))),f326(f326(f253(x43811,x43811),f326(f280(x43811),x43812)),f326(f18(f917(x43811,a905),x43811),f326(f280(x43811),x43812)))))
% 157.29/157.21 [4422]E(f326(f261(f910(x44221)),f326(f326(f9(f910(x44221),f917(x44221,a905),a905),f326(f326(f10(f917(x44221,a905),f917(f917(x44221,a905),a905),f910(x44221)),f234(f917(x44221,a905))),f172(x44221))),x44222)),f161(x44221,x44222))
% 157.29/157.21 [4433]E(f326(f156(f910(x44331),x44331,f113(x44331),f326(f326(f10(f910(x44331),f917(f910(x44331),f910(x44331)),x44331),f326(f9(f910(x44331),f910(x44331),f910(x44331)),f134(x44331))),f326(f326(f9(x44331,f910(x44331),f910(x44331)),f151(x44331)),f113(x44331)))),x44332),f326(f167(x44331),x44332))
% 157.29/157.21 [4473]P24(f917(x44731,x44732),f917(f916(x44731,x44732),a905),f326(f326(f10(f917(f916(x44731,x44732),a905),f917(f916(x44731,x44732),a905),f917(x44731,x44732)),f261(f916(x44731,x44732))),f326(f326(f10(f917(x44731,f917(x44732,a905)),f917(f916(x44731,x44732),a905),f917(x44731,x44732)),f256(x44731,x44732,a905)),f326(f10(x44732,f917(x44732,a905),x44731),f326(f9(x44732,x44732,a905),a323)))),f241(f917(f917(x44731,x44732),a905)))
% 157.29/157.21 [4478]E(f45(a1,f326(f103(a1),f326(f326(f79(a1),x44781),x44781)),f326(f103(a1),f326(f326(f79(a1),x44782),x44782))),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f45(a1,f326(f103(a1),x44781),f326(f103(a1),x44782))))
% 157.29/157.21 [4522]E(f326(f326(f40(x45221,f917(f916(x45221,x45221),a905)),x45222),f326(f326(f9(x45221,f917(f916(x45221,x45221),a905),f917(f916(x45221,x45221),a905)),f326(f326(f10(f916(x45221,x45221),f917(f917(f916(x45221,x45221),a905),f917(f916(x45221,x45221),a905)),x45221),f308(f916(x45221,x45221))),f326(f326(f20(x45221,x45221,f916(x45221,x45221)),f251(x45221,x45221)),f7(x45221)))),f188(f917(f916(x45221,x45221),a905)))),f262(x45221,x45222))
% 157.29/157.21 [4530]E(f202(x45301,f326(f326(f251(a1,a1),f326(f78(a1),f326(f326(f72(f916(a1,a1),a1,x45301,f250(a1,a1)),f212(x45301)),x45302))),f326(f326(f72(f916(a1,a1),a1,x45301,f255(a1,a1)),f212(x45301)),x45302))),f227(x45301,x45302))
% 157.29/157.21 [4611]E(f326(f261(f917(x46111,a905)),f326(f326(f10(f917(f917(x46111,a905),a905),a905,f917(x46111,a905)),f86(f917(x46111,a905))),f326(f326(f9(f917(x46111,a905),f917(f917(x46111,a905),a905),f917(f917(x46111,a905),a905)),f326(f326(f10(f917(f917(x46111,a905),f917(a905,a905)),f917(f917(f917(x46111,a905),a905),f917(f917(x46111,a905),a905)),f917(x46111,a905)),f20(f917(x46111,a905),a905,a905)),f326(f326(f10(f917(f917(x46111,a905),a905),f917(f917(x46111,a905),f917(a905,a905)),f917(x46111,a905)),f326(f10(a905,f917(a905,a905),f917(x46111,a905)),a324)),f326(f326(f9(f917(x46111,a905),f917(f917(x46111,a905),f917(x46111,a905)),f917(f917(x46111,a905),a905)),f326(f326(f10(f917(f917(x46111,a905),a905),f917(f917(f917(x46111,a905),f917(x46111,a905)),f917(f917(x46111,a905),a905)),f917(x46111,a905)),f10(f917(x46111,a905),a905,f917(x46111,a905))),a323)),f78(f917(x46111,a905)))))),f326(f326(f10(f917(f917(x46111,a905),a905),a905,f917(x46111,a905)),f326(f328(f917(x46111,a905)),x46112)),f307(x46111))))),f326(f307(x46111),f326(f78(f917(x46111,a905)),x46112)))
% 157.29/157.21 [4699]~E(f326(f326(f79(a1),x46991),x46991),f326(f326(f3(a1),f326(f326(f79(a1),x46992),x46992)),a97))
% 157.29/157.21 [4703]~P105(f326(f326(f235(a909),f326(f326(f79(a909),x47031),x47032)),x47032))
% 157.29/157.21 [4704]~P105(f326(f326(f235(a909),f326(f326(f79(a909),x47041),x47042)),x47041))
% 157.29/157.21 [3956]E(f326(f326(f3(a909),x39561),f326(f326(f80(a909),f326(f326(f36(a909),x39561),x39562)),x39562)),f45(a909,x39561,x39562))
% 157.29/157.21 [3957]E(f326(f326(f3(a1),x39571),f326(f326(f80(a1),f326(f326(f36(a1),x39571),x39572)),x39572)),f45(a1,x39571,x39572))
% 157.29/157.21 [3990]E(f326(f326(f154(a909,x39901),f326(f164(x39901),x39902)),f139(a909,f326(f301(a909,f2(a909)),f326(f189(f910(x39901)),x39902)))),x39902)
% 157.29/157.21 [4049]E(f326(f284(x40491,x40491,f306(x40491,f188(f917(f916(x40491,x40491),a905)))),x40492),x40492)
% 157.29/157.21 [4175]E(f306(x41751,f326(f326(f110(f917(f916(x41751,x41751),a905)),x41752),f306(x41751,f188(f917(f916(x41751,x41751),a905))))),f306(x41751,x41752))
% 157.29/157.21 [4176]E(f306(x41761,f326(f326(f3(f917(f916(x41761,x41761),a905)),x41762),f306(x41761,f188(f917(f916(x41761,x41761),a905))))),f306(x41761,x41762))
% 157.29/157.21 [4226]E(f326(f326(f3(a1),f326(f326(f3(a1),f326(f326(f79(a1),x42261),x42261)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),x42262),x42262)),a97)),f326(f326(f79(a1),f326(f326(f3(a1),x42261),x42262)),f326(f326(f3(a1),x42261),x42262)))
% 157.29/157.21 [4266]E(f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f79(a1),x42661),x42662)),f326(f326(f79(a1),x42661),x42662))),a97),f326(f326(f79(a1),f326(f326(f79(a1),x42661),x42661)),f326(f326(f3(a1),f326(f326(f79(a1),x42662),x42662)),a97)))
% 157.29/157.21 [4291]E(f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),x42911),x42911)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),x42912),x42912)),a97)),f326(f326(f79(a1),f326(f326(f79(a1),x42911),f326(f326(f3(a1),x42912),a97))),f326(f326(f79(a1),x42911),f326(f326(f3(a1),x42912),a97))))
% 157.29/157.21 [4305]E(f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),x43051),x43052)),f326(f326(f3(a1),x43051),x43052))),a97),f326(f326(f3(a1),f326(f326(f3(a1),f326(f326(f79(a1),x43051),x43051)),a97)),f326(f326(f79(a1),x43052),x43052)))
% 157.29/157.21 [4306]E(f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f79(a1),x43061),x43062)),f326(f326(f79(a1),x43061),x43062))),a97),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),x43061),x43061)),a97)),f326(f326(f79(a1),x43062),x43062)))
% 157.29/157.21 [4354]E(f326(f100(a1),f326(f326(f36(a909),f326(f326(f80(a909),f326(a104,f326(f75(a1),x43541))),f326(a104,f326(f75(a1),x43542)))),f216(f326(a104,f326(f75(a1),x43541)),f326(a104,f326(f75(a1),x43542))))),f218(x43541,x43542))
% 157.29/157.21 [4399]E(f326(f326(f258(f916(a99,a99),a99,f916(a99,a99),f916(x43991,f916(a99,a99))),f266(f326(a5,f326(f189(f910(x43991)),x43992)))),f326(f326(f10(x43991,f917(f916(a99,a99),f916(x43991,f916(a99,a99))),a99),f251(x43991,f916(a99,a99))),f326(f326(f10(a909,x43991,a99),f326(f164(x43991),x43992)),a22))),f274(x43991,x43992))
% 157.29/157.21 [4479]E(f326(f142(a909,f910(x44791),f326(f9(f910(x44791),a909,a909),f326(f326(f10(a909,f917(a909,a909),f910(x44791)),f233(a909)),f189(f910(x44791)))),f2(a909)),f326(f168(f910(x44791)),f179(x44791,x44792))),f326(f189(f910(f910(x44791))),f326(f136(f910(x44791),f326(f326(f10(a905,a905,f910(x44791)),a321),f326(f326(f9(f910(x44791),f910(x44791),a905),a323),f113(x44791)))),x44792)))
% 157.29/157.21 [4485]E(f326(f326(f40(a909,f917(x44851,a905)),f241(f917(a909,a905))),f326(f326(f9(a909,f917(a909,f917(x44851,a905)),f917(x44851,a905)),f326(f326(f10(f917(a909,a905),f917(f917(a909,f917(x44851,a905)),f917(x44851,a905)),a909),f40(a909,f917(x44851,a905))),f301(a909,f2(a909)))),x44852)),f326(f326(f40(a909,f917(x44851,a905)),f241(f917(a909,a905))),x44852))
% 157.29/157.21 [4507]P105(f326(f61(a909),f326(f261(a909),f326(f326(f20(a909,a905,a905),f326(f326(f10(a905,f917(a905,a905),a909),a324),x45071)),f326(f326(f9(a909,a909,a905),f235(a909)),x45072)))))
% 157.29/157.21 [4619]E(f326(f261(f916(f910(x46191),f910(x46191))),f326(f256(f910(x46191),f910(x46191),a905),f326(f326(f20(f910(x46191),f917(f910(x46191),a905),f917(f910(x46191),a905)),f326(f326(f10(f917(f910(x46191),f917(a905,a905)),f917(f917(f910(x46191),a905),f917(f910(x46191),a905)),f910(x46191)),f20(f910(x46191),a905,a905)),f326(f326(f10(f917(f910(x46191),a905),f917(f910(x46191),f917(a905,a905)),f910(x46191)),f326(f10(a905,f917(a905,a905),f910(x46191)),a325)),f326(f326(f9(f910(x46191),f917(f910(x46191),a909),f917(f910(x46191),a905)),f326(f326(f10(f917(a909,a905),f917(f917(f910(x46191),a909),f917(f910(x46191),a905)),f910(x46191)),f10(a909,a905,f910(x46191))),f326(f326(f10(a909,f917(a909,a905),f910(x46191)),f235(a909)),f189(f910(x46191))))),f189(f910(x46191)))))),f326(f326(f20(f910(x46191),f917(f910(x46191),a905),f917(f910(x46191),a905)),f326(f326(f10(f917(f910(x46191),f917(a905,a905)),f917(f917(f910(x46191),a905),f917(f910(x46191),a905)),f910(x46191)),f20(f910(x46191),a905,a905)),f326(f326(f10(f917(f910(x46191),a905),f917(f910(x46191),f917(a905,a905)),f910(x46191)),f326(f10(a905,f917(a905,a905),f910(x46191)),a324)),f326(f326(f9(f910(x46191),f917(f910(x46191),a909),f917(f910(x46191),a905)),f326(f326(f10(f917(a909,a905),f917(f917(f910(x46191),a909),f917(f910(x46191),a905)),f910(x46191)),f10(a909,a905,f910(x46191))),f326(f326(f10(a909,f917(a909,a905),f910(x46191)),a323),f189(f910(x46191))))),f189(f910(x46191)))))),f326(f326(f9(f910(x46191),f917(f916(f910(x46191),f910(x46191)),a905),f917(f910(x46191),a905)),f326(f326(f10(f917(f910(x46191),f917(f917(f916(f910(x46191),f910(x46191)),a905),a905)),f917(f917(f916(f910(x46191),f910(x46191)),a905),f917(f910(x46191),a905)),f910(x46191)),f9(f910(x46191),f917(f916(f910(x46191),f910(x46191)),a905),a905)),f326(f326(f10(f917(f910(x46191),f916(f910(x46191),f910(x46191))),f917(f910(x46191),f917(f917(f916(f910(x46191),f910(x46191)),a905),a905)),f910(x46191)),f326(f10(f916(f910(x46191),f910(x46191)),f917(f917(f916(f910(x46191),f910(x46191)),a905),a905),f910(x46191)),f328(f916(f910(x46191),f910(x46191))))),f251(f910(x46191),f910(x46191))))),f145(x46191,x46192)))))),f146(x46191,x46192))
% 157.29/157.21 [4295]E(f326(f326(f79(a1),f326(f326(f79(a1),f326(f326(f80(a1),x42951),x42952)),f326(f326(f80(a1),x42951),x42952))),x42952),f326(f326(f80(a1),f326(f326(f3(a1),f326(f326(f79(a1),x42951),x42951)),a97)),x42952))
% 157.29/157.21 [4398]E(f326(a104,f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x43981),x43982)),f188(f917(f916(a909,a909),a905)))))),f326(f326(f3(a909),x43981),x43982))
% 157.29/157.21 [4402]E(f326(f326(f288(x44021,x44021,x44021),f326(f326(f110(f917(f916(x44021,x44021),a905)),x44022),f306(x44021,f188(f917(f916(x44021,x44021),a905))))),f306(x44021,f326(f326(f110(f917(f916(x44021,x44021),a905)),x44022),f306(x44021,f188(f917(f916(x44021,x44021),a905)))))),f306(x44021,x44022))
% 157.29/157.21 [4439]E(f267(x44391,f326(f136(f916(a99,x44391),f326(f256(a99,x44391,a905),f326(f326(f10(a905,f917(x44391,a905),a99),f18(a905,x44391)),f326(f235(a99),f2(a99))))),x44392)),f267(x44391,x44392))
% 157.29/157.21 [4440]E(f265(x44401,f326(f136(f916(a99,x44401),f326(f256(a99,x44401,a905),f326(f326(f10(a905,f917(x44401,a905),a99),f18(a905,x44401)),f326(f235(a99),f2(a99))))),x44402)),f265(x44401,x44402))
% 157.29/157.21 [4442]E(f326(f78(a1),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x44421),x44422)),f188(f917(f916(a909,a909),a905)))))),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x44422),x44421)),f188(f917(f916(a909,a909),a905))))))
% 157.29/157.21 [4498]E(f326(f326(f287(f910(a909),x44981),f145(a909,a239)),f326(f326(f9(x44981,f910(f917(x44981,a909)),f910(a909)),f326(f326(f10(f917(f917(x44981,a909),a909),f917(f910(f917(x44981,a909)),f910(a909)),x44981),f154(f917(x44981,a909),a909)),f326(f9(f917(x44981,a909),x44981,a909),f7(f917(x44981,a909))))),x44982)),f153(x44981,x44982))
% 157.29/157.21 [4519]E(f326(f326(f85(a1,a909),f326(f103(a1),f326(f326(f79(a1),x45191),a97))),f326(f326(f20(a1,a909,a909),f326(f326(f9(a1,a909,f917(a909,a909)),f326(f326(f10(a905,f917(a909,f917(a909,a909)),a1),f96(a909)),a193)),f2(a909))),f326(f326(f10(a909,a909,a1),a112),f326(f326(f10(a909,a909,a1),f326(f232(a909),x45192)),a104)))),f326(f326(f232(a909),f326(a112,x45192)),f326(f103(a909),x45191)))
% 157.29/157.21 [4520]E(f326(f326(f85(a1,a909),f326(f103(a1),f326(f326(f79(a1),x45201),a97))),f326(f326(f20(a1,a909,a909),f326(f326(f9(a1,a909,f917(a909,a909)),f326(f326(f10(a905,f917(a909,f917(a909,a909)),a1),f96(a909)),a193)),f326(a112,x45202))),f326(f326(f10(a909,a909,a1),a112),f326(f326(f10(a909,a909,a1),f326(f233(a909),x45202)),a104)))),f326(f326(f233(a909),f326(a112,x45202)),f326(f103(a909),x45201)))
% 157.29/157.21 [4540]E(f326(f142(f910(x45401),f910(x45401),f134(x45401),f113(x45401)),f326(f326(f154(f910(x45401),f910(x45401)),f156(f910(x45401),x45401,f113(x45401),f326(f326(f10(f910(x45401),f917(f910(x45401),f910(x45401)),x45401),f18(f910(x45401),f910(x45401))),f326(f326(f9(x45401,f910(x45401),f910(x45401)),f151(x45401)),f113(x45401))))),x45402)),f326(f326(f154(f910(x45401),x45401),f141(x45401)),f326(f136(f910(x45401),f326(f326(f10(a905,a905,f910(x45401)),a321),f326(f326(f9(f910(x45401),f910(x45401),a905),a323),f113(x45401)))),x45402)))
% 157.29/157.21 [4602]E(f326(f256(a1,a1,a905),f326(f326(f9(a1,f917(a1,a905),f917(a1,a905)),f326(f326(f10(f917(a1,f917(a905,a905)),f917(f917(a1,a905),f917(a1,a905)),a1),f20(a1,a905,a905)),f326(f326(f10(f917(a1,a905),f917(a1,f917(a905,a905)),a1),f326(f10(a905,f917(a905,a905),a1),a324)),f326(f326(f10(f917(a1,a1),f917(a1,a905),a1),f326(f10(a1,a905,a1),f326(a323,x46021))),f326(f326(f10(a1,f917(a1,a1),a1),f79(a1)),f326(f80(a1),x46022)))))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f326(f10(a905,a905,a1),f326(a329,f326(f326(f235(a1),f2(a1)),x46022))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),f2(a1)))),f326(f326(f9(a1,a1,a905),f235(a1)),x46022))))),f326(f326(f10(a905,a905,a1),f326(a329,f326(a321,f326(f326(f235(a1),f2(a1)),x46022)))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f235(a1),x46022))),f326(f326(f9(a1,a1,a905),f234(a1)),f2(a1))))))),f49(x46021,x46022))
% 157.29/157.21 [4605]E(f326(f261(x46051),f326(f326(f10(f917(a909,a905),a905,x46051),f86(a909)),f326(f326(f9(x46051,f917(a909,a905),f917(a909,a905)),f326(f326(f10(f917(a909,f917(a905,a905)),f917(f917(a909,a905),f917(a909,a905)),x46051),f20(a909,a905,a905)),f326(f326(f10(f917(a909,a905),f917(a909,f917(a905,a905)),x46051),f326(f10(a905,f917(a905,a905),a909),a324)),f326(f326(f9(x46051,f917(a909,x46051),f917(a909,a905)),f326(f326(f10(f917(x46051,a905),f917(f917(a909,x46051),f917(a909,a905)),x46051),f10(x46051,a905,a909)),a323)),f326(f164(x46051),x46052))))),f326(f326(f9(a909,a909,a905),f235(a909)),f326(f189(f910(x46051)),x46052))))),f326(f172(x46051),x46052))
% 157.29/157.21 [4412]E(f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),x44121),a97)),x44122)),f326(f326(f3(a1),f326(f326(f79(a1),x44121),a97)),x44122))),a97),f326(f326(f3(a1),f326(f326(f79(a1),x44121),x44121)),f326(f326(f3(a1),f326(f326(f79(a1),x44122),x44122)),a97)))
% 157.29/157.21 [4535]E(f326(f142(f910(f910(x45351)),f910(f910(x45351)),f134(f910(x45351)),f113(f910(x45351))),f326(f326(f154(f910(x45351),f910(f910(x45351))),f156(f910(f910(x45351)),x45351,f113(f910(x45351)),f326(f18(f917(f910(x45351),f910(f910(x45351))),x45351),f326(f326(f9(f910(x45351),f910(f910(x45351)),f910(f910(x45351))),f151(f910(x45351))),f113(f910(x45351)))))),x45352)),f326(f326(f154(f910(x45351),f910(x45351)),f171(x45351)),f326(f136(f910(x45351),f326(f326(f10(a905,a905,f910(x45351)),a321),f326(f326(f9(f910(x45351),f910(x45351),a905),a323),f113(x45351)))),x45352)))
% 157.29/157.21 [4545]E(f326(f326(f85(a1,a909),f326(f103(a1),f326(f326(f79(a1),x45451),a97))),f326(f326(f20(a1,a909,a909),f326(f326(f9(a1,a909,f917(a909,a909)),f326(f326(f10(a905,f917(a909,f917(a909,a909)),a1),f96(a909)),a193)),f2(a909))),f326(f326(f10(a909,a909,a1),a112),f326(f326(f9(a1,a909,a909),f326(f326(f10(a909,f917(a909,a909),a1),f232(a909)),a104)),x45452)))),f326(f326(f232(a909),f326(f103(a909),x45451)),f326(a112,x45452)))
% 157.29/157.21 [4546]E(f326(f326(f85(a1,a909),f326(f103(a1),f326(f326(f79(a1),x45461),a97))),f326(f326(f20(a1,a909,a909),f326(f326(f9(a1,a909,f917(a909,a909)),f326(f326(f10(a905,f917(a909,f917(a909,a909)),a1),f96(a909)),a193)),f326(a112,x45462))),f326(f326(f10(a909,a909,a1),a112),f326(f326(f9(a1,a909,a909),f326(f326(f10(a909,f917(a909,a909),a1),f233(a909)),a104)),x45462)))),f326(f326(f233(a909),f326(f103(a909),x45461)),f326(a112,x45462)))
% 157.29/157.21 [4534]E(f326(f256(x45341,x45341,a905),f326(f326(f20(x45341,a905,f917(x45341,a905)),f326(f326(f10(f917(x45341,f917(a905,a905)),f917(a905,f917(x45341,a905)),x45341),f9(x45341,a905,a905)),f326(f326(f10(f917(x45341,a905),f917(x45341,f917(a905,a905)),x45341),f326(f10(a905,f917(a905,a905),x45341),a324)),a323))),x45342)),f262(x45341,x45342))
% 157.29/157.21 [4579]E(f326(f326(f36(a909),x45791),f326(f326(f79(a909),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97))),x45792)),f326(f326(f36(a909),x45791),f326(a112,f326(a112,f326(a112,x45792)))))
% 157.29/157.21 [4580]E(f45(a909,x45801,f326(f326(f79(a909),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97))),x45802)),f45(a909,x45801,f326(a112,f326(a112,f326(a112,x45802)))))
% 157.29/157.21 [4581]E(f45(a909,f326(f326(f79(a909),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97))),x45811),x45812),f45(a909,f326(a112,f326(a112,f326(a112,x45811))),x45812))
% 157.29/157.21 [4593]E(f123(f326(x45931,f326(f326(f80(a99),f326(f103(a99),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97))),x45932))),f326(f200(x45931),x45932))
% 157.29/157.21 [4594]E(f326(f326(f36(a909),f326(f326(f79(a909),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97))),x45941)),x45942),f326(f326(f36(a909),f326(a112,f326(a112,f326(a112,x45941)))),x45942))
% 157.29/157.21 [4651]~E(f27(x46511,x46512,x46513),a25)
% 157.29/157.21 [4652]~E(f26(x46521,x46522,x46523),a25)
% 157.29/157.21 [4656]~E(f126(x46561,x46562,x46563),f119(x46561))
% 157.29/157.21 [3387]E(f326(f192(x33871,x33872),x33873),f121(x33871,x33872))
% 157.29/157.21 [3406]E(f326(f199(x34061,x34062),x34063),f326(f129(x34061),x34062))
% 157.29/157.21 [3482]E(f326(f326(f154(x34821,x34822),x34823),f113(x34821)),f113(x34822))
% 157.29/157.21 [3522]E(f326(f184(x35221,x35222,x35223),f2(a909)),x35222)
% 157.29/157.21 [3524]E(f326(f326(f181(x35241,x35242),x35243),f113(x35242)),f113(f916(x35241,x35242)))
% 157.29/157.21 [3539]E(f326(f189(f910(x35391)),f169(x35391,x35392,x35393)),x35392)
% 157.29/157.21 [3558]E(f84(x35581,f62(x35581,x35582,x35583)),f326(f63(x35581,x35582),x35583))
% 157.29/157.21 [3562]E(f242(x35621,x35622,f242(x35622,x35621,x35623)),x35623)
% 157.29/157.21 [3582]E(f326(f168(x35821),f169(x35821,x35822,x35823)),f169(x35821,x35822,x35823))
% 157.29/157.21 [3609]E(f140(x36091,x36092,f152(x36091,x36093)),f152(x36091,f140(x36091,x36092,x36093)))
% 157.29/157.21 [3628]E(f326(f250(f910(x36281),f910(x36281)),f166(x36281,x36282,x36283)),f326(f136(x36281,x36282),x36283))
% 157.29/157.21 [3671]E(f326(f326(f151(x36711),x36712),f169(x36711,x36713,x36712)),f169(x36711,f326(a112,x36713),x36712))
% 157.29/157.21 [3703]E(f19(x37031,x37032,x37033,f2(a99)),x37032)
% 157.29/157.21 [3704]E(f21(x37041,x37042,x37043,f2(a99)),x37042)
% 157.29/157.21 [3705]E(f185(x37051,x37052,x37053,f2(a909)),x37052)
% 157.29/157.21 [3712]E(f163(x37121,x37122,x37123,f113(x37121)),f113(x37122))
% 157.29/157.21 [3713]E(f130(x37131,x37132,x37133,f119(x37131)),f119(x37132))
% 157.29/157.21 [3719]E(f326(f326(f164(x37191),f326(f326(f151(x37191),x37192),x37193)),f2(a909)),x37192)
% 157.29/157.21 [3748]E(f59(x37481,x37482,f113(x37481),x37483),f113(f916(x37481,x37482)))
% 157.29/157.21 [3768]P24(x37681,x37682,x37683,f188(f917(x37681,a905)))
% 157.29/157.21 [3871]E(f264(x38711,x38712,x38713),f326(f251(f917(a99,f917(a905,f913(f911(x38711)))),f916(a99,a99)),f41(x38711)))
% 157.29/157.21 [3929]E(f326(f72(x39291,x39292,x39291,x39293),f31(x39291)),x39293)
% 157.29/157.21 [4110]P105(f326(f326(f328(f916(x41101,x41101)),f326(f326(f251(x41101,x41101),x41102),x41102)),f306(x41101,x41103)))
% 157.29/157.21 [4708]~P105(f326(f326(f328(f916(f910(x47081),f910(x47081))),f326(f326(f251(f910(x47081),f910(x47081)),x47082),f113(x47081))),f145(x47081,x47083)))
% 157.29/157.21 [4709]~P105(f326(f326(f328(f916(f910(x47091),f910(x47091))),f326(f326(f251(f910(x47091),f910(x47091)),x47092),f113(x47091))),f147(x47091,x47093)))
% 157.29/157.21 [4710]~P105(f326(f326(f328(f916(f910(x47101),f910(x47101))),f326(f326(f251(f910(x47101),f910(x47101)),x47102),f113(x47101))),f157(x47101,x47103)))
% 157.29/157.21 [4711]~P105(f326(f326(f328(f916(f910(x47111),f910(x47111))),f326(f326(f251(f910(x47111),f910(x47111)),f113(x47111)),x47112)),f145(x47111,x47113)))
% 157.29/157.21 [4712]~P105(f326(f326(f328(f916(f910(x47121),f910(x47121))),f326(f326(f251(f910(x47121),f910(x47121)),f113(x47121)),x47122)),f157(x47121,x47123)))
% 157.29/157.21 [3457]E(f326(f326(f201(x34571),x34572),x34573),f202(x34571,f215(x34572,x34573)))
% 157.29/157.21 [3511]E(f326(f285(x35111,x35112),f326(f285(x35112,x35111),x35113)),x35113)
% 157.29/157.21 [3534]E(f326(f326(f181(x35341,x35342),f113(x35341)),x35343),f113(f916(x35341,x35342)))
% 157.29/157.21 [3537]E(f176(x35371,x35372,f326(f281(a909),x35373)),f326(f326(f175(x35371),x35373),x35372))
% 157.29/157.21 [3555]E(f152(x35551,f326(f136(x35551,x35552),x35553)),f326(f136(x35551,x35552),f152(x35551,x35553)))
% 157.29/157.21 [3556]E(f326(f283(x35561,x35562),f326(f285(x35562,x35561),x35563)),f326(f263(x35562,x35561),x35563))
% 157.29/157.21 [3557]E(f326(f263(x35571,x35572),f326(f285(x35572,x35571),x35573)),f326(f283(x35572,x35571),x35573))
% 157.29/157.21 [3575]E(f326(f136(x35751,x35752),f326(f168(x35751),x35753)),f326(f168(x35751),f326(f136(x35751,x35752),x35753)))
% 157.29/157.21 [3588]E(f326(f326(f138(x35881),x35882),f326(f171(x35881),x35883)),f326(f326(f138(x35881),f326(a112,x35882)),x35883))
% 157.29/157.21 [3604]E(f28(f26(x36041,x36042,x36043)),f326(f326(f79(a909),f28(x36043)),f326(a112,f2(a909))))
% 157.29/157.21 [3605]E(f326(f309(x36051,x36052,x36053),f188(f917(x36051,a905))),f188(f917(x36052,a905)))
% 157.29/157.21 [3606]E(f326(f284(x36061,x36062,x36063),f188(f917(x36061,a905))),f188(f917(x36062,a905)))
% 157.29/157.21 [3607]E(f326(f310(x36071,x36072,x36073),f188(f917(x36072,a905))),f188(f917(x36071,a905)))
% 157.29/157.21 [3608]E(f326(f310(x36081,x36082,x36083),f241(f917(x36082,a905))),f241(f917(x36081,a905)))
% 157.29/157.21 [3634]E(f120(x36341,f126(f911(x36341),x36342,x36343)),f116(x36341,x36342,f120(x36341,x36343)))
% 157.29/157.21 [3636]E(f326(f326(f308(x36361),x36362),f326(f172(x36361),x36363)),f326(f172(x36361),f140(x36361,x36362,x36363)))
% 157.29/157.21 [3723]E(f326(f189(a906),f26(x37231,x37232,x37233)),f326(f326(f79(a909),f326(f189(a906),x37233)),f326(a112,f2(a909))))
% 157.29/157.21 [3724]E(f326(f309(f916(x37241,x37242),x37242,f255(x37241,x37242)),x37243),f326(f283(x37241,x37242),x37243))
% 157.29/157.21 [3725]E(f326(f309(f916(x37251,x37252),x37251,f250(x37251,x37252)),x37253),f326(f263(x37251,x37252),x37253))
% 157.29/157.21 [3740]E(f326(f172(x37401),f169(x37401,f326(a112,x37402),x37403)),f326(f326(f308(x37401),x37403),f188(f917(x37401,a905))))
% 157.29/157.21 [3797]E(f326(f326(f251(x37971,x37972),f326(f250(x37971,x37972),x37973)),f326(f255(x37971,x37972),x37973)),x37973)
% 157.29/157.21 [3804]E(f326(f189(f911(x38041)),f126(x38041,x38042,x38043)),f326(f326(f79(a909),f326(f189(f911(x38041)),x38043)),f326(a112,f2(a909))))
% 157.29/157.21 [3806]E(f326(f326(f256(x38061,x38062,x38061),f18(x38061,x38062)),x38063),f326(f250(x38061,x38062),x38063))
% 157.29/157.21 [3884]E(f28(f27(x38841,x38842,x38843)),f326(f326(f79(a909),f326(f326(f79(a909),f28(x38842)),f28(x38843))),f326(a112,f2(a909))))
% 157.29/157.21 [3934]E(f326(f72(x39341,x39341,x39342,f31(x39341)),x39343),x39343)
% 157.29/157.21 [3942]E(f326(f326(f134(x39421),f169(x39421,x39422,x39423)),f326(f326(f151(x39421),x39423),f113(x39421))),f326(f326(f151(x39421),x39423),f169(x39421,x39422,x39423)))
% 157.29/157.21 [4043]E(f326(f189(a906),f27(x40431,x40432,x40433)),f326(f326(f79(a909),f326(f326(f79(a909),f326(f189(a906),x40432)),f326(f189(a906),x40433))),f326(a112,f2(a909))))
% 157.29/157.21 [4119]P105(f326(f326(f234(f917(x41191,a905)),f326(f172(x41191),f326(f136(x41191,x41192),x41193))),f326(f172(x41191),x41193)))
% 157.29/157.21 [4161]P105(f326(f326(f234(f917(x41611,a905)),f326(f172(x41611),f326(f326(f175(x41611),x41612),x41613))),f326(f172(x41611),x41613)))
% 157.29/157.21 [4162]P105(f326(f326(f234(f917(x41621,a905)),f326(f172(x41621),f326(f326(f138(x41621),x41622),x41623))),f326(f172(x41621),x41623)))
% 157.29/157.21 [4166]P105(f326(f326(f234(f917(x41661,a905)),f326(f172(x41661),f176(x41661,x41662,x41663))),f326(f172(x41661),x41662)))
% 157.29/157.21 [4167]P105(f326(f326(f234(f917(x41671,a905)),f326(f172(x41671),f170(x41671,x41672,x41673))),f326(f172(x41671),x41673)))
% 157.29/157.21 [4188]P24(f916(x41881,x41882),f916(x41882,x41881),f326(f256(x41881,x41882,f916(x41882,x41881)),f326(f9(x41882,x41881,f916(x41882,x41881)),f251(x41882,x41881))),x41883)
% 157.29/157.21 [4199]E(f326(f326(f326(f183(f910(x41991),f910(x41991)),f45(a909,x41992,f326(f189(f910(x41991)),x41993))),f167(x41991)),x41993),f326(f326(f326(f183(f910(x41991),f910(x41991)),x41992),f167(x41991)),x41993))
% 157.29/157.21 [4243]P105(f326(f326(f328(f916(f910(x42431),f910(x42431))),f326(f326(f251(f910(x42431),f910(x42431)),x42432),x42432)),f158(x42431,f306(x42431,x42433))))
% 157.29/157.21 [4385]E(f84(f916(x43851,x43852),f326(f326(f20(f916(x43851,x43852),x43852,a905),f326(f326(f10(x43851,f917(x43852,a905),f916(x43851,x43852)),x43853),f250(x43851,x43852))),f255(x43851,x43852))),f84(f916(x43851,x43852),f326(f256(x43851,x43852,a905),x43853)))
% 157.29/157.21 [4386]E(f89(f916(x43861,x43862),f326(f326(f20(f916(x43861,x43862),x43862,a905),f326(f326(f10(x43861,f917(x43862,a905),f916(x43861,x43862)),x43863),f250(x43861,x43862))),f255(x43861,x43862))),f89(f916(x43861,x43862),f326(f256(x43861,x43862,a905),x43863)))
% 157.29/157.21 [4419]E(f326(f326(f287(f916(a909,x44191),x44191),f319(a909,x44191,a239,x44192)),f326(f326(f20(x44191,x44191,f916(a909,x44191)),f326(f326(f10(a909,f917(x44191,f916(a909,x44191)),x44191),f251(a909,x44191)),x44193)),f7(x44191))),f320(x44191,x44193,x44192))
% 157.29/157.21 [4481]E(f326(f257(x44811,x44811,x44812,x44812,f7(x44811),f7(x44812)),x44813),x44813)
% 157.29/157.21 [4554]E(f326(f142(f910(f910(x45541)),f910(f910(x45541)),f134(f910(x45541)),f113(f910(x45541))),f326(f326(f154(f910(x45541),f910(f910(x45541))),f326(f326(f9(f910(x45541),f910(x45541),f910(f910(x45541))),f326(f326(f10(f917(x45541,f910(x45541)),f917(f910(x45541),f910(f910(x45541))),f910(x45541)),f154(x45541,f910(x45541))),f326(f9(x45541,f910(x45541),f910(x45541)),f151(x45541)))),x45542)),f55(x45541,x45543,x45542))),f55(x45541,f326(a112,x45543),x45542))
% 157.29/157.21 [4610]E(f223(a909,f916(x46101,f911(x46101)),f2(a909),f326(f256(x46101,f911(x46101),a909),f326(f326(f9(x46101,a909,f917(f911(x46101),a909)),f326(f326(f10(f917(f911(x46101),f917(a909,a909)),f917(a909,f917(f911(x46101),a909)),x46101),f9(f911(x46101),a909,a909)),f326(f326(f10(f917(f911(x46101),a909),f917(f911(x46101),f917(a909,a909)),x46101),f326(f10(a909,f917(a909,a909),f911(x46101)),f79(a909))),f326(f326(f9(x46101,f917(f911(x46101),a909),f917(f911(x46101),a909)),f326(f326(f10(f917(a909,a909),f917(f917(f911(x46101),a909),f917(f911(x46101),a909)),x46101),f10(a909,a909,f911(x46101))),f326(f326(f10(a909,f917(a909,a909),x46101),f79(a909)),x46102))),f125(x46101,x46102))))),f77(a909))),f326(f135(x46101),x46103)),f326(f125(x46101,x46102),x46103))
% 157.29/157.21 [4618]E(f326(f326(f85(a1,x46181),f218(f326(f326(f72(f916(a1,a1),a1,x46181,f255(a1,a1)),f212(x46181)),x46182),f326(f326(f72(f916(a1,a1),a1,x46181,f255(a1,a1)),f212(x46181)),x46183))),f326(f326(f20(a1,a1,x46181),f326(f326(f10(a1,f917(a1,x46181),a1),f201(x46181)),f326(f326(f20(a1,a1,a1),f326(f326(f10(a1,f917(a1,a1),a1),f79(a1)),f326(f326(f10(a1,a1,a1),f326(f80(a1),f326(f326(f72(f916(a1,a1),a1,x46181,f250(a1,a1)),f212(x46181)),x46182))),f326(f326(f9(a1,a1,a1),f36(a1)),f326(f326(f72(f916(a1,a1),a1,x46181,f255(a1,a1)),f212(x46181)),x46182))))),f326(f326(f10(a1,a1,a1),f326(f80(a1),f326(f326(f72(f916(a1,a1),a1,x46181,f250(a1,a1)),f212(x46181)),x46183))),f326(f326(f9(a1,a1,a1),f36(a1)),f326(f326(f72(f916(a1,a1),a1,x46181,f255(a1,a1)),f212(x46181)),x46183)))))),f7(a1))),f230(x46181,x46182,x46183))
% 157.29/157.21 [4647]~E(f326(f326(f151(x46471),x46472),x46473),x46473)
% 157.29/157.21 [4654]~E(f326(f326(f151(x46541),x46542),x46543),f113(x46541))
% 157.29/157.21 [4668]~E(f326(f326(f308(x46681),x46682),x46683),f188(f917(x46681,a905)))
% 157.29/157.21 [4690]~E(f326(f309(x46901,f917(x46901,a905),x46902),x46903),f326(f307(x46901),x46903))
% 157.29/157.21 [3516]E(f326(f326(f159(x35161,f113(x35161)),x35162),x35163),f113(x35161))
% 157.29/157.21 [3517]E(f326(f141(x35171),f326(f326(f151(x35171),x35172),x35173)),x35172)
% 157.29/157.21 [3518]E(f326(f171(x35181),f326(f326(f151(x35181),x35182),x35183)),x35183)
% 157.29/157.21 [3561]E(f326(f326(f138(x35611),f77(a909)),f326(f326(f151(x35611),x35612),x35613)),x35613)
% 157.29/157.21 [3595]E(f114(x35951,f326(f326(f138(x35951),x35952),x35953)),f326(f326(f138(x35951),x35952),f114(x35951,x35953)))
% 157.29/157.21 [3597]E(f326(f326(f159(x35971,x35972),x35973),f326(f326(f164(x35971),x35972),x35973)),x35972)
% 157.29/157.21 [3618]E(f326(f326(f308(x36181),x36182),f326(f326(f308(x36181),x36182),x36183)),f326(f326(f308(x36181),x36182),x36183))
% 157.29/157.21 [3631]E(f326(f326(f308(x36311),x36312),f326(f172(x36311),x36313)),f326(f172(x36311),f326(f326(f151(x36311),x36312),x36313)))
% 157.29/157.21 [3633]E(f326(f326(f138(x36331),x36332),f326(f171(x36331),x36333)),f326(f171(x36331),f326(f326(f138(x36331),x36332),x36333)))
% 157.29/157.21 [3645]E(f326(f326(f175(x36451),f77(a909)),f326(f326(f151(x36451),x36452),x36453)),f326(f326(f151(x36451),x36452),f113(x36451)))
% 157.29/157.21 [3688]E(f326(f63(x36881,x36882),f326(f326(f308(x36881),x36883),f188(f917(x36881,a905)))),x36883)
% 157.29/157.21 [3730]E(f326(f326(f79(a909),x37301),f326(f326(f79(a909),x37302),x37303)),f326(f326(f79(a909),x37302),f326(f326(f79(a909),x37301),x37303)))
% 157.29/157.21 [3731]E(f326(f326(f79(a1),x37311),f326(f326(f79(a1),x37312),x37313)),f326(f326(f79(a1),x37312),f326(f326(f79(a1),x37311),x37313)))
% 157.29/157.21 [3736]E(f326(f326(f253(x37361,x37362),f188(f917(x37361,a905))),x37363),f188(f917(f916(x37361,x37362),a905)))
% 157.29/157.21 [3760]E(f326(f326(f110(f917(x37601,a905)),x37602),x37603),f326(f326(f110(f917(x37601,a905)),x37603),x37602))
% 157.29/157.21 [3761]E(f326(f326(f101(f917(x37611,a905)),x37612),x37613),f326(f326(f101(f917(x37611,a905)),x37613),x37612))
% 157.29/157.21 [3763]E(f326(f326(f134(x37631),x37632),f326(f326(f151(x37631),x37633),f113(x37631))),f326(f167(x37631),f326(f326(f151(x37631),x37633),x37632)))
% 157.29/157.21 [3764]E(f326(f326(f134(x37641),f326(f168(x37641),x37642)),f326(f168(x37641),x37643)),f326(f168(x37641),f326(f326(f134(x37641),x37643),x37642)))
% 157.29/157.21 [3774]E(f326(f171(x37741),f326(f326(f175(x37741),f326(a112,x37742)),x37743)),f326(f326(f175(x37741),x37742),f326(f171(x37741),x37743)))
% 157.29/157.21 [3782]P105(f326(f326(f328(x37821),x37822),f326(f326(f308(x37821),x37822),x37823)))
% 157.29/157.21 [3786]E(f326(f326(f39(x37861,f917(x37862,a905)),f188(f917(x37861,a905))),x37863),f241(f917(x37862,a905)))
% 157.29/157.21 [3789]E(f326(f284(x37891,x37891,f262(x37891,x37892)),x37893),f326(f326(f101(f917(x37891,a905)),x37892),x37893))
% 157.29/157.21 [3803]E(f326(f189(f910(x38031)),f326(f326(f151(x38031),x38032),x38033)),f326(f326(f79(a909),f326(f189(f910(x38031)),x38033)),f326(a112,f2(a909))))
% 157.29/157.21 [3808]E(f114(x38081,f326(f326(f134(x38081),x38082),f326(f326(f151(x38081),x38083),f113(x38081)))),x38082)
% 157.29/157.21 [3809]E(f144(x38091,f326(f326(f134(x38091),x38092),f326(f326(f151(x38091),x38093),f113(x38091)))),x38093)
% 157.29/157.21 [3818]E(f326(f326(f134(x38181),f326(f326(f175(x38181),x38182),x38183)),f326(f326(f138(x38181),x38182),x38183)),x38183)
% 157.29/157.21 [3827]E(f326(f326(f3(a909),f326(f326(f79(a909),x38271),x38272)),f326(f326(f79(a909),x38273),x38272)),f326(f326(f3(a909),x38271),x38273))
% 157.29/157.21 [3828]E(f326(f326(f3(a909),f326(f326(f79(a909),x38281),x38282)),f326(f326(f79(a909),x38281),x38283)),f326(f326(f3(a909),x38282),x38283))
% 157.29/157.21 [3834]E(f326(f326(f134(x38341),f326(f168(x38341),x38342)),f326(f326(f151(x38341),x38343),f113(x38341))),f326(f168(x38341),f326(f326(f151(x38341),x38343),x38342)))
% 157.29/157.21 [3836]E(f326(f326(f79(a909),f326(f189(f910(x38361)),x38362)),f326(f189(f910(x38361)),x38363)),f326(f189(f910(x38361)),f326(f326(f134(x38361),x38362),x38363)))
% 157.29/157.21 [3839]E(f326(f326(f79(a909),f326(f189(f910(x38391)),x38392)),f326(f189(f910(x38391)),x38393)),f326(f189(f910(x38391)),f173(x38391,x38392,x38393)))
% 157.29/157.21 [3846]E(f326(f326(f110(f917(x38461,a905)),f326(f172(x38461),x38462)),f326(f172(x38461),x38463)),f326(f172(x38461),f326(f326(f134(x38461),x38462),x38463)))
% 157.29/157.21 [3847]E(f45(a909,f326(f326(f80(a909),x38471),x38472),f326(f326(f80(a909),x38471),x38473)),f326(f326(f80(a909),x38471),f45(a909,x38472,x38473)))
% 157.29/157.21 [3859]E(f326(f326(f175(x38591),f326(f326(f3(a909),x38592),f77(a909))),f326(f171(x38591),x38593)),f326(f171(x38591),f326(f326(f175(x38591),x38592),x38593)))
% 157.29/157.21 [3864]E(f326(f326(f101(f917(x38641,a905)),x38642),f326(f78(f917(x38641,a905)),x38643)),f326(f326(f3(f917(x38641,a905)),x38642),x38643))
% 157.29/157.21 [3865]E(f326(f326(f3(f917(x38651,a905)),x38652),f326(f78(f917(x38651,a905)),x38653)),f326(f326(f101(f917(x38651,a905)),x38652),x38653))
% 157.29/157.21 [3888]E(f326(f326(f253(x38881,x38882),x38883),f326(f18(f917(x38882,a905),x38881),f188(f917(x38882,a905)))),f188(f917(f916(x38881,x38882),a905)))
% 157.29/157.21 [3890]E(f326(f326(f3(a909),f326(f326(f80(a909),x38901),x38902)),f326(f326(f80(a909),x38901),x38903)),f326(f326(f80(a909),x38901),f326(f326(f3(a909),x38902),x38903)))
% 157.29/157.21 [3891]E(f326(f326(f79(a909),f326(f326(f80(a909),x38911),x38912)),f326(f326(f80(a909),x38911),x38913)),f326(f326(f80(a909),x38911),f326(f326(f79(a909),x38912),x38913)))
% 157.29/157.21 [3892]E(f326(f326(f3(a1),f326(f326(f80(a1),x38921),x38922)),f326(f326(f80(a1),x38921),x38923)),f326(f326(f80(a1),x38921),f326(f326(f3(a1),x38922),x38923)))
% 157.29/157.21 [3893]E(f326(f326(f79(a1),f326(f326(f80(a1),x38931),x38932)),f326(f326(f80(a1),x38931),x38933)),f326(f326(f80(a1),x38931),f326(f326(f79(a1),x38932),x38933)))
% 157.29/157.21 [3894]E(f326(f326(f80(a1),f326(f326(f243(a1),x38941),x38942)),f326(f326(f243(a1),x38941),x38943)),f326(f326(f243(a1),x38941),f326(f326(f79(a909),x38942),x38943)))
% 157.29/157.21 [3908]E(f326(f326(f40(x39081,f917(x39082,a905)),x39083),f326(f18(f917(x39082,a905),x39081),f188(f917(x39082,a905)))),f188(f917(x39082,a905)))
% 157.29/157.21 [3910]E(f45(a909,f326(f326(f80(a909),x39101),x39102),f326(f326(f80(a909),x39103),x39102)),f326(f326(f80(a909),f45(a909,x39101,x39103)),x39102))
% 157.29/157.21 [3915]E(f45(a1,f326(f326(f3(a1),x39151),f45(a1,x39152,x39153)),x39153),f45(a1,f326(f326(f3(a1),x39151),x39152),x39153))
% 157.29/157.21 [3916]E(f45(a1,f326(f326(f80(a1),x39161),f45(a1,x39162,x39163)),x39163),f45(a1,f326(f326(f80(a1),x39161),x39162),x39163))
% 157.29/157.21 [3917]P105(f326(f326(f234(f917(x39171,a905)),x39172),f326(f326(f308(x39171),x39173),x39172)))
% 157.29/157.21 [3994]E(f326(f326(f39(f917(x39941,a905),f917(x39941,a905)),x39942),f326(f110(f917(x39941,a905)),x39943)),f326(f326(f110(f917(x39941,a905)),x39943),f38(f917(x39941,a905),x39942)))
% 157.29/157.21 [3995]E(f326(f326(f40(f917(x39951,a905),f917(x39951,a905)),x39952),f326(f101(f917(x39951,a905)),x39953)),f326(f326(f101(f917(x39951,a905)),x39953),f37(f917(x39951,a905),x39952)))
% 157.29/157.21 [4007]E(f326(f172(x40071),f326(f326(f326(f183(f910(x40071),f910(x40071)),x40072),f167(x40071)),x40073)),f326(f172(x40071),x40073))
% 157.29/157.21 [4011]E(f326(f326(f175(x40111),f326(f189(f910(x40111)),f177(x40111,x40112,x40113))),x40113),f177(x40111,x40112,x40113))
% 157.29/157.21 [4015]E(f326(f189(f910(x40151)),f326(f326(f326(f183(f910(x40151),f910(x40151)),x40152),f167(x40151)),x40153)),f326(f189(f910(x40151)),x40153))
% 157.29/157.21 [4018]E(f326(f326(f256(x40181,x40182,x40182),f326(f18(f917(x40182,x40182),x40181),f7(x40182))),x40183),f326(f255(x40181,x40182),x40183))
% 157.29/157.21 [4025]E(f45(a1,f326(f326(f3(a1),f45(a1,x40251,x40252)),x40253),x40252),f45(a1,f326(f326(f3(a1),x40251),x40253),x40252))
% 157.29/157.21 [4026]E(f45(a1,f326(f326(f243(a1),f45(a1,x40261,x40262)),x40263),x40262),f45(a1,f326(f326(f243(a1),x40261),x40263),x40262))
% 157.29/157.21 [4029]E(f326(f326(f40(f917(f916(x40291,x40292),a905),f917(x40292,a905)),x40293),f283(x40291,x40292)),f326(f283(x40291,x40292),f37(f917(f916(x40291,x40292),a905),x40293)))
% 157.29/157.21 [4030]E(f326(f326(f40(f917(f916(x40301,x40302),a905),f917(x40301,a905)),x40303),f263(x40301,x40302)),f326(f263(x40301,x40302),f37(f917(f916(x40301,x40302),a905),x40303)))
% 157.29/157.21 [4054]E(f326(f72(x40541,x40541,x40541,x40542),f326(f326(f183(x40541,x40541),x40543),x40542)),f326(f326(f183(x40541,x40541),f326(a112,x40543)),x40542))
% 157.29/157.21 [4074]E(f326(f326(f138(x40741),f326(f326(f3(a909),f326(f189(f910(x40741)),x40742)),x40743)),f326(f168(x40741),x40742)),f326(f168(x40741),f326(f326(f175(x40741),x40743),x40742)))
% 157.29/157.21 [4075]E(f326(f326(f175(x40751),f326(f326(f3(a909),f326(f189(f910(x40751)),x40752)),x40753)),f326(f168(x40751),x40752)),f326(f168(x40751),f326(f326(f138(x40751),x40753),x40752)))
% 157.29/157.21 [4077]E(f326(f326(f79(a909),f326(f165(a909),f326(f326(f154(x40771,a909),x40772),x40773))),f326(f189(f910(x40771)),x40773)),f155(x40771,x40772,x40773))
% 157.29/157.21 [4097]E(f326(f167(x40971),f326(f326(f326(f183(f910(x40971),f910(x40971)),x40972),f167(x40971)),x40973)),f326(f326(f326(f183(f910(x40971),f910(x40971)),f326(a112,x40972)),f167(x40971)),x40973))
% 157.29/157.21 [4111]P105(f326(f326(f234(a909),f326(f189(f910(x41111)),f326(f136(x41111,x41112),x41113))),f326(f189(f910(x41111)),x41113)))
% 157.29/157.21 [4127]E(f326(f326(f110(f917(f917(x41271,a905),a905)),f326(f307(x41271),x41272)),f326(f309(f917(x41271,a905),f917(x41271,a905),f326(f308(x41271),x41273)),f326(f307(x41271),x41272))),f326(f307(x41271),f326(f326(f308(x41271),x41273),x41272)))
% 157.29/157.21 [4158]P105(f326(f326(f234(a909),f326(f189(f910(x41581)),f177(x41581,x41582,x41583))),f326(f189(f910(x41581)),x41583)))
% 157.29/157.21 [4165]E(f326(f263(x41651,x41652),f326(f261(f916(x41651,x41652)),f326(f256(x41651,x41652,a905),x41653))),f326(f261(x41651),f326(f326(f10(f917(x41652,a905),a905,x41651),f86(x41652)),x41653)))
% 157.29/157.21 [4177]E(f326(f309(a909,a909,f326(f326(f9(a909,a909,a909),f79(a909)),x41771)),f302(a909,x41772,x41773)),f302(a909,f326(f326(f79(a909),x41772),x41771),f326(f326(f79(a909),x41773),x41771)))
% 157.29/157.21 [4191]E(f326(f309(a909,a909,f326(f326(f9(a909,a909,a909),f79(a909)),x41911)),f326(f301(a909,x41912),x41913)),f326(f301(a909,f326(f326(f79(a909),x41912),x41911)),f326(f326(f79(a909),x41913),x41911)))
% 157.29/157.21 [4209]E(f326(f326(f181(x42091,x42092),f326(f326(f154(f916(x42091,x42092),x42091),f250(x42091,x42092)),x42093)),f326(f326(f154(f916(x42091,x42092),x42092),f255(x42091,x42092)),x42093)),x42093)
% 157.29/157.21 [4214]E(f326(f326(f79(a909),f326(f326(f80(a909),x42141),f45(a909,f326(f326(f36(a909),x42142),x42141),x42143))),f45(a909,x42142,x42141)),f45(a909,x42142,f326(f326(f80(a909),x42141),x42143)))
% 157.29/157.21 [4227]E(f326(f326(f134(x42271),x42272),f326(f142(f910(x42271),f910(x42271),f134(x42271),f113(x42271)),x42273)),f326(f142(f910(x42271),f910(x42271),f134(x42271),x42272),x42273))
% 157.29/157.21 [4248]P105(f326(f326(f328(f916(x42481,x42481)),f326(f326(f251(x42481,x42481),x42482),x42482)),f326(f326(f183(f916(x42481,x42481),a905),f2(a909)),x42483)))
% 157.29/157.21 [4253]E(f326(f261(x42531),f326(f326(f10(f917(x42532,a905),a905,x42531),f86(x42532)),f326(f9(x42532,x42531,a905),x42533))),f326(f283(x42532,x42531),f326(f261(f916(x42532,x42531)),f326(f256(x42532,x42531,a905),x42533))))
% 157.29/157.21 [4270]E(f326(f326(f110(f917(x42701,a905)),f326(f326(f40(a909,f917(x42701,a905)),f302(a909,f77(a909),x42702)),x42703)),f326(x42703,f2(a909))),f326(f326(f40(a909,f917(x42701,a905)),f326(f300(a909),x42702)),x42703))
% 157.29/157.21 [4285]E(f326(f142(f910(x42851),f910(x42851),f134(x42851),f113(x42851)),f326(f326(f154(f910(x42851),f910(x42851)),f136(x42851,x42852)),x42853)),f326(f136(x42851,x42852),f326(f142(f910(x42851),f910(x42851),f134(x42851),f113(x42851)),x42853)))
% 157.29/157.21 [4289]E(f326(f255(f910(x42891),f910(x42891)),f166(x42891,x42892,x42893)),f326(f136(x42891,f326(f72(a905,a905,x42891,a321),x42892)),x42893))
% 157.29/157.21 [4300]P23(x43001,x43002,f326(f326(f308(f908(x43001)),f91(x43001,x43003,a25,x43003)),f188(f917(f908(x43001),a905))))
% 157.29/157.21 [4337]E(f326(f326(f79(a1),f326(f326(f79(a1),f326(f326(f80(a1),x43371),f326(f326(f36(a1),x43372),x43371))),f45(a1,x43372,x43371))),x43373),f326(f326(f79(a1),x43372),x43373))
% 157.29/157.21 [4374]E(f326(f326(f79(a1),f326(f326(f79(a1),f326(f326(f80(a1),f326(f326(f36(a1),x43741),x43742)),x43742)),f45(a1,x43741,x43742))),x43743),f326(f326(f79(a1),x43741),x43743))
% 157.29/157.21 [4400]E(f84(f916(x44001,x44002),f326(f256(x44001,x44002,a905),f326(f326(f10(f917(x44002,f916(x44001,x44002)),f917(x44002,a905),x44001),f326(f10(f916(x44001,x44002),a905,x44002),x44003)),f251(x44001,x44002)))),f84(f916(x44001,x44002),x44003))
% 157.29/157.21 [4401]E(f89(f916(x44011,x44012),f326(f256(x44011,x44012,a905),f326(f326(f10(f917(x44012,f916(x44011,x44012)),f917(x44012,a905),x44011),f326(f10(f916(x44011,x44012),a905,x44012),x44013)),f251(x44011,x44012)))),f89(f916(x44011,x44012),x44013))
% 157.29/157.21 [4428]P105(f326(f326(f234(f917(x44281,a905)),f37(f917(x44281,a905),f326(f326(f101(f917(f917(x44281,a905),a905)),x44282),x44283))),f326(f326(f101(f917(x44281,a905)),f37(f917(x44281,a905),x44282)),f37(f917(x44281,a905),x44283))))
% 157.29/157.21 [4429]E(f326(f168(x44291),f326(f326(f326(f183(f910(x44291),f910(x44291)),f326(f326(f3(a909),f326(f189(f910(x44291)),x44292)),f45(a909,x44293,f326(f189(f910(x44291)),x44292)))),f167(x44291)),x44292)),f326(f326(f326(f183(f910(x44291),f910(x44291)),x44293),f167(x44291)),f326(f168(x44291),x44292)))
% 157.29/157.21 [4466]P105(f326(f326(f234(a909),f326(f189(f910(x44661)),f326(f326(f138(x44661),f326(f189(f910(x44661)),f177(x44661,x44662,x44663))),x44663))),f326(f189(f910(x44661)),x44663)))
% 157.29/157.21 [4702]~P105(f326(f62(x47021,x47022,f188(f917(x47021,a905))),x47023))
% 157.29/157.21 [4707]~P105(f326(f326(f328(f916(x47071,x47071)),f326(f326(f251(x47071,x47071),x47072),x47073)),f153(x47071,f113(f917(x47071,a909)))))
% 157.29/157.21 [3775]E(f326(f189(f910(x37751)),f326(f326(f175(x37751),x37752),x37753)),f326(f326(f232(a909),f326(f189(f910(x37751)),x37753)),x37752))
% 157.29/157.21 [3776]E(f326(f189(f910(x37761)),f326(f326(f138(x37761),x37762),x37763)),f326(f326(f3(a909),f326(f189(f910(x37761)),x37763)),x37762))
% 157.29/157.21 [3802]E(f326(f189(f910(f910(x38021))),f55(x38021,x38022,x38023)),f326(f326(f243(a909),f326(f189(f910(x38021)),x38023)),x38022))
% 157.29/157.21 [3820]E(f326(f326(f36(a909),f326(f326(f36(a909),x38201),x38202)),x38203),f326(f326(f36(a909),x38201),f326(f326(f80(a909),x38202),x38203)))
% 157.29/157.21 [3821]E(f326(f326(f3(a909),f326(f326(f3(a909),x38211),x38212)),x38213),f326(f326(f3(a909),x38211),f326(f326(f79(a909),x38212),x38213)))
% 157.29/157.21 [3822]E(f326(f326(f80(a909),f326(f326(f80(a909),x38221),x38222)),x38223),f326(f326(f80(a909),x38221),f326(f326(f80(a909),x38222),x38223)))
% 157.29/157.21 [3823]E(f326(f326(f80(a1),f326(f326(f80(a1),x38231),x38232)),x38233),f326(f326(f80(a1),x38231),f326(f326(f80(a1),x38232),x38233)))
% 157.29/157.21 [3824]E(f326(f326(f79(a909),f326(f326(f79(a909),x38241),x38242)),x38243),f326(f326(f79(a909),x38241),f326(f326(f79(a909),x38242),x38243)))
% 157.29/157.21 [3825]E(f326(f326(f79(a1),f326(f326(f79(a1),x38251),x38252)),x38253),f326(f326(f79(a1),x38251),f326(f326(f79(a1),x38252),x38253)))
% 157.29/157.21 [3826]E(f326(f326(f243(a1),f326(f326(f243(a1),x38261),x38262)),x38263),f326(f326(f243(a1),x38261),f326(f326(f80(a909),x38262),x38263)))
% 157.29/157.21 [3845]E(f162(x38451,f326(f326(f151(f917(x38451,a905)),x38452),x38453)),f174(x38451,x38452,f162(x38451,x38453)))
% 157.29/157.21 [3889]E(f326(f326(f3(a909),f326(f326(f3(a909),x38891),x38892)),x38893),f326(f326(f3(a909),f326(f326(f3(a909),x38891),x38893)),x38892))
% 157.29/157.21 [3897]E(f326(f326(f101(f917(x38971,a905)),x38972),f326(f326(f3(f917(x38971,a905)),x38973),x38972)),f188(f917(x38971,a905)))
% 157.29/157.21 [3901]E(f326(f326(f154(a909,x39011),f326(f18(x39011,a909),x39012)),f139(a909,f326(f301(a909,f2(a909)),x39013))),f169(x39011,x39013,x39012))
% 157.29/157.21 [3940]E(f37(f917(x39401,a905),f326(f326(f308(f917(x39401,a905)),x39402),x39403)),f326(f326(f110(f917(x39401,a905)),x39402),f37(f917(x39401,a905),x39403)))
% 157.29/157.21 [3941]E(f38(f917(x39411,a905),f326(f326(f308(f917(x39411,a905)),x39412),x39413)),f326(f326(f101(f917(x39411,a905)),x39412),f38(f917(x39411,a905),x39413)))
% 157.29/157.21 [3943]E(f169(x39431,f326(f189(f910(x39431)),f326(f136(x39431,f326(a323,x39432)),x39433)),x39432),f326(f136(x39431,f326(a323,x39432)),x39433))
% 157.29/157.21 [3945]E(f326(f326(f3(a909),f326(f326(f80(a909),x39451),x39452)),f326(f326(f80(a909),x39453),x39452)),f326(f326(f80(a909),f326(f326(f3(a909),x39451),x39453)),x39452))
% 157.29/157.21 [3946]E(f326(f326(f79(a909),f326(f326(f80(a909),x39461),x39462)),f326(f326(f80(a909),x39463),x39462)),f326(f326(f80(a909),f326(f326(f79(a909),x39461),x39463)),x39462))
% 157.29/157.21 [3947]E(f326(f326(f3(a1),f326(f326(f80(a1),x39471),x39472)),f326(f326(f80(a1),x39473),x39472)),f326(f326(f80(a1),f326(f326(f3(a1),x39471),x39473)),x39472))
% 157.29/157.21 [3948]E(f326(f326(f79(a1),f326(f326(f80(a1),x39481),x39482)),f326(f326(f80(a1),x39483),x39482)),f326(f326(f80(a1),f326(f326(f79(a1),x39481),x39483)),x39482))
% 157.29/157.21 [3950]E(f326(f326(f232(a909),f326(f326(f3(a909),x39501),x39502)),f326(f326(f3(a909),x39503),x39502)),f326(f326(f3(a909),f326(f326(f232(a909),x39501),x39503)),x39502))
% 157.29/157.21 [3971]E(f326(f326(f101(f917(f910(x39711),a905)),f160(x39711,x39712)),f160(x39711,x39713)),f160(x39711,f326(f326(f101(f917(x39711,a905)),x39712),x39713)))
% 157.29/157.21 [3974]E(f326(f326(f110(f917(x39741,a905)),x39742),f326(f326(f110(f917(x39741,a905)),x39742),x39743)),f326(f326(f110(f917(x39741,a905)),x39742),x39743))
% 157.29/157.21 [3975]E(f326(f326(f110(f917(x39751,a905)),x39752),f326(f326(f3(f917(x39751,a905)),x39753),x39752)),f326(f326(f110(f917(x39751,a905)),x39752),x39753))
% 157.29/157.21 [3976]E(f326(f326(f101(f917(x39761,a905)),x39762),f326(f326(f101(f917(x39761,a905)),x39762),x39763)),f326(f326(f101(f917(x39761,a905)),x39762),x39763))
% 157.29/157.21 [3988]E(f326(f326(f288(x39881,x39882,x39882),x39883),f306(x39882,f188(f917(f916(x39882,x39882),a905)))),x39883)
% 157.29/157.21 [3991]E(f326(f326(f110(f917(x39911,a905)),f326(f326(f308(x39911),x39912),f188(f917(x39911,a905)))),x39913),f326(f326(f308(x39911),x39912),x39913))
% 157.29/157.21 [4010]E(f326(f326(f3(a909),f326(f326(f3(a909),f326(a112,x40101)),x40102)),f326(a112,x40103)),f326(f326(f3(a909),f326(f326(f3(a909),x40101),x40102)),x40103))
% 157.29/157.21 [4038]E(f326(f326(f101(f917(f917(x40381,a905),a905)),f326(f307(x40381),x40382)),f326(f307(x40381),x40383)),f326(f307(x40381),f326(f326(f101(f917(x40381,a905)),x40382),x40383)))
% 157.29/157.21 [4041]E(f326(f326(f110(f917(x40411,a905)),f326(f78(f917(x40411,a905)),x40412)),x40413),f326(f78(f917(x40411,a905)),f326(f326(f3(f917(x40411,a905)),x40412),x40413)))
% 157.29/157.21 [4051]E(f326(f326(f308(x40511),x40512),f326(f326(f3(f917(x40511,a905)),x40513),f326(f326(f308(x40511),x40512),f188(f917(x40511,a905))))),f326(f326(f308(x40511),x40512),x40513))
% 157.29/157.21 [4063]P105(f326(f326(f234(f917(x40631,a905)),x40632),f326(f326(f110(f917(x40631,a905)),x40633),x40632)))
% 157.29/157.21 [4064]P105(f326(f326(f234(f917(x40641,a905)),x40642),f326(f326(f110(f917(x40641,a905)),x40642),x40643)))
% 157.29/157.21 [4068]E(f326(f326(f101(f917(x40681,a905)),f326(f78(f917(x40681,a905)),x40682)),f326(f78(f917(x40681,a905)),x40683)),f326(f78(f917(x40681,a905)),f326(f326(f110(f917(x40681,a905)),x40682),x40683)))
% 157.29/157.21 [4069]E(f326(f326(f110(f917(x40691,a905)),f326(f78(f917(x40691,a905)),x40692)),f326(f78(f917(x40691,a905)),x40693)),f326(f78(f917(x40691,a905)),f326(f326(f101(f917(x40691,a905)),x40692),x40693)))
% 157.29/157.21 [4083]P105(f326(f326(f234(f917(x40831,a905)),f326(f172(x40831),x40832)),f326(f172(x40831),f326(f326(f151(x40831),x40833),x40832))))
% 157.29/157.21 [4095]E(f326(f326(f110(f917(x40951,a905)),f326(f326(f3(f917(x40951,a905)),x40952),x40953)),f326(f326(f101(f917(x40951,a905)),x40952),x40953)),x40952)
% 157.29/157.21 [4145]E(f326(f326(f8(x41451,a1),f326(f326(f10(a909,a1,x41451),f100(a1)),x41452)),x41453),f326(f100(a1),f326(f326(f8(x41451,a909),x41452),x41453)))
% 157.29/157.21 [4146]E(f326(f326(f11(x41461,a1),f326(f326(f10(a909,a1,x41461),f100(a1)),x41462)),x41463),f326(f100(a1),f326(f326(f11(x41461,a909),x41462),x41463)))
% 157.29/157.21 [4193]E(f326(f326(f134(x41931),f177(x41931,x41932,x41933)),f326(f326(f138(x41931),f326(f189(f910(x41931)),f177(x41931,x41932,x41933))),x41933)),x41933)
% 157.29/157.21 [4197]E(f326(f78(f917(f916(x41971,x41972),a905)),f326(f326(f253(x41971,x41972),x41973),f326(f18(f917(x41972,a905),x41971),f241(f917(x41972,a905))))),f326(f326(f253(x41971,x41972),f326(f78(f917(x41971,a905)),x41973)),f326(f18(f917(x41972,a905),x41971),f241(f917(x41972,a905)))))
% 157.29/157.21 [4198]E(f326(f78(f917(f916(x41981,x41982),a905)),f326(f326(f253(x41981,x41982),f241(f917(x41981,a905))),f326(f18(f917(x41982,a905),x41981),x41983))),f326(f326(f253(x41981,x41982),f241(f917(x41981,a905))),f326(f18(f917(x41982,a905),x41981),f326(f78(f917(x41982,a905)),x41983))))
% 157.29/157.21 [4249]E(f326(f326(f40(f917(x42491,a905),f917(x42491,a905)),x42492),f326(f326(f9(f917(x42491,a905),f917(x42491,a905),f917(x42491,a905)),f101(f917(x42491,a905))),x42493)),f326(f326(f101(f917(x42491,a905)),f37(f917(x42491,a905),x42492)),x42493))
% 157.29/157.21 [4255]E(f326(f142(f910(x42551),f910(x42551),f134(x42551),f113(x42551)),f326(f326(f151(f910(x42551)),x42552),x42553)),f326(f326(f134(x42551),x42552),f326(f142(f910(x42551),f910(x42551),f134(x42551),f113(x42551)),x42553)))
% 157.29/157.21 [4276]E(f326(f326(f308(f917(x42761,a905)),f326(f284(x42761,x42761,x42762),f326(f326(f308(x42761),x42763),f188(f917(x42761,a905))))),f188(f917(f917(x42761,a905),a905))),f326(f326(f60(x42761),f326(f326(f308(x42761),x42763),f188(f917(x42761,a905)))),x42762))
% 157.29/157.21 [4286]E(f326(f326(f79(a909),f326(f326(f80(a909),x42861),f326(f326(f36(a909),x42862),x42863))),f326(f326(f36(a909),f326(f326(f80(a909),x42861),f45(a909,x42862,x42863))),x42863)),f326(f326(f36(a909),f326(f326(f80(a909),x42861),x42862)),x42863))
% 157.29/157.21 [4287]E(f326(f326(f79(a1),f326(f326(f80(a1),x42871),f326(f326(f36(a1),x42872),x42873))),f326(f326(f36(a1),f326(f326(f80(a1),x42871),f45(a1,x42872,x42873))),x42873)),f326(f326(f36(a1),f326(f326(f80(a1),x42871),x42872)),x42873))
% 157.29/157.21 [4322]E(f326(f326(f3(f917(x43221,a905)),f326(f172(x43221),x43222)),f326(f326(f308(x43221),x43223),f188(f917(x43221,a905)))),f326(f172(x43221),f326(f136(x43221,f326(f326(f10(a905,a905,x43221),a321),f326(a323,x43223))),x43222)))
% 157.29/157.21 [4372]E(f326(f326(f134(x43721),f326(f142(f910(x43721),f910(x43721),f134(x43721),f113(x43721)),x43722)),f326(f142(f910(x43721),f910(x43721),f134(x43721),f113(x43721)),x43723)),f326(f142(f910(x43721),f910(x43721),f134(x43721),f113(x43721)),f326(f326(f134(f910(x43721)),x43722),x43723)))
% 157.55/157.21 [4375]E(f326(f326(f251(f910(x43751),f910(x43751)),f326(f136(x43751,x43752),x43753)),f326(f136(x43751,f326(f72(a905,a905,x43751,a321),x43752)),x43753)),f166(x43751,x43752,x43753))
% 157.55/157.21 [4378]E(f326(f326(f79(a909),f326(f326(f79(a909),f326(f326(f36(a909),x43781),x43782)),f326(f326(f36(a909),x43783),x43782))),f326(f326(f36(a909),f326(f326(f79(a909),f45(a909,x43781,x43782)),f45(a909,x43783,x43782))),x43782)),f326(f326(f36(a909),f326(f326(f79(a909),x43781),x43783)),x43782))
% 157.55/157.21 [4379]E(f326(f326(f79(a1),f326(f326(f79(a1),f326(f326(f36(a1),x43791),x43792)),f326(f326(f36(a1),x43793),x43792))),f326(f326(f36(a1),f326(f326(f79(a1),f45(a1,x43791,x43792)),f45(a1,x43793,x43792))),x43792)),f326(f326(f36(a1),f326(f326(f79(a1),x43791),x43793)),x43792))
% 157.55/157.21 [4432]E(f326(f326(f101(f917(f910(x44321),a905)),f326(f326(f9(f910(x44321),f917(f910(x44321),a905),a905),f328(f910(x44321))),f161(x44321,x44322))),f326(f326(f9(f910(x44321),f917(f910(x44321),a905),a905),f328(f910(x44321))),f161(x44321,x44323))),f160(x44321,f326(f326(f101(f917(x44321,a905)),f326(f326(f9(x44321,f917(x44321,a905),a905),f328(x44321)),x44322)),f326(f326(f9(x44321,f917(x44321,a905),a905),f328(x44321)),x44323))))
% 157.55/157.21 [4444]E(f326(f261(x44441),f326(f326(f20(x44441,a905,a905),f326(f326(f10(a905,f917(a905,a905),x44441),a325),f326(f326(f9(x44441,x44441,a905),a323),x44442))),f326(f326(f9(x44441,f917(x44441,a905),a905),f328(x44441)),x44443))),f326(f326(f308(x44441),x44442),x44443))
% 157.55/157.21 [4464]E(f326(f326(f85(f910(f910(x44641)),f910(f910(x44641))),f54(x44641,x44642)),f326(f326(f20(f910(f910(x44641)),f910(f910(x44641)),f910(f910(x44641))),f326(f326(f10(f910(f910(x44641)),f917(f910(f910(x44641)),f910(f910(x44641))),f910(f910(x44641))),f134(f910(x44641))),f326(f154(f910(x44641),f910(x44641)),f326(f151(x44641),x44643)))),f7(f910(f910(x44641))))),f54(x44641,f326(f326(f151(x44641),x44643),x44642)))
% 157.55/157.21 [4467]E(f326(f261(x44671),f326(f326(f20(x44671,a905,a905),f326(f326(f10(a905,f917(a905,a905),x44671),a325),f326(f326(f9(x44671,f917(x44671,a905),a905),f328(x44671)),x44672))),f326(f326(f9(x44671,f917(x44671,a905),a905),f328(x44671)),x44673))),f326(f326(f110(f917(x44671,a905)),x44672),x44673))
% 157.55/157.21 [4468]E(f326(f261(x44681),f326(f326(f20(x44681,a905,a905),f326(f326(f10(a905,f917(a905,a905),x44681),a324),f326(f326(f9(x44681,f917(x44681,a905),a905),f328(x44681)),x44682))),f326(f326(f9(x44681,f917(x44681,a905),a905),f328(x44681)),x44683))),f326(f326(f101(f917(x44681,a905)),x44682),x44683))
% 157.55/157.21 [4557]E(f326(f326(f40(x45571,f917(f917(x45571,a905),a905)),x45572),f326(f326(f9(x45571,f917(f917(x45571,a905),a905),f917(f917(x45571,a905),a905)),f326(f326(f10(f917(x45571,a905),f917(f917(f917(x45571,a905),a905),f917(f917(x45571,a905),a905)),x45571),f308(f917(x45571,a905))),f326(f326(f10(f917(x45571,a905),f917(x45571,a905),x45571),f284(x45571,x45571,x45573)),f326(f326(f9(x45571,f917(x45571,a905),f917(x45571,a905)),f308(x45571)),f188(f917(x45571,a905)))))),f188(f917(f917(x45571,a905),a905)))),f326(f326(f60(x45571),x45572),x45573))
% 157.55/157.21 [4559]E(f326(f326(f201(x45591),f326(f326(f80(a1),f326(f326(f72(f916(a1,a1),a1,x45591,f250(a1,a1)),f212(x45591)),x45592)),f326(f326(f72(f916(a1,a1),a1,x45591,f250(a1,a1)),f212(x45591)),x45593))),f326(f326(f80(a1),f326(f326(f72(f916(a1,a1),a1,x45591,f255(a1,a1)),f212(x45591)),x45592)),f326(f326(f72(f916(a1,a1),a1,x45591,f255(a1,a1)),f212(x45591)),x45593))),f228(x45591,x45592,x45593))
% 157.55/157.21 [4562]E(f326(f261(f910(x45621)),f326(f326(f20(f910(x45621),a905,a905),f326(f326(f10(a905,f917(a905,a905),f910(x45621)),a324),f326(f326(f9(f910(x45621),a909,a905),f326(f326(f10(a909,f917(a909,a905),f910(x45621)),a323),f189(f910(x45621)))),x45622))),f326(f326(f9(f910(x45621),f917(x45621,a905),a905),f326(f326(f10(f917(x45621,a905),f917(f917(x45621,a905),a905),f910(x45621)),f234(f917(x45621,a905))),f172(x45621))),f326(f172(x45621),x45623)))),f326(f172(f910(x45621)),f55(x45621,x45622,x45623)))
% 157.55/157.21 [3964]E(f45(a909,f326(f326(f79(a909),f326(f326(f80(a909),x39641),x39642)),x39643),x39642),f45(a909,x39643,x39642))
% 157.55/157.21 [4009]E(f139(a909,f326(f301(a909,f326(f326(f79(a909),x40091),x40092)),x40093)),f326(f326(f138(a909),x40092),f139(a909,f326(f301(a909,x40091),x40093))))
% 157.55/157.21 [4050]E(f326(f326(f79(a1),f326(f100(a1),x40501)),f326(f326(f79(a1),f326(f100(a1),x40502)),x40503)),f326(f326(f79(a1),f326(f100(a1),f326(f326(f79(a909),x40501),x40502))),x40503))
% 157.55/157.21 [4059]E(f326(f326(f110(f917(x40591,a905)),f326(f326(f3(f917(x40591,a905)),x40592),x40593)),x40593),f326(f326(f110(f917(x40591,a905)),x40592),x40593))
% 157.55/157.21 [4060]E(f326(f326(f3(f917(x40601,a905)),f326(f326(f3(f917(x40601,a905)),x40602),x40603)),x40603),f326(f326(f3(f917(x40601,a905)),x40602),x40603))
% 157.55/157.21 [4084]E(f326(f326(f288(x40841,x40841,x40842),f306(x40841,f188(f917(f916(x40841,x40841),a905)))),x40843),x40843)
% 157.55/157.21 [4092]E(f326(f326(f110(f917(x40921,a905)),f326(f280(x40921),x40922)),f326(f280(x40921),x40923)),f326(f280(x40921),f326(f326(f110(f917(f916(x40921,x40921),a905)),x40922),x40923)))
% 157.55/157.21 [4102]E(f265(x41021,f326(f326(f151(f916(a99,x41021)),f326(f326(f251(a99,x41021),f2(a99)),x41022)),x41023)),f265(x41021,x41023))
% 157.55/157.21 [4104]E(f326(f326(f110(f917(x41041,a905)),f37(f917(x41041,a905),x41042)),f37(f917(x41041,a905),x41043)),f37(f917(x41041,a905),f326(f326(f110(f917(f917(x41041,a905),a905)),x41042),x41043)))
% 157.55/157.21 [4105]E(f326(f326(f101(f917(x41051,a905)),f38(f917(x41051,a905),x41052)),f38(f917(x41051,a905),x41053)),f38(f917(x41051,a905),f326(f326(f110(f917(f917(x41051,a905),a905)),x41052),x41053)))
% 157.55/157.21 [4142]E(f326(f326(f288(x41421,x41421,x41421),f326(f326(f183(f916(x41421,x41421),a905),x41422),x41423)),x41423),f326(f326(f183(f916(x41421,x41421),a905),f326(a112,x41422)),x41423))
% 157.55/157.21 [4185]P105(f326(f326(f234(f917(x41851,a905)),f326(f326(f3(f917(x41851,a905)),x41852),x41853)),x41852))
% 157.55/157.21 [4186]P105(f326(f326(f234(f917(x41861,a905)),f326(f326(f101(f917(x41861,a905)),x41862),x41863)),x41863))
% 157.55/157.21 [4187]P105(f326(f326(f234(f917(x41871,a905)),f326(f326(f101(f917(x41871,a905)),x41872),x41873)),x41872))
% 157.55/157.21 [4211]E(f306(x42111,f326(f326(f110(f917(f916(x42111,x42111),a905)),f306(x42111,x42112)),f306(x42111,x42113))),f306(x42111,f326(f326(f110(f917(f916(x42111,x42111),a905)),x42112),x42113)))
% 157.55/157.21 [4215]E(f37(f917(x42151,a905),f326(f326(f308(f917(x42151,a905)),x42152),f326(f326(f308(f917(x42151,a905)),x42153),f188(f917(f917(x42151,a905),a905))))),f326(f326(f110(f917(x42151,a905)),x42152),x42153))
% 157.55/157.21 [4216]E(f38(f917(x42161,a905),f326(f326(f308(f917(x42161,a905)),x42162),f326(f326(f308(f917(x42161,a905)),x42163),f188(f917(f917(x42161,a905),a905))))),f326(f326(f101(f917(x42161,a905)),x42162),x42163))
% 157.55/157.21 [4221]E(f326(f326(f288(x42211,x42211,x42211),f326(f326(f183(f916(x42211,x42211),a905),x42212),x42213)),x42213),f326(f326(f288(x42211,x42211,x42211),x42213),f326(f326(f183(f916(x42211,x42211),a905),x42212),x42213)))
% 157.55/157.21 [4290]E(f326(f326(f110(f917(x42901,a905)),f326(f261(x42901),f326(f326(f9(x42901,x42901,a905),a323),x42902))),x42903),f326(f326(f308(x42901),x42902),x42903))
% 157.55/157.21 [4293]E(f326(a104,f326(f326(f8(x42931,a1),f326(f326(f10(a909,a1,x42931),f100(a1)),x42932)),x42933)),f326(f326(f8(x42931,a909),x42932),x42933))
% 157.55/157.21 [4294]E(f326(a104,f326(f326(f11(x42941,a1),f326(f326(f10(a909,a1,x42941),f100(a1)),x42942)),x42943)),f326(f326(f11(x42941,a909),x42942),x42943))
% 157.55/157.21 [4369]E(f326(f156(f910(x43691),x43691,f326(f171(x43691),x43692),f326(f18(f917(f910(x43691),f910(x43691)),x43691),f326(f326(f9(f910(x43691),f910(x43691),f910(x43691)),f134(x43691)),x43692))),x43693),f326(f171(x43691),f326(f326(f134(x43691),x43693),x43692)))
% 157.55/157.21 [4397]P105(f326(f326(f234(f917(f917(x43971,a905),a905)),f326(f326(f110(f917(f917(x43971,a905),a905)),f326(f307(x43971),x43972)),f326(f307(x43971),x43973))),f326(f307(x43971),f326(f326(f110(f917(x43971,a905)),x43972),x43973))))
% 157.55/157.21 [4486]E(f326(f261(x44861),f326(f326(f20(x44861,a905,a905),f326(f326(f10(a905,f917(a905,a905),x44861),a324),f326(f326(f9(x44861,f917(x44861,a905),a905),f328(x44861)),x44862))),f326(f326(f10(a905,a905,x44861),a321),f326(f326(f9(x44861,f917(x44861,a905),a905),f328(x44861)),x44863)))),f326(f326(f3(f917(x44861,a905)),x44862),x44863))
% 157.55/157.21 [4510]E(f326(f35(a909),f326(f261(a909),f326(f326(f20(a909,a905,a905),f326(f326(f10(a905,f917(a905,a905),a909),a324),f326(f326(f9(a909,a909,a905),f235(a909)),f326(f189(f910(x45101)),x45102)))),f326(f326(f10(x45101,a905,a909),x45103),f326(f164(x45101),x45102))))),f326(f189(f910(x45101)),f326(f136(x45101,x45103),x45102)))
% 157.55/157.21 [4512]E(f326(f189(f910(x45121)),f176(x45121,x45122,x45123)),f326(f35(a909),f326(f261(a909),f326(f326(f20(a909,a905,a905),f326(f326(f10(a905,f917(a905,a905),a909),a324),f326(f326(f9(a909,a909,a905),f235(a909)),f326(f189(f910(x45121)),x45122)))),f326(f326(f9(a909,f917(a909,a905),a905),f328(a909)),x45123)))))
% 157.55/157.21 [4608]E(f326(f326(f101(f917(f916(f910(x46081),f910(x46081)),a905)),f326(f309(f916(f916(x46081,f910(x46081)),f916(x46081,f910(x46081))),f916(f910(x46081),f910(x46081)),f257(f916(x46081,f910(x46081)),f910(x46081),f916(x46081,f910(x46081)),f910(x46081),f326(f256(x46081,f910(x46081),f910(x46081)),f151(x46081)),f326(f256(x46081,f910(x46081),f910(x46081)),f151(x46081)))),f319(x46081,f910(x46081),x46082,f326(f143(x46081,x46082),x46083)))),f326(f261(f916(f910(x46081),f910(x46081))),f326(f256(f910(x46081),f910(x46081),a905),f326(f326(f9(f910(x46081),f917(f910(x46081),a905),f917(f910(x46081),a905)),f326(f326(f10(f917(a905,a905),f917(f917(f910(x46081),a905),f917(f910(x46081),a905)),f910(x46081)),f10(a905,a905,f910(x46081))),f326(f326(f10(a905,f917(a905,a905),f910(x46081)),a324),f326(f326(f9(f910(x46081),a909,a905),f326(f326(f10(a909,f917(a909,a905),f910(x46081)),a323),f189(f910(x46081)))),f326(a112,x46083))))),f326(f326(f9(f910(x46081),a909,a905),f326(f326(f10(a909,f917(a909,a905),f910(x46081)),a323),f189(f910(x46081)))),f326(a112,x46083)))))),f326(f143(x46081,x46082),f326(a112,x46083)))
% 157.55/157.21 [4106]E(f45(a909,f326(a112,f326(f326(f79(a909),f326(f326(f80(a909),x41061),x41062)),x41063)),x41062),f45(a909,f326(a112,x41063),x41062))
% 157.55/157.21 [4355]E(f326(f261(x43551),f326(f326(f20(x43551,a905,a905),f326(f326(f10(a905,f917(a905,a905),x43551),a324),x43552)),x43553)),f326(f326(f101(f917(x43551,a905)),f326(f261(x43551),x43552)),f326(f261(x43551),x43553)))
% 157.55/157.21 [4356]E(f326(f261(x43561),f326(f326(f20(x43561,a905,a905),f326(f326(f10(a905,f917(a905,a905),x43561),a325),x43562)),x43563)),f326(f326(f110(f917(x43561,a905)),f326(f261(x43561),x43562)),f326(f261(x43561),x43563)))
% 157.55/157.21 [4358]E(f326(f326(f134(x43581),f326(f326(f138(x43581),f45(a909,x43582,f326(f189(f910(x43581)),x43583))),x43583)),f326(f326(f175(x43581),f45(a909,x43582,f326(f189(f910(x43581)),x43583))),x43583)),f326(f326(f326(f183(f910(x43581),f910(x43581)),x43582),f167(x43581)),x43583))
% 157.55/157.21 [4364]E(f326(f261(x43641),f326(f326(f20(x43641,a905,a905),f326(f326(f10(a905,f917(a905,a905),x43641),a329),x43642)),x43643)),f326(f326(f110(f917(x43641,a905)),f326(f78(f917(x43641,a905)),f326(f261(x43641),x43642))),f326(f261(x43641),x43643)))
% 157.55/157.21 [4380]E(f326(f326(f79(a909),f326(f189(f910(x43801)),f326(f136(x43801,x43802),x43803))),f326(f189(f910(x43801)),f326(f136(x43801,f326(f326(f10(a905,a905,x43801),a321),x43802)),x43803))),f326(f189(f910(x43801)),x43803))
% 157.55/157.21 [4403]P105(f326(f326(f234(f917(x44031,a905)),f326(f326(f110(f917(x44031,a905)),f38(f917(x44031,a905),x44032)),f38(f917(x44031,a905),x44033))),f38(f917(x44031,a905),f326(f326(f101(f917(f917(x44031,a905),a905)),x44032),x44033))))
% 157.55/157.21 [4417]E(f326(f172(x44171),f326(f136(x44171,f326(f326(f10(a905,a905,x44171),a321),f326(f326(f9(x44171,x44171,a905),a323),x44172))),x44173)),f326(f326(f3(f917(x44171,a905)),f326(f172(x44171),x44173)),f326(f326(f308(x44171),x44172),f188(f917(x44171,a905)))))
% 157.55/157.21 [4426]P105(f326(f326(f234(f917(f916(x44261,x44261),a905)),f326(f326(f110(f917(f916(x44261,x44261),a905)),f306(x44261,x44262)),f306(x44261,x44263))),f306(x44261,f326(f326(f110(f917(f916(x44261,x44261),a905)),x44262),x44263))))
% 157.55/157.21 [4449]E(f326(f326(f80(a909),f326(a112,f326(a112,f2(a909)))),f326(f326(f8(a909,a909),f326(f326(f10(a909,a909,a909),f326(f79(a909),x44491)),f326(f326(f9(a909,a909,a909),f80(a909)),x44492))),f326(f281(a909),x44493))),f326(f326(f80(a909),x44493),f326(f326(f79(a909),x44491),f326(f326(f79(a909),x44491),f326(f326(f80(a909),f326(f326(f3(a909),x44493),f77(a909))),x44492)))))
% 157.55/157.21 [4459]E(f326(f261(x44591),f326(f326(f20(x44591,a905,a905),f326(f326(f10(a905,f917(a905,a905),x44591),a324),f326(f326(f9(x44591,f917(x44591,a905),a905),f328(x44591)),f326(f172(x44591),x44592)))),x44593)),f326(f172(x44591),f326(f136(x44591,x44593),x44592)))
% 157.55/157.21 [4607]E(f326(f261(x46071),f326(f326(f10(f917(a909,a905),a905,x46071),f86(a909)),f326(f326(f9(x46071,f917(a909,a905),f917(a909,a905)),f326(f326(f10(f917(a909,f917(a905,a905)),f917(f917(a909,a905),f917(a909,a905)),x46071),f20(a909,a905,a905)),f326(f326(f10(f917(a909,a905),f917(a909,f917(a905,a905)),x46071),f326(f10(a905,f917(a905,a905),a909),a324)),f326(f326(f9(x46071,f917(a909,x46071),f917(a909,a905)),f326(f326(f10(f917(x46071,a905),f917(f917(a909,x46071),f917(a909,a905)),x46071),f10(x46071,a905,a909)),a323)),f326(f164(x46071),x46072))))),f326(f326(f20(a909,a905,a905),f326(f326(f10(a905,f917(a905,a905),a909),a324),f326(f326(f9(a909,a909,a905),f235(a909)),f326(f189(f910(x46071)),x46072)))),f326(f326(f9(a909,f917(a909,a905),a905),f328(a909)),x46073))))),f326(f172(x46071),f176(x46071,x46072,x46073)))
% 157.55/157.21 [4499]E(f326(f261(x44991),f326(f326(f20(x44991,a905,a905),f326(f326(f10(a905,f917(a905,a905),x44991),a329),f326(f326(f10(a905,a905,x44991),a321),f326(f326(f9(x44991,x44991,a905),a323),x44992)))),x44993)),f326(f326(f308(x44991),x44992),f326(f261(x44991),x44993)))
% 157.55/157.21 [4531]E(f326(f326(f154(f916(x45311,a909),x45311),f250(x45311,a909)),f326(f136(f916(x45311,a909),f326(f326(f9(f916(x45311,a909),f917(a909,a905),a905),f326(f326(f10(a909,f917(f917(a909,a905),a905),f916(x45311,a909)),f328(a909)),f255(x45311,a909))),x45312)),f326(f326(f181(x45311,a909),x45313),f139(a909,f326(f301(a909,f2(a909)),f326(f189(f910(x45311)),x45313)))))),f176(x45311,x45313,x45312))
% 157.55/157.21 [4558]E(f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(f326(f8(a909,a1),f326(f326(f10(a1,a1,a909),f326(f79(a1),x45581)),f326(f326(f9(a909,a1,a1),f326(f326(f10(a1,f917(a1,a1),a909),f80(a1)),f100(a1))),x45582))),f326(f281(a909),x45583))),f326(f326(f80(a1),f326(f100(a1),x45583)),f326(f326(f79(a1),x45581),f326(f326(f79(a1),x45581),f326(f326(f80(a1),f326(f100(a1),f326(f326(f3(a909),x45583),f77(a909)))),x45582)))))
% 157.55/157.21 [4600]E(f326(f261(f916(x46001,x46002)),f326(f256(x46001,x46002,a905),f326(f326(f9(x46001,f917(f916(x46002,x46001),a905),f917(x46002,a905)),f326(f326(f10(f917(x46002,f917(f917(f916(x46002,x46001),a905),a905)),f917(f917(f916(x46002,x46001),a905),f917(x46002,a905)),x46001),f9(x46002,f917(f916(x46002,x46001),a905),a905)),f326(f326(f10(f917(x46002,f916(x46002,x46001)),f917(x46002,f917(f917(f916(x46002,x46001),a905),a905)),x46001),f326(f10(f916(x46002,x46001),f917(f917(f916(x46002,x46001),a905),a905),x46002),f328(f916(x46002,x46001)))),f326(f9(x46002,x46001,f916(x46002,x46001)),f251(x46002,x46001))))),x46003))),f326(f285(x46002,x46001),x46003))
% 157.55/157.21 [4620]E(f326(f261(f910(x46201)),f326(f326(f10(f917(x46201,a905),a905,f910(x46201)),f86(x46201)),f326(f326(f10(f917(x46201,f917(f910(x46201),a905)),f917(x46201,a905),f910(x46201)),f326(f10(f917(f910(x46201),a905),a905,x46201),f86(f910(x46201)))),f326(f326(f9(f910(x46201),f917(x46201,f917(f910(x46201),a905)),f917(x46201,f917(f910(x46201),a905))),f326(f326(f10(f917(x46201,f917(f917(f910(x46201),a905),f917(f910(x46201),a905))),f917(f917(x46201,f917(f910(x46201),a905)),f917(x46201,f917(f910(x46201),a905))),f910(x46201)),f20(x46201,f917(f910(x46201),a905),f917(f910(x46201),a905))),f326(f326(f10(f917(x46201,f917(f910(x46201),f917(a905,a905))),f917(x46201,f917(f917(f910(x46201),a905),f917(f910(x46201),a905))),f910(x46201)),f326(f10(f917(f910(x46201),f917(a905,a905)),f917(f917(f910(x46201),a905),f917(f910(x46201),a905)),x46201),f20(f910(x46201),a905,a905))),f326(f326(f10(f917(x46201,f917(f910(x46201),a905)),f917(x46201,f917(f910(x46201),f917(a905,a905))),f910(x46201)),f326(f10(f917(f910(x46201),a905),f917(f910(x46201),f917(a905,a905)),x46201),f326(f10(a905,f917(a905,a905),f910(x46201)),a324))),f326(f326(f9(f910(x46201),f917(x46201,f917(f910(x46201),f910(x46201))),f917(x46201,f917(f910(x46201),a905))),f326(f326(f10(f917(f917(f910(x46201),f910(x46201)),f917(f910(x46201),a905)),f917(f917(x46201,f917(f910(x46201),f910(x46201))),f917(x46201,f917(f910(x46201),a905))),f910(x46201)),f10(f917(f910(x46201),f910(x46201)),f917(f910(x46201),a905),x46201)),f326(f326(f10(f917(f910(x46201),a905),f917(f917(f910(x46201),f910(x46201)),f917(f910(x46201),a905)),f910(x46201)),f10(f910(x46201),a905,f910(x46201))),a323))),f151(x46201)))))),f326(f326(f9(x46201,f917(f910(x46201),a905),f917(f910(x46201),a905)),f326(f326(f10(f917(a905,a905),f917(f917(f910(x46201),a905),f917(f910(x46201),a905)),x46201),f10(a905,a905,f910(x46201))),f326(f326(f10(a905,f917(a905,a905),x46201),a324),f326(f326(f9(x46201,f917(x46201,a905),a905),f328(x46201)),x46202)))),f326(f326(f9(f910(x46201),f917(f910(x46201),a905),a905),f328(f910(x46201))),x46203)))))),f174(x46201,x46202,x46203))
% 157.55/157.21 [4617]E(f326(f326(f85(a1,f916(a1,a1)),f326(f326(f3(a1),x46171),x46172)),f326(f326(f9(a1,f916(a1,a1),f916(a1,a1)),f326(f326(f20(a1,f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),f326(f326(f10(a905,f917(f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),a1),f96(f916(a1,a1))),f326(f234(a1),f2(a1)))),f326(f251(a1,a1),f326(f326(f79(a1),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x46173)),f77(a1))))),f326(f326(f251(a1,a1),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x46173)),x46171))),f326(f43(x46172),f326(f326(f251(a1,a1),x46173),x46171)))
% 157.55/157.21 [4640]~E(f29(x46401,x46402),f30(x46403,x46404))
% 157.55/157.21 [3661]E(f116(x36611,f326(x36612,x36613),f326(x36614,x36613)),f326(f203(x36611,x36612,x36614),x36613))
% 157.55/157.21 [3714]E(f326(f326(f244(x37141,x37142,x37143),x37144),f2(a909)),x37142)
% 157.55/157.21 [3753]E(f185(x37531,x37532,x37533,f326(a112,x37534)),f326(x37533,x37534))
% 157.55/157.21 [3794]E(f170(x37941,x37942,f170(x37941,x37943,x37944)),f170(x37941,x37943,f170(x37941,x37942,x37944)))
% 157.55/157.21 [3795]E(f126(x37951,x37952,f116(x37951,x37953,x37954)),f116(x37951,f126(x37951,x37952,x37953),x37954))
% 157.55/157.21 [3930]E(f326(f156(x39301,x39302,x39303,x39304),f113(x39302)),x39303)
% 157.55/157.21 [3931]E(f326(f142(x39311,x39312,x39313,x39314),f113(x39312)),x39314)
% 157.55/157.21 [3938]E(f326(f189(f908(x39381)),f91(x39381,x39382,x39383,x39384)),f2(a909))
% 157.55/157.21 [3970]E(f326(f189(f914(x39701,x39702)),f220(x39701,x39702,x39703,x39704)),f2(a909))
% 157.55/157.21 [3993]E(f326(f256(x39931,x39932,x39933),f254(x39931,x39932,x39933,x39934)),x39934)
% 157.55/157.21 [4037]E(f326(f326(f134(x40371),f169(x40371,x40372,x40373)),f169(x40371,x40374,x40373)),f326(f326(f134(x40371),f169(x40371,x40374,x40373)),f169(x40371,x40372,x40373)))
% 157.55/157.21 [4125]E(f326(f326(f258(x41251,x41252,x41253,f916(x41252,x41253)),x41254),f251(x41252,x41253)),x41254)
% 157.55/157.21 [4135]E(f127(x41351,x41352,x41353,x41354,f119(x41352)),x41353)
% 157.55/157.21 [4141]E(f74(x41411,x41412,x41413,x41414,f326(x41413,x41414)),x41413)
% 157.55/157.21 [4410]P41(x44101,x44102,x44103,x44104,f188(f917(x44101,a905)),x44104)
% 157.55/157.21 [3463]E(f326(f326(f18(x34631,x34632),x34633),x34634),x34633)
% 157.55/157.21 [3743]E(f170(x37431,x37432,f326(f136(x37431,x37433),x37434)),f326(f136(x37431,x37433),f170(x37431,x37432,x37434)))
% 157.55/157.21 [3777]E(f326(f326(f64(x37771,x37772,x37773),x37774),f188(f917(x37771,a905))),x37774)
% 157.55/157.21 [3801]E(f326(f326(f164(x38011),f326(f326(f151(x38011),x38012),x38013)),f326(a112,x38014)),f326(f326(f164(x38011),x38013),x38014))
% 157.55/157.21 [3869]E(f326(f326(x38691,x38692),f326(f184(x38693,x38694,x38691),x38692)),f326(f184(x38693,x38694,x38691),f326(a112,x38692)))
% 157.55/157.21 [3911]E(f254(x39111,x39112,x39113,f326(f256(x39111,x39112,x39113),x39114)),x39114)
% 157.55/157.21 [3968]E(f326(f326(f159(x39681,f326(f326(f151(x39681),x39682),x39683)),f2(a909)),x39684),f326(f326(f151(x39681),x39684),x39683))
% 157.55/157.21 [3978]E(f326(f326(f40(f917(x39781,a905),f917(x39782,a905)),x39783),f309(x39781,x39782,x39784)),f326(f309(x39781,x39782,x39784),f37(f917(x39781,a905),x39783)))
% 157.55/157.21 [3979]E(f326(f326(f40(f917(x39791,a905),f917(x39792,a905)),x39793),f310(x39792,x39791,x39794)),f326(f310(x39792,x39791,x39794),f37(f917(x39791,a905),x39793)))
% 157.55/157.21 [4004]E(f120(x40041,f130(x40042,f911(x40041),x40043,x40044)),f326(f118(x40042,x40041,x40044),x40043))
% 157.55/157.21 [4080]E(f326(f125(x40801,x40802),f126(x40801,x40803,x40804)),f326(f326(f79(a909),f326(f326(f79(a909),f326(x40802,x40803)),f326(f125(x40801,x40802),x40804))),f326(a112,f2(a909))))
% 157.55/157.21 [4101]E(f326(f142(x41011,x41012,f326(f9(x41012,x41011,x41011),x41013),x41014),f326(f168(x41012),f113(x41012))),x41014)
% 157.55/157.21 [4205]E(f223(x42051,f916(x42052,f911(x42052)),x42053,f326(f256(x42052,f911(x42052),x42051),x42054),f326(f135(x42052),f119(x42052))),x42053)
% 157.55/157.21 [4340]E(f326(f256(x43401,x43402,x43403),f326(f326(f10(f917(x43402,f916(x43401,x43402)),f917(x43402,x43403),x43401),f326(f10(f916(x43401,x43402),x43403,x43402),x43404)),f251(x43401,x43402))),x43404)
% 157.55/157.21 [3652]E(f326(f255(x36521,x36522),f326(f326(f251(x36521,x36522),x36523),x36524)),x36524)
% 157.55/157.21 [3653]E(f326(f250(x36531,x36532),f326(f326(f251(x36531,x36532),x36533),x36534)),x36533)
% 157.55/157.21 [3686]E(f326(f189(f910(x36861)),f326(f326(f159(x36861,x36862),x36863),x36864)),f326(f189(f910(x36861)),x36862))
% 157.55/157.21 [3687]E(f326(f189(f910(x36871)),f326(f326(f154(x36872,x36871),x36873),x36874)),f326(f189(f910(x36872)),x36874))
% 157.55/157.21 [3708]E(f326(f326(f138(x37081),f326(a112,x37082)),f326(f326(f151(x37081),x37083),x37084)),f326(f326(f138(x37081),x37082),x37084))
% 157.55/157.21 [3772]E(f326(f326(f175(x37721),x37722),f169(x37721,x37723,x37724)),f169(x37721,f326(f326(f232(a909),x37722),x37723),x37724))
% 157.55/157.21 [3773]E(f326(f326(f138(x37731),x37732),f169(x37731,x37733,x37734)),f169(x37731,f326(f326(f3(a909),x37733),x37732),x37734))
% 157.55/157.21 [3779]E(f326(f326(f308(x37791),x37792),f326(f326(f308(x37791),x37793),x37794)),f326(f326(f308(x37791),x37793),f326(f326(f308(x37791),x37792),x37794)))
% 157.55/157.21 [3783]E(f326(f326(f154(x37831,x37832),x37833),f114(x37831,x37834)),f114(x37832,f326(f326(f154(x37831,x37832),x37833),x37834)))
% 157.55/157.21 [3799]E(f326(f168(x37991),f326(f326(f154(x37992,x37991),x37993),x37994)),f326(f326(f154(x37992,x37991),x37993),f326(f168(x37992),x37994)))
% 157.55/157.21 [3800]E(f326(f326(f154(x38001,x38002),x38003),f326(f171(x38001),x38004)),f326(f171(x38002),f326(f326(f154(x38001,x38002),x38003),x38004)))
% 157.55/157.21 [3815]E(f326(f326(f175(x38151),f326(a112,x38152)),f326(f326(f151(x38151),x38153),x38154)),f326(f326(f151(x38151),x38153),f326(f326(f175(x38151),x38152),x38154)))
% 157.55/157.21 [3819]E(f326(f172(x38191),f326(f326(f154(x38192,x38191),x38193),x38194)),f326(f309(x38192,x38191,x38193),f326(f172(x38192),x38194)))
% 157.55/157.21 [3832]E(f326(f326(f154(x38321,x38322),f326(f18(x38322,x38321),x38323)),x38324),f169(x38322,f326(f189(f910(x38321)),x38324),x38323))
% 157.55/157.21 [3868]E(f19(x38681,x38682,x38683,f326(a5,f326(a112,f326(a22,x38684)))),f326(x38683,x38684))
% 157.55/157.21 [3872]E(f326(f326(f134(x38721),f326(f136(x38721,x38722),x38723)),f326(f136(x38721,x38722),x38724)),f326(f136(x38721,x38722),f326(f326(f134(x38721),x38723),x38724)))
% 157.55/157.21 [3885]E(f152(x38851,f326(f326(f154(x38852,x38851),x38853),f152(x38852,x38854))),f152(x38851,f326(f326(f154(x38852,x38851),x38853),x38854)))
% 157.55/157.21 [3900]E(f326(f285(x39001,x39001),f326(f326(f287(x39002,x39001),x39003),x39004)),f326(f326(f287(x39002,x39001),f326(f285(x39002,x39002),x39003)),x39004))
% 157.55/157.21 [3912]E(f326(f326(f288(x39121,x39122,x39123),x39124),f188(f917(f916(x39122,x39123),a905))),f188(f917(f916(x39121,x39123),a905)))
% 157.55/157.21 [3913]E(f326(f326(f175(x39131),f326(f326(f3(a909),x39132),x39133)),f326(f326(f138(x39131),x39133),x39134)),f326(f326(f138(x39131),x39133),f326(f326(f175(x39131),x39132),x39134)))
% 157.55/157.21 [3932]E(f326(f326(f134(x39321),f169(x39321,x39322,x39323)),f169(x39321,x39324,x39323)),f169(x39321,f326(f326(f79(a909),x39322),x39324),x39323))
% 157.55/157.21 [3933]E(f326(f326(f326(f277(x39331),x39332),x39333),x39334),f326(f251(f917(a99,f917(a905,f913(f911(x39331)))),f916(a99,a99)),f326(f42(x39331),x39332)))
% 157.55/157.21 [3961]E(f37(f917(x39611,a905),f326(f309(x39612,f917(x39611,a905),x39613),x39614)),f326(f326(f40(x39612,f917(x39611,a905)),x39614),x39613))
% 157.55/157.21 [3962]E(f38(f917(x39621,a905),f326(f309(x39622,f917(x39621,a905),x39623),x39624)),f326(f326(f39(x39622,f917(x39621,a905)),x39624),x39623))
% 157.55/157.21 [3963]E(f326(f189(f910(f916(x39631,x39632))),f326(f326(f181(x39631,x39632),x39633),x39634)),f326(f326(f232(a909),f326(f189(f910(x39631)),x39633)),f326(f189(f910(x39632)),x39634)))
% 157.55/157.21 [3965]E(f326(f310(x39651,x39652,x39653),f326(f78(f917(x39652,a905)),x39654)),f326(f78(f917(x39651,a905)),f326(f310(x39651,x39652,x39653),x39654)))
% 157.55/157.21 [4014]E(f326(f310(x40141,x40142,x40143),f326(f261(x40142),x40144)),f326(f261(x40141),f326(f326(f10(x40142,a905,x40141),x40144),x40143)))
% 157.55/157.21 [4032]E(f326(f326(f164(x40321),f326(f326(f134(x40321),x40322),f326(f326(f151(x40321),x40323),x40324))),f326(f189(f910(x40321)),x40322)),x40323)
% 157.55/157.21 [4057]E(f326(f309(x40571,x40572,x40573),f326(f310(x40571,x40572,x40573),x40574)),f326(f326(f101(f917(x40572,a905)),x40574),f326(f309(x40571,x40572,x40573),f241(f917(x40571,a905)))))
% 157.55/157.21 [4076]P105(f326(f326(f328(x40761),f326(x40762,x40763)),f326(f309(x40764,x40761,x40762),f241(f917(x40764,a905)))))
% 157.55/157.21 [4085]E(f21(x40851,x40852,x40853,f326(a5,f326(a112,f326(a22,x40854)))),f326(f326(x40853,x40854),f21(x40851,x40852,x40853,x40854)))
% 157.55/157.21 [4089]E(f326(f326(f134(x40891),f169(x40891,x40892,x40893)),f326(f326(f151(x40891),x40893),x40894)),f326(f326(f151(x40891),x40893),f326(f326(f134(x40891),f169(x40891,x40892,x40893)),x40894)))
% 157.55/157.21 [4091]E(f326(f326(f253(x40911,x40912),f326(f172(x40911),x40913)),f326(f18(f917(x40912,a905),x40911),f326(f172(x40912),x40914))),f326(f172(f916(x40911,x40912)),f59(x40911,x40912,x40913,x40914)))
% 157.55/157.21 [4103]E(f155(x41031,x41032,f326(f326(f151(x41031),x41033),x41034)),f326(f326(f79(a909),f326(f326(f79(a909),f326(x41032,x41033)),f155(x41031,x41032,x41034))),f326(a112,f2(a909))))
% 157.55/157.21 [4116]E(f185(f910(x41161),f326(f326(f151(x41161),x41162),x41163),f326(f326(f9(a909,f910(x41161),f910(x41161)),f138(x41161)),x41163),x41164),f326(f326(f138(x41161),x41164),f326(f326(f151(x41161),x41162),x41163)))
% 157.55/157.21 [4117]P24(x41171,f916(x41172,x41171),f330(x41173,x41174,x41172,x41171),f326(f326(f40(x41172,f917(x41171,a905)),x41174),x41173))
% 157.55/157.21 [4126]E(f326(f326(f3(f917(x41261,a905)),f326(f326(f3(f917(x41261,a905)),x41262),x41263)),f326(f326(f308(x41261),x41264),f188(f917(x41261,a905)))),f326(f326(f3(f917(x41261,a905)),x41262),f326(f326(f308(x41261),x41264),x41263)))
% 157.55/157.21 [4139]E(f326(f326(f183(f917(x41391,x41392),f917(x41391,x41392)),x41393),f72(x41392,x41392,x41391,x41394)),f72(x41392,x41392,x41391,f326(f326(f183(x41392,x41392),x41393),x41394)))
% 157.55/157.21 [4210]E(f326(f326(f326(f183(f910(x42101),f910(x42101)),x42102),f167(x42101)),f326(f326(f326(f183(f910(x42101),f910(x42101)),x42103),f167(x42101)),x42104)),f326(f326(f326(f183(f910(x42101),f910(x42101)),f326(f326(f79(a909),x42102),x42103)),f167(x42101)),x42104))
% 157.55/157.21 [4296]P105(f326(f326(f234(f917(x42961,a905)),f326(f172(x42961),f326(f326(f159(x42961,x42962),x42963),x42964))),f326(f326(f308(x42961),x42964),f326(f172(x42961),x42962))))
% 157.55/157.21 [4330]E(f326(f326(f40(f917(x43301,a905),f917(f916(x43301,x43302),a905)),x43303),f326(f326(f9(f917(x43301,a905),f917(x43301,f917(x43302,a905)),f917(f916(x43301,x43302),a905)),f253(x43301,x43302)),x43304)),f326(f326(f253(x43301,x43302),f37(f917(x43301,a905),x43303)),x43304))
% 157.55/157.21 [4368]E(f209(x43681,x43682,x43683,f326(f72(x43682,f917(a99,f917(a99,f917(f916(a99,a99),f917(a99,f911(x43682))))),x43681,f208(x43682)),x43684)),f210(x43681,x43682,x43684,x43683))
% 157.55/157.21 [4383]E(f205(x43831,x43832,x43833,f326(f72(x43832,f917(a99,f917(a99,f917(f916(a99,a99),f917(a99,f911(f913(x43832)))))),x43831,f204(x43832)),x43834)),f206(x43831,x43832,x43834,x43833))
% 157.55/157.21 [4388]P105(f326(f66(x43881,x43882,x43883,x43884,f188(f917(x43881,a905))),x43884))
% 157.55/157.21 [4427]E(f326(f326(f40(x44271,f917(x44272,a905)),x44273),f326(f326(f9(x44271,f917(x44272,a905),f917(x44272,a905)),f326(f326(f10(x44272,f917(f917(x44272,a905),f917(x44272,a905)),x44271),f308(x44272)),x44274)),f188(f917(x44272,a905)))),f326(f309(x44271,x44272,x44274),x44273))
% 157.55/157.21 [4434]P105(f326(f326(f234(f917(x44341,a905)),f326(f283(x44342,x44341),f326(f326(f101(f917(f916(x44342,x44341),a905)),x44343),x44344))),f326(f326(f101(f917(x44341,a905)),f326(f283(x44342,x44341),x44343)),f326(f283(x44342,x44341),x44344))))
% 157.55/157.21 [4435]P105(f326(f326(f234(f917(x44351,a905)),f326(f263(x44351,x44352),f326(f326(f101(f917(f916(x44351,x44352),a905)),x44353),x44354))),f326(f326(f101(f917(x44351,a905)),f326(f263(x44351,x44352),x44353)),f326(f263(x44351,x44352),x44354))))
% 157.55/157.21 [4495]P105(f326(f326(f234(f917(f916(x44951,x44952),a905)),f326(f309(x44952,f916(x44951,x44952),f330(x44953,x44954,x44951,x44952)),f326(f326(f40(x44951,f917(x44952,a905)),x44954),x44953))),f326(f326(f253(x44951,x44952),x44954),x44953)))
% 157.55/157.21 [4496]E(f326(f118(x44961,f916(x44961,x44962),x44963),f326(f326(f10(f917(x44962,f911(f916(x44961,x44962))),f911(f916(x44961,x44962)),x44961),f118(x44962,f916(x44961,x44962),x44964)),f326(f326(f10(f917(x44962,f916(x44961,x44962)),f917(x44962,f911(f916(x44961,x44962))),x44961),f326(f10(f916(x44961,x44962),f911(f916(x44961,x44962)),x44962),f129(f916(x44961,x44962)))),f251(x44961,x44962)))),f131(x44961,x44962,x44963,x44964))
% 157.55/157.21 [4497]E(f275(x44971,x44972,x44973,f326(f72(x44972,f917(a99,f917(a99,f917(f916(a99,a99),f916(f917(a99,f917(a905,f913(f911(x44972)))),f916(a99,a99))))),x44971,f277(x44972)),x44974)),f278(x44971,x44972,x44974,x44973))
% 157.55/157.21 [4537]E(f84(f916(x45371,x45372),f326(f256(x45371,x45372,a905),f326(f326(f9(x45371,f917(x45372,a905),f917(x45372,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x45372,a905),f917(x45372,a905)),x45371),f10(a905,a905,x45372)),f326(f326(f10(a905,f917(a905,a905),x45371),a324),f326(a323,x45373)))),f326(a323,x45374)))),f326(f326(f251(x45371,x45372),x45373),x45374))
% 157.55/157.21 [4538]E(f89(f916(x45381,x45382),f326(f256(x45381,x45382,a905),f326(f326(f9(x45381,f917(x45382,a905),f917(x45382,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x45382,a905),f917(x45382,a905)),x45381),f10(a905,a905,x45382)),f326(f326(f10(a905,f917(a905,a905),x45381),a324),f326(a323,x45383)))),f326(a323,x45384)))),f326(f326(f251(x45381,x45382),x45383),x45384))
% 157.55/157.21 [4609]E(f326(f326(f256(f910(x46091),f910(x46091),f916(f910(x46091),f910(x46091))),f326(f326(f20(f910(x46091),f917(f910(x46091),f916(f910(x46091),f910(x46091))),f917(f910(x46091),f916(f910(x46091),f910(x46091)))),f326(f326(f10(f917(f910(x46091),f917(f916(f910(x46091),f910(x46091)),f916(f910(x46091),f910(x46091)))),f917(f917(f910(x46091),f916(f910(x46091),f910(x46091))),f917(f910(x46091),f916(f910(x46091),f910(x46091)))),f910(x46091)),f20(f910(x46091),f916(f910(x46091),f910(x46091)),f916(f910(x46091),f910(x46091)))),f326(f326(f10(f917(f910(x46091),f916(f910(x46091),f910(x46091))),f917(f910(x46091),f917(f916(f910(x46091),f910(x46091)),f916(f910(x46091),f910(x46091)))),f910(x46091)),f326(f10(f916(f910(x46091),f910(x46091)),f917(f916(f910(x46091),f910(x46091)),f916(f910(x46091),f910(x46091))),f910(x46091)),f326(f96(f916(f910(x46091),f910(x46091))),f326(x46092,x46093)))),f326(f326(f10(f910(x46091),f917(f910(x46091),f916(f910(x46091),f910(x46091))),f910(x46091)),f251(f910(x46091),f910(x46091))),f326(f151(x46091),x46093))))),f326(f326(f9(f910(x46091),f917(f910(x46091),f910(x46091)),f917(f910(x46091),f916(f910(x46091),f910(x46091)))),f326(f326(f10(f917(f910(x46091),f916(f910(x46091),f910(x46091))),f917(f917(f910(x46091),f910(x46091)),f917(f910(x46091),f916(f910(x46091),f910(x46091)))),f910(x46091)),f10(f910(x46091),f916(f910(x46091),f910(x46091)),f910(x46091))),f251(f910(x46091),f910(x46091)))),f326(f151(x46091),x46093)))),f166(x46091,x46092,x46094)),f166(x46091,x46092,f326(f326(f151(x46091),x46093),x46094)))
% 157.55/157.21 [3848]E(f326(f326(f175(x38481),x38482),f326(f326(f175(x38481),x38483),x38484)),f326(f326(f175(x38481),f326(f326(f232(a909),x38482),x38483)),x38484))
% 157.55/157.21 [3849]E(f326(f326(f138(x38491),x38492),f326(f326(f138(x38491),x38493),x38494)),f326(f326(f138(x38491),f326(f326(f79(a909),x38492),x38493)),x38494))
% 157.55/157.21 [3860]E(f326(f326(f134(x38601),f326(f326(f151(x38601),x38602),x38603)),x38604),f326(f326(f151(x38601),x38602),f326(f326(f134(x38601),x38603),x38604)))
% 157.55/157.21 [3861]E(f326(f326(f134(x38611),f326(f326(f134(x38611),x38612),x38613)),x38614),f326(f326(f134(x38611),x38612),f326(f326(f134(x38611),x38613),x38614)))
% 157.55/157.21 [3944]E(f326(f326(f164(x39441),f326(f326(f151(x39441),x39442),x39443)),x39444),f185(x39441,x39442,f326(f164(x39441),x39443),x39444))
% 157.55/157.21 [3953]E(f326(f326(f183(x39531,x39531),x39532),f326(f326(f183(x39531,x39531),x39533),x39534)),f326(f326(f183(x39531,x39531),f326(f326(f80(a909),x39533),x39532)),x39534))
% 157.55/157.21 [3981]E(f326(f326(f110(f917(x39811,a905)),x39812),f326(f326(f308(x39811),x39813),x39814)),f326(f326(f308(x39811),x39813),f326(f326(f110(f917(x39811,a905)),x39812),x39814)))
% 157.55/157.21 [3996]E(f326(f326(f326(f183(x39961,x39961),x39962),x39963),f326(x39963,x39964)),f326(x39963,f326(f326(f326(f183(x39961,x39961),x39962),x39963),x39964)))
% 157.55/157.21 [4005]E(f326(f326(f288(x40051,x40052,x40053),f188(f917(f916(x40051,x40052),a905))),x40054),f188(f917(f916(x40051,x40053),a905)))
% 157.55/157.21 [4020]E(f326(f326(f110(f917(x40201,a905)),f326(f326(f308(x40201),x40202),x40203)),x40204),f326(f326(f308(x40201),x40202),f326(f326(f110(f917(x40201,a905)),x40203),x40204)))
% 157.55/157.21 [4039]E(f326(f35(f916(x40391,x40392)),f326(f326(f253(x40391,x40392),x40393),f326(f18(f917(x40392,a905),x40391),x40394))),f326(f326(f80(a909),f326(f35(x40391),x40393)),f326(f35(x40392),x40394)))
% 157.55/157.21 [4046]E(f326(f326(f101(f917(x40461,a905)),f326(f326(f308(x40461),x40462),x40463)),f326(f326(f308(x40461),x40462),x40464)),f326(f326(f308(x40461),x40462),f326(f326(f101(f917(x40461,a905)),x40463),x40464)))
% 157.55/157.21 [4061]E(f326(f326(f110(f917(x40611,a905)),x40612),f326(f326(f110(f917(x40611,a905)),x40613),x40614)),f326(f326(f110(f917(x40611,a905)),x40613),f326(f326(f110(f917(x40611,a905)),x40612),x40614)))
% 157.55/157.21 [4062]E(f326(f326(f101(f917(x40621,a905)),x40622),f326(f326(f101(f917(x40621,a905)),x40623),x40624)),f326(f326(f101(f917(x40621,a905)),x40623),f326(f326(f101(f917(x40621,a905)),x40622),x40624)))
% 157.55/157.21 [4072]E(f64(x40721,x40722,f326(f326(f10(x40722,f917(x40722,x40722),x40721),x40723),x40724)),f326(f65(x40722,x40721,x40723),x40724))
% 157.55/157.21 [4081]E(f179(x40811,f326(f326(f154(f910(x40812),f910(x40811)),f326(f154(x40812,x40811),x40813)),x40814)),f326(f326(f154(f910(x40812),f910(x40811)),f326(f154(x40812,x40811),x40813)),f179(x40812,x40814)))
% 157.55/157.21 [4100]E(f326(f142(f910(x41001),f910(x41001),f134(x41001),f113(x41001)),f326(f326(f154(x41002,f910(x41001)),x41003),x41004)),f163(x41002,x41001,x41003,x41004))
% 157.55/157.21 [4157]E(f326(f72(x41571,x41571,x41571,f326(f326(f183(x41571,x41571),x41572),x41573)),f326(f326(f183(x41571,x41571),x41574),x41573)),f326(f326(f183(x41571,x41571),f326(f326(f79(a909),x41572),x41574)),x41573))
% 157.55/157.21 [4180]E(f326(f326(f101(f917(x41801,a905)),f326(f326(f110(f917(x41801,a905)),x41802),x41803)),f326(f326(f110(f917(x41801,a905)),x41802),x41804)),f326(f326(f110(f917(x41801,a905)),x41802),f326(f326(f101(f917(x41801,a905)),x41803),x41804)))
% 157.55/157.21 [4181]E(f326(f326(f101(f917(x41811,a905)),f326(f326(f3(f917(x41811,a905)),x41812),x41813)),f326(f326(f3(f917(x41811,a905)),x41812),x41814)),f326(f326(f3(f917(x41811,a905)),x41812),f326(f326(f110(f917(x41811,a905)),x41813),x41814)))
% 157.55/157.21 [4182]E(f326(f326(f110(f917(x41821,a905)),f326(f326(f3(f917(x41821,a905)),x41822),x41823)),f326(f326(f3(f917(x41821,a905)),x41822),x41824)),f326(f326(f3(f917(x41821,a905)),x41822),f326(f326(f101(f917(x41821,a905)),x41823),x41824)))
% 157.55/157.21 [4183]E(f326(f326(f110(f917(x41831,a905)),f326(f326(f101(f917(x41831,a905)),x41832),x41833)),f326(f326(f101(f917(x41831,a905)),x41832),x41834)),f326(f326(f101(f917(x41831,a905)),x41832),f326(f326(f110(f917(x41831,a905)),x41833),x41834)))
% 157.55/157.21 [4184]E(f326(f326(f3(f917(x41841,a905)),f326(f326(f101(f917(x41841,a905)),x41842),x41843)),f326(f326(f101(f917(x41841,a905)),x41842),x41844)),f326(f326(f101(f917(x41841,a905)),x41842),f326(f326(f3(f917(x41841,a905)),x41843),x41844)))
% 157.55/157.21 [4189]E(f326(f35(f916(x41891,x41892)),f326(f326(f253(x41891,x41892),f326(f326(f308(x41891),x41893),f188(f917(x41891,a905)))),f326(f18(f917(x41892,a905),x41891),x41894))),f326(f35(x41892),x41894))
% 157.55/157.21 [4224]E(f326(f326(f40(x42241,f917(x42242,a905)),x42243),f326(f326(f10(f917(x42242,a905),f917(x42242,a905),x42241),f78(f917(x42242,a905))),x42244)),f326(f78(f917(x42242,a905)),f326(f326(f39(x42241,f917(x42242,a905)),x42243),x42244)))
% 157.55/157.21 [4225]E(f326(f326(f39(x42251,f917(x42252,a905)),x42253),f326(f326(f10(f917(x42252,a905),f917(x42252,a905),x42251),f78(f917(x42252,a905))),x42254)),f326(f78(f917(x42252,a905)),f326(f326(f40(x42251,f917(x42252,a905)),x42253),x42254)))
% 157.55/157.21 [4241]E(f326(f326(f288(x42411,x42411,x42411),f326(f326(f183(f916(x42411,x42411),a905),x42412),x42413)),f326(f326(f183(f916(x42411,x42411),a905),x42414),x42413)),f326(f326(f183(f916(x42411,x42411),a905),f326(f326(f79(a909),x42412),x42414)),x42413))
% 157.55/157.21 [4271]E(f326(f326(f39(x42711,f917(f917(x42712,a905),a905)),x42713),f326(f326(f10(f917(x42712,a905),f917(f917(x42712,a905),a905),x42711),f307(x42712)),x42714)),f326(f307(x42712),f326(f326(f39(x42711,f917(x42712,a905)),x42713),x42714)))
% 157.55/157.21 [4303]E(f326(f326(f39(f917(x43031,a905),f917(x43032,a905)),x43033),f326(f326(f9(f917(x43031,a905),f917(x43031,f917(x43032,a905)),f917(x43032,a905)),f39(x43031,f917(x43032,a905))),x43034)),f326(f326(f39(x43031,f917(x43032,a905)),f37(f917(x43031,a905),x43033)),x43034))
% 157.55/157.21 [4304]E(f326(f326(f40(f917(x43041,a905),f917(x43042,a905)),x43043),f326(f326(f9(f917(x43041,a905),f917(x43041,f917(x43042,a905)),f917(x43042,a905)),f40(x43041,f917(x43042,a905))),x43044)),f326(f326(f40(x43041,f917(x43042,a905)),f37(f917(x43041,a905),x43043)),x43044))
% 157.55/157.21 [4309]E(f326(f326(f154(x43091,x43092),x43093),f326(f142(f910(x43091),f910(x43091),f134(x43091),f113(x43091)),x43094)),f326(f142(f910(x43092),f910(x43092),f134(x43092),f113(x43092)),f326(f326(f154(f910(x43091),f910(x43092)),f326(f154(x43091,x43092),x43093)),x43094)))
% 157.55/157.21 [4311]E(f185(f910(x43111),f113(x43111),f326(f326(f10(f910(x43111),f910(x43111),a909),f326(f151(x43111),x43112)),f326(f326(f9(a909,f910(x43111),f910(x43111)),f175(x43111)),x43113)),x43114),f326(f326(f175(x43111),x43114),f326(f326(f151(x43111),x43112),x43113)))
% 157.55/157.21 [4349]P105(f326(f326(f234(f917(x43491,a905)),f326(f309(x43492,x43491,x43493),f326(f310(x43492,x43491,x43493),x43494))),x43494))
% 157.55/157.21 [4351]E(f326(f309(f916(x43511,x43512),f916(x43512,x43511),f326(f256(x43511,x43512,f916(x43512,x43511)),f326(f9(x43512,x43511,f916(x43512,x43511)),f251(x43512,x43511)))),f326(f326(f253(x43511,x43512),x43513),f326(f18(f917(x43512,a905),x43511),x43514))),f326(f326(f253(x43512,x43511),x43514),f326(f18(f917(x43511,a905),x43512),x43513)))
% 157.55/157.21 [4360]E(f326(f326(f40(x43601,f917(x43602,a905)),x43603),f326(f326(f10(f917(x43601,a905),f917(x43602,a905),x43601),f284(x43601,x43602,x43604)),f326(f326(f9(x43601,f917(x43601,a905),f917(x43601,a905)),f308(x43601)),f188(f917(x43601,a905))))),f326(f284(x43601,x43602,x43604),x43603))
% 157.55/157.21 [4361]E(f326(f326(f40(x43611,f917(x43612,a905)),x43613),f326(f326(f10(f917(x43611,a905),f917(x43612,a905),x43611),f310(x43612,x43611,x43614)),f326(f326(f9(x43611,f917(x43611,a905),f917(x43611,a905)),f308(x43611)),f188(f917(x43611,a905))))),f326(f310(x43612,x43611,x43614),x43613))
% 157.55/157.21 [4448]E(f326(f326(f110(f917(x44481,a905)),f326(f326(f110(f917(x44481,a905)),f326(f326(f101(f917(x44481,a905)),x44482),x44483)),f326(f326(f101(f917(x44481,a905)),x44483),x44484))),f326(f326(f101(f917(x44481,a905)),x44484),x44482)),f326(f326(f101(f917(x44481,a905)),f326(f326(f101(f917(x44481,a905)),f326(f326(f110(f917(x44481,a905)),x44482),x44483)),f326(f326(f110(f917(x44481,a905)),x44483),x44484))),f326(f326(f110(f917(x44481,a905)),x44484),x44482)))
% 157.55/157.21 [4511]E(f326(f142(f910(x45111),f910(x45111),f134(x45111),f113(x45111)),f326(f326(f154(x45112,f910(x45111)),f326(f326(f9(x45112,f910(x45111),f910(x45111)),f326(f326(f10(x45111,f917(f910(x45111),f910(x45111)),x45112),f151(x45111)),x45113)),f113(x45111))),x45114)),f326(f326(f154(x45112,x45111),x45113),x45114))
% 157.55/157.21 [4521]E(f326(f326(f85(a1,x45211),f326(f103(a1),f326(f326(f79(a1),x45212),a97))),f326(f326(f20(a1,x45211,x45211),f326(f326(f9(a1,x45211,f917(x45211,x45211)),f326(f326(f10(a905,f917(x45211,f917(x45211,x45211)),a1),f96(x45211)),a193)),x45213)),f326(f326(f10(a909,x45211,a1),x45214),a104))),f185(x45211,x45213,x45214,f326(f103(a909),x45212)))
% 157.55/157.21 [4552]E(f326(f261(x45521),f326(f326(f10(f917(x45522,a905),a905,x45521),f86(x45522)),f326(f326(f10(f917(x45522,a905),f917(x45522,a905),x45521),f326(f20(x45522,a905,a905),f326(f326(f10(a905,f917(a905,a905),x45522),a324),f326(f326(f9(x45522,f917(x45522,a905),a905),f328(x45522)),x45523)))),f326(f9(x45522,x45521,a905),x45524)))),f326(f284(x45522,x45521,f326(f261(f916(x45522,x45521)),f326(f256(x45522,x45521,a905),x45524))),x45523))
% 157.55/157.21 [4706]~P105(f326(f326(f188(f917(x47061,f917(x47062,a905))),x47063),x47064))
% 157.55/157.21 [4008]E(f326(f326(f164(x40081),f326(f326(f134(x40081),x40082),x40083)),f326(f326(f79(a909),f326(f189(f910(x40081)),x40082)),x40084)),f326(f326(f164(x40081),x40083),x40084))
% 157.55/157.21 [4013]E(f326(f326(f138(x40131),x40132),f326(f326(f175(x40131),f326(f326(f79(a909),x40133),x40132)),x40134)),f326(f326(f175(x40131),x40133),f326(f326(f138(x40131),x40132),x40134)))
% 157.55/157.21 [4114]E(f326(f326(f110(f917(x41141,a905)),f326(f283(x41142,x41141),x41143)),f326(f283(x41142,x41141),x41144)),f326(f283(x41142,x41141),f326(f326(f110(f917(f916(x41142,x41141),a905)),x41143),x41144)))
% 157.55/157.21 [4115]E(f326(f326(f110(f917(x41151,a905)),f326(f263(x41151,x41152),x41153)),f326(f263(x41151,x41152),x41154)),f326(f263(x41151,x41152),f326(f326(f110(f917(f916(x41151,x41152),a905)),x41153),x41154)))
% 157.55/157.21 [4120]E(f326(f326(f110(f917(x41201,a905)),f326(f326(f110(f917(x41201,a905)),x41202),x41203)),x41204),f326(f326(f110(f917(x41201,a905)),x41202),f326(f326(f110(f917(x41201,a905)),x41203),x41204)))
% 157.55/157.21 [4121]E(f326(f326(f3(f917(x41211,a905)),f326(f326(f101(f917(x41211,a905)),x41212),x41213)),x41214),f326(f326(f101(f917(x41211,a905)),x41212),f326(f326(f3(f917(x41211,a905)),x41213),x41214)))
% 157.55/157.21 [4122]E(f326(f326(f101(f917(x41221,a905)),f326(f326(f101(f917(x41221,a905)),x41222),x41223)),x41224),f326(f326(f101(f917(x41221,a905)),x41222),f326(f326(f101(f917(x41221,a905)),x41223),x41224)))
% 157.55/157.21 [4159]E(f326(f326(f110(f917(f916(x41591,x41592),a905)),f326(f285(x41592,x41591),x41593)),f326(f285(x41592,x41591),x41594)),f326(f285(x41592,x41591),f326(f326(f110(f917(f916(x41592,x41591),a905)),x41593),x41594)))
% 157.55/157.21 [4160]E(f326(f326(f101(f917(f916(x41601,x41602),a905)),f326(f285(x41602,x41601),x41603)),f326(f285(x41602,x41601),x41604)),f326(f285(x41602,x41601),f326(f326(f101(f917(f916(x41602,x41601),a905)),x41603),x41604)))
% 157.55/157.21 [4173]E(f326(f326(f110(f917(x41731,f917(x41732,a905))),f242(x41732,x41731,x41733)),f242(x41732,x41731,x41734)),f242(x41732,x41731,f326(f326(f110(f917(x41732,f917(x41731,a905))),x41733),x41734)))
% 157.55/157.21 [4174]E(f326(f326(f101(f917(x41741,f917(x41742,a905))),f242(x41742,x41741,x41743)),f242(x41742,x41741,x41744)),f242(x41742,x41741,f326(f326(f101(f917(x41742,f917(x41741,a905))),x41743),x41744)))
% 157.55/157.21 [4228]E(f326(f326(f101(f917(x42281,a905)),f326(f326(f110(f917(x42281,a905)),x42282),x42283)),f326(f326(f110(f917(x42281,a905)),x42284),x42283)),f326(f326(f110(f917(x42281,a905)),f326(f326(f101(f917(x42281,a905)),x42282),x42284)),x42283))
% 157.55/157.21 [4229]E(f326(f326(f110(f917(x42291,a905)),f326(f326(f3(f917(x42291,a905)),x42292),x42293)),f326(f326(f3(f917(x42291,a905)),x42294),x42293)),f326(f326(f3(f917(x42291,a905)),f326(f326(f110(f917(x42291,a905)),x42292),x42294)),x42293))
% 157.55/157.21 [4230]E(f326(f326(f110(f917(x42301,a905)),f326(f326(f101(f917(x42301,a905)),x42302),x42303)),f326(f326(f101(f917(x42301,a905)),x42304),x42303)),f326(f326(f101(f917(x42301,a905)),f326(f326(f110(f917(x42301,a905)),x42302),x42304)),x42303))
% 157.55/157.21 [4231]E(f326(f326(f3(f917(x42311,a905)),f326(f326(f101(f917(x42311,a905)),x42312),x42313)),f326(f326(f101(f917(x42311,a905)),x42314),x42313)),f326(f326(f101(f917(x42311,a905)),f326(f326(f3(f917(x42311,a905)),x42312),x42314)),x42313))
% 157.55/157.21 [4232]E(f326(f326(f3(f917(x42321,a905)),f326(f326(f101(f917(x42321,a905)),x42322),x42323)),f326(f326(f101(f917(x42321,a905)),x42324),x42323)),f326(f326(f3(f917(x42321,a905)),f326(f326(f101(f917(x42321,a905)),x42322),x42323)),x42324))
% 157.55/157.21 [4244]E(f326(f326(f3(f917(x42441,a905)),f326(f326(f3(f917(x42441,a905)),x42442),f326(f326(f308(x42441),x42443),f188(f917(x42441,a905))))),x42444),f326(f326(f3(f917(x42441,a905)),x42442),f326(f326(f308(x42441),x42443),x42444)))
% 157.55/157.21 [4298]E(f326(f326(f110(f917(x42981,a905)),f326(f326(f308(x42981),x42982),f326(f326(f308(x42981),x42983),f188(f917(x42981,a905))))),f326(f280(x42981),x42984)),f326(f280(x42981),f326(f326(f308(f916(x42981,x42981)),f326(f326(f251(x42981,x42981),x42982),x42983)),x42984)))
% 157.55/157.21 [4325]E(f326(f326(f40(a909,f917(x43251,a905)),f326(f300(a909),x43252)),f326(f326(f10(a909,f917(x43251,a905),a909),x43253),f326(f326(f9(a909,a909,a909),f79(a909)),x43254))),f326(f326(f40(a909,f917(x43251,a905)),f302(a909,x43254,f326(f326(f79(a909),x43252),x43254))),x43253))
% 157.55/157.21 [4326]E(f174(x43261,f326(f284(x43261,x43261,x43262),f326(f326(f308(x43261),x43263),f188(f917(x43261,a905)))),f326(f284(f910(x43261),f910(x43261),f158(x43261,x43262)),f326(f326(f308(f910(x43261)),x43264),f188(f917(f910(x43261),a905))))),f326(f284(f910(x43261),f910(x43261),f158(x43261,x43262)),f326(f326(f308(f910(x43261)),f326(f326(f151(x43261),x43263),x43264)),f188(f917(f910(x43261),a905)))))
% 157.55/157.21 [4390]E(f326(f261(x43901),f326(f326(f9(x43901,f917(x43902,a905),a905),f326(f326(f10(x43902,f917(f917(x43902,a905),a905),x43901),f328(x43902)),x43903)),x43904)),f326(f310(x43901,x43902,x43903),x43904))
% 157.55/157.21 [4480]E(f326(f261(x44801),f326(f326(f9(x44801,f917(f916(x44802,x44801),a905),a905),f326(f326(f10(f916(x44802,x44801),f917(f917(f916(x44802,x44801),a905),a905),x44801),f328(f916(x44802,x44801))),f326(f251(x44802,x44801),x44803))),x44804)),f326(f284(x44802,x44801,x44804),f326(f326(f308(x44802),x44803),f188(f917(x44802,a905)))))
% 157.55/157.21 [4494]E(f326(f326(f154(f916(x44941,a909),x44941),f250(x44941,a909)),f326(f136(f916(x44941,a909),f326(f326(f10(a909,a905,f916(x44941,a909)),x44942),f326(f326(f10(a909,a909,f916(x44941,a909)),a112),f255(x44941,a909)))),f326(f326(f181(x44941,a909),x44943),x44944))),f326(f326(f154(f916(x44941,a909),x44941),f250(x44941,a909)),f326(f136(f916(x44941,a909),f326(f326(f10(a909,a905,f916(x44941,a909)),x44942),f255(x44941,a909))),f326(f326(f181(x44941,a909),x44943),f326(f326(f154(a909,a909),a112),x44944)))))
% 157.55/157.21 [4503]P105(f326(f326(f234(f917(f917(x45031,a905),a905)),f326(f326(f40(x45032,f917(f917(x45031,a905),a905)),x45033),f326(f326(f10(f917(x45031,a905),f917(f917(x45031,a905),a905),x45032),f307(x45031)),x45034))),f326(f307(x45031),f326(f326(f40(x45032,f917(x45031,a905)),x45033),x45034))))
% 157.55/157.21 [4544]E(f326(f326(f85(a1,x45441),f326(f103(a1),f326(f326(f79(a1),x45442),a97))),f326(f326(f20(a1,x45441,x45441),f326(f326(f9(a1,x45441,f917(x45441,x45441)),f326(f326(f10(a905,f917(x45441,f917(x45441,x45441)),a1),f96(x45441)),a193)),x45443)),f326(f326(f20(a1,x45441,x45441),f326(f326(f10(a909,f917(x45441,x45441),a1),x45444),a104)),f326(f326(f10(a909,x45441,a1),f184(x45441,x45443,x45444)),a104)))),f326(f184(x45441,x45443,x45444),f326(f103(a909),x45442)))
% 157.55/157.21 [4568]E(f326(f261(f916(x45681,x45682)),f326(f256(x45681,x45682,a905),f326(f326(f9(x45681,f917(x45682,a905),f917(x45682,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x45682,a905),f917(x45682,a905)),x45681),f10(a905,a905,x45682)),f326(f326(f10(a905,f917(a905,a905),x45681),a324),f326(f326(f9(x45681,f917(x45681,a905),a905),f328(x45681)),x45683)))),f326(f326(f9(x45682,f917(x45682,a905),a905),f328(x45682)),x45684)))),f229(x45681,x45682,x45683,x45684))
% 157.55/157.21 [4604]E(f326(f326(f40(x46041,f917(f916(x46041,x46042),a905)),x46043),f326(f326(f20(x46041,f917(x46042,f917(f916(x46041,x46042),a905)),f917(f916(x46041,x46042),a905)),f326(f326(f10(f917(x46042,a905),f917(f917(x46042,f917(f916(x46041,x46042),a905)),f917(f916(x46041,x46042),a905)),x46041),f40(x46042,f917(f916(x46041,x46042),a905))),x46044)),f326(f326(f9(x46041,f917(f916(x46041,x46042),a905),f917(x46042,f917(f916(x46041,x46042),a905))),f326(f326(f10(f917(x46042,f917(f917(f916(x46041,x46042),a905),f917(f916(x46041,x46042),a905))),f917(f917(f916(x46041,x46042),a905),f917(x46042,f917(f916(x46041,x46042),a905))),x46041),f9(x46042,f917(f916(x46041,x46042),a905),f917(f916(x46041,x46042),a905))),f326(f326(f10(f917(x46042,f916(x46041,x46042)),f917(x46042,f917(f917(f916(x46041,x46042),a905),f917(f916(x46041,x46042),a905))),x46041),f326(f10(f916(x46041,x46042),f917(f917(f916(x46041,x46042),a905),f917(f916(x46041,x46042),a905)),x46042),f308(f916(x46041,x46042)))),f251(x46041,x46042)))),f188(f917(f916(x46041,x46042),a905))))),f326(f326(f253(x46041,x46042),x46043),x46044))
% 157.55/157.21 [4168]E(f326(f326(f134(x41681),f326(f326(f175(x41681),x41682),x41683)),f326(f326(f175(x41681),f326(f326(f3(a909),x41682),f326(f189(f910(x41681)),x41683))),x41684)),f326(f326(f175(x41681),x41682),f326(f326(f134(x41681),x41683),x41684)))
% 157.55/157.21 [4169]E(f326(f326(f134(x41691),f326(f326(f138(x41691),x41692),x41693)),f326(f326(f138(x41691),f326(f326(f3(a909),x41692),f326(f189(f910(x41691)),x41693))),x41694)),f326(f326(f138(x41691),x41692),f326(f326(f134(x41691),x41693),x41694)))
% 157.55/157.21 [4218]E(f326(f326(f79(a909),f326(f326(f80(a909),x42181),x42182)),f326(f326(f79(a909),f326(f326(f80(a909),x42183),x42182)),x42184)),f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f79(a909),x42181),x42183)),x42182)),x42184))
% 157.55/157.21 [4366]E(f89(x43661,f326(f326(f9(x43661,x43662,a905),f326(f326(f10(x43662,f917(x43662,a905),x43661),a323),x43663)),x43664)),f326(f90(x43661,x43662,f241(f917(x43661,a905)),x43663),x43664))
% 157.55/157.21 [4414]P105(f326(f326(f234(f917(x44141,a905)),f326(f326(f3(f917(x44141,a905)),f326(f283(x44142,x44141),x44143)),f326(f283(x44142,x44141),x44144))),f326(f283(x44142,x44141),f326(f326(f3(f917(f916(x44142,x44141),a905)),x44143),x44144))))
% 157.55/157.21 [4415]P105(f326(f326(f234(f917(x44151,a905)),f326(f326(f3(f917(x44151,a905)),f326(f263(x44151,x44152),x44153)),f326(f263(x44151,x44152),x44154))),f326(f263(x44151,x44152),f326(f326(f3(f917(f916(x44151,x44152),a905)),x44153),x44154))))
% 157.55/157.21 [4523]E(f326(f326(f79(a1),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x45231),x45232)),f188(f917(f916(a909,a909),a905)))))),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x45233),x45234)),f188(f917(f916(a909,a909),a905)))))),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),f326(f326(f79(a909),x45231),x45233)),f326(f326(f79(a909),x45232),x45234))),f188(f917(f916(a909,a909),a905))))))
% 157.55/157.21 [4563]E(f326(f326(f80(a1),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x45631),x45632)),f188(f917(f916(a909,a909),a905)))))),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x45633),x45634)),f188(f917(f916(a909,a909),a905)))))),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),f326(f326(f79(a909),f326(f326(f80(a909),x45631),x45633)),f326(f326(f80(a909),x45632),x45634))),f326(f326(f79(a909),f326(f326(f80(a909),x45631),x45634)),f326(f326(f80(a909),x45632),x45633)))),f188(f917(f916(a909,a909),a905))))))
% 157.55/157.21 [4584]E(f326(f261(x45841),f326(f326(f10(f917(x45842,a905),a905,x45841),f87(x45842)),f326(f326(f10(f917(x45842,a905),f917(x45842,a905),x45841),f326(f20(x45842,a905,a905),f326(f326(f10(a905,f917(a905,a905),x45842),a329),f326(f326(f9(x45842,f917(x45842,a905),a905),f328(x45842)),x45843)))),f326(f326(f9(x45841,f917(x45842,f917(x45841,a905)),f917(x45842,a905)),f326(f326(f10(f917(f917(x45841,a905),a905),f917(f917(x45842,f917(x45841,a905)),f917(x45842,a905)),x45841),f10(f917(x45841,a905),a905,x45842)),f328(x45841))),x45844)))),f326(f326(f39(x45842,f917(x45841,a905)),x45843),x45844))
% 157.55/157.21 [4616]E(f326(f326(f288(x46161,x46161,x46161),f326(f326(f308(f916(x46161,x46161)),f326(f326(f251(x46161,x46161),x46162),x46163)),x46164)),f306(x46161,f326(f326(f308(f916(x46161,x46161)),f326(f326(f251(x46161,x46161),x46162),x46163)),x46164))),f326(f326(f110(f917(f916(x46161,x46161),a905)),f326(f326(f288(x46161,x46161,x46161),x46164),f306(x46161,x46164))),f326(f261(f916(x46161,x46161)),f326(f256(x46161,x46161,a905),f326(f326(f9(x46161,f917(x46161,a905),f917(x46161,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x46161,a905),f917(x46161,a905)),x46161),f10(a905,a905,x46161)),f326(f326(f10(a905,f917(a905,a905),x46161),a324),f326(f326(f9(x46161,f917(f916(x46161,x46161),a905),a905),f326(f326(f10(f916(x46161,x46161),f917(f917(f916(x46161,x46161),a905),a905),x46161),f328(f916(x46161,x46161))),f326(f326(f9(x46161,x46161,f916(x46161,x46161)),f251(x46161,x46161)),x46162))),f306(x46161,x46164))))),f326(f326(f9(x46161,f917(f916(x46161,x46161),a905),a905),f326(f326(f10(f916(x46161,x46161),f917(f917(f916(x46161,x46161),a905),a905),x46161),f328(f916(x46161,x46161))),f326(f251(x46161,x46161),x46163))),f306(x46161,x46164)))))))
% 157.55/157.21 [4416]E(f326(f136(x44161,f326(f326(f20(x44161,a905,a905),f326(f326(f10(a905,f917(a905,a905),x44161),a324),x44162)),x44163)),x44164),f326(f136(x44161,x44163),f326(f136(x44161,x44162),x44164)))
% 157.55/157.21 [4517]E(f326(f326(f134(x45171),f326(f326(f326(f96(f910(x45171)),f326(f326(f328(a909),f2(a909)),x45172)),f326(f326(f151(x45171),x45173),f113(x45171))),f113(x45171))),f176(x45171,x45174,f326(f261(a909),f326(f326(f9(a909,f917(a909,a905),a905),f326(f326(f10(a909,f917(f917(a909,a905),a905),a909),f328(a909)),a112)),x45172)))),f176(x45171,f326(f326(f151(x45171),x45173),x45174),x45172))
% 157.55/157.21 [4612]E(f326(f261(f916(x46121,x46122)),f326(f326(f10(f917(a909,a905),a905,f916(x46121,x46122)),f86(a909)),f326(f326(f9(f916(x46121,x46122),f917(a909,a905),f917(a909,a905)),f326(f326(f10(f917(a909,f917(a905,a905)),f917(f917(a909,a905),f917(a909,a905)),f916(x46121,x46122)),f20(a909,a905,a905)),f326(f326(f10(f917(a909,a905),f917(a909,f917(a905,a905)),f916(x46121,x46122)),f326(f10(a905,f917(a905,a905),a909),a324)),f326(f326(f9(f916(x46121,x46122),f917(a909,f916(x46121,x46122)),f917(a909,a905)),f326(f326(f10(f917(f916(x46121,x46122),a905),f917(f917(a909,f916(x46121,x46122)),f917(a909,a905)),f916(x46121,x46122)),f10(f916(x46121,x46122),a905,a909)),a323)),f326(f326(f20(a909,x46122,f916(x46121,x46122)),f326(f326(f10(x46121,f917(x46122,f916(x46121,x46122)),a909),f251(x46121,x46122)),f326(f164(x46121),x46123))),f326(f164(x46122),x46124)))))),f326(f326(f9(a909,a909,a905),f235(a909)),f326(f326(f232(a909),f326(f189(f910(x46121)),x46123)),f326(f189(f910(x46122)),x46124)))))),f326(f172(f916(x46121,x46122)),f326(f326(f181(x46121,x46122),x46123),x46124)))
% 157.55/157.21 [4536]E(f326(f261(f916(x45361,x45362)),f326(f256(x45361,x45362,a905),f326(f326(f9(x45361,f917(x45362,a905),f917(x45362,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x45362,a905),f917(x45362,a905)),x45361),f10(a905,a905,x45362)),f326(f326(f10(a905,f917(a905,a905),x45361),a324),x45363))),x45364))),f326(f326(f253(x45361,x45362),f326(f261(x45361),x45363)),f326(f18(f917(x45362,a905),x45361),f326(f261(x45362),x45364))))
% 157.55/157.21 [4539]E(f326(f261(f916(x45391,x45392)),f326(f256(x45391,x45392,a905),f326(f326(f20(x45391,f917(x45392,a905),f917(x45392,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x45392,a905),f917(x45392,a905)),x45391),f10(a905,a905,x45392)),f326(f326(f10(a905,f917(a905,a905),x45391),a324),x45393))),x45394))),f326(f326(f253(x45391,x45392),f326(f261(x45391),x45393)),f326(f326(f10(f917(x45392,a905),f917(x45392,a905),x45391),f261(x45392)),x45394)))
% 157.55/157.21 [4551]E(f326(f261(x45511),f326(f326(f10(f917(x45512,a905),a905,x45511),f87(x45512)),f326(f326(f10(f917(x45512,a905),f917(x45512,a905),x45511),f326(f20(x45512,a905,a905),f326(f326(f10(a905,f917(a905,a905),x45512),a329),f326(f326(f9(x45512,f917(x45512,a905),a905),f328(x45512)),x45513)))),x45514))),f326(f326(f39(x45512,f917(x45511,a905)),x45513),f326(f326(f10(f917(x45511,a905),f917(x45511,a905),x45512),f261(x45511)),f326(f9(x45511,x45512,a905),x45514))))
% 157.55/157.21 [4596]E(f326(f326(f154(f916(x45961,a909),x45961),f250(x45961,a909)),f326(f136(f916(x45961,a909),f326(f326(f9(f916(x45961,a909),f917(a909,a905),a905),f326(f326(f10(a909,f917(f917(a909,a905),a905),f916(x45961,a909)),f328(a909)),f255(x45961,a909))),x45962)),f326(f326(f181(x45961,a909),x45963),f139(a909,f326(f301(a909,x45964),f326(f326(f79(a909),x45964),f326(f189(f910(x45961)),x45963))))))),f326(f326(f154(f916(x45961,a909),x45961),f250(x45961,a909)),f326(f136(f916(x45961,a909),f326(f326(f9(f916(x45961,a909),f917(a909,a905),a905),f326(f326(f10(a909,f917(f917(a909,a905),a905),f916(x45961,a909)),f328(a909)),f326(f326(f9(f916(x45961,a909),a909,a909),f326(f326(f10(a909,f917(a909,a909),f916(x45961,a909)),f79(a909)),f255(x45961,a909))),x45964))),x45962)),f326(f326(f181(x45961,a909),x45963),f139(a909,f326(f301(a909,f2(a909)),f326(f189(f910(x45961)),x45963)))))))
% 157.55/157.21 [4597]E(f326(a112,f326(f326(f233(a909),f326(f189(f910(x45971)),x45972)),f326(f142(a909,f910(x45973),f326(f9(f910(x45973),a909,a909),f326(f326(f10(a909,f917(a909,a909),f910(x45973)),f233(a909)),f326(f326(f9(f910(x45973),a909,a909),f326(f326(f10(a909,f917(a909,a909),f910(x45973)),f3(a909)),f189(f910(x45973)))),f326(a112,f2(a909))))),f2(a909)),f326(f168(f910(x45973)),f326(f136(f910(x45973),f326(f326(f10(a905,a905,f910(x45973)),a321),f326(f326(f9(f910(x45973),f910(x45973),a905),a323),f113(x45973)))),x45974))))),f326(f326(f233(a909),f326(a112,f326(f189(f910(x45971)),x45972))),f326(f142(a909,f910(x45973),f326(f9(f910(x45973),a909,a909),f326(f326(f10(a909,f917(a909,a909),f910(x45973)),f233(a909)),f189(f910(x45973)))),f2(a909)),f326(f168(f910(x45973)),x45974))))
% 157.55/157.21 [4550]E(f326(f326(f134(x45501),f176(x45501,x45502,x45503)),f176(x45501,x45504,f326(f261(a909),f326(f326(f9(a909,f917(a909,a905),a905),f326(f326(f10(a909,f917(f917(a909,a905),a905),a909),f328(a909)),f326(f326(f9(a909,a909,a909),f79(a909)),f326(f189(f910(x45501)),x45502)))),x45503)))),f176(x45501,f326(f326(f134(x45501),x45502),x45504),x45503))
% 157.55/157.21 [4598]E(f38(f917(x45981,a905),f326(f261(f917(x45981,a905)),f326(f326(f10(f917(x45982,a905),a905,f917(x45981,a905)),f86(x45982)),f326(f326(f10(f917(x45982,a905),f917(x45982,a905),f917(x45981,a905)),f326(f20(x45982,a905,a905),f326(f326(f10(a905,f917(a905,a905),x45982),a324),f326(f326(f9(x45982,f917(x45982,a905),a905),f328(x45982)),x45983)))),f326(f326(f9(f917(x45981,a905),f917(x45982,f917(x45981,a905)),f917(x45982,a905)),f326(f326(f10(f917(f917(x45981,a905),a905),f917(f917(x45982,f917(x45981,a905)),f917(x45982,a905)),f917(x45981,a905)),f10(f917(x45981,a905),a905,x45982)),a323)),x45984))))),f326(f326(f39(x45982,f917(x45981,a905)),x45983),x45984))
% 157.55/157.21 [4599]E(f37(f917(x45991,a905),f326(f261(f917(x45991,a905)),f326(f326(f10(f917(x45992,a905),a905,f917(x45991,a905)),f86(x45992)),f326(f326(f10(f917(x45992,a905),f917(x45992,a905),f917(x45991,a905)),f326(f20(x45992,a905,a905),f326(f326(f10(a905,f917(a905,a905),x45992),a324),f326(f326(f9(x45992,f917(x45992,a905),a905),f328(x45992)),x45993)))),f326(f326(f9(f917(x45991,a905),f917(x45992,f917(x45991,a905)),f917(x45992,a905)),f326(f326(f10(f917(f917(x45991,a905),a905),f917(f917(x45992,f917(x45991,a905)),f917(x45992,a905)),f917(x45991,a905)),f10(f917(x45991,a905),a905,x45992)),a323)),x45994))))),f326(f326(f40(x45992,f917(x45991,a905)),x45993),x45994))
% 157.55/157.21 [4606]E(f326(f326(f151(f910(x46061)),f326(f326(f151(x46061),x46062),f326(f142(f910(x46061),f910(x46061),f134(x46061),f113(x46061)),f326(f326(f154(f910(x46061),f910(x46061)),f156(f910(x46061),x46061,f113(x46061),f326(f326(f10(f910(x46061),f917(f910(x46061),f910(x46061)),x46061),f18(f910(x46061),f910(x46061))),f326(f326(f9(x46061,f910(x46061),f910(x46061)),f151(x46061)),f113(x46061))))),x46063)))),f179(x46061,f326(f326(f151(f910(x46061)),x46064),f326(f142(f910(f910(x46061)),f910(f910(x46061)),f134(f910(x46061)),f113(f910(x46061))),f326(f326(f154(f910(x46061),f910(f910(x46061))),f156(f910(f910(x46061)),x46061,f113(f910(x46061)),f326(f18(f917(f910(x46061),f910(f910(x46061))),x46061),f326(f326(f9(f910(x46061),f910(f910(x46061)),f910(f910(x46061))),f151(f910(x46061))),f113(f910(x46061)))))),x46063))))),f179(x46061,f326(f326(f151(f910(x46061)),f326(f326(f151(x46061),x46062),x46064)),x46063)))
% 157.55/157.21 [4613]E(f326(f261(f916(x46131,x46131)),f326(f256(x46131,x46131,a905),f326(f326(f9(x46131,f917(f916(x46132,x46132),a905),f917(x46131,a905)),f326(f326(f10(f917(x46131,f917(f917(f916(x46132,x46132),a905),a905)),f917(f917(f916(x46132,x46132),a905),f917(x46131,a905)),x46131),f9(x46131,f917(f916(x46132,x46132),a905),a905)),f326(f326(f10(f917(x46131,f916(x46132,x46132)),f917(x46131,f917(f917(f916(x46132,x46132),a905),a905)),x46131),f326(f10(f916(x46132,x46132),f917(f917(f916(x46132,x46132),a905),a905),x46131),f328(f916(x46132,x46132)))),f326(f326(f9(x46131,f917(x46131,x46132),f917(x46131,f916(x46132,x46132))),f326(f326(f10(f917(x46132,f916(x46132,x46132)),f917(f917(x46131,x46132),f917(x46131,f916(x46132,x46132))),x46131),f10(x46132,f916(x46132,x46132),x46131)),f326(f326(f10(x46132,f917(x46132,f916(x46132,x46132)),x46131),f251(x46132,x46132)),x46133))),x46133)))),x46134))),f326(f326(f287(x46132,x46131),x46134),x46133))
% 157.55/157.21 [4659]~E(f30(x46591,x46592),f27(x46593,x46594,x46595))
% 157.55/157.21 [4660]~E(f30(x46601,x46602),f26(x46603,x46604,x46605))
% 157.55/157.21 [4661]~E(f29(x46611,x46612),f27(x46613,x46614,x46615))
% 157.55/157.21 [4662]~E(f29(x46621,x46622),f26(x46623,x46624,x46625))
% 157.55/157.21 [4663]~E(f27(x46631,x46632,x46633),f30(x46634,x46635))
% 157.55/157.21 [4664]~E(f27(x46641,x46642,x46643),f29(x46644,x46645))
% 157.55/157.21 [4665]~E(f26(x46651,x46652,x46653),f30(x46654,x46655))
% 157.55/157.21 [4666]~E(f26(x46661,x46662,x46663),f29(x46664,x46665))
% 157.55/157.21 [3744]E(f326(f326(f154(x37441,x37442),x37443),f169(x37441,x37444,x37445)),f169(x37442,x37444,f326(x37443,x37445)))
% 157.55/157.21 [3958]E(f93(x39581,x39582,f91(x39581,x39583,x39584,x39585)),f2(a909))
% 157.55/157.21 [4082]E(f130(x40821,x40822,x40823,f126(x40821,x40824,x40825)),f126(x40822,f326(x40823,x40824),f130(x40821,x40822,x40823,x40825)))
% 157.55/157.21 [4315]E(f326(f74(x43151,x43152,x43153,x43154,x43155),x43154),x43155)
% 157.55/157.21 [4367]E(f252(x43671,x43672,x43673,f242(x43672,x43671,x43674),f242(x43673,x43672,x43675)),f242(x43673,x43671,f252(x43673,x43672,x43671,x43675,x43674)))
% 157.55/157.21 [3937]E(f326(f326(f256(x39371,x39372,x39373),x39374),x39375),f326(f326(x39374,f326(f250(x39371,x39372),x39375)),f326(f255(x39371,x39372),x39375)))
% 157.55/157.21 [3973]E(f326(f326(f326(f65(x39731,x39732,x39733),x39734),x39735),f188(f917(x39732,a905))),x39735)
% 157.55/157.21 [4252]E(f326(f72(f910(x42521),f910(x42522),f910(x42523),f326(f154(x42521,x42522),x42524)),f326(f154(x42523,x42521),x42525)),f326(f154(x42523,x42522),f326(f72(x42521,x42522,x42523,x42524),x42525)))
% 157.55/157.21 [4329]E(f84(x43291,f66(x43292,x43291,x43293,x43294,x43295)),f326(f326(f64(x43292,x43291,x43293),x43294),x43295))
% 157.55/157.21 [4363]E(f326(f326(f79(a909),f326(f326(f79(a909),f326(x43631,f326(f250(x43632,x43633),x43634))),f326(x43635,f326(f255(x43632,x43633),x43634)))),f326(a112,f2(a909))),f260(x43632,x43633,x43631,x43635,x43634))
% 157.55/157.21 [3873]E(f326(f326(f175(x38731),x38732),f326(f326(f154(x38733,x38731),x38734),x38735)),f326(f326(f154(x38733,x38731),x38734),f326(f326(f175(x38733),x38732),x38735)))
% 157.55/157.21 [3874]E(f326(f326(f138(x38741),x38742),f326(f326(f154(x38743,x38741),x38744),x38745)),f326(f326(f154(x38743,x38741),x38744),f326(f326(f138(x38743),x38742),x38745)))
% 157.55/157.21 [3906]E(f326(f326(f154(x39061,x39062),x39063),f326(f326(f151(x39061),x39064),x39065)),f326(f326(f151(x39062),f326(x39063,x39064)),f326(f326(f154(x39061,x39062),x39063),x39065)))
% 157.55/157.21 [3969]E(f326(f309(x39691,x39692,x39693),f326(f326(f308(x39691),x39694),x39695)),f326(f326(f308(x39692),f326(x39693,x39694)),f326(f309(x39691,x39692,x39693),x39695)))
% 157.55/157.21 [3997]E(f173(x39971,f326(f326(f151(x39971),x39972),x39973),f326(f326(f151(x39971),x39974),x39975)),f326(f326(f151(x39971),x39972),f326(f326(f151(x39971),x39974),f173(x39971,x39973,x39975))))
% 157.55/157.21 [4034]E(f326(f326(f181(x40341,x40342),f326(f326(f175(x40341),x40343),x40344)),f326(f326(f175(x40342),x40343),x40345)),f326(f326(f175(f916(x40341,x40342)),x40343),f326(f326(f181(x40341,x40342),x40344),x40345)))
% 157.55/157.21 [4035]E(f326(f326(f181(x40351,x40352),f326(f326(f138(x40351),x40353),x40354)),f326(f326(f138(x40352),x40353),x40355)),f326(f326(f138(f916(x40351,x40352)),x40353),f326(f326(f181(x40351,x40352),x40354),x40355)))
% 157.55/157.21 [4045]E(f326(f326(f159(x40451,f326(f326(f151(x40451),x40452),x40453)),f326(a112,x40454)),x40455),f326(f326(f151(x40451),x40452),f326(f326(f159(x40451,x40453),x40454),x40455)))
% 157.55/157.21 [4048]E(f326(f326(f134(x40481),f326(f326(f154(x40482,x40481),x40483),x40484)),f326(f326(f154(x40482,x40481),x40483),x40485)),f326(f326(f154(x40482,x40481),x40483),f326(f326(f134(x40482),x40484),x40485)))
% 157.55/157.21 [4052]E(f326(f326(x40521,x40522),f326(f326(f244(x40523,x40524,x40521),x40522),x40525)),f326(f326(f244(x40523,x40524,x40521),x40522),f326(a112,x40525)))
% 157.55/157.21 [4086]E(f163(x40861,x40862,x40863,f326(f326(f151(x40861),x40864),x40865)),f326(f326(f134(x40862),f326(x40863,x40864)),f163(x40861,x40862,x40863,x40865)))
% 157.55/157.21 [4098]E(f326(f326(f288(x40981,x40982,x40983),f326(f285(x40982,x40981),x40984)),f326(f285(x40983,x40982),x40985)),f326(f285(x40983,x40981),f326(f326(f288(x40983,x40982,x40981),x40985),x40984)))
% 157.55/157.21 [4130]E(f326(f326(f326(f183(f910(x41301),f910(x41301)),x41302),f167(x41301)),f326(f326(f154(x41303,x41301),x41304),x41305)),f326(f326(f154(x41303,x41301),x41304),f326(f326(f326(f183(f910(x41303),f910(x41303)),x41302),f167(x41303)),x41305)))
% 157.55/157.21 [4131]E(f326(f326(f258(x41311,x41312,x41311,x41313),f326(f251(x41312,x41311),x41314)),x41315),f326(x41315,x41314))
% 157.55/157.21 [4154]E(f155(x41541,x41542,f326(f326(f154(x41543,x41541),x41544),x41545)),f155(x41543,f326(f72(x41541,a909,x41543,x41542),x41544),x41545))
% 157.55/157.21 [4217]E(f177(f916(x42171,x42172),f326(f72(x42172,a905,f916(x42171,x42172),x42173),f255(x42171,x42172)),f326(f326(f181(x42171,x42172),x42174),x42175)),f326(f326(f181(x42171,x42172),x42174),f177(x42172,x42173,x42175)))
% 157.55/157.21 [4222]E(f326(f309(x42221,x42222,f326(f326(f10(x42223,x42222,x42221),x42224),x42225)),f241(f917(x42221,a905))),f326(f309(x42223,x42222,x42224),f326(f309(x42221,x42223,x42225),f241(f917(x42221,a905)))))
% 157.55/157.21 [4235]E(f177(f916(x42351,x42352),f326(f72(x42351,a905,f916(x42351,x42352),x42353),f250(x42351,x42352)),f326(f326(f181(x42351,x42352),x42354),x42355)),f326(f326(f181(x42351,x42352),f177(x42351,x42353,x42354)),x42355))
% 157.55/157.21 [4256]E(f326(f326(f110(f917(x42561,a905)),f326(f310(x42561,x42562,x42563),f326(f326(f308(x42562),x42564),f188(f917(x42562,a905))))),f326(f310(x42561,x42562,x42563),x42565)),f326(f310(x42561,x42562,x42563),f326(f326(f308(x42562),x42564),x42565)))
% 157.55/157.21 [4314]E(f326(f326(f134(f916(x43141,x43142)),f326(f326(f154(x43142,f916(x43141,x43142)),f326(f251(x43141,x43142),x43143)),x43144)),f59(x43141,x43142,x43145,x43144)),f59(x43141,x43142,f326(f326(f151(x43141),x43143),x43145),x43144))
% 157.55/157.21 [4316]E(f326(f326(f154(x43161,x43162),x43163),f177(x43161,f326(f72(x43162,a905,x43161,x43164),x43163),x43165)),f177(x43162,x43164,f326(f326(f154(x43161,x43162),x43163),x43165)))
% 157.55/157.21 [4321]E(f326(f142(x43211,x43212,f326(f9(x43212,x43211,x43211),f326(f9(x43211,x43212,x43211),x43213)),x43214),f326(f168(x43212),f326(f168(x43212),x43215))),f326(f142(x43211,x43212,x43213,x43214),x43215))
% 157.55/157.21 [4424]P105(f326(f326(f234(f917(x44241,a905)),f326(f309(x44242,x44241,x44243),f326(f326(f101(f917(x44242,a905)),x44244),x44245))),f326(f326(f101(f917(x44241,a905)),f326(f309(x44242,x44241,x44243),x44244)),f326(f309(x44242,x44241,x44243),x44245))))
% 157.55/157.21 [4425]P105(f326(f326(f234(f917(x44251,a905)),f326(f284(x44252,x44251,x44253),f326(f326(f101(f917(x44252,a905)),x44254),x44255))),f326(f326(f101(f917(x44251,a905)),f326(f284(x44252,x44251,x44253),x44254)),f326(f284(x44252,x44251,x44253),x44255))))
% 157.55/157.21 [4524]E(f326(f255(x45241,x45242),f326(f257(x45243,x45241,x45242,x45242,x45244,f31(x45242)),x45245)),f326(f255(x45243,x45242),x45245))
% 157.55/157.21 [4525]E(f326(f250(x45251,x45252),f326(f257(x45251,x45251,x45253,x45252,f31(x45251),x45254),x45255)),f326(f250(x45251,x45253),x45255))
% 157.55/157.21 [3715]E(f326(f326(f326(f326(f204(x37151),x37152),x37153),x37154),x37155),f192(x37151,x37152))
% 157.55/157.21 [3716]E(f326(f326(f326(f326(f208(x37161),x37162),x37163),x37164),x37165),f199(x37161,x37162))
% 157.55/157.21 [4087]E(f326(f326(f39(x40871,f917(x40872,a905)),f326(f326(f308(x40871),x40873),x40874)),x40875),f326(f326(f101(f917(x40872,a905)),f326(x40875,x40873)),f326(f326(f39(x40871,f917(x40872,a905)),x40874),x40875)))
% 157.55/157.21 [4088]E(f326(f326(f40(x40881,f917(x40882,a905)),f326(f326(f308(x40881),x40883),x40884)),x40885),f326(f326(f110(f917(x40882,a905)),f326(x40885,x40883)),f326(f326(f40(x40881,f917(x40882,a905)),x40884),x40885)))
% 157.55/157.21 [4138]E(f326(f118(x41381,x41382,f326(x41383,x41384)),f326(f326(f9(x41381,a99,f911(x41382)),x41385),x41384)),f326(f197(x41381,x41382,x41383,x41385),x41384))
% 157.55/157.21 [4148]E(f326(f326(f110(f917(x41481,a905)),f326(f309(x41482,x41481,x41483),x41484)),f326(f309(x41482,x41481,x41483),x41485)),f326(f309(x41482,x41481,x41483),f326(f326(f110(f917(x41482,a905)),x41484),x41485)))
% 157.55/157.21 [4149]E(f326(f326(f110(f917(x41491,a905)),f326(f284(x41492,x41491,x41493),x41494)),f326(f284(x41492,x41491,x41493),x41495)),f326(f284(x41492,x41491,x41493),f326(f326(f110(f917(x41492,a905)),x41494),x41495)))
% 157.55/157.21 [4150]E(f326(f326(f110(f917(x41501,a905)),f326(f310(x41501,x41502,x41503),x41504)),f326(f310(x41501,x41502,x41503),x41505)),f326(f310(x41501,x41502,x41503),f326(f326(f110(f917(x41502,a905)),x41504),x41505)))
% 157.55/157.21 [4151]E(f326(f326(f3(f917(x41511,a905)),f326(f310(x41511,x41512,x41513),x41514)),f326(f310(x41511,x41512,x41513),x41515)),f326(f310(x41511,x41512,x41513),f326(f326(f3(f917(x41512,a905)),x41514),x41515)))
% 157.55/157.21 [4152]E(f326(f326(f101(f917(x41521,a905)),f326(f310(x41521,x41522,x41523),x41524)),f326(f310(x41521,x41522,x41523),x41525)),f326(f310(x41521,x41522,x41523),f326(f326(f101(f917(x41522,a905)),x41524),x41525)))
% 157.55/157.21 [4213]E(f326(f326(f159(x42131,f326(f326(f134(x42131),x42132),f326(f326(f151(x42131),x42133),x42134))),f326(f189(f910(x42131)),x42132)),x42135),f326(f326(f134(x42131),x42132),f326(f326(f151(x42131),x42135),x42134)))
% 157.55/157.21 [4220]E(f326(f326(f39(x42201,f917(x42202,a905)),x42203),f326(f326(f10(f917(x42202,a905),f917(x42202,a905),x42201),f326(f308(x42202),x42204)),x42205)),f326(f326(f308(x42202),x42204),f326(f326(f39(x42201,f917(x42202,a905)),x42203),x42205)))
% 157.55/157.21 [4376]E(f326(f326(f154(x43761,x43762),x43763),f326(f136(x43761,f326(f72(x43762,a905,x43761,x43764),x43763)),x43765)),f326(f136(x43762,x43764),f326(f326(f154(x43761,x43762),x43763),x43765)))
% 157.55/157.21 [4382]E(f326(f189(f910(x43821)),f326(f136(x43821,x43822),f326(f326(f154(x43823,x43821),x43824),x43825))),f326(f189(f910(x43823)),f326(f136(x43823,f326(f72(x43821,a905,x43823,x43822),x43824)),x43825)))
% 157.55/157.21 [4589]E(f326(f156(f910(f916(x45891,x45892)),x45892,f113(f916(x45891,x45892)),f326(f326(f9(x45892,f917(f910(x45892),f910(f916(x45891,x45892))),f917(f910(x45892),f910(f916(x45891,x45892)))),f326(f326(f10(f917(f910(f916(x45891,x45892)),f910(f916(x45891,x45892))),f917(f917(f910(x45892),f910(f916(x45891,x45892))),f917(f910(x45892),f910(f916(x45891,x45892)))),x45892),f10(f910(f916(x45891,x45892)),f910(f916(x45891,x45892)),f910(x45892))),f326(f326(f10(f916(x45891,x45892),f917(f910(f916(x45891,x45892)),f910(f916(x45891,x45892))),x45892),f151(f916(x45891,x45892))),f326(f251(x45891,x45892),x45893)))),f326(f181(x45891,x45892),x45894))),x45895),f326(f326(f181(x45891,x45892),f326(f326(f151(x45891),x45893),x45894)),x45895))
% 157.55/157.21 [4079]E(f326(f326(f159(x40791,f326(f326(f159(x40791,x40792),x40793),x40794)),x40793),x40795),f326(f326(f159(x40791,x40792),x40793),x40795))
% 157.55/157.21 [4132]E(f326(f283(x41321,x41322),f326(f326(f308(f916(x41321,x41322)),f326(f326(f251(x41321,x41322),x41323),x41324)),x41325)),f326(f326(f308(x41322),x41324),f326(f283(x41321,x41322),x41325)))
% 157.55/157.21 [4133]E(f326(f263(x41331,x41332),f326(f326(f308(f916(x41331,x41332)),f326(f326(f251(x41331,x41332),x41333),x41334)),x41335)),f326(f326(f308(x41331),x41333),f326(f263(x41331,x41332),x41335)))
% 157.55/157.21 [4178]E(f122(x41781,x41782,f326(x41783,x41784),f326(f326(f9(x41781,a99,f911(f913(x41782))),x41785),x41784)),f326(f195(x41781,x41782,x41783,x41785),x41784))
% 157.55/157.21 [4206]E(f326(f326(f110(f917(f916(x42061,x42062),a905)),f326(f326(f253(x42061,x42062),x42063),x42064)),f326(f326(f253(x42061,x42062),x42065),x42064)),f326(f326(f253(x42061,x42062),f326(f326(f110(f917(x42061,a905)),x42063),x42065)),x42064))
% 157.55/157.21 [4207]E(f326(f326(f3(f917(f916(x42071,x42072),a905)),f326(f326(f253(x42071,x42072),x42073),x42074)),f326(f326(f253(x42071,x42072),x42075),x42074)),f326(f326(f253(x42071,x42072),f326(f326(f3(f917(x42071,a905)),x42073),x42075)),x42074))
% 157.55/157.21 [4208]E(f326(f326(f101(f917(f916(x42081,x42082),a905)),f326(f326(f253(x42081,x42082),x42083),x42084)),f326(f326(f253(x42081,x42082),x42085),x42084)),f326(f326(f253(x42081,x42082),f326(f326(f101(f917(x42081,a905)),x42083),x42085)),x42084))
% 157.55/157.21 [4267]E(f326(f326(f101(f917(x42671,a905)),f326(f326(f39(x42672,f917(x42671,a905)),x42673),x42674)),f326(f326(f39(x42672,f917(x42671,a905)),x42675),x42674)),f326(f326(f39(x42672,f917(x42671,a905)),f326(f326(f110(f917(x42672,a905)),x42673),x42675)),x42674))
% 157.55/157.21 [4268]E(f326(f326(f110(f917(x42681,a905)),f326(f326(f40(x42682,f917(x42681,a905)),x42683),x42684)),f326(f326(f40(x42682,f917(x42681,a905)),x42685),x42684)),f326(f326(f40(x42682,f917(x42681,a905)),f326(f326(f110(f917(x42682,a905)),x42683),x42685)),x42684))
% 157.55/157.21 [4282]E(f326(f326(f39(x42821,f917(x42822,a905)),x42823),f326(f326(f10(f917(x42822,a905),f917(x42822,a905),x42821),f326(f110(f917(x42822,a905)),x42824)),x42825)),f326(f326(f110(f917(x42822,a905)),x42824),f326(f326(f39(x42821,f917(x42822,a905)),x42823),x42825)))
% 157.55/157.21 [4283]E(f326(f326(f40(x42831,f917(x42832,a905)),x42833),f326(f326(f10(f917(x42832,a905),f917(x42832,a905),x42831),f326(f3(f917(x42832,a905)),x42834)),x42835)),f326(f326(f3(f917(x42832,a905)),x42834),f326(f326(f39(x42831,f917(x42832,a905)),x42833),x42835)))
% 157.55/157.21 [4284]E(f326(f326(f40(x42841,f917(x42842,a905)),x42843),f326(f326(f10(f917(x42842,a905),f917(x42842,a905),x42841),f326(f101(f917(x42842,a905)),x42844)),x42845)),f326(f326(f101(f917(x42842,a905)),x42844),f326(f326(f40(x42841,f917(x42842,a905)),x42843),x42845)))
% 157.55/157.21 [4341]E(f185(f910(x43411),f326(f326(f151(x43411),x43412),x43413),f326(f326(f10(f910(x43411),f910(x43411),a909),f326(f151(x43411),x43414)),f326(f326(f9(a909,x43411,f910(x43411)),f159(x43411,x43413)),x43412)),x43415),f326(f326(f159(x43411,f326(f326(f151(x43411),x43414),x43413)),x43415),x43412))
% 157.55/157.21 [4345]E(f326(f326(f39(x43451,f917(f916(x43452,x43453),a905)),x43454),f326(f326(f10(f917(f916(x43453,x43452),a905),f917(f916(x43452,x43453),a905),x43451),f285(x43453,x43452)),x43455)),f326(f285(x43453,x43452),f326(f326(f39(x43451,f917(f916(x43453,x43452),a905)),x43454),x43455)))
% 157.55/157.21 [4346]E(f326(f326(f40(x43461,f917(f916(x43462,x43463),a905)),x43464),f326(f326(f10(f917(f916(x43463,x43462),a905),f917(f916(x43462,x43463),a905),x43461),f285(x43463,x43462)),x43465)),f326(f285(x43463,x43462),f326(f326(f40(x43461,f917(f916(x43463,x43462),a905)),x43464),x43465)))
% 157.55/157.21 [4447]P105(f326(f326(f234(f917(x44471,a905)),f326(f326(f3(f917(x44471,a905)),f326(f309(x44472,x44471,x44473),x44474)),f326(f309(x44472,x44471,x44473),x44475))),f326(f309(x44472,x44471,x44473),f326(f326(f3(f917(x44472,a905)),x44474),x44475))))
% 157.55/157.21 [4592]E(f326(f156(f910(f916(x45921,x45922)),x45921,f113(f916(x45921,x45922)),f326(f326(f9(x45921,f917(f910(x45921),f910(f916(x45921,x45922))),f917(f910(x45921),f910(f916(x45921,x45922)))),f326(f326(f10(f917(f910(f916(x45921,x45922)),f910(f916(x45921,x45922))),f917(f917(f910(x45921),f910(f916(x45921,x45922))),f917(f910(x45921),f910(f916(x45921,x45922)))),x45921),f10(f910(f916(x45921,x45922)),f910(f916(x45921,x45922)),f910(x45921))),f326(f326(f10(f916(x45921,x45922),f917(f910(f916(x45921,x45922)),f910(f916(x45921,x45922))),x45921),f151(f916(x45921,x45922))),f326(f326(f9(x45921,x45922,f916(x45921,x45922)),f251(x45921,x45922)),x45923)))),f326(f326(f9(f910(x45921),f910(x45922),f910(f916(x45921,x45922))),f181(x45921,x45922)),x45924))),x45925),f326(f326(f181(x45921,x45922),x45925),f326(f326(f151(x45922),x45923),x45924)))
% 157.55/157.21 [4310]E(f326(f326(f110(f917(x43101,a905)),f326(f284(x43102,x43101,x43103),x43104)),f326(f284(x43102,x43101,x43105),x43104)),f326(f284(x43102,x43101,f326(f326(f110(f917(f916(x43102,x43101),a905)),x43103),x43105)),x43104))
% 157.55/157.21 [4347]E(f326(f326(f134(f916(x43471,x43472)),f326(f326(f181(x43471,x43472),x43473),f326(f326(f175(x43472),f326(f189(f910(x43471)),x43473)),x43474))),f326(f326(f181(x43471,x43472),x43475),f326(f326(f138(x43472),f326(f189(f910(x43471)),x43473)),x43474))),f326(f326(f181(x43471,x43472),f326(f326(f134(x43471),x43473),x43475)),x43474))
% 157.55/157.21 [4450]E(f326(f326(f253(x44501,x44502),x44503),f326(f326(f20(x44501,f917(x44502,a905),f917(x44502,a905)),f326(f326(f10(f917(x44502,a905),f917(f917(x44502,a905),f917(x44502,a905)),x44501),f110(f917(x44502,a905))),x44504)),x44505)),f326(f326(f110(f917(f916(x44501,x44502),a905)),f326(f326(f253(x44501,x44502),x44503),x44504)),f326(f326(f253(x44501,x44502),x44503),x44505)))
% 157.55/157.21 [4451]E(f326(f326(f253(x44511,x44512),x44513),f326(f326(f20(x44511,f917(x44512,a905),f917(x44512,a905)),f326(f326(f10(f917(x44512,a905),f917(f917(x44512,a905),f917(x44512,a905)),x44511),f3(f917(x44512,a905))),x44514)),x44515)),f326(f326(f3(f917(f916(x44511,x44512),a905)),f326(f326(f253(x44511,x44512),x44513),x44514)),f326(f326(f253(x44511,x44512),x44513),x44515)))
% 157.55/157.21 [4452]E(f326(f326(f253(x44521,x44522),x44523),f326(f326(f20(x44521,f917(x44522,a905),f917(x44522,a905)),f326(f326(f10(f917(x44522,a905),f917(f917(x44522,a905),f917(x44522,a905)),x44521),f101(f917(x44522,a905))),x44524)),x44525)),f326(f326(f101(f917(f916(x44521,x44522),a905)),f326(f326(f253(x44521,x44522),x44523),x44524)),f326(f326(f253(x44521,x44522),x44523),x44525)))
% 157.55/157.21 [4456]E(f326(f326(f39(x44561,f917(x44562,a905)),x44563),f326(f326(f9(x44561,f917(x44562,a905),f917(x44562,a905)),f326(f326(f10(f917(x44562,a905),f917(f917(x44562,a905),f917(x44562,a905)),x44561),f110(f917(x44562,a905))),x44564)),x44565)),f326(f326(f110(f917(x44562,a905)),f326(f326(f39(x44561,f917(x44562,a905)),x44563),x44564)),x44565))
% 157.55/157.21 [4457]E(f326(f326(f40(x44571,f917(x44572,a905)),x44573),f326(f326(f9(x44571,f917(x44572,a905),f917(x44572,a905)),f326(f326(f10(f917(x44572,a905),f917(f917(x44572,a905),f917(x44572,a905)),x44571),f3(f917(x44572,a905))),x44574)),x44575)),f326(f326(f3(f917(x44572,a905)),f326(f326(f40(x44571,f917(x44572,a905)),x44573),x44574)),x44575))
% 157.55/157.21 [4458]E(f326(f326(f40(x44581,f917(x44582,a905)),x44583),f326(f326(f9(x44581,f917(x44582,a905),f917(x44582,a905)),f326(f326(f10(f917(x44582,a905),f917(f917(x44582,a905),f917(x44582,a905)),x44581),f101(f917(x44582,a905))),x44584)),x44585)),f326(f326(f101(f917(x44582,a905)),f326(f326(f40(x44581,f917(x44582,a905)),x44583),x44584)),x44585))
% 157.55/157.21 [4462]E(f326(f326(f39(x44621,f917(x44622,a905)),x44623),f326(f326(f20(x44621,f917(x44622,a905),f917(x44622,a905)),f326(f326(f10(f917(x44622,a905),f917(f917(x44622,a905),f917(x44622,a905)),x44621),f101(f917(x44622,a905))),x44624)),x44625)),f326(f326(f101(f917(x44622,a905)),f326(f326(f39(x44621,f917(x44622,a905)),x44623),x44624)),f326(f326(f39(x44621,f917(x44622,a905)),x44623),x44625)))
% 157.55/157.21 [4463]E(f326(f326(f40(x44631,f917(x44632,a905)),x44633),f326(f326(f20(x44631,f917(x44632,a905),f917(x44632,a905)),f326(f326(f10(f917(x44632,a905),f917(f917(x44632,a905),f917(x44632,a905)),x44631),f110(f917(x44632,a905))),x44634)),x44635)),f326(f326(f110(f917(x44632,a905)),f326(f326(f40(x44631,f917(x44632,a905)),x44633),x44634)),f326(f326(f40(x44631,f917(x44632,a905)),x44633),x44635)))
% 157.55/157.21 [4476]E(f326(f326(f39(x44761,f917(x44762,a905)),x44763),f326(f326(f20(x44761,f917(x44762,a905),f917(x44762,a905)),f326(f326(f10(f917(x44762,a905),f917(f917(x44762,a905),f917(x44762,a905)),x44761),f101(f917(x44762,a905))),x44764)),x44765)),f326(f326(f101(f917(x44762,a905)),f38(f917(x44762,a905),f326(f309(x44761,f917(x44762,a905),x44764),x44763))),f38(f917(x44762,a905),f326(f309(x44761,f917(x44762,a905),x44765),x44763))))
% 157.55/157.21 [4477]E(f326(f326(f40(x44771,f917(x44772,a905)),x44773),f326(f326(f20(x44771,f917(x44772,a905),f917(x44772,a905)),f326(f326(f10(f917(x44772,a905),f917(f917(x44772,a905),f917(x44772,a905)),x44771),f110(f917(x44772,a905))),x44774)),x44775)),f326(f326(f110(f917(x44772,a905)),f37(f917(x44772,a905),f326(f309(x44771,f917(x44772,a905),x44774),x44773))),f37(f917(x44772,a905),f326(f309(x44771,f917(x44772,a905),x44775),x44773))))
% 157.55/157.21 [4513]E(f326(f326(f138(x45131),f326(f189(f910(x45131)),f177(x45131,x45132,f326(f326(f154(x45133,x45131),x45134),x45135)))),f326(f326(f154(x45133,x45131),x45134),x45135)),f326(f326(f154(x45133,x45131),x45134),f326(f326(f138(x45133),f326(f189(f910(x45133)),f177(x45133,f326(f72(x45131,a905,x45133,x45132),x45134),x45135))),x45135)))
% 157.55/157.21 [4389]E(f326(f326(f134(f916(x43891,x43892)),f326(f326(f181(x43891,x43892),f326(f326(f175(x43891),f326(f189(f910(x43892)),x43893)),x43894)),x43893)),f326(f326(f181(x43891,x43892),f326(f326(f138(x43891),f326(f189(f910(x43892)),x43893)),x43894)),x43895)),f326(f326(f181(x43891,x43892),x43894),f326(f326(f134(x43892),x43893),x43895)))
% 157.55/157.21 [4504]E(f84(x45041,f326(f326(f20(x45041,a905,a905),f326(f326(f10(a905,f917(a905,a905),x45041),a324),f326(f326(f9(x45041,f917(x45041,a905),a905),f328(x45041)),x45042))),f326(f326(f9(x45041,x45043,a905),f326(f326(f10(x45043,f917(x45043,a905),x45041),a323),x45044)),x45045))),f326(f76(x45041,x45043,x45042,x45044),x45045))
% 157.55/157.21 [4505]E(f89(x45051,f326(f326(f20(x45051,a905,a905),f326(f326(f10(a905,f917(a905,a905),x45051),a324),f326(f326(f9(x45051,f917(x45051,a905),a905),f328(x45051)),x45052))),f326(f326(f9(x45051,x45053,a905),f326(f326(f10(x45053,f917(x45053,a905),x45051),a323),x45054)),x45055))),f326(f90(x45051,x45053,x45052,x45054),x45055))
% 157.55/157.21 [4553]E(f326(f326(f85(a1,x45531),f326(f103(a1),f326(f326(f79(a1),x45532),a97))),f326(f326(f20(a1,x45531,x45531),f326(f326(f9(a1,x45531,f917(x45531,x45531)),f326(f326(f10(a905,f917(x45531,f917(x45531,x45531)),a1),f96(x45531)),a193)),f185(x45531,x45533,x45534,x45535))),f326(f326(f10(a909,x45531,a1),x45534),f326(f326(f9(a1,a909,a909),f326(f326(f10(a909,f917(a909,a909),a1),f79(a909)),a104)),x45535)))),f185(x45531,x45533,x45534,f326(f326(f79(a909),f326(f103(a909),x45532)),x45535)))
% 157.55/157.21 [4588]E(f326(f326(f85(a1,x45881),f326(f103(a1),f326(f326(f79(a1),x45882),a97))),f326(f326(f20(a1,x45881,x45881),f326(f326(f9(a1,x45881,f917(x45881,x45881)),f326(f326(f10(a905,f917(x45881,f917(x45881,x45881)),a1),f96(x45881)),a193)),f326(f184(x45881,x45883,x45884),x45885))),f326(f326(f20(a1,x45881,x45881),f326(f326(f10(a909,f917(x45881,x45881),a1),x45884),f326(f326(f9(a1,a909,a909),f326(f326(f10(a909,f917(a909,a909),a1),f79(a909)),a104)),x45885))),f326(f326(f10(a909,x45881,a1),f184(x45881,x45883,x45884)),f326(f326(f9(a1,a909,a909),f326(f326(f10(a909,f917(a909,a909),a1),f79(a909)),a104)),x45885))))),f326(f184(x45881,x45883,x45884),f326(f326(f79(a909),f326(f103(a909),x45882)),x45885)))
% 157.55/157.22 [4621]E(f326(f261(f916(x46211,x46212)),f326(f256(x46211,x46212,a905),f326(f326(f10(f917(x46212,f917(x46213,a905)),f917(x46212,a905),x46211),f326(f10(f917(x46213,a905),a905,x46212),f86(x46213))),f326(f326(f9(x46211,f917(x46212,f917(x46213,a905)),f917(x46212,f917(x46213,a905))),f326(f326(f10(f917(f917(x46213,a905),f917(x46213,a905)),f917(f917(x46212,f917(x46213,a905)),f917(x46212,f917(x46213,a905))),x46211),f10(f917(x46213,a905),f917(x46213,a905),x46212)),f326(f326(f10(f917(x46213,f917(a905,a905)),f917(f917(x46213,a905),f917(x46213,a905)),x46211),f20(x46213,a905,a905)),f326(f326(f10(f917(x46213,a905),f917(x46213,f917(a905,a905)),x46211),f326(f10(a905,f917(a905,a905),x46213),a324)),f326(f326(f9(x46211,f917(f916(x46211,x46213),a905),f917(x46213,a905)),f326(f326(f10(f917(x46213,f917(f917(f916(x46211,x46213),a905),a905)),f917(f917(f916(x46211,x46213),a905),f917(x46213,a905)),x46211),f9(x46213,f917(f916(x46211,x46213),a905),a905)),f326(f326(f10(f917(x46213,f916(x46211,x46213)),f917(x46213,f917(f917(f916(x46211,x46213),a905),a905)),x46211),f326(f10(f916(x46211,x46213),f917(f917(f916(x46211,x46213),a905),a905),x46213),f328(f916(x46211,x46213)))),f251(x46211,x46213)))),x46214))))),f326(f326(f9(x46212,f917(f916(x46213,x46212),a905),f917(x46213,a905)),f326(f326(f10(f917(x46213,f917(f917(f916(x46213,x46212),a905),a905)),f917(f917(f916(x46213,x46212),a905),f917(x46213,a905)),x46212),f9(x46213,f917(f916(x46213,x46212),a905),a905)),f326(f326(f10(f917(x46213,f916(x46213,x46212)),f917(x46213,f917(f917(f916(x46213,x46212),a905),a905)),x46212),f326(f10(f916(x46213,x46212),f917(f917(f916(x46213,x46212),a905),a905),x46213),f328(f916(x46213,x46212)))),f326(f9(x46213,x46212,f916(x46213,x46212)),f251(x46213,x46212))))),x46215))))),f326(f326(f288(x46211,x46213,x46212),x46214),x46215))
% 157.55/157.22 [4685]~E(f26(x46851,x46852,x46853),f27(x46854,x46855,x46856))
% 157.55/157.22 [4236]E(f224(x42361,x42362,x42363,x42364,f220(x42361,x42362,x42365,x42366)),f326(f326(x42364,x42365),x42366))
% 157.55/157.22 [4237]E(f225(x42371,x42372,x42373,x42374,f220(x42371,x42372,x42375,x42376)),f326(f326(x42374,x42375),x42376))
% 157.55/157.22 [4365]E(f127(x43651,x43652,x43653,x43654,f126(x43652,x43655,x43656)),f326(f326(f326(x43654,x43655),x43656),f127(x43651,x43652,x43653,x43654,x43656)))
% 157.55/157.22 [4384]E(f74(x43841,x43842,f74(x43841,x43842,x43843,x43844,x43845),x43844,x43846),f74(x43841,x43842,x43843,x43844,x43846))
% 157.55/157.22 [4492]E(f326(f72(f916(x44921,x44922),x44922,f916(x44923,x44924),f255(x44921,x44922)),f257(x44923,x44921,x44924,x44922,x44925,x44926)),f326(f72(x44924,x44922,f916(x44923,x44924),x44926),f255(x44923,x44924)))
% 157.55/157.22 [4493]E(f326(f72(f916(x44931,x44932),x44931,f916(x44933,x44934),f250(x44931,x44932)),f257(x44933,x44931,x44934,x44932,x44935,x44936)),f326(f72(x44933,x44931,f916(x44933,x44934),x44935),f250(x44933,x44934)))
% 157.55/157.22 [4055]E(f94(x40551,x40552,x40553,f91(x40551,x40554,x40555,x40556)),f326(f326(f326(x40553,x40554),x40555),x40556))
% 157.55/157.22 [4056]E(f95(x40561,x40562,x40563,f91(x40561,x40564,x40565,x40566)),f326(f326(f326(x40563,x40564),x40565),x40566))
% 157.55/157.22 [4108]E(f326(f326(f72(x41081,x41082,x41083,x41084),x41085),x41086),f326(x41084,f326(x41085,x41086)))
% 157.55/157.22 [4246]E(f223(x42461,f916(x42462,f911(x42462)),x42463,f326(f256(x42462,f911(x42462),x42461),x42464),f326(f135(x42462),f126(x42462,x42465,x42466))),f326(f326(x42464,x42465),x42466))
% 157.55/157.22 [4297]E(f226(x42971,x42972,x42973,x42974,f220(x42971,x42972,x42975,x42976)),f326(f326(f79(a909),f326(f326(f79(a909),f326(x42973,x42975)),f326(x42974,x42976))),f326(a112,f2(a909))))
% 157.55/157.22 [3904]E(f326(f326(f256(x39041,x39042,x39043),x39044),f326(f326(f251(x39041,x39042),x39045),x39046)),f326(f326(x39044,x39045),x39046))
% 157.55/157.22 [3966]E(f326(f326(f326(f10(x39661,x39662,x39663),x39664),x39665),x39666),f326(x39664,f326(x39665,x39666)))
% 157.55/157.22 [3967]E(f326(f326(f326(f9(x39671,x39672,x39673),x39674),x39675),x39676),f326(f326(x39674,x39676),x39675))
% 157.55/157.22 [3983]E(f326(f326(f326(f20(x39831,x39832,x39833),x39834),x39835),x39836),f326(f326(x39834,x39836),f326(x39835,x39836)))
% 157.55/157.22 [4006]E(f326(f156(x40061,x40062,x40063,x40064),f326(f326(f151(x40062),x40065),x40066)),f326(f326(x40064,x40065),x40066))
% 157.55/157.22 [4044]E(f169(f916(x40441,x40442),f326(f326(f232(a909),x40443),x40444),f326(f326(f251(x40441,x40442),x40445),x40446)),f326(f326(f181(x40441,x40442),f169(x40441,x40443,x40445)),f169(x40442,x40444,x40446)))
% 157.55/157.22 [4112]E(f326(f326(f151(f916(x41121,x41122)),f326(f326(f251(x41121,x41122),x41123),x41124)),f326(f326(f181(x41121,x41122),x41125),x41126)),f326(f326(f181(x41121,x41122),f326(f326(f151(x41121),x41123),x41125)),f326(f326(f151(x41122),x41124),x41126)))
% 157.55/157.22 [4113]E(f326(f326(f154(x41131,x41132),x41133),f326(f326(f159(x41131,x41134),x41135),x41136)),f326(f326(f159(x41132,f326(f326(f154(x41131,x41132),x41133),x41134)),x41135),f326(x41133,x41136)))
% 157.55/157.22 [4137]E(f326(f326(f254(x41371,x41372,x41373,x41374),x41375),x41376),f326(x41374,f326(f326(f251(x41371,x41372),x41375),x41376)))
% 157.55/157.22 [4153]E(f326(f142(x41531,x41532,x41533,x41534),f326(f326(f151(x41532),x41535),x41536)),f326(f142(x41531,x41532,x41533,f326(f326(x41533,x41534),x41535)),x41536))
% 157.55/157.22 [4179]E(f259(x41791,x41792,x41793,x41794,f326(f326(f251(x41791,x41792),x41795),x41796)),f326(f326(x41794,x41795),x41796))
% 157.55/157.22 [4260]E(f326(f326(f40(x42601,f917(x42602,a905)),x42603),f326(f72(x42604,f917(x42602,a905),x42601,x42605),x42606)),f326(f326(f40(x42604,f917(x42602,a905)),f326(f309(x42601,x42604,x42606),x42603)),x42605))
% 157.55/157.22 [4313]E(f326(f326(f154(x43131,x43132),x43133),f326(f326(f154(x43134,x43131),x43135),x43136)),f326(f326(f154(x43134,x43132),f326(f72(x43131,x43132,x43134,x43133),x43135)),x43136))
% 157.55/157.22 [4319]E(f326(f309(x43191,x43192,f326(f72(x43193,x43192,x43191,x43194),x43195)),x43196),f326(f309(x43193,x43192,x43194),f326(f309(x43191,x43193,x43195),x43196)))
% 157.55/157.22 [4320]E(f326(f310(x43201,x43202,f326(f72(x43203,x43202,x43201,x43204),x43205)),x43206),f326(f310(x43201,x43203,x43205),f326(f310(x43203,x43202,x43204),x43206)))
% 157.55/157.22 [4348]E(f326(f142(x43481,x43482,x43483,f326(f142(x43481,x43482,x43483,x43484),x43485)),x43486),f326(f142(x43481,x43482,x43483,x43484),f326(f326(f134(x43482),x43485),x43486)))
% 157.55/157.22 [4482]E(f326(f257(x44821,x44821,x44822,x44823,f31(x44821),x44824),f326(f326(f251(x44821,x44822),x44825),x44826)),f326(f326(f251(x44821,x44823),x44825),f326(x44824,x44826)))
% 157.55/157.22 [4483]E(f326(f257(x44831,x44832,x44833,x44833,x44834,f31(x44833)),f326(f326(f251(x44831,x44833),x44835),x44836)),f326(f326(f251(x44832,x44833),f326(x44834,x44835)),x44836))
% 157.55/157.22 [4571]E(f326(f326(f154(f916(x45711,x45712),f916(x45711,x45713)),f326(f256(x45711,x45712,f916(x45711,x45713)),f326(f326(f9(x45711,f917(x45712,x45713),f917(x45712,f916(x45711,x45713))),f326(f326(f10(f917(x45713,f916(x45711,x45713)),f917(f917(x45712,x45713),f917(x45712,f916(x45711,x45713))),x45711),f10(x45713,f916(x45711,x45713),x45712)),f251(x45711,x45713))),x45714))),f326(f326(f181(x45711,x45712),x45715),x45716)),f326(f326(f181(x45711,x45713),x45715),f326(f326(f154(x45712,x45713),x45714),x45716)))
% 157.55/157.22 [4163]E(f326(f326(f72(x41631,x41632,x41633,f326(f18(x41632,x41631),x41634)),x41635),x41636),x41634)
% 157.55/157.22 [4195]E(f326(f309(x41951,x41952,x41953),f326(f309(x41954,x41951,x41955),x41956)),f326(f309(x41954,x41952,f326(f326(f10(x41951,x41952,x41954),x41953),x41955)),x41956))
% 157.55/157.22 [4201]E(f326(f326(f39(x42011,f917(x42012,a905)),f326(f309(x42013,x42011,x42014),x42015)),x42016),f326(f326(f39(x42013,f917(x42012,a905)),x42015),f326(f326(f10(x42011,f917(x42012,a905),x42013),x42016),x42014)))
% 157.55/157.22 [4202]E(f326(f326(f40(x42021,f917(x42022,a905)),f326(f309(x42023,x42021,x42024),x42025)),x42026),f326(f326(f40(x42023,f917(x42022,a905)),x42025),f326(f326(f10(x42021,f917(x42022,a905),x42023),x42026),x42024)))
% 157.55/157.22 [4203]E(f326(f326(f39(x42031,f917(x42032,a905)),x42033),f326(f326(f10(x42034,f917(x42032,a905),x42031),x42035),x42036)),f326(f326(f39(x42034,f917(x42032,a905)),f326(f309(x42031,x42034,x42036),x42033)),x42035))
% 157.55/157.22 [4204]E(f326(f326(f40(x42041,f917(x42042,a905)),x42043),f326(f326(f10(x42044,f917(x42042,a905),x42041),x42045),x42046)),f326(f326(f40(x42044,f917(x42042,a905)),f326(f309(x42041,x42044,x42046),x42043)),x42045))
% 157.55/157.22 [4262]E(f326(f326(f40(x42621,f917(x42622,a905)),x42623),f326(f326(f10(f917(x42624,a905),f917(x42622,a905),x42621),f309(x42624,x42622,x42625)),x42626)),f326(f309(x42624,x42622,x42625),f326(f326(f40(x42621,f917(x42624,a905)),x42623),x42626)))
% 157.55/157.22 [4263]E(f326(f326(f40(x42631,f917(x42632,a905)),x42633),f326(f326(f10(f917(x42634,a905),f917(x42632,a905),x42631),f284(x42634,x42632,x42635)),x42636)),f326(f284(x42634,x42632,x42635),f326(f326(f40(x42631,f917(x42634,a905)),x42633),x42636)))
% 157.55/157.22 [4264]E(f326(f326(f39(x42641,f917(x42642,a905)),x42643),f326(f326(f10(f917(x42644,a905),f917(x42642,a905),x42641),f310(x42642,x42644,x42645)),x42646)),f326(f310(x42642,x42644,x42645),f326(f326(f39(x42641,f917(x42644,a905)),x42643),x42646)))
% 157.55/157.22 [4265]E(f326(f326(f40(x42651,f917(x42652,a905)),x42653),f326(f326(f10(f917(x42654,a905),f917(x42652,a905),x42651),f310(x42652,x42654,x42655)),x42656)),f326(f310(x42652,x42654,x42655),f326(f326(f40(x42651,f917(x42654,a905)),x42653),x42656)))
% 157.55/157.22 [4353]E(f326(f142(x43531,x43532,f326(f9(x43532,x43531,x43531),x43533),x43534),f326(f168(x43532),f326(f326(f151(x43532),x43535),x43536))),f326(f326(x43533,x43535),f326(f142(x43531,x43532,f326(f9(x43532,x43531,x43531),x43533),x43534),f326(f168(x43532),x43536))))
% 157.55/157.22 [4411]E(f326(f326(f20(f916(x44111,x44112),x44112,x44113),f326(f326(f10(x44114,f917(x44112,x44113),f916(x44111,x44112)),x44115),f326(f326(f10(x44111,x44114,f916(x44111,x44112)),x44116),f250(x44111,x44112)))),f255(x44111,x44112)),f326(f256(x44111,x44112,x44113),f326(f326(f10(x44114,f917(x44112,x44113),x44111),x44115),x44116)))
% 157.55/157.22 [4418]E(f326(f142(x44181,x44182,f326(f9(x44182,x44181,x44181),x44183),f326(f142(x44181,x44182,f326(f9(x44182,x44181,x44181),x44183),x44184),f326(f168(x44182),x44185))),f326(f168(x44182),x44186)),f326(f142(x44181,x44182,f326(f9(x44182,x44181,x44181),x44183),x44184),f326(f168(x44182),f326(f326(f134(x44182),x44186),x44185))))
% 157.55/157.22 [4420]E(f326(f326(f154(f916(x44201,x44202),f916(x44203,x44202)),f326(f256(x44201,x44202,f916(x44203,x44202)),f326(f326(f10(x44203,f917(x44202,f916(x44203,x44202)),x44201),f251(x44203,x44202)),x44204))),f326(f326(f181(x44201,x44202),x44205),x44206)),f326(f326(f181(x44203,x44202),f326(f326(f154(x44201,x44203),x44204),x44205)),x44206))
% 157.55/157.22 [4465]P105(f326(f326(f234(f917(x44651,a905)),f326(f284(x44652,x44651,x44653),f326(f326(f39(x44654,f917(x44652,a905)),x44655),x44656))),f326(f326(f39(x44654,f917(x44651,a905)),x44655),f326(f326(f10(f917(x44652,a905),f917(x44651,a905),x44654),f284(x44652,x44651,x44653)),x44656))))
% 157.55/157.22 [4275]E(f326(f326(f181(x42751,x42752),f326(f326(f159(x42751,x42753),x42754),f326(f250(x42751,x42752),x42755))),f326(f326(f159(x42752,x42756),x42754),f326(f255(x42751,x42752),x42755))),f326(f326(f159(f916(x42751,x42752),f326(f326(f181(x42751,x42752),x42753),x42756)),x42754),x42755))
% 157.55/157.22 [4336]E(f326(f326(f110(f917(f916(x43361,x43362),a905)),f326(f326(f288(x43361,x43363,x43362),x43364),x43365)),f326(f326(f288(x43361,x43363,x43362),x43364),x43366)),f326(f326(f288(x43361,x43363,x43362),x43364),f326(f326(f110(f917(f916(x43363,x43362),a905)),x43365),x43366)))
% 157.55/157.22 [4430]E(f326(f326(f308(f916(x44301,x44302)),f326(f326(f251(x44301,x44302),x44303),x44304)),f326(f326(f110(f917(f916(x44301,x44302),a905)),f326(f326(f253(x44301,x44302),x44305),f326(f18(f917(x44302,a905),x44301),f326(f326(f308(x44302),x44304),x44306)))),f326(f326(f253(x44301,x44302),f326(f326(f308(x44301),x44303),x44305)),f326(f18(f917(x44302,a905),x44301),x44306)))),f326(f326(f253(x44301,x44302),f326(f326(f308(x44301),x44303),x44305)),f326(f18(f917(x44302,a905),x44301),f326(f326(f308(x44302),x44304),x44306))))
% 157.55/157.22 [4509]E(f326(f326(f101(f917(x45091,a905)),f326(f310(x45091,x45092,f326(f72(f916(x45092,x45093),x45092,x45091,f250(x45092,x45093)),x45094)),x45095)),f326(f310(x45091,x45093,f326(f72(f916(x45092,x45093),x45093,x45091,f255(x45092,x45093)),x45094)),x45096)),f326(f310(x45091,f916(x45092,x45093),x45094),f326(f326(f253(x45092,x45093),x45095),f326(f18(f917(x45093,a905),x45092),x45096))))
% 157.55/157.22 [4359]E(f326(f326(f110(f917(f916(x43591,x43592),a905)),f326(f326(f288(x43591,x43593,x43592),x43594),x43595)),f326(f326(f288(x43591,x43593,x43592),x43596),x43595)),f326(f326(f288(x43591,x43593,x43592),f326(f326(f110(f917(f916(x43591,x43593),a905)),x43594),x43596)),x43595))
% 157.55/157.22 [4490]E(f326(f326(f39(x44901,f917(x44902,a905)),x44903),f326(f326(f9(x44901,f917(x44904,f917(x44902,a905)),f917(x44902,a905)),f326(f326(f10(f917(x44904,a905),f917(f917(x44904,f917(x44902,a905)),f917(x44902,a905)),x44901),f39(x44904,f917(x44902,a905))),x44905)),x44906)),f326(f326(f39(x44904,f917(x44902,a905)),f326(f326(f40(x44901,f917(x44904,a905)),x44903),x44905)),x44906))
% 157.55/157.22 [4491]E(f326(f326(f40(x44911,f917(x44912,a905)),x44913),f326(f326(f9(x44911,f917(x44914,f917(x44912,a905)),f917(x44912,a905)),f326(f326(f10(f917(x44914,a905),f917(f917(x44914,f917(x44912,a905)),f917(x44912,a905)),x44911),f40(x44914,f917(x44912,a905))),x44915)),x44916)),f326(f326(f40(x44914,f917(x44912,a905)),f326(f326(f40(x44911,f917(x44914,a905)),x44913),x44915)),x44916))
% 157.55/157.22 [4543]E(f326(f256(x45431,x45432,f916(x45433,x45434)),f326(f326(f9(x45431,f917(x45432,x45434),f917(x45432,f916(x45433,x45434))),f326(f326(f10(f917(x45434,f916(x45433,x45434)),f917(f917(x45432,x45434),f917(x45432,f916(x45433,x45434))),x45431),f10(x45434,f916(x45433,x45434),x45432)),f326(f326(f10(x45433,f917(x45434,f916(x45433,x45434)),x45431),f251(x45433,x45434)),x45435))),x45436)),f257(x45431,x45433,x45432,x45434,x45435,x45436))
% 157.55/157.22 [4566]E(f326(f309(x45661,x45662,f326(f326(f20(x45661,x45662,x45662),f326(f326(f20(x45661,x45662,f917(x45662,x45662)),f326(f326(f10(a905,f917(x45662,f917(x45662,x45662)),x45661),f96(x45662)),x45663)),x45664)),x45665)),x45666),f326(f326(f110(f917(x45662,a905)),f326(f309(x45661,x45662,x45664),f326(f326(f101(f917(x45661,a905)),x45666),f326(f261(x45661),x45663)))),f326(f309(x45661,x45662,x45665),f326(f326(f101(f917(x45661,a905)),x45666),f326(f261(x45661),f326(f326(f10(a905,a905,x45661),a321),x45663))))))
% 157.55/157.22 [4578]E(f326(f309(x45781,f916(x45782,x45783),f326(f326(f20(x45781,x45783,f916(x45782,x45783)),f326(f326(f10(x45782,f917(x45783,f916(x45782,x45783)),x45781),f251(x45782,x45783)),x45784)),x45785)),x45786),f326(f326(f253(x45782,x45783),f326(f309(x45781,x45782,x45784),x45786)),f326(f326(f10(f917(x45781,a905),f917(x45783,a905),x45782),f309(x45781,x45783,x45785)),f326(f326(f9(x45782,f917(x45781,a905),f917(x45781,a905)),f326(f326(f10(f917(x45781,a905),f917(f917(x45781,a905),f917(x45781,a905)),x45782),f101(f917(x45781,a905))),f326(f326(f10(f917(x45782,a905),f917(x45781,a905),x45782),f310(x45781,x45782,x45784)),f326(f326(f9(x45782,f917(x45782,a905),f917(x45782,a905)),f308(x45782)),f188(f917(x45782,a905)))))),x45786))))
% 157.55/157.22 [4603]E(f245(x46031,x46032,x46033,x46034,x46035,x46036),f326(x46034,f326(f261(x46031),f326(f326(f10(f917(f917(x46033,x46031),a905),a905,x46031),f86(f917(x46033,x46031))),f326(f326(f10(f917(f917(x46033,x46031),a905),f917(f917(x46033,x46031),a905),x46031),f326(f20(f917(x46033,x46031),a905,a905),f326(f326(f10(a905,f917(a905,a905),f917(x46033,x46031)),a324),f326(f326(f9(f917(x46033,x46031),f917(f917(x46033,x46031),a905),a905),f328(f917(x46033,x46031))),x46035)))),f326(f326(f9(x46031,f917(f917(x46033,x46031),x46031),f917(f917(x46033,x46031),a905)),f326(f326(f10(f917(x46031,a905),f917(f917(f917(x46033,x46031),x46031),f917(f917(x46033,x46031),a905)),x46031),f10(x46031,a905,f917(x46033,x46031))),a323)),f326(f326(f9(f917(x46033,x46031),x46033,x46031),f7(f917(x46033,x46031))),x46036)))))))
% 157.55/157.22 [4392]E(f326(f72(x43921,x43922,x43923,x43924),f74(x43923,x43921,x43925,x43926,x43927)),f74(x43923,x43922,f326(f72(x43921,x43922,x43923,x43924),x43925),x43926,f326(x43924,x43927)))
% 157.55/157.22 [4526]E(f326(f255(x45261,x45262),f326(f257(x45263,x45261,x45264,x45262,x45265,x45266),x45267)),f326(x45266,f326(f255(x45263,x45264),x45267)))
% 157.55/157.22 [4527]E(f326(f250(x45271,x45272),f326(f257(x45273,x45271,x45274,x45272,x45275,x45276),x45277)),f326(x45275,f326(f250(x45273,x45274),x45277)))
% 157.55/157.22 [4238]E(f326(f326(f181(x42381,x42382),f326(f326(f159(x42381,x42383),x42384),x42385)),f326(f326(f159(x42382,x42386),x42384),x42387)),f326(f326(f159(f916(x42381,x42382),f326(f326(f181(x42381,x42382),x42383),x42386)),x42384),f326(f326(f251(x42381,x42382),x42385),x42387)))
% 157.55/157.22 [4308]E(f326(f326(f326(f258(x43081,x43082,x43083,x43084),x43085),x43086),x43087),f326(f326(f256(x43082,x43083,x43084),x43086),f326(x43085,x43087)))
% 157.55/157.22 [4318]E(f326(f326(f326(f258(x43181,x43182,x43183,x43184),x43185),x43186),x43187),f326(f326(x43186,f326(f250(x43182,x43183),f326(x43185,x43187))),f326(f255(x43182,x43183),f326(x43185,x43187))))
% 157.55/157.22 [4370]E(f326(f72(x43701,x43702,x43703,x43704),f326(f72(x43705,x43701,x43703,x43706),x43707)),f326(f72(x43705,x43702,x43703,f326(f72(x43701,x43702,x43705,x43704),x43706)),x43707))
% 157.55/157.22 [4547]E(f326(f257(x45471,x45472,x45473,x45473,x45474,f31(x45473)),f326(f257(x45471,x45471,x45475,x45473,f31(x45471),x45476),x45477)),f326(f326(f251(x45472,x45473),f326(x45474,f326(f250(x45471,x45475),x45477))),f326(x45476,f326(f255(x45471,x45475),x45477))))
% 157.55/157.22 [4548]E(f326(f257(x45481,x45481,x45482,x45483,f31(x45481),x45484),f326(f257(x45485,x45481,x45482,x45482,x45486,f31(x45482)),x45487)),f326(f326(f251(x45481,x45483),f326(x45486,f326(f250(x45485,x45482),x45487))),f326(x45484,f326(f255(x45485,x45482),x45487))))
% 157.55/157.22 [4564]E(f326(f257(x45641,x45642,x45643,x45643,x45644,f31(x45643)),f326(f257(x45645,x45641,x45643,x45643,x45646,f31(x45643)),x45647)),f326(f257(x45645,x45642,x45643,x45643,f326(f72(x45641,x45642,x45645,x45644),x45646),f31(x45643)),x45647))
% 157.55/157.22 [4565]E(f326(f257(x45651,x45651,x45652,x45653,f31(x45651),x45654),f326(f257(x45651,x45651,x45655,x45652,f31(x45651),x45656),x45657)),f326(f257(x45651,x45651,x45655,x45653,f31(x45651),f326(f72(x45652,x45653,x45655,x45654),x45656)),x45657))
% 157.55/157.22 [4575]E(f326(f257(x45751,x45752,x45753,x45753,x45754,f31(x45753)),f326(f257(x45751,x45751,x45755,x45753,f31(x45751),x45756),x45757)),f326(f257(x45752,x45752,x45755,x45753,f31(x45752),x45756),f326(f257(x45751,x45752,x45755,x45755,x45754,f31(x45755)),x45757)))
% 157.55/157.22 [4272]E(f326(f326(f288(x42721,x42722,x42723),f326(f326(f288(x42721,x42724,x42722),x42725),x42726)),x42727),f326(f326(f288(x42721,x42724,x42723),x42725),f326(f326(f288(x42724,x42722,x42723),x42726),x42727)))
% 157.55/157.22 [4342]E(f326(f326(f256(x43421,x43422,x43423),f326(f72(x43424,f917(x43422,x43423),x43421,x43425),x43426)),x43427),f326(f326(x43425,f326(x43426,f326(f250(x43421,x43422),x43427))),f326(f255(x43421,x43422),x43427)))
% 157.55/157.22 [4423]E(f326(f142(x44231,x44232,f326(f9(x44232,x44231,x44231),x44233),x44234),f326(f168(x44232),f326(f326(f154(x44235,x44232),x44236),x44237))),f326(f142(x44231,x44235,f326(f9(x44235,x44231,x44231),f326(f72(x44232,f917(x44231,x44231),x44235,x44233),x44236)),x44234),f326(f168(x44235),x44237)))
% 157.55/157.22 [4371]E(f326(f326(f40(x43711,f917(f916(x43712,x43713),a905)),x43714),f326(f326(f10(f917(f916(x43715,x43713),a905),f917(f916(x43712,x43713),a905),x43711),f326(f288(x43712,x43715,x43713),x43716)),x43717)),f326(f326(f288(x43712,x43715,x43713),x43716),f326(f326(f40(x43711,f917(f916(x43715,x43713),a905)),x43714),x43717)))
% 157.55/157.22 [4514]E(f326(f326(f40(x45141,f917(f916(x45142,x45143),a905)),x45144),f326(f326(f9(x45141,f917(f916(x45145,x45143),a905),f917(f916(x45142,x45143),a905)),f326(f326(f10(f917(f916(x45142,x45145),a905),f917(f917(f916(x45145,x45143),a905),f917(f916(x45142,x45143),a905)),x45141),f288(x45142,x45145,x45143)),x45146)),x45147)),f326(f326(f288(x45142,x45145,x45143),f326(f326(f40(x45141,f917(f916(x45142,x45145),a905)),x45144),x45146)),x45147))
% 157.55/157.22 [4515]E(f326(f142(x45151,x45152,f326(f326(f9(x45151,f917(x45152,x45153),f917(x45152,x45151)),f326(f326(f10(f917(x45153,x45151),f917(f917(x45152,x45153),f917(x45152,x45151)),x45151),f10(x45153,x45151,x45152)),x45154)),x45155),x45156),x45157),f326(f142(x45151,x45153,x45154,x45156),f326(f326(f154(x45152,x45153),x45155),x45157)))
% 157.55/157.22 [4576]E(f326(f326(f39(x45761,f917(x45762,a905)),x45763),f326(f326(f10(f917(x45764,f917(x45762,a905)),f917(x45762,a905),x45761),f326(f39(x45764,f917(x45762,a905)),x45765)),f326(f326(f9(x45761,f917(x45764,f917(x45762,a905)),f917(x45764,f917(x45762,a905))),f326(f326(f10(f917(f917(x45762,a905),f917(x45762,a905)),f917(f917(x45764,f917(x45762,a905)),f917(x45764,f917(x45762,a905))),x45761),f10(f917(x45762,a905),f917(x45762,a905),x45764)),f326(f326(f10(f917(x45762,a905),f917(f917(x45762,a905),f917(x45762,a905)),x45761),f110(f917(x45762,a905))),x45766))),x45767))),f326(f326(f110(f917(x45762,a905)),f326(f326(f39(x45761,f917(x45762,a905)),x45763),x45766)),f326(f326(f39(x45764,f917(x45762,a905)),x45765),x45767)))
% 157.55/157.22 [4577]E(f326(f326(f40(x45771,f917(x45772,a905)),x45773),f326(f326(f10(f917(x45774,f917(x45772,a905)),f917(x45772,a905),x45771),f326(f40(x45774,f917(x45772,a905)),x45775)),f326(f326(f9(x45771,f917(x45774,f917(x45772,a905)),f917(x45774,f917(x45772,a905))),f326(f326(f10(f917(f917(x45772,a905),f917(x45772,a905)),f917(f917(x45774,f917(x45772,a905)),f917(x45774,f917(x45772,a905))),x45771),f10(f917(x45772,a905),f917(x45772,a905),x45774)),f326(f326(f10(f917(x45772,a905),f917(f917(x45772,a905),f917(x45772,a905)),x45771),f101(f917(x45772,a905))),x45776))),x45777))),f326(f326(f101(f917(x45772,a905)),f326(f326(f40(x45771,f917(x45772,a905)),x45773),x45776)),f326(f326(f40(x45774,f917(x45772,a905)),x45775),x45777)))
% 157.55/157.22 [4569]E(f197(x45691,x45692,f326(f326(f326(x45693,x45694),x45695),x45696),f326(f326(f9(x45691,f916(a99,a99),f917(a99,f911(x45692))),f326(f326(f9(x45691,a99,f917(f916(a99,a99),f917(a99,f911(x45692)))),f326(f326(f9(x45691,a99,f917(a99,f917(f916(a99,a99),f917(a99,f911(x45692))))),x45697),x45694)),x45695)),x45696)),f326(f326(f326(f209(x45691,x45692,x45693,x45697),x45694),x45695),x45696))
% 157.55/157.22 [4583]E(f198(x45831,x45832,f326(f326(f326(x45833,x45834),x45835),x45836),f326(f326(f9(x45831,f916(a99,a99),f917(a99,f911(x45832))),f326(f326(f9(x45831,a99,f917(f916(a99,a99),f917(a99,f911(x45832)))),f326(f326(f9(x45831,a99,f917(a99,f917(f916(a99,a99),f917(a99,f911(x45832))))),x45837),x45834)),x45835)),x45836)),f211(x45831,x45832,x45833,x45837,x45834,x45835,x45836))
% 157.55/157.22 [4574]E(f195(x45741,x45742,f326(f326(f326(x45743,x45744),x45745),x45746),f326(f326(f9(x45741,f916(a99,a99),f917(a99,f911(f913(x45742)))),f326(f326(f9(x45741,a99,f917(f916(a99,a99),f917(a99,f911(f913(x45742))))),f326(f326(f9(x45741,a99,f917(a99,f917(f916(a99,a99),f917(a99,f911(f913(x45742)))))),x45747),x45744)),x45745)),x45746)),f326(f326(f326(f205(x45741,x45742,x45743,x45747),x45744),x45745),x45746))
% 157.55/157.22 [4585]E(f196(x45851,x45852,f326(f326(f326(x45853,x45854),x45855),x45856),f326(f326(f9(x45851,f916(a99,a99),f917(a99,f911(f913(x45852)))),f326(f326(f9(x45851,a99,f917(f916(a99,a99),f917(a99,f911(f913(x45852))))),f326(f326(f9(x45851,a99,f917(a99,f917(f916(a99,a99),f917(a99,f911(f913(x45852)))))),x45857),x45854)),x45855)),x45856)),f207(x45851,x45852,x45853,x45857,x45854,x45855,x45856))
% 157.55/157.22 [4484]E(f326(f257(x44841,x44842,x44843,x44844,x44845,x44846),f326(f326(f251(x44841,x44843),x44847),x44848)),f326(f326(f251(x44842,x44844),f326(x44845,x44847)),f326(x44846,x44848)))
% 157.55/157.22 [4587]E(f326(f326(f154(f916(x45871,x45872),f916(x45873,x45874)),f326(f256(x45871,x45872,f916(x45873,x45874)),f326(f326(f9(x45871,f917(x45872,x45874),f917(x45872,f916(x45873,x45874))),f326(f326(f10(f917(x45874,f916(x45873,x45874)),f917(f917(x45872,x45874),f917(x45872,f916(x45873,x45874))),x45871),f10(x45874,f916(x45873,x45874),x45872)),f326(f326(f10(x45873,f917(x45874,f916(x45873,x45874)),x45871),f251(x45873,x45874)),x45875))),x45876))),f326(f326(f181(x45871,x45872),x45877),x45878)),f326(f326(f181(x45873,x45874),f326(f326(f154(x45871,x45873),x45875),x45877)),f326(f326(f154(x45872,x45874),x45876),x45878)))
% 157.55/157.22 [4590]E(f326(f326(f154(f916(x45901,x45902),x45903),f326(f256(x45901,x45902,x45903),f326(f326(f10(f917(x45902,f916(x45901,x45904)),f917(x45902,x45903),x45901),f326(f10(f916(x45901,x45904),x45903,x45902),x45905)),f326(f326(f9(x45901,f917(x45902,x45904),f917(x45902,f916(x45901,x45904))),f326(f326(f10(f917(x45904,f916(x45901,x45904)),f917(f917(x45902,x45904),f917(x45902,f916(x45901,x45904))),x45901),f10(x45904,f916(x45901,x45904),x45902)),f251(x45901,x45904))),x45906)))),f326(f326(f181(x45901,x45902),x45907),x45908)),f326(f326(f154(f916(x45901,x45904),x45903),x45905),f326(f326(f181(x45901,x45904),x45907),f326(f326(f154(x45902,x45904),x45906),x45908))))
% 157.55/157.22 [4518]E(f326(f326(f154(f916(x45181,x45182),x45183),f326(f256(x45181,x45182,x45183),f326(f326(f10(f917(x45182,f916(x45184,x45182)),f917(x45182,x45183),x45181),f326(f10(f916(x45184,x45182),x45183,x45182),x45185)),f326(f326(f10(x45184,f917(x45182,f916(x45184,x45182)),x45181),f251(x45184,x45182)),x45186)))),f326(f326(f181(x45181,x45182),x45187),x45188)),f326(f326(f154(f916(x45184,x45182),x45183),x45185),f326(f326(f181(x45184,x45182),f326(f326(f154(x45181,x45184),x45186),x45187)),x45188)))
% 157.55/157.22 [4475]E(f326(f326(f256(x44751,x44752,x44753),f326(f326(f10(f917(x44752,f916(x44754,x44755)),f917(x44752,x44753),x44751),f326(f10(f916(x44754,x44755),x44753,x44752),f326(f256(x44754,x44755,x44753),x44756))),x44757)),x44758),f326(f326(f256(x44754,x44755,x44753),x44756),f326(f326(f256(x44751,x44752,f916(x44754,x44755)),x44757),x44758)))
% 157.55/157.22 [4591]E(f326(f326(f40(f916(x45911,x45912),f917(f916(x45913,x45914),a905)),f326(f326(f253(x45911,x45912),x45915),f326(f18(f917(x45912,a905),x45911),x45916))),f326(f256(x45911,x45912,f917(f916(x45913,x45914),a905)),f326(f326(f9(x45911,f917(x45912,f917(x45913,f917(x45914,a905))),f917(x45912,f917(f916(x45913,x45914),a905))),f326(f326(f10(f917(f917(x45913,f917(x45914,a905)),f917(f916(x45913,x45914),a905)),f917(f917(x45912,f917(x45913,f917(x45914,a905))),f917(x45912,f917(f916(x45913,x45914),a905))),x45911),f10(f917(x45913,f917(x45914,a905)),f917(f916(x45913,x45914),a905),x45912)),f326(f326(f10(f917(x45913,a905),f917(f917(x45913,f917(x45914,a905)),f917(f916(x45913,x45914),a905)),x45911),f253(x45913,x45914)),x45917))),f326(f326(f10(f917(x45914,a905),f917(x45913,f917(x45914,a905)),x45912),f18(f917(x45914,a905),x45913)),x45918)))),f326(f326(f253(x45913,x45914),f326(f326(f40(x45911,f917(x45913,a905)),x45915),x45917)),f326(f18(f917(x45914,a905),x45913),f326(f326(f40(x45912,f917(x45914,a905)),x45916),x45918))))
% 157.55/157.22 [4532]E(f326(f326(f258(x45321,x45322,x45323,x45324),f326(f326(f258(x45321,x45325,x45326,f916(x45322,x45323)),x45327),x45328)),x45329),f326(f326(f258(x45321,x45325,x45326,x45324),x45327),f326(f326(f9(x45325,f917(x45322,f917(x45323,x45324)),f917(x45326,x45324)),f326(f326(f10(f917(x45326,f916(x45322,x45323)),f917(f917(x45322,f917(x45323,x45324)),f917(x45326,x45324)),x45325),f258(x45326,x45322,x45323,x45324)),x45328)),x45329)))
% 157.55/157.22 [4561]E(f326(f72(f916(x45611,x45612),f916(x45613,x45614),f916(x45615,x45616),f257(x45611,x45613,x45612,x45614,x45617,x45618)),f257(x45615,x45611,x45616,x45612,x45619,x456110)),f257(x45615,x45613,x45616,x45614,f326(f72(x45611,x45613,x45615,x45617),x45619),f326(f72(x45612,x45614,x45616,x45618),x456110)))
% 157.55/157.22 [4567]E(f326(f257(x45671,x45672,x45673,x45674,x45675,x45676),f326(f257(x45677,x45671,x45678,x45673,x45679,x456710),x456711)),f326(f257(x45677,x45672,x45678,x45674,f326(f72(x45671,x45672,x45677,x45675),x45679),f326(f72(x45673,x45674,x45678,x45676),x456710)),x456711))
% 157.55/157.22 [4714]~P3(x47141)+P3(f913(x47141))
% 157.55/157.22 [4715]~P61(x47151)+P61(f913(x47151))
% 157.55/157.22 [4716]~P103(x47161)+P103(f910(x47161))
% 157.55/157.22 [4719]~P142(x47191)+~E(f77(x47191),f2(x47191))
% 157.55/157.22 [4721]~E(x47211,f2(a99))+E(f326(a24,x47211),f2(a1))
% 157.55/157.22 [4722]~E(x47221,f2(a1))+E(f81(a1,x47221),f2(a1))
% 157.55/157.22 [4728]~P143(x47281)+P27(x47281,f2(x47281))
% 157.55/157.22 [4730]~P108(x47301)+P12(x47301,f113(x47301))
% 157.55/157.22 [4739]P105(x47391)+P105(f326(a321,x47391))
% 157.55/157.22 [4793]~P143(x47931)+~P27(x47931,f77(x47931))
% 157.55/157.22 [4834]~P105(x48341)+~P105(f326(a321,x48341))
% 157.55/157.22 [4855]E(f326(a104,x48551),f2(a909))+~P105(f326(a193,x48551))
% 157.55/157.22 [4921]~P67(x49211)+P15(x49211,x49211,f80(x49211))
% 157.55/157.22 [4922]~P100(x49221)+P13(x49221,x49221,f110(x49221))
% 157.55/157.22 [4923]~P96(x49231)+P13(x49231,x49231,f80(x49231))
% 157.55/157.22 [4924]~P101(x49241)+P13(x49241,x49241,f101(x49241))
% 157.55/157.22 [4925]~P108(x49251)+P13(x49251,x49251,f232(x49251))
% 157.55/157.22 [4926]~P108(x49261)+P13(x49261,x49261,f233(x49261))
% 157.55/157.22 [4725]~E(x47251,f2(a909))+E(f326(f100(a1),x47251),f2(a1))
% 157.55/157.22 [4732]~P94(x47321)+E(f326(f103(x47321),a82),f2(x47321))
% 157.55/157.22 [4735]~E(f575(x47351),f2(a909))+E(f326(f165(a909),x47351),f2(a909))
% 157.55/157.22 [4736]~P107(x47361)+E(f236(x47361,f234(x47361)),f232(x47361))
% 157.55/157.22 [4737]~P107(x47371)+E(f237(x47371,f234(x47371)),f233(x47371))
% 157.55/157.22 [4738]~P90(x47381)+E(f81(x47381,f2(x47381)),f2(x47381))
% 157.55/157.22 [4747]~P143(x47471)+E(f326(f100(x47471),f77(a909)),f77(x47471))
% 157.55/157.22 [4748]~P143(x47481)+E(f326(f100(x47481),f2(a909)),f2(x47481))
% 157.55/157.22 [4749]~P140(x47491)+E(f326(f102(x47491),f77(a1)),f77(x47491))
% 157.55/157.22 [4750]~P140(x47501)+E(f326(f102(x47501),f2(a1)),f2(x47501))
% 157.55/157.22 [4751]E(x47511,f2(a909))+~E(f326(f100(a1),x47511),f2(a1))
% 157.55/157.22 [4787]~P118(x47871)+E(f326(f75(x47871),f77(x47871)),f77(x47871))
% 157.55/157.22 [4788]~P86(x47881)+E(f326(f75(x47881),f2(x47881)),f2(x47881))
% 157.55/157.22 [4789]~P95(x47891)+E(f326(f78(x47891),f188(x47891)),f241(x47891))
% 157.55/157.22 [4790]~P73(x47901)+E(f326(f78(x47901),f2(x47901)),f2(x47901))
% 157.55/157.22 [4791]~P95(x47911)+E(f326(f78(x47911),f241(x47911)),f188(x47911))
% 157.55/157.22 [4792]~P82(x47921)+E(f326(f165(x47921),f113(x47921)),f2(x47921))
% 157.55/157.22 [4810]~P35(x48101)+P39(f326(f172(a1),x48101))
% 157.55/157.22 [4839]~P94(x48391)+E(f326(f78(x48391),f77(x48391)),f326(f103(x48391),a97))
% 157.55/157.22 [4854]~P94(x48541)+P27(x48541,f326(f103(x48541),a82))
% 157.55/157.22 [4880]P35(x48801)+~P39(f326(f172(a1),x48801))
% 157.55/157.22 [4927]E(f326(f100(a1),f326(a104,x49271)),x49271)+P105(f326(a193,x49271))
% 157.55/157.22 [4997]~P115(x49971)+E(f244(x49971,f77(x49971),f80(x49971)),f243(x49971))
% 157.55/157.22 [5030]~P94(x50301)+~P27(x50301,f326(f103(x50301),a97))
% 157.55/157.22 [5183]E(f326(f75(a1),x51831),x51831)+P105(f326(f326(f235(a1),x51831),f2(a1)))
% 157.55/157.22 [5201]~E(f326(a104,x52011),f2(a909))+P105(f326(f326(f234(a1),x52011),f2(a1)))
% 157.55/157.22 [5267]~P105(f326(a193,x52671))+P105(f326(f326(f235(a1),x52671),f2(a1)))
% 157.55/157.22 [5307]~P124(x53071)+P105(f326(f326(f234(x53071),f2(x53071)),f77(x53071)))
% 157.55/157.22 [5308]~P140(x53081)+P105(f326(f326(f328(x53081),f77(x53081)),f109(x53081)))
% 157.55/157.22 [5309]~P143(x53091)+P105(f326(f326(f328(x53091),f77(x53091)),f186(x53091)))
% 157.55/157.22 [5310]~P140(x53101)+P105(f326(f326(f328(x53101),f2(x53101)),f109(x53101)))
% 157.55/157.22 [5311]~P143(x53111)+P105(f326(f326(f328(x53111),f2(x53111)),f186(x53111)))
% 157.55/157.22 [5312]~P124(x53121)+P105(f326(f326(f235(x53121),f2(x53121)),f77(x53121)))
% 157.55/157.22 [5365]E(x53651,f77(a909))+~P105(f326(f326(f286(a909),x53651),f77(a909)))
% 157.55/157.22 [5366]E(x53661,f2(a909))+~P105(f326(f326(f234(a909),x53661),f2(a909)))
% 157.55/157.22 [5408]E(f326(a104,x54081),f2(a909))+~P105(f326(f326(f234(a1),x54081),f2(a1)))
% 157.55/157.22 [5471]P105(f326(a193,x54711))+~P105(f326(f326(f235(a1),x54711),f2(a1)))
% 157.55/157.22 [5478]~P108(x54781)+P15(x54781,f910(x54781),f148(x54781,x54781,f7(x54781)))
% 157.55/157.22 [5496]P39(x54961)+~P105(f326(f326(f234(a1),f2(a1)),f332(x54961)))
% 157.55/157.22 [5501]E(f326(f75(a1),x55011),f326(f78(a1),x55011))+~P105(f326(f326(f235(a1),x55011),f2(a1)))
% 157.55/157.22 [5674]~P124(x56741)+~P105(f326(f326(f234(x56741),f77(x56741)),f2(x56741)))
% 157.55/157.22 [5675]~P124(x56751)+~P105(f326(f326(f235(x56751),f77(x56751)),f2(x56751)))
% 157.55/157.22 [5691]~E(x56911,f2(a909))+P105(f326(f326(f234(a1),f326(f100(a1),x56911)),f2(a1)))
% 157.55/157.22 [5692]~E(x56921,f2(a1))+P105(f326(f326(f235(a1),f326(f75(a1),x56921)),f77(a1)))
% 157.55/157.22 [5815]~P82(x58151)+E(f142(x58151,x58151,f79(x58151),f2(x58151)),f165(x58151))
% 157.55/157.22 [5998]~P102(x59981)+P24(a909,x59981,f100(x59981),f241(f917(a909,a905)))
% 157.55/157.22 [6198]E(x61981,f2(a909))+~P105(f326(f326(f234(a1),f326(f100(a1),x61981)),f2(a1)))
% 157.55/157.22 [6199]E(x61991,f2(a1))+~P105(f326(f326(f235(a1),f326(f75(a1),x61991)),f77(a1)))
% 157.55/157.22 [7003]~P105(f326(f326(f235(a1),x70031),f2(a1)))+P105(f326(f326(f235(a1),f326(f326(f79(a1),x70031),x70031)),f2(a1)))
% 157.55/157.22 [7558]P105(f326(f326(f235(a1),x75581),f2(a1)))+~P105(f326(f326(f235(a1),f326(f326(f79(a1),x75581),x75581)),f2(a1)))
% 157.55/157.22 [8099]E(x80991,f326(a5,f2(a909)))+P105(f326(f326(f235(a909),f326(f326(f3(a909),f326(a22,x80991)),f326(a112,f2(a909)))),f326(a22,x80991)))
% 157.55/157.22 [8856]~P105(f326(f326(f235(a1),x88561),f2(a1)))+P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),x88561),x88561)),a97)),f2(a1)))
% 157.55/157.22 [8953]~P105(f326(f326(f235(a1),x89531),f2(a1)))+P105(f326(f326(f235(a1),f326(f326(f79(a1),f326(f326(f79(a1),f77(a1)),x89531)),x89531)),f2(a1)))
% 157.55/157.22 [9271]P105(f326(f326(f235(a1),x92711),f2(a1)))+~P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),x92711),x92711)),a97)),f2(a1)))
% 157.55/157.22 [9332]P105(f326(f326(f235(a1),x93321),f2(a1)))+~P105(f326(f326(f235(a1),f326(f326(f79(a1),f326(f326(f79(a1),f77(a1)),x93321)),x93321)),f2(a1)))
% 157.55/157.22 [4828]~E(a82,x48281)+E(f326(f326(f79(a1),x48281),x48281),a82)
% 157.55/157.22 [4829]~E(x48291,a82)+E(f326(f326(f79(a1),x48291),x48291),a82)
% 157.55/157.22 [4840]E(x48401,f2(a1))+E(f326(f326(f36(a1),x48401),x48401),f77(a1))
% 157.55/157.22 [4974]E(x49741,a82)+~E(f326(f326(f79(a1),x49741),x49741),a82)
% 157.55/157.22 [4975]E(a82,x49751)+~E(f326(f326(f79(a1),x49751),x49751),a82)
% 157.55/157.22 [4987]~P4(x49871)+E(f37(x49871,f188(f917(x49871,a905))),f188(x49871))
% 157.55/157.22 [4988]~P4(x49881)+E(f37(x49881,f241(f917(x49881,a905))),f241(x49881))
% 157.55/157.22 [4989]~P4(x49891)+E(f38(x49891,f188(f917(x49891,a905))),f241(x49891))
% 157.55/157.22 [4990]~P4(x49901)+E(f38(x49901,f241(f917(x49901,a905))),f188(x49901))
% 157.55/157.22 [4991]~P108(x49911)+E(f139(x49911,f188(f917(x49911,a905))),f113(x49911))
% 157.55/157.22 [5138]E(x51381,f2(a909))+P105(f326(f326(f235(a909),f2(a909)),x51381))
% 157.55/157.22 [5158]~P5(x51581)+P105(f326(f326(f234(a1),f2(a1)),x51581))
% 157.55/157.22 [5192]~E(f326(f103(a909),x51921),f2(a909))+P105(f326(f326(f234(a1),x51921),a82))
% 157.55/157.22 [5197]P39(x51971)+P105(f326(f326(f328(a1),f332(x51971)),x51971))
% 157.55/157.22 [5198]E(x51981,f326(a5,f2(a909)))+P105(f326(f326(f234(a99),f77(a99)),x51981))
% 157.55/157.22 [5239]P105(f326(a193,x52391))+P105(f326(f326(f234(a1),f2(a1)),x52391))
% 157.55/157.22 [5289]E(f326(f100(a1),f326(a104,x52891)),f2(a1))+P105(f326(f326(f234(a1),f2(a1)),x52891))
% 157.55/157.22 [5346]E(f326(f100(a1),f326(f103(a909),x53461)),f326(f103(a1),x53461))+P105(f326(a193,f326(f103(a1),x53461)))
% 157.55/157.22 [5372]E(f326(f103(a909),x53721),f2(a909))+~P105(f326(a193,f326(f103(a1),x53721)))
% 157.55/157.22 [5373]E(f326(f103(a909),x53731),f2(a909))+~P105(f326(f326(f234(a1),x53731),a82))
% 157.55/157.22 [5405]P5(x54051)+~P105(f326(f326(f234(a1),f2(a1)),x54051))
% 157.55/157.22 [5481]E(f326(a112,f813(x54811)),x54811)+~P105(f326(f326(f235(a909),f2(a909)),x54811))
% 157.55/157.22 [5490]E(f326(a112,f326(f103(a909),x54901)),f77(a909))+~P105(f326(a193,f326(f103(a1),x54901)))
% 157.55/157.22 [5497]E(f326(f100(a1),f339(x54971)),x54971)+~P105(f326(f326(f235(a1),f2(a1)),x54971))
% 157.55/157.22 [5504]~E(x55041,f326(a5,f2(a909)))+~P105(f326(f326(f234(a99),f77(a99)),x55041))
% 157.55/157.22 [5511]E(f326(f100(a1),f326(f103(a909),x55111)),f2(a1))+~P105(f326(a193,f326(f103(a1),x55111)))
% 157.55/157.22 [5537]E(f326(f165(a909),x55371),f2(a909))+P105(f326(f326(f328(a909),f575(x55371)),f326(f172(a909),x55371)))
% 157.55/157.22 [5558]E(f326(f100(a1),f326(a104,x55581)),x55581)+~P105(f326(f326(f234(a1),f2(a1)),x55581))
% 157.55/157.22 [5566]~P105(f326(a193,x55661))+~P105(f326(f326(f234(a1),f2(a1)),x55661))
% 157.55/157.22 [5667]E(f326(f326(f79(a909),f77(a909)),f326(f103(a909),x56671)),f77(a909))+~P105(f326(f326(f235(a1),x56671),a82))
% 157.55/157.22 [5734]E(x57341,f2(a909))+~P105(f326(f326(f235(a909),x57341),f326(a112,f2(a909))))
% 157.55/157.22 [5756]E(x57561,f326(a112,f2(a909)))+~P105(f326(f326(f286(a909),x57561),f326(a112,f2(a909))))
% 157.55/157.22 [5774]E(f326(f326(f3(a909),f326(f103(a909),x57741)),f77(a909)),f2(a909))+~P105(f326(f326(f234(a1),x57741),a82))
% 157.55/157.22 [5775]E(f326(f326(f79(a909),f326(f103(a909),x57751)),f77(a909)),f77(a909))+~P105(f326(f326(f235(a1),x57751),a82))
% 157.55/157.22 [5787]~P39(x57871)+E(f326(f35(a909),f326(f309(a1,a909,a104),x57871)),f326(f35(a1),x57871))
% 157.55/157.22 [5816]~P108(x58161)+E(f236(x58161,f326(f9(x58161,x58161,a905),f234(x58161))),f233(x58161))
% 157.55/157.22 [5817]~P108(x58171)+E(f237(x58171,f326(f9(x58171,x58171,a905),f234(x58171))),f232(x58171))
% 157.55/157.22 [5827]E(f45(a909,f326(a112,f2(a909)),f326(f103(a909),x58271)),f326(a112,f2(a909)))+~P105(f326(a193,f326(f103(a1),x58271)))
% 157.55/157.22 [5836]~P105(f326(f326(f235(a1),f2(a1)),x58361))+P105(f326(f326(f234(a1),f77(a1)),x58361))
% 157.55/157.22 [5837]P105(f326(f326(f235(a1),f2(a1)),x58371))+~P105(f326(f326(f234(a1),f77(a1)),x58371))
% 157.55/157.22 [5848]E(f326(a112,f326(f326(f3(a909),x58481),f77(a909))),x58481)+~P105(f326(f326(f235(a909),f2(a909)),x58481))
% 157.55/157.22 [5904]P105(f326(f326(f235(a909),f2(a909)),f339(x59041)))+~P105(f326(f326(f235(a1),f2(a1)),x59041))
% 157.55/157.22 [5965]E(f45(a1,f326(f103(a1),a97),x59651),f326(f326(f3(a1),x59651),f77(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x59651))
% 157.55/157.22 [6011]~P105(f326(f326(f235(a1),a82),x60111))+P105(f326(f326(f235(a909),f2(a909)),f326(f103(a909),x60111)))
% 157.55/157.22 [6016]E(f326(a22,f802(x60161)),x60161)+~P105(f326(f326(f328(a909),x60161),f241(f917(a909,a905))))
% 157.55/157.22 [6065]P105(f326(f326(f235(a909),f2(a909)),f326(a104,x60651)))+~P105(f326(f326(f235(a1),f2(a1)),x60651))
% 157.55/157.22 [6114]~P105(f326(f326(f235(a909),f2(a909)),x61141))+P105(f326(f326(f235(a1),f2(a1)),f326(f100(a1),x61141)))
% 157.55/157.22 [6150]~P105(f326(f326(f235(a909),f2(a909)),f326(a104,x61501)))+P105(f326(f326(f235(a1),f2(a1)),x61501))
% 157.55/157.22 [6165]~P39(x61651)+E(f326(f309(a909,a1,f100(a1)),f326(f309(a1,a909,a104),x61651)),x61651)
% 157.55/157.22 [6178]P105(f326(f326(f235(a1),a82),x61781))+~P105(f326(f326(f235(a909),f2(a909)),f326(f103(a909),x61781)))
% 157.55/157.22 [6236]P105(f326(f326(f235(a909),f2(a909)),x62361))+~P105(f326(f326(f235(a1),f2(a1)),f326(f100(a1),x62361)))
% 157.55/157.22 [6352]E(f326(f309(a909,a1,f100(a1)),f326(f281(a909),f326(a104,x63521))),f326(f301(a1,f2(a1)),x63521))+~P105(f326(f326(f234(a1),f2(a1)),x63521))
% 157.55/157.22 [6368]~P124(x63681)+P105(f326(f326(f235(x63681),f2(x63681)),f326(f326(f79(x63681),f77(x63681)),f77(x63681))))
% 157.55/157.22 [6418]P105(f326(f326(f235(a909),f326(a112,f2(a909))),f326(a104,x64181)))+~P105(f326(f326(f235(a1),f77(a1)),x64181))
% 157.55/157.22 [6517]E(x65171,f2(a1))+P105(f326(f49(f2(a1),x65171),f326(f326(f251(a1,a1),f2(a1)),f2(a1))))
% 157.55/157.22 [6685]~P105(f326(f326(f235(a909),f326(a112,f2(a909))),f326(a104,x66851)))+P105(f326(f326(f235(a1),f77(a1)),x66851))
% 157.55/157.22 [7113]~P117(x71131)+P36(x71131,f326(f261(f916(x71131,x71131)),f326(f256(x71131,x71131,a905),f235(x71131))))
% 157.55/157.22 [5721]E(f326(f103(a909),f326(f326(f3(a1),x57211),a97)),f326(a112,f326(f103(a909),x57211)))+P105(f326(a193,f326(f103(a1),x57211)))
% 157.55/157.22 [5737]~P35(x57371)+E(f326(f326(f154(a909,a1),f100(a1)),f326(f326(f154(a1,a909),a104),x57371)),x57371)
% 157.55/157.22 [5854]E(f326(f78(a1),f326(f100(a1),f326(a112,f375(x58541)))),x58541)+~P105(f326(f326(f235(a1),x58541),f2(a1)))
% 157.55/157.22 [5864]E(f326(f326(f79(a909),f77(a909)),f326(f103(a909),x58641)),f326(f103(a909),f326(f326(f3(a1),x58641),a97)))+P105(f326(f326(f235(a1),x58641),a82))
% 157.55/157.22 [5906]E(f326(f326(f36(a1),f326(f103(a1),a97)),x59061),f326(f103(a1),a97))+~P105(f326(f326(f235(a1),f2(a1)),x59061))
% 157.55/157.22 [6007]E(f326(f326(f3(a909),f326(f103(a909),x60071)),f77(a909)),f326(f103(a909),f326(f326(f79(a1),x60071),a97)))+P105(f326(f326(f234(a1),x60071),a82))
% 157.55/157.22 [6008]E(f326(f326(f79(a909),f326(f103(a909),x60081)),f77(a909)),f326(f103(a909),f326(f326(f3(a1),x60081),a97)))+P105(f326(f326(f235(a1),x60081),a82))
% 157.55/157.22 [6052]E(f326(a104,f326(f326(f79(a1),f77(a1)),x60521)),f326(a112,f326(a104,x60521)))+~P105(f326(f326(f234(a1),f2(a1)),x60521))
% 157.55/157.22 [6086]E(f326(a112,f326(f326(f3(a909),x60861),f326(a112,f2(a909)))),x60861)+~P105(f326(f326(f235(a909),f2(a909)),x60861))
% 157.55/157.22 [6302]E(f45(a909,f326(a112,f2(a909)),f326(f103(a909),x63021)),f326(a104,f45(a1,f77(a1),f326(f103(a1),x63021))))+P105(f326(a193,f326(f103(a1),x63021)))
% 157.55/157.22 [6345]~P105(f326(f326(f234(a1),a82),x63451))+P105(f326(f326(f234(a1),a82),f326(f326(f79(a1),x63451),x63451)))
% 157.55/157.22 [6346]~P105(f326(f326(f235(a1),a97),x63461))+P105(f326(f326(f234(a1),a97),f326(f326(f79(a1),x63461),x63461)))
% 157.55/157.22 [6347]~P105(f326(f326(f235(a1),a82),x63471))+P105(f326(f326(f235(a1),a82),f326(f326(f79(a1),x63471),x63471)))
% 157.55/157.22 [6348]~P105(f326(f326(f235(a1),a97),x63481))+P105(f326(f326(f235(a1),a97),f326(f326(f79(a1),x63481),x63481)))
% 157.55/157.22 [6531]~P105(f326(f61(x65311),f241(f917(x65311,a905))))+P105(f326(f61(f913(x65311)),f241(f917(f913(x65311),a905))))
% 157.55/157.22 [6615]~P105(f326(f326(f234(a1),f2(a1)),x66151))+P105(f326(f326(f235(a1),f2(a1)),f326(f326(f79(a1),f77(a1)),x66151)))
% 157.55/157.22 [6622]E(f326(f250(a1,a1),f47(f77(a1),f326(f103(a1),x66221))),f326(f326(f36(a1),f77(a1)),f326(f103(a1),x66221)))+~P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x66221)))
% 157.55/157.22 [6644]E(f326(f255(a1,a1),f47(f77(a1),f326(f103(a1),x66441))),f45(a1,f77(a1),f326(f103(a1),x66441)))+~P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x66441)))
% 157.55/157.22 [6656]P105(f326(f61(x66561),f241(f917(x66561,a905))))+~P105(f326(f61(f913(x66561)),f241(f917(f913(x66561),a905))))
% 157.55/157.22 [6686]P105(f326(f326(f234(a1),a82),x66861))+~P105(f326(f326(f234(a1),a82),f326(f326(f79(a1),x66861),x66861)))
% 157.55/157.22 [6687]P105(f326(f326(f235(a1),a82),x66871))+~P105(f326(f326(f235(a1),a82),f326(f326(f79(a1),x66871),x66871)))
% 157.55/157.22 [6688]P105(f326(f326(f235(a1),a97),x66881))+~P105(f326(f326(f234(a1),a97),f326(f326(f79(a1),x66881),x66881)))
% 157.55/157.22 [6689]P105(f326(f326(f235(a1),a97),x66891))+~P105(f326(f326(f235(a1),a97),f326(f326(f79(a1),x66891),x66891)))
% 157.55/157.22 [7007]~P105(f326(f61(x70071),f241(f917(x70071,a905))))+P105(f326(f326(f235(a909),f2(a909)),f326(f35(x70071),f241(f917(x70071,a905)))))
% 157.55/157.22 [7597]P105(f326(f61(a909),x75971))+~P105(f326(f61(a1),f326(f309(a909,a1,f100(a1)),x75971)))
% 157.55/157.22 [5642]~E(a97,x56421)+E(f326(f326(f3(a1),f326(f326(f79(a1),x56421),x56421)),a97),a97)
% 157.55/157.22 [5643]~E(x56431,a97)+E(f326(f326(f3(a1),f326(f326(f79(a1),x56431),x56431)),a97),a97)
% 157.55/157.22 [6173]E(x61731,a97)+~E(f326(f326(f3(a1),f326(f326(f79(a1),x61731),x61731)),a97),a97)
% 157.55/157.22 [6174]E(a97,x61741)+~E(f326(f326(f3(a1),f326(f326(f79(a1),x61741),x61741)),a97),a97)
% 157.55/157.22 [6584]~E(f326(f103(a909),x65841),f2(a909))+P105(f326(a193,f326(f103(a1),f326(f326(f79(a1),x65841),a97))))
% 157.55/157.22 [6937]~P105(f326(a193,f326(f103(a1),x69371)))+P105(f326(a193,f326(f103(a1),f326(f326(f79(a1),x69371),x69371))))
% 157.55/157.22 [6938]~P105(f326(f326(f234(a1),x69381),a82))+P105(f326(f326(f234(a1),f326(f326(f79(a1),x69381),x69381)),a82))
% 157.55/157.22 [6939]~P105(f326(f326(f234(a1),x69391),a97))+P105(f326(f326(f234(a1),f326(f326(f79(a1),x69391),x69391)),a97))
% 157.55/157.22 [6940]~P105(f326(f326(f235(a1),x69401),a82))+P105(f326(f326(f235(a1),f326(f326(f79(a1),x69401),x69401)),a82))
% 157.55/157.22 [6941]~P105(f326(f326(f234(a1),x69411),a97))+P105(f326(f326(f235(a1),f326(f326(f79(a1),x69411),x69411)),a97))
% 157.55/157.22 [7260]E(f326(f103(a909),x72601),f2(a909))+~P105(f326(a193,f326(f103(a1),f326(f326(f79(a1),x72601),a97))))
% 157.55/157.22 [7513]~P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x75131)))+P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),f326(f326(f79(a1),x75131),x75131))))
% 157.55/157.22 [7514]P105(f326(a193,f326(f103(a1),x75141)))+~P105(f326(a193,f326(f103(a1),f326(f326(f79(a1),x75141),x75141))))
% 157.55/157.22 [7515]P105(f326(f326(f234(a1),x75151),a82))+~P105(f326(f326(f234(a1),f326(f326(f79(a1),x75151),x75151)),a82))
% 157.55/157.22 [7516]P105(f326(f326(f234(a1),x75161),a97))+~P105(f326(f326(f234(a1),f326(f326(f79(a1),x75161),x75161)),a97))
% 157.55/157.22 [7517]P105(f326(f326(f234(a1),x75171),a97))+~P105(f326(f326(f235(a1),f326(f326(f79(a1),x75171),x75171)),a97))
% 157.55/157.22 [7518]P105(f326(f326(f235(a1),x75181),a82))+~P105(f326(f326(f235(a1),f326(f326(f79(a1),x75181),x75181)),a82))
% 157.55/157.22 [7873]E(f326(a107,f518(x78731)),x78731)+~P105(f326(f326(f328(f917(f916(a909,a909),a905)),x78731),a98))
% 157.55/157.22 [6504]~P94(x65041)+E(f326(f103(x65041),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f77(x65041))
% 157.55/157.22 [6987]~P105(f326(a193,f326(f103(a1),x69871)))+E(f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),x69871),x69871)),a97)),f2(a909))
% 157.55/157.22 [8045]~P105(f326(f326(f235(a1),f326(f103(a1),x80451)),f2(a1)))+E(f326(f250(a1,a1),f326(a51,f50(f326(f78(a1),f77(a1)),f326(f78(a1),f326(f103(a1),x80451))))),f326(f326(f36(a1),f77(a1)),f326(f103(a1),x80451)))
% 157.55/157.22 [8058]~P105(f326(f326(f235(a1),f326(f103(a1),x80581)),f2(a1)))+E(f326(f255(a1,a1),f326(a51,f50(f326(f78(a1),f77(a1)),f326(f78(a1),f326(f103(a1),x80581))))),f45(a1,f77(a1),f326(f103(a1),x80581)))
% 157.55/157.22 [8106]~P105(f326(f326(f234(a1),a82),x81061))+P105(f326(f326(f234(a1),a82),f326(f326(f3(a1),f326(f326(f79(a1),x81061),x81061)),a97)))
% 157.55/157.22 [8107]~P105(f326(f326(f234(a1),a97),x81071))+P105(f326(f326(f234(a1),a97),f326(f326(f3(a1),f326(f326(f79(a1),x81071),x81071)),a97)))
% 157.55/157.22 [8108]~P105(f326(f326(f234(a1),a82),x81081))+P105(f326(f326(f235(a1),a82),f326(f326(f3(a1),f326(f326(f79(a1),x81081),x81081)),a97)))
% 157.55/157.22 [8109]~P105(f326(f326(f235(a1),a97),x81091))+P105(f326(f326(f235(a1),a97),f326(f326(f3(a1),f326(f326(f79(a1),x81091),x81091)),a97)))
% 157.55/157.22 [8401]~P94(x84011)+~P27(x84011,f326(f103(x84011),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))
% 157.55/157.22 [8582]P105(f326(f326(f234(a1),a82),x85821))+~P105(f326(f326(f234(a1),a82),f326(f326(f3(a1),f326(f326(f79(a1),x85821),x85821)),a97)))
% 157.55/157.22 [8583]P105(f326(f326(f234(a1),a82),x85831))+~P105(f326(f326(f235(a1),a82),f326(f326(f3(a1),f326(f326(f79(a1),x85831),x85831)),a97)))
% 157.55/157.22 [8584]P105(f326(f326(f234(a1),a97),x85841))+~P105(f326(f326(f234(a1),a97),f326(f326(f3(a1),f326(f326(f79(a1),x85841),x85841)),a97)))
% 157.55/157.22 [8585]P105(f326(f326(f235(a1),a97),x85851))+~P105(f326(f326(f235(a1),a97),f326(f326(f3(a1),f326(f326(f79(a1),x85851),x85851)),a97)))
% 157.55/157.22 [8903]E(f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),x89031),x89031)),a97)),f326(f326(f85(a909,a909),f326(f103(a909),x89031)),f326(f326(f10(a909,a909,a909),a112),f326(f326(f20(a909,a909,a909),f79(a909)),f7(a909)))))+P105(f326(a193,f326(f103(a1),x89031)))
% 157.55/157.22 [9751]E(x97511,f188(f917(f916(a909,a909),a905)))+P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),x97511),f188(f917(f916(a909,a909),a905)))),a33))
% 157.55/157.22 [8830]~P105(f326(a193,f326(f103(a1),x88301)))+P105(f326(a193,f326(f103(a1),f326(f326(f3(a1),f326(f326(f79(a1),x88301),x88301)),a97))))
% 157.55/157.22 [8831]~P105(f326(f326(f235(a1),x88311),a82))+P105(f326(f326(f234(a1),f326(f326(f3(a1),f326(f326(f79(a1),x88311),x88311)),a97)),a82))
% 157.55/157.22 [8832]~P105(f326(f326(f234(a1),x88321),a97))+P105(f326(f326(f234(a1),f326(f326(f3(a1),f326(f326(f79(a1),x88321),x88321)),a97)),a97))
% 157.55/157.22 [8833]~P105(f326(f326(f235(a1),x88331),a82))+P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),x88331),x88331)),a97)),a82))
% 157.55/157.22 [8834]~P105(f326(f326(f235(a1),x88341),a97))+P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),x88341),x88341)),a97)),a97))
% 157.55/157.22 [8944]~P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x89441)))+P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),f326(f326(f3(a1),f326(f326(f79(a1),x89441),x89441)),a97))))
% 157.55/157.22 [9102]~P94(x91021)+E(f326(f326(f79(x91021),f77(x91021)),f77(x91021)),f326(f103(x91021),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))
% 157.55/157.22 [9255]P105(f326(a193,f326(f103(a1),x92551)))+~P105(f326(a193,f326(f103(a1),f326(f326(f3(a1),f326(f326(f79(a1),x92551),x92551)),a97))))
% 157.55/157.22 [9256]P105(f326(f326(f234(a1),x92561),a97))+~P105(f326(f326(f234(a1),f326(f326(f3(a1),f326(f326(f79(a1),x92561),x92561)),a97)),a97))
% 157.55/157.22 [9257]P105(f326(f326(f235(a1),x92571),a82))+~P105(f326(f326(f234(a1),f326(f326(f3(a1),f326(f326(f79(a1),x92571),x92571)),a97)),a82))
% 157.55/157.22 [9258]P105(f326(f326(f235(a1),x92581),a82))+~P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),x92581),x92581)),a97)),a82))
% 157.55/157.22 [9259]P105(f326(f326(f235(a1),x92591),a97))+~P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),x92591),x92591)),a97)),a97))
% 157.55/157.22 [9796]~P105(f326(f61(f916(a909,a909)),x97961))+P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),f188(f917(f916(a909,a909),a905))),x97961)),a69))
% 157.55/157.22 [9581]~P143(x95811)+E(f326(f326(f243(x95811),f77(x95811)),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f77(x95811))
% 157.55/157.22 [9582]~P143(x95821)+E(f326(f326(f243(x95821),f2(x95821)),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f2(x95821))
% 157.55/157.22 [10020]~P105(f326(f326(f235(a909),f77(a909)),x100201))+P105(f326(f326(f235(a909),f2(a909)),f326(f326(f36(a909),x100201),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))
% 157.55/157.22 [10026]~P105(f326(f326(f235(a909),f2(a909)),x100261))+P105(f326(f326(f235(a909),f2(a909)),f326(f326(f36(a909),f326(f326(f79(a909),x100261),f77(a909))),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))
% 157.55/157.22 [10065]~E(f45(a909,x100651,f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f77(a909))+P105(f326(f326(f235(a909),f2(a909)),f45(a909,x100651,f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))
% 157.55/157.22 [10095]E(f45(a909,x100951,f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f77(a909))+~P105(f326(f326(f235(a909),f2(a909)),f45(a909,x100951,f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))
% 157.55/157.22 [4756]~P6(x47561,x47562)+P42(x47561,x47562)
% 157.55/157.22 [4757]~P36(x47571,x47572)+P56(x47571,x47572)
% 157.55/157.22 [4758]~P43(x47581,x47582)+P56(x47581,x47582)
% 157.55/157.22 [4760]~P6(x47601,x47602)+P48(x47601,x47602)
% 157.55/157.22 [4762]~P14(x47621,x47622)+P48(x47621,x47622)
% 157.55/157.22 [4764]~P6(x47641,x47642)+P49(x47641,x47642)
% 157.55/157.22 [4766]~P14(x47661,x47662)+P49(x47661,x47662)
% 157.55/157.22 [4767]~P6(x47671,x47672)+P14(x47671,x47672)
% 157.55/157.22 [4717]~E(x47171,x47172)+E(f268(x47171,x47172),f77(a99))
% 157.55/157.22 [4720]E(f216(x47201,x47202),x47201)+~E(x47202,f2(a909))
% 157.55/157.22 [4727]~E(x47272,f113(x47271))+E(f152(x47271,x47272),f113(x47271))
% 157.55/157.22 [4746]~E(f152(x47462,x47461),f113(x47462))+E(x47461,f113(x47462))
% 157.55/157.22 [4771]~P1(x47712)+P1(f917(x47711,x47712))
% 157.55/157.22 [4772]~P106(x47722)+P106(f917(x47721,x47722))
% 157.55/157.22 [4773]~P107(x47732)+P107(f917(x47731,x47732))
% 157.55/157.22 [4774]~P109(x47742)+P109(f917(x47741,x47742))
% 157.55/157.22 [4775]~P2(x47752)+P2(f917(x47751,x47752))
% 157.55/157.22 [4776]~P77(x47762)+P77(f917(x47761,x47762))
% 157.55/157.22 [4777]~P97(x47772)+P78(f917(x47771,x47772))
% 157.55/157.22 [4778]~P77(x47782)+P100(f917(x47781,x47782))
% 157.55/157.22 [4779]~P77(x47792)+P101(f917(x47791,x47792))
% 157.55/157.22 [4780]~P98(x47802)+P98(f917(x47801,x47802))
% 157.55/157.22 [4781]~P4(x47812)+P4(f917(x47811,x47812))
% 157.55/157.22 [4782]~P95(x47822)+P95(f917(x47821,x47822))
% 157.55/157.22 [4783]~P89(x47832)+P89(f917(x47831,x47832))
% 157.55/157.22 [4784]~P116(x47842)+P116(f917(x47841,x47842))
% 157.55/157.22 [4785]~P97(x47852)+P99(f917(x47851,x47852))
% 157.55/157.22 [4786]~P97(x47862)+P97(f917(x47861,x47862))
% 157.55/157.22 [4799]E(x47991,x47992)+~E(f326(a112,x47991),f326(a112,x47992))
% 157.55/157.22 [4800]E(x48001,x48002)+~E(f326(a107,x48001),f326(a107,x48002))
% 157.55/157.22 [4801]E(x48011,x48012)+~E(f326(a5,x48011),f326(a5,x48012))
% 157.55/157.22 [4803]E(x48031,x48032)+~E(f326(a22,x48031),f326(a22,x48032))
% 157.55/157.22 [4856]P38(x48561,x48562)+~E(f700(x48562,x48561),f701(x48562,x48561))
% 157.55/157.22 [4886]~P56(x48861,x48862)+P38(x48861,f306(x48861,x48862))
% 157.55/157.22 [4887]~P50(x48871,x48872)+P50(x48871,f306(x48871,x48872))
% 157.55/157.22 [4900]~P59(x49001)+E(f45(x49001,x49002,x49002),f2(x49001))
% 157.55/157.22 [4934]~P36(x49341,x49342)+P36(f910(x49341),f146(x49341,x49342))
% 157.55/157.22 [4935]~P36(x49351,x49352)+P36(f910(x49351),f145(x49351,x49352))
% 157.55/157.22 [4936]~P37(x49361,x49362)+P37(f910(x49361),f147(x49361,x49362))
% 157.55/157.22 [4937]~P37(x49371,x49372)+P37(f910(x49371),f158(x49371,x49372))
% 157.55/157.22 [4938]~P50(x49381,x49382)+P50(f910(x49381),f158(x49381,x49382))
% 157.55/157.22 [5035]~P36(x50351,x50352)+P36(f917(x50351,a905),f317(x50351,x50352))
% 157.55/157.22 [5036]~P36(x50361,x50362)+P36(f917(x50361,a905),f318(x50361,x50362))
% 157.55/157.22 [5167]~P5(x51671)+P39(f302(a1,x51671,x51672))
% 157.55/157.22 [5270]~P36(x52701,x52702)+P58(x52701,f67(x52701,x52701,x52702))
% 157.55/157.22 [5781]~P79(x57811)+P24(x57811,x57811,f78(x57811),x57812)
% 157.55/157.22 [4741]~E(x47412,f113(x47411))+E(f326(f167(x47411),x47412),f113(x47411))
% 157.55/157.22 [4742]~E(x47422,f113(x47421))+E(f326(f168(x47421),x47422),f113(x47421))
% 157.55/157.22 [4805]E(x48051,f326(a104,x48052))+~E(f326(f100(a1),x48051),x48052)
% 157.55/157.22 [4808]E(x48081,f113(x48082))+~E(f326(f167(x48082),x48081),f113(x48082))
% 157.55/157.22 [4809]E(x48091,f113(x48092))+~E(f326(f168(x48092),x48091),f113(x48092))
% 157.55/157.22 [4825]~P94(x48251)+E(f326(f103(x48251),x48252),f326(f102(x48251),x48252))
% 157.55/157.22 [4833]~P3(x48331)+P105(f326(f61(x48331),x48332))
% 157.55/157.22 [4841]~E(f659(x48412,x48411),f113(x48411))+E(f179(x48411,x48412),f113(f910(x48411)))
% 157.55/157.22 [4850]~E(x48502,f113(x48501))+E(f326(f172(x48501),x48502),f188(f917(x48501,a905)))
% 157.55/157.22 [4851]~E(x48512,f113(x48511))+E(f188(f917(x48511,a905)),f326(f172(x48511),x48512))
% 157.55/157.22 [4853]E(x48531,x48532)+~E(f326(f100(a1),x48531),f326(f100(a1),x48532))
% 157.55/157.22 [4857]E(f214(x48571,x48572),f2(a909))+P105(f326(f61(x48571),x48572))
% 157.55/157.22 [4875]~P118(x48751)+E(f81(x48751,f81(x48751,x48752)),f81(x48751,x48752))
% 157.55/157.22 [4889]~P112(x48891)+E(f326(f326(f243(x48891),x48892),f77(a909)),x48892)
% 157.55/157.22 [4890]~P81(x48901)+E(f326(f326(f243(x48901),x48902),f77(a909)),x48902)
% 157.55/157.22 [4891]~P50(x48911,x48912)+E(f326(f285(x48911,x48911),x48912),x48912)
% 157.55/157.22 [4895]E(x48951,x48952)+E(f268(x48951,x48952),f326(f326(f79(a99),x48952),f77(a99)))
% 157.55/157.22 [4898]E(f326(f35(x48981),x48982),f2(a909))+P105(f326(f61(x48981),x48982))
% 157.55/157.22 [4901]~E(f152(x49011,x49012),x49012)+P105(f326(f137(x49011),x49012))
% 157.55/157.22 [4904]~P78(x49041)+E(f326(f326(f110(x49041),x49042),f188(x49041)),x49042)
% 157.55/157.22 [4905]~P73(x49051)+E(f326(f326(f3(x49051),x49052),f2(x49051)),x49052)
% 157.55/157.22 [4906]~P112(x49061)+E(f326(f326(f80(x49061),x49062),f77(x49061)),x49062)
% 157.55/157.22 [4907]~P74(x49071)+E(f326(f326(f80(x49071),x49072),f77(x49071)),x49072)
% 157.55/157.22 [4908]~P81(x49081)+E(f326(f326(f80(x49081),x49082),f77(x49081)),x49082)
% 157.55/157.22 [4909]~P99(x49091)+E(f326(f326(f101(x49091),x49092),f241(x49091)),x49092)
% 157.55/157.22 [4910]~P69(x49101)+E(f326(f326(f79(x49101),x49102),f2(x49101)),x49102)
% 157.55/157.22 [4911]~P112(x49111)+E(f326(f326(f79(x49111),x49112),f2(x49111)),x49112)
% 157.55/157.22 [4912]~P82(x49121)+E(f326(f326(f79(x49121),x49122),f2(x49121)),x49122)
% 157.55/157.22 [4913]~P121(x49131)+E(f326(f326(f290(x49131),x49132),f77(x49131)),x49132)
% 157.55/157.22 [4914]~P59(x49141)+E(f326(f326(f36(x49141),x49142),f77(x49141)),x49142)
% 157.55/157.22 [4915]~P112(x49151)+E(f326(f326(f243(x49151),x49152),f2(a909)),f77(x49151))
% 157.55/157.22 [4916]~P115(x49161)+E(f326(f326(f243(x49161),x49162),f2(a909)),f77(x49161))
% 157.55/157.22 [4917]~E(x49172,f188(f917(x49171,a905)))+E(f326(f35(x49171),x49172),f2(a909))
% 157.55/157.22 [4928]~P59(x49281)+E(f45(x49281,x49282,f2(x49281)),x49282)
% 157.55/157.22 [4939]~P99(x49391)+E(f326(f326(f110(x49391),x49392),f241(x49391)),f241(x49391))
% 157.55/157.22 [4940]~P112(x49401)+E(f326(f326(f80(x49401),x49402),f2(x49401)),f2(x49401))
% 157.55/157.22 [4941]~P130(x49411)+E(f326(f326(f80(x49411),x49412),f2(x49411)),f2(x49411))
% 157.55/157.22 [4942]~P78(x49421)+E(f326(f326(f101(x49421),x49422),f188(x49421)),f188(x49421))
% 157.55/157.22 [4943]~P122(x49431)+E(f326(f326(f290(x49431),x49432),f2(x49431)),f2(x49431))
% 157.55/157.22 [4944]~P59(x49441)+E(f326(f326(f36(x49441),x49442),f2(x49441)),f2(x49441))
% 157.55/157.22 [4946]~P59(x49461)+E(f45(x49461,x49462,f77(x49461)),f2(x49461))
% 157.55/157.22 [4947]~P59(x49471)+E(f45(x49471,f2(x49471),x49472),f2(x49471))
% 157.55/157.22 [4976]E(x49761,f2(a909))+E(f55(x49762,x49761,f113(x49762)),f113(f910(x49762)))
% 157.55/157.22 [4999]P50(x49991,x49992)+~E(f326(f285(x49991,x49991),x49992),x49992)
% 157.55/157.22 [5000]P36(x50001,x50002)+~E(f576(x50002,x50001),f188(f917(x50001,a905)))
% 157.55/157.22 [5001]E(x50011,f113(x50012))+~E(f326(f172(x50012),x50011),f188(f917(x50012,a905)))
% 157.55/157.22 [5002]E(x50021,f113(x50022))+~E(f188(f917(x50022,a905)),f326(f172(x50022),x50021))
% 157.55/157.22 [5005]~E(x50051,x50052)+P105(f326(f326(a323,x50051),x50052))
% 157.55/157.22 [5015]P105(x50151)+P105(f326(f326(a329,x50151),x50152))
% 157.55/157.22 [5016]E(x50161,f113(x50162))+E(f326(f326(f164(x50162),x50161),f2(a909)),f326(f141(x50162),x50161))
% 157.55/157.22 [5019]E(f152(x50191,x50192),x50192)+~P105(f326(f137(x50191),x50192))
% 157.55/157.22 [5026]~P105(x50262)+P105(f326(f326(a329,x50261),x50262))
% 157.55/157.22 [5027]~P105(x50272)+P105(f326(f326(a325,x50271),x50272))
% 157.55/157.22 [5028]~P105(x50281)+P105(f326(f326(a325,x50281),x50282))
% 157.55/157.22 [5038]~E(f660(x50382,x50381),f666(x50382,x50381))+P105(f326(f137(x50381),x50382))
% 157.55/157.22 [5045]E(f326(f261(x50451),x50452),f188(f917(x50451,a905)))+P105(f326(x50452,f531(x50452)))
% 157.55/157.22 [5046]E(f188(f917(x50461,a905)),f326(f261(x50461),x50462))+P105(f326(x50462,f545(x50462)))
% 157.55/157.22 [5119]~P118(x51191)+E(f326(f326(f80(x51191),x51192),f81(x51191,x51192)),f326(f75(x51191),x51192))
% 157.55/157.22 [5131]~E(x51311,f2(a1))+E(f46(x51311,x51312),f326(f326(f251(a1,a1),f2(a1)),f2(a1)))
% 157.55/157.22 [5163]~P56(x51631,x51632)+P56(x51631,f326(f285(x51631,x51631),x51632))
% 157.55/157.22 [5164]~P37(x51641,x51642)+P37(x51641,f326(f285(x51641,x51641),x51642))
% 157.55/157.22 [5165]~P38(x51651,x51652)+P38(x51651,f326(f285(x51651,x51651),x51652))
% 157.55/157.22 [5166]~P50(x51661,x51662)+P50(x51661,f326(f285(x51661,x51661),x51662))
% 157.55/157.22 [5188]E(x51881,x51882)+~P105(f326(f326(a323,x51881),x51882))
% 157.55/157.22 [5199]P105(x51991)+~P105(f326(f326(a324,x51992),x51991))
% 157.55/157.22 [5200]P105(x52001)+~P105(f326(f326(a324,x52001),x52002))
% 157.55/157.22 [5205]~P116(x52051)+P105(f326(f326(f234(x52051),x52052),f241(x52051)))
% 157.55/157.22 [5206]~P112(x52061)+P105(f326(f326(f286(x52061),x52062),f2(x52061)))
% 157.55/157.22 [5210]E(x52101,x52102)+~E(f326(x52101,f333(x52102,x52101)),f326(x52102,f333(x52102,x52101)))
% 157.55/157.22 [5241]E(x52411,f2(a909))+E(f216(x52411,f45(a909,x52412,x52411)),f216(x52412,x52411))
% 157.55/157.22 [5246]~P108(x52461)+P12(x52461,f326(f326(f151(x52461),x52462),f113(x52461)))
% 157.55/157.22 [5248]E(x52481,f2(a1))+P105(f326(f49(x52482,x52481),f46(x52482,x52481)))
% 157.55/157.22 [5265]~P14(x52652,x52651)+P105(f326(f326(x52651,f794(x52651)),f794(x52651)))
% 157.55/157.22 [5268]~E(x52681,x52682)+P105(f326(f326(f235(a909),x52681),f326(a112,x52682)))
% 157.55/157.22 [5278]~E(x52781,f2(a909))+P105(f326(f326(f235(a909),x52781),f326(a112,x52782)))
% 157.55/157.22 [5288]P105(f326(x52881,x52882))+P105(f326(f326(f234(a1),f2(a1)),f364(x52881)))
% 157.55/157.22 [5351]E(f326(f326(f308(x53512),f368(x53512,x53511)),f411(x53512,x53511)),x53511)+E(x53511,f188(f917(x53512,a905)))
% 157.55/157.22 [5352]P56(x53521,x53522)+~P56(x53521,f326(f285(x53521,x53521),x53522))
% 157.55/157.22 [5353]P37(x53531,x53532)+~P37(x53531,f326(f285(x53531,x53531),x53532))
% 157.55/157.22 [5354]P38(x53541,x53542)+~P38(x53541,f326(f285(x53541,x53541),x53542))
% 157.55/157.22 [5355]P50(x53551,x53552)+~P50(x53551,f326(f285(x53551,x53551),x53552))
% 157.55/157.22 [5358]~E(f45(a909,x53582,x53581),f2(a909))+E(f326(f326(f80(a909),x53581),f369(x53581,x53582)),x53582)
% 157.55/157.22 [5359]~E(f45(a1,x53592,x53591),f2(a1))+E(f326(f326(f80(a1),x53591),f335(x53591,x53592)),x53592)
% 157.55/157.22 [5386]~P105(f326(x53861,x53862))+P105(f326(f326(f234(a1),f2(a1)),f334(x53861)))
% 157.55/157.22 [5397]E(f326(f326(f3(a909),f326(a104,x53971)),f326(a104,x53972)),f326(a104,x53971))+~P105(f326(a193,x53972))
% 157.55/157.22 [5426]E(f271(x54261,x54262),f77(a99))+~P105(f326(f326(f234(a99),x54261),f77(a99)))
% 157.55/157.22 [5512]~P105(f326(f326(a921,x55121),x55122))+P105(f326(f326(a922,x55121),x55122))
% 157.55/157.22 [5523]E(f326(f326(f164(x55231),x55232),f660(x55232,x55231)),f326(f326(f164(x55231),x55232),f666(x55232,x55231)))+P105(f326(f137(x55231),x55232))
% 157.55/157.22 [5567]~P105(f326(x55671,f89(x55672,x55671)))+P105(f326(x55671,f590(x55672,x55671)))
% 157.55/157.22 [5632]P58(x56321,x56322)+~P105(f326(f314(x56321,x56322),f546(x56322,x56321)))
% 157.55/157.22 [5778]~P14(x57782,x57781)+P105(f326(f326(x57781,f795(x57781,x57782)),f795(x57781,x57782)))
% 157.55/157.22 [5779]~P14(x57792,x57791)+P105(f326(f326(x57791,f799(x57791,x57792)),f799(x57791,x57792)))
% 157.55/157.22 [5788]~E(f326(a112,f45(a909,x57881,x57882)),x57882)+E(f45(a909,f326(a112,x57881),x57882),f2(a909))
% 157.55/157.22 [5843]P36(x58431,x58432)+P105(f326(f326(f328(x58431),f611(x58432,x58431)),f612(x58432,x58431)))
% 157.55/157.22 [5850]~P94(x58501)+P105(f326(f326(f328(x58501),f326(f103(x58501),x58502)),f109(x58501)))
% 157.55/157.22 [5851]~P140(x58511)+P105(f326(f326(f328(x58511),f326(f100(x58511),x58512)),f109(x58511)))
% 157.55/157.22 [5852]~P143(x58521)+P105(f326(f326(f328(x58521),f326(f100(x58521),x58522)),f186(x58521)))
% 157.55/157.22 [5853]~P140(x58531)+P105(f326(f326(f328(x58531),f326(f102(x58531),x58532)),f109(x58531)))
% 157.55/157.22 [5996]~P37(x59961,x59962)+E(f326(f326(f288(x59961,x59961,x59961),x59962),f306(x59961,x59962)),x59962)
% 157.55/157.22 [6010]E(f326(a112,f45(a909,x60101,x60102)),x60102)+E(f45(a909,f326(a112,x60101),x60102),f326(a112,f45(a909,x60101,x60102)))
% 157.55/157.22 [6430]P36(x64301,x64302)+~P105(f326(f326(f328(x64301),f547(x64302,x64301)),f315(x64301,x64302)))
% 157.55/157.22 [6467]~P124(x64671)+~P105(f326(f326(f235(x64671),f326(f100(x64671),x64672)),f2(x64671)))
% 157.55/157.22 [6468]~P86(x64681)+~P105(f326(f326(f235(x64681),f326(f75(x64681),x64682)),f2(x64681)))
% 157.55/157.22 [6500]E(x65001,f188(f917(x65002,a905)))+~P105(f326(f326(f328(x65002),f368(x65002,x65001)),f411(x65002,x65001)))
% 157.55/157.22 [6558]P105(f326(f326(f235(a1),x65581),f45(a1,x65582,x65581)))+~P105(f326(f326(f235(a1),x65581),f2(a1)))
% 157.55/157.22 [6658]E(f326(f326(f308(a909),f326(a112,x66581)),f302(a909,x66582,x66581)),f302(a909,x66582,f326(a112,x66581)))+~P105(f326(f326(f234(a909),x66582),f326(a112,x66581)))
% 157.55/157.22 [6749]~P108(x67491)+P12(x67491,f150(x67491,x67491,f7(x67491),x67492))
% 157.55/157.22 [6880]E(f326(f167(x68801),x68802),x68802)+~P105(f326(f326(f234(a909),f326(f189(f910(x68801)),x68802)),f77(a909)))
% 157.55/157.22 [6902]~P86(x69021)+P105(f326(f326(f234(x69021),f326(f78(x69021),f326(f75(x69021),x69022))),f2(x69021)))
% 157.55/157.22 [6933]~P36(x69331,x69332)+P36(x69331,f326(f326(f288(x69331,x69331,x69331),x69332),f306(x69331,x69332)))
% 157.55/157.22 [6934]~P50(x69341,x69342)+P50(x69341,f326(f326(f288(x69341,x69341,x69341),x69342),f306(x69341,x69342)))
% 157.55/157.22 [7154]~P105(f326(f326(f235(a1),x71542),f2(a1)))+P105(f326(f326(f234(a1),f45(a1,x71541,x71542)),f2(a1)))
% 157.55/157.22 [7555]~P143(x75551)+E(f190(x75551,f326(f326(f9(x75551,x75551,x75551),f79(x75551)),f77(x75551)),x75552,f2(x75551)),f326(f100(x75551),x75552))
% 157.55/157.22 [7583]~P126(x75831)+~P105(f326(f326(f235(x75831),f326(f326(f80(x75831),x75832),x75832)),f2(x75831)))
% 157.55/157.22 [10187]~P118(x101871)+~P105(f326(f326(f235(x101871),f326(f326(f243(x101871),x101872),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f2(x101871)))
% 157.55/157.22 [4806]~E(x48062,f113(x48061))+E(f326(f189(f910(x48061)),x48062),f2(a909))
% 157.55/157.22 [4842]~E(x48421,f2(a909))+E(f326(f326(f79(a909),x48421),x48422),x48422)
% 157.55/157.22 [4843]~E(x48432,f2(a909))+E(f326(f326(f80(a909),x48431),x48432),f2(a909))
% 157.55/157.22 [4845]~E(x48451,f2(a909))+E(f326(f326(f80(a909),x48451),x48452),f2(a909))
% 157.55/157.22 [4846]~E(x48462,f2(a1))+E(f326(f326(f36(a1),x48461),x48462),f2(a1))
% 157.55/157.22 [4847]~E(x48472,f2(a909))+E(f326(f326(f243(a909),x48471),x48472),f77(a909))
% 157.55/157.22 [4858]E(x48581,f113(x48582))+~E(f326(f189(f910(x48582)),x48581),f2(a909))
% 157.55/157.22 [4859]~P77(x48591)+E(f326(f326(f110(x48591),x48592),x48592),x48592)
% 157.55/157.22 [4861]~P100(x48611)+E(f326(f326(f110(x48611),x48612),x48612),x48612)
% 157.55/157.22 [4863]~P96(x48631)+E(f326(f326(f80(x48631),x48632),x48632),x48632)
% 157.55/157.22 [4864]~P77(x48641)+E(f326(f326(f101(x48641),x48642),x48642),x48642)
% 157.55/157.22 [4866]~P101(x48661)+E(f326(f326(f101(x48661),x48662),x48662),x48662)
% 157.55/157.22 [4868]~P108(x48681)+E(f326(f326(f232(x48681),x48682),x48682),x48682)
% 157.55/157.22 [4870]~P108(x48701)+E(f326(f326(f233(x48701),x48702),x48702),x48702)
% 157.55/157.22 [4888]~P73(x48881)+E(f326(f326(f3(x48881),x48882),x48882),f2(x48881))
% 157.55/157.22 [4902]~P73(x49021)+E(f326(f78(x49021),f326(f78(x49021),x49022)),x49022)
% 157.55/157.22 [4903]~P95(x49031)+E(f326(f78(x49031),f326(f78(x49031),x49032)),x49032)
% 157.55/157.22 [4920]~E(x49202,f2(a909))+E(f326(f326(f243(a909),x49201),x49202),f326(a112,f2(a909)))
% 157.55/157.22 [4955]~P78(x49551)+E(f326(f326(f110(x49551),f188(x49551)),x49552),x49552)
% 157.55/157.22 [4956]~P112(x49561)+E(f326(f326(f80(x49561),f77(x49561)),x49562),x49562)
% 157.55/157.22 [4957]~P74(x49571)+E(f326(f326(f80(x49571),f77(x49571)),x49572),x49572)
% 157.55/157.22 [4958]~P81(x49581)+E(f326(f326(f80(x49581),f77(x49581)),x49582),x49582)
% 157.55/157.22 [4959]~P99(x49591)+E(f326(f326(f101(x49591),f241(x49591)),x49592),x49592)
% 157.55/157.22 [4960]~P69(x49601)+E(f326(f326(f79(x49601),f2(x49601)),x49602),x49602)
% 157.55/157.22 [4961]~P112(x49611)+E(f326(f326(f79(x49611),f2(x49611)),x49612),x49612)
% 157.55/157.22 [4962]~P82(x49621)+E(f326(f326(f79(x49621),f2(x49621)),x49622),x49622)
% 157.55/157.22 [4980]~P99(x49801)+E(f326(f326(f110(x49801),f241(x49801)),x49802),f241(x49801))
% 157.55/157.22 [4981]~P112(x49811)+E(f326(f326(f80(x49811),f2(x49811)),x49812),f2(x49811))
% 157.55/157.22 [4982]~P130(x49821)+E(f326(f326(f80(x49821),f2(x49821)),x49822),f2(x49821))
% 157.55/157.22 [4983]~P78(x49831)+E(f326(f326(f101(x49831),f188(x49831)),x49832),f188(x49831))
% 157.55/157.22 [4984]~P121(x49841)+E(f326(f326(f290(x49841),f2(x49841)),x49842),f2(x49841))
% 157.55/157.22 [4985]~P59(x49851)+E(f326(f326(f36(x49851),f2(x49851)),x49852),f2(x49851))
% 157.55/157.22 [4986]~P81(x49861)+E(f326(f326(f243(x49861),f77(x49861)),x49862),f77(x49861))
% 157.55/157.22 [4994]E(x49941,f113(x49942))+E(f144(x49942,f326(f168(x49942),x49941)),f326(f141(x49942),x49941))
% 157.55/157.22 [4995]E(x49951,f113(x49952))+E(f326(f141(x49952),f326(f168(x49952),x49951)),f144(x49952,x49951))
% 157.55/157.22 [4996]E(x49961,f2(a909))+~E(f326(f326(f79(a909),x49962),x49961),x49962)
% 157.55/157.22 [5003]~P94(x50031)+E(f326(f102(x50031),f326(f103(a1),x50032)),f326(f103(x50031),x50032))
% 157.55/157.22 [5004]~P140(x50041)+E(f326(f102(x50041),f326(f100(a1),x50042)),f326(f100(x50041),x50042))
% 157.55/157.22 [5011]E(x50111,f77(a909))+~E(f326(f326(f80(a909),x50112),x50111),f77(a909))
% 157.55/157.22 [5012]E(x50121,f77(a909))+~E(f326(f326(f80(a909),x50121),x50122),f77(a909))
% 157.55/157.22 [5013]E(x50131,f2(a909))+~E(f326(f326(f79(a909),x50132),x50131),f2(a909))
% 157.55/157.22 [5014]E(x50141,f2(a909))+~E(f326(f326(f79(a909),x50141),x50142),f2(a909))
% 157.55/157.22 [5031]~P118(x50311)+E(f326(f75(x50311),f326(f100(x50311),x50312)),f326(f100(x50311),x50312))
% 157.55/157.22 [5032]~P86(x50321)+E(f326(f75(x50321),f326(f75(x50321),x50322)),f326(f75(x50321),x50322))
% 157.55/157.22 [5033]~P86(x50331)+E(f326(f75(x50331),f326(f78(x50331),x50332)),f326(f75(x50331),x50332))
% 157.55/157.22 [5034]~P69(x50341)+E(f326(f165(x50341),f326(f168(x50341),x50342)),f326(f165(x50341),x50342))
% 157.55/157.22 [5039]~E(x50391,f326(a112,f2(a909)))+E(f326(f326(f243(a909),x50391),x50392),f326(a112,f2(a909)))
% 157.55/157.22 [5048]~P73(x50481)+E(f326(f326(f3(x50481),f2(x50481)),x50482),f326(f78(x50481),x50482))
% 157.55/157.22 [5049]~E(x50492,f2(a909))+E(f139(a909,f326(f301(a909,x50491),x50492)),f113(a909))
% 157.55/157.22 [5058]~P94(x50581)+E(f326(f326(f79(x50581),x50582),f326(f103(x50581),a82)),x50582)
% 157.55/157.22 [5059]E(x50591,f2(a1))+E(f47(f326(f75(a1),x50592),f326(f75(a1),x50591)),f53(x50592,x50591))
% 157.55/157.22 [5075]~E(x50751,x50752)+P105(f326(f326(f234(a909),x50751),x50752))
% 157.55/157.22 [5079]~E(x50791,x50792)+P105(f326(f326(f286(a909),x50791),x50792))
% 157.55/157.22 [5086]~E(x50861,f2(a99))+E(f326(f326(f79(a909),f326(a22,x50861)),x50862),x50862)
% 157.55/157.22 [5100]~P5(x51001)+P5(f326(f326(f243(a1),x51001),x51002))
% 157.55/157.22 [5101]~P95(x51011)+E(f326(f326(f110(x51011),x51012),f326(f78(x51011),x51012)),f241(x51011))
% 157.55/157.22 [5102]~P95(x51021)+E(f326(f326(f101(x51021),x51022),f326(f78(x51021),x51022)),f188(x51021))
% 157.55/157.22 [5103]~P73(x51031)+E(f326(f326(f79(x51031),x51032),f326(f78(x51031),x51032)),f2(x51031))
% 157.55/157.22 [5128]E(x51281,f2(a909))+~E(f326(f78(a1),f326(f100(a1),x51282)),f326(f100(a1),x51281))
% 157.55/157.22 [5129]E(x51291,f2(a909))+~E(f326(f78(a1),f326(f100(a1),x51291)),f326(f100(a1),x51292))
% 157.55/157.22 [5139]E(f194(x51391,x51392),f2(a1))+P105(f326(f326(f234(a1),x51392),x51391))
% 157.55/157.22 [5140]E(f178(x51401,x51402),f113(a1))+P105(f326(f326(f234(a1),x51401),x51402))
% 157.55/157.22 [5141]E(f240(x51411,x51412),f2(a99))+P105(f326(f326(f235(a99),x51411),x51412))
% 157.55/157.22 [5154]E(x51541,f326(a112,f2(a909)))+~E(f326(f326(f80(a909),x51542),x51541),f326(a112,f2(a909)))
% 157.55/157.22 [5155]E(x51551,f326(a112,f2(a909)))+~E(f326(f326(f80(a909),x51551),x51552),f326(a112,f2(a909)))
% 157.55/157.22 [5156]~P106(x51561)+P105(f326(f326(f234(x51561),x51562),x51562))
% 157.55/157.22 [5157]~P112(x51571)+P105(f326(f326(f286(x51571),x51572),x51572))
% 157.55/157.22 [5160]~P94(x51601)+E(f326(f326(f80(x51601),x51602),f326(f103(x51601),a97)),f326(f78(x51601),x51602))
% 157.55/157.22 [5180]~P94(x51801)+E(f326(f78(x51801),f326(f103(x51801),x51802)),f326(f103(x51801),f326(f78(a1),x51802)))
% 157.55/157.22 [5181]~P140(x51811)+E(f326(f78(x51811),f326(f102(x51811),x51812)),f326(f102(x51811),f326(f78(a1),x51812)))
% 157.55/157.22 [5211]~E(x52111,f326(a112,x52112))+P105(f326(f326(f235(a909),f2(a909)),x52111))
% 157.55/157.22 [5229]~P108(x52291)+E(f326(f78(f917(x52291,a905)),f326(f281(x52291),x52292)),f326(f282(x52291),x52292))
% 157.55/157.22 [5230]~P108(x52301)+E(f326(f78(f917(x52301,a905)),f326(f300(x52301),x52302)),f326(f303(x52301),x52302))
% 157.55/157.22 [5231]~P108(x52311)+E(f326(f78(f917(x52311,a905)),f326(f303(x52311),x52312)),f326(f300(x52311),x52312))
% 157.55/157.22 [5232]~P108(x52321)+E(f326(f78(f917(x52321,a905)),f326(f282(x52321),x52322)),f326(f281(x52321),x52322))
% 157.55/157.22 [5240]~E(f326(f100(a1),x52402),x52401)+P105(f326(f326(f234(a1),f2(a1)),x52401))
% 157.55/157.22 [5247]~E(x52472,f2(a1))+E(f53(x52471,x52472),f326(f326(f251(a1,a1),f2(a1)),f326(f75(a1),x52471)))
% 157.55/157.22 [5249]~P1(x52491)+P105(f326(f326(f234(x52491),f188(x52491)),x52492))
% 157.55/157.22 [5250]~P112(x52501)+P105(f326(f326(f286(x52501),f77(x52501)),x52502))
% 157.55/157.22 [5283]E(x52831,x52832)+~E(f326(f326(f79(a1),x52831),x52831),f326(f326(f79(a1),x52832),x52832))
% 157.55/157.22 [5287]~P105(f326(x52871,x52872))+P105(f326(x52871,f326(a104,f334(x52871))))
% 157.55/157.22 [5313]~P118(x53131)+E(f326(f326(f80(x53131),f81(x53131,x53132)),f326(f75(x53131),x53132)),x53132)
% 157.55/157.22 [5320]~E(x53202,f2(a909))+E(f84(f916(a909,a909),f48(x53201,x53202)),f326(f326(f251(a909,a909),f2(a909)),x53201))
% 157.55/157.22 [5325]~E(x53251,x53252)+~P105(f326(f326(f235(a909),x53251),x53252))
% 157.55/157.22 [5326]~E(x53261,x53262)+~P105(f326(f326(f235(a1),x53261),x53262))
% 157.55/157.22 [5329]~P143(x53291)+E(f326(f326(f79(x53291),f77(x53291)),f326(f100(x53291),x53292)),f326(f100(x53291),f326(a112,x53292)))
% 157.55/157.22 [5333]~E(x53331,f2(a909))+~P105(f326(f326(f235(a909),x53332),x53331))
% 157.55/157.22 [5347]E(f152(x53471,x53472),x53472)+~E(f326(f189(f910(x53471)),f152(x53471,x53472)),f326(f189(f910(x53471)),x53472))
% 157.55/157.22 [5348]E(f326(f35(x53481),f326(f172(x53481),x53482)),f326(f189(f910(x53481)),x53482))+~P105(f326(f137(x53481),x53482))
% 157.55/157.22 [5363]~P105(f326(x53631,f336(x53631)))+P105(f326(x53631,f326(f100(a1),x53632)))
% 157.55/157.22 [5374]E(f240(x53741,x53742),x53742)+~P105(f326(f326(f235(a99),x53741),x53742))
% 157.55/157.22 [5376]E(f271(x53761,x53762),f77(a99))+~P105(f326(f326(f235(a99),x53762),x53761))
% 157.55/157.22 [5377]E(f178(x53771,x53772),f113(a1))+~P105(f326(f326(f235(a1),x53772),x53771))
% 157.55/157.22 [5378]E(f128(x53781,x53782),f115(a1))+~P105(f326(f326(f235(a1),x53781),x53782))
% 157.55/157.22 [5380]~P109(x53801)+E(f302(x53801,x53802,x53802),f326(f326(f308(x53801),x53802),f188(f917(x53801,a905))))
% 157.55/157.22 [5400]~E(f326(f326(f3(a909),x54001),x54002),f2(a909))+P105(f326(f326(f234(a909),x54001),x54002))
% 157.55/157.22 [5423]~E(x54232,f2(a909))+E(f55(x54231,x54232,f113(x54231)),f326(f326(f151(f910(x54231)),f113(x54231)),f113(f910(x54231))))
% 157.55/157.22 [5427]~P106(x54271)+~P105(f326(f326(f235(x54271),x54272),x54272))
% 157.55/157.22 [5429]~E(f45(a1,x54291,x54292),f2(a1))+E(f45(a1,x54291,f326(f78(a1),x54292)),f2(a1))
% 157.55/157.22 [5431]~E(f45(a1,x54311,x54312),f2(a1))+E(f45(a1,f326(f78(a1),x54311),x54312),f2(a1))
% 157.55/157.22 [5439]E(f326(f301(a909,x54391),f326(a112,x54392)),f188(f917(a909,a905)))+P105(f326(f326(f234(a909),x54391),x54392))
% 157.55/157.22 [5463]E(f139(a909,f326(f301(a909,x54631),x54632)),f113(a909))+P105(f326(f326(f235(a909),x54631),x54632))
% 157.55/157.22 [5468]~E(f326(f35(x54681),f326(f172(x54681),x54682)),f326(f189(f910(x54681)),x54682))+P105(f326(f137(x54681),x54682))
% 157.55/157.22 [5472]~P105(f326(f137(x54721),x54722))+P105(f326(f137(x54721),f326(f167(x54721),x54722)))
% 157.55/157.22 [5473]~P105(f326(f137(x54731),x54732))+P105(f326(f137(x54731),f326(f171(x54731),x54732)))
% 157.55/157.22 [5474]~P105(f326(f137(x54741),x54742))+P105(f326(f137(x54741),f326(f168(x54741),x54742)))
% 157.55/157.22 [5482]P105(f326(x54821,x54822))+~P105(f326(x54821,f326(a104,f364(x54821))))
% 157.55/157.22 [5483]P105(f326(f326(f234(a909),x54832),x54831))+P105(f326(f326(f234(a909),x54831),x54832))
% 157.55/157.22 [5484]P105(f326(f326(f234(a1),x54842),x54841))+P105(f326(f326(f234(a1),x54841),x54842))
% 157.55/157.22 [5488]~P86(x54881)+P105(f326(f326(f234(x54881),x54882),f326(f75(x54881),x54882)))
% 157.55/157.22 [5491]P105(f326(x54911,f337(x54911)))+~P105(f326(x54911,f326(f100(a1),x54912)))
% 157.55/157.22 [5516]E(f326(f326(f3(a909),x55161),x55162),f2(a909))+~P105(f326(f326(f234(a909),x55161),x55162))
% 157.55/157.22 [5517]E(f326(f326(f36(a909),x55171),x55172),f2(a909))+~P105(f326(f326(f235(a909),x55171),x55172))
% 157.55/157.22 [5535]E(f45(a909,x55351,x55352),x55351)+~P105(f326(f326(f235(a909),x55351),x55352))
% 157.55/157.22 [5543]E(f45(a1,x55431,f326(f78(a1),x55432)),f291(x55431,x55432))+P105(f326(f326(f234(a1),f2(a1)),x55432))
% 157.55/157.22 [5556]E(f326(f326(f3(a1),x55561),x55562),f194(x55561,x55562))+~P105(f326(f326(f234(a1),x55562),x55561))
% 157.55/157.22 [5576]P105(f326(f326(f234(a1),f2(a1)),f336(x55761)))+P105(f326(x55761,f326(f100(a1),x55762)))
% 157.55/157.22 [5589]~P124(x55891)+P105(f326(f326(f234(x55891),f2(x55891)),f326(f100(x55891),x55892)))
% 157.55/157.22 [5590]~P86(x55901)+P105(f326(f326(f234(x55901),f2(x55901)),f326(f75(x55901),x55902)))
% 157.55/157.22 [5618]E(f326(f326(f79(a909),x56181),f591(x56182,x56181)),x56182)+~P105(f326(f326(f234(a909),x56181),x56182))
% 157.55/157.22 [5633]E(f302(a1,x56331,x56332),f188(f917(a1,a905)))+~P105(f326(f326(f235(a1),x56332),x56331))
% 157.55/157.22 [5635]~P118(x56351)+E(f326(f326(f80(x56351),f326(f75(x56351),x56352)),f326(f75(x56351),x56352)),f326(f326(f80(x56351),x56352),x56352))
% 157.55/157.22 [5641]E(f139(a909,f326(f301(a909,x56411),f326(a112,x56412))),f113(a909))+P105(f326(f326(f234(a909),x56411),x56412))
% 157.55/157.22 [5645]E(f326(f326(f36(a1),x56451),x56452),f292(x56451,x56452))+~P105(f326(f326(f234(a1),f2(a1)),x56452))
% 157.55/157.22 [5665]P105(f326(f137(x56651),x56652))+~P105(f326(f137(x56651),f326(f167(x56651),x56652)))
% 157.55/157.22 [5666]P105(f326(f137(x56661),x56662))+~P105(f326(f137(x56661),f326(f168(x56661),x56662)))
% 157.55/157.22 [5693]P105(f326(f61(a909),x56931))+P105(f326(f326(f328(a909),f373(x56931,x56932)),x56931))
% 157.55/157.22 [5694]P105(f326(f61(a909),x56941))+P105(f326(f326(f328(a909),f404(x56941,x56942)),x56941))
% 157.55/157.22 [5697]P105(f326(f326(f235(a909),x56972),f326(a112,x56971)))+P105(f326(f326(f235(a909),x56971),x56972))
% 157.55/157.22 [5698]E(f45(a1,x56981,x56982),f291(x56981,x56982))+~P105(f326(f326(f234(a1),f2(a1)),x56982))
% 157.55/157.22 [5702]E(f139(a909,f326(f301(a909,x57021),x57022)),f113(a909))+~P105(f326(f326(f234(a909),x57022),x57021))
% 157.55/157.22 [5703]~P79(x57031)+E(f326(f309(x57031,x57031,f78(x57031)),f326(f281(x57031),x57032)),f326(f303(x57031),f326(f78(x57031),x57032)))
% 157.55/157.22 [5704]~P79(x57041)+E(f326(f309(x57041,x57041,f78(x57041)),f326(f300(x57041),x57042)),f326(f282(x57041),f326(f78(x57041),x57042)))
% 157.55/157.22 [5705]~P79(x57051)+E(f326(f309(x57051,x57051,f78(x57051)),f326(f303(x57051),x57052)),f326(f281(x57051),f326(f78(x57051),x57052)))
% 157.55/157.22 [5706]~P79(x57061)+E(f326(f309(x57061,x57061,f78(x57061)),f326(f282(x57061),x57062)),f326(f300(x57061),f326(f78(x57061),x57062)))
% 157.55/157.22 [5717]E(x57171,f188(f917(x57172,a905)))+P105(f326(f326(f328(x57172),f374(x57171,x57172)),x57171))
% 157.55/157.22 [5718]E(x57181,f188(f917(x57182,a905)))+P105(f326(f326(f328(x57182),f391(x57181,x57182)),x57181))
% 157.55/157.22 [5729]~P105(f326(f326(f235(a909),x57291),x57292))+P105(f326(f326(f234(a909),x57291),x57292))
% 157.55/157.22 [5730]~P105(f326(f326(f235(a1),x57301),x57302))+P105(f326(f326(f234(a1),x57301),x57302))
% 157.55/157.22 [5746]E(f47(x57461,x57462),f326(f326(f251(a1,a1),f2(a1)),x57461))+~P105(f326(f326(f235(a1),x57461),x57462))
% 157.55/157.22 [5748]E(f215(f326(f78(a1),x57481),f326(f78(a1),x57482)),f215(x57481,x57482))+~P105(f326(f326(f235(a1),x57482),f2(a1)))
% 157.55/157.22 [5760]E(x57601,x57602)+~E(f326(a5,f326(a112,f326(a22,x57601))),f326(a5,f326(a112,f326(a22,x57602))))
% 157.55/157.22 [5765]E(f47(x57651,x57652),f326(f326(f251(a1,a1),f2(a1)),x57651))+~P105(f326(f326(f234(a1),x57652),f2(a1)))
% 157.55/157.22 [5794]E(f45(a909,f326(f103(a909),x57941),f326(f103(a909),x57942)),f2(a909))+~P105(f326(a193,f326(f103(a1),x57941)))
% 157.55/157.22 [5808]P105(f326(f326(f234(a1),f2(a1)),f337(x58081)))+~P105(f326(x58081,f326(f100(a1),x58082)))
% 157.55/157.22 [5841]P39(f302(a1,x58411,x58412))+~P105(f326(f326(f234(a1),f2(a1)),x58411))
% 157.55/157.22 [5846]~P105(f326(f61(x58461),x58462))+P105(f326(f61(f917(x58461,a905)),f326(f307(x58461),x58462)))
% 157.55/157.22 [5859]E(f326(f326(f79(a1),x58591),f326(f100(a1),f340(x58592,x58591))),x58592)+~P105(f326(f326(f234(a1),x58591),x58592))
% 157.55/157.22 [5867]P105(f326(f326(f234(a909),x58671),x58672))+P105(f326(f326(f234(a909),f326(a112,x58672)),x58671))
% 157.55/157.22 [5911]E(f326(f326(f36(a909),f326(f103(a909),x59111)),f326(f103(a909),x59112)),f2(a909))+~P105(f326(a193,f326(f103(a1),x59111)))
% 157.55/157.22 [5912]E(f326(f326(f80(a909),f326(f103(a909),x59121)),f326(f103(a909),x59122)),f2(a909))+~P105(f326(f326(f235(a1),x59121),a82))
% 157.55/157.22 [5914]P105(f326(f326(f234(a909),x59141),f326(a112,x59142)))+~P105(f326(f326(f234(a909),x59141),x59142))
% 157.55/157.22 [5916]P105(f326(f326(f235(a909),x59161),f326(a112,x59162)))+~P105(f326(f326(f234(a909),x59161),x59162))
% 157.55/157.22 [5918]P105(f326(f326(f235(a909),x59181),f326(a112,x59182)))+~P105(f326(f326(f235(a909),x59181),x59182))
% 157.55/157.22 [5921]~E(x59211,x59212)+P105(f326(f326(f235(a1),x59211),f326(f326(f79(a1),x59212),f77(a1))))
% 157.55/157.22 [5924]E(f45(a1,x59241,x59242),f2(a1))+E(f326(f326(f3(a1),x59242),f45(a1,x59241,x59242)),f45(a1,f326(f78(a1),x59241),x59242))
% 157.55/157.22 [5933]E(x59331,f113(x59332))+P105(f326(f326(f328(x59332),f144(x59332,x59331)),f326(f172(x59332),x59331)))
% 157.55/157.22 [5945]E(f84(f916(a909,a909),f48(x59451,x59452)),f326(f326(f251(a909,a909),f2(a909)),x59451))+~P105(f326(f326(f235(a909),x59451),x59452))
% 157.55/157.22 [5989]E(f326(f326(f3(a909),f326(f103(a909),x59891)),f326(f103(a909),x59892)),f326(f103(a909),x59891))+~P105(f326(f326(f235(a1),x59892),a82))
% 157.55/157.22 [5990]E(f326(f326(f79(a909),f326(f103(a909),x59901)),f326(f103(a909),x59902)),f326(f103(a909),x59902))+~P105(f326(f326(f235(a1),x59901),a82))
% 157.55/157.22 [5997]E(f326(a112,f326(f326(f79(a909),x59971),f796(x59972,x59971))),x59972)+~P105(f326(f326(f235(a909),x59971),x59972))
% 157.55/157.22 [6021]P105(f326(x60211,x60212))+~P105(f326(x60211,f326(a88,f567(x60212,x60211))))
% 157.55/157.22 [6022]P105(f326(x60221,x60222))+~P105(f326(x60221,f326(a5,f811(x60222,x60221))))
% 157.55/157.22 [6031]~P105(f326(f326(f235(a909),x60311),f326(a112,x60312)))+P105(f326(f326(f234(a909),x60311),x60312))
% 157.55/157.22 [6077]E(f326(f326(f308(a909),x60771),f326(f301(a909,x60772),x60771)),f326(f301(a909,x60772),f326(a112,x60771)))+~P105(f326(f326(f234(a909),x60772),x60771))
% 157.55/157.22 [6079]E(x60791,f113(x60792))+E(f326(f326(f134(x60792),f114(x60792,x60791)),f326(f326(f151(x60792),f144(x60792,x60791)),f113(x60792))),x60791)
% 157.55/157.22 [6096]P105(f326(f61(x60961),x60962))+~P105(f326(f326(f235(a909),f2(a909)),f326(f35(x60961),x60962)))
% 157.55/157.22 [6099]~E(x60991,f188(f917(x60992,a905)))+~P105(f326(f326(f235(a909),f2(a909)),f326(f35(x60992),x60991)))
% 157.55/157.22 [6111]~P105(f326(f326(f235(a909),x61111),x61112))+P105(f326(f326(f234(a909),f326(a112,x61111)),x61112))
% 157.55/157.22 [6115]~P108(x61151)+E(f150(x61151,x61151,f7(x61151),f152(x61151,x61152)),f139(x61151,f326(f172(x61151),x61152)))
% 157.55/157.22 [6118]E(x61181,f113(x61182))+P105(f326(f326(f328(x61182),f326(f141(x61182),x61181)),f326(f172(x61182),x61181)))
% 157.55/157.22 [6124]~P124(x61241)+P105(f326(f326(f235(x61241),x61242),f326(f326(f79(x61241),x61242),f77(x61241))))
% 157.55/157.22 [6126]~P86(x61261)+P105(f326(f326(f234(x61261),f326(f78(x61261),x61262)),f326(f75(x61261),x61262)))
% 157.55/157.22 [6140]~E(x61401,x61402)+E(f289(a909,f286(a909),x61401,x61402),f326(f326(f308(a909),x61401),f188(f917(a909,a905))))
% 157.55/157.22 [6158]P105(f326(f61(a909),x61581))+~P105(f326(f326(f234(a909),f404(x61581,x61582)),x61582))
% 157.55/157.22 [6159]P105(f326(f61(a909),x61591))+~P105(f326(f326(f235(a909),f373(x61591,x61592)),x61592))
% 157.55/157.22 [6162]~P105(f326(f61(f916(x61621,x61621)),x61622))+P105(f326(f61(x61621),f326(f280(x61621),x61622)))
% 157.55/157.22 [6217]E(f289(a909,f286(a909),x62171,x62172),f188(f917(a909,a905)))+P105(f326(f326(f286(a909),x62171),x62172))
% 157.55/157.22 [6220]~P105(f326(f326(f235(a909),x62202),f326(a112,x62201)))+~P105(f326(f326(f235(a909),x62201),x62202))
% 157.55/157.22 [6221]~P109(x62211)+E(f326(f326(f101(f917(x62211,a905)),f326(f300(x62211),x62212)),f326(f282(x62211),x62212)),f326(f326(f308(x62211),x62212),f188(f917(x62211,a905))))
% 157.55/157.22 [6233]P105(f326(f61(x62331),x62332))+~P105(f326(f61(f917(x62331,a905)),f326(f307(x62331),x62332)))
% 157.55/157.22 [6255]P105(f326(f326(f234(a909),f326(a112,x62551)),f326(a112,x62552)))+~P105(f326(f326(f234(a909),x62551),x62552))
% 157.55/157.22 [6256]P105(f326(f326(f234(a909),f326(a22,x62561)),f326(a22,x62562)))+~P105(f326(f326(f234(a99),x62561),x62562))
% 157.55/157.22 [6257]P105(f326(f326(f234(a99),f326(a5,x62571)),f326(a5,x62572)))+~P105(f326(f326(f234(a909),x62571),x62572))
% 157.55/157.22 [6259]P105(f326(f326(f235(a909),f326(a112,x62591)),f326(a112,x62592)))+~P105(f326(f326(f235(a909),x62591),x62592))
% 157.55/157.22 [6260]P105(f326(f326(f235(a909),f326(a22,x62601)),f326(a22,x62602)))+~P105(f326(f326(f235(a99),x62601),x62602))
% 157.55/157.22 [6261]P105(f326(f326(f235(a99),f326(a5,x62611)),f326(a5,x62612)))+~P105(f326(f326(f235(a909),x62611),x62612))
% 157.55/157.22 [6266]E(x62661,x62662)+~E(f326(f309(a909,a1,f100(a1)),x62661),f326(f309(a909,a1,f100(a1)),x62662))
% 157.55/157.22 [6282]P105(f326(f326(f234(a909),x62821),x62822))+~P105(f326(f326(f234(a909),f326(a112,x62821)),x62822))
% 157.55/157.22 [6285]P105(f326(f326(f235(a909),x62851),x62852))+~P105(f326(f326(f234(a909),f326(a112,x62851)),x62852))
% 157.55/157.22 [6286]P105(f326(f326(f235(a909),x62861),x62862))+~P105(f326(f326(f235(a909),f326(a112,x62861)),x62862))
% 157.55/157.22 [6305]E(f45(a1,x63051,x63052),f2(a1))+E(f326(f326(f3(a1),f45(a1,x63051,x63052)),x63052),f45(a1,x63051,f326(f78(a1),x63052)))
% 157.55/157.22 [6371]E(f326(f35(f917(x63711,a905)),f326(f307(x63711),x63712)),f326(f326(f243(a909),f326(a112,f326(a112,f2(a909)))),f326(f35(x63711),x63712)))+~P105(f326(f61(x63711),x63712))
% 157.55/157.22 [6374]E(x63741,f113(x63742))+E(f326(f326(f164(x63742),x63741),f326(f326(f3(a909),f326(f189(f910(x63742)),x63741)),f77(a909))),f144(x63742,x63741))
% 157.55/157.22 [6396]E(x63961,f113(x63962))+E(f326(f326(f134(x63962),f326(f171(x63962),x63961)),f326(f326(f151(x63962),f326(f141(x63962),x63961)),f113(x63962))),f326(f167(x63962),x63961))
% 157.55/157.22 [6427]~P105(f326(f61(x64271),f37(f917(x64271,a905),x64272)))+P105(f326(f61(f917(x64271,a905)),x64272))
% 157.55/157.22 [6449]P105(f326(f326(f234(a909),f326(f103(a909),x64491)),f326(f103(a909),x64492)))+~P105(f326(f326(f234(a1),x64491),a82))
% 157.55/157.22 [6470]~P105(f326(f326(f235(a1),x64701),x64702))+P105(f326(f326(f234(a1),x64701),f326(f326(f3(a1),x64702),f77(a1))))
% 157.55/157.22 [6471]~P105(f326(f326(f234(a1),x64711),x64712))+P105(f326(f326(f235(a1),x64711),f326(f326(f79(a1),x64712),f77(a1))))
% 157.55/157.22 [6472]~P105(f326(f326(f235(a1),x64721),x64722))+P105(f326(f326(f235(a1),x64721),f326(f326(f79(a1),x64722),f77(a1))))
% 157.55/157.22 [6474]~P105(f326(f326(f234(a1),x64741),x64742))+P105(f326(f326(f234(a909),f326(f103(a909),x64741)),f326(f103(a909),x64742)))
% 157.55/157.22 [6475]~P105(f326(f326(f234(a1),x64751),x64752))+P105(f326(f326(f234(a1),f326(f103(a1),x64751)),f326(f103(a1),x64752)))
% 157.55/157.22 [6477]~P105(f326(f326(f234(a909),x64771),x64772))+P105(f326(f326(f234(a1),f326(f100(a1),x64771)),f326(f100(a1),x64772)))
% 157.55/157.22 [6478]~P105(f326(f326(f235(a1),x64781),x64782))+P105(f326(f326(f235(a1),f326(f103(a1),x64781)),f326(f103(a1),x64782)))
% 157.55/157.22 [6480]~P105(f326(f326(f235(a909),x64801),x64802))+P105(f326(f326(f235(a1),f326(f100(a1),x64801)),f326(f100(a1),x64802)))
% 157.55/157.22 [6501]~P105(f326(f326(f234(a909),x65011),x65012))+~P105(f326(f326(f234(a909),f326(a112,x65012)),x65011))
% 157.55/157.22 [6544]~P105(f326(f326(f234(a909),f326(a112,x65441)),f326(a112,x65442)))+P105(f326(f326(f234(a909),x65441),x65442))
% 157.55/157.22 [6545]~P105(f326(f326(f234(a99),f326(a5,x65451)),f326(a5,x65452)))+P105(f326(f326(f234(a909),x65451),x65452))
% 157.55/157.22 [6546]~P105(f326(f326(f234(a909),f326(a22,x65461)),f326(a22,x65462)))+P105(f326(f326(f234(a99),x65461),x65462))
% 157.55/157.22 [6548]~P105(f326(f326(f235(a909),f326(a112,x65481)),f326(a112,x65482)))+P105(f326(f326(f235(a909),x65481),x65482))
% 157.55/157.22 [6549]~P105(f326(f326(f235(a99),f326(a5,x65491)),f326(a5,x65492)))+P105(f326(f326(f235(a909),x65491),x65492))
% 157.55/157.22 [6550]~P105(f326(f326(f235(a909),f326(a104,x65501)),f326(a104,x65502)))+P105(f326(f326(f235(a1),x65501),x65502))
% 157.55/157.22 [6551]~P105(f326(f326(f235(a909),f326(a22,x65511)),f326(a22,x65512)))+P105(f326(f326(f235(a99),x65511),x65512))
% 157.55/157.22 [6590]~P105(f326(f326(f235(a909),f326(a104,x65902)),f326(a104,x65901)))+P105(f326(f326(f235(a1),f2(a1)),x65901))
% 157.55/157.22 [6621]P105(f326(f326(f234(a1),f2(a1)),f45(a1,x66211,x66212)))+~P105(f326(f326(f235(a1),f2(a1)),x66212))
% 157.55/157.22 [6783]P36(x67831,x67832)+~E(f326(f326(f288(x67831,x67831,x67831),x67832),x67832),f188(f917(f916(x67831,x67831),a905)))
% 157.55/157.22 [6799]~P36(x67991,x67992)+P36(x67991,f326(f326(f288(x67991,x67991,x67991),x67992),x67992))
% 157.55/157.22 [6810]P105(f326(f326(f234(a1),x68101),x68102))+~P105(f326(f326(f235(a1),x68101),f326(f326(f79(a1),x68102),f77(a1))))
% 157.55/157.22 [6811]P105(f326(f326(f235(a1),x68111),x68112))+~P105(f326(f326(f234(a1),x68111),f326(f326(f3(a1),x68112),f77(a1))))
% 157.55/157.22 [6814]P105(f326(f326(f234(a909),x68141),x68142))+~P105(f326(f326(f234(a1),f326(f100(a1),x68141)),f326(f100(a1),x68142)))
% 157.55/157.22 [6815]P105(f326(f326(f234(a1),x68151),x68152))+~P105(f326(f326(f234(a1),f326(f103(a1),x68151)),f326(f103(a1),x68152)))
% 157.55/157.22 [6817]P105(f326(f326(f235(a909),x68171),x68172))+~P105(f326(f326(f235(a1),f326(f100(a1),x68171)),f326(f100(a1),x68172)))
% 157.55/157.22 [6818]P105(f326(f326(f235(a1),x68181),x68182))+~P105(f326(f326(f235(a909),f326(f103(a909),x68181)),f326(f103(a909),x68182)))
% 157.55/157.22 [6819]P105(f326(f326(f235(a1),x68191),x68192))+~P105(f326(f326(f235(a1),f326(f103(a1),x68191)),f326(f103(a1),x68192)))
% 157.55/157.22 [6891]~E(f289(a909,f286(a909),x68911,x68912),f188(f917(a909,a905)))+~P105(f326(f326(f286(a909),x68911),x68912))
% 157.55/157.22 [6915]~E(f691(x69152,x69151),f113(x69151))+E(f326(f142(f910(x69151),f910(x69151),f134(x69151),f113(x69151)),x69152),f113(x69151))
% 157.55/157.22 [6916]~E(f692(x69162,x69161),f113(x69161))+E(f326(f142(f910(x69161),f910(x69161),f134(x69161),f113(x69161)),x69162),f113(x69161))
% 157.55/157.22 [6920]~P4(x69201)+E(f326(f142(x69201,x69201,f110(x69201),f188(x69201)),x69202),f37(x69201,f326(f172(x69201),x69202)))
% 157.55/157.22 [6921]~P4(x69211)+E(f326(f142(x69211,x69211,f101(x69211),f241(x69211)),x69212),f38(x69211,f326(f172(x69211),x69212)))
% 157.55/157.22 [6935]E(x69351,f2(a99))+E(f326(f326(f79(a909),f326(a22,f326(f326(f3(a99),x69351),f77(a99)))),f326(a112,x69352)),f326(f326(f79(a909),f326(a22,x69351)),x69352))
% 157.55/157.22 [6984]P105(f326(f326(f235(a1),f326(f326(f3(a1),x69841),x69842)),f2(a1)))+~P105(f326(f326(f235(a1),x69841),x69842))
% 157.55/157.22 [7009]~P108(x70091)+E(f326(f326(f110(f917(x70091,a905)),f326(f326(f308(x70091),x70092),f188(f917(x70091,a905)))),f326(f303(x70091),x70092)),f326(f282(x70091),x70092))
% 157.55/157.22 [7082]~P58(x70821,x70822)+P36(x70821,f326(f261(f916(x70821,x70821)),f326(f256(x70821,x70821,a905),x70822)))
% 157.55/157.22 [7083]~P58(x70831,x70832)+P56(x70831,f326(f261(f916(x70831,x70831)),f326(f256(x70831,x70831,a905),x70832)))
% 157.55/157.22 [7084]~P48(x70841,x70842)+P37(x70841,f326(f261(f916(x70841,x70841)),f326(f256(x70841,x70841,a905),x70842)))
% 157.55/157.22 [7085]~P49(x70851,x70852)+P50(x70851,f326(f261(f916(x70851,x70851)),f326(f256(x70851,x70851,a905),x70852)))
% 157.55/157.22 [7086]E(x70861,f188(f917(x70862,a905)))+~P105(f326(f326(f234(f917(x70862,a905)),x70861),f188(f917(x70862,a905))))
% 157.55/157.22 [7170]~P105(f326(f326(f235(a909),f2(a909)),x71702))+P105(f326(f326(f234(a909),f45(a909,x71701,x71702)),x71702))
% 157.55/157.22 [7171]~P105(f326(f326(f234(a1),f2(a1)),x71711))+P105(f326(f326(f234(a1),f45(a1,x71711,x71712)),x71711))
% 157.55/157.22 [7172]~P105(f326(f326(f235(a909),f2(a909)),x71722))+P105(f326(f326(f235(a909),f45(a909,x71721,x71722)),x71722))
% 157.55/157.22 [7174]~P105(f326(f326(f235(a1),f2(a1)),x71742))+P105(f326(f326(f235(a1),f45(a1,x71741,x71742)),x71742))
% 157.55/157.22 [7250]~P109(x72501)+E(f326(f326(f3(f917(x72501,a905)),f326(f326(f308(x72501),x72502),f188(f917(x72501,a905)))),f326(f281(x72501),x72502)),f326(f326(f308(x72501),x72502),f188(f917(x72501,a905))))
% 157.55/157.22 [7323]~P42(x73231,x73232)+P51(x73231,f241(f917(x73231,a905)),f326(f261(f916(x73231,x73231)),f326(f256(x73231,x73231,a905),x73232)))
% 157.55/157.22 [7324]P105(f326(x73241,x73242))+P105(f326(f326(f328(f917(f916(a909,a909),a905)),f567(x73242,x73241)),a98))
% 157.55/157.22 [7368]E(f326(f326(f134(a909),f139(a909,f326(f301(a909,x73681),x73682))),f326(f326(f151(a909),x73682),f113(a909))),f139(a909,f326(f301(a909,x73681),f326(a112,x73682))))+~P105(f326(f326(f234(a909),x73681),x73682))
% 157.55/157.22 [7522]E(x75221,f2(a909))+~E(f326(f142(a909,a909,f79(a909),x75221),x75222),f2(a909))
% 157.55/157.22 [7547]~P105(f326(f326(f235(a1),f326(f326(f3(a1),x75471),x75472)),f2(a1)))+P105(f326(f326(f235(a1),x75471),x75472))
% 157.55/157.22 [7574]P36(x75741,x75742)+~P36(x75741,f326(f326(f288(x75741,x75741,x75741),x75742),x75742))
% 157.55/157.22 [7600]~P105(f326(f326(f234(a909),f326(a112,x76001)),x76002))+P105(f185(a905,a238,f326(f234(a909),x76001),x76002))
% 157.55/157.22 [7752]P24(a909,a909,f326(f326(f9(a909,a909,a909),f3(a909)),x77521),x77522)+P105(f326(f326(f328(a909),f578(x77521,x77522)),x77522))
% 157.55/157.22 [7808]E(f326(f326(f326(f65(a909,x78081,f79(a909)),f326(f18(a909,x78081),f77(a909))),f2(a909)),x78082),f326(f35(x78081),x78082))+~P105(f326(f61(x78081),x78082))
% 157.55/157.22 [7849]P24(a909,a909,f326(f326(f9(a909,a909,a909),f3(a909)),x78491),x78492)+~P105(f326(f326(f234(a909),x78491),f578(x78491,x78492)))
% 157.55/157.22 [7905]P36(x79051,x79052)+P105(f326(f326(f234(f917(x79051,a905)),f576(x79052,x79051)),f326(f284(x79051,x79051,x79052),f576(x79052,x79051))))
% 157.55/157.22 [7910]P58(x79101,x79102)+~P36(x79101,f326(f261(f916(x79101,x79101)),f326(f256(x79101,x79101,a905),x79102)))
% 157.55/157.22 [7911]P48(x79111,x79112)+~P37(x79111,f326(f261(f916(x79111,x79111)),f326(f256(x79111,x79111,a905),x79112)))
% 157.55/157.22 [7912]P49(x79121,x79122)+~P50(x79121,f326(f261(f916(x79121,x79121)),f326(f256(x79121,x79121,a905),x79122)))
% 157.55/157.22 [7978]P105(f326(f326(f234(a909),f326(a112,x79781)),x79782))+~P105(f185(a905,a238,f326(f234(a909),x79781),x79782))
% 157.55/157.22 [8033]P105(f326(f326(f328(f916(a909,a909)),f326(f326(f251(a909,a909),x80331),x80332)),f306(a909,a316)))+~P105(f326(f326(f234(a909),x80331),x80332))
% 157.55/157.22 [8128]P42(x81281,x81282)+~P51(x81281,f241(f917(x81281,a905)),f326(f261(f916(x81281,x81281)),f326(f256(x81281,x81281,a905),x81282)))
% 157.55/157.22 [8183]~P105(f326(f137(x81831),x81832))+P105(f326(f137(f917(x81831,a905)),f326(f326(f154(f910(x81831),f917(x81831,a905)),f172(x81831)),f54(x81831,x81832))))
% 157.55/157.22 [8379]~P36(x83791,f326(f285(x83791,x83791),x83792))+P36(x83791,f326(f285(x83791,x83791),f326(f326(f288(x83791,x83791,x83791),x83792),f306(x83791,x83792))))
% 157.55/157.22 [8477]P25(x84771,a909,f817(x84772,x84771),x84772,f326(f301(a909,f2(a909)),f326(f35(x84771),x84772)))+~P105(f326(f61(x84771),x84772))
% 157.55/157.22 [8478]P25(a909,x84781,f818(x84782,x84781),f326(f301(a909,f2(a909)),f326(f35(x84781),x84782)),x84782)+~P105(f326(f61(x84781),x84782))
% 157.55/157.22 [8495]P25(a909,x84951,f819(x84952,x84951),f302(a909,f77(a909),f326(f35(x84951),x84952)),x84952)+~P105(f326(f61(x84951),x84952))
% 157.55/157.22 [8504]P105(f326(f61(f916(x85041,x85041)),f326(f326(f288(x85041,x85041,x85041),x85042),f306(x85041,x85042))))+~P105(f326(f61(f916(x85041,x85041)),x85042))
% 157.55/157.22 [8531]E(x85311,f2(a1))+P105(f326(f49(x85312,x85311),f326(f326(f251(a1,a1),f326(f326(f36(a1),x85312),x85311)),f45(a1,x85312,x85311))))
% 157.55/157.22 [8544]~P105(f326(f326(f328(f916(a909,a909)),f326(f326(f251(a909,a909),x85441),x85442)),f306(a909,a316)))+P105(f326(f326(f234(a909),x85441),x85442))
% 157.55/157.22 [8560]~P82(x85601)+E(f326(f142(x85601,x85601,f326(f9(x85601,x85601,x85601),f79(x85601)),f2(x85601)),f326(f168(x85601),x85602)),f326(f142(x85601,x85601,f79(x85601),f2(x85601)),x85602))
% 157.55/157.22 [8730]~P108(x87301)+E(f326(f142(f910(x87301),x87301,f326(f9(x87301,f910(x87301),f910(x87301)),f148(x87301,x87301,f7(x87301))),f113(x87301)),x87302),f150(x87301,x87301,f7(x87301),x87302))
% 157.55/157.22 [8841]~P56(x88411,f326(f261(f916(x88411,x88411)),f326(f256(x88411,x88411,a905),x88412)))+P56(x88411,f326(f261(f916(x88411,x88411)),f326(f256(x88411,x88411,a905),f242(x88411,x88411,x88412))))
% 157.55/157.22 [8855]P105(f326(f326(f328(f916(a909,a909)),f326(f326(f251(a909,a909),x88551),x88552)),f326(f326(f288(a909,a909,a909),a316),f306(a909,a316))))+~P105(f326(f326(f235(a909),x88551),x88552))
% 157.55/157.22 [8901]~P105(f326(f61(f916(x89011,x89011)),f326(f326(f288(x89011,x89011,x89011),x89012),f306(x89011,x89012))))+P105(f326(f61(f916(x89011,x89011)),x89012))
% 157.55/157.22 [8959]~P56(x89591,f326(f261(f916(x89591,x89591)),f326(f256(x89591,x89591,a905),f242(x89591,x89591,x89592))))+P56(x89591,f326(f261(f916(x89591,x89591)),f326(f256(x89591,x89591,a905),x89592)))
% 157.55/157.22 [9156]P56(x91561,x91562)+P105(f326(f326(f328(f916(x91561,x91561)),f326(f326(f251(x91561,x91561),f602(x91562,x91561)),f602(x91562,x91561))),f326(f326(f288(x91561,x91561,x91561),x91562),f306(x91561,x91562))))
% 157.55/157.22 [9157]P56(x91571,x91572)+P105(f326(f326(f328(f916(x91571,x91571)),f326(f326(f251(x91571,x91571),f616(x91572,x91571)),f616(x91572,x91571))),f326(f326(f288(x91571,x91571,x91571),x91572),f306(x91571,x91572))))
% 157.55/157.22 [9274]~P105(f326(f326(f328(f916(a909,a909)),f326(f326(f251(a909,a909),x92741),x92742)),f326(f326(f288(a909,a909,a909),a316),f306(a909,a316))))+P105(f326(f326(f235(a909),x92741),x92742))
% 157.55/157.22 [5225]~P94(x52251)+E(f326(f326(f79(x52251),f326(f103(x52251),a82)),x52252),x52252)
% 157.55/157.22 [5255]~P95(x52551)+E(f326(f326(f110(x52551),f326(f78(x52551),x52552)),x52552),f241(x52551))
% 157.55/157.22 [5256]~P95(x52561)+E(f326(f326(f101(x52561),f326(f78(x52561),x52562)),x52562),f188(x52561))
% 157.55/157.22 [5257]~P66(x52571)+E(f326(f326(f79(x52571),f326(f78(x52571),x52572)),x52572),f2(x52571))
% 157.55/157.22 [5258]~P73(x52581)+E(f326(f326(f79(x52581),f326(f78(x52581),x52582)),x52582),f2(x52581))
% 157.55/157.22 [5291]~P94(x52911)+E(f326(f326(f80(x52911),f326(f103(x52911),a97)),x52912),f326(f78(x52911),x52912))
% 157.55/157.22 [5455]~P114(x54551)+E(f326(f326(f80(x54551),f326(f78(x54551),f77(x54551))),x54552),f326(f78(x54551),x54552))
% 157.55/157.22 [5500]E(f326(f75(a1),x55001),f77(a1))+~E(f326(f75(a1),f326(f326(f80(a1),x55001),x55002)),f77(a1))
% 157.55/157.22 [5592]~P94(x55921)+E(f326(f326(f79(x55921),f77(x55921)),f326(f103(x55921),x55922)),f326(f103(x55921),f326(f326(f3(a1),x55922),a97)))
% 157.55/157.22 [5646]~P77(x56461)+E(f12(x56461,f326(f326(f308(x56461),x56462),f188(f917(x56461,a905)))),x56462)
% 157.55/157.22 [5647]~P77(x56471)+E(f13(x56471,f326(f326(f308(x56471),x56472),f188(f917(x56471,a905)))),x56472)
% 157.55/157.22 [5648]~P4(x56481)+E(f37(x56481,f326(f326(f308(x56481),x56482),f188(f917(x56481,a905)))),x56482)
% 157.55/157.22 [5649]~P108(x56491)+E(f16(x56491,f326(f326(f308(x56491),x56492),f188(f917(x56491,a905)))),x56492)
% 157.55/157.22 [5650]~P4(x56501)+E(f38(x56501,f326(f326(f308(x56501),x56502),f188(f917(x56501,a905)))),x56502)
% 157.55/157.22 [5651]~P108(x56511)+E(f17(x56511,f326(f326(f308(x56511),x56512),f188(f917(x56511,a905)))),x56512)
% 157.55/157.22 [5673]E(f326(f326(f79(a909),x56731),f326(f326(f3(a909),x56732),x56731)),x56732)+P105(f326(f326(f235(a909),x56732),x56731))
% 157.55/157.22 [5712]E(x57121,f113(x57122))+P105(f326(f326(f235(a909),f2(a909)),f326(f189(f910(x57122)),x57121)))
% 157.55/157.22 [5838]~P108(x58381)+E(f14(x58381,f232(x58381),f326(f326(f308(x58381),x58382),f188(f917(x58381,a905)))),x58382)
% 157.55/157.22 [5839]~P108(x58391)+E(f15(x58391,f233(x58391),f326(f326(f308(x58391),x58392),f188(f917(x58391,a905)))),x58392)
% 157.55/157.22 [5900]E(f326(f326(f3(a909),x59001),f326(f326(f3(a909),x59001),x59002)),x59002)+~P105(f326(f326(f234(a909),x59002),x59001))
% 157.55/157.22 [5901]E(f326(f326(f79(a909),x59011),f326(f326(f3(a909),x59012),x59011)),x59012)+~P105(f326(f326(f234(a909),x59011),x59012))
% 157.55/157.22 [5923]E(f45(a909,f326(f326(f3(a909),x59231),x59232),x59232),f45(a909,x59231,x59232))+P105(f326(f326(f235(a909),x59231),x59232))
% 157.55/157.22 [5934]E(f326(f78(a1),f326(f326(f36(a1),x59341),f326(f78(a1),x59342))),f292(x59341,x59342))+P105(f326(f326(f234(a1),f2(a1)),x59342))
% 157.55/157.22 [5936]~E(x59362,f2(a909))+P105(f326(f326(f235(a909),f2(a909)),f326(f326(f243(a909),x59361),x59362)))
% 157.55/157.22 [5999]~P94(x59991)+E(f326(f326(f79(x59991),f326(f78(x59991),f77(x59991))),f326(f103(x59991),x59992)),f326(f103(x59991),f326(f326(f79(a1),x59992),a97)))
% 157.55/157.22 [6001]E(f326(f326(f243(a909),f326(f103(a909),x60011)),x60012),f326(f326(f243(a909),f2(a909)),x60012))+~P105(f326(a193,f326(f103(a1),x60011)))
% 157.55/157.22 [6103]E(f326(f141(a909),f139(a909,f326(f301(a909,x61031),x61032))),x61031)+~P105(f326(f326(f235(a909),x61031),x61032))
% 157.55/157.22 [6119]E(f326(f326(f80(a909),f326(f103(a909),x61191)),f326(f103(a909),x61192)),f326(f103(a909),f326(f326(f80(a1),x61191),x61192)))+P105(f326(f326(f235(a1),x61191),a82))
% 157.55/157.22 [6125]~P126(x61251)+P105(f326(f326(f234(x61251),f2(x61251)),f326(f326(f80(x61251),x61252),x61252)))
% 157.55/157.22 [6137]E(f326(f326(f3(a909),f326(a112,x61371)),x61372),f326(a112,f326(f326(f3(a909),x61371),x61372)))+~P105(f326(f326(f234(a909),x61372),x61371))
% 157.55/157.22 [6141]E(f45(a909,f326(f326(f3(a909),x61411),x61412),x61412),f45(a909,x61411,x61412))+~P105(f326(f326(f234(a909),x61412),x61411))
% 157.55/157.22 [6194]E(f326(f326(f243(a909),f326(a104,x61941)),x61942),f326(a104,f326(f326(f243(a1),x61941),x61942)))+~P105(f326(f326(f234(a1),f2(a1)),x61941))
% 157.55/157.22 [6212]P105(f326(f137(x62121),x62122))+P105(f326(f326(f235(a909),f660(x62122,x62121)),f326(f189(f910(x62121)),x62122)))
% 157.55/157.22 [6213]P105(f326(f137(x62131),x62132))+P105(f326(f326(f235(a909),f666(x62132,x62131)),f326(f189(f910(x62131)),x62132)))
% 157.55/157.22 [6227]~E(x62271,f113(x62272))+~P105(f326(f326(f235(a909),f2(a909)),f326(f189(f910(x62272)),x62271)))
% 157.55/157.22 [6238]E(f144(a909,f139(a909,f326(f301(a909,x62381),x62382))),f326(f326(f3(a909),x62382),f77(a909)))+~P105(f326(f326(f235(a909),x62381),x62382))
% 157.55/157.22 [6241]E(f326(f326(f79(a1),x62411),f326(f100(a1),f326(a112,f342(x62412,x62411)))),x62412)+~P105(f326(f326(f235(a1),x62411),x62412))
% 157.55/157.22 [6248]E(x62481,f2(a909))+E(f326(f326(f80(a909),x62482),f326(f326(f243(a909),x62482),f326(f326(f3(a909),x62481),f77(a909)))),f326(f326(f243(a909),x62482),x62481))
% 157.55/157.22 [6276]E(f326(f326(f80(a909),f326(a104,x62761)),f326(a104,x62762)),f326(a104,f326(f326(f80(a1),x62761),x62762)))+~P105(f326(f326(f234(a1),f2(a1)),x62761))
% 157.55/157.22 [6277]E(f326(f326(f36(a909),f326(a104,x62771)),f326(a104,x62772)),f326(a104,f326(f326(f36(a1),x62771),x62772)))+~P105(f326(f326(f234(a1),f2(a1)),x62771))
% 157.55/157.22 [6291]~P112(x62911)+E(f326(f326(f79(x62911),x62912),x62912),f326(f326(f80(x62911),f326(f326(f79(x62911),f77(x62911)),f77(x62911))),x62912))
% 157.55/157.22 [6314]E(f326(f326(f3(a1),f326(f100(a1),x63141)),f326(f100(a1),x63142)),f326(f100(a1),f326(f326(f3(a909),x63141),x63142)))+~P105(f326(f326(f234(a909),x63142),x63141))
% 157.55/157.22 [6316]E(f326(f326(f251(a1,a1),f326(f103(a1),a97)),f326(f326(f79(a1),x63161),x63162)),f50(x63161,x63162))+~P105(f326(f326(f234(a1),x63162),f2(a1)))
% 157.55/157.22 [6349]E(f179(x63491,x63492),f113(f910(x63491)))+P105(f326(f326(f328(f910(x63491)),f659(x63492,x63491)),f326(f172(f910(x63491)),x63492)))
% 157.55/157.22 [6358]E(f116(a1,f326(f129(a1),x63581),f128(x63582,f326(f326(f79(a1),x63581),f77(a1)))),f128(x63582,x63581))+P105(f326(f326(f235(a1),x63582),x63581))
% 157.55/157.22 [6412]~P105(f326(f326(f286(a909),x64121),x64122))+P105(f326(f326(f286(a909),x64121),f326(f326(f79(a909),x64122),x64121)))
% 157.55/157.22 [6433]E(f326(f326(f151(a1),x64331),f178(f326(f326(f79(a1),x64331),f77(a1)),x64332)),f178(x64331,x64332))+~P105(f326(f326(f234(a1),x64331),x64332))
% 157.55/157.22 [6473]~P105(f326(f326(f235(a909),x64732),x64731))+P105(f326(f326(f235(a909),f2(a909)),f326(f326(f3(a909),x64731),x64732)))
% 157.55/157.22 [6506]~P105(f326(f326(f235(a909),x65061),f326(a104,x65062)))+P105(f326(f326(f235(a1),f326(f100(a1),x65061)),x65062))
% 157.55/157.22 [6535]~P108(x65351)+E(f326(f326(f110(f917(x65351,a905)),f326(f281(x65351),x65352)),f326(f326(f308(x65351),x65352),f188(f917(x65351,a905)))),f326(f300(x65351),x65352))
% 157.55/157.22 [6536]~P105(f326(f326(f234(a1),f2(a1)),x65361))+P105(f326(f326(f234(a1),f2(a1)),f326(f326(f243(a1),x65361),x65362)))
% 157.55/157.22 [6539]~P105(f326(f326(f235(a909),f2(a909)),x65391))+P105(f326(f326(f235(a909),f2(a909)),f326(f326(f243(a909),x65391),x65392)))
% 157.55/157.22 [6566]~E(f326(x65661,f2(a909)),f2(a909))+E(f326(f326(f8(a909,a909),x65661),f302(a909,f326(a112,f2(a909)),x65662)),f326(f326(f8(a909,a909),x65661),f302(a909,f2(a909),x65662)))
% 157.55/157.22 [6629]~P94(x66291)+E(f326(f326(f80(x66291),f326(f326(f79(x66291),f77(x66291)),f77(x66291))),f326(f103(x66291),x66292)),f326(f103(x66291),f326(f326(f79(a1),x66292),x66292)))
% 157.55/157.22 [6646]E(f326(f326(f308(a1),x66461),f302(a1,f326(f326(f79(a1),x66461),f77(a1)),x66462)),f302(a1,x66461,x66462))+P105(f326(f326(f235(a1),x66462),x66461))
% 157.55/157.22 [6647]P105(f326(f326(f235(a909),x66471),f326(a104,x66472)))+~P105(f326(f326(f235(a1),f326(f100(a1),x66471)),x66472))
% 157.55/157.22 [6746]P105(f326(f326(f286(a909),x67461),x67462))+~P105(f326(f326(f286(a909),x67461),f326(f326(f79(a909),x67462),x67461)))
% 157.55/157.22 [6751]E(f326(a104,f326(f326(f36(a1),f326(f103(a1),x67511)),f326(f103(a1),x67512))),f326(f326(f36(a909),f326(f103(a909),x67511)),f326(f103(a909),x67512)))+P105(f326(a193,f326(f103(a1),x67511)))
% 157.55/157.22 [6812]P105(f326(f326(f235(a909),x68121),x68122))+~P105(f326(f326(f235(a909),f2(a909)),f326(f326(f3(a909),x68122),x68121)))
% 157.55/157.22 [6855]P105(f326(f326(f235(a909),f2(a909)),x68551))+~P105(f326(f326(f235(a909),f2(a909)),f326(f326(f80(a909),x68552),x68551)))
% 157.55/157.22 [6856]P105(f326(f326(f235(a909),f2(a909)),x68561))+~P105(f326(f326(f235(a909),f2(a909)),f326(f326(f80(a909),x68561),x68562)))
% 157.55/157.22 [6875]~P105(f326(f326(f234(a1),x68751),f2(a1)))+E(f326(f326(f80(a909),f326(a104,f326(f78(a1),x68751))),f326(a104,f326(f78(a1),x68752))),f326(a104,f326(f326(f80(a1),x68751),x68752)))
% 157.55/157.22 [6932]~E(x69322,f188(f917(x69321,a905)))+P105(f326(f326(f234(f917(x69321,a905)),x69322),f326(f78(f917(x69321,a905)),x69322)))
% 157.55/157.22 [6994]~P94(x69941)+E(f326(f326(f79(x69941),f326(f326(f79(x69941),f2(x69941)),f326(f103(x69941),x69942))),f326(f103(x69941),x69942)),f326(f103(x69941),f326(f326(f79(a1),x69942),x69942)))
% 157.55/157.22 [7048]~P105(f326(f326(f235(a1),x70481),x70482))+P105(f326(f326(f234(a1),f326(f326(f79(a1),x70481),f77(a1))),x70482))
% 157.55/157.22 [7114]E(x71141,f2(a909))+~P105(f326(f326(f234(a1),f326(f100(a1),x71142)),f326(f78(a1),f326(f100(a1),x71141))))
% 157.55/157.22 [7115]E(x71151,f2(a909))+~P105(f326(f326(f234(a1),f326(f100(a1),x71151)),f326(f78(a1),f326(f100(a1),x71152))))
% 157.55/157.22 [7218]E(f326(f326(f251(a1,a1),f326(f103(a1),a97)),f326(f326(f79(a1),x72181),x72182)),f50(x72181,x72182))+~P105(f326(f326(f234(a1),f2(a1)),f326(f326(f79(a1),x72181),x72182)))
% 157.55/157.22 [7262]~P26(x72621,x72622)+P36(x72621,f326(f250(f917(f916(x72621,x72621),a905),f917(f916(x72621,x72621),a905)),x72622))
% 157.55/157.22 [7281]~P105(f326(f326(f234(a909),f326(a112,f2(a909))),x72811))+P105(f326(f326(f234(a909),f326(a112,f2(a909))),f326(f326(f243(a909),x72811),x72812)))
% 157.55/157.22 [7461]~P105(f326(f326(f234(a1),x74611),x74612))+P105(f326(f326(f234(a1),f326(f326(f79(a1),x74611),x74611)),f326(f326(f79(a1),x74612),x74612)))
% 157.55/157.22 [7466]~P105(f326(f326(f235(a1),x74661),x74662))+P105(f326(f326(f235(a1),f326(f326(f79(a1),x74661),x74661)),f326(f326(f79(a1),x74662),x74662)))
% 157.55/157.22 [7523]~P105(f326(f326(f235(a909),f2(a909)),x75231))+P105(f326(f326(f235(a909),f326(f326(f3(a909),x75231),f326(a112,x75232))),x75231))
% 157.55/157.22 [7556]P105(f326(f326(f234(a909),f326(a112,f2(a909))),x75561))+~P105(f326(f326(f234(a909),f326(a112,f2(a909))),f326(f326(f80(a909),x75562),x75561)))
% 157.55/157.22 [7557]P105(f326(f326(f234(a909),f326(a112,f2(a909))),x75571))+~P105(f326(f326(f234(a909),f326(a112,f2(a909))),f326(f326(f80(a909),x75571),x75572)))
% 157.55/157.22 [7561]P105(f326(f326(f234(a909),f326(f326(f164(a909),x75611),x75612)),f326(f165(a909),x75611)))+~P105(f326(f326(f235(a909),x75612),f326(f189(f910(a909)),x75611)))
% 157.55/157.22 [7599]P105(f326(f326(f235(a1),x75991),x75992))+~P105(f326(f326(f234(a1),f326(f326(f79(a1),x75991),f77(a1))),x75992))
% 157.55/157.22 [7641]P105(f326(f61(x76411),f241(f917(x76411,a905))))+~P105(f326(f61(f917(x76412,x76411)),f241(f917(f917(x76412,x76411),a905))))
% 157.55/157.22 [7642]P105(f326(f61(x76421),f241(f917(x76421,a905))))+~P105(f326(f61(f915(x76422,x76421)),f241(f917(f915(x76422,x76421),a905))))
% 157.55/157.22 [7643]P105(f326(f61(x76431),f241(f917(x76431,a905))))+~P105(f326(f61(f915(x76431,x76432)),f241(f917(f915(x76431,x76432),a905))))
% 157.55/157.22 [7681]E(x76811,f188(f917(x76812,a905)))+~P105(f326(f326(f234(f917(x76812,a905)),x76811),f326(f78(f917(x76812,a905)),x76811)))
% 157.55/157.22 [7818]E(f326(f142(f910(x78181),f910(x78181),f134(x78181),f113(x78181)),x78182),f113(x78181))+P105(f326(f326(f328(f910(x78181)),f691(x78182,x78181)),f326(f172(f910(x78181)),x78182)))
% 157.55/157.22 [7819]E(f326(f142(f910(x78191),f910(x78191),f134(x78191),f113(x78191)),x78192),f113(x78191))+P105(f326(f326(f328(f910(x78191)),f692(x78192,x78191)),f326(f172(f910(x78191)),x78192)))
% 157.55/157.22 [8051]P105(f326(f326(f234(a1),x80511),x80512))+~P105(f326(f326(f234(a1),f326(f326(f79(a1),x80511),x80511)),f326(f326(f79(a1),x80512),x80512)))
% 157.55/157.22 [8056]P105(f326(f326(f235(a1),x80561),x80562))+~P105(f326(f326(f235(a1),f326(f326(f79(a1),x80561),x80561)),f326(f326(f79(a1),x80562),x80562)))
% 157.55/157.22 [8148]~P112(x81481)+E(f326(f326(f80(x81481),f326(f326(f79(x81481),f77(x81481)),f77(x81481))),f326(f326(f8(a909,x81481),f100(x81481)),f302(a909,f77(a909),x81482))),f326(f326(f80(x81481),f326(f100(x81481),x81482)),f326(f326(f79(x81481),f326(f100(x81481),x81482)),f77(x81481))))
% 157.55/157.22 [8197]P105(f326(f326(f328(a909),x81971),x81972))+~P105(f326(f326(f328(a1),f326(f100(a1),x81971)),f326(f309(a909,a1,f100(a1)),x81972)))
% 157.55/157.22 [8351]~P105(f326(f61(x83511),x83512))+E(f326(f309(a909,x83511,f549(x83512,x83511)),f326(f261(a909),f326(f326(f9(a909,a909,a905),f235(a909)),f550(x83512,x83511)))),x83512)
% 157.55/157.22 [8628]P52(x86281,x86282)+P105(f326(f326(f328(f916(x86281,x86281)),f326(f326(f251(x86281,x86281),f476(x86282,x86281)),f476(x86282,x86281))),x86282))
% 157.55/157.22 [8629]P37(x86291,x86292)+P105(f326(f326(f328(f916(x86291,x86291)),f326(f326(f251(x86291,x86291),f788(x86292,x86291)),f792(x86292,x86291))),x86292))
% 157.55/157.22 [8630]P37(x86301,x86302)+P105(f326(f326(f328(f916(x86301,x86301)),f326(f326(f251(x86301,x86301),f792(x86302,x86301)),f793(x86302,x86301))),x86302))
% 157.55/157.22 [8631]P38(x86311,x86312)+P105(f326(f326(f328(f916(x86311,x86311)),f326(f326(f251(x86311,x86311),f701(x86312,x86311)),f700(x86312,x86311))),x86312))
% 157.55/157.22 [8632]P38(x86321,x86322)+P105(f326(f326(f328(f916(x86321,x86321)),f326(f326(f251(x86321,x86321),f700(x86322,x86321)),f701(x86322,x86321))),x86322))
% 157.55/157.22 [8633]P50(x86331,x86332)+P105(f326(f326(f328(f916(x86331,x86331)),f326(f326(f251(x86331,x86331),f797(x86332,x86331)),f798(x86332,x86331))),x86332))
% 157.55/157.22 [8773]~P94(x87731)+E(f326(f326(f3(x87731),f77(x87731)),f326(f103(x87731),x87732)),f326(f103(x87731),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f78(a1),x87732))))
% 157.55/157.22 [8898]~P105(f326(f326(f235(f917(a909,a905)),x88981),x88982))+P105(f326(f326(f235(f917(a1,a905)),f326(f309(a909,a1,f100(a1)),x88981)),f326(f309(a909,a1,f100(a1)),x88982)))
% 157.55/157.22 [8932]~P105(f326(f326(f235(a1),x89321),x89322))+P105(f326(f326(f234(a1),f326(f326(f3(a1),f326(f326(f79(a1),x89321),x89321)),a97)),f326(f326(f79(a1),x89322),x89322)))
% 157.55/157.22 [8934]~P105(f326(f326(f235(a1),x89341),x89342))+P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),x89341),x89341)),a97)),f326(f326(f79(a1),x89342),x89342)))
% 157.55/157.22 [9007]~P105(f326(f326(f328(a909),x90071),f326(f172(a909),x90072)))+P105(f326(f326(f234(a909),x90071),f326(f142(a909,a909,f79(a909),f2(a909)),x90072)))
% 157.55/157.22 [9096]P45(x90961,x90962)+~P105(f326(f326(f328(f916(x90961,x90961)),f326(f326(f251(x90961,x90961),f387(x90962,x90961)),f387(x90962,x90961))),x90962))
% 157.55/157.22 [9097]P37(x90971,x90972)+~P105(f326(f326(f328(f916(x90971,x90971)),f326(f326(f251(x90971,x90971),f788(x90972,x90971)),f793(x90972,x90971))),x90972))
% 157.55/157.22 [9098]P50(x90981,x90982)+~P105(f326(f326(f328(f916(x90981,x90981)),f326(f326(f251(x90981,x90981),f798(x90982,x90981)),f797(x90982,x90981))),x90982))
% 157.55/157.22 [9237]~P105(f326(f326(f234(f917(a1,a905)),f326(f309(a909,a1,f100(a1)),x92371)),f326(f309(a909,a1,f100(a1)),x92372)))+P105(f326(f326(f234(f917(a909,a905)),x92371),x92372))
% 157.55/157.22 [9238]~P105(f326(f326(f235(f917(a1,a905)),f326(f309(a909,a1,f100(a1)),x92381)),f326(f309(a909,a1,f100(a1)),x92382)))+P105(f326(f326(f235(f917(a909,a905)),x92381),x92382))
% 157.55/157.22 [9322]P105(f326(f326(f235(a1),x93221),x93222))+~P105(f326(f326(f234(a1),f326(f326(f3(a1),f326(f326(f79(a1),x93221),x93221)),a97)),f326(f326(f79(a1),x93222),x93222)))
% 157.55/157.22 [9324]P105(f326(f326(f235(a1),x93241),x93242))+~P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),x93241),x93241)),a97)),f326(f326(f79(a1),x93242),x93242)))
% 157.55/157.22 [10206]~P103(x102061)+E(f116(f910(x102061),f326(f129(f910(x102061)),f113(x102061)),f326(f326(f326(f96(f911(f910(x102061))),f326(f326(f235(a1),f2(a1)),x102062)),f326(f118(f916(x102061,f910(x102061)),f910(x102061),f131(x102061,f910(x102061),f132(x102061,f326(f326(f3(a1),x102062),f77(a1))),f132(f910(x102061),f326(f326(f3(a1),x102062),f77(a1))))),f326(f256(x102061,f910(x102061),f911(f910(x102061))),f326(f326(f10(f917(f910(x102061),f910(x102061)),f917(f910(x102061),f911(f910(x102061))),x102061),f326(f10(f910(x102061),f911(f910(x102061)),f910(x102061)),f129(f910(x102061)))),f151(x102061))))),f115(f910(x102061)))),f132(f910(x102061),x102062))
% 157.55/157.22 [10228]~P105(f326(f61(x102281),x102282))+E(f326(f189(f910(x102281)),f89(f910(x102281),f326(f326(f20(f910(x102281),a905,a905),f326(f326(f10(a905,f917(a905,a905),f910(x102281)),a324),f326(f326(f9(f910(x102281),f917(x102281,a905),a905),f326(f326(f10(f917(x102281,a905),f917(f917(x102281,a905),a905),f910(x102281)),a323),f172(x102281))),x102282))),f137(x102281)))),f214(x102281,x102282))
% 157.55/157.22 [6237]E(f326(f326(f79(a909),f326(f326(f3(a909),x62371),x62372)),x62372),x62371)+~P105(f326(f326(f234(a909),x62372),x62371))
% 157.55/157.22 [6310]E(f326(f326(f36(a909),f326(f326(f80(a909),x63101),x63102)),x63102),x63101)+~P105(f326(f326(f235(a909),f2(a909)),x63102))
% 157.55/157.22 [6311]E(f326(f326(f36(a909),f326(f326(f80(a909),x63111),x63112)),x63111),x63112)+~P105(f326(f326(f235(a909),f2(a909)),x63111))
% 157.55/157.22 [6315]~P69(x63151)+E(f326(f326(f8(a909,x63151),f326(f164(x63151),x63152)),f326(f301(a909,f2(a909)),f326(f189(f910(x63151)),x63152))),f326(f165(x63151),x63152))
% 157.55/157.22 [6425]E(f45(a909,f326(a112,f326(f326(f80(a909),x64251),x64252)),x64251),f77(a909))+~P105(f326(f326(f235(a909),f77(a909)),x64251))
% 157.55/157.22 [6431]E(f326(a112,f326(f326(f79(a909),f326(f103(a909),x64311)),x64312)),f326(f326(f79(a909),f77(a909)),x64312))+~P105(f326(a193,f326(f103(a1),x64311)))
% 157.55/157.22 [6460]E(f326(a104,f326(f326(f243(a1),f326(f103(a1),x64601)),x64602)),f326(f326(f243(a909),f326(f103(a909),x64601)),x64602))+P105(f326(a193,f326(f103(a1),x64601)))
% 157.55/157.22 [6701]E(f326(f326(f3(a909),x67011),f326(f103(a909),f326(f326(f79(a1),x67012),a97))),f326(f326(f3(a909),f326(a112,x67011)),f326(f103(a909),x67012)))+~P105(f326(f326(f235(a1),a82),x67012))
% 157.55/157.22 [6782]E(x67821,f2(a909))+E(f326(a112,f326(f326(f79(a909),f326(f326(f3(a909),x67821),f77(a909))),x67822)),f326(f326(f79(a909),x67821),x67822))
% 157.55/157.22 [6825]E(x68251,f2(a1))+P105(f326(f326(f235(a1),f2(a1)),f326(f326(f243(a1),f326(f75(a1),x68251)),x68252)))
% 157.55/157.22 [6840]~E(x68402,f2(a909))+P105(f326(f326(f235(a1),f2(a1)),f326(f326(f243(a1),f326(f75(a1),x68401)),x68402)))
% 157.55/157.22 [6878]E(x68781,f2(a909))+E(f326(f326(f79(a909),x68782),f326(f326(f80(a909),f326(f326(f3(a909),x68781),f77(a909))),x68782)),f326(f326(f80(a909),x68781),x68782))
% 157.55/157.22 [6925]~P105(f326(f326(f234(a1),x69251),x69252))+P105(f326(f326(f235(a1),f326(f326(f79(a1),x69251),a97)),x69252))
% 157.55/157.22 [7051]E(f326(f326(f151(a909),x70511),f139(a909,f326(f301(a909,f326(a112,x70511)),x70512))),f139(a909,f326(f301(a909,x70511),x70512)))+~P105(f326(f326(f235(a909),x70511),x70512))
% 157.55/157.22 [7253]E(x72531,x72532)+~E(f326(f326(f3(a1),f326(f326(f79(a1),x72531),x72531)),a97),f326(f326(f3(a1),f326(f326(f79(a1),x72532),x72532)),a97))
% 157.55/157.22 [7256]E(x72561,f113(x72562))+E(f265(x72562,f326(f326(f154(x72562,f916(a99,x72562)),f326(f251(a99,x72562),f77(a99))),x72561)),f274(x72562,x72561))
% 157.55/157.22 [7493]P105(f326(f326(f234(a1),x74931),x74932))+~P105(f326(f326(f235(a1),f326(f326(f79(a1),x74931),a97)),x74932))
% 157.55/157.22 [7958]~P105(f326(f326(f235(a909),x79581),x79582))+P105(f326(f326(f328(f916(a909,a909)),f326(f326(f251(a909,a909),x79581),x79582)),a239))
% 157.55/157.22 [8174]~P105(f326(f326(f235(a99),f2(a99)),x81741))+P105(f326(f326(f235(a99),f326(f250(a99,f916(a99,a99)),f326(f266(x81741),x81742))),x81741))
% 157.55/157.22 [8432]~P37(x84321,x84322)+P37(x84321,f326(f326(f110(f917(f916(x84321,x84321),a905)),x84322),f306(x84321,f188(f917(f916(x84321,x84321),a905)))))
% 157.55/157.22 [8433]~P38(x84331,x84332)+P38(x84331,f326(f326(f110(f917(f916(x84331,x84331),a905)),x84332),f306(x84331,f188(f917(f916(x84331,x84331),a905)))))
% 157.55/157.22 [8481]~P86(x84811)+P105(f326(f326(f234(x84811),f326(f75(x84811),f326(f165(x84811),x84812))),f326(f165(x84811),f326(f326(f154(x84811,x84811),f75(x84811)),x84812))))
% 157.55/157.22 [8506]P105(f326(f326(f235(a909),x85061),x85062))+~P105(f326(f326(f328(f916(a909,a909)),f326(f326(f251(a909,a909),x85061),x85062)),a239))
% 157.55/157.22 [8652]E(f326(f326(f251(x86521,x86521),f614(x86522,x86521)),f614(x86522,x86521)),x86522)+~P105(f326(f326(f328(f916(x86521,x86521)),x86522),f306(x86521,f188(f917(f916(x86521,x86521),a905)))))
% 157.55/157.22 [8695]E(f326(f301(a909,x86951),f326(f326(f79(a909),x86951),f326(f35(a909),x86952))),x86952)+~P105(f326(f326(f234(f917(a909,a905)),x86952),f326(f301(a909,x86951),f326(f326(f79(a909),x86951),f326(f35(a909),x86952)))))
% 157.55/157.22 [8925]P38(x89251,x89252)+~P38(x89251,f326(f326(f110(f917(f916(x89251,x89251),a905)),x89252),f306(x89251,f188(f917(f916(x89251,x89251),a905)))))
% 157.55/157.22 [9051]E(f326(f326(f36(a1),f326(f103(a1),f326(f326(f3(a1),f326(f326(f79(a1),x90511),x90511)),a97))),f326(f103(a1),f326(f326(f79(a1),x90512),x90512))),f326(f326(f36(a1),f326(f103(a1),x90511)),f326(f103(a1),x90512)))+~P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x90512)))
% 157.55/157.22 [9141]~P37(x91411,x91412)+P105(f326(f326(f234(f917(f916(x91411,x91411),a905)),f326(f326(f288(x91411,x91411,x91411),x91412),x91412)),x91412))
% 157.55/157.22 [9167]E(f177(f910(x91671),f326(f326(f10(a905,a905,f910(x91671)),a321),f326(f326(f9(f910(x91671),f910(x91671),a905),a323),f113(x91671))),x91672),f179(x91671,f179(x91671,x91672)))+~P12(a909,f326(f168(a909),f326(f326(f154(f910(x91671),a909),f189(f910(x91671))),x91672)))
% 157.55/157.22 [9170]E(f326(f326(f36(a1),f326(f103(a1),f326(f326(f3(a1),f326(f326(f79(a1),x91701),x91701)),a97))),f326(f103(a1),f326(f326(f79(a1),x91702),x91702))),f326(f326(f36(a1),f326(f326(f79(a1),f326(f103(a1),x91701)),f77(a1))),f326(f103(a1),x91702)))+P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x91702)))
% 157.55/157.22 [10001]P105(f326(a193,x100012))+E(f326(f326(f85(a1,a909),f326(f326(f3(a1),x100011),x100012)),f326(f326(f20(a1,a909,a909),f326(f326(f9(a1,a909,f917(a909,a909)),f326(f326(f10(a905,f917(a909,f917(a909,a909)),a1),f96(a909)),a193)),f2(a909))),a104)),f326(f326(f3(a909),f326(a104,x100011)),f326(a104,x100012)))
% 157.55/157.22 [10009]E(f326(f326(f85(a1,a909),f326(f103(a1),f326(f326(f79(a1),x100091),f326(f78(a1),x100092)))),f326(f326(f20(a1,a909,a909),f326(f326(f9(a1,a909,f917(a909,a909)),f326(f326(f10(a905,f917(a909,f917(a909,a909)),a1),f96(a909)),a193)),f2(a909))),a104)),f326(f326(f3(a909),f326(f103(a909),x100091)),f326(f103(a909),x100092)))+P105(f326(f326(f235(a1),x100092),a82))
% 157.55/157.22 [10010]~P26(x100101,x100102)+P105(f326(f326(f234(f917(f916(x100101,x100101),a905)),f326(f326(f288(x100101,x100101,x100101),f326(f250(f917(f916(x100101,x100101),a905),f917(f916(x100101,x100101),a905)),x100102)),f326(f255(f917(f916(x100101,x100101),a905),f917(f916(x100101,x100101),a905)),x100102))),f326(f250(f917(f916(x100101,x100101),a905),f917(f916(x100101,x100101),a905)),x100102)))
% 157.55/157.22 [10066]~E(f326(f35(a909),f326(f261(a909),f326(f326(f20(a909,a905,a905),f326(f326(f10(a905,f917(a905,a905),a909),a324),f326(f326(f9(a909,f917(a909,a905),a905),f328(a909)),x100661))),f326(f326(f9(a909,a909,a905),f235(a909)),f326(a112,x100662))))),f2(a909))+~P105(f326(f326(f328(a909),f2(a909)),x100661))
% 157.55/157.22 [10077]E(f298(a909,f326(f326(f20(a909,f917(a909,a905),f917(a909,a905)),f326(f326(f10(f917(a909,f917(a905,a905)),f917(f917(a909,a905),f917(a909,a905)),a909),f20(a909,a905,a905)),f326(f326(f10(f917(a909,a905),f917(a909,f917(a905,a905)),a909),f326(f10(a905,f917(a905,a905),a909),a324)),f286(a909)))),f326(f326(f10(f917(a909,a905),f917(a909,a905),a909),f326(f10(a905,a905,a909),a321)),f326(f9(a909,a909,a905),f286(a909)))),x100771,x100772),f188(f917(a909,a905)))+~P105(f326(f326(f286(a909),x100772),x100771))
% 157.55/157.22 [10082]E(f299(a909,f286(a909),f326(f326(f20(a909,f917(a909,a905),f917(a909,a905)),f326(f326(f10(f917(a909,f917(a905,a905)),f917(f917(a909,a905),f917(a909,a905)),a909),f20(a909,a905,a905)),f326(f326(f10(f917(a909,a905),f917(a909,f917(a905,a905)),a909),f326(f10(a905,f917(a905,a905),a909),a324)),f286(a909)))),f326(f326(f10(f917(a909,a905),f917(a909,a905),a909),f326(f10(a905,a905,a909),a321)),f326(f9(a909,a909,a905),f286(a909)))),x100821,x100822),f188(f917(a909,a905)))+P105(f326(f326(f286(a909),x100821),x100822))
% 157.55/157.22 [10083]E(f296(a909,f286(a909),f326(f326(f20(a909,f917(a909,a905),f917(a909,a905)),f326(f326(f10(f917(a909,f917(a905,a905)),f917(f917(a909,a905),f917(a909,a905)),a909),f20(a909,a905,a905)),f326(f326(f10(f917(a909,a905),f917(a909,f917(a905,a905)),a909),f326(f10(a905,f917(a905,a905),a909),a324)),f286(a909)))),f326(f326(f10(f917(a909,a905),f917(a909,a905),a909),f326(f10(a905,a905,a909),a321)),f326(f9(a909,a909,a905),f286(a909)))),x100831,x100832),f188(f917(a909,a905)))+P105(f326(f326(f286(a909),x100831),x100832))
% 157.55/157.22 [10087]E(f299(a909,f286(a909),f326(f326(f20(a909,f917(a909,a905),f917(a909,a905)),f326(f326(f10(f917(a909,f917(a905,a905)),f917(f917(a909,a905),f917(a909,a905)),a909),f20(a909,a905,a905)),f326(f326(f10(f917(a909,a905),f917(a909,f917(a905,a905)),a909),f326(f10(a905,f917(a905,a905),a909),a324)),f286(a909)))),f326(f326(f10(f917(a909,a905),f917(a909,a905),a909),f326(f10(a905,a905,a909),a321)),f326(f9(a909,a909,a905),f286(a909)))),x100871,x100872),f188(f917(a909,a905)))+~P105(f326(f326(f286(a909),x100872),x100871))
% 157.55/157.22 [10089]E(f296(a909,f286(a909),f326(f326(f20(a909,f917(a909,a905),f917(a909,a905)),f326(f326(f10(f917(a909,f917(a905,a905)),f917(f917(a909,a905),f917(a909,a905)),a909),f20(a909,a905,a905)),f326(f326(f10(f917(a909,a905),f917(a909,f917(a905,a905)),a909),f326(f10(a905,f917(a905,a905),a909),a324)),f286(a909)))),f326(f326(f10(f917(a909,a905),f917(a909,a905),a909),f326(f10(a905,a905,a909),a321)),f326(f9(a909,a909,a905),f286(a909)))),x100891,x100892),f188(f917(a909,a905)))+~P105(f326(f326(f286(a909),x100892),x100891))
% 157.55/157.22 [10133]E(f45(a1,f326(f103(a1),f326(f326(f3(a1),f326(f326(f79(a1),x101331),x101331)),a97)),f326(f103(a1),f326(f326(f79(a1),x101332),x101332))),f326(f326(f79(a1),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f45(a1,f326(f103(a1),x101331),f326(f103(a1),x101332)))),f77(a1)))+~P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x101332)))
% 157.55/157.22 [10142]E(f45(a1,f326(f103(a1),f326(f326(f3(a1),f326(f326(f79(a1),x101421),x101421)),a97)),f326(f103(a1),f326(f326(f79(a1),x101422),x101422))),f326(f326(f3(a1),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f45(a1,f326(f326(f79(a1),f326(f103(a1),x101421)),f77(a1)),f326(f103(a1),x101422)))),f77(a1)))+P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x101422)))
% 157.55/157.22 [10196]~P4(x101961)+E(f37(x101961,f326(f261(x101961),f326(f326(f10(f917(x101961,a905),a905,x101961),f87(x101961)),f326(f326(f10(f917(x101961,a905),f917(x101961,a905),x101961),f326(f20(x101961,a905,a905),f326(f326(f10(a905,f917(a905,a905),x101961),a329),f326(f326(f9(x101961,f917(x101961,a905),a905),f328(x101961)),x101962)))),f234(x101961))))),f38(x101961,x101962))
% 157.55/157.22 [10221]~P36(x102211,x102212)+P58(x102211,f326(f326(f9(x102211,f917(f916(x102211,x102211),a905),f917(x102211,a905)),f326(f326(f10(f917(x102211,f917(f917(f916(x102211,x102211),a905),a905)),f917(f917(f916(x102211,x102211),a905),f917(x102211,a905)),x102211),f9(x102211,f917(f916(x102211,x102211),a905),a905)),f326(f326(f10(f917(x102211,f916(x102211,x102211)),f917(x102211,f917(f917(f916(x102211,x102211),a905),a905)),x102211),f326(f10(f916(x102211,x102211),f917(f917(f916(x102211,x102211),a905),a905),x102211),f328(f916(x102211,x102211)))),f251(x102211,x102211)))),x102212))
% 157.55/157.22 [10222]~P7(x102221,f241(f917(x102221,a905)),x102222)+P6(x102221,f326(f326(f9(x102221,f917(f916(x102221,x102221),a905),f917(x102221,a905)),f326(f326(f10(f917(x102221,f917(f917(f916(x102221,x102221),a905),a905)),f917(f917(f916(x102221,x102221),a905),f917(x102221,a905)),x102221),f9(x102221,f917(f916(x102221,x102221),a905),a905)),f326(f326(f10(f917(x102221,f916(x102221,x102221)),f917(x102221,f917(f917(f916(x102221,x102221),a905),a905)),x102221),f326(f10(f916(x102221,x102221),f917(f917(f916(x102221,x102221),a905),a905),x102221),f328(f916(x102221,x102221)))),f251(x102221,x102221)))),x102222))
% 157.55/157.22 [10264]P36(x102641,x102642)+~P58(x102641,f326(f326(f9(x102641,f917(f916(x102641,x102641),a905),f917(x102641,a905)),f326(f326(f10(f917(x102641,f917(f917(f916(x102641,x102641),a905),a905)),f917(f917(f916(x102641,x102641),a905),f917(x102641,a905)),x102641),f9(x102641,f917(f916(x102641,x102641),a905),a905)),f326(f326(f10(f917(x102641,f916(x102641,x102641)),f917(x102641,f917(f917(f916(x102641,x102641),a905),a905)),x102641),f326(f10(f916(x102641,x102641),f917(f917(f916(x102641,x102641),a905),a905),x102641),f328(f916(x102641,x102641)))),f251(x102641,x102641)))),x102642))
% 157.55/157.22 [10265]P7(x102651,f241(f917(x102651,a905)),x102652)+~P6(x102651,f326(f326(f9(x102651,f917(f916(x102651,x102651),a905),f917(x102651,a905)),f326(f326(f10(f917(x102651,f917(f917(f916(x102651,x102651),a905),a905)),f917(f917(f916(x102651,x102651),a905),f917(x102651,a905)),x102651),f9(x102651,f917(f916(x102651,x102651),a905),a905)),f326(f326(f10(f917(x102651,f916(x102651,x102651)),f917(x102651,f917(f917(f916(x102651,x102651),a905),a905)),x102651),f326(f10(f916(x102651,x102651),f917(f917(f916(x102651,x102651),a905),a905),x102651),f328(f916(x102651,x102651)))),f251(x102651,x102651)))),x102652))
% 157.55/157.22 [7441]E(f326(f326(f79(a909),f326(f103(a909),f326(f326(f3(a1),x74411),a97))),x74412),f326(a112,f326(f326(f79(a909),f326(f103(a909),x74411)),x74412)))+P105(f326(a193,f326(f103(a1),x74411)))
% 157.55/157.22 [7876]~P94(x78761)+E(f326(f326(f79(x78761),f326(f326(f79(x78761),f77(x78761)),f326(f103(x78761),x78762))),f326(f103(x78761),x78762)),f326(f103(x78761),f326(f326(f3(a1),f326(f326(f79(a1),x78762),x78762)),a97)))
% 157.55/157.22 [8508]~P105(f326(f326(f234(a1),x85081),x85082))+P105(f326(f326(f234(a1),f326(f326(f79(a1),x85081),x85081)),f326(f326(f3(a1),f326(f326(f79(a1),x85082),x85082)),a97)))
% 157.55/157.22 [8510]~P105(f326(f326(f234(a1),x85101),x85102))+P105(f326(f326(f235(a1),f326(f326(f79(a1),x85101),x85101)),f326(f326(f3(a1),f326(f326(f79(a1),x85102),x85102)),a97)))
% 157.55/157.22 [8936]P105(f326(f326(f234(a1),x89361),x89362))+~P105(f326(f326(f234(a1),f326(f326(f79(a1),x89361),x89361)),f326(f326(f3(a1),f326(f326(f79(a1),x89362),x89362)),a97)))
% 157.55/157.22 [8938]P105(f326(f326(f234(a1),x89381),x89382))+~P105(f326(f326(f235(a1),f326(f326(f79(a1),x89381),x89381)),f326(f326(f3(a1),f326(f326(f79(a1),x89382),x89382)),a97)))
% 157.55/157.22 [9226]~P105(f326(f326(f234(a1),x92261),x92262))+P105(f326(f326(f234(a1),f326(f326(f3(a1),f326(f326(f79(a1),x92261),x92261)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),x92262),x92262)),a97)))
% 157.55/157.22 [9228]~P105(f326(f326(f235(a1),x92281),x92282))+P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),x92281),x92281)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),x92282),x92282)),a97)))
% 157.55/157.22 [9492]P105(f326(f326(f234(a1),x94921),x94922))+~P105(f326(f326(f234(a1),f326(f326(f3(a1),f326(f326(f79(a1),x94921),x94921)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),x94922),x94922)),a97)))
% 157.55/157.22 [9494]P105(f326(f326(f235(a1),x94941),x94942))+~P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),x94941),x94941)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),x94942),x94942)),a97)))
% 157.55/157.22 [9527]~P105(f326(f61(x95271),x95272))+P105(f326(f61(f917(x95271,a905)),f326(f261(f917(x95271,a905)),f326(f326(f9(f917(x95271,a905),f917(x95271,a905),a905),f234(f917(x95271,a905))),x95272))))
% 157.55/157.22 [9576]~E(f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),x95761),f188(f917(f916(a909,a909),a905)))),f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),x95762),f188(f917(f916(a909,a909),a905)))))+P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),x95761),x95762)),a108))
% 157.55/157.22 [9662]E(f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),x96621),f188(f917(f916(a909,a909),a905)))),f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),x96622),f188(f917(f916(a909,a909),a905)))))+~P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),x96621),x96622)),a108))
% 157.55/157.22 [9698]P105(f326(f326(f234(a1),f2(a1)),f637(x96981,x96982)))+E(f326(f261(a1),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),f2(a1)))),x96981)),f326(f261(a1),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),f2(a1)))),x96982)))
% 157.55/157.22 [10204]~P4(x102041)+E(f38(x102041,f326(f261(x102041),f326(f326(f10(f917(x102041,a905),a905,x102041),f87(x102041)),f326(f326(f10(f917(x102041,a905),f917(x102041,a905),x102041),f326(f20(x102041,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102041),a329),f326(f326(f9(x102041,f917(x102041,a905),a905),f328(x102041)),x102042)))),f326(f9(x102041,x102041,a905),f234(x102041)))))),f37(x102041,x102042))
% 157.55/157.22 [10227]P105(f326(f326(f328(a909),f2(a909)),x102271))+E(f326(f35(a909),f326(f261(a909),f326(f326(f20(a909,a905,a905),f326(f326(f10(a905,f917(a905,a905),a909),a324),f326(f326(f9(a909,f917(a909,a905),a905),f326(f326(f10(a909,f917(f917(a909,a905),a905),a909),f328(a909)),a112)),x102271))),f326(f326(f9(a909,a909,a905),f235(a909)),x102272)))),f326(f35(a909),f326(f261(a909),f326(f326(f20(a909,a905,a905),f326(f326(f10(a905,f917(a905,a905),a909),a324),f326(f326(f9(a909,f917(a909,a905),a905),f328(a909)),x102271))),f326(f326(f9(a909,a909,a905),f235(a909)),f326(a112,x102272))))))
% 157.55/157.22 [7746]~P94(x77461)+E(f326(f326(f80(x77461),x77462),f326(f103(x77461),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),x77462)
% 157.55/157.22 [8003]~P94(x80031)+E(f326(f326(f79(x80031),f326(f103(x80031),x80032)),f77(x80031)),f326(f103(x80031),f326(f326(f79(a1),x80032),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))
% 157.55/157.22 [8146]P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x81462)))+E(f326(f326(f243(a1),x81461),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),x81462),x81462)),a97))),f77(a1))
% 157.55/157.22 [9552]~P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x95522)))+E(f326(f326(f243(a1),x95521),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),x95522),x95522)),a97))),f326(f326(f85(a1,a1),f326(f326(f243(a1),x95521),f326(f103(a909),x95522))),f326(f326(f20(a1,a1,a1),f326(f326(f10(a1,f917(a1,a1),a1),f80(a1)),f326(f80(a1),x95521))),f7(a1))))
% 157.55/157.22 [9920]~P105(f326(f326(f234(a909),f645(x99202,x99201)),f326(x99201,f645(x99202,x99201))))+P105(f326(f61(a909),f326(f261(a909),f326(f326(f9(a909,a909,a905),f326(f326(f10(a909,f917(a909,a905),a909),f234(a909)),x99201)),x99202))))
% 157.55/157.22 [10056]~P105(f326(f326(f234(a909),f326(f103(a909),x100561)),f326(a112,x100562)))+P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x100561),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f9(a1,a909,a905),f326(f326(f10(a909,f917(a909,a905),a1),f234(a909)),a104)),x100562))))
% 157.55/157.22 [10057]~P105(f326(f326(f235(a909),f326(f103(a909),x100571)),f326(a112,x100572)))+P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x100571),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f9(a1,a909,a905),f326(f326(f10(a909,f917(a909,a905),a1),f235(a909)),a104)),x100572))))
% 157.55/157.22 [10117]P105(f326(f326(f234(a909),f326(f103(a909),x101171)),f326(a112,x101172)))+~P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x101171),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f9(a1,a909,a905),f326(f326(f10(a909,f917(a909,a905),a1),f234(a909)),a104)),x101172))))
% 157.55/157.22 [10118]P105(f326(f326(f235(a909),f326(f103(a909),x101181)),f326(a112,x101182)))+~P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x101181),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f9(a1,a909,a905),f326(f326(f10(a909,f917(a909,a905),a1),f235(a909)),a104)),x101182))))
% 157.55/157.22 [10148]~P105(f326(f326(f234(a909),f326(a112,x101482)),f326(f103(a909),x101481)))+P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x101481),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f10(a909,a905,a1),f326(f234(a909),x101482)),a104)))))
% 157.55/157.22 [10149]~P105(f326(f326(f235(a909),f326(a112,x101492)),f326(f103(a909),x101491)))+P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x101491),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f10(a909,a905,a1),f326(f235(a909),x101492)),a104)))))
% 157.55/157.22 [10194]P105(f326(f326(f234(a909),f326(a112,x101941)),f326(f103(a909),x101942)))+~P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x101942),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f10(a909,a905,a1),f326(f234(a909),x101941)),a104)))))
% 157.55/157.22 [10195]P105(f326(f326(f235(a909),f326(a112,x101951)),f326(f103(a909),x101952)))+~P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x101952),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f10(a909,a905,a1),f326(f235(a909),x101951)),a104)))))
% 157.55/157.22 [10274]~P105(f326(f326(f328(a909),f2(a909)),x102741))+E(f326(a112,f326(f35(a909),f326(f261(a909),f326(f326(f20(a909,a905,a905),f326(f326(f10(a905,f917(a905,a905),a909),a324),f326(f326(f9(a909,f917(a909,a905),a905),f326(f326(f10(a909,f917(f917(a909,a905),a905),a909),f328(a909)),a112)),x102741))),f326(f326(f9(a909,a909,a905),f235(a909)),x102742))))),f326(f35(a909),f326(f261(a909),f326(f326(f20(a909,a905,a905),f326(f326(f10(a905,f917(a905,a905),a909),a324),f326(f326(f9(a909,f917(a909,a905),a905),f328(a909)),x102741))),f326(f326(f9(a909,a909,a905),f235(a909)),f326(a112,x102742))))))
% 157.55/157.22 [8678]~P94(x86781)+E(f326(f326(f80(x86781),f326(f103(x86781),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),x86782),x86782)
% 157.55/157.22 [8739]~P94(x87391)+E(f326(f326(f79(x87391),f77(x87391)),f326(f103(x87391),x87392)),f326(f103(x87391),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),x87392)))
% 157.55/157.22 [8801]~P94(x88011)+E(f326(f326(f3(x88011),f326(f103(x88011),x88012)),f77(x88011)),f326(f103(x88011),f326(f326(f79(a1),x88012),f326(f78(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.55/157.22 [8955]~P105(f326(f326(f235(a909),f326(f103(a909),a82)),x89552))+E(f326(f326(f3(a909),x89551),f326(f326(f3(a909),x89552),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(f326(f3(a909),f326(a112,x89551)),x89552))
% 157.55/157.22 [9594]~P112(x95941)+E(f326(f326(f80(x95941),x95942),x95942),f326(f326(f243(x95941),x95942),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.55/157.22 [9595]~P81(x95951)+E(f326(f326(f243(x95951),x95952),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(f326(f80(x95951),x95952),x95952))
% 157.55/157.22 [9597]~P94(x95971)+E(f326(f326(f80(x95971),x95972),f326(f103(x95971),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(f326(f79(x95971),x95972),x95972))
% 157.55/157.22 [9838]~P118(x98381)+E(f326(f326(f243(x98381),f326(f75(x98381),x98382)),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(f326(f243(x98381),x98382),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.55/157.22 [9839]~P140(x98391)+E(f326(f326(f243(x98391),f326(f78(x98391),x98392)),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(f326(f243(x98391),x98392),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.55/157.22 [9835]~P94(x98351)+E(f326(f326(f80(x98351),f326(f103(x98351),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x98352),f326(f326(f79(x98351),x98352),x98352))
% 157.55/157.22 [9953]~P118(x99531)+E(f326(f75(x99531),f326(f326(f243(x99531),x99532),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x99531),x99532),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.55/157.22 [10017]~P118(x100171)+P105(f326(f326(f234(x100171),f2(x100171)),f326(f326(f243(x100171),x100172),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))
% 157.55/157.22 [10185]~E(f326(a112,x101852),f326(f103(a909),x101851))+P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x101851),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f9(a1,a909,a905),f326(f326(f10(a909,f917(a909,a905),a1),a323),a104)),x101852)))))
% 157.55/157.22 [10186]~E(f326(f103(a909),x101861),f326(a112,x101862))+P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x101861),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f9(a1,a909,a905),f326(f326(f10(a909,f917(a909,a905),a1),a323),a104)),x101862)))))
% 157.55/157.22 [10230]E(f326(a112,x102301),f326(f103(a909),x102302))+~P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x102302),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f9(a1,a909,a905),f326(f326(f10(a909,f917(a909,a905),a1),a323),a104)),x102301)))))
% 157.55/157.22 [10231]E(f326(f103(a909),x102311),f326(a112,x102312))+~P105(f326(f326(f85(a1,a905),f326(f103(a1),f326(f326(f79(a1),x102311),a97))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a329),f326(f326(f10(a905,a905,a1),a321),a193))),f326(f326(f9(a1,a909,a905),f326(f326(f10(a909,f917(a909,a905),a1),a323),a104)),x102312)))))
% 157.55/157.22 [10275]~P14(x102751,x102752)+P105(f326(f326(f328(f917(x102751,a905)),f805(x102752,x102751)),f326(f326(f10(f917(x102751,a905),a905,f917(x102751,a905)),f86(x102751)),f326(f326(f10(f917(x102751,a905),f917(x102751,a905),f917(x102751,a905)),f326(f20(x102751,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102751),a324),f326(f326(f20(x102751,x102751,a905),x102752),f7(x102751))))),f326(f326(f9(f917(x102751,a905),f917(x102751,f917(x102751,a905)),f917(x102751,a905)),f326(f326(f10(f917(f917(x102751,a905),a905),f917(f917(x102751,f917(x102751,a905)),f917(x102751,a905)),f917(x102751,a905)),f10(f917(x102751,a905),a905,x102751)),a323)),x102752)))))
% 157.55/157.22 [10015]~P94(x100151)+E(f326(f326(f243(x100151),f326(f103(x100151),a97)),f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x100152)),f77(x100151))
% 157.55/157.22 [10016]~P140(x100161)+E(f326(f326(f243(x100161),f326(f78(x100161),f77(x100161))),f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x100162)),f77(x100161))
% 157.55/157.22 [10019]~P81(x100191)+E(f326(f326(f243(x100191),x100192),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),a97))),f326(f326(f80(x100191),f326(f326(f80(x100191),x100192),x100192)),x100192))
% 157.55/157.22 [10210]~P105(f326(f326(f234(a1),f2(a1)),x102102))+E(f45(a1,f326(f326(f79(a1),f77(a1)),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x102101)),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x102102)),f326(f326(f79(a1),f77(a1)),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f45(a1,x102101,x102102))))
% 157.55/157.22 [10233]~P105(f326(f326(f234(a1),f2(a1)),x102332))+E(f326(f326(f36(a1),f326(f326(f79(a1),f77(a1)),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x102331))),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x102332)),f326(f326(f36(a1),x102331),x102332))
% 157.55/157.22 [10235]~P105(f326(f326(f234(a1),x102352),f2(a1)))+E(f326(f326(f36(a1),f326(f326(f79(a1),f77(a1)),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x102351))),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x102352)),f326(f326(f36(a1),f326(f326(f79(a1),x102351),f77(a1))),x102352))
% 157.55/157.22 [10236]~P105(f326(f326(f234(a1),x102362),f2(a1)))+E(f45(a1,f326(f326(f79(a1),f77(a1)),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x102361)),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x102362)),f326(f326(f3(a1),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f45(a1,f326(f326(f79(a1),x102361),f77(a1)),x102362))),f77(a1)))
% 157.55/157.22 [10108]~P94(x101081)+E(f326(f326(f243(x101081),f326(f103(x101081),a97)),f326(a112,f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x101082))),f326(f103(x101081),a97))
% 157.55/157.22 [10110]~P140(x101101)+E(f326(f326(f243(x101101),f326(f78(x101101),f77(x101101))),f326(a112,f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x101102))),f326(f78(x101101),f77(x101101)))
% 157.55/157.22 [5089]P37(x50891,x50892)+~P7(x50891,x50893,x50892)
% 157.55/157.22 [5091]P50(x50911,x50912)+~P7(x50911,x50913,x50912)
% 157.55/157.22 [5264]~P7(x52641,x52642,x52643)+P51(x52641,x52642,x52643)
% 157.55/157.22 [8212]~E(x82122,x82123)+P33(x82121,x82121,a323,x82122,x82123)
% 157.55/157.22 [8752]E(x87521,x87522)+~P33(x87523,x87523,a323,x87521,x87522)
% 157.55/157.22 [4893]E(f169(x48931,x48932,x48933),f113(x48931))+~E(x48932,f2(a909))
% 157.55/157.22 [5061]~E(f169(x50612,x50611,x50613),f113(x50612))+E(x50611,f2(a909))
% 157.55/157.22 [5269]~P36(x52691,x52693)+P36(x52691,f320(x52691,x52692,x52693))
% 157.55/157.22 [5379]~P28(x53791,x53792,x53793)+P30(a1,x53791,f178(x53792,x53793))
% 157.55/157.22 [5453]P28(x54531,x54532,x54533)+~P30(a1,x54531,f178(x54532,x54533))
% 157.55/157.22 [5524]~P7(x55241,x55242,x55243)+P7(f910(x55241),f161(x55241,x55242),f158(x55241,x55243))
% 157.55/157.22 [5525]~P51(x55251,x55252,x55253)+P51(f910(x55251),f161(x55251,x55252),f158(x55251,x55253))
% 157.55/157.22 [5638]P53(x56381,x56382,x56383)+~E(f592(x56383,x56382,x56381),f593(x56383,x56382,x56381))
% 157.55/157.22 [5639]P54(x56391,x56392,x56393)+~E(f608(x56393,x56392,x56391),f609(x56393,x56392,x56391))
% 157.55/157.22 [8218]~E(x82182,x82183)+P25(x82181,x82181,f31(x82181),x82182,x82183)
% 157.55/157.22 [8760]E(x87601,x87602)+~P25(x87603,x87603,f31(x87603),x87601,x87602)
% 157.55/157.22 [4848]~E(f326(f168(x48482),x48481),x48483)+E(x48481,f326(f168(x48482),x48483))
% 157.55/157.22 [4849]~E(x48492,f326(f168(x48491),x48493))+E(f326(f168(x48491),x48492),x48493)
% 157.55/157.22 [4899]E(x48991,x48992)+~E(f326(f168(x48993),x48991),f326(f168(x48993),x48992))
% 157.55/157.22 [5115]~P6(x51153,x51151)+P105(f326(f326(x51151,x51152),x51152))
% 157.55/157.22 [5116]~P42(x51163,x51161)+P105(f326(f326(x51161,x51162),x51162))
% 157.55/157.22 [5118]~P58(x51181,x51182)+P105(f326(f314(x51181,x51182),x51183))
% 157.55/157.22 [5184]~P36(x51841,x51842)+P36(f910(x51841),f326(f143(x51841,x51842),x51843))
% 157.55/157.22 [5189]~P105(f326(x51892,x51893))+~E(f326(f261(x51891),x51892),f188(f917(x51891,a905)))
% 157.55/157.22 [5190]~P105(f326(x51902,x51903))+~E(f188(f917(x51901,a905)),f326(f261(x51901),x51902))
% 157.55/157.22 [5202]E(x52021,f2(a909))+E(f144(x52022,f169(x52022,x52021,x52023)),x52023)
% 157.55/157.22 [5221]~P105(f326(x52211,x52213))+P105(f326(x52211,f89(x52212,x52211)))
% 157.55/157.22 [5222]~P105(f326(x52221,x52223))+P105(f326(x52221,f732(x52221,x52222)))
% 157.55/157.22 [5234]E(x52341,f2(a909))+E(f326(f141(x52342),f169(x52342,x52341,x52343)),x52343)
% 157.55/157.22 [5340]~E(x53402,x53403)+P105(f326(f326(f328(x53401),x53402),f326(a323,x53403)))
% 157.55/157.22 [5356]~E(x53562,f2(a909))+E(f326(f172(x53561),f169(x53561,x53562,x53563)),f188(f917(x53561,a905)))
% 157.55/157.22 [5401]E(f326(f168(x54011),x54012),f326(f326(f151(x54011),x54013),f113(x54011)))+~E(x54012,f326(f326(f151(x54011),x54013),f113(x54011)))
% 157.55/157.22 [5402]~E(x54023,f326(f326(f151(x54021),x54022),f113(x54021)))+E(f326(f326(f151(x54021),x54022),f113(x54021)),f326(f168(x54021),x54023))
% 157.55/157.22 [5449]~P32(x54491,x54492,x54493)+P32(x54491,x54492,f326(f168(x54491),x54493))
% 157.55/157.22 [5450]~P30(x54501,x54502,x54503)+P30(x54501,x54502,f326(f168(x54501),x54503))
% 157.55/157.22 [5454]E(f326(f35(x54541),f812(x54542,x54543,x54541)),x54542)+~E(f326(f35(x54541),x54543),f326(a112,x54542))
% 157.55/157.22 [5461]~P36(x54611,x54613)+P105(f326(f326(f328(x54611),x54612),f315(x54611,x54613)))
% 157.55/157.22 [5465]~E(f326(f168(x54652),x54651),f326(f326(f151(x54652),x54653),f113(x54652)))+E(x54651,f326(f326(f151(x54652),x54653),f113(x54652)))
% 157.55/157.22 [5466]~E(f326(f326(f151(x54662),x54663),f113(x54662)),f326(f168(x54662),x54661))+E(x54661,f326(f326(f151(x54662),x54663),f113(x54662)))
% 157.55/157.22 [5489]E(f84(f916(a909,a909),f48(x54891,x54892)),x54893)+~P105(f326(f48(x54891,x54892),x54893))
% 157.55/157.22 [5528]P32(x55281,x55282,x55283)+~P32(x55281,x55282,f326(f168(x55281),x55283))
% 157.55/157.22 [5529]P30(x55291,x55292,x55293)+~P30(x55291,x55292,f326(f168(x55291),x55293))
% 157.55/157.22 [5568]P105(f326(f326(x55681,x55682),x55682))+~P105(f326(f269(x55683,x55681),x55682))
% 157.55/157.22 [5569]~P105(f326(f326(x55692,x55693),x55693))+P105(f326(f269(x55691,x55692),x55693))
% 157.55/157.22 [5591]~E(x55912,f113(x55911))+P105(f326(f326(f328(f910(x55911)),x55912),f161(x55911,x55913)))
% 157.55/157.22 [5601]~P51(x56011,x56012,x56013)+P51(x56011,x56012,f326(f285(x56011,x56011),x56013))
% 157.55/157.22 [5602]~P54(x56021,x56022,x56023)+P54(x56021,x56022,f326(f285(x56021,x56021),x56023))
% 157.55/157.22 [5619]~P59(x56191)+E(f45(x56191,f45(x56191,x56192,x56193),x56193),f45(x56191,x56192,x56193))
% 157.55/157.22 [5723]E(x57231,x57232)+~P105(f326(f326(f328(x57233),x57231),f326(a323,x57232)))
% 157.55/157.22 [5770]~P143(x57701)+E(f190(x57701,x57702,f2(a909),x57703),x57703)
% 157.55/157.22 [5792]P51(x57921,x57922,x57923)+~P51(x57921,x57922,f326(f285(x57921,x57921),x57923))
% 157.55/157.22 [5793]P54(x57931,x57932,x57933)+~P54(x57931,x57932,f326(f285(x57931,x57931),x57933))
% 157.55/157.22 [5797]~P108(x57972)+E(f150(x57971,x57972,x57973,f113(x57971)),f113(x57971))
% 157.55/157.22 [5809]E(f170(x58091,x58092,f152(x58091,x58093)),f152(x58091,f170(x58091,x58092,x58093)))+~P105(f326(f137(x58091),x58093))
% 157.55/157.22 [5908]~P105(f326(f326(x59083,x59082),x59082))+P105(f326(f326(f328(x59081),x59082),f269(x59081,x59083)))
% 157.55/157.22 [5910]E(f326(f136(x59101,x59102),x59103),f113(x59101))+P105(f326(x59102,f667(x59103,x59102,x59101)))
% 157.55/157.22 [5978]E(f68(x59781,x59782,x59783),x59782)+P105(f326(x59783,f733(x59782,x59781,x59783)))
% 157.55/157.22 [6070]~P105(f326(f137(x60701),x60702))+P105(f326(f137(x60701),f176(x60701,x60702,x60703)))
% 157.55/157.22 [6071]~P105(f326(f137(x60711),x60713))+P105(f326(f137(x60711),f170(x60711,x60712,x60713)))
% 157.55/157.22 [6072]~P105(f326(f137(x60721),x60723))+P105(f326(f137(x60721),f177(x60721,x60722,x60723)))
% 157.55/157.22 [6073]~P105(f326(f137(x60731),x60733))+P105(f326(f137(x60731),f140(x60731,x60732,x60733)))
% 157.55/157.22 [6074]~P145(x60741,x60743,x60742)+P105(f326(x60741,f45(a1,x60742,x60743)))
% 157.55/157.22 [6090]~P32(x60903,x60901,x60902)+P105(f326(x60901,f745(x60902,x60901,x60903)))
% 157.55/157.22 [6091]~P34(x60913,x60911,x60912)+P105(f326(x60911,f751(x60912,x60911,x60913)))
% 157.55/157.22 [6092]~P34(x60923,x60921,x60922)+P105(f326(x60921,f761(x60922,x60921,x60923)))
% 157.55/157.22 [6093]~P32(x60933,x60931,x60932)+P105(f326(x60931,f775(x60931,x60932,x60933)))
% 157.55/157.22 [6094]~P32(x60943,x60941,x60942)+P105(f326(x60941,f784(x60942,x60941,x60943)))
% 157.55/157.22 [6098]P105(f326(f326(x60981,x60982),x60982))+~P105(f326(f326(f328(x60983),x60982),f269(x60983,x60981)))
% 157.55/157.22 [6113]E(f326(f136(x61131,x61132),x61133),f177(x61131,x61132,x61133))+P105(f326(x61132,f716(x61133,x61132,x61131)))
% 157.55/157.22 [6153]~P105(f326(f137(x61531),x61533))+P105(f326(f137(f910(x61531)),f55(x61531,x61532,x61533)))
% 157.55/157.22 [6188]~P109(x61881)+E(f326(f326(f101(f917(x61881,a905)),f326(f281(x61881),x61882)),f302(x61881,x61882,x61883)),f188(f917(x61881,a905)))
% 157.55/157.22 [6189]~P109(x61891)+E(f326(f326(f101(f917(x61891,a905)),f326(f300(x61891),x61892)),f305(x61891,x61892,x61893)),f188(f917(x61891,a905)))
% 157.55/157.22 [6190]~P109(x61901)+E(f326(f326(f101(f917(x61901,a905)),f326(f300(x61901),x61902)),f304(x61901,x61902,x61903)),f188(f917(x61901,a905)))
% 157.55/157.22 [6421]E(f326(f136(x64211,x64212),x64213),x64213)+~P105(f326(x64212,f668(x64213,x64212,x64211)))
% 157.55/157.22 [6423]E(f326(f326(f308(x64231),f874(x64232,x64233,x64231)),f812(x64232,x64233,x64231)),x64233)+~E(f326(f35(x64231),x64233),f326(a112,x64232))
% 157.55/157.22 [6438]P145(x64381,x64382,x64383)+~P105(f326(x64381,f45(a1,x64383,x64382)))
% 157.55/157.22 [6488]P30(x64881,x64882,x64883)+~P105(f326(x64882,f752(x64883,x64882,x64881)))
% 157.55/157.22 [6489]P30(x64891,x64892,x64893)+~P105(f326(x64892,f759(x64892,x64893,x64891)))
% 157.55/157.22 [6490]P30(x64901,x64902,x64903)+~P105(f326(x64902,f760(x64903,x64902,x64901)))
% 157.55/157.22 [6491]P28(x64911,x64912,x64913)+~P105(f326(x64911,f776(x64913,x64912,x64911)))
% 157.55/157.22 [6492]P29(x64921,x64922,x64923)+~P105(f326(x64921,f824(x64923,x64922,x64921)))
% 157.55/157.22 [6494]E(f177(x64941,x64942,x64943),x64943)+~P105(f326(x64942,f712(x64943,x64942,x64941)))
% 157.55/157.22 [6573]~P105(f326(x65732,f568(x65733,x65732,x65731)))+P105(f326(f247(x65731,x65732),x65733))
% 157.55/157.22 [6574]~P105(f326(x65742,f669(x65743,x65742,x65741)))+P105(f326(f160(x65741,x65742),x65743))
% 157.55/157.22 [6826]~P105(f326(f314(x68261,x68262),f382(x68263,x68262,x68261)))+P105(f326(f314(x68261,x68262),x68263))
% 157.55/157.22 [6827]~P105(f326(f314(x68271,x68272),f388(x68273,x68272,x68271)))+P105(f326(f314(x68271,x68272),x68273))
% 157.55/157.22 [7442]~P59(x74421)+E(f326(f326(f79(x74421),f326(f326(f80(x74421),x74422),f326(f326(f36(x74421),x74423),x74422))),f45(x74421,x74423,x74422)),x74423)
% 157.55/157.22 [7471]P28(x74711,x74712,x74713)+P105(f326(f326(f328(a1),f776(x74713,x74712,x74711)),f302(a1,x74712,x74713)))
% 157.55/157.22 [7897]E(f326(f326(f251(x78971,x78971),f474(x78972,x78973,x78971)),f474(x78972,x78973,x78971)),x78973)+~P105(f326(f326(f328(f916(x78971,x78971)),x78973),f262(x78971,x78972)))
% 157.55/157.22 [8011]~P105(f326(f326(f328(x80111),f519(x80113,x80112,x80111)),f315(x80111,x80113)))+P105(f326(f326(f328(x80111),x80112),f315(x80111,x80113)))
% 157.55/157.22 [8012]~P105(f326(f326(f328(x80121),f595(x80123,x80122,x80121)),f315(x80121,x80123)))+P105(f326(f326(f328(x80121),x80122),f315(x80121,x80123)))
% 157.55/157.22 [8013]~P105(f326(f326(f328(x80131),f597(x80133,x80132,x80131)),f315(x80131,x80133)))+P105(f326(f326(f328(x80131),x80132),f315(x80131,x80133)))
% 157.55/157.22 [8105]P32(a1,x81051,f178(x81052,x81053))+P28(f326(f72(a905,a905,a1,a321),x81051),x81052,x81053)
% 157.55/157.22 [8193]~P59(x81931)+E(f326(f326(f79(x81931),f326(f326(f80(x81931),f326(f326(f36(x81931),x81932),x81933)),x81933)),f45(x81931,x81932,x81933)),x81932)
% 157.55/157.22 [8239]~E(f326(f35(x82391),x82392),f326(a112,x82393))+~P105(f326(f326(f328(x82391),f874(x82393,x82392,x82391)),f812(x82393,x82392,x82391)))
% 157.55/157.22 [8670]~P32(a1,x86701,f178(x86702,x86703))+~P28(f326(f72(a905,a905,a1,a321),x86701),x86702,x86703)
% 157.55/157.22 [8857]P105(f326(f326(f234(f917(f916(x88571,x88571),a905)),f306(x88571,x88572)),f306(x88571,x88573)))+~P105(f326(f326(f234(f917(f916(x88571,x88571),a905)),x88572),f306(x88571,x88573)))
% 157.55/157.22 [9137]E(x91371,f113(x91372))+~P105(f326(f326(f328(f916(f910(x91372),f910(x91372))),f326(f326(f251(f910(x91372),f910(x91372)),x91371),f113(x91372))),f158(x91372,x91373)))
% 157.55/157.22 [9161]E(x91611,f113(x91612))+~P105(f326(f326(f328(f916(f910(x91612),f910(x91612))),f326(f326(f251(f910(x91612),f910(x91612)),f113(x91612)),x91611)),f158(x91612,x91613)))
% 157.55/157.22 [9286]E(f326(f326(f151(x92861),f685(x92862,x92863,x92861)),f686(x92862,x92863,x92861)),x92863)+~P105(f326(f326(f328(f916(f910(x92861),f910(x92861))),f326(f326(f251(f910(x92861),f910(x92861)),f113(x92861)),x92863)),f147(x92861,x92862)))
% 157.55/157.22 [9520]~P126(x95201)+~P105(f326(f326(f235(x95201),f326(f326(f79(x95201),f326(f326(f80(x95201),x95202),x95202)),f326(f326(f80(x95201),x95203),x95203))),f2(x95201)))
% 157.55/157.22 [9569]P105(f326(f61(x95691),x95692))+~P105(f326(f326(f328(f916(f917(x95691,a905),f917(x95691,a905))),f326(f326(f251(f917(x95691,a905),f917(x95691,a905)),x95693),x95692)),f313(x95691)))
% 157.55/157.22 [9864]~P46(x98641,x98642,x98643)+P105(f326(f326(f234(a1),f326(f326(f72(f916(a1,a1),a1,x98641,f250(a1,a1)),f212(x98641)),f230(x98641,x98642,f227(x98641,x98643)))),f2(a1)))
% 157.55/157.22 [9865]~P47(x98651,x98652,x98653)+P105(f326(f326(f235(a1),f326(f326(f72(f916(a1,a1),a1,x98651,f250(a1,a1)),f212(x98651)),f230(x98651,x98652,f227(x98651,x98653)))),f2(a1)))
% 157.55/157.22 [9983]P47(x99831,x99832,x99833)+~P105(f326(f326(f235(a1),f326(f326(f72(f916(a1,a1),a1,x99831,f250(a1,a1)),f212(x99831)),f230(x99831,x99832,f227(x99831,x99833)))),f2(a1)))
% 157.55/157.22 [9984]P46(x99841,x99842,x99843)+~P105(f326(f326(f234(a1),f326(f326(f72(f916(a1,a1),a1,x99841,f250(a1,a1)),f212(x99841)),f230(x99841,x99842,f227(x99841,x99843)))),f2(a1)))
% 157.55/157.22 [10335]~P118(x103351)+~P105(f326(f326(f235(x103351),f326(f326(f79(x103351),f326(f326(f243(x103351),x103352),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x103351),x103353),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))),f2(x103351)))
% 157.55/157.22 [4878]~E(x48783,f113(x48781))+E(f326(f326(f134(x48781),x48782),x48783),x48782)
% 157.55/157.22 [4879]~E(x48792,f113(x48791))+E(f326(f326(f134(x48791),x48792),x48793),x48793)
% 157.55/157.22 [4885]~E(x48852,f2(a909))+E(f326(f326(f175(x48851),x48852),x48853),f113(x48851))
% 157.55/157.22 [4894]~E(x48943,f113(x48941))+E(f326(f326(f175(x48941),x48942),x48943),f113(x48941))
% 157.55/157.22 [4933]~E(x49331,x49333)+E(x49331,f326(f326(f134(x49332),f113(x49332)),x49333))
% 157.55/157.22 [5024]~P1(x50242)+E(f326(f188(f917(x50241,x50242)),x50243),f188(x50242))
% 157.55/157.22 [5025]~P116(x50252)+E(f326(f241(f917(x50251,x50252)),x50253),f241(x50252))
% 157.55/157.22 [5043]E(x50431,f113(x50432))+~E(f326(f326(f134(x50432),x50433),x50431),x50433)
% 157.55/157.22 [5044]E(x50441,f113(x50442))+~E(f326(f326(f134(x50442),x50441),x50443),x50443)
% 157.55/157.22 [5052]E(x50521,f113(x50522))+~E(f326(f326(f134(x50522),x50523),x50521),f113(x50522))
% 157.55/157.22 [5053]E(x50531,f113(x50532))+~E(f326(f326(f134(x50532),x50531),x50533),f113(x50532))
% 157.55/157.22 [5082]~E(x50822,f2(a909))+E(f326(f326(f80(a909),x50821),x50822),f326(f326(f80(a909),x50823),x50822))
% 157.55/157.22 [5084]~E(x50841,f2(a909))+E(f326(f326(f80(a909),x50841),x50842),f326(f326(f80(a909),x50841),x50843))
% 157.55/157.22 [5142]~P77(x51421)+E(f326(f326(f110(x51421),x51422),x51423),f326(f326(f110(x51421),x51423),x51422))
% 157.55/157.22 [5144]~P100(x51441)+E(f326(f326(f110(x51441),x51442),x51443),f326(f326(f110(x51441),x51443),x51442))
% 157.55/157.22 [5145]~P112(x51451)+E(f326(f326(f80(x51451),x51452),x51453),f326(f326(f80(x51451),x51453),x51452))
% 157.55/157.22 [5146]~P77(x51461)+E(f326(f326(f101(x51461),x51462),x51463),f326(f326(f101(x51461),x51463),x51462))
% 157.55/157.22 [5148]~P101(x51481)+E(f326(f326(f101(x51481),x51482),x51483),f326(f326(f101(x51481),x51483),x51482))
% 157.55/157.22 [5149]~P112(x51491)+E(f326(f326(f79(x51491),x51492),x51493),f326(f326(f79(x51491),x51493),x51492))
% 157.55/157.22 [5151]~P108(x51511)+E(f326(f326(f232(x51511),x51512),x51513),f326(f326(f232(x51511),x51513),x51512))
% 157.55/157.22 [5153]~P108(x51531)+E(f326(f326(f233(x51531),x51532),x51533),f326(f326(f233(x51531),x51533),x51532))
% 157.55/157.22 [5216]E(f45(a909,x52161,x52162),f2(a909))+~E(x52161,f326(f326(f80(a909),x52162),x52163))
% 157.55/157.22 [5217]E(f45(a1,x52171,x52172),f2(a1))+~E(x52171,f326(f326(f80(a1),x52172),x52173))
% 157.55/157.22 [5281]E(x52811,x52812)+~E(f326(f326(f79(a909),x52813),x52811),f326(f326(f79(a909),x52813),x52812))
% 157.55/157.22 [5282]E(x52821,x52822)+~E(f326(f326(f79(a909),x52821),x52823),f326(f326(f79(a909),x52822),x52823))
% 157.55/157.22 [5292]~P95(x52921)+E(f326(f326(f101(x52921),x52922),f326(f78(x52921),x52923)),f326(f326(f3(x52921),x52922),x52923))
% 157.55/157.22 [5293]~P66(x52931)+E(f326(f326(f79(x52931),x52932),f326(f78(x52931),x52933)),f326(f326(f3(x52931),x52932),x52933))
% 157.55/157.22 [5294]~P73(x52941)+E(f326(f326(f79(x52941),x52942),f326(f78(x52941),x52943)),f326(f326(f3(x52941),x52942),x52943))
% 157.55/157.22 [5295]~P114(x52951)+E(f326(f326(f79(x52951),x52952),f326(f78(x52951),x52953)),f326(f326(f3(x52951),x52952),x52953))
% 157.55/157.22 [5296]~P73(x52961)+E(f326(f326(f3(x52961),x52962),f326(f78(x52961),x52963)),f326(f326(f79(x52961),x52962),x52963))
% 157.55/157.22 [5334]~P105(f326(x53343,x53342))+P105(f326(f326(f328(x53341),x53342),x53343))
% 157.55/157.22 [5336]~P69(x53362)+E(f326(f326(f8(x53361,x53362),x53363),f188(f917(x53361,a905))),f2(x53362))
% 157.55/157.22 [5338]~P74(x53382)+E(f326(f326(f11(x53381,x53382),x53383),f188(f917(x53381,a905))),f77(x53382))
% 157.55/157.22 [5391]~E(x53912,f326(f326(f79(a909),x53911),x53913))+P105(f326(f326(f234(a909),x53911),x53912))
% 157.55/157.22 [5394]~E(x53942,f188(f917(x53941,a905)))+E(f326(f326(f60(x53941),x53942),x53943),f188(f917(f917(x53941,a905),a905)))
% 157.55/157.22 [5395]~E(x53952,f188(f917(x53951,a905)))+E(f188(f917(f917(x53951,a905),a905)),f326(f326(f60(x53951),x53952),x53953))
% 157.55/157.22 [5469]~E(f326(f283(x54692,x54693),x54691),f188(f917(x54693,a905)))+E(x54691,f188(f917(f916(x54692,x54693),a905)))
% 157.55/157.22 [5470]~E(f326(f263(x54702,x54703),x54701),f188(f917(x54702,a905)))+E(x54701,f188(f917(f916(x54702,x54703),a905)))
% 157.55/157.22 [5502]E(f326(f283(x55021,x55022),x55023),f188(f917(x55022,a905)))+~E(x55023,f188(f917(f916(x55021,x55022),a905)))
% 157.55/157.22 [5503]E(f326(f263(x55031,x55032),x55033),f188(f917(x55031,a905)))+~E(x55033,f188(f917(f916(x55031,x55032),a905)))
% 157.55/157.22 [5506]E(f273(x55061,x55062,x55063),f326(f326(f3(a99),x55062),x55063))+P105(f326(f326(f235(a99),x55062),x55063))
% 157.55/157.22 [5522]P105(f326(x55221,x55222))+~P105(f326(f326(f328(x55223),x55222),x55221))
% 157.55/157.22 [5561]E(x55611,x55612)+~E(f326(f78(f917(x55613,a905)),x55611),f326(f78(f917(x55613,a905)),x55612))
% 157.55/157.22 [5572]~E(x55721,f188(f917(x55722,a905)))+~P105(f326(f326(f328(x55722),x55723),x55721))
% 157.55/157.22 [5603]~E(x56032,f326(f326(f79(a1),x56031),f326(f100(a1),x56033)))+P105(f326(f326(f234(a1),x56031),x56032))
% 157.55/157.22 [5617]E(f326(f326(f308(x56171),x56172),x56173),x56173)+~P105(f326(f326(f328(x56171),x56172),x56173))
% 157.55/157.22 [5628]E(x56281,f188(f917(x56282,a905)))+~E(f326(f326(f60(x56282),x56281),x56283),f188(f917(f917(x56282,a905),a905)))
% 157.55/157.22 [5629]E(x56291,f188(f917(x56292,a905)))+~E(f188(f917(f917(x56292,a905),a905)),f326(f326(f60(x56292),x56291),x56293))
% 157.55/157.22 [5636]~P110(x56361)+E(f326(f326(f80(x56361),f326(f78(x56361),x56362)),f326(f78(x56361),x56363)),f326(f326(f80(x56361),x56362),x56363))
% 157.55/157.22 [5637]~P62(x56371)+E(f326(f326(f290(x56371),f326(f78(x56371),x56372)),f326(f78(x56371),x56373)),f326(f326(f290(x56371),x56372),x56373))
% 157.55/157.22 [5669]~P105(f326(x56693,x56692))+P105(f326(f326(f328(x56691),x56692),f326(f261(x56691),x56693)))
% 157.55/157.22 [5696]E(x56961,f2(a909))+E(f326(f172(x56962),f169(x56962,x56961,x56963)),f326(f326(f308(x56962),x56963),f188(f917(x56962,a905))))
% 157.55/157.22 [5716]E(f170(x57161,x57162,x57163),x57163)+P105(f326(f326(f328(x57161),x57162),f326(f172(x57161),x57163)))
% 157.55/157.22 [5801]~P105(f326(f137(x58011),x58013))+P105(f326(f137(x58011),f326(f136(x58011,x58012),x58013)))
% 157.55/157.22 [5844]~P59(x58441)+E(f326(f326(f36(x58441),f45(x58441,x58442,x58443)),x58443),f2(x58441))
% 157.55/157.22 [5863]E(f176(x58631,f326(f326(f151(x58631),x58632),f113(x58631)),x58633),f113(x58631))+P105(f326(f326(f328(a909),f2(a909)),x58633))
% 157.55/157.22 [5869]E(x58691,f2(a909))+E(f326(f171(x58692),f169(x58692,x58691,x58693)),f169(x58692,f326(f326(f3(a909),x58691),f77(a909)),x58693))
% 157.55/157.22 [5920]E(f326(f326(f151(x59201),x59202),x59203),f140(x59201,x59202,x59203))+P105(f326(f326(f328(x59201),x59202),f326(f172(x59201),x59203)))
% 157.55/157.22 [5929]E(x59291,x59292)+~E(f326(f326(f80(a909),f326(a112,x59293)),x59291),f326(f326(f80(a909),f326(a112,x59293)),x59292))
% 157.55/157.22 [5930]~E(x59302,f326(f326(f79(a1),x59301),f326(f100(a1),f326(a112,x59303))))+P105(f326(f326(f235(a1),x59301),x59302))
% 157.55/157.22 [6000]~P29(x60001,x60002,x60003)+P30(a909,x60001,f139(a909,f326(f301(a909,x60002),x60003)))
% 157.55/157.22 [6051]~E(x60513,f113(x60511))+E(f326(f326(f326(f183(f910(x60511),f910(x60511)),x60512),f167(x60511)),x60513),f113(x60511))
% 157.55/157.22 [6055]P105(f326(x60551,x60552))+~P105(f326(f326(f328(x60553),x60552),f326(f261(x60553),x60551)))
% 157.55/157.22 [6085]E(x60851,x60852)+~E(f326(f326(f308(x60853),x60851),f188(f917(x60853,a905))),f326(f326(f308(x60853),x60852),f188(f917(x60853,a905))))
% 157.55/157.22 [6100]~P109(x61001)+E(f326(f326(f101(f917(x61001,a905)),f326(f281(x61001),x61002)),f326(f301(x61001,x61002),x61003)),f188(f917(x61001,a905)))
% 157.55/157.22 [6139]E(f140(x61391,x61392,x61393),x61393)+~P105(f326(f326(f328(x61391),x61392),f326(f172(x61391),x61393)))
% 157.55/157.22 [6161]~P79(x61611)+E(f326(f309(x61611,x61611,f78(x61611)),f326(f301(x61611,x61612),x61613)),f304(x61611,f326(f78(x61611),x61613),f326(f78(x61611),x61612)))
% 157.55/157.22 [6172]E(f326(f189(f910(x61721)),f170(x61721,x61722,x61723)),f326(f189(f910(x61721)),x61723))+P105(f326(f326(f328(x61721),x61722),f326(f172(x61721),x61723)))
% 157.55/157.22 [6226]~P109(x62261)+E(f326(f326(f101(f917(x62261,a905)),f326(f301(x62261,x62262),x62263)),f326(f282(x62261),x62263)),f188(f917(x62261,a905)))
% 157.55/157.22 [6246]~P79(x62461)+E(f326(f309(x62461,x62461,f78(x62461)),f302(x62461,x62462,x62463)),f302(x62461,f326(f78(x62461),x62463),f326(f78(x62461),x62462)))
% 157.55/157.22 [6247]~P79(x62471)+E(f326(f309(x62471,x62471,f78(x62471)),f305(x62471,x62472,x62473)),f305(x62471,f326(f78(x62471),x62473),f326(f78(x62471),x62472)))
% 157.55/157.22 [6312]E(f176(x63121,f326(f326(f151(x63121),x63122),f113(x63121)),x63123),f326(f326(f151(x63121),x63122),f113(x63121)))+~P105(f326(f326(f328(a909),f2(a909)),x63123))
% 157.55/157.22 [6317]P29(x63171,x63172,x63173)+~P30(a909,x63171,f139(a909,f326(f301(a909,x63172),x63173)))
% 157.55/157.22 [6320]~P79(x63201)+E(f326(f309(x63201,x63201,f78(x63201)),f304(x63201,x63202,x63203)),f326(f301(x63201,f326(f78(x63201),x63203)),f326(f78(x63201),x63202)))
% 157.55/157.22 [6341]~P60(x63411)+E(f45(x63411,f326(f78(x63411),f45(x63411,x63412,x63413)),x63413),f45(x63411,f326(f78(x63411),x63412),x63413))
% 157.55/157.22 [6436]~P105(f326(f61(f916(x64362,x64361)),x64363))+P105(f326(f61(x64361),f326(f283(x64362,x64361),x64363)))
% 157.55/157.22 [6437]~P105(f326(f61(f916(x64371,x64372)),x64373))+P105(f326(f61(x64371),f326(f263(x64371,x64372),x64373)))
% 157.55/157.22 [6442]~P109(x64421)+E(f326(f326(f101(f917(x64421,a905)),f302(x64421,x64422,x64423)),f326(f303(x64421),x64423)),f188(f917(x64421,a905)))
% 157.55/157.22 [6443]~P109(x64431)+E(f326(f326(f101(f917(x64431,a905)),f305(x64431,x64432,x64433)),f326(f282(x64431),x64433)),f188(f917(x64431,a905)))
% 157.55/157.22 [6444]~P109(x64441)+E(f326(f326(f101(f917(x64441,a905)),f304(x64441,x64442,x64443)),f326(f303(x64441),x64443)),f188(f917(x64441,a905)))
% 157.55/157.22 [6515]E(f326(f326(f164(x65151),x65152),f652(x65152,x65153,x65151)),x65153)+~P105(f326(f326(f328(x65151),x65153),f326(f172(x65151),x65152)))
% 157.55/157.22 [6657]E(x66571,f113(x66572))+~E(f326(f326(f326(f183(f910(x66572),f910(x66572)),x66573),f167(x66572)),x66571),f113(x66572))
% 157.55/157.22 [6762]~P105(f326(f61(f916(x67622,x67621)),x67623))+P105(f326(f61(f916(x67621,x67622)),f326(f285(x67622,x67621),x67623)))
% 157.55/157.22 [6785]E(x67851,x67852)+~E(f289(a909,f286(a909),x67853,x67851),f326(f326(f308(a909),x67852),f188(f917(a909,a905))))
% 157.55/157.22 [6786]E(x67861,x67862)+~E(f289(a909,f286(a909),x67861,x67862),f326(f326(f308(a909),x67863),f188(f917(a909,a905))))
% 157.55/157.22 [6917]P54(x69171,x69172,x69173)+P105(f326(f326(f328(x69171),f609(x69173,x69172,x69171)),x69172))
% 157.55/157.22 [6918]P54(x69181,x69182,x69183)+P105(f326(f326(f328(x69181),f608(x69183,x69182,x69181)),x69182))
% 157.55/157.22 [6928]P105(f326(f314(x69281,x69282),x69283))+P105(f326(f326(x69282,f382(x69283,x69282,x69281)),x69283))
% 157.55/157.22 [6929]P105(f326(f314(x69291,x69292),x69293))+P105(f326(f326(x69292,f388(x69293,x69292,x69291)),x69293))
% 157.55/157.22 [6960]E(f326(f189(f910(x69601)),f170(x69601,x69602,x69603)),f326(f326(f3(a909),f326(f189(f910(x69601)),x69603)),f77(a909)))+~P105(f326(f326(f328(x69601),x69602),f326(f172(x69601),x69603)))
% 157.55/157.22 [6999]P105(f326(f247(x69991,x69992),x69993))+P105(f326(f326(f328(x69991),f568(x69993,x69992,x69991)),x69993))
% 157.55/157.22 [7008]~P105(f326(f61(f916(x70082,x70081)),f326(f285(x70081,x70082),x70083)))+P105(f326(f61(f916(x70081,x70082)),x70083))
% 157.55/157.22 [7063]~P105(f326(f326(f328(x70631),x70632),f326(f172(x70631),f114(x70631,x70633))))+P105(f326(f326(f328(x70631),x70632),f326(f172(x70631),x70633)))
% 157.55/157.22 [7097]E(f326(f136(x70971,x70972),x70973),x70973)+P105(f326(f326(f328(x70971),f668(x70973,x70972,x70971)),f326(f172(x70971),x70973)))
% 157.55/157.22 [7112]E(f326(f136(x71121,x71122),x71123),f113(x71121))+P105(f326(f326(f328(x71121),f667(x71123,x71122,x71121)),f326(f172(x71121),x71123)))
% 157.55/157.22 [7138]P30(x71381,x71382,x71383)+P105(f326(f326(f328(x71381),f752(x71383,x71382,x71381)),f326(f172(x71381),x71383)))
% 157.55/157.22 [7139]P30(x71391,x71392,x71393)+P105(f326(f326(f328(x71391),f760(x71393,x71392,x71391)),f326(f172(x71391),x71393)))
% 157.55/157.22 [7140]P30(x71401,x71402,x71403)+P105(f326(f326(f328(x71401),f759(x71402,x71403,x71401)),f326(f172(x71401),x71403)))
% 157.55/157.22 [7143]E(f177(x71431,x71432,x71433),x71433)+P105(f326(f326(f328(x71431),f712(x71433,x71432,x71431)),f326(f172(x71431),x71433)))
% 157.55/157.22 [7219]P105(f326(f160(x72191,x72192),x72193))+P105(f326(f326(f328(x72191),f669(x72193,x72192,x72191)),f326(f172(x72191),x72193)))
% 157.55/157.22 [7228]~P32(x72281,x72283,x72282)+P105(f326(f326(f328(x72281),f745(x72282,x72283,x72281)),f326(f172(x72281),x72282)))
% 157.55/157.22 [7229]~P34(x72291,x72293,x72292)+P105(f326(f326(f328(x72291),f751(x72292,x72293,x72291)),f326(f172(x72291),x72292)))
% 157.55/157.22 [7230]~P34(x72301,x72303,x72302)+P105(f326(f326(f328(x72301),f761(x72302,x72303,x72301)),f326(f172(x72301),x72302)))
% 157.55/157.22 [7231]~P32(x72311,x72312,x72313)+P105(f326(f326(f328(x72311),f775(x72312,x72313,x72311)),f326(f172(x72311),x72313)))
% 157.55/157.22 [7232]~P32(x72321,x72323,x72322)+P105(f326(f326(f328(x72321),f784(x72322,x72323,x72321)),f326(f172(x72321),x72322)))
% 157.55/157.22 [7266]P105(f326(f326(f328(x72661),x72662),f893(x72663,x72662,x72661)))+~P105(f326(f326(f328(x72661),x72662),f37(f917(x72661,a905),x72663)))
% 157.55/157.22 [7267]~P69(x72671)+E(f326(f326(f79(x72671),f326(f326(f8(a909,x72671),x72672),f326(f281(a909),x72673))),f326(x72672,x72673)),f326(f326(f8(a909,x72671),x72672),f326(f281(a909),f326(a112,x72673))))
% 157.55/157.22 [7279]P29(x72791,x72792,x72793)+P105(f326(f326(f328(a909),f824(x72793,x72792,x72791)),f326(f301(a909,x72792),x72793)))
% 157.55/157.22 [7357]~P32(x73572,x73571,x73573)+P105(f326(x73571,f326(f326(f164(x73572),x73573),f748(x73573,x73571,x73572))))
% 157.55/157.22 [7369]~P105(f326(f326(f328(x73691),x73692),f384(x73692,x73693,x73691)))+P105(f326(f326(f328(x73691),x73692),f38(f917(x73691,a905),x73693)))
% 157.55/157.22 [7402]~P69(x74021)+E(f326(f326(f79(x74021),f326(f326(f8(a909,x74021),x74022),f326(f300(a909),x74023))),f326(x74022,f326(a112,x74023))),f326(f326(f8(a909,x74021),x74022),f326(f300(a909),f326(a112,x74023))))
% 157.55/157.22 [7545]P105(f326(f326(f328(f910(x75451)),x75452),f161(x75451,x75453)))+P105(f326(f326(f328(x75451),f653(x75453,x75452,x75451)),f326(f172(x75451),x75452)))
% 157.55/157.22 [7559]~P105(f326(f326(f328(f910(x75591)),x75592),f161(x75591,f315(x75591,x75593))))+P105(f326(f326(f328(f910(x75591)),x75592),f315(f910(x75591),f157(x75591,x75593))))
% 157.55/157.22 [7584]~P105(f326(f326(f328(f910(x75841)),x75842),f315(f910(x75841),f157(x75841,x75843))))+P105(f326(f326(f328(f910(x75841)),x75842),f161(x75841,f315(x75841,x75843))))
% 157.55/157.22 [7617]E(f326(f326(f326(f183(f910(x76171),f910(x76171)),x76172),f167(x76171)),x76173),x76173)+~P105(f326(f326(f234(a909),f326(f189(f910(x76171)),x76173)),f77(a909)))
% 157.55/157.22 [7650]E(f326(f326(f134(x76501),f749(x76502,x76503,x76501)),f326(f326(f151(x76501),x76503),f750(x76502,x76503,x76501))),x76502)+~P105(f326(f326(f328(x76501),x76503),f326(f172(x76501),x76502)))
% 157.55/157.22 [7651]E(f326(f326(f134(x76511),f754(x76512,x76513,x76511)),f326(f326(f151(x76511),x76513),f755(x76512,x76513,x76511))),x76512)+~P105(f326(f326(f328(x76511),x76513),f326(f172(x76511),x76512)))
% 157.55/157.22 [7652]E(f326(f326(f134(x76521),f756(x76522,x76523,x76521)),f326(f326(f151(x76521),x76523),f758(x76522,x76523,x76521))),x76522)+~P105(f326(f326(f328(x76521),x76523),f326(f172(x76521),x76522)))
% 157.55/157.22 [7673]~P24(x76731,x76732,x76733,f241(f917(x76731,a905)))+P24(f910(x76731),f910(x76732),f326(f154(x76731,x76732),x76733),f241(f917(f910(x76731),a905)))
% 157.55/157.22 [7820]E(x78201,f326(f326(f79(a909),f326(f326(f80(a909),f326(f250(a909,a909),x78202)),x78203)),f326(f255(a909,a909),x78202)))+~P105(f326(f48(x78201,x78203),x78202))
% 157.55/157.22 [7828]P24(x78281,x78282,x78283,f241(f917(x78281,a905)))+~P24(f910(x78281),f910(x78282),f326(f154(x78281,x78282),x78283),f241(f917(f910(x78281),a905)))
% 157.55/157.22 [7872]P105(f326(f326(f328(f917(x78721,a905)),f384(x78722,x78723,x78721)),x78723))+P105(f326(f326(f328(x78721),x78722),f38(f917(x78721,a905),x78723)))
% 157.55/157.22 [7961]P105(f326(f326(f328(f910(x79611)),x79612),f161(x79611,x79613)))+~P105(f326(f326(f328(x79611),f653(x79613,x79612,x79611)),x79613))
% 157.55/157.22 [8060]P30(x80601,x80602,x80603)+~P105(f326(x80602,f326(f326(f164(x80601),x80603),f757(x80603,x80602,x80601))))
% 157.55/157.22 [8084]E(x80841,x80842)+~E(f326(f326(f9(x80843,f917(x80843,a905),a905),f328(x80843)),x80841),f326(f326(f9(x80843,f917(x80843,a905),a905),f328(x80843)),x80842))
% 157.55/157.22 [8092]~P105(f326(f326(f328(f916(x80921,x80921)),x80923),f262(x80921,x80922)))+P105(f326(f326(f328(x80921),f474(x80922,x80923,x80921)),x80922))
% 157.55/157.22 [8094]~P105(f326(f326(f328(x80941),x80943),f37(f917(x80941,a905),x80942)))+P105(f326(f326(f328(f917(x80941,a905)),f893(x80942,x80943,x80941)),x80942))
% 157.55/157.22 [8213]P24(x82131,x82132,f90(x82132,x82131,f241(f917(x82132,a905)),x82133),f241(f917(x82131,a905)))+~E(f326(f309(x82132,x82131,x82133),f241(f917(x82132,a905))),f241(f917(x82131,a905)))
% 157.55/157.22 [8267]~P105(f326(f326(f328(x82671),x82672),f326(f172(x82671),f754(x82673,x82672,x82671))))+~P105(f326(f326(f328(x82671),x82672),f326(f172(x82671),x82673)))
% 157.55/157.22 [8268]~P105(f326(f326(f328(x82681),x82682),f326(f172(x82681),f758(x82683,x82682,x82681))))+~P105(f326(f326(f328(x82681),x82682),f326(f172(x82681),x82683)))
% 157.55/157.22 [8292]P29(f326(f72(a905,a905,a909,a321),x82921),x82922,x82923)+P32(a909,x82921,f139(a909,f326(f301(a909,x82922),x82923)))
% 157.55/157.22 [8452]E(x84521,f113(x84522))+P105(f326(f326(f328(x84522),f326(f250(x84522,f916(a99,a99)),f326(f274(x84522,x84521),x84523))),f326(f172(x84522),x84521)))
% 157.55/157.22 [8549]~P68(x85491)+E(f326(f142(x85491,x85491,f326(f9(x85491,x85491,x85491),f79(x85491)),x85492),f326(f168(x85491),x85493)),f326(f142(x85491,x85491,f79(x85491),x85492),x85493))
% 157.55/157.22 [8740]~P24(x87402,x87401,x87403,f241(f917(x87402,a905)))+E(f326(f309(x87401,x87402,f90(x87402,x87401,f241(f917(x87402,a905)),x87403)),f241(f917(x87401,a905))),f241(f917(x87402,a905)))
% 157.55/157.22 [8810]~P29(f326(f72(a905,a905,a909,a321),x88101),x88102,x88103)+~P32(a909,x88101,f139(a909,f326(f301(a909,x88102),x88103)))
% 157.55/157.22 [9057]~P108(x90571)+E(f326(f172(x90571),f149(x90571,x90571,f7(x90571),x90572,x90573)),f326(f326(f308(x90571),x90572),f326(f172(x90571),x90573)))
% 157.55/157.22 [9066]~E(f326(x90663,f326(f90(x90661,x90662,f241(f917(x90661,a905)),x90663),f804(x90663,x90662,x90661))),f804(x90663,x90662,x90661))+E(f326(f309(x90661,x90662,x90663),f241(f917(x90661,a905))),f241(f917(x90662,a905)))
% 157.55/157.22 [9068]P105(f326(f326(f235(a909),f2(a909)),f617(x90681,x90682,x90683)))+~P105(f326(f326(f328(f916(x90683,x90683)),x90682),f326(f326(f288(x90683,x90683,x90683),x90681),f306(x90683,x90681))))
% 157.55/157.22 [9343]~P56(x93431,x93432)+~P105(f326(f326(f328(f916(x93431,x93431)),f326(f326(f251(x93431,x93431),x93433),x93433)),f326(f326(f288(x93431,x93431,x93431),x93432),f306(x93431,x93432))))
% 157.55/157.22 [9475]~E(f326(f326(f101(f917(f916(x94751,x94751),a905)),f326(f285(x94751,x94751),x94752)),f306(x94751,x94752)),f188(f917(f916(x94751,x94751),a905)))+~P105(f326(f326(f328(f916(x94751,x94751)),f326(f326(f251(x94751,x94751),x94753),x94753)),f326(f326(f288(x94751,x94751,x94751),x94752),f306(x94751,x94752))))
% 157.55/157.22 [9655]~P105(f326(f61(x96551),x96552))+P105(f326(f326(f234(a909),f326(f35(x96551),f326(f326(f3(f917(x96551,a905)),x96552),f326(f326(f308(x96551),x96553),f188(f917(x96551,a905)))))),f326(f35(x96551),x96552)))
% 157.55/157.22 [5204]~E(x52043,f113(x52041))+E(f144(x52041,f326(f326(f151(x52041),x52042),x52043)),x52042)
% 157.55/157.22 [5213]~E(x52133,f113(x52131))+E(f114(x52131,f326(f326(f151(x52131),x52132),x52133)),f113(x52131))
% 157.55/157.22 [5243]E(x52431,f113(x52432))+E(f144(x52432,f326(f326(f151(x52432),x52433),x52431)),f144(x52432,x52431))
% 157.55/157.22 [5245]E(x52451,f113(x52452))+E(f144(x52452,f326(f326(f134(x52452),x52453),x52451)),f144(x52452,x52451))
% 157.55/157.22 [5251]~E(x52513,f113(x52511))+E(f114(x52511,f326(f326(f134(x52511),x52512),x52513)),f114(x52511,x52512))
% 157.55/157.22 [5253]~E(x52533,f113(x52531))+E(f144(x52531,f326(f326(f134(x52531),x52532),x52533)),f144(x52531,x52532))
% 157.55/157.22 [5286]E(x52861,f113(x52862))+E(f326(f141(x52862),f326(f326(f134(x52862),x52861),x52863)),f326(f141(x52862),x52861))
% 157.55/157.22 [5314]~E(x53142,f113(x53141))+E(f326(f141(x53141),f326(f326(f134(x53141),x53142),x53143)),f326(f141(x53141),x53143))
% 157.55/157.22 [5367]~P77(x53671)+E(f326(f326(f110(x53671),x53672),f326(f326(f101(x53671),x53672),x53673)),x53672)
% 157.55/157.22 [5368]~P77(x53681)+E(f326(f326(f101(x53681),x53682),f326(f326(f110(x53681),x53682),x53683)),x53682)
% 157.55/157.22 [5369]~P108(x53691)+E(f326(f326(f232(x53691),x53692),f326(f326(f233(x53691),x53692),x53693)),x53692)
% 157.55/157.22 [5370]~P108(x53701)+E(f326(f326(f233(x53701),x53702),f326(f326(f232(x53701),x53702),x53703)),x53702)
% 157.55/157.22 [5389]~P59(x53891)+E(f45(x53891,f326(f326(f80(x53891),x53892),x53893),x53893),f2(x53891))
% 157.55/157.22 [5390]~P59(x53901)+E(f45(x53901,f326(f326(f80(x53901),x53902),x53903),x53902),f2(x53901))
% 157.55/157.22 [5464]~P66(x54641)+E(f326(f78(x54641),f326(f326(f3(x54641),x54642),x54643)),f326(f326(f3(x54641),x54643),x54642))
% 157.55/157.22 [5526]E(x55261,f113(x55262))+E(f114(x55262,f326(f326(f151(x55262),x55263),x55261)),f326(f326(f151(x55262),x55263),f114(x55262,x55261)))
% 157.55/157.22 [5527]E(x55271,f113(x55272))+E(f114(x55272,f326(f326(f134(x55272),x55273),x55271)),f326(f326(f134(x55272),x55273),f114(x55272,x55271)))
% 157.55/157.22 [5530]~P4(x55301)+E(f37(x55301,f326(f326(f308(x55301),x55302),x55303)),f326(f326(f110(x55301),x55302),f37(x55301,x55303)))
% 157.55/157.22 [5531]~P4(x55311)+E(f38(x55311,f326(f326(f308(x55311),x55312),x55313)),f326(f326(f101(x55311),x55312),f38(x55311,x55313)))
% 157.55/157.22 [5577]~P77(x55771)+E(f326(f326(f110(x55771),x55772),f326(f326(f110(x55771),x55772),x55773)),f326(f326(f110(x55771),x55772),x55773))
% 157.55/157.22 [5579]~P100(x55791)+E(f326(f326(f110(x55791),x55792),f326(f326(f110(x55791),x55792),x55793)),f326(f326(f110(x55791),x55792),x55793))
% 157.55/157.22 [5580]~P96(x55801)+E(f326(f326(f80(x55801),x55802),f326(f326(f80(x55801),x55802),x55803)),f326(f326(f80(x55801),x55802),x55803))
% 157.55/157.22 [5581]~P77(x55811)+E(f326(f326(f101(x55811),x55812),f326(f326(f101(x55811),x55812),x55813)),f326(f326(f101(x55811),x55812),x55813))
% 157.55/157.22 [5583]~P101(x55831)+E(f326(f326(f101(x55831),x55832),f326(f326(f101(x55831),x55832),x55833)),f326(f326(f101(x55831),x55832),x55833))
% 157.55/157.22 [5585]~P108(x55851)+E(f326(f326(f232(x55851),x55852),f326(f326(f232(x55851),x55852),x55853)),f326(f326(f232(x55851),x55852),x55853))
% 157.55/157.22 [5587]~P108(x55871)+E(f326(f326(f233(x55871),x55872),f326(f326(f233(x55871),x55872),x55873)),f326(f326(f233(x55871),x55872),x55873))
% 157.55/157.22 [5594]~P59(x55941)+E(f45(x55941,f326(f326(f79(x55941),x55942),x55943),x55943),f45(x55941,x55942,x55943))
% 157.55/157.22 [5595]~P59(x55951)+E(f45(x55951,f326(f326(f79(x55951),x55952),x55953),x55952),f45(x55951,x55953,x55952))
% 157.55/157.22 [5604]~P110(x56041)+E(f326(f326(f80(x56041),x56042),f326(f78(x56041),x56043)),f326(f78(x56041),f326(f326(f80(x56041),x56042),x56043)))
% 157.55/157.22 [5605]~P62(x56051)+E(f326(f326(f290(x56051),x56052),f326(f78(x56051),x56053)),f326(f78(x56051),f326(f326(f290(x56051),x56052),x56053)))
% 157.55/157.22 [5606]~P82(x56061)+E(f326(f326(f79(x56061),x56062),f326(f165(x56061),x56063)),f326(f165(x56061),f326(f326(f151(x56061),x56062),x56063)))
% 157.55/157.22 [5634]~P110(x56341)+E(f326(f326(f80(x56341),f326(f78(x56341),x56342)),x56343),f326(f326(f80(x56341),x56342),f326(f78(x56341),x56343)))
% 157.55/157.22 [5640]~P7(x56401,x56402,x56403)+E(f37(f917(x56401,a905),f326(f326(f60(x56401),x56402),x56403)),x56402)
% 157.55/157.22 [5708]~P115(x57081)+E(f326(f326(f80(x57081),x57082),f326(f326(f243(x57081),x57082),x57083)),f326(f326(f243(x57081),x57082),f326(a112,x57083)))
% 157.55/157.22 [5709]~P112(x57091)+E(f326(f326(f80(x57091),x57092),f326(f326(f243(x57091),x57092),x57093)),f326(f326(f243(x57091),x57092),f326(a112,x57093)))
% 157.55/157.22 [5719]~P73(x57191)+E(f326(f326(f79(x57191),f326(f78(x57191),x57192)),f326(f326(f79(x57191),x57192),x57193)),x57193)
% 157.55/157.22 [5742]~P143(x57421)+E(f326(f326(f243(x57421),f326(f100(x57421),x57422)),x57423),f326(f100(x57421),f326(f326(f243(a909),x57422),x57423)))
% 157.55/157.22 [5743]~P140(x57431)+E(f326(f326(f243(x57431),f326(f102(x57431),x57432)),x57433),f326(f102(x57431),f326(f326(f243(a1),x57432),x57433)))
% 157.55/157.22 [5749]~P86(x57491)+E(f326(f75(x57491),f326(f326(f3(x57491),x57492),x57493)),f326(f75(x57491),f326(f326(f3(x57491),x57493),x57492)))
% 157.55/157.22 [5751]~P118(x57511)+E(f326(f326(f80(x57511),f81(x57511,x57512)),f81(x57511,x57513)),f81(x57511,f326(f326(f80(x57511),x57512),x57513)))
% 157.55/157.22 [5755]E(x57551,f113(x57552))+E(f326(f326(f134(x57552),f326(f171(x57552),x57551)),x57553),f326(f171(x57552),f326(f326(f134(x57552),x57551),x57553)))
% 157.55/157.22 [5761]~E(x57612,f326(a112,f326(f326(f79(a909),x57611),x57613)))+P105(f326(f326(f235(a909),x57611),x57612))
% 157.55/157.22 [5762]~P118(x57621)+E(f326(f326(f243(x57621),f326(f75(x57621),x57622)),x57623),f326(f75(x57621),f326(f326(f243(x57621),x57622),x57623)))
% 157.55/157.22 [5763]~P110(x57631)+E(f326(f326(f80(x57631),f326(f78(x57631),x57632)),x57633),f326(f78(x57631),f326(f326(f80(x57631),x57632),x57633)))
% 157.55/157.22 [5764]~P121(x57641)+E(f326(f326(f290(x57641),f326(f78(x57641),x57642)),x57643),f326(f78(x57641),f326(f326(f290(x57641),x57642),x57643)))
% 157.55/157.22 [5862]E(f577(x58621,x58622,x58623),f594(x58621,x58622,x58623))+E(f326(f326(f101(f917(x58623,a905)),x58622),x58621),f188(f917(x58623,a905)))
% 157.55/157.22 [5877]~P69(x58772)+E(f326(f326(f8(x58771,x58772),f326(f18(x58772,x58771),f2(x58772))),x58773),f2(x58772))
% 157.55/157.22 [5878]~P74(x58782)+E(f326(f326(f11(x58781,x58782),f326(f18(x58782,x58781),f77(x58782))),x58783),f77(x58782))
% 157.55/157.22 [5880]~P94(x58801)+E(f326(f326(f3(x58801),f326(f103(x58801),x58802)),f326(f103(x58801),x58803)),f326(f103(x58801),f326(f326(f3(a1),x58802),x58803)))
% 157.55/157.22 [5883]~P143(x58831)+E(f326(f326(f80(x58831),f326(f100(x58831),x58832)),f326(f100(x58831),x58833)),f326(f100(x58831),f326(f326(f80(a909),x58832),x58833)))
% 157.55/157.22 [5884]~P143(x58841)+E(f326(f326(f79(x58841),f326(f100(x58841),x58842)),f326(f100(x58841),x58843)),f326(f100(x58841),f326(f326(f79(a909),x58842),x58843)))
% 157.55/157.22 [5885]~P140(x58851)+E(f326(f326(f3(x58851),f326(f102(x58851),x58852)),f326(f102(x58851),x58853)),f326(f102(x58851),f326(f326(f3(a1),x58852),x58853)))
% 157.55/157.22 [5886]~P140(x58861)+E(f326(f326(f80(x58861),f326(f102(x58861),x58862)),f326(f102(x58861),x58863)),f326(f102(x58861),f326(f326(f80(a1),x58862),x58863)))
% 157.55/157.22 [5887]~P140(x58871)+E(f326(f326(f79(x58871),f326(f102(x58871),x58872)),f326(f102(x58871),x58873)),f326(f102(x58871),f326(f326(f79(a1),x58872),x58873)))
% 157.55/157.22 [5888]~P94(x58881)+E(f326(f326(f80(x58881),f326(f103(x58881),x58882)),f326(f103(x58881),x58883)),f326(f103(x58881),f326(f326(f80(a1),x58882),x58883)))
% 157.55/157.22 [5889]~P94(x58891)+E(f326(f326(f79(x58891),f326(f103(x58891),x58892)),f326(f103(x58891),x58893)),f326(f103(x58891),f326(f326(f79(a1),x58892),x58893)))
% 157.55/157.22 [5937]~E(x59373,x59372)+P105(f326(f326(f234(f917(x59371,a905)),x59372),x59373))
% 157.55/157.22 [5943]~E(x59432,x59433)+P105(f326(f326(f234(f917(x59431,a905)),x59432),x59433))
% 157.55/157.22 [5948]~P118(x59481)+E(f326(f326(f80(x59481),f326(f75(x59481),x59482)),f326(f75(x59481),x59483)),f326(f75(x59481),f326(f326(f80(x59481),x59482),x59483)))
% 157.55/157.22 [5949]~P64(x59491)+E(f326(f326(f290(x59491),f326(f75(x59491),x59492)),f326(f75(x59491),x59493)),f326(f75(x59491),f326(f326(f290(x59491),x59492),x59493)))
% 157.55/157.22 [5950]~P95(x59501)+E(f326(f326(f101(x59501),f326(f78(x59501),x59502)),f326(f78(x59501),x59503)),f326(f78(x59501),f326(f326(f110(x59501),x59502),x59503)))
% 157.55/157.22 [5951]~P95(x59511)+E(f326(f326(f110(x59511),f326(f78(x59511),x59512)),f326(f78(x59511),x59513)),f326(f78(x59511),f326(f326(f101(x59511),x59512),x59513)))
% 157.55/157.22 [5952]~P73(x59521)+E(f326(f326(f79(x59521),f326(f78(x59521),x59522)),f326(f78(x59521),x59523)),f326(f78(x59521),f326(f326(f79(x59521),x59523),x59522)))
% 157.55/157.22 [5953]~P66(x59531)+E(f326(f326(f79(x59531),f326(f78(x59531),x59532)),f326(f78(x59531),x59533)),f326(f78(x59531),f326(f326(f79(x59531),x59532),x59533)))
% 157.55/157.22 [5954]~P75(x59541)+E(f326(f326(f233(x59541),f326(f78(x59541),x59542)),f326(f78(x59541),x59543)),f326(f78(x59541),f326(f326(f232(x59541),x59542),x59543)))
% 157.55/157.22 [5955]~P75(x59551)+E(f326(f326(f232(x59551),f326(f78(x59551),x59552)),f326(f78(x59551),x59553)),f326(f78(x59551),f326(f326(f233(x59551),x59552),x59553)))
% 157.55/157.22 [5956]~P82(x59561)+E(f326(f326(f79(x59561),f326(f165(x59561),x59562)),f326(f165(x59561),x59563)),f326(f165(x59561),f326(f326(f134(x59561),x59562),x59563)))
% 157.55/157.22 [5957]E(x59571,f188(f917(x59572,a905)))+~E(f326(f326(f110(f917(x59572,a905)),x59573),x59571),f188(f917(x59572,a905)))
% 157.55/157.22 [5958]E(x59581,f188(f917(x59582,a905)))+~E(f326(f326(f110(f917(x59582,a905)),x59581),x59583),f188(f917(x59582,a905)))
% 157.55/157.22 [5959]~P146(x59591,x59593,x59592)+P105(f326(x59591,f326(f326(f36(a1),x59592),x59593)))
% 157.55/157.22 [6024]~P105(f326(f61(x60241),x60243))+P105(f326(f61(x60241),f326(f326(f308(x60241),x60242),x60243)))
% 157.55/157.22 [6025]~P105(f326(f137(x60251),x60253))+P105(f326(f137(x60251),f326(f326(f175(x60251),x60252),x60253)))
% 157.55/157.22 [6026]~P105(f326(f137(x60261),x60263))+P105(f326(f137(x60261),f326(f326(f138(x60261),x60262),x60263)))
% 157.55/157.22 [6056]~P77(x60561)+P105(f326(f326(f234(x60561),x60562),f326(f326(f110(x60561),x60563),x60562)))
% 157.55/157.22 [6057]~P100(x60571)+P105(f326(f326(f234(x60571),x60572),f326(f326(f110(x60571),x60573),x60572)))
% 157.55/157.22 [6058]~P77(x60581)+P105(f326(f326(f234(x60581),x60582),f326(f326(f110(x60581),x60582),x60583)))
% 157.55/157.22 [6059]~P100(x60591)+P105(f326(f326(f234(x60591),x60592),f326(f326(f110(x60591),x60592),x60593)))
% 157.55/157.22 [6060]~P108(x60601)+P105(f326(f326(f234(x60601),x60602),f326(f326(f233(x60601),x60603),x60602)))
% 157.55/157.22 [6061]~P108(x60611)+P105(f326(f326(f234(x60611),x60612),f326(f326(f233(x60611),x60612),x60613)))
% 157.55/157.22 [6075]~E(x60751,f2(a909))+E(f326(f326(f36(a909),f326(f326(f80(a909),x60751),x60752)),f326(f326(f80(a909),x60751),x60753)),f2(a909))
% 157.55/157.22 [6155]~P94(x61551)+E(f326(f326(f3(x61551),f326(f103(x61551),x61552)),f326(f103(x61551),x61553)),f326(f103(x61551),f326(f326(f79(a1),x61552),f326(f78(a1),x61553))))
% 157.55/157.22 [6214]E(x62141,f2(a909))+E(f326(f326(f36(a909),f326(f326(f80(a909),x62141),x62142)),f326(f326(f80(a909),x62141),x62143)),f326(f326(f36(a909),x62142),x62143))
% 157.55/157.22 [6244]E(f152(x62441,f326(f326(f151(x62441),x62442),x62443)),f326(f326(f151(x62441),x62442),f152(x62441,x62443)))+P105(f326(f326(f328(x62441),x62442),f326(f172(x62441),x62443)))
% 157.55/157.22 [6280]P146(x62801,x62802,x62803)+~P105(f326(x62801,f326(f326(f36(a1),x62803),x62802)))
% 157.55/157.22 [6354]E(x63541,f113(x63542))+E(f326(f326(f151(x63542),f326(f141(x63542),x63541)),f326(f326(f175(x63542),x63543),f326(f171(x63542),x63541))),f326(f326(f175(x63542),f326(a112,x63543)),x63541))
% 157.55/157.22 [6361]E(f326(f326(f3(f917(x63611,a905)),x63612),x63613),x63612)+~E(f326(f326(f101(f917(x63611,a905)),x63612),x63613),f188(f917(x63611,a905)))
% 157.55/157.22 [6375]E(f152(x63751,f326(f326(f151(x63751),x63752),x63753)),f152(x63751,x63753))+~P105(f326(f326(f328(x63751),x63752),f326(f172(x63751),x63753)))
% 157.55/157.22 [6405]~P105(f326(f326(f234(a909),x64051),x64053))+P105(f326(f326(f234(a909),x64051),f326(f326(f79(a909),x64052),x64053)))
% 157.55/157.22 [6407]~P105(f326(f326(f234(a909),x64071),x64072))+P105(f326(f326(f234(a909),x64071),f326(f326(f79(a909),x64072),x64073)))
% 157.55/157.22 [6409]~P105(f326(f326(f235(a909),x64091),x64093))+P105(f326(f326(f235(a909),x64091),f326(f326(f79(a909),x64092),x64093)))
% 157.55/157.22 [6411]~P105(f326(f326(f235(a909),x64111),x64112))+P105(f326(f326(f235(a909),x64111),f326(f326(f79(a909),x64112),x64113)))
% 157.55/157.22 [6450]P105(f326(f61(x64501),x64502))+~P105(f326(f61(x64501),f326(f326(f308(x64501),x64503),x64502)))
% 157.55/157.22 [6451]P105(f326(f137(x64511),x64512))+~P105(f326(f137(x64511),f326(f326(f151(x64511),x64513),x64512)))
% 157.55/157.22 [6452]P105(f326(f137(x64521),x64522))+~P105(f326(f137(x64521),f326(f326(f134(x64521),x64523),x64522)))
% 157.55/157.22 [6453]P105(f326(f137(x64531),x64532))+~P105(f326(f137(x64531),f326(f326(f134(x64531),x64532),x64533)))
% 157.55/157.22 [6505]~P112(x65051)+E(f326(f326(f79(x65051),x65052),f326(f326(f80(x65051),x65053),x65052)),f326(f326(f80(x65051),f326(f326(f79(x65051),x65053),f77(x65051))),x65052))
% 157.55/157.22 [6552]~E(x65521,x65522)+~P105(f326(f326(f235(f917(x65523,a905)),x65521),x65522))
% 157.55/157.22 [6595]P105(f326(f326(f328(x65951),x65952),x65953))+P105(f326(f326(f328(x65951),x65952),f326(f78(f917(x65951,a905)),x65953)))
% 157.55/157.22 [6601]E(f144(x66011,f326(f326(f138(x66011),x66012),x66013)),f144(x66011,x66013))+~P105(f326(f326(f235(a909),x66012),f326(f189(f910(x66011)),x66013)))
% 157.55/157.22 [6602]E(f326(f326(f175(x66021),x66022),f114(x66021,x66023)),f326(f326(f175(x66021),x66022),x66023))+~P105(f326(f326(f235(a909),x66022),f326(f189(f910(x66021)),x66023)))
% 157.55/157.22 [6659]E(f326(f326(f326(f183(f910(x66591),f910(x66591)),x66592),f167(x66591)),x66593),x66593)+~E(f45(a909,x66592,f326(f189(f910(x66591)),x66593)),f2(a909))
% 157.55/157.22 [6666]~P7(x66661,x66663,x66662)+E(f326(f326(f288(x66661,x66661,x66661),f326(f285(x66661,x66661),x66662)),x66662),x66662)
% 157.55/157.22 [6709]~E(f326(f326(f110(f917(x67091,a905)),x67092),x67093),x67093)+P105(f326(f326(f234(f917(x67091,a905)),x67092),x67093))
% 157.55/157.22 [6714]~P53(x67141,x67141,x67143)+P53(x67141,x67141,f326(f326(f183(f916(x67141,x67141),a905),x67142),x67143))
% 157.55/157.22 [6717]~P105(f326(f326(f328(x67171),x67173),f326(f172(x67171),x67172)))+P105(f326(f326(f235(a909),f2(a909)),f326(f189(f910(x67171)),x67172)))
% 157.55/157.22 [6744]~P86(x67441)+E(f326(f75(x67441),f326(f326(f79(x67441),f326(f75(x67441),x67442)),f326(f75(x67441),x67443))),f326(f326(f79(x67441),f326(f75(x67441),x67442)),f326(f75(x67441),x67443)))
% 157.55/157.22 [6755]E(f326(f326(f36(a909),f326(f326(f80(a909),x67551),x67552)),f326(f326(f80(a909),x67551),x67553)),f326(f326(f36(a909),x67552),x67553))+~P105(f326(f326(f235(a909),f2(a909)),x67551))
% 157.55/157.22 [6897]~P105(f326(f61(x68971),x68973))+E(f326(f326(f64(x68971,f917(x68971,a905),f308(x68971)),x68972),x68973),f326(f326(f110(f917(x68971,a905)),x68973),x68972))
% 157.55/157.22 [6953]E(f326(f326(f110(f917(x69531,a905)),x69532),x69533),x69532)+~P105(f326(f326(f234(f917(x69531,a905)),x69533),x69532))
% 157.55/157.22 [6955]E(f326(f326(f110(f917(x69551,a905)),x69552),x69553),x69553)+~P105(f326(f326(f234(f917(x69551,a905)),x69552),x69553))
% 157.55/157.22 [6956]E(f326(f326(f101(f917(x69561,a905)),x69562),x69563),x69563)+~P105(f326(f326(f234(f917(x69561,a905)),x69563),x69562))
% 157.55/157.22 [6957]E(f326(f326(f101(f917(x69571,a905)),x69572),x69573),x69572)+~P105(f326(f326(f234(f917(x69571,a905)),x69572),x69573))
% 157.55/157.22 [7006]~P105(f326(f137(x70061),x70062))+E(f326(f326(f3(f917(x70061,a905)),f326(f172(x70061),x70062)),f326(f326(f308(x70061),x70063),f188(f917(x70061,a905)))),f326(f172(x70061),f170(x70061,x70063,x70062)))
% 157.55/157.22 [7058]P36(x70581,x70582)+~P36(x70581,f326(f326(f183(f916(x70581,x70581),a905),x70583),x70582))
% 157.55/157.22 [7124]P105(f326(f49(x71241,x71242),f326(a51,x71243)))+~P105(f326(f49(f326(f78(a1),x71241),f326(f78(a1),x71242)),x71243))
% 157.55/157.22 [7129]E(f326(f326(f3(f917(x71291,a905)),f326(f326(f308(x71291),x71292),x71293)),f326(f326(f308(x71291),x71292),f188(f917(x71291,a905)))),x71293)+P105(f326(f326(f328(x71291),x71292),x71293))
% 157.55/157.22 [7152]E(f326(f326(f101(f917(x71521,a905)),f326(f172(x71521),x71522)),f326(f172(x71521),x71523)),f188(f917(x71521,a905)))+~P105(f326(f137(x71521),f326(f326(f134(x71521),x71522),x71523)))
% 157.55/157.22 [7167]~P105(f326(f326(f328(x71671),x71672),f326(f172(x71671),x71673)))+~P105(f326(f137(x71671),f326(f326(f151(x71671),x71672),x71673)))
% 157.55/157.22 [7238]P30(x72381,x72382,x72383)+P105(f326(f326(f235(a909),f757(x72383,x72382,x72381)),f326(f189(f910(x72381)),x72383)))
% 157.55/157.22 [7248]E(f326(f326(f101(f917(x72481,a905)),x72482),x72483),f188(f917(x72481,a905)))+P105(f326(f326(f328(x72481),f577(x72483,x72482,x72481)),x72482))
% 157.55/157.22 [7249]E(f326(f326(f101(f917(x72491,a905)),x72492),x72493),f188(f917(x72491,a905)))+P105(f326(f326(f328(x72491),f594(x72493,x72492,x72491)),x72493))
% 157.55/157.22 [7252]E(f114(x72521,f326(f326(f175(x72521),x72522),x72523)),f326(f326(f175(x72521),f326(f326(f3(a909),x72522),f77(a909))),x72523))+~P105(f326(f326(f234(a909),x72522),f326(f189(f910(x72521)),x72523)))
% 157.55/157.22 [7312]~P32(x73123,x73122,x73121)+P105(f326(f326(f235(a909),f748(x73121,x73122,x73123)),f326(f189(f910(x73123)),x73121)))
% 157.55/157.22 [7330]P105(f326(f326(f235(a909),f2(a909)),x73301))+P105(f326(f326(f234(a909),f326(f326(f80(a909),x73302),x73301)),f326(f326(f80(a909),x73303),x73301)))
% 157.55/157.22 [7331]P105(f326(f326(f235(a909),f2(a909)),x73311))+P105(f326(f326(f234(a909),f326(f326(f80(a909),x73311),x73312)),f326(f326(f80(a909),x73311),x73313)))
% 157.55/157.22 [7334]~P105(f326(f326(f328(x73341),x73342),x73343))+~P105(f326(f326(f328(x73341),x73342),f326(f78(f917(x73341,a905)),x73343)))
% 157.55/157.22 [7340]~P105(f326(f326(f235(f917(x73401,a905)),x73402),x73403))+P105(f326(f326(f234(f917(x73401,a905)),x73402),x73403))
% 157.55/157.22 [7450]~P105(f326(f326(f234(a909),x74503),x74502))+P105(f326(f326(f234(a909),f326(f326(f3(a909),x74501),x74502)),f326(f326(f3(a909),x74501),x74503)))
% 157.55/157.22 [7451]~P105(f326(f326(f234(a909),x74511),x74513))+P105(f326(f326(f234(a909),f326(f326(f3(a909),x74511),x74512)),f326(f326(f3(a909),x74513),x74512)))
% 157.55/157.22 [7453]~P105(f326(f326(f234(a909),x74532),x74533))+P105(f326(f326(f234(a909),f326(f326(f80(a909),x74531),x74532)),f326(f326(f80(a909),x74531),x74533)))
% 157.55/157.22 [7455]~P105(f326(f326(f234(a909),x74551),x74553))+P105(f326(f326(f234(a909),f326(f326(f80(a909),x74551),x74552)),f326(f326(f80(a909),x74553),x74552)))
% 157.55/157.22 [7456]~P105(f326(f326(f234(a909),x74562),x74563))+P105(f326(f326(f234(a909),f326(f326(f79(a909),x74561),x74562)),f326(f326(f79(a909),x74561),x74563)))
% 157.55/157.22 [7457]~P105(f326(f326(f234(a909),x74571),x74573))+P105(f326(f326(f234(a909),f326(f326(f79(a909),x74571),x74572)),f326(f326(f79(a909),x74573),x74572)))
% 157.55/157.22 [7458]~P105(f326(f326(f234(a909),x74581),x74583))+P105(f326(f326(f234(a909),f326(f326(f36(a909),x74581),x74582)),f326(f326(f36(a909),x74583),x74582)))
% 157.55/157.22 [7459]~P105(f326(f326(f234(a1),x74592),x74593))+P105(f326(f326(f234(a1),f326(f326(f79(a1),x74591),x74592)),f326(f326(f79(a1),x74591),x74593)))
% 157.55/157.22 [7462]~P105(f326(f326(f235(a909),x74622),x74623))+P105(f326(f326(f235(a909),f326(f326(f79(a909),x74621),x74622)),f326(f326(f79(a909),x74621),x74623)))
% 157.55/157.22 [7463]~P105(f326(f326(f235(a909),x74631),x74633))+P105(f326(f326(f235(a909),f326(f326(f79(a909),x74631),x74632)),f326(f326(f79(a909),x74633),x74632)))
% 157.55/157.22 [7464]~P105(f326(f326(f235(a1),x74641),x74643))+P105(f326(f326(f235(a1),f326(f326(f79(a1),x74641),x74642)),f326(f326(f79(a1),x74643),x74642)))
% 157.55/157.22 [7544]E(x75441,x75442)+~P105(f326(f326(f328(x75443),x75441),f326(f326(f308(x75443),x75442),f188(f917(x75443,a905)))))
% 157.55/157.22 [7546]~E(f326(f326(f101(f917(x75461,a905)),x75462),x75463),f188(f917(x75461,a905)))+P105(f326(f326(f234(f917(x75461,a905)),x75462),f326(f78(f917(x75461,a905)),x75463)))
% 157.55/157.22 [7551]P105(f326(f326(f328(f917(x75511,a905)),x75512),f326(f307(x75511),x75513)))+~P105(f326(f326(f234(f917(x75511,a905)),x75512),x75513))
% 157.55/157.22 [7601]E(f326(f326(f151(x76011),f326(f326(f164(x76011),x76012),x76013)),f326(f326(f138(x76011),f326(a112,x76013)),x76012)),f326(f326(f138(x76011),x76013),x76012))+~P105(f326(f326(f235(a909),x76013),f326(f189(f910(x76011)),x76012)))
% 157.55/157.22 [7627]P105(f326(f326(f328(f916(x76271,x76271)),x76272),f306(x76271,x76273)))+~P105(f326(f326(f328(f916(x76271,x76271)),x76272),x76273))
% 157.55/157.22 [7636]~P105(f326(f326(f328(f917(x76361,a905)),x76362),f326(f307(x76361),x76363)))+P105(f326(f326(f234(f917(x76361,a905)),x76362),x76363))
% 157.55/157.22 [7679]P105(f326(f326(f234(f917(x76791,a905)),x76792),f37(f917(x76791,a905),x76793)))+~P105(f326(f326(f328(f917(x76791,a905)),x76792),x76793))
% 157.55/157.22 [7702]~P140(x77021)+E(f326(f326(f80(x77021),f326(f326(f243(x77021),f326(f78(x77021),f77(x77021))),x77022)),f326(f326(f243(x77021),x77023),x77022)),f326(f326(f243(x77021),f326(f78(x77021),x77023)),x77022))
% 157.55/157.22 [7724]E(f326(f326(f164(x77241),x77242),f326(f326(f3(a909),f326(f189(f910(x77241)),x77242)),f326(a112,x77243))),f326(f326(f164(x77241),f326(f168(x77241),x77242)),x77243))+~P105(f326(f326(f235(a909),x77243),f326(f189(f910(x77241)),x77242)))
% 157.55/157.22 [7741]~E(f326(f326(f101(f917(x77411,a905)),f722(x77413,x77412,x77411)),x77413),f188(f917(x77411,a905)))+E(f326(f326(f101(f917(x77411,a905)),f37(f917(x77411,a905),x77412)),x77413),f188(f917(x77411,a905)))
% 157.55/157.22 [7803]~P105(f326(f326(f328(x78033),x78032),f326(f172(x78033),x78031)))+P105(f326(f326(f235(a909),f652(x78031,x78032,x78033)),f326(f189(f910(x78033)),x78031)))
% 157.55/157.22 [7811]P105(f326(f326(f328(x78111),f326(f326(f164(x78111),x78112),x78113)),f326(f172(x78111),x78112)))+~P105(f326(f326(f235(a909),x78113),f326(f189(f910(x78111)),x78112)))
% 157.55/157.22 [7908]~P105(f326(x79082,f713(x79083,x79082,x79081)))+E(f326(f326(f138(x79081),f326(f189(f910(x79081)),f177(x79081,x79082,x79083))),x79083),f113(x79081))
% 157.55/157.22 [7921]P105(f326(f326(f234(f917(f910(x79211),a905)),f161(x79211,x79212)),f161(x79211,x79213)))+~P105(f326(f326(f234(f917(x79211,a905)),x79212),x79213))
% 157.55/157.22 [7922]P105(f326(f326(f234(f917(f910(x79221),a905)),f160(x79221,x79222)),f160(x79221,x79223)))+~P105(f326(f326(f234(f917(x79221,a905)),x79222),x79223))
% 157.55/157.22 [7948]E(f326(f326(f101(f917(x79481,a905)),f37(f917(x79481,a905),x79482)),x79483),f188(f917(x79481,a905)))+P105(f326(f326(f328(f917(x79481,a905)),f722(x79483,x79482,x79481)),x79482))
% 157.55/157.22 [7950]~P105(f326(f326(f328(f917(x79501,a905)),x79503),x79502))+P105(f326(f326(f234(f917(x79501,a905)),f38(f917(x79501,a905),x79502)),x79503))
% 157.55/157.22 [7952]E(f326(f326(f101(f917(x79521,a905)),x79522),x79523),f188(f917(x79521,a905)))+~P105(f326(f326(f234(f917(x79521,a905)),x79522),f326(f78(f917(x79521,a905)),x79523)))
% 157.55/157.22 [7998]E(f326(f326(f3(a909),f326(f326(f79(a909),f326(f165(a909),x79981)),x79982)),f326(f326(f164(a909),x79981),x79983)),f326(f165(a909),f326(f326(f159(a909,x79981),x79983),x79982)))+~P105(f326(f326(f235(a909),x79983),f326(f189(f910(a909)),x79981)))
% 157.55/157.22 [8049]P105(f326(f326(f234(a909),x80491),x80492))+~P105(f326(f326(f234(a909),f326(f326(f79(a909),x80493),x80491)),f326(f326(f79(a909),x80493),x80492)))
% 157.55/157.22 [8052]P105(f326(f326(f235(a909),x80521),x80522))+~P105(f326(f326(f235(a909),f326(f326(f79(a909),x80523),x80521)),f326(f326(f79(a909),x80523),x80522)))
% 157.55/157.22 [8053]P105(f326(f326(f235(a909),x80531),x80532))+~P105(f326(f326(f235(a909),f326(f326(f80(a909),x80533),x80531)),f326(f326(f80(a909),x80533),x80532)))
% 157.55/157.22 [8054]P105(f326(f326(f235(a909),x80541),x80542))+~P105(f326(f326(f235(a909),f326(f326(f80(a909),x80541),x80543)),f326(f326(f80(a909),x80542),x80543)))
% 157.55/157.22 [8082]P105(f326(f326(f235(a909),f2(a909)),x80821))+~P105(f326(f326(f235(a909),f326(f326(f80(a909),x80822),x80821)),f326(f326(f80(a909),x80823),x80821)))
% 157.55/157.22 [8083]P105(f326(f326(f235(a909),f2(a909)),x80831))+~P105(f326(f326(f235(a909),f326(f326(f80(a909),x80831),x80832)),f326(f326(f80(a909),x80831),x80833)))
% 157.55/157.22 [8156]E(f246(x81561,x81562,x81563),x81562)+~P105(f326(f326(f234(f917(x81561,a905)),x81563),f326(f326(f308(x81561),x81562),f188(f917(x81561,a905)))))
% 157.55/157.22 [8206]~P105(f326(f137(x82061),x82063))+E(f326(f136(x82061,f326(f326(f10(a905,a905,x82061),a321),f326(a323,x82062))),x82063),f170(x82061,x82062,x82063))
% 157.55/157.22 [8231]E(f326(f326(f138(x82311),f326(f189(f910(x82311)),f177(x82311,x82312,x82313))),x82313),f113(x82311))+P105(f326(f326(f328(x82311),f713(x82313,x82312,x82311)),f326(f172(x82311),x82313)))
% 157.55/157.22 [8235]E(f326(f326(f134(x82351),f326(f326(f175(x82351),x82352),x82353)),f326(f326(f151(x82351),f326(f326(f164(x82351),x82353),x82352)),f113(x82351))),f326(f326(f175(x82351),f326(a112,x82352)),x82353))+~P105(f326(f326(f235(a909),x82352),f326(f189(f910(x82351)),x82353)))
% 157.55/157.22 [8297]E(f326(f136(x82971,f326(f326(f10(a905,a905,x82971),a321),f326(a323,x82972))),x82973),x82973)+P105(f326(f326(f328(x82971),x82972),f326(f172(x82971),x82973)))
% 157.55/157.22 [8303]P105(f326(f326(f234(f917(f917(x83031,a905),a905)),f247(x83031,x83032)),f247(x83031,x83033)))+~P105(f326(f326(f234(f917(x83031,a905)),x83032),x83033))
% 157.55/157.22 [8342]~P105(f326(f137(x83421),x83423))+P105(f326(f137(x83421),f326(f326(f326(f183(f910(x83421),f910(x83421)),x83422),f167(x83421)),x83423)))
% 157.55/157.22 [8348]~P105(f326(f326(f235(a909),x83482),x83483))+P105(f326(f326(f235(a909),f326(f326(f80(a909),f326(a112,x83481)),x83482)),f326(f326(f80(a909),f326(a112,x83481)),x83483)))
% 157.55/157.22 [8368]P105(f326(f326(f234(f917(f917(x83681,a905),a905)),f326(f307(x83681),x83682)),f326(f307(x83681),x83683)))+~P105(f326(f326(f234(f917(x83681,a905)),x83682),x83683))
% 157.55/157.22 [8437]~E(f326(f309(x84371,x84372,x84373),f241(f917(x84371,a905))),f241(f917(x84372,a905)))+E(f326(f72(x84371,x84372,x84372,x84373),f90(x84371,x84372,f241(f917(x84371,a905)),x84373)),f31(x84372))
% 157.55/157.22 [8530]~P105(f326(f326(f234(f917(x85301,a905)),x85303),x85302))+P105(f326(f326(f234(f917(x85301,a905)),f326(f78(f917(x85301,a905)),x85302)),f326(f78(f917(x85301,a905)),x85303)))
% 157.55/157.22 [8563]E(f326(f309(a909,a909,f326(f326(f9(a909,a909,a909),f3(a909)),x85631)),f326(f301(a909,x85632),x85633)),f326(f301(a909,f326(f326(f3(a909),x85632),x85631)),f326(f326(f3(a909),x85633),x85631)))+~P105(f326(f326(f235(a909),x85631),x85633))
% 157.55/157.22 [8589]~P82(x85891)+E(f326(f326(f79(x85891),x85892),f326(f142(x85891,x85891,f79(x85891),f2(x85891)),x85893)),f326(f142(x85891,x85891,f79(x85891),x85892),x85893))
% 157.55/157.22 [8664]~P86(x86641)+P105(f326(f326(f234(x86641),f326(f75(x86641),f326(f326(f3(x86641),x86642),x86643))),f326(f326(f79(x86641),f326(f75(x86641),x86642)),f326(f75(x86641),x86643))))
% 157.55/157.22 [8665]~P86(x86651)+P105(f326(f326(f234(x86651),f326(f75(x86651),f326(f326(f79(x86651),x86652),x86653))),f326(f326(f79(x86651),f326(f75(x86651),x86652)),f326(f75(x86651),x86653))))
% 157.55/157.22 [8676]E(f326(f326(f79(a1),f326(f326(f80(a1),x86761),f45(a1,f326(f326(f36(a1),x86762),x86761),x86763))),f45(a1,x86762,x86761)),f45(a1,x86762,f326(f326(f80(a1),x86761),x86763)))+~P105(f326(f326(f235(a1),f2(a1)),x86763))
% 157.55/157.22 [8682]E(f326(f326(f134(x86821),f326(f326(f175(x86821),x86822),x86823)),f326(f326(f151(x86821),f326(f141(x86821),f326(f326(f138(x86821),x86822),x86823))),f113(x86821))),f326(f326(f175(x86821),f326(a112,x86822)),x86823))+~P105(f326(f326(f235(a909),x86822),f326(f189(f910(x86821)),x86823)))
% 157.55/157.22 [8702]E(f326(f267(x87021,f326(f326(f154(x87021,f916(a99,x87021)),f326(f251(a99,x87021),f77(a99))),x87022)),f326(a5,x87023)),f326(f326(f164(x87021),x87022),x87023))+~P105(f326(f326(f235(a909),x87023),f326(f189(f910(x87021)),x87022)))
% 157.55/157.22 [8770]P105(f326(f326(f328(f916(x87701,x87701)),x87702),f326(f326(f288(x87701,x87701,x87701),x87703),f306(x87701,x87703))))+~P105(f326(f326(f328(f916(x87701,x87701)),x87702),x87703))
% 157.55/157.22 [8781]E(f326(f309(x87811,x87812,x87813),f241(f917(x87811,a905))),f241(f917(x87812,a905)))+~E(f326(f72(x87811,x87812,x87812,x87813),f90(x87811,x87812,f241(f917(x87811,a905)),x87813)),f31(x87812))
% 157.55/157.22 [8790]P105(f326(f326(f234(a909),x87901),x87902))+~P105(f326(f326(f234(a909),f326(f326(f80(a909),f326(a112,x87903)),x87901)),f326(f326(f80(a909),f326(a112,x87903)),x87902)))
% 157.55/157.22 [8806]P105(f326(f326(f234(f917(x88061,a905)),x88062),x88063))+~P105(f326(f326(f234(f917(x88061,a905)),f326(f78(f917(x88061,a905)),x88063)),f326(f78(f917(x88061,a905)),x88062)))
% 157.55/157.22 [8829]P105(f326(f137(x88291),x88292))+~P105(f326(f137(x88291),f326(f326(f326(f183(f910(x88291),f910(x88291)),x88293),f167(x88291)),x88292)))
% 157.55/157.22 [8902]E(f326(f284(x89021,x89021,f306(x89021,x89022)),x89023),x89023)+~P105(f326(f326(f234(f917(x89021,a905)),f326(f284(x89021,x89021,x89022),x89023)),x89023))
% 157.55/157.22 [8950]~P108(x89501)+P12(x89501,f326(f136(x89501,f326(f326(f9(x89501,x89501,a905),a323),f326(x89502,x89503))),x89503))
% 157.55/157.22 [8957]~P105(f326(f326(f234(a909),x89571),x89572))+P105(f326(f326(f234(a909),x89571),f326(f142(a909,a909,f79(a909),x89572),x89573)))
% 157.55/157.22 [9043]~P105(f326(f326(f328(f916(x90431,x90431)),x90432),f306(x90431,x90433)))+P105(f326(f326(f328(f916(x90431,x90431)),x90432),f326(f326(f183(f916(x90431,x90431),a905),f615(x90433,x90432,x90431)),x90433)))
% 157.55/157.22 [9124]~P82(x91241)+E(f326(f326(f79(x91241),x91242),f326(f142(x91241,x91241,f326(f9(x91241,x91241,x91241),f79(x91241)),f2(x91241)),f326(f168(x91241),x91243))),f326(f142(x91241,x91241,f79(x91241),x91242),x91243))
% 157.55/157.22 [9241]~P25(x92412,x92411,x92413,f241(f917(x92412,a905)),f241(f917(x92411,a905)))+E(f90(x92411,x92412,f241(f917(x92411,a905)),f90(x92412,x92411,f241(f917(x92412,a905)),x92413)),x92413)
% 157.55/157.22 [9391]P53(x93911,x93912,x93913)+P105(f326(f326(f328(f916(x93911,x93912)),f326(f326(f251(x93911,x93912),f606(x93913,x93912,x93911)),f593(x93913,x93912,x93911))),x93913))
% 157.55/157.22 [9392]P53(x93921,x93922,x93923)+P105(f326(f326(f328(f916(x93921,x93922)),f326(f326(f251(x93921,x93922),f606(x93923,x93922,x93921)),f592(x93923,x93922,x93921))),x93923))
% 157.55/157.22 [9460]~P105(f326(f326(f328(f916(x94601,x94601)),x94602),f326(f326(f288(x94601,x94601,x94601),x94603),f306(x94601,x94603))))+P105(f326(f326(f328(f916(x94601,x94601)),x94602),f326(f326(f183(f916(x94601,x94601),a905),f617(x94603,x94602,x94601)),x94603)))
% 157.55/157.22 [9461]~P105(f326(x94611,f326(f326(f164(x94612),x94613),f326(f189(f910(x94612)),f177(x94612,x94611,x94613)))))+~P105(f326(f326(f235(a909),f326(f189(f910(x94612)),f177(x94612,x94611,x94613))),f326(f189(f910(x94612)),x94613)))
% 157.55/157.22 [9550]~P105(f326(f326(f234(f917(x95501,a905)),x95502),x95503))+P105(f326(f326(f234(f917(x95501,a905)),f326(f326(f9(x95501,f917(x95501,a905),a905),f328(x95501)),x95502)),f326(f326(f9(x95501,f917(x95501,a905),a905),f328(x95501)),x95503)))
% 157.55/157.22 [9607]~P105(f326(f326(f328(f916(f917(x96071,a905),f917(x96071,a905))),f326(f326(f251(f917(x96071,a905),f917(x96071,a905)),x96072),x96073)),f313(x96071)))+P105(f326(f326(f235(f917(x96071,a905)),x96072),x96073))
% 157.55/157.22 [9631]P54(x96311,x96312,x96313)+~P105(f326(f326(f328(f916(x96311,x96311)),f326(f326(f251(x96311,x96311),f609(x96313,x96312,x96311)),f608(x96313,x96312,x96311))),x96313))
% 157.55/157.22 [9632]P54(x96321,x96322,x96323)+~P105(f326(f326(f328(f916(x96321,x96321)),f326(f326(f251(x96321,x96321),f608(x96323,x96322,x96321)),f609(x96323,x96322,x96321))),x96323))
% 157.55/157.22 [9669]~P105(f326(f326(f328(f916(f910(x96691),f910(x96691))),f326(f326(f251(f910(x96691),f910(x96691)),x96692),x96692)),f147(x96691,x96693)))+P105(f326(f326(f328(f916(x96691,x96691)),f326(f326(f251(x96691,x96691),f651(x96692,x96693,x96691)),f651(x96692,x96693,x96691))),x96693))
% 157.55/157.22 [9719]P105(f326(f326(f234(f917(x97191,a905)),x97192),x97193))+~P105(f326(f326(f234(f917(x97191,a905)),f326(f326(f9(x97191,f917(x97191,a905),a905),f328(x97191)),x97192)),f326(f326(f9(x97191,f917(x97191,a905),a905),f328(x97191)),x97193)))
% 157.55/157.22 [9800]E(f326(f326(f3(a909),f326(f326(f8(a909,a909),x98001),f326(f281(a909),x98002))),f326(f326(f8(a909,a909),x98003),f326(f281(a909),x98002))),f326(f326(f8(a909,a909),f326(f326(f20(a909,a909,a909),f326(f326(f10(a909,f917(a909,a909),a909),f3(a909)),x98001)),x98003)),f326(f281(a909),x98002)))+~P105(f326(f326(f234(a909),f326(x98003,f407(x98002,x98001,x98003))),f326(x98001,f407(x98002,x98001,x98003))))
% 157.55/157.22 [5798]~P73(x57981)+E(f326(f326(f3(x57981),f326(f326(f79(x57981),x57982),x57983)),x57983),x57982)
% 157.55/157.22 [5799]~P73(x57991)+E(f326(f326(f79(x57991),f326(f326(f3(x57991),x57992),x57993)),x57993),x57992)
% 157.55/157.22 [6033]~P73(x60331)+E(f326(f326(f79(x60331),x60332),f326(f326(f79(x60331),f326(f78(x60331),x60332)),x60333)),x60333)
% 157.55/157.22 [6116]~P81(x61161)+E(f326(f326(f80(x61161),f326(f326(f243(x61161),x61162),x61163)),x61162),f326(f326(f243(x61161),x61162),f326(a112,x61163)))
% 157.55/157.22 [6117]~P112(x61171)+E(f326(f326(f80(x61171),f326(f326(f243(x61171),x61172),x61173)),x61172),f326(f326(f243(x61171),x61172),f326(a112,x61173)))
% 157.55/157.22 [6338]~P118(x63381)+E(f326(f75(x63381),f326(f326(f243(x63381),f326(f78(x63381),x63382)),x63383)),f326(f75(x63381),f326(f326(f243(x63381),x63382),x63383)))
% 157.55/157.22 [6384]~P81(x63841)+E(f326(f326(f80(x63841),f326(f326(f243(x63841),x63842),x63843)),x63842),f326(f326(f80(x63841),x63842),f326(f326(f243(x63841),x63842),x63843)))
% 157.55/157.22 [6441]E(f326(f326(f3(a99),f326(f326(f79(a99),x64411),x64412)),x64413),f273(x64411,x64412,x64413))+~P105(f326(f326(f235(a99),x64412),x64413))
% 157.55/157.22 [6464]~E(f326(f326(f138(x64641),x64643),x64642),f113(x64641))+P105(f326(f326(f234(a909),f326(f189(f910(x64641)),x64642)),x64643))
% 157.55/157.22 [6600]E(f326(f326(f80(a909),f326(f103(a909),x66001)),f326(f326(f80(a909),f326(f103(a909),x66002)),x66003)),f2(a909))+~P105(f326(f326(f235(a1),x66001),a82))
% 157.55/157.22 [6616]~P62(x66161)+E(f326(f326(f243(x66161),f326(f326(f290(x66161),f77(x66161)),x66162)),x66163),f326(f326(f290(x66161),f77(x66161)),f326(f326(f243(x66161),x66162),x66163)))
% 157.55/157.22 [6695]E(f326(f326(f3(a909),f326(f326(f79(a909),x66951),x66952)),x66953),f326(f326(f3(a909),x66951),f326(f326(f3(a909),x66953),x66952)))+~P105(f326(f326(f234(a909),x66952),x66953))
% 157.55/157.22 [6697]E(f326(f326(f3(a909),f326(f326(f79(a909),x66971),x66972)),x66973),f326(f326(f79(a909),x66971),f326(f326(f3(a909),x66972),x66973)))+~P105(f326(f326(f234(a909),x66973),x66972))
% 157.55/157.22 [6735]~P77(x67351)+P105(f326(f326(f234(x67351),f326(f326(f101(x67351),x67352),x67353)),x67353))
% 157.55/157.22 [6736]~P101(x67361)+P105(f326(f326(f234(x67361),f326(f326(f101(x67361),x67362),x67363)),x67363))
% 157.55/157.22 [6737]~P77(x67371)+P105(f326(f326(f234(x67371),f326(f326(f101(x67371),x67372),x67373)),x67372))
% 157.55/157.22 [6738]~P101(x67381)+P105(f326(f326(f234(x67381),f326(f326(f101(x67381),x67382),x67383)),x67382))
% 157.55/157.22 [6739]~P108(x67391)+P105(f326(f326(f234(x67391),f326(f326(f232(x67391),x67392),x67393)),x67393))
% 157.55/157.22 [6740]~P108(x67401)+P105(f326(f326(f234(x67401),f326(f326(f232(x67401),x67402),x67403)),x67402))
% 157.55/157.22 [6754]E(f326(f326(f36(a1),f326(f326(f36(a1),x67541),x67542)),x67543),f326(f326(f36(a1),x67541),f326(f326(f80(a1),x67542),x67543)))+~P105(f326(f326(f235(a1),f2(a1)),x67543))
% 157.55/157.22 [6808]~P112(x68081)+E(f326(f326(f79(x68081),f326(f326(f80(x68081),x68082),x68083)),x68083),f326(f326(f80(x68081),f326(f326(f79(x68081),x68082),f77(x68081))),x68083))
% 157.55/157.22 [6809]~P94(x68091)+E(f326(f326(f80(x68091),f326(f78(x68091),f326(f103(x68091),x68092))),x68093),f326(f326(f80(x68091),f326(f103(x68091),f326(f78(a1),x68092))),x68093))
% 157.55/157.22 [6881]~P82(x68811)+E(f326(f165(x68811),f326(f326(f154(x68812,x68811),f326(f18(x68811,x68812),f2(x68811))),x68813)),f2(x68811))
% 157.55/157.22 [6899]E(f326(f326(f79(a909),f326(f103(a909),x68991)),f326(f326(f79(a909),f326(f103(a909),x68992)),x68993)),f326(f326(f79(a909),f326(f103(a909),x68992)),x68993))+~P105(f326(a193,f326(f103(a1),x68991)))
% 157.55/157.22 [6913]~P4(x69131)+E(f37(x69131,f326(f326(f308(x69131),x69132),f326(f326(f308(x69131),x69133),f188(f917(x69131,a905))))),f326(f326(f110(x69131),x69132),x69133))
% 157.55/157.22 [6914]~P4(x69141)+E(f38(x69141,f326(f326(f308(x69141),x69142),f326(f326(f308(x69141),x69143),f188(f917(x69141,a905))))),f326(f326(f101(x69141),x69142),x69143))
% 157.55/157.22 [6936]E(f326(f326(f175(x69361),x69362),x69363),x69363)+~P105(f326(f326(f234(a909),f326(f189(f910(x69361)),x69363)),x69362))
% 157.55/157.22 [6948]E(f326(f326(f138(x69481),x69482),x69483),f113(x69481))+~P105(f326(f326(f234(a909),f326(f189(f910(x69481)),x69483)),x69482))
% 157.55/157.22 [6959]E(f326(f326(f79(a909),f326(f326(f3(a909),x69591),x69592)),x69593),f326(f326(f3(a909),f326(f326(f79(a909),x69591),x69593)),x69592))+~P105(f326(f326(f234(a909),x69592),x69591))
% 157.55/157.22 [6973]~P105(f326(f326(f235(a909),x69731),x69733))+P105(f326(f326(f235(a909),f326(f326(f3(a909),x69731),x69732)),x69733))
% 157.55/157.22 [7000]~P108(x70001)+E(f170(x70001,x70002,f326(f326(f148(x70001,x70001,f7(x70001)),x70002),x70003)),x70003)
% 157.55/157.22 [7087]E(f326(f326(f3(a909),f326(f326(f79(a909),x70871),x70872)),f326(a112,x70873)),f326(f326(f3(a909),x70871),f326(a112,f326(f326(f3(a909),x70873),x70872))))+~P105(f326(f326(f234(a909),x70872),x70873))
% 157.55/157.22 [7088]~P118(x70881)+P105(f326(f326(f234(x70881),f2(x70881)),f326(f326(f243(x70881),f326(f75(x70881),x70882)),x70883)))
% 157.55/157.22 [7136]P23(x71361,x71362,x71363)+~P105(f326(f326(f234(f917(f908(x71361),a905)),x71363),x71362))
% 157.55/157.22 [7179]~P105(f326(f61(x71791),x71792))+P105(f326(f61(x71791),f326(f326(f3(f917(x71791,a905)),x71792),x71793)))
% 157.55/157.22 [7180]~P105(f326(f61(x71801),x71803))+P105(f326(f61(x71801),f326(f326(f101(f917(x71801,a905)),x71802),x71803)))
% 157.55/157.22 [7181]~P105(f326(f61(x71811),x71812))+P105(f326(f61(x71811),f326(f326(f101(f917(x71811,a905)),x71812),x71813)))
% 157.55/157.22 [7320]~P36(x73201,x73203)+P36(x73201,f326(f326(f101(f917(f916(x73201,x73201),a905)),x73202),x73203))
% 157.55/157.22 [7321]~P36(x73211,x73212)+P36(x73211,f326(f326(f101(f917(f916(x73211,x73211),a905)),x73212),x73213))
% 157.55/157.22 [7446]~P77(x74461)+E(f12(x74461,f326(f172(x74461),f326(f326(f151(x74461),x74462),x74463))),f326(f142(x74461,x74461,f110(x74461),x74462),x74463))
% 157.55/157.22 [7447]~P77(x74471)+E(f13(x74471,f326(f172(x74471),f326(f326(f151(x74471),x74472),x74473))),f326(f142(x74471,x74471,f101(x74471),x74472),x74473))
% 157.55/157.22 [7448]~P108(x74481)+E(f16(x74481,f326(f172(x74481),f326(f326(f151(x74481),x74482),x74483))),f326(f142(x74481,x74481,f232(x74481),x74482),x74483))
% 157.55/157.22 [7449]~P108(x74491)+E(f17(x74491,f326(f172(x74491),f326(f326(f151(x74491),x74492),x74493))),f326(f142(x74491,x74491,f233(x74491),x74492),x74493))
% 157.55/157.22 [7512]~P105(f326(f61(x75121),x75122))+P105(f326(f326(f234(a909),f326(f35(x75121),x75122)),f326(f35(x75121),f326(f326(f308(x75121),x75123),x75122))))
% 157.55/157.22 [7519]E(f326(f326(f110(f917(a909,a905)),f326(f301(a909,x75191),x75192)),f326(f301(a909,x75192),f326(f326(f79(a909),x75192),x75193))),f326(f301(a909,x75191),f326(f326(f79(a909),x75192),x75193)))+~P105(f326(f326(f234(a909),x75191),x75192))
% 157.55/157.22 [7528]P105(f326(f326(f234(a909),x75281),x75282))+~P105(f326(f326(f234(a909),f326(f326(f79(a909),x75283),x75281)),x75282))
% 157.55/157.22 [7529]P105(f326(f326(f234(a909),x75291),x75292))+~P105(f326(f326(f234(a909),f326(f326(f79(a909),x75291),x75293)),x75292))
% 157.55/157.22 [7530]P105(f326(f326(f235(a909),x75301),x75302))+~P105(f326(f326(f235(a909),f326(f326(f79(a909),x75301),x75303)),x75302))
% 157.55/157.22 [7568]~P108(x75681)+E(f14(x75681,f232(x75681),f326(f172(x75681),f326(f326(f151(x75681),x75682),x75683))),f326(f142(x75681,x75681,f232(x75681),x75682),x75683))
% 157.55/157.22 [7569]~P108(x75691)+E(f15(x75691,f233(x75691),f326(f172(x75691),f326(f326(f151(x75691),x75692),x75693))),f326(f142(x75691,x75691,f233(x75691),x75692),x75693))
% 157.55/157.22 [7573]~E(x75732,f188(f917(f916(x75731,x75731),a905)))+P105(f326(f326(f234(f917(f916(x75731,x75731),a905)),x75732),x75733))
% 157.55/157.22 [7674]E(f326(f326(f110(f917(x76741,a905)),x76742),f326(f326(f3(f917(x76741,a905)),x76743),x76742)),x76743)+~P105(f326(f326(f234(f917(x76741,a905)),x76742),x76743))
% 157.55/157.22 [7675]~P105(f326(f326(f234(a909),x76751),f326(f326(f79(a909),x76753),x76752)))+P105(f326(f326(f234(a909),f326(f326(f3(a909),x76751),x76752)),x76753))
% 157.55/157.22 [7676]~P105(f326(f326(f235(a909),x76761),f326(f326(f3(a909),x76763),x76762)))+P105(f326(f326(f235(a909),f326(f326(f79(a909),x76761),x76762)),x76763))
% 157.55/157.22 [7731]E(x77311,f113(x77312))+E(f326(f141(x77312),f326(f326(f326(f183(f910(x77312),f910(x77312)),x77313),f167(x77312)),x77311)),f326(f326(f164(x77312),x77311),f45(a909,x77313,f326(f189(f910(x77312)),x77311))))
% 157.55/157.22 [7740]E(f326(f326(f308(x77401),x77402),f326(f326(f3(f917(x77401,a905)),x77403),f326(f326(f308(x77401),x77402),f188(f917(x77401,a905))))),x77403)+~P105(f326(f326(f328(x77401),x77402),x77403))
% 157.55/157.22 [7899]P105(f326(f326(f234(a909),x78991),f326(f326(f79(a909),x78992),x78993)))+~P105(f326(f326(f234(a909),f326(f326(f3(a909),x78991),x78993)),x78992))
% 157.55/157.22 [7900]P105(f326(f326(f235(a909),x79001),f326(f326(f3(a909),x79002),x79003)))+~P105(f326(f326(f235(a909),f326(f326(f79(a909),x79001),x79003)),x79002))
% 157.55/157.22 [7925]P105(f326(f61(x79251),x79252))+~P105(f326(f61(x79251),f326(f326(f110(f917(x79251,a905)),x79253),x79252)))
% 157.55/157.22 [7926]P105(f326(f61(x79261),x79262))+~P105(f326(f61(x79261),f326(f326(f110(f917(x79261,a905)),x79262),x79263)))
% 157.55/157.22 [7997]~P45(x79971,x79973)+P105(f326(f326(f328(f916(x79971,x79971)),f326(f326(f251(x79971,x79971),x79972),x79972)),x79973))
% 157.55/157.22 [8129]E(f326(f326(f164(a909),f139(a909,f326(f301(a909,x81291),x81292))),x81293),f326(f326(f79(a909),x81291),x81293))+~P105(f326(f326(f235(a909),f326(f326(f79(a909),x81291),x81293)),x81292))
% 157.55/157.22 [8195]E(f326(f326(f175(a909),x81951),f139(a909,f326(f301(a909,x81952),x81953))),f139(a909,f326(f301(a909,x81952),f326(f326(f79(a909),x81952),x81951))))+~P105(f326(f326(f234(a909),f326(f326(f79(a909),x81952),x81951)),x81953))
% 157.55/157.22 [8252]~P94(x82521)+E(f326(f326(f243(x82521),x82522),f326(f103(a909),f326(f326(f79(a1),x82523),x82523))),f326(f326(f85(x82521,x82521),f326(f326(f243(x82521),x82522),f326(f103(a909),x82523))),f326(f326(f20(x82521,x82521,x82521),f80(x82521)),f7(x82521))))
% 157.55/157.22 [8511]E(f326(f326(f134(x85111),f326(f326(f175(x85111),x85112),x85113)),f326(f326(f151(x85111),f326(f326(f164(x85111),x85113),x85112)),f326(f326(f138(x85111),f326(a112,x85112)),x85113))),x85113)+~P105(f326(f326(f235(a909),x85112),f326(f189(f910(x85111)),x85113)))
% 157.55/157.22 [8518]P105(f326(f326(f234(f917(x85181,a905)),f314(x85181,x85182)),f314(x85181,x85183)))+~P105(f326(f326(f234(f917(x85181,f917(x85181,a905))),x85183),x85182))
% 157.55/157.22 [8519]~P54(x85191,x85192,x85193)+P54(x85191,x85192,f326(f326(f3(f917(f916(x85191,x85191),a905)),x85193),f306(x85191,f188(f917(f916(x85191,x85191),a905)))))
% 157.55/157.22 [8538]P105(f326(f326(f234(f917(x85381,a905)),f315(x85381,x85382)),f315(x85381,x85383)))+~P105(f326(f326(f234(f917(f916(x85381,x85381),a905)),x85383),x85382))
% 157.55/157.22 [8545]~P126(x85451)+P105(f326(f326(f234(x85451),f2(x85451)),f326(f326(f79(x85451),f326(f326(f80(x85451),x85452),x85452)),f326(f326(f80(x85451),x85453),x85453))))
% 157.55/157.22 [8578]P105(f326(f326(f234(f917(x85781,a905)),f326(f280(x85781),x85782)),f326(f280(x85781),x85783)))+~P105(f326(f326(f234(f917(f916(x85781,x85781),a905)),x85782),x85783))
% 157.55/157.22 [8607]~P52(x86071,x86072)+~P105(f326(f326(f328(f916(x86071,x86071)),f326(f326(f251(x86071,x86071),x86073),x86073)),x86072))
% 157.55/157.22 [8609]~P36(x86091,x86092)+~P105(f326(f326(f328(f916(x86091,x86091)),f326(f326(f251(x86091,x86091),x86093),x86093)),x86092))
% 157.55/157.22 [8666]P105(f326(f326(f234(f917(x86661,a905)),f37(f917(x86661,a905),x86662)),f37(f917(x86661,a905),x86663)))+~P105(f326(f326(f234(f917(f917(x86661,a905),a905)),x86662),x86663))
% 157.55/157.22 [8667]P105(f326(f326(f234(f917(x86671,a905)),f38(f917(x86671,a905),x86672)),f38(f917(x86671,a905),x86673)))+~P105(f326(f326(f234(f917(f917(x86671,a905),a905)),x86673),x86672))
% 157.55/157.22 [8721]~P7(x87211,x87213,x87212)+P105(f326(f326(f234(f917(f916(x87211,x87211),a905)),x87212),f326(f326(f253(x87211,x87211),x87213),f326(f18(f917(x87211,a905),x87211),x87213))))
% 157.55/157.22 [8722]~P51(x87221,x87223,x87222)+P105(f326(f326(f234(f917(f916(x87221,x87221),a905)),x87222),f326(f326(f253(x87221,x87221),x87223),f326(f18(f917(x87221,a905),x87221),x87223))))
% 157.55/157.22 [8771]~P86(x87711)+P105(f326(f326(f234(x87711),f326(f326(f3(x87711),f326(f75(x87711),x87712)),f326(f75(x87711),x87713))),f326(f75(x87711),f326(f326(f3(x87711),x87713),x87712))))
% 157.55/157.22 [8772]~P86(x87721)+P105(f326(f326(f234(x87721),f326(f326(f3(x87721),f326(f75(x87721),x87722)),f326(f75(x87721),x87723))),f326(f75(x87721),f326(f326(f3(x87721),x87722),x87723))))
% 157.55/157.22 [8804]P105(f326(f326(f234(f917(f916(x88041,x88041),a905)),f306(x88041,x88042)),f306(x88041,x88043)))+~P105(f326(f326(f234(f917(f916(x88041,x88041),a905)),x88042),x88043))
% 157.55/157.22 [8915]~P24(x89152,x89151,x89153,f241(f917(x89152,a905)))+E(f326(f72(x89151,x89152,x89152,f90(x89152,x89151,f241(f917(x89152,a905)),x89153)),x89153),f31(x89152))
% 157.55/157.22 [8975]P54(x89751,x89752,x89753)+~P54(x89751,x89752,f326(f326(f3(f917(f916(x89751,x89751),a905)),x89753),f306(x89751,f188(f917(f916(x89751,x89751),a905)))))
% 157.55/157.22 [8995]P105(f326(f326(f234(f917(f916(f910(x89951),f910(x89951)),a905)),f157(x89951,x89952)),f157(x89951,x89953)))+~P105(f326(f326(f234(f917(f916(x89951,x89951),a905)),x89952),x89953))
% 157.55/157.22 [8996]P105(f326(f326(f234(f917(f916(f910(x89961),f910(x89961)),a905)),f158(x89961,x89962)),f158(x89961,x89963)))+~P105(f326(f326(f234(f917(f916(x89961,x89961),a905)),x89962),x89963))
% 157.55/157.22 [9017]~P51(x90171,x90173,x90172)+P105(f326(f326(f234(f917(f916(x90171,x90171),a905)),x90172),f326(f326(f288(x90171,x90171,x90171),f326(f285(x90171,x90171),x90172)),x90172)))
% 157.55/157.22 [9069]~P105(f326(f137(x90691),x90692))+E(f326(f136(x90691,f326(f326(f9(x90691,f917(x90691,a905),a905),f328(x90691)),f326(f172(x90691),f176(x90691,x90692,x90693)))),x90692),f176(x90691,x90692,x90693))
% 157.55/157.22 [9122]E(x91221,x91222)+~P105(f326(f326(f328(f916(x91223,x91223)),f326(f326(f251(x91223,x91223),x91221),x91222)),f306(x91223,f188(f917(f916(x91223,x91223),a905)))))
% 157.55/157.22 [9204]P105(f326(f326(f328(x92041),x92042),f315(x92041,x92043)))+P105(f326(f326(f328(f916(x92041,x92041)),f326(f326(f251(x92041,x92041),f519(x92043,x92042,x92041)),x92042)),x92043))
% 157.55/157.22 [9205]P105(f326(f326(f328(x92051),x92052),f315(x92051,x92053)))+P105(f326(f326(f328(f916(x92051,x92051)),f326(f326(f251(x92051,x92051),f595(x92053,x92052,x92051)),x92052)),x92053))
% 157.55/157.22 [9206]P105(f326(f326(f328(x92061),x92062),f315(x92061,x92063)))+P105(f326(f326(f328(f916(x92061,x92061)),f326(f326(f251(x92061,x92061),f597(x92063,x92062,x92061)),x92062)),x92063))
% 157.55/157.22 [9242]P24(x92421,x92422,x92423,f241(f917(x92421,a905)))+~E(f326(f72(x92422,x92421,x92421,f90(x92421,x92422,f241(f917(x92421,a905)),x92423)),x92423),f31(x92421))
% 157.55/157.22 [9295]~P105(f326(f326(f328(f910(x92951)),x92953),f161(x92951,x92952)))+P105(f326(f160(x92951,f326(f326(f9(x92951,f917(x92951,a905),a905),f328(x92951)),x92952)),x92953))
% 157.55/157.22 [9318]P105(f326(x93183,x93182))+E(f326(f261(x93181),f326(f326(f20(x93181,a905,a905),f326(f326(f10(a905,f917(a905,a905),x93181),a324),f326(a323,x93182))),x93183)),f188(f917(x93181,a905)))
% 157.55/157.22 [9334]~P86(x93341)+P105(f326(f326(f234(x93341),f326(f75(x93341),f326(f326(f3(x93341),f326(f75(x93341),x93342)),f326(f75(x93341),x93343)))),f326(f75(x93341),f326(f326(f3(x93341),x93342),x93343))))
% 157.55/157.22 [9348]~P105(f326(x93483,x93482))+E(f326(f261(x93481),f326(f326(f20(x93481,a905,a905),f326(f326(f10(a905,f917(a905,a905),x93481),a324),f326(a323,x93482))),x93483)),f326(f326(f308(x93481),x93482),f188(f917(x93481,a905))))
% 157.55/157.22 [9355]~P105(f326(f326(f328(f917(x93551,a905)),x93553),f326(f307(x93551),x93552)))+P105(f326(f247(x93551,f326(f326(f9(x93551,f917(x93551,a905),a905),f328(x93551)),x93552)),x93553))
% 157.55/157.22 [9390]P36(x93901,x93902)+P105(f326(f326(f328(f916(x93901,x93901)),f326(f326(f251(x93901,x93901),f326(f560(x93902,x93901),f326(a112,x93903))),f326(f560(x93902,x93901),x93903))),x93902))
% 157.55/157.22 [9529]P105(f326(f326(f328(f910(x95291)),x95292),f161(x95291,x95293)))+~P105(f326(f160(x95291,f326(f326(f9(x95291,f917(x95291,a905),a905),f328(x95291)),x95293)),x95292))
% 157.55/157.22 [9542]P105(f326(f326(f328(f917(x95421,a905)),x95422),f326(f307(x95421),x95423)))+~P105(f326(f247(x95421,f326(f326(f9(x95421,f917(x95421,a905),a905),f328(x95421)),x95423)),x95422))
% 157.55/157.22 [9602]P105(f326(f326(f328(x96021),f326(f267(x96021,x96022),x96023)),f326(f172(x96021),f326(f326(f154(f916(a99,x96021),x96021),f255(a99,x96021)),x96022))))+~P105(f326(f326(f235(a99),x96023),f326(f165(a99),f326(f326(f154(f916(a99,x96021),a99),f250(a99,x96021)),x96022))))
% 157.55/157.22 [9648]P105(f326(f326(f234(f917(f916(f910(x96481),f910(x96481)),a905)),f158(x96481,x96482)),f326(f326(f253(f910(x96481),f910(x96481)),f161(x96481,x96483)),f326(f18(f917(f910(x96481),a905),f910(x96481)),f161(x96481,x96483)))))+~P105(f326(f326(f234(f917(f916(x96481,x96481),a905)),x96482),f326(f326(f253(x96481,x96481),x96483),f326(f18(f917(x96481,a905),x96481),x96483))))
% 157.55/157.22 [9672]P105(f326(f326(f328(x96721),f326(f250(x96721,f916(a99,a99)),f326(f265(x96721,x96722),x96723))),f326(f172(x96721),f326(f326(f154(f916(a99,x96721),x96721),f255(a99,x96721)),x96722))))+~P105(f326(f326(f235(a99),f2(a99)),f326(f165(a99),f326(f326(f154(f916(a99,x96721),a99),f250(a99,x96721)),x96722))))
% 157.55/157.22 [9687]~P105(f326(f326(f234(f917(f916(x96871,x96871),a905)),x96872),f326(f326(f253(x96871,x96871),x96873),f326(f18(f917(x96871,a905),x96871),x96873))))+P105(f326(f326(f234(f917(f916(x96871,x96871),a905)),f326(f326(f288(x96871,x96871,x96871),x96872),f306(x96871,x96872))),f326(f326(f253(x96871,x96871),x96873),f326(f18(f917(x96871,a905),x96871),x96873))))
% 157.55/157.22 [9986]~P36(x99861,x99862)+~P105(f326(f326(f328(f916(x99861,x99861)),f326(f326(f251(x99861,x99861),f326(x99863,f326(a112,f561(x99862,x99861,x99863)))),f326(x99863,f561(x99862,x99861,x99863)))),x99862))
% 157.55/157.22 [9987]~P36(x99871,x99872)+~P105(f326(f326(f328(f916(x99871,x99871)),f326(f326(f251(x99871,x99871),f326(x99873,f326(a112,f603(x99873,x99872,x99871)))),f326(x99873,f603(x99873,x99872,x99871)))),x99872))
% 157.55/157.22 [10244]P105(f326(f326(f234(f917(f916(f917(x102441,a905),f917(x102441,a905)),a905)),f326(f326(f288(f917(x102441,a905),f917(x102441,a905),f917(x102441,a905)),f317(x102441,x102442)),f326(f326(f110(f917(f916(f917(x102441,a905),f917(x102441,a905)),a905)),f317(x102441,x102443)),f326(f326(f308(f916(f917(x102441,a905),f917(x102441,a905))),f326(f326(f251(f917(x102441,a905),f917(x102441,a905)),f188(f917(x102441,a905))),f188(f917(x102441,a905)))),f188(f917(f916(f917(x102441,a905),f917(x102441,a905)),a905)))))),f317(x102441,x102442)))+~P105(f326(f326(f234(f917(f916(x102441,x102441),a905)),f326(f326(f288(x102441,x102441,x102441),x102442),x102443)),x102442))
% 157.55/157.22 [10245]P105(f326(f326(f234(f917(f916(f917(x102451,a905),f917(x102451,a905)),a905)),f326(f326(f288(f917(x102451,a905),f917(x102451,a905),f917(x102451,a905)),f318(x102451,x102452)),f326(f326(f110(f917(f916(f917(x102451,a905),f917(x102451,a905)),a905)),f318(x102451,x102453)),f326(f326(f308(f916(f917(x102451,a905),f917(x102451,a905))),f326(f326(f251(f917(x102451,a905),f917(x102451,a905)),f188(f917(x102451,a905))),f188(f917(x102451,a905)))),f188(f917(f916(f917(x102451,a905),f917(x102451,a905)),a905)))))),f318(x102451,x102452)))+~P105(f326(f326(f234(f917(f916(x102451,x102451),a905)),f326(f326(f288(x102451,x102451,x102451),x102452),x102453)),x102452))
% 157.55/157.22 [7445]~P105(f326(f326(f234(a909),x74452),x74451))+E(f326(f326(f3(a909),f326(a112,f326(f326(f3(a909),x74451),x74452))),x74453),f326(f326(f3(a909),f326(a112,x74451)),f326(f326(f79(a909),x74452),x74453)))
% 157.55/157.22 [7484]~P59(x74841)+E(f326(f326(f79(x74841),f45(x74841,x74842,x74843)),f326(f326(f80(x74841),f326(f326(f36(x74841),x74842),x74843)),x74843)),x74842)
% 157.55/157.22 [7680]E(f326(f326(f80(a909),f326(f103(a909),x76801)),f326(f326(f80(a909),f326(f103(a909),x76802)),x76803)),f326(f326(f80(a909),f326(f103(a909),f326(f326(f80(a1),x76801),x76802))),x76803))+P105(f326(f326(f235(a1),x76801),a82))
% 157.55/157.22 [8138]~P105(f326(f326(f234(a909),x81383),x81382))+P105(f326(f326(f234(a909),x81381),f326(f326(f3(a909),f326(f326(f79(a909),x81382),x81381)),x81383)))
% 157.55/157.22 [8333]~P105(f326(f326(f234(a909),x83331),x83332))+E(f326(f326(f134(a909),f139(a909,f326(f301(a909,x83331),x83332))),f139(a909,f326(f301(a909,x83332),f326(f326(f79(a909),x83332),x83333)))),f139(a909,f326(f301(a909,x83331),f326(f326(f79(a909),x83332),x83333))))
% 157.55/157.22 [8586]~P105(f326(f61(x85861),x85862))+E(f326(a112,f326(f35(x85861),f326(f326(f3(f917(x85861,a905)),x85862),f326(f326(f308(x85861),x85863),f188(f917(x85861,a905)))))),f326(f35(x85861),f326(f326(f308(x85861),x85863),x85862)))
% 157.55/157.22 [8625]~P105(f326(f61(x86251),x86252))+E(f326(f326(f79(a909),f77(a909)),f326(f35(x86251),f326(f326(f3(f917(x86251,a905)),x86252),f326(f326(f308(x86251),x86253),f188(f917(x86251,a905)))))),f326(f35(x86251),f326(f326(f308(x86251),x86253),x86252)))
% 157.55/157.22 [8813]E(f326(f326(f3(a909),f326(f35(x88131),x88132)),f326(f35(x88131),f326(f326(f101(f917(x88131,a905)),x88132),x88133))),f326(f35(x88131),f326(f326(f3(f917(x88131,a905)),x88132),x88133)))+~P105(f326(f61(x88131),f326(f326(f101(f917(x88131,a905)),x88132),x88133)))
% 157.55/157.22 [9064]~P5(f326(x90642,f398(x90642,x90643,x90641)))+E(f326(f100(a1),f326(f326(f8(x90641,a909),f326(f326(f10(a1,a909,x90641),a104),x90642)),x90643)),f326(f326(f8(x90641,a1),x90642),x90643))
% 157.55/157.22 [9065]~P5(f326(x90652,f399(x90652,x90653,x90651)))+E(f326(f100(a1),f326(f326(f11(x90651,a909),f326(f326(f10(a1,a909,x90651),a104),x90652)),x90653)),f326(f326(f11(x90651,a1),x90652),x90653))
% 157.55/157.22 [9105]~P105(f326(f61(x91051),x91053))+P105(f326(f326(f234(a909),f326(f326(f3(a909),f326(f35(x91051),x91052)),f326(f35(x91051),x91053))),f326(f35(x91051),f326(f326(f3(f917(x91051,a905)),x91052),x91053))))
% 157.55/157.22 [9132]P105(f326(f326(f328(x91321),f398(x91322,x91323,x91321)),x91323))+E(f326(f100(a1),f326(f326(f8(x91321,a909),f326(f326(f10(a1,a909,x91321),a104),x91322)),x91323)),f326(f326(f8(x91321,a1),x91322),x91323))
% 157.55/157.22 [9133]P105(f326(f326(f328(x91331),f399(x91332,x91333,x91331)),x91333))+E(f326(f100(a1),f326(f326(f11(x91331,a909),f326(f326(f10(a1,a909,x91331),a104),x91332)),x91333)),f326(f326(f11(x91331,a1),x91332),x91333))
% 157.55/157.22 [9196]E(f84(x91961,f326(f326(f9(x91961,f917(x91961,a905),a905),f328(x91961)),f326(f326(f3(f917(x91961,a905)),x91962),f326(f326(f308(x91961),x91963),f188(f917(x91961,a905)))))),f246(x91961,x91963,x91962))+P105(f326(f326(f234(f917(x91961,a905)),x91962),f326(f326(f308(x91961),x91963),f188(f917(x91961,a905)))))
% 157.55/157.22 [9543]E(f326(f326(f154(f910(x95431),x95431),f326(f326(f9(f910(x95431),a909,x95431),f164(x95431)),x95432)),f326(f136(f910(x95431),f326(f326(f10(a909,a905,f910(x95431)),f326(f235(a909),x95432)),f189(f910(x95431)))),x95433)),f326(f326(f164(f910(x95431)),f179(x95431,x95433)),x95432))+~P105(f326(f326(f235(a909),x95432),f326(f189(f910(f910(x95431))),f179(x95431,x95433))))
% 157.55/157.22 [9622]E(f326(f136(x96221,x96222),x96223),f177(x96221,x96222,x96223))+P105(f326(f326(f328(x96221),f716(x96223,x96222,x96221)),f326(f172(x96221),f326(f326(f138(x96221),f326(f189(f910(x96221)),f177(x96221,x96222,x96223))),x96223))))
% 157.55/157.22 [9760]E(f326(f326(f138(x97601),f326(f189(f910(x97601)),f177(x97601,x97602,x97603))),x97603),f113(x97601))+~P105(f326(x97602,f326(f141(x97601),f326(f326(f138(x97601),f326(f189(f910(x97601)),f177(x97601,x97602,x97603))),x97603))))
% 157.55/157.22 [9853]~P105(f326(f326(f328(f916(x98531,x98531)),x98532),f306(x98531,x98533)))+P105(f326(f326(f328(f916(x98531,x98531)),x98532),f326(f326(f40(a909,f917(f916(x98531,x98531),a905)),f241(f917(a909,a905))),f326(f326(f9(a909,f917(f916(x98531,x98531),a905),f917(f916(x98531,x98531),a905)),f183(f916(x98531,x98531),a905)),x98533))))
% 157.55/157.22 [9913]~P105(f326(f326(f234(f917(x99131,a905)),f326(f326(f40(a909,f917(x99131,a905)),f326(f301(a909,f2(a909)),f478(x99133,x99132,x99131))),x99132)),x99133))+P105(f326(f326(f234(f917(x99131,a905)),f326(f326(f40(a909,f917(x99131,a905)),f241(f917(a909,a905))),x99132)),x99133))
% 157.55/157.22 [9959]~P105(f326(f326(f235(a1),f2(a1)),x99593))+P105(f326(f326(f235(a1),x99591),f326(f326(f79(a1),x99592),f326(f326(f80(a1),f326(f326(f79(a1),f326(f75(a1),f326(f326(f3(a1),x99592),x99591))),f77(a1))),x99593))))
% 157.55/157.22 [9973]~P36(x99731,f326(f326(f110(f917(f916(x99731,x99731),a905)),x99732),x99733))+P36(x99731,f326(f326(f110(f917(f916(x99731,x99731),a905)),f326(f326(f110(f917(f916(x99731,x99731),a905)),f326(f326(f288(x99731,x99731,x99731),x99732),x99732)),f326(f326(f288(x99731,x99731,x99731),x99733),x99732))),x99733))
% 157.55/157.22 [10049]P36(x100491,f326(f326(f110(f917(f916(x100491,x100491),a905)),x100492),x100493))+~P36(x100491,f326(f326(f110(f917(f916(x100491,x100491),a905)),f326(f326(f110(f917(f916(x100491,x100491),a905)),f326(f326(f288(x100491,x100491,x100491),x100492),x100492)),f326(f326(f288(x100491,x100491,x100491),x100493),x100492))),x100493))
% 157.55/157.22 [9625]~P140(x96251)+E(f326(f102(x96251),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x96252),x96253)),f188(f917(f916(a909,a909),a905)))))),f326(f326(f3(x96251),f326(f100(x96251),x96252)),f326(f100(x96251),x96253)))
% 157.55/157.22 [9707]P105(f326(x97073,x97072))+E(f326(f261(x97071),f326(f326(f20(x97071,a905,a905),f326(f326(f10(a905,f917(a905,a905),x97071),a324),f326(f326(f9(x97071,x97071,a905),a323),x97072))),x97073)),f188(f917(x97071,a905)))
% 157.55/157.22 [9709]~P105(f326(x97093,x97092))+E(f326(f261(x97091),f326(f326(f20(x97091,a905,a905),f326(f326(f10(a905,f917(a905,a905),x97091),a324),f326(f326(f9(x97091,x97091,a905),a323),x97092))),x97093)),f326(f326(f308(x97091),x97092),f188(f917(x97091,a905))))
% 157.55/157.22 [9939]E(x99391,x99392)+P105(f326(f326(f242(x99393,x99393,f326(f326(f10(f917(x99393,a905),f917(x99393,a905),x99393),f326(f10(a905,a905,x99393),a321)),a323)),x99391),x99392))
% 157.55/157.22 [10028]~E(x100281,x100282)+~P105(f326(f326(f242(x100283,x100283,f326(f326(f10(f917(x100283,a905),f917(x100283,a905),x100283),f326(f10(a905,a905,x100283),a321)),a323)),x100281),x100282))
% 157.55/157.22 [10041]~P105(f326(f61(x100411),x100413))+E(f326(f326(f64(x100411,f917(x100411,a905),f326(f326(f10(f917(x100411,a905),f917(f917(x100411,a905),f917(x100411,a905)),x100411),f326(f9(f917(x100411,a905),f917(x100411,a905),f917(x100411,a905)),f3(f917(x100411,a905)))),f326(f326(f9(x100411,f917(x100411,a905),f917(x100411,a905)),f308(x100411)),f188(f917(x100411,a905))))),x100412),x100413),f326(f326(f3(f917(x100411,a905)),x100412),x100413))
% 157.55/157.22 [10071]~P105(f326(f326(f235(a1),f2(a1)),x100713))+P105(f326(f326(f235(a1),f326(f326(f3(a1),x100711),f326(f326(f80(a1),f326(f326(f79(a1),f326(f75(a1),f326(f326(f3(a1),x100711),x100712))),f77(a1))),x100713))),x100712))
% 157.55/157.22 [10331]~P105(f326(f326(f328(x103311),x103313),f315(x103311,x103312)))+P105(f326(f314(x103311,f326(f326(f9(x103311,f917(f916(x103311,x103311),a905),f917(x103311,a905)),f326(f326(f10(f917(x103311,f917(f917(f916(x103311,x103311),a905),a905)),f917(f917(f916(x103311,x103311),a905),f917(x103311,a905)),x103311),f9(x103311,f917(f916(x103311,x103311),a905),a905)),f326(f326(f10(f917(x103311,f916(x103311,x103311)),f917(x103311,f917(f917(f916(x103311,x103311),a905),a905)),x103311),f326(f10(f916(x103311,x103311),f917(f917(f916(x103311,x103311),a905),a905),x103311),f328(f916(x103311,x103311)))),f251(x103311,x103311)))),x103312)),x103313))
% 157.55/157.22 [10345]P105(f326(f326(f328(x103451),x103452),f315(x103451,x103453)))+~P105(f326(f314(x103451,f326(f326(f9(x103451,f917(f916(x103451,x103451),a905),f917(x103451,a905)),f326(f326(f10(f917(x103451,f917(f917(f916(x103451,x103451),a905),a905)),f917(f917(f916(x103451,x103451),a905),f917(x103451,a905)),x103451),f9(x103451,f917(f916(x103451,x103451),a905),a905)),f326(f326(f10(f917(x103451,f916(x103451,x103451)),f917(x103451,f917(f917(f916(x103451,x103451),a905),a905)),x103451),f326(f10(f916(x103451,x103451),f917(f917(f916(x103451,x103451),a905),a905),x103451),f328(f916(x103451,x103451)))),f251(x103451,x103451)))),x103453)),x103452))
% 157.55/157.22 [9911]~P105(f326(f61(x99111),f326(f261(x99111),x99113)))+P105(f326(f61(x99111),f326(f261(x99111),f326(f326(f20(x99111,a905,a905),f326(f326(f10(a905,f917(a905,a905),x99111),a324),x99112)),x99113))))
% 157.55/157.22 [9912]~P105(f326(f61(x99121),f326(f261(x99121),x99122)))+P105(f326(f61(x99121),f326(f261(x99121),f326(f326(f20(x99121,a905,a905),f326(f326(f10(a905,f917(a905,a905),x99121),a324),x99122)),x99123))))
% 157.55/157.22 [10007]P105(f326(f61(x100071),f326(f261(x100071),x100072)))+~P105(f326(f61(x100071),f326(f261(x100071),f326(f326(f20(x100071,a905,a905),f326(f326(f10(a905,f917(a905,a905),x100071),a325),x100073)),x100072))))
% 157.55/157.22 [10008]P105(f326(f61(x100081),f326(f261(x100081),x100082)))+~P105(f326(f61(x100081),f326(f261(x100081),f326(f326(f20(x100081,a905,a905),f326(f326(f10(a905,f917(a905,a905),x100081),a325),x100082)),x100083))))
% 157.55/157.22 [10308]~P105(f326(f61(x103081),x103082))+P105(f326(f61(f910(x103081)),f326(f261(f910(x103081)),f326(f326(f20(f910(x103081),a905,a905),f326(f326(f10(a905,f917(a905,a905),f910(x103081)),a324),f326(f326(f9(f910(x103081),f917(x103081,a905),a905),f326(f326(f10(f917(x103081,a905),f917(f917(x103081,a905),a905),f910(x103081)),f234(f917(x103081,a905))),f172(x103081))),x103082))),f326(f326(f9(f910(x103081),a909,a905),f326(f326(f10(a909,f917(a909,a905),f910(x103081)),a323),f189(f910(x103081)))),x103083)))))
% 157.55/157.22 [10309]~P105(f326(f61(x103091),x103092))+P105(f326(f61(f910(x103091)),f326(f261(f910(x103091)),f326(f326(f20(f910(x103091),a905,a905),f326(f326(f10(a905,f917(a905,a905),f910(x103091)),a324),f326(f326(f9(f910(x103091),f917(x103091,a905),a905),f326(f326(f10(f917(x103091,a905),f917(f917(x103091,a905),a905),f910(x103091)),f234(f917(x103091,a905))),f172(x103091))),x103092))),f326(f326(f9(f910(x103091),a909,a905),f326(f326(f10(a909,f917(a909,a905),f910(x103091)),f234(a909)),f189(f910(x103091)))),x103093)))))
% 157.55/157.22 [10021]~P112(x100211)+E(f326(f326(f243(x100211),x100212),f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x100213)),f326(f326(f80(x100211),f326(f326(f243(x100211),x100212),x100213)),f326(f326(f243(x100211),x100212),x100213)))
% 157.55/157.22 [10052]~P81(x100521)+E(f326(f326(f243(x100521),f326(f326(f243(x100521),x100522),x100523)),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(f326(f243(x100521),x100522),f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x100523)))
% 157.55/157.22 [10109]~P140(x101091)+E(f326(f326(f243(x101091),f326(f78(x101091),x101092)),f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x101093)),f326(f326(f243(x101091),x101092),f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x101093)))
% 157.55/157.22 [10253]~P118(x102531)+P105(f326(f326(f234(x102531),f2(x102531)),f326(f326(f79(x102531),f326(f326(f243(x102531),x102532),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x102531),x102533),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))))
% 157.55/157.22 [10119]~P112(x101191)+E(f326(f326(f243(x101191),x101192),f326(a112,f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x101193))),f326(f326(f80(x101191),x101192),f326(f326(f80(x101191),f326(f326(f243(x101191),x101192),x101193)),f326(f326(f243(x101191),x101192),x101193))))
% 157.55/157.22 [10169]~P81(x101691)+E(f326(f326(f80(x101691),x101692),f326(f326(f243(x101691),f326(f326(f243(x101691),x101692),x101693)),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x101691),x101692),f326(a112,f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x101693))))
% 157.55/157.22 [10209]~P118(x102091)+P105(f326(f326(f234(x102091),f2(x102091)),f326(f326(f243(x102091),x102092),f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x102093))))
% 157.55/157.22 [10284]~P94(x102841)+E(f326(f326(f3(x102841),f326(f326(f79(x102841),f326(f326(f243(x102841),x102842),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x102841),x102843),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))),f326(f326(f80(x102841),f326(f326(f80(x102841),f326(f103(x102841),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x102842)),x102843)),f326(f326(f243(x102841),f326(f326(f3(x102841),x102842),x102843)),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.55/157.22 [10285]~P94(x102851)+E(f326(f326(f79(x102851),f326(f326(f79(x102851),f326(f326(f243(x102851),x102852),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x102851),x102853),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))),f326(f326(f80(x102851),f326(f326(f80(x102851),f326(f103(x102851),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x102852)),x102853)),f326(f326(f243(x102851),f326(f326(f79(x102851),x102852),x102853)),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.55/157.22 [4821]E(x48211,x48212)+~E(f30(x48213,x48211),f30(x48214,x48212))
% 157.55/157.22 [4822]E(x48221,x48222)+~E(f30(x48221,x48223),f30(x48222,x48224))
% 157.55/157.22 [4823]E(x48231,x48232)+~E(f29(x48233,x48231),f29(x48234,x48232))
% 157.55/157.22 [4824]E(x48241,x48242)+~E(f29(x48241,x48243),f29(x48242,x48244))
% 157.55/157.22 [7942]P24(x79421,x79422,x79423,x79424)+~E(f506(x79424,x79423,x79422,x79421),f514(x79424,x79423,x79422,x79421))
% 157.55/157.22 [8229]P33(x82291,x82292,x82293,x82294,f113(x82292))+~E(x82294,f113(x82291))
% 157.55/157.22 [8230]P33(x82301,x82302,x82303,f113(x82301),x82304)+~E(x82304,f113(x82302))
% 157.55/157.22 [8761]~P33(x87612,x87613,x87614,x87611,f113(x87613))+E(x87611,f113(x87612))
% 157.55/157.22 [8762]~P33(x87623,x87622,x87624,f113(x87623),x87621)+E(x87621,f113(x87622))
% 157.55/157.22 [5209]~P16(x52093,x52091,x52094)+E(f326(f326(x52091,x52092),x52092),x52092)
% 157.55/157.22 [5462]P105(f326(x54622,x54624))+E(f326(f136(x54621,x54622),f169(x54621,x54623,x54624)),f113(x54621))
% 157.55/157.22 [5499]~E(x54994,f188(f917(x54991,a905)))+E(f326(f309(x54991,x54992,x54993),x54994),f188(f917(x54992,a905)))
% 157.55/157.22 [5747]~P105(f326(x57472,x57474))+E(f326(f136(x57471,x57472),f169(x57471,x57473,x57474)),f169(x57471,x57473,x57474))
% 157.55/157.22 [5777]~E(f326(f309(x57772,x57773,x57774),x57771),f188(f917(x57773,a905)))+E(x57771,f188(f917(x57772,a905)))
% 157.55/157.22 [5964]~P6(x59641,x59643)+E(f270(x59641,x59642,f269(x59641,x59643),x59644),x59644)
% 157.55/157.22 [6076]~P108(x60762)+E(f326(f326(f148(x60761,x60762,x60763),x60764),f113(x60761)),f326(f326(f151(x60761),x60764),f113(x60761)))
% 157.55/157.22 [6435]~E(x64351,f188(f917(x64352,a905)))+~P105(f326(f62(x64352,x64353,x64351),x64354))
% 157.55/157.22 [6457]~P57(x64571,x64573,x64574,x64572)+P105(f326(f61(x64571),x64572))
% 157.55/157.22 [6459]~P57(x64591,x64593,x64592,x64594)+P105(f326(f61(x64591),x64592))
% 157.55/157.22 [6466]~P57(x64662,x64663,x64664,x64661)+~E(x64661,f188(f917(x64662,a905)))
% 157.55/157.22 [6499]~P109(x64991)+E(f326(f326(f101(f917(x64991,a905)),f326(f301(x64991,x64992),x64993)),f302(x64991,x64993,x64994)),f188(f917(x64991,a905)))
% 157.55/157.22 [6527]~P105(f326(f326(x65273,x65274),x65272))+P105(f326(f326(f328(x65271),x65272),f293(x65271,x65273,x65274)))
% 157.55/157.22 [6528]~P105(f326(f326(x65283,x65284),x65282))+P105(f326(f326(f328(x65281),x65282),f294(x65281,x65283,x65284)))
% 157.55/157.22 [6529]~P105(f326(f326(x65293,x65292),x65294))+P105(f326(f326(f328(x65291),x65292),f295(x65291,x65293,x65294)))
% 157.55/157.22 [6530]~P105(f326(f326(x65303,x65302),x65304))+P105(f326(f326(f328(x65301),x65302),f297(x65301,x65303,x65304)))
% 157.55/157.22 [6670]~P109(x66701)+E(f326(f326(f101(f917(x66701,a905)),f302(x66701,x66702,x66703)),f305(x66701,x66703,x66704)),f188(f917(x66701,a905)))
% 157.55/157.22 [6671]~P109(x66711)+E(f326(f326(f101(f917(x66711,a905)),f302(x66711,x66712,x66713)),f304(x66711,x66713,x66714)),f188(f917(x66711,a905)))
% 157.55/157.22 [6672]~P109(x66721)+E(f326(f326(f101(f917(x66721,a905)),f305(x66721,x66722,x66723)),f302(x66721,x66723,x66724)),f188(f917(x66721,a905)))
% 157.55/157.22 [6673]~P109(x66731)+E(f326(f326(f101(f917(x66731,a905)),f304(x66731,x66732,x66733)),f305(x66731,x66733,x66734)),f188(f917(x66731,a905)))
% 157.55/157.22 [6674]~P109(x66741)+E(f326(f326(f101(f917(x66741,a905)),f304(x66741,x66742,x66743)),f304(x66741,x66743,x66744)),f188(f917(x66741,a905)))
% 157.55/157.22 [6712]P105(f326(f326(x67121,x67122),f559(x67122,x67121)))+~P105(f326(f248(x67123,x67124,x67121),x67122))
% 157.55/157.22 [6793]~P108(x67932)+E(f326(f172(x67931),f150(x67931,x67932,x67933,x67934)),f326(f172(x67931),x67934))
% 157.55/157.22 [6845]~P143(x68451)+E(f190(x68451,x68452,f326(a112,x68453),x68454),f190(x68451,x68452,x68453,f326(x68452,x68454)))
% 157.55/157.22 [6908]~P105(f326(f326(f328(x69084),x69083),f293(x69084,x69081,x69082)))+P105(f326(f326(x69081,x69082),x69083))
% 157.55/157.22 [6909]~P105(f326(f326(f328(x69094),x69093),f294(x69094,x69091,x69092)))+P105(f326(f326(x69091,x69092),x69093))
% 157.55/157.22 [6910]~P105(f326(f326(f328(x69104),x69102),f295(x69104,x69101,x69103)))+P105(f326(f326(x69101,x69102),x69103))
% 157.55/157.22 [6911]~P105(f326(f326(f328(x69114),x69112),f297(x69114,x69111,x69113)))+P105(f326(f326(x69111,x69112),x69113))
% 157.55/157.22 [6985]E(f326(f35(f915(x69851,x69852)),f312(x69851,x69852,x69853,x69854)),f2(a909))+P105(f326(f61(x69852),x69854))
% 157.55/157.22 [6986]E(f326(f35(f915(x69861,x69862)),f312(x69861,x69862,x69863,x69864)),f2(a909))+P105(f326(f61(x69861),x69863))
% 157.55/157.22 [7187]~P13(x71874,x71871,x71872)+E(f326(f72(x71871,x71871,x71871,f326(x71872,x71873)),f326(x71872,x71873)),f326(x71872,x71873))
% 157.55/157.22 [7427]E(f276(x74271,x74272,x74273,x74274),f326(f251(f917(a99,f917(a905,f913(f911(x74271)))),f916(a99,a99)),f41(x74271)))+~P105(f326(f326(f234(a99),x74273),f2(a99)))
% 157.55/157.22 [8061]~E(x80612,x80613)+P105(f326(f326(f328(f916(x80611,x80611)),f326(f326(f251(x80611,x80611),x80612),x80613)),f306(x80611,x80614)))
% 157.55/157.22 [8090]~P24(x80901,x80902,x80903,f241(f917(x80901,a905)))+E(f326(f76(x80901,x80902,f241(f917(x80901,a905)),x80903),f326(x80903,x80904)),x80904)
% 157.55/157.22 [8091]~P24(x80911,x80912,x80913,f241(f917(x80911,a905)))+E(f326(f90(x80911,x80912,f241(f917(x80911,a905)),x80913),f326(x80913,x80914)),x80914)
% 157.55/157.22 [8178]~P105(f326(f326(f328(f910(x81781)),f326(f326(f151(x81781),x81784),x81782)),f161(x81781,x81783)))+P105(f326(f326(f328(f910(x81781)),x81782),f161(x81781,x81783)))
% 157.55/157.22 [8179]~P105(f326(f326(f328(f910(x81791)),f326(f326(f134(x81791),x81794),x81792)),f161(x81791,x81793)))+P105(f326(f326(f328(f910(x81791)),x81792),f161(x81791,x81793)))
% 157.55/157.22 [8180]~P105(f326(f326(f328(f910(x81801)),f326(f326(f134(x81801),x81802),x81804)),f161(x81801,x81803)))+P105(f326(f326(f328(f910(x81801)),x81802),f161(x81801,x81803)))
% 157.55/157.22 [8191]~P108(x81911)+P12(x81911,f326(f326(f154(x81912,x81911),x81913),f150(x81912,x81911,x81913,x81914)))
% 157.55/157.22 [8291]P24(x82914,x82913,x82911,x82912)+E(f326(x82911,f506(x82912,x82911,x82913,x82914)),f326(x82911,f514(x82912,x82911,x82913,x82914)))
% 157.55/157.22 [8397]~P24(x83972,x83971,x83974,x83973)+P24(x83971,x83972,f76(x83972,x83971,x83973,x83974),f326(f309(x83972,x83971,x83974),x83973))
% 157.55/157.22 [8536]P36(f916(x85362,x85364),f279(x85362,x85364,x85361,x85363))+P105(f326(x85361,f565(x85362,x85363,x85364,x85361)))
% 157.55/157.22 [8650]E(x86501,x86502)+~P105(f326(f326(f328(f916(x86503,x86503)),f326(f326(f251(x86503,x86503),x86501),x86502)),f262(x86503,x86504)))
% 157.55/157.22 [8713]~P105(f326(f61(f915(x87133,x87131)),f312(x87133,x87131,x87134,x87132)))+P105(f326(f61(x87131),x87132))
% 157.55/157.22 [8714]~P105(f326(f61(f915(x87141,x87143)),f312(x87141,x87143,x87142,x87144)))+P105(f326(f61(x87141),x87142))
% 157.55/157.22 [8723]~P24(x87231,x87232,x87233,x87234)+P25(x87231,x87232,x87233,x87234,f326(f309(x87231,x87232,x87233),x87234))
% 157.55/157.22 [8724]P10(x87241,x87242,x87243,x87244)+~E(f326(x87244,f825(x87242,x87244,x87243,x87241)),f326(x87244,f826(x87242,x87244,x87243,x87241)))
% 157.55/157.22 [8814]~P25(x88142,x88143,x88144,x88141,f188(f917(x88143,a905)))+E(x88141,f188(f917(x88142,a905)))
% 157.55/157.22 [8815]~P25(x88153,x88152,x88154,f188(f917(x88153,a905)),x88151)+E(x88151,f188(f917(x88152,a905)))
% 157.55/157.22 [8907]P36(f916(x89071,x89072),f279(x89071,x89072,x89073,x89074))+~P36(x89072,f326(x89074,f565(x89071,x89074,x89072,x89073)))
% 157.55/157.22 [9465]E(f326(f326(f159(x94651,x94652),f662(x94653,x94654,x94652,x94651)),f663(x94653,x94654,x94652,x94651)),x94654)+~P105(f326(f326(f328(f916(f910(x94651),f910(x94651))),f326(f326(f251(f910(x94651),f910(x94651)),x94652),x94654)),f157(x94651,x94653)))
% 157.55/157.22 [9470]~P105(f326(f326(f328(f916(f910(x94701),f910(x94701))),f326(f326(f251(f910(x94701),f910(x94701)),x94702),x94703)),f145(x94701,x94704)))+P105(f326(f326(f328(f916(f910(x94701),f910(x94701))),f326(f326(f251(f910(x94701),f910(x94701)),x94702),x94703)),f147(x94701,x94704)))
% 157.55/157.22 [9579]P105(f326(f61(x95791),x95792))+~P105(f326(f326(f328(f916(f917(x95791,a905),f917(x95791,a905))),f326(f326(f251(f917(x95791,a905),f917(x95791,a905)),x95793),x95792)),f318(x95791,x95794)))
% 157.55/157.22 [9580]P105(f326(f61(x95801),x95802))+~P105(f326(f326(f328(f916(f917(x95801,a905),f917(x95801,a905))),f326(f326(f251(f917(x95801,a905),f917(x95801,a905)),x95802),x95803)),f318(x95801,x95804)))
% 157.55/157.22 [9583]~E(x95831,f188(f917(x95832,a905)))+~P105(f326(f326(f328(f916(f917(x95832,a905),f917(x95832,a905))),f326(f326(f251(f917(x95832,a905),f917(x95832,a905)),x95833),x95831)),f318(x95832,x95834)))
% 157.55/157.22 [10220]P10(x102201,x102202,x102203,x102204)+~P105(f326(f326(f256(x102201,x102201,a905),f326(f326(f9(x102201,f917(x102201,x102202),f917(x102201,a905)),f326(f326(f10(f917(x102202,a905),f917(f917(x102201,x102202),f917(x102201,a905)),x102201),f10(x102202,a905,x102201)),f326(f326(f10(x102202,f917(x102202,a905),x102201),a323),x102204))),x102204)),f572(x102204,x102203,x102202,x102201)))
% 157.55/157.22 [5107]~E(x51072,f113(x51071))+E(f326(f326(f159(x51071,x51072),x51073),x51074),f113(x51071))
% 157.55/157.22 [5108]~E(x51084,f113(x51081))+E(f326(f326(f154(x51081,x51082),x51083),x51084),f113(x51082))
% 157.55/157.22 [5342]E(x53421,f113(x53422))+~E(f326(f326(f154(x53422,x53423),x53424),x53421),f113(x53423))
% 157.55/157.22 [5343]E(x53431,f113(x53432))+~E(f326(f326(f159(x53432,x53431),x53433),x53434),f113(x53432))
% 157.55/157.22 [5381]E(x53811,x53812)+~E(f326(f326(f134(x53813),x53814),x53811),f326(f326(f134(x53813),x53814),x53812))
% 157.55/157.22 [5382]E(x53821,x53822)+~E(f326(f326(f134(x53823),x53821),x53824),f326(f326(f134(x53823),x53822),x53824))
% 157.55/157.22 [5536]P105(f326(x55363,x55362))+E(f170(x55361,x55362,f326(f136(x55361,x55363),x55364)),f326(f136(x55361,x55363),x55364))
% 157.55/157.22 [5538]~P105(f326(x55382,x55383))+P32(x55381,x55382,f326(f326(f151(x55381),x55383),x55384))
% 157.55/157.22 [5548]E(x55481,x55482)+~E(f139(a909,f326(f301(a909,x55481),x55483)),f326(f326(f151(a909),x55482),x55484))
% 157.55/157.22 [5597]~P26(x55972,x55973)+P26(x55971,f326(f326(f73(x55972,x55971),x55973),x55974))
% 157.55/157.22 [5598]~P36(x55982,x55983)+P36(x55981,f326(f326(f287(x55982,x55981),x55983),x55984))
% 157.55/157.22 [5599]~P37(x55992,x55993)+P37(x55991,f326(f326(f287(x55992,x55991),x55993),x55994))
% 157.55/157.22 [5600]~P50(x56002,x56003)+P50(x56001,f326(f326(f287(x56002,x56001),x56003),x56004))
% 157.55/157.22 [5731]~P32(x57311,x57312,x57314)+P32(x57311,x57312,f326(f326(f151(x57311),x57313),x57314))
% 157.55/157.22 [5732]~P32(x57321,x57322,x57324)+P32(x57321,x57322,f326(f326(f134(x57321),x57323),x57324))
% 157.55/157.22 [5733]~P32(x57331,x57332,x57333)+P32(x57331,x57332,f326(f326(f134(x57331),x57333),x57334))
% 157.55/157.22 [5820]~E(x58201,f113(x58202))+~E(f326(f326(f134(x58202),x58203),f326(f326(f151(x58202),x58204),f113(x58202))),x58201)
% 157.55/157.22 [5845]~P30(x58453,x58451,f326(f326(f151(x58453),x58452),x58454))+P105(f326(x58451,x58452))
% 157.55/157.22 [5855]E(f114(x58551,x58552),x58553)+~E(f326(f326(f134(x58551),x58553),f326(f326(f151(x58551),x58554),f113(x58551))),x58552)
% 157.55/157.22 [5856]E(f144(x58561,x58562),x58563)+~E(f326(f326(f134(x58561),x58564),f326(f326(f151(x58561),x58563),f113(x58561))),x58562)
% 157.55/157.22 [5966]~E(f139(a909,f326(f301(a909,x59661),x59662)),f326(f326(f151(a909),x59663),x59664))+P105(f326(f326(f235(a909),x59661),x59662))
% 157.55/157.22 [5984]P30(x59841,x59842,x59843)+~P30(x59841,x59842,f326(f326(f151(x59841),x59844),x59843))
% 157.55/157.22 [5985]P30(x59851,x59852,x59853)+~P30(x59851,x59852,f326(f326(f134(x59851),x59854),x59853))
% 157.55/157.22 [5986]P30(x59861,x59862,x59863)+~P30(x59861,x59862,f326(f326(f134(x59861),x59863),x59864))
% 157.55/157.22 [6179]E(x61791,f326(f326(f134(x61792),f326(f168(x61792),x61793)),f326(f326(f151(x61792),x61794),f113(x61792))))+~E(f326(f168(x61792),x61791),f326(f326(f151(x61792),x61794),x61793))
% 157.55/157.22 [6356]~P109(x63561)+E(f326(f326(f101(f917(x63561,a905)),f326(f301(x63561,x63562),x63563)),f326(f301(x63561,x63563),x63564)),f188(f917(x63561,a905)))
% 157.55/157.22 [6367]E(f326(f326(f164(x63671),f169(x63671,x63672,x63673)),x63674),x63673)+~P105(f326(f326(f235(a909),x63674),x63672))
% 157.55/157.22 [6394]~P69(x63941)+E(f326(f165(x63941),f326(f326(f154(a1,x63941),x63942),f178(x63943,x63944))),f326(f326(f8(a1,x63941),x63942),f326(f172(a1),f178(x63943,x63944))))
% 157.55/157.22 [6395]~P69(x63951)+E(f326(f326(f8(a1,x63951),x63952),f326(f172(a1),f178(x63953,x63954))),f326(f165(x63951),f326(f326(f154(a1,x63951),x63952),f178(x63953,x63954))))
% 157.55/157.22 [6540]~E(x65402,f326(f326(f134(x65401),f326(f168(x65401),x65404)),f326(f326(f151(x65401),x65403),f113(x65401))))+E(f326(f168(x65401),x65402),f326(f326(f151(x65401),x65403),x65404))
% 157.55/157.22 [6556]~P18(x65562,x65563,x65564,x65561)+E(f326(x65561,f188(f917(x65562,a905))),f31(x65563))
% 157.55/157.22 [6581]~P109(x65811)+E(f326(f326(f101(f917(x65811,a905)),f305(x65811,x65812,x65813)),f326(f301(x65811,x65813),x65814)),f188(f917(x65811,a905)))
% 157.55/157.22 [6796]E(x67961,f188(f917(x67962,a905)))+~E(f312(x67963,x67962,x67964,x67961),f188(f917(f915(x67963,x67962),a905)))
% 157.55/157.22 [6797]E(x67971,f188(f917(x67972,a905)))+~E(f312(x67972,x67973,x67971,x67974),f188(f917(f915(x67972,x67973),a905)))
% 157.55/157.22 [6866]~P108(x68662)+E(f326(f189(f910(x68661)),f150(x68661,x68662,x68663,x68664)),f326(f189(f910(x68661)),x68664))
% 157.55/157.22 [6877]~P105(f326(f249(x68773,x68774,x68771),x68772))+P105(f326(f326(x68771,f548(x68772,x68771)),x68772))
% 157.55/157.22 [6919]~P105(f326(f61(x69192),x69194))+P105(f326(f61(x69191),f326(f309(x69192,x69191,x69193),x69194)))
% 157.55/157.22 [7148]~P24(x71482,x71481,x71483,x71484)+E(f326(f35(x71481),f326(f309(x71482,x71481,x71483),x71484)),f326(f35(x71482),x71484))
% 157.55/157.22 [7166]E(f326(f309(x71661,x71662,x71663),f326(f310(x71661,x71662,x71663),x71664)),x71664)+~E(f326(f309(x71661,x71662,x71663),f241(f917(x71661,a905))),f241(f917(x71662,a905)))
% 157.55/157.22 [7582]~P24(x75821,x75822,x75823,f241(f917(x75821,a905)))+E(f326(f310(x75821,x75822,x75823),f326(f309(x75821,x75822,x75823),x75824)),x75824)
% 157.55/157.22 [7860]E(x78601,x78602)+~P105(f326(f326(f328(x78603),x78601),f326(f172(x78603),f169(x78603,x78604,x78602))))
% 157.55/157.22 [7869]~E(x78691,f2(a909))+~P105(f326(f326(f328(x78692),x78693),f326(f172(x78692),f169(x78692,x78691,x78694))))
% 157.55/157.22 [7902]P105(f326(x79021,x79022))+~P105(f326(f326(f328(x79023),x79022),f326(f172(x79023),f177(x79023,x79021,x79024))))
% 157.55/157.22 [8008]~P105(f326(f326(f328(f910(x80081)),f326(f326(f151(x80081),x80082),x80084)),f161(x80081,x80083)))+P105(f326(f326(f328(x80081),x80082),x80083))
% 157.55/157.22 [8135]~P105(f326(f326(f328(x81351),x81352),f326(f172(x81351),f176(x81351,x81353,x81354))))+P105(f326(f326(f328(x81351),x81352),f326(f172(x81351),x81353)))
% 157.55/157.22 [8136]~P105(f326(f326(f328(x81361),x81362),f326(f172(x81361),f170(x81361,x81364,x81363))))+P105(f326(f326(f328(x81361),x81362),f326(f172(x81361),x81363)))
% 157.55/157.22 [8137]~P105(f326(f326(f328(x81371),x81372),f326(f172(x81371),f177(x81371,x81374,x81373))))+P105(f326(f326(f328(x81371),x81372),f326(f172(x81371),x81373)))
% 157.55/157.22 [8147]E(f326(f189(f910(x81471)),x81472),x81473)+~P105(f326(f326(f328(f910(x81471)),x81472),f326(f172(f910(x81471)),f55(x81471,x81473,x81474))))
% 157.55/157.22 [8242]P105(f326(x82423,x82422))+E(f326(f136(x82421,f326(f326(f10(a905,a905,x82421),a321),f326(a323,x82422))),f326(f136(x82421,x82423),x82424)),f326(f136(x82421,x82423),x82424))
% 157.55/157.22 [8349]E(f326(f326(f164(x83491),f177(x83491,x83492,x83493)),x83494),f326(f326(f164(x83491),x83493),x83494))+~P105(f326(f326(f235(a909),x83494),f326(f189(f910(x83491)),f177(x83491,x83492,x83493))))
% 157.55/157.22 [8435]~P69(x84351)+E(f326(f326(f8(a909,x84351),f326(f326(f10(a909,x84351,a909),x84352),a112)),f326(f301(a909,x84353),x84354)),f326(f326(f8(a909,x84351),x84352),f326(f301(a909,f326(a112,x84353)),f326(a112,x84354))))
% 157.55/157.22 [8444]~P69(x84441)+E(f326(f326(f8(a909,x84441),f326(f326(f10(a909,x84441,a909),x84442),a112)),f302(a909,x84443,x84444)),f326(f326(f8(a909,x84441),x84442),f302(a909,f326(a112,x84443),f326(a112,x84444))))
% 157.55/157.22 [8571]~P24(x85711,x85713,x85714,f241(f917(x85711,a905)))+P24(x85711,f917(x85712,x85713),f326(f326(f10(x85713,f917(x85712,x85713),x85711),f18(x85713,x85712)),x85714),f241(f917(x85711,a905)))
% 157.55/157.22 [8655]~P24(x86552,x86551,x86554,x86553)+E(f326(f309(x86551,x86552,f76(x86552,x86551,x86553,x86554)),f326(f309(x86552,x86551,x86554),x86553)),x86553)
% 157.55/157.22 [8715]~P105(f326(f326(f328(f916(x87151,x87151)),f326(f326(f251(x87151,x87151),x87152),x87154)),f262(x87151,x87153)))+P105(f326(f326(f328(x87151),x87152),x87153))
% 157.55/157.22 [8838]~P24(x88382,x88381,x88383,f241(f917(x88382,a905)))+E(f326(f309(x88381,x88382,f90(x88382,x88381,f241(f917(x88382,a905)),x88383)),f326(f309(x88382,x88381,x88383),x88384)),x88384)
% 157.55/157.22 [8913]~P25(x89131,x89132,x89133,x89134,f241(f917(x89132,a905)))+E(f326(f309(x89131,x89132,x89133),f241(f917(x89131,a905))),f241(f917(x89132,a905)))
% 157.55/157.22 [8946]~E(f326(f326(f8(x89461,a909),x89464),x89463),f326(a112,x89462))+P105(f326(f326(f328(x89461),f890(x89462,x89463,x89464,x89461)),x89463))
% 157.55/157.22 [8967]~E(f326(f326(f8(x89674,a909),x89671),x89673),f326(a112,x89672))+P105(f326(f326(f235(a909),f2(a909)),f326(x89671,f890(x89672,x89673,x89671,x89674))))
% 157.55/157.22 [8978]~P105(f326(f61(x89782),x89784))+P105(f326(f326(f234(a909),f326(f35(x89781),f326(f309(x89782,x89781,x89783),x89784))),f326(f35(x89782),x89784)))
% 157.55/157.22 [8979]E(f326(f326(f251(x89791,x89792),f635(x89793,x89794,x89792,x89791)),f636(x89793,x89794,x89792,x89791)),x89794)+~P105(f326(f326(f328(f916(x89791,x89792)),x89794),f326(f285(x89792,x89791),x89793)))
% 157.55/157.22 [8987]P24(x89871,x89872,x89873,x89874)+P105(f326(f326(f328(x89871),f506(x89874,x89873,x89872,x89871)),x89874))
% 157.55/157.22 [8988]P24(x89881,x89882,x89883,x89884)+P105(f326(f326(f328(x89881),f514(x89884,x89883,x89882,x89881)),x89884))
% 157.55/157.22 [9056]P10(x90561,x90562,x90563,x90564)+P105(f326(f326(f328(f916(x90561,x90561)),f572(x90564,x90563,x90562,x90561)),x90563))
% 157.55/157.22 [9110]P105(f326(x91101,x91102))+~P105(f326(x91101,f326(f326(f251(x91103,x91104),f390(x91104,x91103,x91101)),f393(x91104,x91103,x91101))))
% 157.55/157.22 [9127]E(f326(f189(f910(x91271)),x91272),f326(f189(f910(x91271)),x91273))+~P105(f326(f326(f328(f916(f910(x91271),f910(x91271))),f326(f326(f251(f910(x91271),f910(x91271)),x91272),x91273)),f145(x91271,x91274)))
% 157.55/157.22 [9128]E(f326(f189(f910(x91281)),x91282),f326(f189(f910(x91281)),x91283))+~P105(f326(f326(f328(f916(f910(x91281),f910(x91281))),f326(f326(f251(f910(x91281),f910(x91281)),x91282),x91283)),f157(x91281,x91284)))
% 157.55/157.22 [9131]E(f326(f189(f910(x91311)),x91312),f326(f189(f910(x91311)),x91313))+~P105(f326(f326(f328(f916(f910(x91311),f910(x91311))),f326(f326(f251(f910(x91311),f910(x91311)),x91312),x91313)),f158(x91311,x91314)))
% 157.55/157.22 [9200]P105(f326(f326(f234(a909),f155(x92001,x92002,x92003)),f155(x92001,x92004,x92003)))+P105(f326(f326(f328(x92001),f661(x92004,x92002,x92003,x92001)),f326(f172(x92001),x92003)))
% 157.55/157.22 [9203]E(f326(f189(f910(x92031)),x92032),f326(f189(f910(x92031)),x92033))+~P105(f326(f326(f328(f916(f910(x92031),f910(x92031))),f326(f326(f251(f910(x92031),f910(x92031)),x92032),x92033)),f306(f910(x92031),f157(x92031,x92034))))
% 157.55/157.22 [9436]~P24(x94361,x94362,x94363,x94364)+~P105(f326(f326(f235(a909),f326(f35(x94362),f326(f309(x94361,x94362,x94363),x94364))),f326(f35(x94361),x94364)))
% 157.55/157.22 [9483]~P105(f326(f326(f328(f916(f910(x94831),f910(x94831))),f326(f326(f251(f910(x94831),f910(x94831)),x94832),x94833)),f157(x94831,x94834)))+P105(f326(f326(f328(f916(f910(x94831),f910(x94831))),f326(f326(f251(f910(x94831),f910(x94831)),x94832),x94833)),f158(x94831,f306(x94831,x94834))))
% 157.55/157.22 [9487]~P105(f326(f326(f328(f916(f910(x94871),f910(x94871))),f326(f326(f251(f910(x94871),f910(x94871)),x94872),x94873)),f158(x94871,x94874)))+P105(f326(f326(f328(f916(f910(x94871),f910(x94871))),f326(f326(f251(f910(x94871),f910(x94871)),x94872),x94873)),f306(f910(x94871),f157(x94871,x94874))))
% 157.55/157.22 [9503]P105(f326(f326(f328(f916(x95031,x95031)),f326(f326(f251(x95031,x95031),x95032),x95033)),f306(x95031,x95034)))+~P105(f326(f326(f328(f916(x95031,x95031)),f326(f326(f251(x95031,x95031),x95032),x95033)),f326(f326(f288(x95031,x95031,x95031),x95034),f306(x95031,x95034))))
% 157.55/157.22 [9688]E(f326(f326(f134(x96881),f678(x96882,x96883,x96884,x96881)),f326(f326(f151(x96881),f679(x96882,x96883,x96884,x96881)),f682(x96882,x96883,x96884,x96881))),x96884)+~P105(f326(f326(f328(f916(f910(x96881),f910(x96881))),f326(f326(f251(f910(x96881),f910(x96881)),x96884),x96883)),f157(x96881,x96882)))
% 157.55/157.22 [9689]E(f326(f326(f134(x96891),f678(x96892,x96893,x96894,x96891)),f326(f326(f151(x96891),f681(x96892,x96893,x96894,x96891)),f682(x96892,x96893,x96894,x96891))),x96893)+~P105(f326(f326(f328(f916(f910(x96891),f910(x96891))),f326(f326(f251(f910(x96891),f910(x96891)),x96894),x96893)),f157(x96891,x96892)))
% 157.55/157.22 [9767]P105(f326(f326(f328(f916(x97671,x97671)),f326(f326(f251(x97671,x97671),x97672),f631(x97673,x97674,x97672,x97671))),f306(x97671,x97673)))+~P105(f326(f326(f328(f916(x97671,x97671)),f326(f326(f251(x97671,x97671),x97672),x97674)),f326(f326(f288(x97671,x97671,x97671),x97673),f306(x97671,x97673))))
% 157.55/157.22 [9836]P105(f326(f326(f234(a909),f155(x98361,x98362,x98363)),f155(x98361,x98364,x98363)))+~P105(f326(f326(f235(a909),f326(x98362,f661(x98364,x98362,x98363,x98361))),f326(x98364,f661(x98364,x98362,x98363,x98361))))
% 157.55/157.22 [9907]P105(f326(f326(f328(f916(x99071,x99071)),f326(f326(f251(x99071,x99071),f622(x99072,x99073,x99074,x99071)),x99073)),f306(x99071,x99072)))+~P105(f326(f326(f328(f916(x99071,x99071)),f326(f326(f251(x99071,x99071),x99074),x99073)),f326(f326(f288(x99071,x99071,x99071),x99072),f306(x99071,x99072))))
% 157.55/157.22 [5362]~E(x53622,x53623)+E(f170(x53621,x53622,f326(f326(f151(x53621),x53623),x53624)),x53624)
% 157.55/157.22 [5492]P105(f326(x54922,x54923))+E(f177(x54921,x54922,f326(f326(f151(x54921),x54923),x54924)),f113(x54921))
% 157.55/157.22 [5560]~P89(x55602)+E(f326(f326(f78(f917(x55601,x55602)),x55603),x55604),f326(f78(x55602),f326(x55603,x55604)))
% 157.55/157.22 [5573]~E(x55732,f2(a909))+E(f326(f326(f138(x55731),x55732),f326(f326(f151(x55731),x55733),x55734)),f326(f326(f151(x55731),x55733),x55734))
% 157.55/157.22 [5574]P105(f326(x55742,x55743))+E(f326(f136(x55741,x55742),f326(f326(f151(x55741),x55743),x55744)),f326(f136(x55741,x55742),x55744))
% 157.55/157.22 [5714]~E(x57142,x57144)+P105(f326(f326(f326(f308(x57141),x57142),x57143),x57144))
% 157.55/157.22 [5722]E(x57221,f113(x57222))+E(f144(x57223,f326(f326(f154(x57222,x57223),x57224),x57221)),f326(x57224,f144(x57222,x57221)))
% 157.55/157.22 [5736]~E(x57361,f63(x57362,x57364))+E(f326(x57361,f326(f326(f308(x57362),x57363),f188(f917(x57362,a905)))),x57363)
% 157.55/157.22 [5772]E(x57721,f113(x57722))+E(f326(f141(x57723),f326(f326(f154(x57722,x57723),x57724),x57721)),f326(x57724,f326(f141(x57722),x57721)))
% 157.55/157.22 [5875]~P105(f326(x58753,x58754))+P105(f326(f326(f326(f308(x58751),x58752),x58753),x58754))
% 157.55/157.22 [6003]~P17(x60032,x60034,x60031)+E(f326(x60031,f326(f326(f308(x60032),x60033),f188(f917(x60032,a905)))),x60033)
% 157.55/157.22 [6029]~E(x60292,x60293)+P105(f326(f326(f328(x60291),x60292),f326(f326(f308(x60291),x60293),x60294)))
% 157.55/157.22 [6034]~P77(x60341)+E(f326(f326(f110(x60341),x60342),f326(f326(f110(x60341),x60343),x60344)),f326(f326(f110(x60341),x60343),f326(f326(f110(x60341),x60342),x60344)))
% 157.55/157.22 [6036]~P100(x60361)+E(f326(f326(f110(x60361),x60362),f326(f326(f110(x60361),x60363),x60364)),f326(f326(f110(x60361),x60363),f326(f326(f110(x60361),x60362),x60364)))
% 157.55/157.22 [6037]~P112(x60371)+E(f326(f326(f80(x60371),x60372),f326(f326(f80(x60371),x60373),x60374)),f326(f326(f80(x60371),x60373),f326(f326(f80(x60371),x60372),x60374)))
% 157.55/157.22 [6038]~P77(x60381)+E(f326(f326(f101(x60381),x60382),f326(f326(f101(x60381),x60383),x60384)),f326(f326(f101(x60381),x60383),f326(f326(f101(x60381),x60382),x60384)))
% 157.55/157.22 [6040]~P101(x60401)+E(f326(f326(f101(x60401),x60402),f326(f326(f101(x60401),x60403),x60404)),f326(f326(f101(x60401),x60403),f326(f326(f101(x60401),x60402),x60404)))
% 157.55/157.22 [6041]~P112(x60411)+E(f326(f326(f79(x60411),x60412),f326(f326(f79(x60411),x60413),x60414)),f326(f326(f79(x60411),x60413),f326(f326(f79(x60411),x60412),x60414)))
% 157.55/157.22 [6043]~P108(x60431)+E(f326(f326(f232(x60431),x60432),f326(f326(f232(x60431),x60433),x60434)),f326(f326(f232(x60431),x60433),f326(f326(f232(x60431),x60432),x60434)))
% 157.55/157.22 [6045]~P108(x60451)+E(f326(f326(f233(x60451),x60452),f326(f326(f233(x60451),x60453),x60454)),f326(f326(f233(x60451),x60453),f326(f326(f233(x60451),x60452),x60454)))
% 157.55/157.22 [6050]E(x60501,x60502)+E(f170(x60503,x60501,f326(f326(f151(x60503),x60502),x60504)),f326(f326(f151(x60503),x60502),f170(x60503,x60501,x60504)))
% 157.55/157.22 [6063]~P105(f326(x60632,x60633))+E(f326(f136(x60631,x60632),f326(f326(f151(x60631),x60633),x60634)),f326(f326(f151(x60631),x60633),f326(f136(x60631,x60632),x60634)))
% 157.55/157.22 [6200]~P105(f326(x62002,x62003))+E(f177(x62001,x62002,f326(f326(f151(x62001),x62003),x62004)),f326(f326(f151(x62001),x62003),f177(x62001,x62002,x62004)))
% 157.55/157.22 [6264]E(x62641,f188(f917(x62642,a905)))+E(f326(f326(f39(x62642,f917(x62643,a905)),x62641),f326(f18(f917(x62643,a905),x62642),x62644)),x62644)
% 157.55/157.22 [6265]E(x62651,f188(f917(x62652,a905)))+E(f326(f326(f40(x62652,f917(x62653,a905)),x62651),f326(f18(f917(x62653,a905),x62652),x62654)),x62654)
% 157.55/157.22 [6274]~E(x62744,f188(f917(x62742,a905)))+E(f326(f326(f253(x62741,x62742),x62743),f326(f18(f917(x62742,a905),x62741),x62744)),f188(f917(f916(x62741,x62742),a905)))
% 157.55/157.22 [6275]~E(x62753,f188(f917(x62751,a905)))+E(f326(f326(f253(x62751,x62752),x62753),f326(f18(f917(x62752,a905),x62751),x62754)),f188(f917(f916(x62751,x62752),a905)))
% 157.55/157.22 [6329]E(x63291,f2(a909))+E(f326(f326(f138(x63292),x63291),f326(f326(f151(x63292),x63293),x63294)),f326(f326(f138(x63292),f326(f326(f3(a909),x63291),f77(a909))),x63294))
% 157.55/157.22 [6350]E(x63501,f188(f917(x63502,a905)))+E(f326(f309(x63502,x63503,f326(f18(x63503,x63502),x63504)),x63501),f326(f326(f308(x63503),x63504),f188(f917(x63503,a905))))
% 157.55/157.22 [6353]E(f326(f310(x63531,x63532,f326(f18(x63532,x63531),x63533)),x63534),f188(f917(x63531,a905)))+P105(f326(f326(f328(x63532),x63533),x63534))
% 157.55/157.22 [6419]~E(x64193,f188(f917(x64191,a905)))+E(f326(f326(f39(x64191,f917(x64192,a905)),x64193),f326(f18(f917(x64192,a905),x64191),x64194)),f241(f917(x64192,a905)))
% 157.55/157.22 [6420]~E(x64203,f188(f917(x64201,a905)))+E(f326(f326(f40(x64201,f917(x64202,a905)),x64203),f326(f18(f917(x64202,a905),x64201),x64204)),f188(f917(x64202,a905)))
% 157.55/157.22 [6422]~P59(x64221)+E(f45(x64221,f326(f326(f80(x64221),x64222),x64223),f326(f326(f80(x64221),x64222),x64224)),f326(f326(f80(x64221),x64222),f45(x64221,x64223,x64224)))
% 157.55/157.22 [6591]E(f326(f310(x65911,x65912,f326(f18(x65912,x65911),x65913)),x65914),f241(f917(x65911,a905)))+~P105(f326(f326(f328(x65912),x65913),x65914))
% 157.55/157.22 [6614]~P105(f326(f326(f328(x66141),x66142),x66144))+P105(f326(f326(f328(x66141),x66142),f326(f326(f308(x66141),x66143),x66144)))
% 157.55/157.22 [6619]P105(f326(x66191,x66192))+~P105(f326(f160(x66193,x66191),f326(f326(f151(x66193),x66192),x66194)))
% 157.55/157.22 [6628]~E(x66283,f326(f326(f3(a909),f326(f189(f910(x66281)),x66282)),f77(a909)))+E(f114(x66281,f326(f326(f159(x66281,x66282),x66283),x66284)),f114(x66281,x66282))
% 157.55/157.22 [6648]~P108(x66481)+E(f326(f326(f101(f917(x66481,a905)),f326(f300(x66481),x66482)),f302(x66481,x66483,x66484)),f302(x66481,x66483,f326(f326(f232(x66481),x66482),x66484)))
% 157.55/157.22 [6649]~P108(x66491)+E(f326(f326(f101(f917(x66491,a905)),f326(f282(x66491),x66492)),f302(x66491,x66493,x66494)),f302(x66491,f326(f326(f233(x66491),x66492),x66493),x66494))
% 157.55/157.22 [6665]E(f326(f326(f101(f917(x66651,a905)),x66652),f326(f326(f308(x66651),x66653),x66654)),f326(f326(f101(f917(x66651,a905)),x66652),x66654))+P105(f326(f326(f328(x66651),x66653),x66652))
% 157.55/157.22 [6677]E(f170(x66771,x66772,f326(f326(f134(x66771),x66773),x66774)),f326(f326(f134(x66771),x66773),f170(x66771,x66772,x66774)))+P105(f326(f326(f328(x66771),x66772),f326(f172(x66771),x66773)))
% 157.55/157.22 [6682]~P81(x66821)+E(f326(f326(f80(x66821),f326(f326(f243(x66821),x66822),x66823)),f326(f326(f243(x66821),x66822),x66824)),f326(f326(f243(x66821),x66822),f326(f326(f79(a909),x66823),x66824)))
% 157.55/157.22 [6683]~P112(x66831)+E(f326(f326(f80(x66831),f326(f326(f243(x66831),x66832),x66833)),f326(f326(f243(x66831),x66832),x66834)),f326(f326(f243(x66831),x66832),f326(f326(f79(a909),x66833),x66834)))
% 157.55/157.22 [6720]~P98(x67201)+E(f326(f326(f101(x67201),f326(f326(f110(x67201),x67202),x67203)),f326(f326(f110(x67201),x67202),x67204)),f326(f326(f110(x67201),x67202),f326(f326(f101(x67201),x67203),x67204)))
% 157.55/157.22 [6721]~P112(x67211)+E(f326(f326(f79(x67211),f326(f326(f80(x67211),x67212),x67213)),f326(f326(f80(x67211),x67212),x67214)),f326(f326(f80(x67211),x67212),f326(f326(f79(x67211),x67213),x67214)))
% 157.55/157.22 [6722]~P98(x67221)+E(f326(f326(f110(x67221),f326(f326(f101(x67221),x67222),x67223)),f326(f326(f101(x67221),x67222),x67224)),f326(f326(f101(x67221),x67222),f326(f326(f110(x67221),x67223),x67224)))
% 157.55/157.22 [6723]~P108(x67231)+E(f326(f326(f233(x67231),f326(f326(f232(x67231),x67232),x67233)),f326(f326(f232(x67231),x67232),x67234)),f326(f326(f232(x67231),x67232),f326(f326(f233(x67231),x67233),x67234)))
% 157.55/157.22 [6724]~P108(x67241)+E(f326(f326(f232(x67241),f326(f326(f233(x67241),x67242),x67243)),f326(f326(f233(x67241),x67242),x67244)),f326(f326(f233(x67241),x67242),f326(f326(f232(x67241),x67243),x67244)))
% 157.55/157.22 [6757]~P59(x67571)+E(f45(x67571,f326(f326(f80(x67571),x67572),x67573),f326(f326(f80(x67571),x67574),x67573)),f326(f326(f80(x67571),f45(x67571,x67572,x67574)),x67573))
% 157.55/157.22 [6760]~E(f326(f189(f910(x67601)),x67603),f326(f189(f910(x67602)),x67604))+E(f326(f326(f154(f916(x67601,x67602),x67602),f255(x67601,x67602)),f326(f326(f181(x67601,x67602),x67603),x67604)),x67604)
% 157.55/157.22 [6761]~E(f326(f189(f910(x67611)),x67613),f326(f189(f910(x67612)),x67614))+E(f326(f326(f154(f916(x67611,x67612),x67611),f250(x67611,x67612)),f326(f326(f181(x67611,x67612),x67613),x67614)),x67613)
% 157.55/157.22 [6766]P105(f326(f160(x67661,x67662),x67663))+~P105(f326(f160(x67661,x67662),f326(f326(f151(x67661),x67664),x67663)))
% 157.55/157.22 [6767]P105(f326(f160(x67671,x67672),x67673))+~P105(f326(f160(x67671,x67672),f326(f326(f134(x67671),x67674),x67673)))
% 157.55/157.22 [6768]P105(f326(f160(x67681,x67682),x67683))+~P105(f326(f160(x67681,x67682),f326(f326(f134(x67681),x67683),x67684)))
% 157.55/157.22 [6773]~P60(x67731)+E(f45(x67731,f326(f326(f3(x67731),x67732),f45(x67731,x67733,x67734)),x67734),f45(x67731,f326(f326(f3(x67731),x67732),x67733),x67734))
% 157.55/157.22 [6774]~P59(x67741)+E(f45(x67741,f326(f326(f80(x67741),x67742),f45(x67741,x67743,x67744)),x67744),f45(x67741,f326(f326(f80(x67741),x67742),x67743),x67744))
% 157.55/157.22 [6776]~P59(x67761)+E(f45(x67761,f326(f326(f79(x67761),x67762),f45(x67761,x67763,x67764)),x67764),f45(x67761,f326(f326(f79(x67761),x67762),x67763),x67764))
% 157.55/157.22 [6858]~P108(x68581)+E(f326(f326(f101(f917(x68581,a905)),f302(x68581,x68582,x68583)),f326(f300(x68581),x68584)),f302(x68581,x68582,f326(f326(f232(x68581),x68583),x68584)))
% 157.55/157.22 [6859]~P108(x68591)+E(f326(f326(f101(f917(x68591,a905)),f302(x68591,x68592,x68593)),f326(f282(x68591),x68594)),f302(x68591,f326(f326(f233(x68591),x68592),x68594),x68593))
% 157.55/157.22 [6862]~E(f326(f189(f910(x68621)),x68623),f326(f189(f910(x68622)),x68624))+E(f326(f326(f181(x68621,x68622),f326(f168(x68621),x68623)),f326(f168(x68622),x68624)),f326(f168(f916(x68621,x68622)),f326(f326(f181(x68621,x68622),x68623),x68624)))
% 157.55/157.22 [6874]E(x68741,f326(f326(f3(a909),f326(f189(f910(x68742)),x68743)),f77(a909)))+E(f114(x68742,f326(f326(f159(x68742,x68743),x68741),x68744)),f326(f326(f159(x68742,f114(x68742,x68743)),x68741),x68744))
% 157.55/157.22 [6888]~P105(f326(f137(x68882),x68884))+P105(f326(f137(f916(x68881,x68882)),f326(f326(f181(x68881,x68882),x68883),x68884)))
% 157.55/157.22 [6889]~P105(f326(f137(x68891),x68893))+P105(f326(f137(f916(x68891,x68892)),f326(f326(f181(x68891,x68892),x68893),x68894)))
% 157.55/157.22 [7151]E(f326(f326(f36(a909),x71511),x71512),x71513)+~P105(f326(f48(x71511,x71512),f326(f326(f251(a909,a909),x71513),x71514)))
% 157.55/157.22 [7175]E(f45(a909,x71751,x71752),x71753)+~P105(f326(f48(x71751,x71752),f326(f326(f251(a909,a909),x71754),x71753)))
% 157.55/157.22 [7178]P105(f326(f137(x71781),x71782))+~P105(f326(f137(x71783),f326(f326(f154(x71781,x71783),x71784),x71782)))
% 157.55/157.22 [7261]E(f170(x72611,x72612,f326(f326(f134(x72611),x72613),x72614)),f326(f326(f134(x72611),f170(x72611,x72612,x72613)),x72614))+~P105(f326(f326(f328(x72611),x72612),f326(f172(x72611),x72613)))
% 157.55/157.22 [7352]~P60(x73521)+E(f45(x73521,f326(f326(f3(x73521),f45(x73521,x73522,x73523)),x73524),x73523),f45(x73521,f326(f326(f3(x73521),x73522),x73524),x73523))
% 157.55/157.22 [7355]~P59(x73551)+E(f45(x73551,f326(f326(f80(x73551),f45(x73551,x73552,x73553)),x73554),x73553),f45(x73551,f326(f326(f80(x73551),x73552),x73554),x73553))
% 157.55/157.22 [7356]~P59(x73561)+E(f45(x73561,f326(f326(f79(x73561),f45(x73561,x73562,x73563)),x73564),x73563),f45(x73561,f326(f326(f79(x73561),x73562),x73564),x73563))
% 157.55/157.22 [7553]~E(x75531,f326(f326(f151(x75532),x75533),x75534))+~P105(f326(f326(f234(a909),f326(f189(f910(x75532)),x75531)),f326(f189(f910(x75532)),x75534)))
% 157.55/157.22 [7753]P24(x77531,x77532,x77533,f326(f172(x77531),x77534))+~P105(f326(f137(x77532),f326(f326(f154(x77531,x77532),x77533),x77534)))
% 157.55/157.22 [7826]~P105(f326(f326(f234(f917(x78261,a905)),x78262),x78264))+P105(f326(f326(f234(f917(x78261,a905)),x78262),f326(f326(f308(x78261),x78263),x78264)))
% 157.55/157.22 [7861]~P60(x78611)+E(f45(x78611,f326(f326(f3(x78611),f45(x78611,x78612,x78613)),f45(x78611,x78614,x78613)),x78613),f45(x78611,f326(f326(f3(x78611),x78612),x78614),x78613))
% 157.55/157.22 [7862]~P59(x78621)+E(f45(x78621,f326(f326(f80(x78621),f45(x78621,x78622,x78623)),f45(x78621,x78624,x78623)),x78623),f45(x78621,f326(f326(f80(x78621),x78622),x78624),x78623))
% 157.55/157.22 [7863]~P59(x78631)+E(f45(x78631,f326(f326(f79(x78631),f45(x78631,x78632,x78633)),f45(x78631,x78634,x78633)),x78633),f45(x78631,f326(f326(f79(x78631),x78632),x78634),x78633))
% 157.55/157.22 [7965]~E(f326(x79654,f447(x79654,x79653,x79651,x79652)),f188(f917(x79652,a905)))+E(f326(f326(f40(x79651,f917(x79652,a905)),x79653),x79654),f188(f917(x79652,a905)))
% 157.55/157.22 [7966]~E(f326(x79664,f414(x79664,x79663,x79661,x79662)),f241(f917(x79662,a905)))+E(f326(f326(f39(x79661,f917(x79662,a905)),x79663),x79664),f241(f917(x79662,a905)))
% 157.55/157.22 [7967]~E(f326(x79674,f415(x79674,x79673,x79672,x79671)),f241(f917(x79672,a905)))+E(f326(f326(f39(x79671,f917(x79672,a905)),x79673),x79674),f241(f917(x79672,a905)))
% 157.55/157.22 [7968]~E(f326(x79684,f448(x79684,x79683,x79682,x79681)),f188(f917(x79682,a905)))+E(f326(f326(f40(x79681,f917(x79682,a905)),x79683),x79684),f188(f917(x79682,a905)))
% 157.55/157.22 [8350]P105(f326(x83501,x83502))+~P105(f326(f326(f328(x83503),x83502),f326(f326(f101(f917(x83503,a905)),x83504),f326(f261(x83503),x83501))))
% 157.55/157.22 [8387]~P105(f326(f326(f234(f917(x83871,a905)),x83873),x83874))+P105(f326(f326(f234(f917(x83871,a905)),f326(f326(f308(x83871),x83872),x83873)),f326(f326(f308(x83871),x83872),x83874)))
% 157.55/157.22 [8564]P105(f326(x85642,x85643))+E(f326(f326(f138(x85641),f326(f189(f910(x85641)),f177(x85641,x85642,f326(f326(f151(x85641),x85643),x85644)))),f326(f326(f151(x85641),x85643),x85644)),f326(f326(f151(x85641),x85643),x85644))
% 157.55/157.22 [8669]~P105(f326(f326(f235(a909),f326(x86694,x86692)),f326(x86694,x86693)))+P105(f326(f326(f328(f916(x86691,x86691)),f326(f326(f251(x86691,x86691),x86692),x86693)),f326(f326(f287(a909,x86691),a239),x86694)))
% 157.55/157.22 [8765]~P105(f326(x87652,f735(x87654,x87652,x87653,x87651)))+E(f177(x87651,x87652,f326(f326(f134(x87651),x87653),x87654)),f326(f326(f134(x87651),x87653),f177(x87651,x87652,x87654)))
% 157.55/157.22 [8842]P24(f910(x88421),f910(x88422),f326(f154(x88421,x88422),x88423),x88424)+~P24(x88421,x88422,x88423,f37(f917(x88421,a905),f326(f309(f910(x88421),f917(x88421,a905),f172(x88421)),x88424)))
% 157.55/157.22 [8917]~P105(f326(x89172,x89173))+E(f326(f326(f138(x89171),f326(f189(f910(x89171)),f177(x89171,x89172,f326(f326(f151(x89171),x89173),x89174)))),f326(f326(f151(x89171),x89173),x89174)),f326(f326(f138(x89171),f326(f189(f910(x89171)),f177(x89171,x89172,x89174))),x89174))
% 157.55/157.22 [8958]~E(x89582,x89583)+E(f326(f136(x89581,f326(f326(f10(a905,a905,x89581),a321),f326(a323,x89582))),f326(f326(f151(x89581),x89583),x89584)),f326(f136(x89581,f326(f326(f10(a905,a905,x89581),a321),f326(a323,x89582))),x89584))
% 157.55/157.22 [8968]E(f326(f326(f40(x89681,f917(x89682,a905)),x89683),x89684),f188(f917(x89682,a905)))+P105(f326(f326(f328(x89681),f447(x89684,x89683,x89681,x89682)),x89683))
% 157.55/157.22 [8969]E(f326(f326(f39(x89691,f917(x89692,a905)),x89693),x89694),f241(f917(x89692,a905)))+P105(f326(f326(f328(x89691),f414(x89694,x89693,x89691,x89692)),x89693))
% 157.55/157.22 [8970]E(f326(f326(f39(x89701,f917(x89702,a905)),x89703),x89704),f241(f917(x89702,a905)))+P105(f326(f326(f328(x89701),f415(x89704,x89703,x89702,x89701)),x89703))
% 157.55/157.22 [8971]E(f326(f326(f40(x89711,f917(x89712,a905)),x89713),x89714),f188(f917(x89712,a905)))+P105(f326(f326(f328(x89711),f448(x89714,x89713,x89712,x89711)),x89713))
% 157.55/157.22 [9009]P105(f326(f326(f235(a909),f326(x90091,x90092)),f326(x90091,x90093)))+~P105(f326(f326(f328(f916(x90094,x90094)),f326(f326(f251(x90094,x90094),x90092),x90093)),f326(f326(f287(a909,x90094),a239),x90091)))
% 157.55/157.22 [9035]E(f177(x90351,x90352,f326(f326(f134(x90351),x90353),x90354)),f326(f326(f134(x90351),x90353),f177(x90351,x90352,x90354)))+P105(f326(f326(f328(x90351),f735(x90354,x90352,x90353,x90351)),f326(f172(x90351),x90353)))
% 157.55/157.22 [9086]~P25(x90861,x90862,x90863,f241(f917(x90861,a905)),f241(f917(x90862,a905)))+E(f326(f309(x90861,x90862,x90863),f326(f78(f917(x90861,a905)),x90864)),f326(f78(f917(x90862,a905)),f326(f309(x90861,x90862,x90863),x90864)))
% 157.55/157.22 [9189]P105(f326(f326(f328(x91891),f502(x91892,x91893,x91894,x91891)),x91893))+~P105(f326(f326(f328(f917(x91891,a905)),x91894),f326(f326(f60(x91891),x91893),x91892)))
% 157.55/157.22 [9192]E(x91921,x91922)+~P105(f326(f326(f328(f916(x91923,x91923)),f326(f326(f251(x91923,x91923),x91921),x91922)),f326(f326(f183(f916(x91923,x91923),a905),f2(a909)),x91924)))
% 157.55/157.22 [9273]E(f326(f284(x92731,x92731,x92732),f326(f326(f308(x92731),f502(x92732,x92733,x92734,x92731)),f188(f917(x92731,a905)))),x92734)+~P105(f326(f326(f328(f917(x92731,a905)),x92734),f326(f326(f60(x92731),x92733),x92732)))
% 157.55/157.22 [9278]~P105(f326(f326(f328(f916(x92781,x92781)),f326(f326(f251(x92781,x92781),x92783),x92782)),f306(x92781,x92784)))+P105(f326(f326(f328(f916(x92781,x92781)),f326(f326(f251(x92781,x92781),x92782),x92783)),f306(x92781,f326(f285(x92781,x92781),x92784))))
% 157.55/157.22 [9291]~P59(x92911)+E(f326(f326(f79(x92911),f326(f326(f79(x92911),f326(f326(f80(x92911),x92912),f326(f326(f36(x92911),x92913),x92912))),f45(x92911,x92913,x92912))),x92914),f326(f326(f79(x92911),x92913),x92914))
% 157.55/157.22 [9302]~P105(f326(f326(f328(x93021),x93023),x93024))+P105(f326(f326(f328(f917(x93021,a905)),f326(f284(x93021,x93021,x93022),f326(f326(f308(x93021),x93023),f188(f917(x93021,a905))))),f326(f326(f60(x93021),x93024),x93022)))
% 157.55/157.22 [9314]P105(f326(f326(f328(f916(x93141,x93141)),f326(f326(f251(x93141,x93141),x93142),x93143)),f306(x93141,x93144)))+~P105(f326(f326(f328(f916(x93141,x93141)),f326(f326(f251(x93141,x93141),x93143),x93142)),f306(x93141,f326(f285(x93141,x93141),x93144))))
% 157.55/157.22 [9397]E(f326(f326(f159(x93971,f326(f168(x93971),x93972)),f326(f326(f3(a909),f326(f326(f3(a909),f326(f189(f910(x93971)),x93972)),x93973)),f77(a909))),x93974),f326(f168(x93971),f326(f326(f159(x93971,x93972),x93973),x93974)))+~P105(f326(f326(f235(a909),x93973),f326(f189(f910(x93971)),x93972)))
% 157.55/157.22 [9400]~P105(f326(x94002,f730(x94004,x94002,x94003,x94001)))+E(f326(f326(f138(x94001),f326(f189(f910(x94001)),f177(x94001,x94002,f326(f326(f134(x94001),x94003),x94004)))),f326(f326(f134(x94001),x94003),x94004)),f326(f326(f138(x94001),f326(f189(f910(x94001)),f177(x94001,x94002,x94004))),x94004))
% 157.55/157.22 [9444]~P24(x94442,x94441,x94443,f241(f917(x94442,a905)))+P105(f326(f326(f234(f917(x94441,a905)),f326(f309(x94442,x94441,x94443),f326(f78(f917(x94442,a905)),x94444))),f326(f78(f917(x94441,a905)),f326(f309(x94442,x94441,x94443),x94444))))
% 157.55/157.22 [9456]~P4(x94561)+E(f326(f142(x94561,x94562,f326(f9(x94562,x94561,x94561),f326(f326(f10(x94561,f917(x94561,x94561),x94562),f101(x94561)),x94563)),f241(x94561)),x94564),f326(f326(f39(x94562,x94561),f326(f172(x94562),x94564)),x94563))
% 157.55/157.22 [9457]~P4(x94571)+E(f326(f142(x94571,x94572,f326(f9(x94572,x94571,x94571),f326(f326(f10(x94571,f917(x94571,x94571),x94572),f110(x94571)),x94573)),f188(x94571)),x94574),f326(f326(f40(x94572,x94571),f326(f172(x94572),x94574)),x94573))
% 157.55/157.22 [9467]E(f326(f326(f138(x94671),f326(f189(f910(x94671)),f177(x94671,x94672,f326(f326(f134(x94671),x94673),x94674)))),f326(f326(f134(x94671),x94673),x94674)),f326(f326(f138(x94671),f326(f189(f910(x94671)),f177(x94671,x94672,x94674))),x94674))+P105(f326(f326(f328(x94671),f730(x94674,x94672,x94673,x94671)),f326(f172(x94671),x94673)))
% 157.55/157.22 [9537]~P105(f326(f326(f328(f916(f910(x95374),f910(x95374))),f326(f326(f251(f910(x95374),f910(x95374)),x95373),x95372)),f157(x95374,x95371)))+P105(f326(f326(f235(a909),f662(x95371,x95372,x95373,x95374)),f326(f189(f910(x95374)),x95373)))
% 157.55/157.22 [9538]~P59(x95381)+E(f326(f326(f79(x95381),f326(f326(f79(x95381),f326(f326(f80(x95381),f326(f326(f36(x95381),x95382),x95383)),x95383)),f45(x95381,x95382,x95383))),x95384),f326(f326(f79(x95381),x95382),x95384))
% 157.55/157.22 [9565]~P105(f326(f326(f328(f916(f910(x95651),f910(x95651))),f326(f326(f251(f910(x95651),f910(x95651)),x95652),x95653)),f326(f285(f910(x95651),f910(x95651)),f157(x95651,x95654))))+P105(f326(f326(f328(f916(f910(x95651),f910(x95651))),f326(f326(f251(f910(x95651),f910(x95651)),x95652),x95653)),f157(x95651,f326(f285(x95651,x95651),x95654))))
% 157.55/157.22 [9566]P105(f326(f326(f328(f916(f910(x95661),f910(x95661))),f326(f326(f251(f910(x95661),f910(x95661)),x95662),x95663)),f326(f285(f910(x95661),f910(x95661)),f157(x95661,x95664))))+~P105(f326(f326(f328(f916(f910(x95661),f910(x95661))),f326(f326(f251(f910(x95661),f910(x95661)),x95662),x95663)),f157(x95661,f326(f285(x95661,x95661),x95664))))
% 157.55/157.22 [9605]~P105(f326(f326(f328(x96051),x96053),f326(f263(x96051,x96052),x96054)))+P105(f326(f326(f328(f916(x96051,x96052)),f326(f326(f251(x96051,x96052),x96053),f562(x96054,x96052,x96053,x96051))),x96054))
% 157.55/157.22 [9606]~P105(f326(f326(f328(x96061),x96063),f326(f263(x96061,x96062),x96064)))+P105(f326(f326(f328(f916(x96061,x96062)),f326(f326(f251(x96061,x96062),x96063),f563(x96064,x96062,x96063,x96061))),x96064))
% 157.55/157.22 [9762]~P105(f326(f326(f328(f916(x97621,x97621)),f326(f326(f251(x97621,x97621),x97622),x97624)),f326(f326(f288(x97621,x97621,x97621),x97623),f306(x97621,x97623))))+P105(f326(f326(f328(f916(x97621,x97621)),f326(f326(f251(x97621,x97621),x97622),f622(x97623,x97624,x97622,x97621))),x97623))
% 157.55/157.22 [9921]P10(x99211,x99212,x99213,x99214)+P105(f326(f326(f328(f916(x99211,x99211)),f326(f326(f251(x99211,x99211),f826(x99212,x99214,x99213,x99211)),f825(x99212,x99214,x99213,x99211))),x99213))
% 157.55/157.22 [9928]~P105(f326(f326(f328(f916(x99282,x99281)),x99284),f326(f285(x99281,x99282),x99283)))+P105(f326(f326(f328(f916(x99281,x99282)),f326(f326(f251(x99281,x99282),f636(x99283,x99284,x99281,x99282)),f635(x99283,x99284,x99281,x99282))),x99283))
% 157.55/157.22 [9952]~P105(f326(f326(f328(f916(f910(x99521),f910(x99521))),f326(f326(f251(f910(x99521),f910(x99521)),x99524),x99523)),f157(x99521,x99522)))+P105(f326(f326(f328(f916(x99521,x99521)),f326(f326(f251(x99521,x99521),f679(x99522,x99523,x99524,x99521)),f681(x99522,x99523,x99524,x99521))),x99522))
% 157.55/157.22 [10043]~P105(f326(f326(f328(f916(f910(x100431),f910(x100431))),f326(f326(f251(f910(x100431),f910(x100431)),x100432),x100434)),f157(x100431,x100433)))+P105(f326(f326(f328(f916(x100431,x100431)),f326(f326(f251(x100431,x100431),f326(f326(f164(x100431),x100432),f662(x100433,x100434,x100432,x100431))),f663(x100433,x100434,x100432,x100431))),x100433))
% 157.55/157.22 [10063]~P105(f326(f61(x100632),x100634))+E(f326(f326(f326(f65(f917(x100631,a905),x100632,f110(f917(x100631,a905))),f326(f326(f9(x100632,f917(x100631,a905),f917(x100631,a905)),f326(f326(f10(x100631,f917(f917(x100631,a905),f917(x100631,a905)),x100632),f308(x100631)),x100633)),f188(f917(x100631,a905)))),f188(f917(x100631,a905))),x100634),f326(f309(x100632,x100631,x100633),x100634))
% 157.55/157.22 [10174]~P24(x101741,x101742,x101743,f241(f917(x101741,a905)))+P105(f326(f326(f234(f917(x101741,a905)),f326(f310(x101741,x101742,x101743),f326(f326(f308(x101742),x101744),f188(f917(x101742,a905))))),f326(f326(f308(x101741),f84(x101741,f326(f326(f9(x101741,x101742,a905),f326(f326(f10(x101742,f917(x101742,a905),x101741),a323),x101743)),x101744))),f188(f917(x101741,a905)))))
% 157.55/157.22 [5783]~E(f326(f326(f134(x57831),x57832),x57834),x57833)+E(f326(f326(f175(x57831),f326(f189(f910(x57831)),x57832)),x57833),x57832)
% 157.55/157.22 [5784]~E(f326(f326(f134(x57842),x57843),x57841),x57844)+E(x57841,f326(f326(f138(x57842),f326(f189(f910(x57842)),x57843)),x57844))
% 157.55/157.22 [5795]~E(x57954,f2(a909))+E(f326(f326(f164(x57951),f326(f326(f151(x57951),x57952),x57953)),x57954),x57952)
% 157.55/157.22 [6342]~P112(x63421)+E(f326(f326(f243(x63421),f326(f326(f243(x63421),x63422),x63423)),x63424),f326(f326(f243(x63421),x63422),f326(f326(f80(a909),x63423),x63424)))
% 157.55/157.22 [6343]~P81(x63431)+E(f326(f326(f243(x63431),f326(f326(f243(x63431),x63432),x63433)),x63434),f326(f326(f243(x63431),x63432),f326(f326(f80(a909),x63433),x63434)))
% 157.55/157.22 [6351]E(x63511,f2(a909))+E(f326(f326(f164(x63512),f326(f326(f151(x63512),x63513),x63514)),x63511),f326(f326(f164(x63512),x63514),f326(f326(f3(a909),x63511),f77(a909))))
% 157.55/157.22 [6377]~P121(x63771)+E(f326(f326(f290(x63771),f326(f326(f80(x63771),x63772),x63773)),x63774),f326(f326(f80(x63771),x63772),f326(f326(f290(x63771),x63773),x63774)))
% 157.55/157.22 [6379]~P77(x63791)+E(f326(f326(f110(x63791),f326(f326(f110(x63791),x63792),x63793)),x63794),f326(f326(f110(x63791),x63792),f326(f326(f110(x63791),x63793),x63794)))
% 157.55/157.22 [6381]~P100(x63811)+E(f326(f326(f110(x63811),f326(f326(f110(x63811),x63812),x63813)),x63814),f326(f326(f110(x63811),x63812),f326(f326(f110(x63811),x63813),x63814)))
% 157.55/157.22 [6382]~P67(x63821)+E(f326(f326(f80(x63821),f326(f326(f80(x63821),x63822),x63823)),x63824),f326(f326(f80(x63821),x63822),f326(f326(f80(x63821),x63823),x63824)))
% 157.55/157.22 [6383]~P112(x63831)+E(f326(f326(f80(x63831),f326(f326(f80(x63831),x63832),x63833)),x63834),f326(f326(f80(x63831),x63832),f326(f326(f80(x63831),x63833),x63834)))
% 157.55/157.22 [6385]~P77(x63851)+E(f326(f326(f101(x63851),f326(f326(f101(x63851),x63852),x63853)),x63854),f326(f326(f101(x63851),x63852),f326(f326(f101(x63851),x63853),x63854)))
% 157.55/157.22 [6387]~P101(x63871)+E(f326(f326(f101(x63871),f326(f326(f101(x63871),x63872),x63873)),x63874),f326(f326(f101(x63871),x63872),f326(f326(f101(x63871),x63873),x63874)))
% 157.55/157.22 [6388]~P68(x63881)+E(f326(f326(f79(x63881),f326(f326(f79(x63881),x63882),x63883)),x63884),f326(f326(f79(x63881),x63882),f326(f326(f79(x63881),x63883),x63884)))
% 157.55/157.22 [6389]~P112(x63891)+E(f326(f326(f79(x63891),f326(f326(f79(x63891),x63892),x63893)),x63894),f326(f326(f79(x63891),x63892),f326(f326(f79(x63891),x63893),x63894)))
% 157.55/157.22 [6391]~P108(x63911)+E(f326(f326(f232(x63911),f326(f326(f232(x63911),x63912),x63913)),x63914),f326(f326(f232(x63911),x63912),f326(f326(f232(x63911),x63913),x63914)))
% 157.55/157.22 [6393]~P108(x63931)+E(f326(f326(f233(x63931),f326(f326(f233(x63931),x63932),x63933)),x63934),f326(f326(f233(x63931),x63932),f326(f326(f233(x63931),x63933),x63934)))
% 157.55/157.22 [6402]~P59(x64021)+E(f45(x64021,f326(f326(f79(x64021),x64022),f326(f326(f80(x64021),x64023),x64024)),x64024),f45(x64021,x64022,x64024))
% 157.55/157.22 [6403]~P59(x64031)+E(f45(x64031,f326(f326(f79(x64031),x64032),f326(f326(f80(x64031),x64033),x64034)),x64033),f45(x64031,x64032,x64033))
% 157.55/157.22 [6541]E(f326(f326(f164(x65411),f326(f326(f175(x65411),x65412),x65413)),x65414),f326(f326(f164(x65411),x65413),x65414))+~P105(f326(f326(f235(a909),x65414),x65412))
% 157.55/157.22 [6716]~E(x67162,x67164)+P105(f326(f326(f172(x67161),f326(f326(f151(x67161),x67162),x67163)),x67164))
% 157.55/157.22 [6718]~P112(x67181)+E(f326(f326(f80(x67181),f326(f326(f80(x67181),x67182),x67183)),x67184),f326(f326(f80(x67181),f326(f326(f80(x67181),x67182),x67184)),x67183))
% 157.55/157.22 [6719]~P112(x67191)+E(f326(f326(f79(x67191),f326(f326(f79(x67191),x67192),x67193)),x67194),f326(f326(f79(x67191),f326(f326(f79(x67191),x67192),x67194)),x67193))
% 157.55/157.22 [6779]~P143(x67792)+E(f326(f326(f8(x67791,x67792),f326(f18(x67792,x67791),x67793)),x67794),f326(f326(f80(x67792),f326(f100(x67792),f326(f35(x67791),x67794))),x67793))
% 157.55/157.22 [6951]E(f326(f326(f101(f917(x69511,a905)),f326(f326(f308(x69511),x69512),x69513)),x69514),f326(f326(f101(f917(x69511,a905)),x69513),x69514))+P105(f326(f326(f328(x69511),x69512),x69514))
% 157.55/157.22 [7018]~P98(x70181)+E(f326(f326(f101(x70181),f326(f326(f110(x70181),x70182),x70183)),f326(f326(f110(x70181),x70184),x70183)),f326(f326(f110(x70181),f326(f326(f101(x70181),x70182),x70184)),x70183))
% 157.55/157.22 [7019]~P79(x70191)+E(f326(f326(f232(x70191),f326(f326(f3(x70191),x70192),x70193)),f326(f326(f3(x70191),x70194),x70193)),f326(f326(f3(x70191),f326(f326(f232(x70191),x70192),x70194)),x70193))
% 157.55/157.22 [7020]~P79(x70201)+E(f326(f326(f233(x70201),f326(f326(f3(x70201),x70202),x70203)),f326(f326(f3(x70201),x70204),x70203)),f326(f326(f3(x70201),f326(f326(f233(x70201),x70202),x70204)),x70203))
% 157.55/157.22 [7022]~P113(x70221)+E(f326(f326(f79(x70221),f326(f326(f80(x70221),x70222),x70223)),f326(f326(f80(x70221),x70224),x70223)),f326(f326(f80(x70221),f326(f326(f79(x70221),x70222),x70224)),x70223))
% 157.55/157.22 [7023]~P98(x70231)+E(f326(f326(f110(x70231),f326(f326(f101(x70231),x70232),x70233)),f326(f326(f101(x70231),x70234),x70233)),f326(f326(f101(x70231),f326(f326(f110(x70231),x70232),x70234)),x70233))
% 157.55/157.22 [7024]~P84(x70241)+E(f326(f326(f232(x70241),f326(f326(f79(x70241),x70242),x70243)),f326(f326(f79(x70241),x70244),x70243)),f326(f326(f79(x70241),f326(f326(f232(x70241),x70242),x70244)),x70243))
% 157.55/157.22 [7025]~P84(x70251)+E(f326(f326(f233(x70251),f326(f326(f79(x70251),x70252),x70253)),f326(f326(f79(x70251),x70254),x70253)),f326(f326(f79(x70251),f326(f326(f233(x70251),x70252),x70254)),x70253))
% 157.55/157.22 [7026]~P121(x70261)+E(f326(f326(f3(x70261),f326(f326(f290(x70261),x70262),x70263)),f326(f326(f290(x70261),x70264),x70263)),f326(f326(f290(x70261),f326(f326(f3(x70261),x70262),x70264)),x70263))
% 157.55/157.22 [7027]~P121(x70271)+E(f326(f326(f79(x70271),f326(f326(f290(x70271),x70272),x70273)),f326(f326(f290(x70271),x70274),x70273)),f326(f326(f290(x70271),f326(f326(f79(x70271),x70272),x70274)),x70273))
% 157.55/157.22 [7028]~P108(x70281)+E(f326(f326(f233(x70281),f326(f326(f232(x70281),x70282),x70283)),f326(f326(f232(x70281),x70284),x70283)),f326(f326(f232(x70281),f326(f326(f233(x70281),x70282),x70284)),x70283))
% 157.55/157.22 [7029]~P112(x70291)+E(f326(f326(f80(x70291),f326(f326(f243(x70291),x70292),x70293)),f326(f326(f243(x70291),x70294),x70293)),f326(f326(f243(x70291),f326(f326(f80(x70291),x70292),x70294)),x70293))
% 157.55/157.22 [7030]~P74(x70301)+E(f326(f326(f80(x70301),f326(f326(f243(x70301),x70302),x70303)),f326(f326(f243(x70301),x70304),x70303)),f326(f326(f243(x70301),f326(f326(f80(x70301),x70302),x70304)),x70303))
% 157.55/157.22 [7031]~P62(x70311)+E(f326(f326(f290(x70311),f326(f326(f243(x70311),x70312),x70313)),f326(f326(f243(x70311),x70314),x70313)),f326(f326(f243(x70311),f326(f326(f290(x70311),x70312),x70314)),x70313))
% 157.55/157.22 [7032]~P108(x70321)+E(f326(f326(f232(x70321),f326(f326(f233(x70321),x70322),x70323)),f326(f326(f233(x70321),x70324),x70323)),f326(f326(f233(x70321),f326(f326(f232(x70321),x70322),x70324)),x70323))
% 157.55/157.22 [7033]~P112(x70331)+E(f326(f326(f79(x70331),f326(f326(f80(x70331),x70332),x70333)),f326(f326(f80(x70331),x70334),x70333)),f326(f326(f80(x70331),f326(f326(f79(x70331),x70332),x70334)),x70333))
% 157.55/157.22 [7064]E(f326(f326(f159(x70641,x70642),x70643),x70644),x70642)+~P105(f326(f326(f234(a909),f326(f189(f910(x70641)),x70642)),x70643))
% 157.55/157.22 [7090]~P105(f326(x70903,x70904))+P105(f326(f326(f326(f110(f917(x70901,a905)),x70902),x70903),x70904))
% 157.55/157.22 [7092]~P105(f326(x70922,x70924))+P105(f326(f326(f326(f110(f917(x70921,a905)),x70922),x70923),x70924))
% 157.55/157.22 [7111]E(f326(f326(f164(x71111),f326(f326(f134(x71111),x71112),x71113)),x71114),f326(f326(f164(x71111),x71112),x71114))+~P105(f326(f326(f235(a909),x71114),f326(f189(f910(x71111)),x71112)))
% 157.55/157.22 [7122]E(f326(f326(f3(f917(x71221,a905)),f326(f326(f308(x71221),x71222),x71223)),x71224),f326(f326(f3(f917(x71221,a905)),x71223),x71224))+~P105(f326(f326(f328(x71221),x71222),x71224))
% 157.55/157.22 [7164]~E(f139(a909,f326(f301(a909,x71641),x71642)),f326(f326(f151(a909),x71644),x71643))+E(f139(a909,f326(f301(a909,f326(f326(f79(a909),x71641),f77(a909))),x71642)),x71643)
% 157.55/157.22 [7186]~P105(f326(f326(f172(x71861),x71863),x71864))+P105(f326(f326(f172(x71861),f326(f326(f151(x71861),x71862),x71863)),x71864))
% 157.55/157.22 [7236]E(x72361,f2(a909))+E(f326(f326(f151(x72362),x72363),f326(f326(f175(x72362),f326(f326(f3(a909),x72361),f77(a909))),x72364)),f326(f326(f175(x72362),x72361),f326(f326(f151(x72362),x72363),x72364)))
% 157.55/157.22 [7336]E(f326(f326(f164(x73361),x73362),f326(f326(f3(a909),x73363),f326(f189(f910(x73361)),x73364))),f326(f326(f164(x73361),f326(f326(f134(x73361),x73364),x73362)),x73363))+P105(f326(f326(f235(a909),x73363),f326(f189(f910(x73361)),x73364)))
% 157.55/157.22 [7365]E(f326(f326(f101(f917(x73651,a905)),x73652),f326(f326(f308(x73651),x73653),x73654)),f326(f326(f308(x73651),x73653),f326(f326(f101(f917(x73651,a905)),x73652),x73654)))+~P105(f326(f326(f328(x73651),x73653),x73652))
% 157.55/157.22 [7403]E(f326(f326(f164(x74031),f326(f326(f159(x74031,x74032),x74033),x74034)),x74033),x74034)+~P105(f326(f326(f235(a909),x74033),f326(f189(f910(x74031)),x74032)))
% 157.55/157.22 [7425]E(x74251,f188(f917(x74252,a905)))+E(f326(f309(f916(x74253,x74252),x74253,f250(x74253,x74252)),f326(f326(f253(x74253,x74252),x74254),f326(f18(f917(x74252,a905),x74253),x74251))),x74254)
% 157.55/157.22 [7426]E(x74261,f188(f917(x74262,a905)))+E(f326(f309(f916(x74262,x74263),x74263,f255(x74262,x74263)),f326(f326(f253(x74262,x74263),x74261),f326(f18(f917(x74263,a905),x74262),x74264))),x74264)
% 157.55/157.22 [7503]E(f326(f326(f3(f917(x75031,a905)),f326(f326(f308(x75031),x75032),x75033)),x75034),f326(f326(f308(x75031),x75032),f326(f326(f3(f917(x75031,a905)),x75033),x75034)))+P105(f326(f326(f328(x75031),x75032),x75034))
% 157.55/157.22 [7539]~E(x75394,f188(f917(x75392,a905)))+E(f326(f309(f916(x75391,x75392),x75391,f250(x75391,x75392)),f326(f326(f253(x75391,x75392),x75393),f326(f18(f917(x75392,a905),x75391),x75394))),f188(f917(x75391,a905)))
% 157.55/157.22 [7540]~E(x75403,f188(f917(x75401,a905)))+E(f326(f309(f916(x75401,x75402),x75402,f255(x75401,x75402)),f326(f326(f253(x75401,x75402),x75403),f326(f18(f917(x75402,a905),x75401),x75404))),f188(f917(x75402,a905)))
% 157.55/157.22 [7591]~P105(f326(f326(f328(x75911),x75912),x75914))+P105(f326(f326(f328(x75911),x75912),f326(f326(f110(f917(x75911,a905)),x75913),x75914)))
% 157.55/157.22 [7594]~P105(f326(f326(f328(x75941),x75942),x75943))+P105(f326(f326(f328(x75941),x75942),f326(f326(f110(f917(x75941,a905)),x75943),x75944)))
% 157.55/157.22 [7612]E(f326(f326(f101(f917(x76121,a905)),f326(f326(f308(x76121),x76122),x76123)),x76124),f326(f326(f308(x76121),x76122),f326(f326(f101(f917(x76121,a905)),x76123),x76124)))+~P105(f326(f326(f328(x76121),x76122),x76124))
% 157.55/157.22 [7883]P105(f326(x78831,x78832))+~P105(f326(f326(f326(f101(f917(x78833,a905)),x78834),x78831),x78832))
% 157.55/157.22 [7884]P105(f326(x78841,x78842))+~P105(f326(f326(f326(f101(f917(x78843,a905)),x78841),x78844),x78842))
% 157.55/157.22 [7885]E(f326(f326(f8(x78851,a909),x78852),f326(f326(f3(f917(x78851,a905)),x78853),f326(f326(f308(x78851),x78854),f188(f917(x78851,a905))))),f326(f326(f8(x78851,a909),x78852),x78853))+P105(f326(f326(f328(x78851),x78854),x78853))
% 157.55/157.22 [7890]~P69(x78901)+E(f326(f165(x78901),f326(f326(f154(a909,x78901),x78902),f139(a909,f326(f301(a909,x78903),x78904)))),f326(f326(f8(a909,x78901),x78902),f326(f172(a909),f139(a909,f326(f301(a909,x78903),x78904)))))
% 157.55/157.22 [7891]~P69(x78911)+E(f326(f326(f8(a909,x78911),x78912),f326(f172(a909),f139(a909,f326(f301(a909,x78913),x78914)))),f326(f165(x78911),f326(f326(f154(a909,x78911),x78912),f139(a909,f326(f301(a909,x78913),x78914)))))
% 157.55/157.22 [8001]~E(x80013,x80014)+P105(f326(f62(x80011,x80012,f326(f326(f308(x80011),x80013),f188(f917(x80011,a905)))),x80014))
% 157.55/157.22 [8097]P105(f326(f326(f328(x80971),x80972),f326(f172(x80971),x80973)))+~P105(f326(f326(f328(x80971),x80972),f326(f172(x80971),f326(f326(f175(x80971),x80974),x80973))))
% 157.55/157.22 [8098]P105(f326(f326(f328(x80981),x80982),f326(f172(x80981),x80983)))+~P105(f326(f326(f328(x80981),x80982),f326(f172(x80981),f326(f326(f138(x80981),x80984),x80983))))
% 157.55/157.22 [8168]P105(f326(f326(f328(x81681),x81682),x81683))+~P105(f326(f326(f328(x81681),x81682),f326(f326(f3(f917(x81681,a905)),x81683),x81684)))
% 157.55/157.22 [8170]P105(f326(f326(f328(x81701),x81702),x81703))+~P105(f326(f326(f328(x81701),x81702),f326(f326(f101(f917(x81701,a905)),x81704),x81703)))
% 157.55/157.22 [8173]P105(f326(f326(f328(x81731),x81732),x81733))+~P105(f326(f326(f328(x81731),x81732),f326(f326(f101(f917(x81731,a905)),x81733),x81734)))
% 157.55/157.22 [8188]E(f326(f326(f134(x81881),f326(f326(f175(x81881),x81882),x81883)),f326(f326(f151(x81881),x81884),f326(f326(f138(x81881),f326(a112,x81882)),x81883))),f326(f326(f159(x81881,x81883),x81882),x81884))+~P105(f326(f326(f235(a909),x81882),f326(f189(f910(x81881)),x81883)))
% 157.55/157.22 [8211]P105(f326(f326(f328(x82111),x82112),x82113))+~P105(f326(f326(f234(f917(x82111,a905)),f326(f326(f308(x82111),x82112),x82114)),x82113))
% 157.55/157.22 [8248]~P105(f326(f326(f328(x82481),x82482),x82483))+~P105(f326(f326(f328(x82481),x82482),f326(f326(f3(f917(x82481,a905)),x82484),x82483)))
% 157.55/157.22 [8278]~P105(f326(f326(f235(a909),x82784),f326(f189(f910(x82781)),x82783)))+P105(f326(f326(f328(x82781),x82782),f326(f172(x82781),f326(f326(f159(x82781,x82783),x82784),x82782))))
% 157.55/157.22 [8329]E(f326(f326(f164(x83291),f326(f326(f138(x83291),x83292),x83293)),x83294),f326(f326(f164(x83291),x83293),f326(f326(f79(a909),x83292),x83294)))+~P105(f326(f326(f234(a909),f326(f326(f79(a909),x83292),x83294)),f326(f189(f910(x83291)),x83293)))
% 157.55/157.22 [8338]~P143(x83382)+E(f326(f326(f8(x83381,x83382),f326(f326(f10(a909,x83382,x83381),f100(x83382)),x83383)),x83384),f326(f100(x83382),f326(f326(f8(x83381,a909),x83383),x83384)))
% 157.55/157.22 [8339]~P140(x83392)+E(f326(f326(f8(x83391,x83392),f326(f326(f10(a1,x83392,x83391),f102(x83392)),x83393)),x83394),f326(f102(x83392),f326(f326(f8(x83391,a1),x83393),x83394)))
% 157.55/157.22 [8389]~P65(x83892)+E(f326(f326(f11(x83891,x83892),f326(f326(f10(x83892,x83892,x83891),f75(x83892)),x83893)),x83894),f326(f75(x83892),f326(f326(f11(x83891,x83892),x83893),x83894)))
% 157.55/157.22 [8390]~P66(x83902)+E(f326(f326(f8(x83901,x83902),f326(f326(f10(x83902,x83902,x83901),f78(x83902)),x83903)),x83904),f326(f78(x83902),f326(f326(f8(x83901,x83902),x83903),x83904)))
% 157.55/157.22 [8392]E(f326(f326(f8(x83921,a909),x83922),f326(f326(f3(f917(x83921,a905)),x83923),f326(f326(f308(x83921),x83924),f188(f917(x83921,a905))))),f326(f326(f3(a909),f326(f326(f8(x83921,a909),x83922),x83923)),f326(x83922,x83924)))+~P105(f326(f326(f328(x83921),x83924),x83923))
% 157.55/157.22 [8411]P105(f326(f326(f234(f917(x84111,a905)),x84112),x84113))+~P105(f326(f326(f234(f917(x84111,a905)),f326(f326(f308(x84111),x84114),x84112)),x84113))
% 157.55/157.22 [8534]~E(f326(f309(x85342,x85343,x85341),f241(f917(x85342,a905))),f241(f917(x85343,a905)))+E(f326(x85341,f326(f90(x85342,x85343,f241(f917(x85342,a905)),x85341),x85344)),x85344)
% 157.55/157.22 [8616]P36(x86161,x86162)+~P36(x86161,f326(f326(f308(f916(x86161,x86161)),f326(f326(f251(x86161,x86161),x86163),x86164)),x86162))
% 157.55/157.22 [8617]P56(x86171,x86172)+~P56(x86171,f326(f326(f308(f916(x86171,x86171)),f326(f326(f251(x86171,x86171),x86173),x86174)),x86172))
% 157.55/157.22 [8622]~P108(x86221)+E(f326(f326(f148(x86221,x86221,f7(x86221)),x86222),f326(f326(f148(x86221,x86221,f7(x86221)),x86223),x86224)),f326(f326(f148(x86221,x86221,f7(x86221)),x86223),f326(f326(f148(x86221,x86221,f7(x86221)),x86222),x86224)))
% 157.55/157.22 [8637]E(x86371,x86372)+~P105(f326(f62(x86373,x86374,f326(f326(f308(x86373),x86371),f188(f917(x86373,a905)))),x86372))
% 157.55/157.22 [8646]E(f326(f326(f134(x86461),f326(f326(f175(x86461),x86462),x86463)),f326(f326(f175(x86461),x86464),f326(f326(f138(x86461),x86462),x86463))),f326(f326(f175(x86461),f326(f326(f79(a909),x86462),x86464)),x86463))+~P105(f326(f326(f234(a909),f326(f326(f79(a909),x86462),x86464)),f326(f189(f910(x86461)),x86463)))
% 157.55/157.22 [8685]P105(f326(f61(x86851),x86852))+~E(x86852,f326(f309(a909,x86851,x86853),f326(f261(a909),f326(f326(f9(a909,a909,a905),f235(a909)),x86854))))
% 157.55/157.22 [8705]~P91(x87051)+E(f326(f142(x87051,x87051,f79(x87051),f326(f326(f79(x87051),x87052),x87053)),x87054),f326(f326(f79(x87051),x87052),f326(f142(x87051,x87051,f79(x87051),x87053),x87054)))
% 157.55/157.22 [8741]P105(f326(f326(f234(f917(x87411,a905)),f326(f263(x87411,x87412),x87413)),f326(f263(x87411,x87412),x87414)))+~P105(f326(f326(f234(f917(f916(x87411,x87412),a905)),x87413),x87414))
% 157.55/157.22 [8753]~P105(f326(f326(f234(a909),x87532),x87534))+P105(f326(f326(f234(f917(x87531,a905)),f326(f172(x87531),f326(f326(f175(x87531),x87532),x87533))),f326(f172(x87531),f326(f326(f175(x87531),x87534),x87533))))
% 157.55/157.22 [8754]~P105(f326(f326(f234(a909),x87544),x87542))+P105(f326(f326(f234(f917(x87541,a905)),f326(f172(x87541),f326(f326(f138(x87541),x87542),x87543))),f326(f172(x87541),f326(f326(f138(x87541),x87544),x87543))))
% 157.55/157.22 [8811]~P105(f326(f61(x88111),f326(f326(f3(f917(x88111,a905)),x88112),x88114)))+P105(f326(f61(x88111),f326(f326(f3(f917(x88111,a905)),x88112),f326(f326(f308(x88111),x88113),x88114))))
% 157.55/157.22 [8853]P105(f326(f326(f328(f916(x88531,x88531)),x88532),f306(x88531,x88533)))+~P105(f326(f326(f328(f916(x88531,x88531)),x88532),f326(f326(f183(f916(x88531,x88531),a905),x88534),x88533)))
% 157.55/157.22 [8939]~P105(f326(f61(x89391),f326(f326(f3(f917(x89391,a905)),x89392),f326(f326(f308(x89391),x89394),x89393))))+P105(f326(f61(x89391),f326(f326(f3(f917(x89391,a905)),x89392),x89393)))
% 157.55/157.22 [9150]~P77(x91501)+P105(f326(f326(f234(x91501),f326(f326(f110(x91501),x91502),f326(f326(f101(x91501),x91503),x91504))),f326(f326(f101(x91501),f326(f326(f110(x91501),x91502),x91503)),f326(f326(f110(x91501),x91502),x91504))))
% 157.55/157.22 [9151]~P108(x91511)+P105(f326(f326(f234(x91511),f326(f326(f233(x91511),x91512),f326(f326(f232(x91511),x91513),x91514))),f326(f326(f232(x91511),f326(f326(f233(x91511),x91512),x91513)),f326(f326(f233(x91511),x91512),x91514))))
% 157.55/157.22 [9298]E(x92981,x92982)+~P105(f326(f326(f328(f916(x92983,x92983)),f326(f326(f251(x92983,x92983),x92981),x92982)),f326(f172(f916(x92983,x92983)),f326(f326(f181(x92983,x92983),x92984),x92984))))
% 157.55/157.22 [9328]~P105(f326(f326(f328(f916(x93281,x93281)),f326(f326(f251(x93281,x93281),x93283),x93282)),f306(x93281,x93284)))+~P36(x93281,f326(f326(f308(f916(x93281,x93281)),f326(f326(f251(x93281,x93281),x93282),x93283)),x93284))
% 157.55/157.22 [9329]~P105(f326(f326(f328(f916(x93291,x93291)),f326(f326(f251(x93291,x93291),x93293),x93292)),f306(x93291,x93294)))+~P56(x93291,f326(f326(f308(f916(x93291,x93291)),f326(f326(f251(x93291,x93291),x93292),x93293)),x93294))
% 157.55/157.22 [9333]E(x93331,x93332)+E(f326(f136(x93333,f326(f326(f10(a905,a905,x93333),a321),f326(a323,x93331))),f326(f326(f151(x93333),x93332),x93334)),f326(f326(f151(x93333),x93332),f326(f136(x93333,f326(f326(f10(a905,a905,x93333),a321),f326(a323,x93331))),x93334)))
% 157.55/157.22 [9361]~P25(x93612,x93611,x93613,f241(f917(x93612,a905)),f241(f917(x93611,a905)))+E(f326(f309(x93611,x93612,f90(x93612,x93611,f241(f917(x93612,a905)),x93613)),x93614),f326(f310(x93612,x93611,x93613),x93614))
% 157.55/157.22 [9376]~P77(x93761)+P105(f326(f326(f234(x93761),f326(f326(f110(x93761),f326(f326(f101(x93761),x93762),x93763)),f326(f326(f101(x93761),x93762),x93764))),f326(f326(f101(x93761),x93762),f326(f326(f110(x93761),x93763),x93764))))
% 157.55/157.22 [9377]~P108(x93771)+P105(f326(f326(f234(x93771),f326(f326(f233(x93771),f326(f326(f232(x93771),x93772),x93773)),f326(f326(f232(x93771),x93772),x93774))),f326(f326(f232(x93771),x93772),f326(f326(f233(x93771),x93773),x93774))))
% 157.55/157.22 [9438]~P25(x94382,x94381,x94384,f241(f917(x94382,a905)),f241(f917(x94381,a905)))+E(f326(f261(x94381),f326(f326(f10(x94382,a905,x94381),x94383),f90(x94382,x94381,f241(f917(x94382,a905)),x94384))),f326(f309(x94382,x94381,x94384),f326(f261(x94382),x94383)))
% 157.55/157.22 [9452]~E(f326(f309(x94522,x94521,x94523),f241(f917(x94522,a905))),f241(f917(x94521,a905)))+P105(f326(f326(f234(f917(x94521,a905)),f326(f78(f917(x94521,a905)),f326(f309(x94522,x94521,x94523),x94524))),f326(f309(x94522,x94521,x94523),f326(f78(f917(x94522,a905)),x94524))))
% 157.55/157.22 [9775]P105(f326(f326(f328(f916(x97751,x97751)),f326(f326(f251(x97751,x97751),x97752),x97753)),f326(f285(x97751,x97751),f326(f326(f288(x97751,x97751,x97751),x97754),f306(x97751,x97754)))))+~P105(f326(f326(f328(f916(x97751,x97751)),f326(f326(f251(x97751,x97751),x97752),x97753)),f326(f326(f288(x97751,x97751,x97751),f326(f285(x97751,x97751),x97754)),f306(x97751,f326(f285(x97751,x97751),x97754)))))
% 157.55/157.22 [9776]~P105(f326(f326(f328(f916(x97761,x97761)),f326(f326(f251(x97761,x97761),x97762),x97763)),f326(f285(x97761,x97761),f326(f326(f288(x97761,x97761,x97761),x97764),f306(x97761,x97764)))))+P105(f326(f326(f328(f916(x97761,x97761)),f326(f326(f251(x97761,x97761),x97762),x97763)),f326(f326(f288(x97761,x97761,x97761),f326(f285(x97761,x97761),x97764)),f306(x97761,f326(f285(x97761,x97761),x97764)))))
% 157.55/157.22 [9797]~P105(f326(f326(f328(x97972),x97974),f326(f283(x97971,x97972),x97973)))+P105(f326(f326(f328(f916(x97971,x97972)),f326(f326(f251(x97971,x97972),f556(x97973,x97971,x97974,x97972)),x97974)),x97973))
% 157.55/157.22 [9798]~P105(f326(f326(f328(x97982),x97984),f326(f283(x97981,x97982),x97983)))+P105(f326(f326(f328(f916(x97981,x97982)),f326(f326(f251(x97981,x97982),f557(x97983,x97981,x97984,x97982)),x97984)),x97983))
% 157.55/157.22 [9824]~P105(f326(f326(f328(x98241),x98244),f326(f326(f110(f917(x98241,a905)),x98242),x98243)))+P105(f326(f326(f326(f110(f917(x98241,a905)),f326(f326(f9(x98241,f917(x98241,a905),a905),f328(x98241)),x98242)),f326(f326(f9(x98241,f917(x98241,a905),a905),f328(x98241)),x98243)),x98244))
% 157.55/157.22 [9825]~P105(f326(f326(f328(x98251),x98254),f326(f326(f101(f917(x98251,a905)),x98252),x98253)))+P105(f326(f326(f326(f101(f917(x98251,a905)),f326(f326(f9(x98251,f917(x98251,a905),a905),f328(x98251)),x98252)),f326(f326(f9(x98251,f917(x98251,a905),a905),f328(x98251)),x98253)),x98254))
% 157.55/157.22 [9905]~P105(f326(f326(f328(f916(x99051,x99051)),f326(f326(f251(x99051,x99051),x99054),x99053)),f326(f326(f288(x99051,x99051,x99051),x99052),f306(x99051,x99052))))+P105(f326(f326(f328(f916(x99051,x99051)),f326(f326(f251(x99051,x99051),f631(x99052,x99053,x99054,x99051)),x99053)),x99052))
% 157.55/157.22 [9940]P105(f326(f326(f328(x99401),x99402),f326(f326(f110(f917(x99401,a905)),x99403),x99404)))+~P105(f326(f326(f326(f110(f917(x99401,a905)),f326(f326(f9(x99401,f917(x99401,a905),a905),f328(x99401)),x99403)),f326(f326(f9(x99401,f917(x99401,a905),a905),f328(x99401)),x99404)),x99402))
% 157.55/157.22 [9941]P105(f326(f326(f328(x99411),x99412),f326(f326(f101(f917(x99411,a905)),x99413),x99414)))+~P105(f326(f326(f326(f101(f917(x99411,a905)),f326(f326(f9(x99411,f917(x99411,a905),a905),f328(x99411)),x99413)),f326(f326(f9(x99411,f917(x99411,a905),a905),f328(x99411)),x99414)),x99412))
% 157.55/157.22 [10225]P31(x102251,f326(f326(f9(x102251,f917(f916(x102251,x102251),a905),f917(x102251,a905)),f326(f326(f10(f917(x102251,f917(f917(f916(x102251,x102251),a905),a905)),f917(f917(f916(x102251,x102251),a905),f917(x102251,a905)),x102251),f9(x102251,f917(f916(x102251,x102251),a905),a905)),f326(f326(f10(f917(x102251,f916(x102251,x102251)),f917(x102251,f917(f917(f916(x102251,x102251),a905),a905)),x102251),f326(f10(f916(x102251,x102251),f917(f917(f916(x102251,x102251),a905),a905),x102251),f328(f916(x102251,x102251)))),f251(x102251,x102251)))),x102252),x102253,x102254)+~P105(f326(f326(f328(f916(f910(x102251),f910(x102251))),f326(f326(f251(f910(x102251),f910(x102251)),x102253),x102254)),f158(x102251,x102252)))
% 157.55/157.22 [10229]P57(x102291,f326(f326(f9(x102291,f917(f916(x102291,x102291),a905),f917(x102291,a905)),f326(f326(f10(f917(x102291,f917(f917(f916(x102291,x102291),a905),a905)),f917(f917(f916(x102291,x102291),a905),f917(x102291,a905)),x102291),f9(x102291,f917(f916(x102291,x102291),a905),a905)),f326(f326(f10(f917(x102291,f916(x102291,x102291)),f917(x102291,f917(f917(f916(x102291,x102291),a905),a905)),x102291),f326(f10(f916(x102291,x102291),f917(f917(f916(x102291,x102291),a905),a905),x102291),f328(f916(x102291,x102291)))),f251(x102291,x102291)))),x102292),x102293,x102294)+~P105(f326(f326(f328(f916(f917(x102291,a905),f917(x102291,a905))),f326(f326(f251(f917(x102291,a905),f917(x102291,a905)),x102293),x102294)),f318(x102291,x102292)))
% 157.55/157.22 [10263]E(x102631,x102632)+~E(f326(f326(f9(x102633,f917(f916(x102633,x102634),a905),f917(x102634,a905)),f326(f326(f10(f917(x102634,f917(f917(f916(x102633,x102634),a905),a905)),f917(f917(f916(x102633,x102634),a905),f917(x102634,a905)),x102633),f9(x102634,f917(f916(x102633,x102634),a905),a905)),f326(f326(f10(f917(x102634,f916(x102633,x102634)),f917(x102634,f917(f917(f916(x102633,x102634),a905),a905)),x102633),f326(f10(f916(x102633,x102634),f917(f917(f916(x102633,x102634),a905),a905),x102634),f328(f916(x102633,x102634)))),f251(x102633,x102634)))),x102631),f326(f326(f9(x102633,f917(f916(x102633,x102634),a905),f917(x102634,a905)),f326(f326(f10(f917(x102634,f917(f917(f916(x102633,x102634),a905),a905)),f917(f917(f916(x102633,x102634),a905),f917(x102634,a905)),x102633),f9(x102634,f917(f916(x102633,x102634),a905),a905)),f326(f326(f10(f917(x102634,f916(x102633,x102634)),f917(x102634,f917(f917(f916(x102633,x102634),a905),a905)),x102633),f326(f10(f916(x102633,x102634),f917(f917(f916(x102633,x102634),a905),a905),x102634),f328(f916(x102633,x102634)))),f251(x102633,x102634)))),x102632))
% 157.55/157.22 [10266]~P31(x102661,f326(f326(f9(x102661,f917(f916(x102661,x102661),a905),f917(x102661,a905)),f326(f326(f10(f917(x102661,f917(f917(f916(x102661,x102661),a905),a905)),f917(f917(f916(x102661,x102661),a905),f917(x102661,a905)),x102661),f9(x102661,f917(f916(x102661,x102661),a905),a905)),f326(f326(f10(f917(x102661,f916(x102661,x102661)),f917(x102661,f917(f917(f916(x102661,x102661),a905),a905)),x102661),f326(f10(f916(x102661,x102661),f917(f917(f916(x102661,x102661),a905),a905),x102661),f328(f916(x102661,x102661)))),f251(x102661,x102661)))),x102664),x102662,x102663)+P105(f326(f326(f328(f916(f910(x102661),f910(x102661))),f326(f326(f251(f910(x102661),f910(x102661)),x102662),x102663)),f158(x102661,x102664)))
% 157.55/157.22 [10267]~P57(x102671,f326(f326(f9(x102671,f917(f916(x102671,x102671),a905),f917(x102671,a905)),f326(f326(f10(f917(x102671,f917(f917(f916(x102671,x102671),a905),a905)),f917(f917(f916(x102671,x102671),a905),f917(x102671,a905)),x102671),f9(x102671,f917(f916(x102671,x102671),a905),a905)),f326(f326(f10(f917(x102671,f916(x102671,x102671)),f917(x102671,f917(f917(f916(x102671,x102671),a905),a905)),x102671),f326(f10(f916(x102671,x102671),f917(f917(f916(x102671,x102671),a905),a905),x102671),f328(f916(x102671,x102671)))),f251(x102671,x102671)))),x102674),x102672,x102673)+P105(f326(f326(f328(f916(f917(x102671,a905),f917(x102671,a905))),f326(f326(f251(f917(x102671,a905),f917(x102671,a905)),x102672),x102673)),f318(x102671,x102674)))
% 157.55/157.22 [7661]~P94(x76611)+E(f326(f326(f80(x76611),f326(f103(x76611),x76612)),f326(f326(f80(x76611),f326(f103(x76611),x76613)),x76614)),f326(f326(f80(x76611),f326(f103(x76611),f326(f326(f80(a1),x76612),x76613))),x76614))
% 157.55/157.22 [7662]~P94(x76621)+E(f326(f326(f79(x76621),f326(f103(x76621),x76622)),f326(f326(f3(x76621),f326(f103(x76621),x76623)),x76624)),f326(f326(f3(x76621),f326(f103(x76621),f326(f326(f79(a1),x76622),x76623))),x76624))
% 157.55/157.22 [7663]~P94(x76631)+E(f326(f326(f79(x76631),f326(f103(x76631),x76632)),f326(f326(f79(x76631),f326(f103(x76631),x76633)),x76634)),f326(f326(f79(x76631),f326(f103(x76631),f326(f326(f79(a1),x76632),x76633))),x76634))
% 157.55/157.22 [7703]~P143(x77031)+E(f326(f165(x77031),f326(f326(f154(x77032,x77031),f326(f18(x77031,x77032),x77033)),x77034)),f326(f326(f80(x77031),f326(f100(x77031),f326(f189(f910(x77032)),x77034))),x77033))
% 157.55/157.22 [7939]E(f326(f267(x79391,f326(f326(f151(f916(a99,x79391)),x79392),x79393)),x79394),f326(f255(a99,x79391),x79392))+~P105(f326(f326(f235(a99),x79394),f326(f250(a99,x79391),x79392)))
% 157.55/157.22 [7979]~P94(x79791)+E(f326(f326(f79(x79791),f326(f103(x79791),x79792)),f326(f326(f3(x79791),x79793),f326(f103(x79791),x79794))),f326(f326(f79(x79791),f326(f103(x79791),f326(f326(f79(a1),x79792),f326(f78(a1),x79794)))),x79793))
% 157.55/157.22 [8110]E(f326(f267(x81101,x81102),f326(f326(f3(a99),x81103),f326(f250(a99,x81101),x81104))),f326(f267(x81101,f326(f326(f151(f916(a99,x81101)),x81104),x81102)),x81103))+P105(f326(f326(f235(a99),x81103),f326(f250(a99,x81101),x81104)))
% 157.55/157.22 [8540]~P105(f326(f326(f328(x85401),x85402),f326(f172(x85401),f114(x85401,x85404))))+P105(f326(f326(f328(x85401),x85402),f326(f172(x85401),f114(x85401,f326(f326(f134(x85401),x85403),x85404)))))
% 157.55/157.22 [8541]~P105(f326(f326(f328(x85411),x85412),f326(f172(x85411),f114(x85411,x85413))))+P105(f326(f326(f328(x85411),x85412),f326(f172(x85411),f114(x85411,f326(f326(f134(x85411),x85413),x85414)))))
% 157.55/157.22 [8559]E(f326(f326(f110(f917(x85591,a905)),f326(f326(f101(f917(x85591,a905)),x85592),x85593)),x85594),f326(f326(f101(f917(x85591,a905)),x85592),f326(f326(f110(f917(x85591,a905)),x85593),x85594)))+~P105(f326(f326(f234(f917(x85591,a905)),x85594),x85592))
% 157.55/157.22 [8867]~E(f326(f326(f110(f917(x88671,a905)),f326(f326(f101(f917(x88671,a905)),x88673),x88674)),x88672),f326(f326(f101(f917(x88671,a905)),x88673),f326(f326(f110(f917(x88671,a905)),x88674),x88672)))+P105(f326(f326(f234(f917(x88671,a905)),x88672),x88673))
% 157.55/157.22 [9155]~P105(f326(f326(f234(f917(x91551,a905)),x91552),f326(f326(f110(f917(x91551,a905)),x91553),x91554)))+P105(f326(f326(f234(f917(x91551,a905)),f326(f326(f3(f917(x91551,a905)),x91552),x91553)),x91554))
% 157.55/157.22 [9270]~E(f326(f309(x92701,x92702,x92703),f241(f917(x92701,a905))),f241(f917(x92702,a905)))+E(f326(f309(x92701,x92702,x92703),f326(f309(x92702,x92701,f90(x92701,x92702,f241(f917(x92701,a905)),x92703)),x92704)),x92704)
% 157.55/157.22 [9275]P105(f326(f326(f234(f917(x92751,a905)),x92752),f326(f326(f110(f917(x92751,a905)),x92753),x92754)))+~P105(f326(f326(f234(f917(x92751,a905)),f326(f326(f3(f917(x92751,a905)),x92752),x92753)),x92754))
% 157.55/157.22 [9357]~P86(x93571)+E(f326(f75(x93571),f326(f326(f8(x93572,x93571),f326(f326(f10(x93571,x93571,x93572),f75(x93571)),x93573)),x93574)),f326(f326(f8(x93572,x93571),f326(f326(f10(x93571,x93571,x93572),f75(x93571)),x93573)),x93574))
% 157.55/157.22 [9528]~P86(x95281)+P105(f326(f326(f234(x95281),f2(x95281)),f326(f326(f8(x95282,x95281),f326(f326(f10(x95281,x95281,x95282),f75(x95281)),x95283)),x95284)))
% 157.55/157.22 [9532]~P66(x95321)+E(f326(f165(x95321),f326(f326(f154(x95322,x95321),f326(f72(x95321,x95321,x95322,f78(x95321)),x95323)),x95324)),f326(f78(x95321),f326(f165(x95321),f326(f326(f154(x95322,x95321),x95323),x95324))))
% 157.55/157.22 [9671]~P86(x96711)+P105(f326(f326(f234(x96711),f326(f75(x96711),f326(f326(f8(x96712,x96711),x96713),x96714))),f326(f326(f8(x96712,x96711),f326(f326(f10(x96711,x96711,x96712),f75(x96711)),x96713)),x96714)))
% 157.55/157.22 [9700]~E(f326(f326(f79(a909),x97001),x97004),f326(f326(f79(a909),x97003),x97002))+P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),f326(f326(f251(a909,a909),x97001),x97002)),f326(f326(f251(a909,a909),x97003),x97004))),a108))
% 157.55/157.22 [9701]~P105(f326(f326(f235(a909),x97011),x97013))+P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),f326(f326(f251(a909,a909),x97011),x97012)),f326(f326(f251(a909,a909),x97013),x97014))),a32))
% 157.55/157.22 [9702]~P105(f326(f326(f235(a909),x97021),x97023))+P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),f326(f326(f251(a909,a909),x97021),x97022)),f326(f326(f251(a909,a909),x97023),x97024))),a70))
% 157.55/157.22 [9849]E(f326(f326(f79(a909),x98491),x98492),f326(f326(f79(a909),x98493),x98494))+~P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),f326(f326(f251(a909,a909),x98491),x98494)),f326(f326(f251(a909,a909),x98493),x98492))),a108))
% 157.55/157.22 [9880]E(f326(f326(f164(x98801),f326(f326(f138(x98801),f326(f189(f910(x98801)),f177(x98801,x98802,x98803))),x98803)),x98804),f326(f326(f164(x98801),x98803),f326(f326(f79(a909),x98804),f326(f189(f910(x98801)),f177(x98801,x98802,x98803)))))+~P105(f326(f326(f235(a909),x98804),f326(f189(f910(x98801)),f326(f326(f138(x98801),f326(f189(f910(x98801)),f177(x98801,x98802,x98803))),x98803))))
% 157.55/157.22 [9896]~P105(f326(f326(f328(x98962),x98964),f326(f326(f39(x98961,f917(x98962,a905)),f241(f917(x98961,a905))),x98963)))+P105(f326(f326(f326(f39(x98961,f917(x98962,a905)),f241(f917(x98961,a905))),f326(f326(f10(f917(x98962,a905),f917(x98962,a905),x98961),f326(f9(x98962,f917(x98962,a905),a905),f328(x98962))),x98963)),x98964))
% 157.55/157.22 [9897]~P105(f326(f326(f328(x98972),x98974),f326(f326(f40(x98971,f917(x98972,a905)),f241(f917(x98971,a905))),x98973)))+P105(f326(f326(f326(f40(x98971,f917(x98972,a905)),f241(f917(x98971,a905))),f326(f326(f10(f917(x98972,a905),f917(x98972,a905),x98971),f326(f9(x98972,f917(x98972,a905),a905),f328(x98972))),x98973)),x98974))
% 157.55/157.22 [9966]~P105(f326(f49(x99661,x99662),f326(f326(f251(a1,a1),x99664),x99663)))+P105(f326(f49(f326(f78(a1),x99661),x99662),f326(f326(f251(a1,a1),f326(f326(f326(f96(a1),f326(f326(a323,x99663),f2(a1))),f326(f78(a1),x99664)),f326(f326(f3(a1),f326(f78(a1),x99664)),f77(a1)))),f326(f326(f326(f96(a1),f326(f326(a323,x99663),f2(a1))),f2(a1)),f326(f326(f3(a1),x99662),x99663)))))
% 157.55/157.22 [9978]P105(f326(f326(f328(x99781),x99782),f326(f326(f39(x99783,f917(x99781,a905)),f241(f917(x99783,a905))),x99784)))+~P105(f326(f326(f326(f39(x99783,f917(x99781,a905)),f241(f917(x99783,a905))),f326(f326(f10(f917(x99781,a905),f917(x99781,a905),x99783),f326(f9(x99781,f917(x99781,a905),a905),f328(x99781))),x99784)),x99782))
% 157.55/157.22 [9979]P105(f326(f326(f328(x99791),x99792),f326(f326(f40(x99793,f917(x99791,a905)),f241(f917(x99793,a905))),x99794)))+~P105(f326(f326(f326(f40(x99793,f917(x99791,a905)),f241(f917(x99793,a905))),f326(f326(f10(f917(x99791,a905),f917(x99791,a905),x99793),f326(f9(x99791,f917(x99791,a905),a905),f328(x99791))),x99794)),x99792))
% 157.55/157.22 [9991]E(f326(f326(f40(a909,f917(x99911,a905)),f241(f917(a909,a905))),x99912),f326(f326(f40(a909,f917(x99911,a905)),f241(f917(a909,a905))),x99913))+~E(f326(f326(f40(a909,f917(x99911,a905)),f326(f301(a909,f2(a909)),f479(x99912,x99914,x99913,x99911))),x99913),f326(f326(f40(a909,f917(x99911,a905)),f326(f301(a909,f2(a909)),f326(f326(f79(a909),f479(x99912,x99914,x99913,x99911)),x99914))),x99912))
% 157.55/157.22 [10343]~P105(f326(f326(f234(f917(f916(x103431,x103432),a905)),x103433),x103434))+P105(f326(f326(f234(f917(x103431,f917(x103432,a905))),f326(f326(f9(x103431,f917(f916(x103431,x103432),a905),f917(x103432,a905)),f326(f326(f10(f917(x103432,f917(f917(f916(x103431,x103432),a905),a905)),f917(f917(f916(x103431,x103432),a905),f917(x103432,a905)),x103431),f9(x103432,f917(f916(x103431,x103432),a905),a905)),f326(f326(f10(f917(x103432,f916(x103431,x103432)),f917(x103432,f917(f917(f916(x103431,x103432),a905),a905)),x103431),f326(f10(f916(x103431,x103432),f917(f917(f916(x103431,x103432),a905),a905),x103432),f328(f916(x103431,x103432)))),f251(x103431,x103432)))),x103433)),f326(f326(f9(x103431,f917(f916(x103431,x103432),a905),f917(x103432,a905)),f326(f326(f10(f917(x103432,f917(f917(f916(x103431,x103432),a905),a905)),f917(f917(f916(x103431,x103432),a905),f917(x103432,a905)),x103431),f9(x103432,f917(f916(x103431,x103432),a905),a905)),f326(f326(f10(f917(x103432,f916(x103431,x103432)),f917(x103432,f917(f917(f916(x103431,x103432),a905),a905)),x103431),f326(f10(f916(x103431,x103432),f917(f917(f916(x103431,x103432),a905),a905),x103432),f328(f916(x103431,x103432)))),f251(x103431,x103432)))),x103434)))
% 157.55/157.22 [10359]P105(f326(f326(f234(f917(f916(x103591,x103592),a905)),x103593),x103594))+~P105(f326(f326(f234(f917(x103591,f917(x103592,a905))),f326(f326(f9(x103591,f917(f916(x103591,x103592),a905),f917(x103592,a905)),f326(f326(f10(f917(x103592,f917(f917(f916(x103591,x103592),a905),a905)),f917(f917(f916(x103591,x103592),a905),f917(x103592,a905)),x103591),f9(x103592,f917(f916(x103591,x103592),a905),a905)),f326(f326(f10(f917(x103592,f916(x103591,x103592)),f917(x103592,f917(f917(f916(x103591,x103592),a905),a905)),x103591),f326(f10(f916(x103591,x103592),f917(f917(f916(x103591,x103592),a905),a905),x103592),f328(f916(x103591,x103592)))),f251(x103591,x103592)))),x103593)),f326(f326(f9(x103591,f917(f916(x103591,x103592),a905),f917(x103592,a905)),f326(f326(f10(f917(x103592,f917(f917(f916(x103591,x103592),a905),a905)),f917(f917(f916(x103591,x103592),a905),f917(x103592,a905)),x103591),f9(x103592,f917(f916(x103591,x103592),a905),a905)),f326(f326(f10(f917(x103592,f916(x103591,x103592)),f917(x103592,f917(f917(f916(x103591,x103592),a905),a905)),x103591),f326(f10(f916(x103591,x103592),f917(f917(f916(x103591,x103592),a905),a905),x103592),f328(f916(x103591,x103592)))),f251(x103591,x103592)))),x103594)))
% 157.55/157.22 [9403]~P105(f326(f326(f328(f916(x94031,x94031)),x94032),f306(x94031,x94034)))+P105(f326(f326(f328(f916(x94031,x94031)),x94032),f306(x94031,f326(f326(f110(f917(f916(x94031,x94031),a905)),x94033),x94034))))
% 157.55/157.22 [9404]~P105(f326(f326(f328(f916(x94041,x94041)),x94042),f306(x94041,x94043)))+P105(f326(f326(f328(f916(x94041,x94041)),x94042),f306(x94041,f326(f326(f110(f917(f916(x94041,x94041),a905)),x94043),x94044))))
% 157.55/157.22 [10078]~P105(f326(f326(f234(a909),f326(f326(f79(a909),x100781),x100784)),f326(f326(f79(a909),x100783),x100782)))+P105(f326(f326(f234(a1),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x100781),x100782)),f188(f917(f916(a909,a909),a905)))))),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x100783),x100784)),f188(f917(f916(a909,a909),a905)))))))
% 157.55/157.22 [10079]~P105(f326(f326(f235(a909),f326(f326(f79(a909),x100791),x100794)),f326(f326(f79(a909),x100793),x100792)))+P105(f326(f326(f235(a1),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x100791),x100792)),f188(f917(f916(a909,a909),a905)))))),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x100793),x100794)),f188(f917(f916(a909,a909),a905)))))))
% 157.55/157.22 [10167]P105(f326(f326(f234(a909),f326(f326(f79(a909),x101671),x101672)),f326(f326(f79(a909),x101673),x101674)))+~P105(f326(f326(f234(a1),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x101671),x101674)),f188(f917(f916(a909,a909),a905)))))),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x101673),x101672)),f188(f917(f916(a909,a909),a905)))))))
% 157.55/157.22 [10168]P105(f326(f326(f235(a909),f326(f326(f79(a909),x101681),x101682)),f326(f326(f79(a909),x101683),x101684)))+~P105(f326(f326(f235(a1),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x101681),x101684)),f188(f917(f916(a909,a909),a905)))))),f326(a88,f326(f284(f916(a909,a909),f916(a909,a909),a108),f326(f326(f308(f916(a909,a909)),f326(f326(f251(a909,a909),x101683),x101682)),f188(f917(f916(a909,a909),a905)))))))
% 157.55/157.22 [10211]P105(f326(f326(f234(f917(x102111,a905)),f326(f326(f40(a909,f917(x102111,a905)),f241(f917(a909,a905))),x102112)),f326(f326(f40(a909,f917(x102111,a905)),f241(f917(a909,a905))),x102113)))+~P105(f326(f326(f234(f917(x102111,a905)),f326(f326(f40(a909,f917(x102111,a905)),f326(f301(a909,f2(a909)),f477(x102113,x102114,x102112,x102111))),x102112)),f326(f326(f40(a909,f917(x102111,a905)),f326(f301(a909,f2(a909)),f326(f326(f79(a909),f477(x102113,x102114,x102112,x102111)),x102114))),x102113)))
% 157.55/157.22 [10270]P105(f326(f326(f234(a99),x102704),f2(a99)))+E(f326(f326(f258(f916(a99,a99),f916(x102701,f917(a912,a322)),f916(a99,a99),f916(f917(a99,f917(a905,f913(f911(x102701)))),f916(a99,a99))),f326(x102702,x102703)),f326(f326(f10(f917(f917(a99,f917(a905,f913(f911(x102701)))),f917(f916(a99,a99),f916(f917(a99,f917(a905,f913(f911(x102701)))),f916(a99,a99)))),f917(f916(a99,a99),f916(f917(a99,f917(a905,f913(f911(x102701)))),f916(a99,a99))),f916(x102701,f917(a912,a322))),f326(f258(f916(a99,a99),f917(a99,f917(a905,f913(f911(x102701)))),f916(a99,a99),f916(f917(a99,f917(a905,f913(f911(x102701)))),f916(a99,a99))),f276(x102701,x102702,f326(f326(f3(a99),x102704),f77(a99)),x102703))),f326(f326(f10(f917(f917(a99,f917(a905,f913(f911(x102701)))),f917(a99,f917(a905,f913(f911(x102701))))),f917(f917(a99,f917(a905,f913(f911(x102701)))),f917(f916(a99,a99),f916(f917(a99,f917(a905,f913(f911(x102701)))),f916(a99,a99)))),f916(x102701,f917(a912,a322))),f326(f10(f917(a99,f917(a905,f913(f911(x102701)))),f917(f916(a99,a99),f916(f917(a99,f917(a905,f913(f911(x102701)))),f916(a99,a99))),f917(a99,f917(a905,f913(f911(x102701))))),f251(f917(a99,f917(a905,f913(f911(x102701)))),f916(a99,a99)))),f326(f326(f10(f917(a99,f917(a905,f913(f911(x102701)))),f917(f917(a99,f917(a905,f913(f911(x102701)))),f917(a99,f917(a905,f913(f911(x102701))))),f916(x102701,f917(a912,a322))),f44(x102701)),f326(f326(f10(x102701,f917(a99,f917(a905,f913(f911(x102701)))),f916(x102701,f917(a912,a322))),f42(x102701)),f250(x102701,f917(a912,a322))))))),f276(x102701,x102702,x102704,x102703))
% 157.55/157.22 [10332]~P105(f326(f326(f328(x103322),x103324),f326(f283(x103321,x103322),x103323)))+P105(f326(f249(x103321,x103322,f326(f326(f9(x103321,f917(f916(x103321,x103322),a905),f917(x103322,a905)),f326(f326(f10(f917(x103322,f917(f917(f916(x103321,x103322),a905),a905)),f917(f917(f916(x103321,x103322),a905),f917(x103322,a905)),x103321),f9(x103322,f917(f916(x103321,x103322),a905),a905)),f326(f326(f10(f917(x103322,f916(x103321,x103322)),f917(x103322,f917(f917(f916(x103321,x103322),a905),a905)),x103321),f326(f10(f916(x103321,x103322),f917(f917(f916(x103321,x103322),a905),a905),x103322),f328(f916(x103321,x103322)))),f251(x103321,x103322)))),x103323)),x103324))
% 157.55/157.22 [10333]~P105(f326(f326(f328(x103331),x103334),f326(f263(x103331,x103332),x103333)))+P105(f326(f248(x103331,x103332,f326(f326(f9(x103331,f917(f916(x103331,x103332),a905),f917(x103332,a905)),f326(f326(f10(f917(x103332,f917(f917(f916(x103331,x103332),a905),a905)),f917(f917(f916(x103331,x103332),a905),f917(x103332,a905)),x103331),f9(x103332,f917(f916(x103331,x103332),a905),a905)),f326(f326(f10(f917(x103332,f916(x103331,x103332)),f917(x103332,f917(f917(f916(x103331,x103332),a905),a905)),x103331),f326(f10(f916(x103331,x103332),f917(f917(f916(x103331,x103332),a905),a905),x103332),f328(f916(x103331,x103332)))),f251(x103331,x103332)))),x103333)),x103334))
% 157.55/157.22 [10346]P105(f326(f326(f328(x103461),x103462),f326(f283(x103463,x103461),x103464)))+~P105(f326(f249(x103463,x103461,f326(f326(f9(x103463,f917(f916(x103463,x103461),a905),f917(x103461,a905)),f326(f326(f10(f917(x103461,f917(f917(f916(x103463,x103461),a905),a905)),f917(f917(f916(x103463,x103461),a905),f917(x103461,a905)),x103463),f9(x103461,f917(f916(x103463,x103461),a905),a905)),f326(f326(f10(f917(x103461,f916(x103463,x103461)),f917(x103461,f917(f917(f916(x103463,x103461),a905),a905)),x103463),f326(f10(f916(x103463,x103461),f917(f917(f916(x103463,x103461),a905),a905),x103461),f328(f916(x103463,x103461)))),f251(x103463,x103461)))),x103464)),x103462))
% 157.55/157.22 [10347]P105(f326(f326(f328(x103471),x103472),f326(f263(x103471,x103473),x103474)))+~P105(f326(f248(x103471,x103473,f326(f326(f9(x103471,f917(f916(x103471,x103473),a905),f917(x103473,a905)),f326(f326(f10(f917(x103473,f917(f917(f916(x103471,x103473),a905),a905)),f917(f917(f916(x103471,x103473),a905),f917(x103473,a905)),x103471),f9(x103473,f917(f916(x103471,x103473),a905),a905)),f326(f326(f10(f917(x103473,f916(x103471,x103473)),f917(x103473,f917(f917(f916(x103471,x103473),a905),a905)),x103471),f326(f10(f916(x103471,x103473),f917(f917(f916(x103471,x103473),a905),a905),x103473),f328(f916(x103471,x103473)))),f251(x103471,x103473)))),x103474)),x103472))
% 157.55/157.22 [10002]P105(f326(f160(x100021,x100022),x100023))+~P105(f326(f160(x100021,f326(f326(f20(x100021,a905,a905),f326(f326(f10(a905,f917(a905,a905),x100021),a324),x100024)),x100022)),x100023))
% 157.55/157.22 [10003]P105(f326(f160(x100031,x100032),x100033))+~P105(f326(f160(x100031,f326(f326(f20(x100031,a905,a905),f326(f326(f10(a905,f917(a905,a905),x100031),a324),x100032)),x100034)),x100033))
% 157.55/157.22 [10090]~P112(x100901)+E(f326(f326(f80(x100901),f326(f326(f79(x100901),f77(x100901)),f77(x100901))),f326(f326(f8(a909,x100901),f326(f326(f10(x100901,x100901,a909),f326(f79(x100901),x100902)),f326(f326(f9(a909,x100901,x100901),f326(f326(f10(x100901,f917(x100901,x100901),a909),f80(x100901)),f100(x100901))),x100903))),f326(f281(a909),x100904))),f326(f326(f80(x100901),f326(f100(x100901),x100904)),f326(f326(f79(x100901),x100902),f326(f326(f79(x100901),x100902),f326(f326(f80(x100901),f326(f100(x100901),f326(f326(f3(a909),x100904),f77(a909)))),x100903)))))
% 157.55/157.22 [10232]P105(f326(x102321,f566(x102322,x102323,x102324,x102321)))+P36(x102322,f326(f261(f916(x102322,x102322)),f326(f256(x102322,x102322,a905),f326(f326(f10(f917(x102322,a905),f917(x102322,a905),x102322),f326(f20(x102322,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102322),a324),x102321))),f326(f326(f9(x102322,f917(x102322,x102322),f917(x102322,a905)),f326(f326(f10(f917(x102322,a905),f917(f917(x102322,x102322),f917(x102322,a905)),x102322),f10(x102322,a905,x102322)),a323)),x102323)))))
% 157.55/157.22 [10246]~P105(f326(f326(f235(a909),f326(x102464,f326(x102463,f566(x102461,x102463,x102464,x102462)))),f326(x102464,f566(x102461,x102463,x102464,x102462))))+P36(x102461,f326(f261(f916(x102461,x102461)),f326(f256(x102461,x102461,a905),f326(f326(f10(f917(x102461,a905),f917(x102461,a905),x102461),f326(f20(x102461,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102461),a324),x102462))),f326(f326(f9(x102461,f917(x102461,x102461),f917(x102461,a905)),f326(f326(f10(f917(x102461,a905),f917(f917(x102461,x102461),f917(x102461,a905)),x102461),f10(x102461,a905,x102461)),a323)),x102463)))))
% 157.55/157.22 [10317]~P4(x103171)+E(f37(x103171,f326(f261(x103171),f326(f326(f10(f917(f917(x103172,x103171),a905),a905,x103171),f86(f917(x103172,x103171))),f326(f326(f10(f917(f917(x103172,x103171),a905),f917(f917(x103172,x103171),a905),x103171),f326(f20(f917(x103172,x103171),a905,a905),f326(f326(f10(a905,f917(a905,a905),f917(x103172,x103171)),a324),f326(f326(f9(f917(x103172,x103171),f917(f917(x103172,x103171),a905),a905),f328(f917(x103172,x103171))),x103173)))),f326(f326(f9(x103171,f917(f917(x103172,x103171),x103171),f917(f917(x103172,x103171),a905)),f326(f326(f10(f917(x103171,a905),f917(f917(f917(x103172,x103171),x103171),f917(f917(x103172,x103171),a905)),x103171),f10(x103171,a905,f917(x103172,x103171))),a323)),f326(f326(f9(f917(x103172,x103171),x103172,x103171),f7(f917(x103172,x103171))),x103174)))))),f326(f37(f917(x103172,x103171),x103173),x103174))
% 157.55/157.22 [10318]~P4(x103181)+E(f37(x103181,f326(f261(x103181),f326(f326(f10(f917(f917(x103182,x103181),a905),a905,x103181),f86(f917(x103182,x103181))),f326(f326(f10(f917(f917(x103182,x103181),a905),f917(f917(x103182,x103181),a905),x103181),f326(f20(f917(x103182,x103181),a905,a905),f326(f326(f10(a905,f917(a905,a905),f917(x103182,x103181)),a324),f326(f326(f9(f917(x103182,x103181),f917(f917(x103182,x103181),a905),a905),f328(f917(x103182,x103181))),x103183)))),f326(f326(f9(x103181,f917(f917(x103182,x103181),x103181),f917(f917(x103182,x103181),a905)),f326(f326(f10(f917(x103181,a905),f917(f917(f917(x103182,x103181),x103181),f917(f917(x103182,x103181),a905)),x103181),f10(x103181,a905,f917(x103182,x103181))),a323)),f326(f326(f9(f917(x103182,x103181),x103182,x103181),f7(f917(x103182,x103181))),x103184)))))),f326(f37(f917(x103182,x103181),x103183),x103184))
% 157.55/157.22 [10319]~P4(x103191)+E(f38(x103191,f326(f261(x103191),f326(f326(f10(f917(f917(x103192,x103191),a905),a905,x103191),f86(f917(x103192,x103191))),f326(f326(f10(f917(f917(x103192,x103191),a905),f917(f917(x103192,x103191),a905),x103191),f326(f20(f917(x103192,x103191),a905,a905),f326(f326(f10(a905,f917(a905,a905),f917(x103192,x103191)),a324),f326(f326(f9(f917(x103192,x103191),f917(f917(x103192,x103191),a905),a905),f328(f917(x103192,x103191))),x103193)))),f326(f326(f9(x103191,f917(f917(x103192,x103191),x103191),f917(f917(x103192,x103191),a905)),f326(f326(f10(f917(x103191,a905),f917(f917(f917(x103192,x103191),x103191),f917(f917(x103192,x103191),a905)),x103191),f10(x103191,a905,f917(x103192,x103191))),a323)),f326(f326(f9(f917(x103192,x103191),x103192,x103191),f7(f917(x103192,x103191))),x103194)))))),f326(f38(f917(x103192,x103191),x103193),x103194))
% 157.55/157.22 [10320]~P4(x103201)+E(f38(x103201,f326(f261(x103201),f326(f326(f10(f917(f917(x103202,x103201),a905),a905,x103201),f86(f917(x103202,x103201))),f326(f326(f10(f917(f917(x103202,x103201),a905),f917(f917(x103202,x103201),a905),x103201),f326(f20(f917(x103202,x103201),a905,a905),f326(f326(f10(a905,f917(a905,a905),f917(x103202,x103201)),a324),f326(f326(f9(f917(x103202,x103201),f917(f917(x103202,x103201),a905),a905),f328(f917(x103202,x103201))),x103203)))),f326(f326(f9(x103201,f917(f917(x103202,x103201),x103201),f917(f917(x103202,x103201),a905)),f326(f326(f10(f917(x103201,a905),f917(f917(f917(x103202,x103201),x103201),f917(f917(x103202,x103201),a905)),x103201),f10(x103201,a905,f917(x103202,x103201))),a323)),f326(f326(f9(f917(x103202,x103201),x103202,x103201),f7(f917(x103202,x103201))),x103204)))))),f326(f38(f917(x103202,x103201),x103203),x103204))
% 157.55/157.22 [10372]~P105(f326(f326(f328(f916(x103721,x103721)),f326(f326(f251(x103721,x103721),x103723),x103724)),f326(f326(f110(f917(f916(x103721,x103721),a905)),x103722),f306(x103721,f188(f917(f916(x103721,x103721),a905))))))+P105(f326(f326(f326(f326(f110(f917(x103721,f917(x103721,a905))),f326(f326(f9(x103721,f917(f916(x103721,x103721),a905),f917(x103721,a905)),f326(f326(f10(f917(x103721,f917(f917(f916(x103721,x103721),a905),a905)),f917(f917(f916(x103721,x103721),a905),f917(x103721,a905)),x103721),f9(x103721,f917(f916(x103721,x103721),a905),a905)),f326(f326(f10(f917(x103721,f916(x103721,x103721)),f917(x103721,f917(f917(f916(x103721,x103721),a905),a905)),x103721),f326(f10(f916(x103721,x103721),f917(f917(f916(x103721,x103721),a905),a905),x103721),f328(f916(x103721,x103721)))),f251(x103721,x103721)))),x103722)),a323),x103723),x103724))
% 157.55/157.22 [10382]P105(f326(f326(f328(f916(x103821,x103821)),f326(f326(f251(x103821,x103821),x103822),x103823)),f326(f326(f110(f917(f916(x103821,x103821),a905)),x103824),f306(x103821,f188(f917(f916(x103821,x103821),a905))))))+~P105(f326(f326(f326(f326(f110(f917(x103821,f917(x103821,a905))),f326(f326(f9(x103821,f917(f916(x103821,x103821),a905),f917(x103821,a905)),f326(f326(f10(f917(x103821,f917(f917(f916(x103821,x103821),a905),a905)),f917(f917(f916(x103821,x103821),a905),f917(x103821,a905)),x103821),f9(x103821,f917(f916(x103821,x103821),a905),a905)),f326(f326(f10(f917(x103821,f916(x103821,x103821)),f917(x103821,f917(f917(f916(x103821,x103821),a905),a905)),x103821),f326(f10(f916(x103821,x103821),f917(f917(f916(x103821,x103821),a905),a905),x103821),f328(f916(x103821,x103821)))),f251(x103821,x103821)))),x103824)),a323),x103822),x103823))
% 157.55/157.22 [10328]E(f326(f326(f151(f910(x103281)),f326(f326(f151(x103281),x103282),f326(f142(f910(x103281),f910(x103281),f134(x103281),f113(x103281)),f326(f326(f154(f910(x103281),f910(x103281)),f156(f910(x103281),x103281,f113(x103281),f326(f326(f10(f910(x103281),f917(f910(x103281),f910(x103281)),x103281),f18(f910(x103281),f910(x103281))),f326(f326(f9(x103281,f910(x103281),f910(x103281)),f151(x103281)),f113(x103281))))),x103283)))),f179(x103281,f326(f326(f151(f910(x103281)),x103284),f326(f142(f910(f910(x103281)),f910(f910(x103281)),f134(f910(x103281)),f113(f910(x103281))),f326(f326(f154(f910(x103281),f910(f910(x103281))),f156(f910(f910(x103281)),x103281,f113(f910(x103281)),f326(f18(f917(f910(x103281),f910(f910(x103281))),x103281),f326(f326(f9(f910(x103281),f910(f910(x103281)),f910(f910(x103281))),f151(f910(x103281))),f113(f910(x103281)))))),x103283))))),f179(x103281,f326(f326(f151(f910(x103281)),f326(f326(f151(x103281),x103282),x103284)),x103283)))+~P105(f326(f314(f910(f910(x103281)),f180(x103281)),f326(f326(f151(f910(x103281)),f326(f326(f151(x103281),x103282),x103284)),x103283)))
% 157.55/157.22 [10371]~P105(f326(f61(x103712),f326(f261(x103712),x103714)))+P105(f326(f61(x103711),f326(f261(x103711),f326(f326(f10(f917(x103712,a905),a905,x103711),f86(x103712)),f326(f326(f9(x103711,f917(x103712,a905),f917(x103712,a905)),f326(f326(f10(f917(x103712,f917(a905,a905)),f917(f917(x103712,a905),f917(x103712,a905)),x103711),f20(x103712,a905,a905)),f326(f326(f10(f917(x103712,a905),f917(x103712,f917(a905,a905)),x103711),f326(f10(a905,f917(a905,a905),x103712),a324)),f326(f326(f9(x103711,f917(x103712,x103711),f917(x103712,a905)),f326(f326(f10(f917(x103711,a905),f917(f917(x103712,x103711),f917(x103712,a905)),x103711),f10(x103711,a905,x103712)),a323)),x103713)))),x103714)))))
% 157.55/157.22 [8905]P24(x89051,x89052,x89053,x89054)+~P25(x89051,x89052,x89053,x89054,x89055)
% 157.55/157.22 [5415]E(x54151,x54152)+~E(f169(x54153,x54151,x54154),f169(x54153,x54152,x54155))
% 157.55/157.22 [5416]E(x54161,x54162)+~E(f126(x54163,x54164,x54161),f126(x54163,x54165,x54162))
% 157.55/157.22 [5417]E(x54171,x54172)+~E(f126(x54173,x54171,x54174),f126(x54173,x54172,x54175))
% 157.55/157.22 [8241]~E(f326(x82413,x82414),x82415)+E(f74(x82411,x82412,x82413,x82414,x82415),x82413)
% 157.55/157.22 [8763]~E(f74(x87634,x87635,x87631,x87632,x87633),x87631)+E(f326(x87631,x87632),x87633)
% 157.55/157.22 [9374]~P25(x93742,x93741,x93744,x93743,x93745)+P25(x93741,x93742,f76(x93742,x93741,x93743,x93744),x93745,x93743)
% 157.55/157.22 [9375]~P25(x93752,x93751,x93754,x93753,x93755)+P25(x93751,x93752,f90(x93752,x93751,x93753,x93754),x93755,x93753)
% 157.55/157.22 [6230]P105(f326(f249(x62301,x62302,x62303),x62304))+~P105(f326(f326(x62303,x62305),x62304))
% 157.55/157.22 [6232]P105(f326(f248(x62321,x62322,x62323),x62324))+~P105(f326(f326(x62323,x62324),x62325))
% 157.55/157.22 [6707]~E(x67075,f2(a99))+E(f326(f196(x67071,x67072,x67073,x67074),x67075),f124(x67072))
% 157.55/157.22 [6708]~E(x67085,f2(a99))+E(f326(f198(x67081,x67082,x67083,x67084),x67085),f115(x67082))
% 157.55/157.22 [6847]~E(x68473,f2(a99))+E(f326(f272(x68471,x68472,x68473,x68474),x68475),f326(f251(x68471,x68472),x68475))
% 157.55/157.22 [7895]~P19(x78954,x78951,x78952,x78955)+E(f326(f72(x78951,x78951,x78951,f326(x78952,x78953)),f326(x78952,x78953)),f326(x78952,x78953))
% 157.55/157.22 [8279]~P15(x82795,x82791,x82792)+E(f326(f72(x82791,x82791,x82791,f326(x82792,x82793)),f326(x82792,x82794)),f326(f72(x82791,x82791,x82791,f326(x82792,x82794)),f326(x82792,x82793)))
% 157.55/157.22 [8599]P105(f326(f326(f328(f916(x85991,x85991)),f326(f326(f251(x85991,x85991),x85992),x85993)),f320(x85991,x85994,x85995)))+~P105(f326(f326(f235(a909),f326(x85994,x85992)),f326(x85994,x85993)))
% 157.55/157.22 [8691]~P105(f326(f326(f328(x86914),x86913),f298(x86914,x86911,x86912,x86915)))+P105(f326(f326(x86911,x86912),x86913))
% 157.55/157.22 [8692]~P105(f326(f326(f328(x86924),x86923),f289(x86924,x86921,x86922,x86925)))+P105(f326(f326(x86921,x86922),x86923))
% 157.55/157.22 [8693]~P105(f326(f326(f328(x86934),x86932),f298(x86934,x86931,x86935,x86933)))+P105(f326(f326(x86931,x86932),x86933))
% 157.55/157.22 [8694]~P105(f326(f326(f328(x86944),x86942),f289(x86944,x86941,x86945,x86943)))+P105(f326(f326(x86941,x86942),x86943))
% 157.55/157.22 [8775]~P25(x87751,x87753,x87755,x87752,x87754)+E(f326(f35(x87751),x87752),f326(f35(x87753),x87754))
% 157.55/157.22 [8823]~P25(x88231,x88232,x88233,x88234,x88235)+E(f326(f309(x88231,x88232,x88233),x88234),x88235)
% 157.55/157.22 [8843]~P55(x88432,x88431,x88435,x88433,x88434)+E(f326(f309(x88431,x88432,x88433),x88434),f241(f917(x88432,a905)))
% 157.55/157.22 [9287]~P33(x92871,x92872,x92873,x92874,x92875)+P33(x92871,x92872,x92873,f326(f168(x92871),x92874),f326(f168(x92872),x92875))
% 157.55/157.22 [9289]~P33(x92891,x92892,x92893,f326(f168(x92891),x92894),x92895)+P33(x92891,x92892,x92893,x92894,f326(f168(x92892),x92895))
% 157.55/157.22 [9290]~P33(x92901,x92902,x92903,x92904,f326(f168(x92902),x92905))+P33(x92901,x92902,x92903,f326(f168(x92901),x92904),x92905)
% 157.55/157.22 [9296]P33(x92961,x92962,x92963,x92964,x92965)+~P33(x92961,x92962,x92963,f326(f168(x92961),x92964),f326(f168(x92962),x92965))
% 157.55/157.22 [9690]P105(f326(f326(f328(f916(f910(x96901),f910(x96901))),f326(f326(f251(f910(x96901),f910(x96901)),f326(f326(f151(x96901),x96902),x96903)),f326(f326(f151(x96901),x96902),x96904))),f157(x96901,x96905)))+~P105(f326(f326(f328(f916(f910(x96901),f910(x96901))),f326(f326(f251(f910(x96901),f910(x96901)),x96903),x96904)),f157(x96901,x96905)))
% 157.55/157.22 [9691]P105(f326(f326(f328(f916(f910(x96911),f910(x96911))),f326(f326(f251(f910(x96911),f910(x96911)),f326(f326(f134(x96911),x96912),x96913)),f326(f326(f134(x96911),x96912),x96914))),f147(x96911,x96915)))+~P105(f326(f326(f328(f916(f910(x96911),f910(x96911))),f326(f326(f251(f910(x96911),f910(x96911)),x96913),x96914)),f147(x96911,x96915)))
% 157.55/157.22 [9887]E(f326(f326(f151(x98871),f647(x98872,x98873,x98874,x98875,x98871)),f650(x98872,x98873,x98874,x98875,x98871)),x98875)+~P105(f326(f326(f328(f916(f910(x98871),f910(x98871))),f326(f326(f251(f910(x98871),f910(x98871)),x98875),f326(f326(f151(x98871),x98874),x98873))),f158(x98871,x98872)))
% 157.55/157.22 [9908]E(f326(f326(f151(x99081),f648(x99082,x99083,x99084,x99085,x99081)),f649(x99082,x99083,x99084,x99085,x99081)),x99083)+~P105(f326(f326(f328(f916(f910(x99081),f910(x99081))),f326(f326(f251(f910(x99081),f910(x99081)),f326(f326(f151(x99081),x99085),x99084)),x99083)),f158(x99081,x99082)))
% 157.55/157.22 [10053]~P105(f326(f326(f328(f916(f910(x100531),f910(x100531))),f326(f326(f251(f910(x100531),f910(x100531)),f326(f326(f151(x100531),x100535),x100532)),x100534)),f158(x100531,x100533)))+P105(f326(f326(f328(f916(f910(x100531),f910(x100531))),f326(f326(f251(f910(x100531),f910(x100531)),x100532),f649(x100533,x100534,x100532,x100535,x100531))),f158(x100531,x100533)))
% 157.55/157.22 [10134]~P105(f326(f326(f328(f916(f910(x101341),f910(x101341))),f326(f326(f251(f910(x101341),f910(x101341)),x101345),f326(f326(f151(x101341),x101344),x101343))),f158(x101341,x101342)))+P105(f326(f326(f328(f916(f910(x101341),f910(x101341))),f326(f326(f251(f910(x101341),f910(x101341)),f650(x101342,x101343,x101344,x101345,x101341)),x101343)),f158(x101341,x101342)))
% 157.55/157.22 [10321]P105(f326(f326(f328(f916(x103211,x103211)),f326(f326(f251(x103211,x103211),f326(x103212,f326(f326(f79(a909),x103213),x103214))),f326(x103212,x103213))),f306(x103211,x103215)))+~P105(f326(f326(f328(f916(x103211,x103211)),f326(f326(f251(x103211,x103211),f326(x103212,f326(a112,f607(x103214,x103213,x103215,x103212,x103211)))),f326(x103212,f607(x103214,x103213,x103215,x103212,x103211)))),f306(x103211,x103215)))
% 157.55/157.22 [5383]E(x53831,x53832)+~E(f326(f326(f151(x53833),x53834),x53831),f326(f326(f151(x53833),x53835),x53832))
% 157.55/157.22 [5384]E(x53841,x53842)+~E(f326(f326(f151(x53843),x53841),x53844),f326(f326(f151(x53843),x53842),x53845))
% 157.55/157.22 [5432]P105(f326(x54321,x54322))+~E(f326(f136(x54323,x54321),x54324),f326(f326(f151(x54323),x54322),x54325))
% 157.55/157.22 [5433]P105(f326(x54331,x54332))+~E(f326(f326(f151(x54333),x54332),x54334),f326(f136(x54333,x54331),x54335))
% 157.55/157.22 [5593]~E(f326(f326(f138(x55931),x55933),x55932),f326(f326(f151(x55931),x55934),x55935))+E(f326(f326(f164(x55931),x55932),x55933),x55934)
% 157.55/157.22 [5735]~P13(x57354,x57355,x57351)+E(f326(f326(x57351,x57352),f326(f326(x57351,x57352),x57353)),f326(f326(x57351,x57352),x57353))
% 157.55/157.22 [6288]~E(x62884,f2(a99))+E(f326(f326(f117(x62881,x62882,x62883),x62884),x62885),f326(f326(f251(f910(x62882),x62881),f113(x62882)),x62885))
% 157.55/157.22 [6360]~P108(x63602)+~E(f326(f326(f148(x63601,x63602,x63603),x63604),x63605),f113(x63601))
% 157.55/157.22 [6747]E(x67471,x67472)+~E(f326(f326(f134(x67473),x67474),f326(f326(f151(x67473),x67471),f113(x67473))),f326(f326(f134(x67473),x67475),f326(f326(f151(x67473),x67472),f113(x67473))))
% 157.55/157.22 [6748]E(x67481,x67482)+~E(f326(f326(f134(x67483),x67481),f326(f326(f151(x67483),x67484),f113(x67483))),f326(f326(f134(x67483),x67482),f326(f326(f151(x67483),x67485),f113(x67483))))
% 157.55/157.22 [7062]E(f326(f326(f308(x70621),f326(x70622,x70623)),f326(f309(x70624,x70621,x70622),x70625)),f326(f309(x70624,x70621,x70622),x70625))+~P105(f326(f326(f328(x70624),x70623),x70625))
% 157.55/157.22 [7069]~P105(f326(x70694,f326(x70693,x70695)))+P105(f326(f326(f310(x70691,x70692,x70693),x70694),x70695))
% 157.55/157.22 [7072]~P105(f326(f326(x70723,x70725),x70724))+P105(f326(f326(f242(x70721,x70722,x70723),x70724),x70725))
% 157.55/157.22 [7168]~E(f326(f309(x71681,x71682,x71683),x71684),x71685)+E(f326(f309(f917(x71681,a905),f917(x71682,a905),f309(x71681,x71682,x71683)),f326(f307(x71681),x71684)),f326(f307(x71682),x71685))
% 157.55/157.22 [7196]E(f326(f270(x71961,x71962,x71963,x71964),x71965),f326(x71964,x71965))+~P105(f326(f326(f328(x71961),x71965),x71963))
% 157.55/157.22 [7511]P24(x75111,x75112,x75113,x75114)+~P24(x75111,x75112,x75113,f326(f326(f308(x75111),x75115),x75114))
% 157.55/157.22 [7575]P105(f326(x75751,x75752))+~P105(f326(f326(f92(x75753,x75754,x75751),x75755),x75752))
% 157.55/157.22 [7616]~P105(f326(f326(f328(x76164),x76163),x76165))+P105(f326(f326(f328(x76161),f326(x76162,x76163)),f326(f309(x76164,x76161,x76162),x76165)))
% 157.55/157.22 [7637]~P108(x76372)+E(f150(x76371,x76372,x76373,f326(f136(x76371,x76374),x76375)),f326(f136(x76371,x76374),f150(x76371,x76372,x76373,x76375)))
% 157.55/157.22 [7667]P105(f326(x76671,f326(x76672,x76673)))+~P105(f326(f326(f310(x76674,x76675,x76672),x76671),x76673))
% 157.55/157.22 [7670]P105(f326(f326(x76701,x76702),x76703))+~P105(f326(f326(f242(x76704,x76705,x76701),x76703),x76702))
% 157.55/157.22 [7671]P105(f326(f326(x76711,x76712),x76713))+~P105(f326(f326(f92(x76714,x76711,x76715),x76712),x76713))
% 157.55/157.22 [7733]~P105(f326(f326(f328(x77333),f326(x77334,x77332)),x77335))+P105(f326(f326(f328(x77331),x77332),f326(f310(x77331,x77333,x77334),x77335)))
% 157.55/157.22 [8123]~P105(f326(f326(f328(x81235),x81233),f326(f310(x81235,x81231,x81232),x81234)))+P105(f326(f326(f328(x81231),f326(x81232,x81233)),x81234))
% 157.55/157.22 [8416]~P15(x84162,x84161,x84163)+E(f326(f142(x84161,x84162,f326(f9(x84162,x84161,x84161),x84163),x84164),f152(x84162,x84165)),f326(f326(f64(x84162,x84161,x84163),x84164),f326(f172(x84162),x84165)))
% 157.55/157.22 [8438]E(f326(x84381,f480(x84382,x84381,x84383,x84384)),x84384)+~P105(f326(f326(f328(x84385),x84384),f326(f309(x84383,x84385,x84381),x84382)))
% 157.55/157.22 [8738]~E(x87382,f326(f326(f151(x87381),x87384),x87385))+P105(f326(f326(f328(f916(f910(x87381),f910(x87381))),f326(f326(f251(f910(x87381),f910(x87381)),f113(x87381)),x87382)),f147(x87381,x87383)))
% 157.55/157.22 [8784]E(f326(x87841,f326(f90(x87842,x87843,x87844,x87841),x87845)),x87845)+~P105(f326(f326(f328(x87843),x87845),f326(f309(x87842,x87843,x87841),x87844)))
% 157.55/157.22 [8787]P24(x87871,x87872,f90(x87872,x87871,x87873,x87874),x87875)+~P105(f326(f326(f234(f917(x87871,a905)),x87875),f326(f309(x87872,x87871,x87874),x87873)))
% 157.55/157.22 [8794]~P33(x87941,x87943,x87945,x87942,x87944)+E(f326(f189(f910(x87941)),x87942),f326(f189(f910(x87943)),x87944))
% 157.55/157.22 [8805]P105(f326(f326(f234(f917(x88051,a905)),f326(f326(f39(x88052,f917(x88051,a905)),x88053),x88054)),f326(x88054,x88055)))+~P105(f326(f326(f328(x88052),x88055),x88053))
% 157.55/157.22 [8859]~P55(x88591,x88592,x88593,x88595,x88594)+E(f326(f309(x88591,x88592,x88593),f241(f917(x88591,a905))),x88594)
% 157.55/157.22 [9084]E(f326(f136(x90841,x90842),f736(x90843,x90844,x90845,x90842,x90841)),x90843)+~E(f326(f136(x90841,x90842),x90845),f326(f326(f151(x90841),x90844),x90843))
% 157.55/157.22 [9085]E(f326(f136(x90851,x90852),f737(x90853,x90852,x90854,x90855,x90851)),x90854)+~E(f326(f326(f151(x90851),x90855),x90854),f326(f136(x90851,x90852),x90853))
% 157.55/157.22 [9176]E(f326(f189(f910(x91761)),x91762),x91763)+~P105(f326(f326(f328(f916(f910(x91761),f910(x91761))),f326(f326(f251(f910(x91761),f910(x91761)),x91764),x91762)),f326(f143(x91761,x91765),x91763)))
% 157.55/157.22 [9177]E(f326(f189(f910(x91771)),x91772),x91773)+~P105(f326(f326(f328(f916(f910(x91771),f910(x91771))),f326(f326(f251(f910(x91771),f910(x91771)),x91772),x91774)),f326(f143(x91771,x91775),x91773)))
% 157.55/157.22 [9246]P105(f326(f326(f328(x92461),f480(x92462,x92463,x92461,x92464)),x92462))+~P105(f326(f326(f328(x92465),x92464),f326(f309(x92461,x92465,x92463),x92462)))
% 157.55/157.22 [9401]E(f326(f309(x94011,x94012,x94013),f482(x94014,x94013,x94011,x94015,x94012)),x94015)+~P105(f326(f326(f234(f917(x94012,a905)),x94015),f326(f309(x94011,x94012,x94013),x94014)))
% 157.55/157.22 [9708]P105(f326(f326(f328(f916(f910(x97081),f910(x97081))),f326(f326(f251(f910(x97081),f910(x97081)),f326(f326(f151(x97081),x97082),x97083)),f326(f326(f151(x97081),x97082),x97084))),f306(f910(x97081),f157(x97081,x97085))))+~P105(f326(f326(f328(f916(f910(x97081),f910(x97081))),f326(f326(f251(f910(x97081),f910(x97081)),x97083),x97084)),f306(f910(x97081),f157(x97081,x97085))))
% 157.55/157.22 [9739]~E(f326(x97393,f689(x97395,x97394,x97393,x97392,x97391)),f326(x97395,f689(x97395,x97394,x97393,x97392,x97391)))+E(f326(f326(f154(x97391,x97392),x97393),x97394),f326(f326(f154(x97391,x97392),x97395),x97394))
% 157.55/157.22 [9815]~E(f326(f136(x98151,x98155),x98154),f326(f326(f151(x98151),x98153),x98152))+E(f326(f326(f134(x98151),f740(x98152,x98153,x98154,x98155,x98151)),f326(f326(f151(x98151),x98153),f736(x98152,x98153,x98154,x98155,x98151))),x98154)
% 157.55/157.22 [9816]~E(f326(f326(f151(x98161),x98165),x98164),f326(f136(x98161,x98163),x98162))+E(f326(f326(f134(x98161),f738(x98162,x98163,x98164,x98165,x98161)),f326(f326(f151(x98161),x98165),f737(x98162,x98163,x98164,x98165,x98161))),x98162)
% 157.55/157.22 [9820]E(f326(f326(f154(x98201,x98202),x98203),x98204),f326(f326(f154(x98201,x98202),x98205),x98204))+P105(f326(f326(f328(x98201),f689(x98203,x98204,x98205,x98202,x98201)),f326(f172(x98201),x98204)))
% 157.55/157.22 [9850]~P105(f326(f326(f328(x98505),x98504),f326(f284(x98501,x98505,x98503),x98502)))+P105(f326(f326(f328(x98501),f499(x98502,x98503,x98501,x98504,x98505)),x98502))
% 157.55/157.22 [9851]~P105(f326(f326(f328(x98515),x98514),f326(f284(x98511,x98515,x98513),x98512)))+P105(f326(f326(f328(x98511),f503(x98512,x98513,x98511,x98514,x98515)),x98512))
% 157.55/157.22 [9881]~P105(f326(f326(f234(f917(x98815,a905)),x98814),f326(f309(x98811,x98815,x98813),x98812)))+P105(f326(f326(f234(f917(x98811,a905)),f482(x98812,x98813,x98811,x98814,x98815)),x98812))
% 157.55/157.22 [10323]E(x103231,f2(a99))+E(f223(f916(f910(x103232),x103233),f916(x103232,x103233),f326(f326(f251(f910(x103232),x103233),f113(x103232)),x103234),f326(f256(x103232,x103233,f916(f910(x103232),x103233)),f326(f326(f9(x103232,f917(x103233,f916(f910(x103232),x103233)),f917(x103233,f916(f910(x103232),x103233))),f326(f326(f10(f917(f916(f910(x103232),x103233),f916(f910(x103232),x103233)),f917(f917(x103233,f916(f910(x103232),x103233)),f917(x103233,f916(f910(x103232),x103233))),x103232),f10(f916(f910(x103232),x103233),f916(f910(x103232),x103233),x103233)),f326(f326(f10(f917(f910(x103232),f917(x103233,f916(f910(x103232),x103233))),f917(f916(f910(x103232),x103233),f916(f910(x103232),x103233)),x103232),f256(f910(x103232),x103233,f916(f910(x103232),x103233))),f326(f326(f10(f917(f910(x103232),f910(x103232)),f917(f910(x103232),f917(x103233,f916(f910(x103232),x103233))),x103232),f326(f10(f910(x103232),f917(x103233,f916(f910(x103232),x103233)),f910(x103232)),f251(f910(x103232),x103233))),f151(x103232))))),f326(f117(x103233,x103232,x103235),f326(f326(f3(a99),x103231),f77(a99))))),f326(x103235,x103234)),f326(f326(f117(x103233,x103232,x103235),x103231),x103234))
% 157.55/157.22 [6168]E(x61681,x61682)+~E(f326(f255(x61683,x61684),f326(f326(f251(x61683,x61684),x61685),x61681)),x61682)
% 157.55/157.22 [6169]E(x61691,x61692)+~E(f326(f250(x61693,x61694),f326(f326(f251(x61693,x61694),x61691),x61695)),x61692)
% 157.55/157.22 [6434]~E(x64343,f326(f326(f134(x64341),x64344),f326(f326(f151(x64341),x64342),x64345)))+P105(f326(f326(f328(x64341),x64342),f326(f172(x64341),x64343)))
% 157.55/157.22 [6834]E(f326(f309(x68341,x68342,f326(f18(x68342,x68341),x68343)),x68344),f326(f326(f308(x68342),x68343),f188(f917(x68342,a905))))+~P105(f326(f326(f328(x68341),x68345),x68344))
% 157.55/157.22 [6907]E(f326(f326(f110(f917(x69071,a905)),f326(f172(x69071),x69072)),f326(f172(x69071),x69073)),f326(f172(x69071),x69074))+~E(f166(x69071,x69075,x69074),f326(f326(f251(f910(x69071),f910(x69071)),x69072),x69073))
% 157.55/157.22 [7005]~P108(x70052)+E(f326(f189(f910(x70051)),f326(f326(f148(x70051,x70052,x70053),x70054),x70055)),f326(a112,f326(f189(f910(x70051)),x70055)))
% 157.55/157.22 [7017]~P108(x70172)+E(f326(f172(x70171),f326(f326(f148(x70171,x70172,x70173),x70174),x70175)),f326(f326(f308(x70171),x70174),f326(f172(x70171),x70175)))
% 157.55/157.22 [7290]~P112(x72901)+E(f326(f326(f80(x72901),f326(f326(f80(x72901),x72902),x72903)),f326(f326(f80(x72901),x72904),x72905)),f326(f326(f80(x72901),f326(f326(f80(x72901),x72902),x72904)),f326(f326(f80(x72901),x72903),x72905)))
% 157.55/157.22 [7291]~P112(x72911)+E(f326(f326(f79(x72911),f326(f326(f79(x72911),x72912),x72913)),f326(f326(f79(x72911),x72914),x72915)),f326(f326(f79(x72911),f326(f326(f79(x72911),x72912),x72914)),f326(f326(f79(x72911),x72913),x72915)))
% 157.55/157.22 [7292]~P62(x72921)+E(f326(f326(f290(x72921),f326(f326(f80(x72921),x72922),x72923)),f326(f326(f80(x72921),x72924),x72925)),f326(f326(f80(x72921),f326(f326(f290(x72921),x72922),x72924)),f326(f326(f290(x72921),x72923),x72925)))
% 157.55/157.22 [7306]~P108(x73061)+E(f302(x73061,f326(f326(f233(x73061),x73062),x73063),f326(f326(f232(x73061),x73064),x73065)),f326(f326(f101(f917(x73061,a905)),f302(x73061,x73062,x73064)),f302(x73061,x73063,x73065)))
% 157.55/157.22 [7307]~P108(x73071)+E(f305(x73071,f326(f326(f233(x73071),x73072),x73073),f326(f326(f232(x73071),x73074),x73075)),f326(f326(f101(f917(x73071,a905)),f305(x73071,x73072,x73074)),f305(x73071,x73073,x73075)))
% 157.55/157.22 [7308]~P108(x73081)+E(f304(x73081,f326(f326(f233(x73081),x73082),x73083),f326(f326(f232(x73081),x73084),x73085)),f326(f326(f101(f917(x73081,a905)),f304(x73081,x73082,x73084)),f304(x73081,x73083,x73085)))
% 157.55/157.22 [7309]~P108(x73091)+E(f326(f326(f101(f917(x73091,a905)),f326(f301(x73091,x73092),x73093)),f326(f301(x73091,x73094),x73095)),f326(f301(x73091,f326(f326(f233(x73091),x73092),x73094)),f326(f326(f232(x73091),x73093),x73095)))
% 157.55/157.22 [7428]~P105(f326(x74281,f389(x74283,x74282,x74281)))+P105(f326(x74281,f326(f326(f251(x74282,x74283),x74284),x74285)))
% 157.55/157.22 [7542]~E(x75422,f326(x75424,x75425))+P105(f326(f326(f328(x75421),x75422),f326(f309(x75423,x75421,x75424),f241(f917(x75423,a905)))))
% 157.55/157.22 [7613]~P15(x76133,x76132,x76134)+P15(x76131,x76132,f326(f326(f10(x76133,f917(x76132,x76132),x76131),x76134),x76135))
% 157.55/157.22 [7614]~P13(x76143,x76142,x76144)+P13(x76141,x76142,f326(f326(f10(x76143,f917(x76142,x76142),x76141),x76144),x76145))
% 157.55/157.22 [7750]~P24(x77501,x77502,x77503,x77504)+P24(x77501,x77502,x77503,f326(f326(f3(f917(x77501,a905)),x77504),x77505))
% 157.55/157.22 [7904]~P105(f326(f326(x79043,x79044),x79045))+P105(f326(f326(f256(x79041,x79042,a905),x79043),f326(f326(f251(x79041,x79042),x79044),x79045)))
% 157.55/157.22 [8014]~P105(f326(x80142,x80144))+~E(f326(f326(f138(x80141),f326(f189(f910(x80141)),f177(x80141,x80142,x80143))),x80143),f326(f326(f151(x80141),x80144),x80145))
% 157.55/157.22 [8034]P24(x80341,x80342,x80343,x80344)+~P24(x80341,x80342,x80343,f326(f326(f110(f917(x80341,a905)),x80345),x80344))
% 157.55/157.22 [8035]P24(x80351,x80352,x80353,x80354)+~P24(x80351,x80352,x80353,f326(f326(f110(f917(x80351,a905)),x80354),x80355))
% 157.55/157.22 [8081]~P108(x80812)+E(f326(f326(f148(x80811,x80812,x80813),x80814),f150(x80811,x80812,x80813,x80815)),f150(x80811,x80812,x80813,f326(f326(f151(x80811),x80814),x80815)))
% 157.55/157.22 [8393]~P13(x83932,x83931,x83933)+E(f326(f142(x83931,x83932,f326(f9(x83932,x83931,x83931),x83933),x83934),x83935),f326(f326(f64(x83932,x83931,x83933),x83934),f326(f172(x83932),x83935)))
% 157.55/157.22 [8421]~E(f326(f326(f138(x84211),f326(f189(f910(x84211)),f177(x84211,x84212,x84213))),x84213),f326(f326(f151(x84211),x84214),x84215))+E(f326(f326(f134(x84211),f177(x84211,x84212,x84213)),f326(f326(f151(x84211),x84214),x84215)),x84213)
% 157.55/157.22 [8448]P105(f326(f326(x84481,x84482),x84483))+~P105(f326(f326(f256(x84484,x84485,a905),x84481),f326(f326(f251(x84484,x84485),x84482),x84483)))
% 157.55/157.22 [8922]P105(f326(f326(f234(f917(x89221,a905)),f326(f309(x89222,x89221,x89223),x89224)),f326(f309(x89222,x89221,x89223),x89225)))+~P105(f326(f326(f234(f917(x89222,a905)),x89224),x89225))
% 157.55/157.22 [8923]P105(f326(f326(f234(f917(x89231,a905)),f326(f310(x89231,x89232,x89233),x89234)),f326(f310(x89231,x89232,x89233),x89235)))+~P105(f326(f326(f234(f917(x89232,a905)),x89234),x89235))
% 157.55/157.22 [9002]E(x90021,f2(a99))+E(f326(f326(f258(x90022,x90023,x90022,f916(x90023,x90022)),f326(x90024,x90025)),f272(x90023,x90022,f326(f326(f3(a99),x90021),f77(a99)),x90024)),f326(f272(x90023,x90022,x90021,x90024),x90025))
% 157.55/157.22 [9109]P105(f326(f326(f254(x91091,x91092,a905,x91093),x91094),x91095))+~P105(f326(x91093,f326(f326(f251(x91091,x91092),x91094),x91095)))
% 157.55/157.22 [9380]~P105(f326(f326(f254(x93802,x93803,a905,x93801),x93804),x93805))+P105(f326(x93801,f326(f326(f251(x93802,x93803),x93804),x93805)))
% 157.55/157.22 [9560]~P105(f326(f326(f328(x95602),x95605),f326(f309(x95601,x95602,x95604),x95603)))+P105(f326(f326(f328(x95601),f326(f90(x95601,x95602,x95603,x95604),x95605)),x95603))
% 157.55/157.22 [9650]~P105(f326(f61(x96503),f326(f309(x96502,x96503,x96505),f241(f917(x96502,a905)))))+P105(f326(f61(x96501),f326(f309(x96502,x96501,f326(f326(f10(x96503,x96501,x96502),x96504),x96505)),f241(f917(x96502,a905)))))
% 157.55/157.22 [9675]P105(f326(f326(f234(f917(f917(x96751,a905),a905)),f326(f309(f917(x96752,a905),f917(x96751,a905),f309(x96752,x96751,x96753)),f326(f307(x96752),x96754))),f326(f307(x96751),x96755)))+~P105(f326(f326(f234(f917(x96751,a905)),f326(f309(x96752,x96751,x96753),x96754)),x96755))
% 157.55/157.22 [9747]E(x97471,x97472)+~P105(f326(f66(x97473,x97474,x97475,x97471,f188(f917(x97473,a905))),x97472))
% 157.55/157.22 [9763]E(f326(f326(f251(x97631,x97632),f539(x97633,x97634,x97635,x97632,x97631)),f540(x97633,x97634,x97635,x97632,x97631)),x97635)+~P105(f326(f326(f328(f916(x97631,x97632)),x97635),f326(f326(f253(x97631,x97632),x97634),x97633)))
% 157.55/157.22 [9856]P105(f326(f326(f328(x98561),f539(x98562,x98563,x98564,x98565,x98561)),x98563))+~P105(f326(f326(f328(f916(x98561,x98565)),x98564),f326(f326(f253(x98561,x98565),x98563),x98562)))
% 157.55/157.22 [10011]P105(f326(f326(f328(x100111),f540(x100112,x100113,x100114,x100111,x100115)),f326(x100112,f539(x100112,x100113,x100114,x100111,x100115))))+~P105(f326(f326(f328(f916(x100115,x100111)),x100114),f326(f326(f253(x100115,x100111),x100113),x100112)))
% 157.55/157.22 [10031]P105(f326(f326(f328(f916(x100311,x100311)),f326(f326(f251(x100311,x100311),x100312),f628(x100313,x100314,x100315,x100312,x100311))),x100313))+~P105(f326(f326(f328(f916(x100311,x100311)),f326(f326(f251(x100311,x100311),x100312),x100315)),f326(f326(f183(f916(x100311,x100311),a905),f326(a112,x100314)),x100313)))
% 157.55/157.22 [10032]P105(f326(f326(f328(f916(x100321,x100321)),f326(f326(f251(x100321,x100321),x100322),f629(x100323,x100324,x100325,x100322,x100321))),x100323))+~P105(f326(f326(f328(f916(x100321,x100321)),f326(f326(f251(x100321,x100321),x100322),x100325)),f326(f326(f183(f916(x100321,x100321),a905),f326(a112,x100324)),x100323)))
% 157.55/157.22 [10038]~P23(x100381,x100382,f326(f326(f308(f908(x100381)),f91(x100381,f92(x100381,x100383,x100384),x100385,x100383)),f188(f917(f908(x100381),a905))))+P23(x100381,x100382,f326(f326(f308(f908(x100381)),f91(x100381,x100383,f29(x100384,x100385),f92(x100381,x100383,f326(f72(a905,a905,a907,a321),x100384)))),f188(f917(f908(x100381),a905))))
% 157.55/157.22 [10050]~P105(f326(f326(f328(f916(f910(x100501),f910(x100501))),f326(f326(f251(f910(x100501),f910(x100501)),f326(f326(f151(x100501),x100502),x100505)),x100504)),f158(x100501,x100503)))+P105(f326(f326(f328(f916(x100501,x100501)),f326(f326(f251(x100501,x100501),x100502),f648(x100503,x100504,x100505,x100502,x100501))),x100503))
% 157.55/157.22 [6512]P105(f326(x65122,x65124))+E(f177(x65121,x65122,f326(f326(f134(x65121),x65123),f326(f326(f151(x65121),x65124),x65125))),f177(x65121,x65122,x65123))
% 157.55/157.22 [6561]~P77(x65612)+E(f326(f326(f326(f110(f917(x65611,x65612)),x65613),x65614),x65615),f326(f326(f110(x65612),f326(x65613,x65615)),f326(x65614,x65615)))
% 157.55/157.22 [6563]~P2(x65632)+E(f326(f326(f326(f3(f917(x65631,x65632)),x65633),x65634),x65635),f326(f326(f3(x65632),f326(x65633,x65635)),f326(x65634,x65635)))
% 157.55/157.22 [6565]~P77(x65652)+E(f326(f326(f326(f101(f917(x65651,x65652)),x65653),x65654),x65655),f326(f326(f101(x65652),f326(x65653,x65655)),f326(x65654,x65655)))
% 157.55/157.22 [6582]E(x65821,x65822)+E(f326(f326(f164(x65823),f326(f326(f159(x65823,x65824),x65821),x65825)),x65822),f326(f326(f164(x65823),x65824),x65822))
% 157.55/157.22 [6852]~E(x68524,f188(f917(x68523,a905)))+E(f326(f326(f110(f917(x68521,a905)),x68522),f326(f326(f40(x68523,f917(x68521,a905)),x68524),x68525)),x68522)
% 157.55/157.22 [6853]~E(x68534,f188(f917(x68533,a905)))+E(f326(f326(f3(f917(x68531,a905)),x68532),f326(f326(f40(x68533,f917(x68531,a905)),x68534),x68535)),x68532)
% 157.55/157.22 [6854]~E(x68544,f188(f917(x68543,a905)))+E(f326(f326(f101(f917(x68541,a905)),x68542),f326(f326(f39(x68543,f917(x68541,a905)),x68544),x68545)),x68542)
% 157.55/157.22 [6870]~E(x68704,f188(f917(x68703,a905)))+E(f326(f326(f308(x68701),x68702),f326(f326(f40(x68703,f917(x68701,a905)),x68704),x68705)),f326(f326(f308(x68701),x68702),f188(f917(x68701,a905))))
% 157.55/157.22 [7659]E(f326(f326(f164(x76591),f326(f326(f154(x76592,x76591),x76593),x76594)),x76595),f326(x76593,f326(f326(f164(x76592),x76594),x76595)))+~P105(f326(f326(f235(a909),x76595),f326(f189(f910(x76592)),x76594)))
% 157.55/157.22 [7721]E(f326(f326(f110(f917(x77211,a905)),f326(x77212,x77213)),f326(f326(f40(x77214,f917(x77211,a905)),x77215),x77212)),f326(f326(f40(x77214,f917(x77211,a905)),x77215),x77212))+~P105(f326(f326(f328(x77214),x77213),x77215))
% 157.55/157.22 [7722]E(f326(f326(f101(f917(x77221,a905)),f326(x77222,x77223)),f326(f326(f39(x77224,f917(x77221,a905)),x77225),x77222)),f326(f326(f39(x77224,f917(x77221,a905)),x77225),x77222))+~P105(f326(f326(f328(x77224),x77223),x77225))
% 157.55/157.22 [8316]~E(x83163,f188(f917(x83161,a905)))+E(f326(f326(f40(x83161,f917(x83162,a905)),x83163),f326(f326(f10(f917(x83162,a905),f917(x83162,a905),x83161),f326(f308(x83162),x83164)),x83165)),f188(f917(x83162,a905)))
% 157.55/157.22 [8321]~P105(f326(f326(f328(x83214),x83213),x83215))+P105(f326(f326(f234(f917(x83211,a905)),f326(x83212,x83213)),f326(f326(f40(x83214,f917(x83211,a905)),x83215),x83212)))
% 157.55/157.22 [8447]~E(f326(x84474,x84472),x84475)+P105(f326(f326(f328(x84471),x84472),f326(f310(x84471,x84473,x84474),f326(f326(f308(x84473),x84475),f188(f917(x84473,a905))))))
% 157.55/157.22 [8494]~P53(x84941,x84942,f326(f285(x84942,x84941),x84943))+E(f326(f326(f101(f917(x84941,a905)),f326(f284(x84942,x84941,x84943),x84944)),f326(f284(x84942,x84941,x84943),x84945)),f326(f284(x84942,x84941,x84943),f326(f326(f101(f917(x84942,a905)),x84944),x84945)))
% 157.55/157.22 [8568]E(x85681,f2(a99))+E(f326(f118(x85682,x85683,f326(x85684,f326(f326(f3(a99),x85681),f77(a99)))),f326(f326(f9(x85682,a99,f911(x85683)),x85685),x85681)),f326(f198(x85682,x85683,x85684,x85685),x85681))
% 157.55/157.22 [8606]E(x86061,f188(f917(x86062,a905)))+E(f326(f326(f40(x86062,f917(x86063,a905)),x86061),f326(f326(f10(f917(x86063,a905),f917(x86063,a905),x86062),f326(f308(x86063),x86064)),x86065)),f326(f326(f308(x86063),x86064),f326(f326(f40(x86062,f917(x86063,a905)),x86061),x86065)))
% 157.55/157.22 [8656]~P24(x86562,x86561,x86563,f241(f917(x86562,a905)))+E(f326(f326(f3(f917(x86561,a905)),f326(f309(x86562,x86561,x86563),x86564)),f326(f309(x86562,x86561,x86563),x86565)),f326(f309(x86562,x86561,x86563),f326(f326(f3(f917(x86562,a905)),x86564),x86565)))
% 157.55/157.22 [8657]~P24(x86572,x86571,x86573,f241(f917(x86572,a905)))+E(f326(f326(f101(f917(x86571,a905)),f326(f309(x86572,x86571,x86573),x86574)),f326(f309(x86572,x86571,x86573),x86575)),f326(f309(x86572,x86571,x86573),f326(f326(f101(f917(x86572,a905)),x86574),x86575)))
% 157.55/157.22 [8725]~P105(f326(f326(f67(x87251,x87252,x87255),x87253),x87254))+P105(f326(f326(f328(f916(x87251,x87252)),f326(f326(f251(x87251,x87252),x87253),x87254)),x87255))
% 157.55/157.22 [8757]P105(f326(f326(f328(x87571),x87572),f326(f283(x87573,x87571),x87574)))+~P105(f326(f326(f328(f916(x87573,x87571)),f326(f326(f251(x87573,x87571),x87575),x87572)),x87574))
% 157.55/157.22 [8759]P105(f326(f326(f328(x87591),x87592),f326(f263(x87591,x87593),x87594)))+~P105(f326(f326(f328(f916(x87591,x87593)),f326(f326(f251(x87591,x87593),x87592),x87595)),x87594))
% 157.55/157.22 [8906]P105(f326(f326(f67(x89061,x89062,x89063),x89064),x89065))+~P105(f326(f326(f328(f916(x89061,x89062)),f326(f326(f251(x89061,x89062),x89064),x89065)),x89063))
% 157.55/157.22 [8945]E(f326(x89451,x89452),x89453)+~P105(f326(f326(f328(x89454),x89452),f326(f310(x89454,x89455,x89451),f326(f326(f308(x89455),x89453),f188(f917(x89455,a905))))))
% 157.55/157.22 [9173]P105(f326(f326(f328(f916(x91731,x91732)),f326(f326(f251(x91731,x91732),x91733),x91734)),f326(f285(x91732,x91731),x91735)))+~P105(f326(f326(f328(f916(x91732,x91731)),f326(f326(f251(x91732,x91731),x91734),x91733)),x91735))
% 157.55/157.22 [9191]~P105(f326(f326(x91911,x91915),x91914))+P105(f326(f326(x91911,f326(f255(x91912,x91913),f326(f326(f251(x91912,x91913),x91914),x91915))),f326(f250(x91912,x91913),f326(f326(f251(x91912,x91913),x91914),x91915))))
% 157.55/157.22 [9221]~P105(f326(f326(f328(f916(x92212,x92211)),f326(f326(f251(x92212,x92211),x92214),x92213)),f326(f285(x92211,x92212),x92215)))+P105(f326(f326(f328(f916(x92211,x92212)),f326(f326(f251(x92211,x92212),x92213),x92214)),x92215))
% 157.55/157.22 [9253]~P105(f326(f326(f328(f916(x92533,x92531)),f326(f326(f251(x92533,x92531),x92535),x92532)),x92534))+P105(f326(f326(f328(x92531),x92532),f326(f284(x92533,x92531,x92534),f326(f326(f308(x92533),x92535),f188(f917(x92533,a905))))))
% 157.55/157.22 [9300]P105(f326(f326(f328(f916(x93001,x93002)),f326(f326(f251(x93001,x93002),x93003),x93004)),x93005))+~P105(f326(f326(f328(x93002),x93004),f326(f284(x93001,x93002,x93005),f326(f326(f308(x93001),x93003),f188(f917(x93001,a905))))))
% 157.55/157.22 [9387]~P69(x93871)+E(f326(f326(f8(a909,x93871),x93872),f302(a909,f326(f326(f79(a909),x93873),x93874),f326(f326(f79(a909),x93875),x93874))),f326(f326(f8(a909,x93871),f326(f326(f10(a909,x93871,a909),x93872),f326(f326(f9(a909,a909,a909),f79(a909)),x93874))),f302(a909,x93873,x93875)))
% 157.55/157.22 [9406]~P69(x94061)+E(f326(f326(f8(a909,x94061),x94062),f326(f301(a909,f326(f326(f79(a909),x94063),x94064)),f326(f326(f79(a909),x94065),x94064))),f326(f326(f8(a909,x94061),f326(f326(f10(a909,x94061,a909),x94062),f326(f326(f9(a909,a909,a909),f79(a909)),x94064))),f326(f301(a909,x94063),x94065)))
% 157.55/157.22 [9462]~P24(x94621,x94622,x94623,f241(f917(x94621,a905)))+E(f326(f326(f154(x94621,x94622),x94623),f326(f136(x94621,f326(f326(f10(a905,a905,x94621),a321),f326(a323,x94624))),x94625)),f326(f136(x94622,f326(f326(f10(a905,a905,x94622),a321),f326(a323,f326(x94623,x94624)))),f326(f326(f154(x94621,x94622),x94623),x94625)))
% 157.55/157.22 [9480]~P24(x94801,x94802,x94803,f326(f326(f308(x94801),x94804),f326(f172(x94801),x94805)))+E(f326(f326(f154(x94801,x94802),x94803),f326(f136(x94801,f326(f326(f10(a905,a905,x94801),a321),f326(a323,x94804))),x94805)),f326(f136(x94802,f326(f326(f10(a905,a905,x94802),a321),f326(a323,f326(x94803,x94804)))),f326(f326(f154(x94801,x94802),x94803),x94805)))
% 157.55/157.22 [9638]P105(f326(f326(f328(f916(f910(x96381),f910(x96381))),f326(f326(f251(f910(x96381),f910(x96381)),f326(f326(f151(x96381),x96382),x96383)),f326(f326(f151(x96381),x96384),x96383))),f157(x96381,x96385)))+~P105(f326(f326(f328(f916(x96381,x96381)),f326(f326(f251(x96381,x96381),x96382),x96384)),x96385))
% 157.55/157.22 [9758]E(f326(f326(f308(x97581),f538(x97582,x97583,x97584,x97585,x97581)),f554(x97582,x97583,x97584,x97585,x97581)),f326(f326(f308(x97581),x97584),x97583))+~P105(f326(f62(x97581,x97585,f326(f326(f308(x97581),x97584),x97583)),x97582))
% 157.55/157.22 [9759]E(f326(f326(f308(x97591),f564(x97592,x97593,x97594,x97595,x97591)),f573(x97592,x97593,x97594,x97595,x97591)),f326(f326(f308(x97591),x97594),x97593))+~P105(f326(f62(x97591,x97595,f326(f326(f308(x97591),x97594),x97593)),x97592))
% 157.55/157.22 [9841]P105(f326(f326(f328(x98411),f428(x98412,x98413,x98414,x98415,x98411)),x98414))+P105(f326(f326(f326(f39(x98411,f917(x98415,a905)),x98414),x98413),x98412))
% 157.55/157.22 [9846]P105(f326(f326(f328(x98461),f419(x98462,x98463,x98461,x98464,x98465)),x98463))+P105(f326(f326(f328(x98465),x98464),f326(f326(f39(x98461,f917(x98465,a905)),x98463),x98462)))
% 157.55/157.22 [9854]P105(f326(f326(f328(x98541),f420(x98542,x98543,x98541,x98544,x98545)),x98543))+P105(f326(f326(f234(f917(x98545,a905)),x98544),f326(f326(f39(x98541,f917(x98545,a905)),x98543),x98542)))
% 157.55/157.22 [9855]P105(f326(f326(f328(x98551),f830(x98552,x98553,x98554,x98555,x98551)),x98555))+P105(f326(f326(f234(f917(x98554,a905)),x98553),f326(f326(f39(x98551,f917(x98554,a905)),x98555),x98552)))
% 157.55/157.22 [9857]P105(f326(f326(x98571,f471(x98572,x98571,x98573,x98574,x98575)),x98572))+~P105(f326(f326(f326(f40(x98575,f917(x98574,a905)),x98573),x98571),x98572))
% 157.55/157.22 [9861]P105(f326(f326(f328(x98611),f471(x98612,x98613,x98614,x98615,x98611)),x98614))+~P105(f326(f326(f326(f40(x98611,f917(x98615,a905)),x98614),x98613),x98612))
% 157.55/157.22 [9862]P51(x98624,f326(f326(f39(x98621,f917(x98624,a905)),x98625),x98623),f326(f326(f39(x98621,f917(f916(x98624,x98624),a905)),x98625),x98622))+P105(f326(f326(f328(x98621),f768(x98622,x98623,x98624,x98625,x98621)),x98625))
% 157.55/157.22 [9863]P51(x98634,f326(f326(f40(x98631,f917(x98634,a905)),x98635),x98633),f326(f326(f40(x98631,f917(f916(x98634,x98634),a905)),x98635),x98632))+P105(f326(f326(f328(x98631),f823(x98632,x98633,x98634,x98635,x98631)),x98635))
% 157.55/157.22 [9873]P105(f326(f326(f328(x98731),f466(x98732,x98733,x98731,x98734,x98735)),x98733))+~P105(f326(f326(f328(x98735),x98734),f326(f326(f40(x98731,f917(x98735,a905)),x98733),x98732)))
% 157.55/157.22 [9879]P105(f326(f326(f328(x98791),x98792),f326(x98793,f466(x98793,x98794,x98795,x98792,x98791))))+~P105(f326(f326(f328(x98791),x98792),f326(f326(f40(x98795,f917(x98791,a905)),x98794),x98793)))
% 157.55/157.22 [9960]~P105(f326(f326(x99604,f428(x99605,x99604,x99603,x99602,x99601)),x99605))+P105(f326(f326(f326(f39(x99601,f917(x99602,a905)),x99603),x99604),x99605))
% 157.55/157.22 [9963]~P105(f326(f326(f328(x99631),x99632),f326(x99635,f419(x99635,x99634,x99633,x99632,x99631))))+P105(f326(f326(f328(x99631),x99632),f326(f326(f39(x99633,f917(x99631,a905)),x99634),x99635)))
% 157.55/157.22 [9967]~P51(x99671,f326(x99674,f768(x99675,x99674,x99671,x99673,x99672)),f326(x99675,f768(x99675,x99674,x99671,x99673,x99672)))+P51(x99671,f326(f326(f39(x99672,f917(x99671,a905)),x99673),x99674),f326(f326(f39(x99672,f917(f916(x99671,x99671),a905)),x99673),x99675))
% 157.55/157.22 [9968]~P51(x99681,f326(x99684,f823(x99685,x99684,x99681,x99683,x99682)),f326(x99685,f823(x99685,x99684,x99681,x99683,x99682)))+P51(x99681,f326(f326(f40(x99682,f917(x99681,a905)),x99683),x99684),f326(f326(f40(x99682,f917(f916(x99681,x99681),a905)),x99683),x99685))
% 157.55/157.22 [9969]~P105(f326(f326(f234(f917(x99691,a905)),x99692),f326(x99695,f420(x99695,x99694,x99693,x99692,x99691))))+P105(f326(f326(f234(f917(x99691,a905)),x99692),f326(f326(f39(x99693,f917(x99691,a905)),x99694),x99695)))
% 157.55/157.22 [9970]~P105(f326(f326(f234(f917(x99701,a905)),x99702),f326(x99705,f830(x99705,x99702,x99701,x99704,x99703))))+P105(f326(f326(f234(f917(x99701,a905)),x99702),f326(f326(f39(x99703,f917(x99701,a905)),x99704),x99705)))
% 157.55/157.22 [10035]~P105(f326(f326(f328(x100351),f538(x100355,x100354,x100353,x100352,x100351)),f554(x100355,x100354,x100353,x100352,x100351)))+~P105(f326(f62(x100351,x100352,f326(f326(f308(x100351),x100353),x100354)),x100355))
% 157.55/157.22 [10036]~P105(f326(f326(f328(x100361),f564(x100365,x100364,x100363,x100362,x100361)),f573(x100365,x100364,x100363,x100362,x100361)))+~P105(f326(f62(x100361,x100362,f326(f326(f308(x100361),x100363),x100364)),x100365))
% 157.55/157.22 [10037]~P105(f326(f326(f328(f916(x100371,x100371)),f326(f326(f251(x100371,x100371),x100372),x100375)),f326(f326(f183(f916(x100371,x100371),a905),f326(a112,x100374)),x100373)))+P105(f326(f326(f328(f916(x100371,x100371)),f326(f326(f251(x100371,x100371),x100372),f630(x100373,x100374,x100375,x100372,x100371))),f326(f326(f183(f916(x100371,x100371),a905),x100374),x100373)))
% 157.55/157.22 [10044]P105(f326(f66(x100441,x100441,x100442,f538(x100443,x100444,x100445,x100442,x100441),f554(x100443,x100444,x100445,x100442,x100441)),x100443))+~P105(f326(f62(x100441,x100442,f326(f326(f308(x100441),x100445),x100444)),x100443))
% 157.55/157.22 [10045]P105(f326(f66(x100451,x100451,x100452,f564(x100453,x100454,x100455,x100452,x100451),f573(x100453,x100454,x100455,x100452,x100451)),x100453))+~P105(f326(f62(x100451,x100452,f326(f326(f308(x100451),x100455),x100454)),x100453))
% 157.55/157.22 [10055]~P108(x100551)+P12(x100551,f326(f326(f154(x100552,x100551),x100553),f326(f136(x100552,f326(f326(f9(x100552,x100551,a905),f326(f326(f10(x100551,f917(x100551,a905),x100552),a323),x100553)),f326(x100554,x100555))),x100555)))
% 157.55/157.22 [10106]~P105(f326(f326(f328(x101062),x101065),f326(f284(x101061,x101062,x101064),x101063)))+P105(f326(f326(f328(f916(x101061,x101062)),f326(f326(f251(x101061,x101062),f499(x101063,x101064,x101061,x101065,x101062)),x101065)),x101064))
% 157.55/157.22 [10107]~P105(f326(f326(f328(x101072),x101075),f326(f284(x101071,x101072,x101074),x101073)))+P105(f326(f326(f328(f916(x101071,x101072)),f326(f326(f251(x101071,x101072),f503(x101073,x101074,x101071,x101075,x101072)),x101075)),x101074))
% 157.55/157.22 [10127]~P105(f326(f326(f328(f916(x101271,x101271)),f326(f326(f251(x101271,x101271),x101275),x101274)),f326(f326(f183(f916(x101271,x101271),a905),f326(a112,x101273)),x101272)))+P105(f326(f326(f328(f916(x101271,x101271)),f326(f326(f251(x101271,x101271),f630(x101272,x101273,x101274,x101275,x101271)),x101274)),x101272))
% 157.55/157.22 [10130]~P105(f326(f326(f328(f916(x101301,x101301)),f326(f326(f251(x101301,x101301),x101305),x101304)),f326(f326(f183(f916(x101301,x101301),a905),f326(a112,x101303)),x101302)))+P105(f326(f326(f328(f916(x101301,x101301)),f326(f326(f251(x101301,x101301),f628(x101302,x101303,x101304,x101305,x101301)),x101304)),f326(f326(f183(f916(x101301,x101301),a905),x101303),x101302)))
% 157.55/157.22 [10131]~P105(f326(f326(f328(f916(x101311,x101311)),f326(f326(f251(x101311,x101311),x101315),x101314)),f326(f326(f183(f916(x101311,x101311),a905),f326(a112,x101313)),x101312)))+P105(f326(f326(f328(f916(x101311,x101311)),f326(f326(f251(x101311,x101311),f629(x101312,x101313,x101314,x101315,x101311)),x101314)),f326(f326(f183(f916(x101311,x101311),a905),x101313),x101312)))
% 157.55/157.22 [10132]~P105(f326(f326(f328(f916(f910(x101321),f910(x101321))),f326(f326(f251(f910(x101321),f910(x101321)),x101325),f326(f326(f151(x101321),x101324),x101323))),f158(x101321,x101322)))+P105(f326(f326(f328(f916(x101321,x101321)),f326(f326(f251(x101321,x101321),f647(x101322,x101323,x101324,x101325,x101321)),x101324)),x101322))
% 157.55/157.22 [7742]~E(x77423,f188(f917(x77422,a905)))+E(f326(f326(f110(f917(x77421,a905)),f326(f326(f40(x77422,f917(x77421,a905)),x77423),x77424)),x77425),x77425)
% 157.55/157.22 [7743]~E(x77433,f188(f917(x77432,a905)))+E(f326(f326(f101(f917(x77431,a905)),f326(f326(f39(x77432,f917(x77431,a905)),x77433),x77434)),x77435),x77435)
% 157.55/157.22 [8162]~E(x81623,f188(f917(x81622,a905)))+E(f326(f326(f3(f917(x81621,a905)),f326(f326(f39(x81622,f917(x81621,a905)),x81623),x81624)),x81625),f326(f326(f3(f917(x81621,a905)),f241(f917(x81621,a905))),x81625))
% 157.55/157.22 [8290]E(f326(f326(f159(x82901,f326(f326(f134(x82901),x82902),x82903)),x82904),x82905),f326(f326(f134(x82901),f326(f326(f159(x82901,x82902),x82904),x82905)),x82903))+~P105(f326(f326(f235(a909),x82904),f326(f189(f910(x82901)),x82902)))
% 157.55/157.22 [8558]E(f326(f326(f164(x85581),f326(f326(f154(a909,x85581),x85582),f139(a909,f326(f301(a909,x85583),x85584)))),x85585),f326(x85582,f326(f326(f79(a909),x85583),x85585)))+~P105(f326(f326(f235(a909),x85585),f326(f326(f3(a909),x85584),x85583)))
% 157.55/157.22 [8572]E(x85721,f2(a99))+E(f122(x85722,x85723,f326(x85724,f326(f326(f3(a99),x85721),f77(a99))),f326(f326(f9(x85722,a99,f911(f913(x85723))),x85725),x85721)),f326(f196(x85722,x85723,x85724,x85725),x85721))
% 157.55/157.22 [8596]~E(x85963,f188(f917(x85961,a905)))+E(f326(f326(f39(x85961,f917(x85962,a905)),x85963),f326(f326(f10(f917(x85962,a905),f917(x85962,a905),x85961),f326(f3(f917(x85962,a905)),x85964)),x85965)),f241(f917(x85962,a905)))
% 157.55/157.22 [8597]~E(x85973,f188(f917(x85971,a905)))+E(f326(f326(f39(x85971,f917(x85972,a905)),x85973),f326(f326(f10(f917(x85972,a905),f917(x85972,a905),x85971),f326(f101(f917(x85972,a905)),x85974)),x85975)),f241(f917(x85972,a905)))
% 157.55/157.22 [8598]~E(x85983,f188(f917(x85981,a905)))+E(f326(f326(f40(x85981,f917(x85982,a905)),x85983),f326(f326(f10(f917(x85982,a905),f917(x85982,a905),x85981),f326(f110(f917(x85982,a905)),x85984)),x85985)),f188(f917(x85982,a905)))
% 157.55/157.22 [8600]~P144(x86002)+E(f326(f326(f8(x86001,x86002),f326(f326(f10(x86002,x86002,x86001),f326(f80(x86002),x86003)),x86004)),x86005),f326(f326(f80(x86002),x86003),f326(f326(f8(x86001,x86002),x86004),x86005)))
% 157.55/157.22 [8890]E(x88901,f188(f917(x88902,a905)))+E(f326(f326(f39(x88902,f917(x88903,a905)),x88901),f326(f326(f10(f917(x88903,a905),f917(x88903,a905),x88902),f326(f3(f917(x88903,a905)),x88904)),x88905)),f326(f326(f3(f917(x88903,a905)),x88904),f326(f326(f40(x88902,f917(x88903,a905)),x88901),x88905)))
% 157.55/157.22 [8891]E(x88911,f188(f917(x88912,a905)))+E(f326(f326(f39(x88912,f917(x88913,a905)),x88911),f326(f326(f10(f917(x88913,a905),f917(x88913,a905),x88912),f326(f101(f917(x88913,a905)),x88914)),x88915)),f326(f326(f101(f917(x88913,a905)),x88914),f326(f326(f39(x88912,f917(x88913,a905)),x88911),x88915)))
% 157.55/157.22 [8892]E(x88921,f188(f917(x88922,a905)))+E(f326(f326(f40(x88922,f917(x88923,a905)),x88921),f326(f326(f10(f917(x88923,a905),f917(x88923,a905),x88922),f326(f110(f917(x88923,a905)),x88924)),x88925)),f326(f326(f110(f917(x88923,a905)),x88924),f326(f326(f40(x88922,f917(x88923,a905)),x88921),x88925)))
% 157.55/157.22 [9091]~P105(f326(f326(f235(a909),f326(x90914,x90912)),f326(x90914,x90913)))+P105(f326(f326(f328(f916(x90911,x90911)),f326(f326(f251(x90911,x90911),x90912),x90913)),f153(x90911,f326(f326(f151(f917(x90911,a909)),x90914),x90915))))
% 157.55/157.22 [9353]~P24(x93532,x93531,x93533,f326(f326(f110(f917(x93532,a905)),x93534),x93535))+E(f326(f326(f101(f917(x93531,a905)),f326(f309(x93532,x93531,x93533),f326(f326(f3(f917(x93532,a905)),x93534),x93535))),f326(f309(x93532,x93531,x93533),f326(f326(f3(f917(x93532,a905)),x93535),x93534))),f188(f917(x93531,a905)))
% 157.55/157.22 [9604]~P24(x96043,x96041,x96045,f241(f917(x96043,a905)))+E(f326(f72(x96041,x96042,x96043,f326(f72(x96043,x96042,x96041,x96044),f90(x96043,x96041,f241(f917(x96043,a905)),x96045))),x96045),x96044)
% 157.55/157.22 [9634]~P105(f326(f326(f234(f917(x96343,a905)),f326(f284(x96341,x96343,x96344),x96342)),x96345))+P105(f326(f326(f234(f917(x96341,a905)),x96342),f326(f78(f917(x96341,a905)),f326(f284(x96343,x96341,f326(f285(x96341,x96343),x96344)),f326(f78(f917(x96343,a905)),x96345)))))
% 157.55/157.22 [9659]~P24(x96591,x96592,x96593,f326(f326(f308(x96591),x96594),x96595))+~P105(f326(f326(f328(x96592),f326(x96593,x96594)),f326(f309(x96591,x96592,x96593),f326(f326(f3(f917(x96591,a905)),x96595),f326(f326(f308(x96591),x96594),f188(f917(x96591,a905)))))))
% 157.55/157.22 [9712]P105(f326(f326(f234(f917(x97121,a905)),f326(f284(x97122,x97121,x97123),x97124)),x97125))+~P105(f326(f326(f234(f917(x97122,a905)),x97124),f326(f78(f917(x97122,a905)),f326(f284(x97121,x97122,f326(f285(x97122,x97121),x97123)),f326(f78(f917(x97121,a905)),x97125)))))
% 157.55/157.22 [9785]~P86(x97851)+P105(f326(f326(f234(x97851),f326(f75(x97851),f326(f326(f3(x97851),f326(f326(f79(x97851),x97852),x97853)),f326(f326(f79(x97851),x97854),x97855)))),f326(f326(f79(x97851),f326(f75(x97851),f326(f326(f3(x97851),x97852),x97854))),f326(f75(x97851),f326(f326(f3(x97851),x97853),x97855)))))
% 157.55/157.22 [9894]P105(f326(f326(f328(x98941),f467(x98942,x98943,x98944,x98941,x98945)),x98944))+P105(f326(f326(f234(f917(x98945,a905)),f326(f326(f40(x98941,f917(x98945,a905)),x98944),x98943)),x98942))
% 157.55/157.22 [10073]~P105(f326(f326(f234(f917(x100731,a905)),f326(x100734,f467(x100735,x100734,x100733,x100732,x100731))),x100735))+P105(f326(f326(f234(f917(x100731,a905)),f326(f326(f40(x100732,f917(x100731,a905)),x100733),x100734)),x100735))
% 157.55/157.22 [8704]E(f326(f326(f134(x87041),x87042),f326(f326(f159(x87041,x87043),f326(f326(f3(a909),x87044),f326(f189(f910(x87041)),x87042))),x87045)),f326(f326(f159(x87041,f326(f326(f134(x87041),x87042),x87043)),x87044),x87045))+P105(f326(f326(f235(a909),x87044),f326(f189(f910(x87041)),x87042)))
% 157.55/157.22 [8732]~P138(x87321)+E(f326(f326(f79(x87321),f326(f326(f80(x87321),x87322),x87323)),f326(f326(f79(x87321),f326(f326(f80(x87321),x87324),x87323)),x87325)),f326(f326(f79(x87321),f326(f326(f80(x87321),f326(f326(f79(x87321),x87322),x87324)),x87323)),x87325))
% 157.55/157.22 [9309]~P144(x93091)+E(f326(f165(x93091),f326(f326(f154(x93092,x93091),f326(f326(f10(x93091,x93091,x93092),f326(f80(x93091),x93093)),x93094)),x93095)),f326(f326(f80(x93091),x93093),f326(f165(x93091),f326(f326(f154(x93092,x93091),x93094),x93095))))
% 157.55/157.22 [9479]E(f326(f189(f910(x94791)),f326(f326(f175(x94791),f326(f326(f232(a909),f326(f189(f910(x94791)),x94792)),f326(f189(f910(x94793)),x94794))),x94792)),f326(f189(f910(x94793)),f326(f326(f175(x94793),f326(f326(f232(a909),f326(f189(f910(x94791)),x94792)),f326(f189(f910(x94793)),x94794))),x94794)))+P105(f326(x94795,f326(f326(f181(x94791,x94793),x94792),x94794)))
% 157.55/157.22 [9722]~P144(x97222)+E(f326(f326(f8(x97221,x97222),f326(f326(f9(x97221,x97222,x97222),f326(f326(f10(x97222,f917(x97222,x97222),x97221),f80(x97222)),x97223)),x97224)),x97225),f326(f326(f80(x97222),f326(f326(f8(x97221,x97222),x97223),x97225)),x97224))
% 157.55/157.22 [9723]~P63(x97232)+E(f326(f326(f8(x97231,x97232),f326(f326(f9(x97231,x97232,x97232),f326(f326(f10(x97232,f917(x97232,x97232),x97231),f290(x97232)),x97233)),x97234)),x97235),f326(f326(f290(x97232),f326(f326(f8(x97231,x97232),x97233),x97235)),x97234))
% 157.55/157.22 [9730]~P66(x97302)+E(f326(f326(f8(x97301,x97302),f326(f326(f20(x97301,x97302,x97302),f326(f326(f10(x97302,f917(x97302,x97302),x97301),f3(x97302)),x97303)),x97304)),x97305),f326(f326(f3(x97302),f326(f326(f8(x97301,x97302),x97303),x97305)),f326(f326(f8(x97301,x97302),x97304),x97305)))
% 157.55/157.22 [9731]~P69(x97312)+E(f326(f326(f8(x97311,x97312),f326(f326(f20(x97311,x97312,x97312),f326(f326(f10(x97312,f917(x97312,x97312),x97311),f79(x97312)),x97313)),x97314)),x97315),f326(f326(f79(x97312),f326(f326(f8(x97311,x97312),x97313),x97315)),f326(f326(f8(x97311,x97312),x97314),x97315)))
% 157.55/157.22 [9732]~P74(x97322)+E(f326(f326(f11(x97321,x97322),f326(f326(f20(x97321,x97322,x97322),f326(f326(f10(x97322,f917(x97322,x97322),x97321),f80(x97322)),x97323)),x97324)),x97325),f326(f326(f80(x97322),f326(f326(f11(x97321,x97322),x97323),x97325)),f326(f326(f11(x97321,x97322),x97324),x97325)))
% 157.55/157.22 [9770]~E(x97703,f188(f917(x97701,a905)))+E(f326(f326(f39(x97701,f917(x97702,a905)),x97703),f326(f326(f9(x97701,f917(x97702,a905),f917(x97702,a905)),f326(f326(f10(f917(x97702,a905),f917(f917(x97702,a905),f917(x97702,a905)),x97701),f3(f917(x97702,a905))),x97704)),x97705)),f241(f917(x97702,a905)))
% 157.55/157.22 [9771]~E(x97713,f188(f917(x97711,a905)))+E(f326(f326(f39(x97711,f917(x97712,a905)),x97713),f326(f326(f9(x97711,f917(x97712,a905),f917(x97712,a905)),f326(f326(f10(f917(x97712,a905),f917(f917(x97712,a905),f917(x97712,a905)),x97711),f101(f917(x97712,a905))),x97714)),x97715)),f241(f917(x97712,a905)))
% 157.55/157.22 [9772]~E(x97723,f188(f917(x97721,a905)))+E(f326(f326(f40(x97721,f917(x97722,a905)),x97723),f326(f326(f9(x97721,f917(x97722,a905),f917(x97722,a905)),f326(f326(f10(f917(x97722,a905),f917(f917(x97722,a905),f917(x97722,a905)),x97721),f110(f917(x97722,a905))),x97724)),x97725)),f188(f917(x97722,a905)))
% 157.55/157.22 [9793]E(x97931,f188(f917(x97932,a905)))+E(f326(f326(f39(x97932,f917(x97933,a905)),x97931),f326(f326(f9(x97932,f917(x97933,a905),f917(x97933,a905)),f326(f326(f10(f917(x97933,a905),f917(f917(x97933,a905),f917(x97933,a905)),x97932),f3(f917(x97933,a905))),x97934)),x97935)),f326(f326(f3(f917(x97933,a905)),f326(f326(f39(x97932,f917(x97933,a905)),x97931),x97934)),x97935))
% 157.55/157.22 [9794]E(x97941,f188(f917(x97942,a905)))+E(f326(f326(f39(x97942,f917(x97943,a905)),x97941),f326(f326(f9(x97942,f917(x97943,a905),f917(x97943,a905)),f326(f326(f10(f917(x97943,a905),f917(f917(x97943,a905),f917(x97943,a905)),x97942),f101(f917(x97943,a905))),x97944)),x97945)),f326(f326(f101(f917(x97943,a905)),f326(f326(f39(x97942,f917(x97943,a905)),x97941),x97944)),x97945))
% 157.55/157.22 [9795]E(x97951,f188(f917(x97952,a905)))+E(f326(f326(f40(x97952,f917(x97953,a905)),x97951),f326(f326(f9(x97952,f917(x97953,a905),f917(x97953,a905)),f326(f326(f10(f917(x97953,a905),f917(f917(x97953,a905),f917(x97953,a905)),x97952),f110(f917(x97953,a905))),x97954)),x97955)),f326(f326(f110(f917(x97953,a905)),f326(f326(f40(x97952,f917(x97953,a905)),x97951),x97954)),x97955))
% 157.55/157.22 [9358]~P105(f326(f326(f234(a909),x93581),x93584))+E(f326(f326(f3(a909),f326(f326(f79(a909),f326(f326(f80(a909),x93581),x93582)),x93583)),f326(f326(f79(a909),f326(f326(f80(a909),x93584),x93582)),x93585)),f326(f326(f3(a909),x93583),f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x93584),x93581)),x93582)),x93585)))
% 157.55/157.22 [9943]~P144(x99431)+E(f326(f165(x99431),f326(f326(f154(x99432,x99431),f326(f326(f9(x99432,x99431,x99431),f326(f326(f10(x99431,f917(x99431,x99431),x99432),f80(x99431)),x99433)),x99434)),x99435)),f326(f326(f80(x99431),f326(f165(x99431),f326(f326(f154(x99432,x99431),x99433),x99435))),x99434))
% 157.55/157.22 [9949]~P66(x99491)+E(f326(f165(x99491),f326(f326(f154(x99492,x99491),f326(f326(f20(x99492,x99491,x99491),f326(f326(f10(x99491,f917(x99491,x99491),x99492),f3(x99491)),x99493)),x99494)),x99495)),f326(f326(f3(x99491),f326(f165(x99491),f326(f326(f154(x99492,x99491),x99493),x99495))),f326(f165(x99491),f326(f326(f154(x99492,x99491),x99494),x99495))))
% 157.55/157.22 [9950]~P69(x99501)+E(f326(f165(x99501),f326(f326(f154(x99502,x99501),f326(f326(f20(x99502,x99501,x99501),f326(f326(f10(x99501,f917(x99501,x99501),x99502),f79(x99501)),x99503)),x99504)),x99505)),f326(f326(f79(x99501),f326(f165(x99501),f326(f326(f154(x99502,x99501),x99503),x99505))),f326(f165(x99501),f326(f326(f154(x99502,x99501),x99504),x99505))))
% 157.55/157.22 [10098]P105(f326(x100981,f326(f326(f181(x100982,x100983),x100984),x100985)))+~P105(f326(x100981,f326(f326(f181(x100982,x100983),f326(f326(f175(x100982),f326(f326(f232(a909),f326(f189(f910(x100982)),x100984)),f326(f189(f910(x100983)),x100985))),x100984)),f326(f326(f175(x100983),f326(f326(f232(a909),f326(f189(f910(x100982)),x100984)),f326(f189(f910(x100983)),x100985))),x100985))))
% 157.55/157.22 [10358]~P105(f326(f326(f328(f916(x103582,x103581)),f326(f326(f251(x103582,x103581),x103584),x103585)),f326(f285(x103581,x103582),x103583)))+P105(f326(f326(f242(x103581,x103582,f326(f326(f9(x103581,f917(f916(x103581,x103582),a905),f917(x103582,a905)),f326(f326(f10(f917(x103582,f917(f917(f916(x103581,x103582),a905),a905)),f917(f917(f916(x103581,x103582),a905),f917(x103582,a905)),x103581),f9(x103582,f917(f916(x103581,x103582),a905),a905)),f326(f326(f10(f917(x103582,f916(x103581,x103582)),f917(x103582,f917(f917(f916(x103581,x103582),a905),a905)),x103581),f326(f10(f916(x103581,x103582),f917(f917(f916(x103581,x103582),a905),a905),x103582),f328(f916(x103581,x103582)))),f251(x103581,x103582)))),x103583)),x103584),x103585))
% 157.55/157.22 [10368]P105(f326(f326(f328(f916(x103681,x103682)),f326(f326(f251(x103681,x103682),x103683),x103684)),f326(f285(x103682,x103681),x103685)))+~P105(f326(f326(f242(x103682,x103681,f326(f326(f9(x103682,f917(f916(x103682,x103681),a905),f917(x103681,a905)),f326(f326(f10(f917(x103681,f917(f917(f916(x103682,x103681),a905),a905)),f917(f917(f916(x103682,x103681),a905),f917(x103681,a905)),x103682),f9(x103681,f917(f916(x103682,x103681),a905),a905)),f326(f326(f10(f917(x103681,f916(x103682,x103681)),f917(x103681,f917(f917(f916(x103682,x103681),a905),a905)),x103682),f326(f10(f916(x103682,x103681),f917(f917(f916(x103682,x103681),a905),a905),x103681),f328(f916(x103682,x103681)))),f251(x103682,x103681)))),x103685)),x103683),x103684))
% 157.55/157.22 [9603]~P105(f326(f326(f234(a909),x96034),x96031))+E(f326(f326(f3(a909),f326(f326(f79(a909),f326(f326(f80(a909),x96031),x96032)),x96033)),f326(f326(f79(a909),f326(f326(f80(a909),x96034),x96032)),x96035)),f326(f326(f3(a909),f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x96031),x96034)),x96032)),x96033)),x96035))
% 157.55/157.22 [5409]E(x54091,x54092)+~E(f27(x54093,x54094,x54091),f27(x54095,x54096,x54092))
% 157.55/157.22 [5410]E(x54101,x54102)+~E(f27(x54103,x54101,x54104),f27(x54105,x54102,x54106))
% 157.55/157.22 [5411]E(x54111,x54112)+~E(f27(x54111,x54113,x54114),f27(x54112,x54115,x54116))
% 157.55/157.22 [5412]E(x54121,x54122)+~E(f26(x54123,x54124,x54121),f26(x54125,x54126,x54122))
% 157.55/157.22 [5413]E(x54131,x54132)+~E(f26(x54133,x54131,x54134),f26(x54135,x54132,x54136))
% 157.55/157.22 [5414]E(x54141,x54142)+~E(f26(x54141,x54143,x54144),f26(x54142,x54145,x54146))
% 157.55/157.22 [7439]E(x74391,x74392)+~E(f220(x74393,x74394,x74395,x74391),f220(x74393,x74394,x74396,x74392))
% 157.55/157.22 [7440]E(x74401,x74402)+~E(f220(x74403,x74404,x74401,x74405),f220(x74403,x74404,x74402,x74406))
% 157.55/157.22 [8543]~P18(x85435,x85431,x85432,x85436)+E(f326(f72(x85431,x85431,x85431,f326(x85432,x85433)),f326(x85432,x85434)),f326(f72(x85431,x85431,x85431,f326(x85432,x85434)),f326(x85432,x85433)))
% 157.55/157.22 [8776]~P55(x87764,x87765,x87762,x87761,x87766)+E(f326(x87761,f326(x87762,x87763)),x87763)
% 157.55/157.22 [8943]P24(x89431,x89432,x89433,x89434)+~P24(x89431,x89435,f326(f72(x89432,x89435,x89431,x89436),x89433),x89434)
% 157.55/157.22 [9016]~E(x90166,x90164)+E(f326(f74(x90161,x90162,x90163,x90164,x90165),x90166),x90165)
% 157.55/157.22 [9022]E(x90221,x90222)+E(f326(f74(x90223,x90224,x90225,x90222,x90226),x90221),f326(x90225,x90221))
% 157.55/157.22 [9034]~P24(x90344,x90342,f326(f72(x90341,x90342,x90344,x90343),x90345),x90346)+P24(x90341,x90342,x90343,f326(f309(x90344,x90341,x90345),x90346))
% 157.55/157.22 [9733]P105(f326(f61(x97331),x97332))+~P105(f326(f66(x97331,x97333,x97334,x97335,x97332),x97336))
% 157.55/157.22 [9742]~P105(f326(f326(f328(x97424),x97423),f299(x97424,x97425,x97421,x97422,x97426)))+P105(f326(f326(x97421,x97422),x97423))
% 157.55/157.22 [9743]~P105(f326(f326(f328(x97434),x97433),f296(x97434,x97431,x97435,x97432,x97436)))+P105(f326(f326(x97431,x97432),x97433))
% 157.55/157.22 [9744]~P105(f326(f326(f328(x97444),x97442),f299(x97444,x97441,x97445,x97446,x97443)))+P105(f326(f326(x97441,x97442),x97443))
% 157.55/157.22 [9745]~P105(f326(f326(f328(x97454),x97452),f296(x97454,x97455,x97451,x97456,x97453)))+P105(f326(f326(x97451,x97452),x97453))
% 157.55/157.22 [10247]P11(x102471,x102472,x102473,x102474,x102475,x102476)+~E(f326(f326(x102476,f845(x102473,x102476,x102475,x102472,x102474,x102471)),f847(x102473,x102476,x102475,x102472,x102474,x102471)),f326(f326(x102476,f846(x102473,x102476,x102475,x102472,x102474,x102471)),f848(x102473,x102476,x102475,x102472,x102474,x102471)))
% 157.55/157.22 [5926]E(x59261,x59262)+~E(f326(f326(f251(x59263,x59264),x59265),x59261),f326(f326(f251(x59263,x59264),x59266),x59262))
% 157.55/157.22 [5928]E(x59281,x59282)+~E(f326(f326(f251(x59283,x59284),x59281),x59285),f326(f326(f251(x59283,x59284),x59282),x59286))
% 157.55/157.22 [6069]~P15(x60695,x60696,x60691)+E(f326(f326(x60691,x60692),f326(f326(x60691,x60693),x60694)),f326(f326(x60691,x60693),f326(f326(x60691,x60692),x60694)))
% 157.55/157.22 [7505]~P31(x75054,x75051,f326(f326(f151(x75054),x75052),x75055),f326(f326(f151(x75054),x75053),x75056))+P105(f326(f326(x75051,x75052),x75053))
% 157.55/157.22 [7857]P31(x78571,x78572,x78573,x78574)+~P31(x78571,x78572,f326(f326(f151(x78571),x78575),x78573),f326(f326(f151(x78571),x78576),x78574))
% 157.55/157.22 [8880]~P55(x88805,x88801,x88802,x88806,x88804)+P105(f326(f326(f328(x88801),f326(x88802,x88803)),x88804))
% 157.55/157.22 [9082]~E(x90823,f326(f326(f151(x90821),x90825),x90826))+P105(f326(f326(f328(f916(f910(x90821),f910(x90821))),f326(f326(f251(f910(x90821),f910(x90821)),x90822),f326(f326(f134(x90821),x90822),x90823))),f147(x90821,x90824)))
% 157.55/157.22 [9315]~P33(x93151,x93152,x93153,x93155,x93156)+P33(x93151,x93152,x93153,f326(f326(f175(x93151),x93154),x93155),f326(f326(f175(x93152),x93154),x93156))
% 157.55/157.22 [9316]~P33(x93161,x93162,x93163,x93165,x93166)+P33(x93161,x93162,x93163,f326(f326(f138(x93161),x93164),x93165),f326(f326(f138(x93162),x93164),x93166))
% 157.55/157.22 [9570]E(f326(f309(x95701,x95702,f74(x95701,x95702,x95703,x95704,x95705)),x95706),f326(f309(x95701,x95702,x95703),x95706))+P105(f326(f326(f328(x95701),x95704),x95706))
% 157.55/157.22 [9573]E(f326(f326(f154(x95731,x95732),f74(x95731,x95732,x95733,x95734,x95735)),x95736),f326(f326(f154(x95731,x95732),x95733),x95736))+P105(f326(f326(f328(x95731),x95734),f326(f172(x95731),x95736)))
% 157.55/157.22 [9805]~P22(x98054,x98052,x98055,x98053,x98056,x98051)+E(f326(x98051,f188(f917(x98052,a905))),x98053)
% 157.55/157.22 [10039]~E(f326(x100394,f326(f250(x100391,x100393),x100395)),f326(x100396,f326(f250(x100391,x100393),x100395)))+E(f326(f257(x100391,x100392,x100393,x100393,x100394,f31(x100393)),x100395),f326(f257(x100391,x100392,x100393,x100393,x100396,f31(x100393)),x100395))
% 157.55/157.22 [10040]~E(f326(x100404,f326(f255(x100401,x100402),x100405)),f326(x100406,f326(f255(x100401,x100402),x100405)))+E(f326(f257(x100401,x100401,x100402,x100403,f31(x100401),x100404),x100405),f326(f257(x100401,x100401,x100402,x100403,f31(x100401),x100406),x100405))
% 157.55/157.22 [10093]~E(f326(f257(x100932,x100936,x100933,x100933,x100931,f31(x100933)),x100934),f326(f257(x100932,x100936,x100933,x100933,x100935,f31(x100933)),x100934))+E(f326(x100931,f326(f250(x100932,x100933),x100934)),f326(x100935,f326(f250(x100932,x100933),x100934)))
% 157.55/157.22 [10094]~E(f326(f257(x100942,x100942,x100943,x100946,f31(x100942),x100941),x100944),f326(f257(x100942,x100942,x100943,x100946,f31(x100942),x100945),x100944))+E(f326(x100941,f326(f255(x100942,x100943),x100944)),f326(x100945,f326(f255(x100942,x100943),x100944)))
% 157.55/157.22 [8983]P105(f326(f326(f328(x89831),x89832),x89833))+~P105(f326(f326(f328(f916(x89831,x89834)),f326(f326(f251(x89831,x89834),x89832),x89835)),f326(f326(f253(x89831,x89834),x89833),x89836)))
% 157.55/157.22 [8999]P105(f326(f326(f328(x89991),x89992),f326(x89993,x89994)))+~P105(f326(f326(f328(f916(x89995,x89991)),f326(f326(f251(x89995,x89991),x89994),x89992)),f326(f326(f253(x89995,x89991),x89996),x89993)))
% 157.55/157.22 [9429]P105(f326(f326(f328(f916(x94291,x94291)),f326(f326(f251(x94291,x94291),f326(x94292,x94293)),f326(x94292,x94294))),x94295))+~P105(f326(f326(f328(f916(x94296,x94296)),f326(f326(f251(x94296,x94296),x94293),x94294)),f326(f326(f287(x94291,x94296),x94295),x94292)))
% 157.55/157.22 [9449]~P105(f326(f326(f328(f916(x94494,x94494)),f326(f326(f251(x94494,x94494),f326(x94496,x94492)),f326(x94496,x94493))),x94495))+P105(f326(f326(f328(f916(x94491,x94491)),f326(f326(f251(x94491,x94491),x94492),x94493)),f326(f326(f287(x94494,x94491),x94495),x94496)))
% 157.55/157.22 [10096]E(f326(f326(f251(x100961,x100962),f639(x100963,x100964,x100965,x100966,x100962,x100961)),f640(x100963,x100964,x100965,x100966,x100962,x100961)),x100966)+~P105(f326(f326(f328(f916(x100961,x100962)),x100966),f326(f326(f288(x100961,x100965,x100962),x100964),x100963)))
% 157.55/157.22 [10313]~P105(f326(f326(f328(f916(x103131,x103136)),x103135),f326(f326(f288(x103131,x103132,x103136),x103134),x103133)))+P105(f326(f326(f328(f916(x103131,x103132)),f326(f326(f251(x103131,x103132),f639(x103133,x103134,x103132,x103135,x103136,x103131)),f641(x103133,x103134,x103132,x103135,x103136,x103131))),x103134))
% 157.55/157.22 [10314]~P105(f326(f326(f328(f916(x103146,x103142)),x103145),f326(f326(f288(x103146,x103141,x103142),x103144),x103143)))+P105(f326(f326(f328(f916(x103141,x103142)),f326(f326(f251(x103141,x103142),f641(x103143,x103144,x103141,x103145,x103142,x103146)),f640(x103143,x103144,x103141,x103145,x103142,x103146))),x103143))
% 157.55/157.22 [10315]P11(x103151,x103152,x103153,x103154,x103155,x103156)+P105(f326(f326(f328(f916(x103152,x103152)),f326(f326(f251(x103152,x103152),f848(x103153,x103156,x103155,x103152,x103154,x103151)),f847(x103153,x103156,x103155,x103152,x103154,x103151))),x103155))
% 157.55/157.22 [10316]P11(x103161,x103162,x103163,x103164,x103165,x103166)+P105(f326(f326(f328(f916(x103161,x103161)),f326(f326(f251(x103161,x103161),f846(x103163,x103166,x103165,x103162,x103164,x103161)),f845(x103163,x103166,x103165,x103162,x103164,x103161))),x103164))
% 157.55/157.22 [7927]~P4(x79272)+E(f326(f326(f39(x79271,x79272),x79273),f326(f326(f9(x79271,x79274,x79272),x79275),x79276)),f326(f326(f326(f39(x79271,f917(x79274,x79272)),x79273),x79275),x79276))
% 157.55/157.22 [7928]~P4(x79282)+E(f326(f326(f40(x79281,x79282),x79283),f326(f326(f9(x79281,x79284,x79282),x79285),x79286)),f326(f326(f326(f40(x79281,f917(x79284,x79282)),x79283),x79285),x79286))
% 157.55/157.22 [8687]E(f326(f326(f40(x86871,f917(x86872,a905)),x86873),f326(f326(f10(f917(x86872,a905),f917(x86872,a905),x86871),f326(f308(x86872),x86874)),x86875)),f326(f326(f308(x86872),x86874),f326(f326(f40(x86871,f917(x86872,a905)),x86873),x86875)))+~P105(f326(f326(f328(x86871),x86876),x86873))
% 157.55/157.22 [9135]~P4(x91352)+E(f326(f326(f39(x91351,x91352),x91353),f326(f326(f10(f917(x91354,x91352),x91352,x91351),f326(f39(x91354,x91352),x91355)),f326(f9(x91354,x91351,x91352),x91356))),f326(f326(f39(x91354,x91352),x91355),f326(f326(f10(f917(x91351,x91352),x91352,x91354),f326(f39(x91351,x91352),x91353)),x91356)))
% 157.55/157.22 [9136]~P4(x91362)+E(f326(f326(f40(x91361,x91362),x91363),f326(f326(f10(f917(x91364,x91362),x91362,x91361),f326(f40(x91364,x91362),x91365)),f326(f9(x91364,x91361,x91362),x91366))),f326(f326(f40(x91364,x91362),x91365),f326(f326(f10(f917(x91361,x91362),x91362,x91364),f326(f40(x91361,x91362),x91363)),x91366)))
% 157.55/157.22 [9340]P105(f326(f326(f328(x93401),x93402),f326(f172(x93401),x93403)))+~P105(f326(f326(f328(f916(x93404,x93401)),f326(f326(f251(x93404,x93401),x93405),x93402)),f326(f172(f916(x93404,x93401)),f326(f326(f181(x93404,x93401),x93406),x93403))))
% 157.55/157.22 [9341]P105(f326(f326(f328(x93411),x93412),f326(f172(x93411),x93413)))+~P105(f326(f326(f328(f916(x93411,x93414)),f326(f326(f251(x93411,x93414),x93412),x93415)),f326(f172(f916(x93411,x93414)),f326(f326(f181(x93411,x93414),x93413),x93416))))
% 157.55/157.22 [9445]P105(f326(f326(f234(f917(x94451,a905)),f326(f284(x94452,x94451,x94453),x94454)),x94455))+~P105(f326(f326(f234(f917(f916(x94452,x94451),a905)),x94453),f326(f326(f253(x94452,x94451),x94456),f326(f18(f917(x94451,a905),x94452),x94455))))
% 157.55/157.22 [9450]~P25(x94504,x94502,x94505,f241(f917(x94504,a905)),f241(f917(x94502,a905)))+E(f326(f326(f39(x94501,f917(x94502,a905)),x94503),f326(f326(f10(f917(x94504,a905),f917(x94502,a905),x94501),f309(x94504,x94502,x94505)),x94506)),f326(f309(x94504,x94502,x94505),f326(f326(f39(x94501,f917(x94504,a905)),x94503),x94506)))
% 157.55/157.22 [9637]P105(f326(f326(f328(f916(f910(x96371),f910(x96371))),f326(f326(f251(f910(x96371),f910(x96371)),f326(f326(f151(x96371),x96372),x96373)),f326(f326(f151(x96371),x96374),x96375))),f147(x96371,x96376)))+~P105(f326(f326(f328(f916(x96371,x96371)),f326(f326(f251(x96371,x96371),x96372),x96374)),x96376))
% 157.55/157.22 [10092]E(f326(f326(f251(x100921,x100922),f583(x100923,x100924,x100925,x100922,x100921,x100926)),f586(x100923,x100924,x100925,x100922,x100921,x100926)),x100926)+P105(f326(f326(f328(x100925),x100924),f326(f326(f256(x100921,x100922,f917(x100925,a905)),x100923),x100926)))
% 157.55/157.22 [10099]E(f326(f326(f251(x100991,x100992),f584(x100993,x100994,x100992,x100991,x100995,x100996)),f585(x100993,x100994,x100992,x100991,x100995,x100996)),x100993)+~P105(f326(f326(f328(x100996),x100995),f326(f326(f256(x100991,x100992,f917(x100996,a905)),x100994),x100993)))
% 157.55/157.22 [10261]P105(f326(f326(f328(x102611),x102612),f326(f326(x102613,f584(x102614,x102613,x102615,x102616,x102612,x102611)),f585(x102614,x102613,x102615,x102616,x102612,x102611))))+~P105(f326(f326(f328(x102611),x102612),f326(f326(f256(x102616,x102615,f917(x102611,a905)),x102613),x102614)))
% 157.55/157.22 [10286]~P105(f326(f326(f328(x102861),x102862),f326(f326(x102865,f583(x102865,x102862,x102861,x102864,x102863,x102866)),f586(x102865,x102862,x102861,x102864,x102863,x102866))))+P105(f326(f326(f328(x102861),x102862),f326(f326(f256(x102863,x102864,f917(x102861,a905)),x102865),x102866)))
% 157.55/157.22 [8588]E(x85881,x85882)+E(f326(f326(f159(x85883,f326(f326(f159(x85883,x85884),x85881),x85885)),x85882),x85886),f326(f326(f159(x85883,f326(f326(f159(x85883,x85884),x85882),x85886)),x85881),x85885))
% 157.55/157.22 [9697]~P105(f326(f326(f328(x96973),x96976),x96975))+E(f326(f326(f308(x96971),x96972),f326(f309(x96973,x96971,x96974),f326(f326(f3(f917(x96973,a905)),x96975),f326(f326(f308(x96973),x96976),f188(f917(x96973,a905)))))),f326(f309(x96973,x96971,f74(x96973,x96971,x96974,x96976,x96972)),x96975))
% 157.55/157.22 [9214]~P105(f326(f326(x92144,x92145),x92146))+P105(f326(f326(f326(f326(f110(f917(x92141,f917(x92142,a905))),x92143),x92144),x92145),x92146))
% 157.55/157.22 [9216]~P105(f326(f326(x92163,x92165),x92166))+P105(f326(f326(f326(f326(f110(f917(x92161,f917(x92162,a905))),x92163),x92164),x92165),x92166))
% 157.55/157.22 [9500]P105(f326(f326(x95001,x95002),x95003))+~P105(f326(f326(f326(f326(f101(f917(x95004,f917(x95005,a905))),x95006),x95001),x95002),x95003))
% 157.55/157.22 [9501]P105(f326(f326(x95011,x95012),x95013))+~P105(f326(f326(f326(f326(f101(f917(x95014,f917(x95015,a905))),x95011),x95016),x95012),x95013))
% 157.55/157.22 [9931]~P69(x99312)+E(f326(f326(f8(x99311,x99312),f326(f326(f9(x99311,f917(x99313,a905),x99312),f326(f326(f10(f917(x99313,x99312),f917(f917(x99313,a905),x99312),x99311),f8(x99313,x99312)),x99314)),x99315)),x99316),f326(f326(f8(f916(x99311,x99313),x99312),f326(f256(x99311,x99313,x99312),x99314)),f326(f326(f253(x99311,x99313),x99316),f326(f18(f917(x99313,a905),x99311),x99315))))
% 157.55/157.22 [9932]~P74(x99322)+E(f326(f326(f11(x99321,x99322),f326(f326(f9(x99321,f917(x99323,a905),x99322),f326(f326(f10(f917(x99323,x99322),f917(f917(x99323,a905),x99322),x99321),f11(x99323,x99322)),x99324)),x99325)),x99326),f326(f326(f11(f916(x99321,x99323),x99322),f326(f256(x99321,x99323,x99322),x99324)),f326(f326(f253(x99321,x99323),x99326),f326(f18(f917(x99323,a905),x99321),x99325))))
% 157.55/157.22 [10064]~P69(x100642)+E(f326(f326(f8(x100641,x100642),f326(f326(f9(x100641,f917(x100643,a905),x100642),f326(f326(f10(f917(x100643,x100642),f917(f917(x100643,a905),x100642),x100641),f8(x100643,x100642)),f326(f9(x100643,x100641,x100642),x100644))),x100645)),x100646),f326(f326(f8(x100643,x100642),f326(f326(f9(x100643,f917(x100641,a905),x100642),f326(f326(f10(f917(x100641,x100642),f917(f917(x100641,a905),x100642),x100643),f8(x100641,x100642)),x100644)),x100646)),x100645))
% 157.55/157.22 [10380]~P105(f326(f326(f328(f916(x103801,x103802)),f326(f326(f251(x103801,x103802),x103805),x103806)),f326(f326(f110(f917(f916(x103801,x103802),a905)),x103803),x103804)))+P105(f326(f326(f326(f326(f110(f917(x103801,f917(x103802,a905))),f326(f326(f9(x103801,f917(f916(x103801,x103802),a905),f917(x103802,a905)),f326(f326(f10(f917(x103802,f917(f917(f916(x103801,x103802),a905),a905)),f917(f917(f916(x103801,x103802),a905),f917(x103802,a905)),x103801),f9(x103802,f917(f916(x103801,x103802),a905),a905)),f326(f326(f10(f917(x103802,f916(x103801,x103802)),f917(x103802,f917(f917(f916(x103801,x103802),a905),a905)),x103801),f326(f10(f916(x103801,x103802),f917(f917(f916(x103801,x103802),a905),a905),x103802),f328(f916(x103801,x103802)))),f251(x103801,x103802)))),x103803)),f326(f326(f9(x103801,f917(f916(x103801,x103802),a905),f917(x103802,a905)),f326(f326(f10(f917(x103802,f917(f917(f916(x103801,x103802),a905),a905)),f917(f917(f916(x103801,x103802),a905),f917(x103802,a905)),x103801),f9(x103802,f917(f916(x103801,x103802),a905),a905)),f326(f326(f10(f917(x103802,f916(x103801,x103802)),f917(x103802,f917(f917(f916(x103801,x103802),a905),a905)),x103801),f326(f10(f916(x103801,x103802),f917(f917(f916(x103801,x103802),a905),a905),x103802),f328(f916(x103801,x103802)))),f251(x103801,x103802)))),x103804)),x103805),x103806))
% 157.55/157.22 [10381]~P105(f326(f326(f328(f916(x103811,x103812)),f326(f326(f251(x103811,x103812),x103815),x103816)),f326(f326(f101(f917(f916(x103811,x103812),a905)),x103813),x103814)))+P105(f326(f326(f326(f326(f101(f917(x103811,f917(x103812,a905))),f326(f326(f9(x103811,f917(f916(x103811,x103812),a905),f917(x103812,a905)),f326(f326(f10(f917(x103812,f917(f917(f916(x103811,x103812),a905),a905)),f917(f917(f916(x103811,x103812),a905),f917(x103812,a905)),x103811),f9(x103812,f917(f916(x103811,x103812),a905),a905)),f326(f326(f10(f917(x103812,f916(x103811,x103812)),f917(x103812,f917(f917(f916(x103811,x103812),a905),a905)),x103811),f326(f10(f916(x103811,x103812),f917(f917(f916(x103811,x103812),a905),a905),x103812),f328(f916(x103811,x103812)))),f251(x103811,x103812)))),x103813)),f326(f326(f9(x103811,f917(f916(x103811,x103812),a905),f917(x103812,a905)),f326(f326(f10(f917(x103812,f917(f917(f916(x103811,x103812),a905),a905)),f917(f917(f916(x103811,x103812),a905),f917(x103812,a905)),x103811),f9(x103812,f917(f916(x103811,x103812),a905),a905)),f326(f326(f10(f917(x103812,f916(x103811,x103812)),f917(x103812,f917(f917(f916(x103811,x103812),a905),a905)),x103811),f326(f10(f916(x103811,x103812),f917(f917(f916(x103811,x103812),a905),a905),x103812),f328(f916(x103811,x103812)))),f251(x103811,x103812)))),x103814)),x103815),x103816))
% 157.55/157.22 [10390]P105(f326(f326(f328(f916(x103901,x103902)),f326(f326(f251(x103901,x103902),x103903),x103904)),f326(f326(f110(f917(f916(x103901,x103902),a905)),x103905),x103906)))+~P105(f326(f326(f326(f326(f110(f917(x103901,f917(x103902,a905))),f326(f326(f9(x103901,f917(f916(x103901,x103902),a905),f917(x103902,a905)),f326(f326(f10(f917(x103902,f917(f917(f916(x103901,x103902),a905),a905)),f917(f917(f916(x103901,x103902),a905),f917(x103902,a905)),x103901),f9(x103902,f917(f916(x103901,x103902),a905),a905)),f326(f326(f10(f917(x103902,f916(x103901,x103902)),f917(x103902,f917(f917(f916(x103901,x103902),a905),a905)),x103901),f326(f10(f916(x103901,x103902),f917(f917(f916(x103901,x103902),a905),a905),x103902),f328(f916(x103901,x103902)))),f251(x103901,x103902)))),x103905)),f326(f326(f9(x103901,f917(f916(x103901,x103902),a905),f917(x103902,a905)),f326(f326(f10(f917(x103902,f917(f917(f916(x103901,x103902),a905),a905)),f917(f917(f916(x103901,x103902),a905),f917(x103902,a905)),x103901),f9(x103902,f917(f916(x103901,x103902),a905),a905)),f326(f326(f10(f917(x103902,f916(x103901,x103902)),f917(x103902,f917(f917(f916(x103901,x103902),a905),a905)),x103901),f326(f10(f916(x103901,x103902),f917(f917(f916(x103901,x103902),a905),a905),x103902),f328(f916(x103901,x103902)))),f251(x103901,x103902)))),x103906)),x103903),x103904))
% 157.55/157.22 [10391]P105(f326(f326(f328(f916(x103911,x103912)),f326(f326(f251(x103911,x103912),x103913),x103914)),f326(f326(f101(f917(f916(x103911,x103912),a905)),x103915),x103916)))+~P105(f326(f326(f326(f326(f101(f917(x103911,f917(x103912,a905))),f326(f326(f9(x103911,f917(f916(x103911,x103912),a905),f917(x103912,a905)),f326(f326(f10(f917(x103912,f917(f917(f916(x103911,x103912),a905),a905)),f917(f917(f916(x103911,x103912),a905),f917(x103912,a905)),x103911),f9(x103912,f917(f916(x103911,x103912),a905),a905)),f326(f326(f10(f917(x103912,f916(x103911,x103912)),f917(x103912,f917(f917(f916(x103911,x103912),a905),a905)),x103911),f326(f10(f916(x103911,x103912),f917(f917(f916(x103911,x103912),a905),a905),x103912),f328(f916(x103911,x103912)))),f251(x103911,x103912)))),x103915)),f326(f326(f9(x103911,f917(f916(x103911,x103912),a905),f917(x103912,a905)),f326(f326(f10(f917(x103912,f917(f917(f916(x103911,x103912),a905),a905)),f917(f917(f916(x103911,x103912),a905),f917(x103912,a905)),x103911),f9(x103912,f917(f916(x103911,x103912),a905),a905)),f326(f326(f10(f917(x103912,f916(x103911,x103912)),f917(x103912,f917(f917(f916(x103911,x103912),a905),a905)),x103911),f326(f10(f916(x103911,x103912),f917(f917(f916(x103911,x103912),a905),a905),x103912),f328(f916(x103911,x103912)))),f251(x103911,x103912)))),x103916)),x103913),x103914))
% 157.55/157.22 [10374]~P105(f326(f326(f328(f916(x103742,x103743)),f326(f326(f251(x103742,x103743),x103745),x103746)),f326(f326(f39(x103741,f917(f916(x103742,x103743),a905)),f241(f917(x103741,a905))),x103744)))+P105(f326(f326(f326(f326(f39(x103741,f917(x103742,f917(x103743,a905))),f241(f917(x103741,a905))),f326(f326(f10(f917(f916(x103742,x103743),a905),f917(x103742,f917(x103743,a905)),x103741),f326(f9(x103742,f917(f916(x103742,x103743),a905),f917(x103743,a905)),f326(f326(f10(f917(x103743,f917(f917(f916(x103742,x103743),a905),a905)),f917(f917(f916(x103742,x103743),a905),f917(x103743,a905)),x103742),f9(x103743,f917(f916(x103742,x103743),a905),a905)),f326(f326(f10(f917(x103743,f916(x103742,x103743)),f917(x103743,f917(f917(f916(x103742,x103743),a905),a905)),x103742),f326(f10(f916(x103742,x103743),f917(f917(f916(x103742,x103743),a905),a905),x103743),f328(f916(x103742,x103743)))),f251(x103742,x103743))))),x103744)),x103745),x103746))
% 157.55/157.22 [10375]~P105(f326(f326(f328(f916(x103752,x103753)),f326(f326(f251(x103752,x103753),x103755),x103756)),f326(f326(f40(x103751,f917(f916(x103752,x103753),a905)),f241(f917(x103751,a905))),x103754)))+P105(f326(f326(f326(f326(f40(x103751,f917(x103752,f917(x103753,a905))),f241(f917(x103751,a905))),f326(f326(f10(f917(f916(x103752,x103753),a905),f917(x103752,f917(x103753,a905)),x103751),f326(f9(x103752,f917(f916(x103752,x103753),a905),f917(x103753,a905)),f326(f326(f10(f917(x103753,f917(f917(f916(x103752,x103753),a905),a905)),f917(f917(f916(x103752,x103753),a905),f917(x103753,a905)),x103752),f9(x103753,f917(f916(x103752,x103753),a905),a905)),f326(f326(f10(f917(x103753,f916(x103752,x103753)),f917(x103753,f917(f917(f916(x103752,x103753),a905),a905)),x103752),f326(f10(f916(x103752,x103753),f917(f917(f916(x103752,x103753),a905),a905),x103753),f328(f916(x103752,x103753)))),f251(x103752,x103753))))),x103754)),x103755),x103756))
% 157.55/157.22 [10384]P105(f326(f326(f328(f916(x103841,x103842)),f326(f326(f251(x103841,x103842),x103843),x103844)),f326(f326(f39(x103845,f917(f916(x103841,x103842),a905)),f241(f917(x103845,a905))),x103846)))+~P105(f326(f326(f326(f326(f39(x103845,f917(x103841,f917(x103842,a905))),f241(f917(x103845,a905))),f326(f326(f10(f917(f916(x103841,x103842),a905),f917(x103841,f917(x103842,a905)),x103845),f326(f9(x103841,f917(f916(x103841,x103842),a905),f917(x103842,a905)),f326(f326(f10(f917(x103842,f917(f917(f916(x103841,x103842),a905),a905)),f917(f917(f916(x103841,x103842),a905),f917(x103842,a905)),x103841),f9(x103842,f917(f916(x103841,x103842),a905),a905)),f326(f326(f10(f917(x103842,f916(x103841,x103842)),f917(x103842,f917(f917(f916(x103841,x103842),a905),a905)),x103841),f326(f10(f916(x103841,x103842),f917(f917(f916(x103841,x103842),a905),a905),x103842),f328(f916(x103841,x103842)))),f251(x103841,x103842))))),x103846)),x103843),x103844))
% 157.55/157.22 [10385]P105(f326(f326(f328(f916(x103851,x103852)),f326(f326(f251(x103851,x103852),x103853),x103854)),f326(f326(f40(x103855,f917(f916(x103851,x103852),a905)),f241(f917(x103855,a905))),x103856)))+~P105(f326(f326(f326(f326(f40(x103855,f917(x103851,f917(x103852,a905))),f241(f917(x103855,a905))),f326(f326(f10(f917(f916(x103851,x103852),a905),f917(x103851,f917(x103852,a905)),x103855),f326(f9(x103851,f917(f916(x103851,x103852),a905),f917(x103852,a905)),f326(f326(f10(f917(x103852,f917(f917(f916(x103851,x103852),a905),a905)),f917(f917(f916(x103851,x103852),a905),f917(x103852,a905)),x103851),f9(x103852,f917(f916(x103851,x103852),a905),a905)),f326(f326(f10(f917(x103852,f916(x103851,x103852)),f917(x103852,f917(f917(f916(x103851,x103852),a905),a905)),x103851),f326(f10(f916(x103851,x103852),f917(f917(f916(x103851,x103852),a905),a905),x103852),f328(f916(x103851,x103852)))),f251(x103851,x103852))))),x103856)),x103853),x103854))
% 157.55/157.22 [7436]E(x74361,x74362)+~E(f91(x74363,x74364,x74365,x74361),f91(x74363,x74366,x74367,x74362))
% 157.55/157.22 [7437]E(x74371,x74372)+~E(f91(x74373,x74374,x74371,x74375),f91(x74373,x74376,x74372,x74377))
% 157.55/157.22 [7438]E(x74381,x74382)+~E(f91(x74383,x74381,x74384,x74385),f91(x74383,x74382,x74386,x74387))
% 157.55/157.22 [7609]E(f326(x76091,f326(x76092,x76093)),f326(x76094,x76093))+~E(f326(f72(x76095,x76096,x76097,x76091),x76092),x76094)
% 157.55/157.22 [9713]E(x97131,x97132)+E(f74(x97133,x97134,f74(x97133,x97134,x97135,x97131,x97136),x97132,x97137),f74(x97133,x97134,f74(x97133,x97134,x97135,x97132,x97137),x97131,x97136))
% 157.55/157.22 [9804]~P21(x98043,x98044,x98041,x98045,x98046,x98047)+E(f326(f326(x98041,x98042),x98042),x98042)
% 157.55/157.22 [6170]~E(f326(f326(f154(x61701,x61705),x61706),x61702),f326(f326(f154(x61703,x61705),x61707),x61704))+E(f326(f189(f910(x61701)),x61702),f326(f189(f910(x61703)),x61704))
% 157.55/157.22 [8619]E(f326(x86191,f326(x86192,x86193)),f326(x86194,x86193))+~E(f326(f72(x86195,x86196,x86197,x86191),x86192),f326(f72(x86196,x86196,x86197,f31(x86196)),x86194))
% 157.55/157.22 [8972]~P33(x89724,x89725,x89721,f326(f326(f151(x89724),x89722),x89726),f326(f326(f151(x89725),x89723),x89727))+P105(f326(f326(x89721,x89722),x89723))
% 157.55/157.22 [9347]P33(x93471,x93472,x93473,x93474,x93475)+~P33(x93471,x93472,x93473,f326(f326(f151(x93471),x93476),x93474),f326(f326(f151(x93472),x93477),x93475))
% 157.55/157.22 [9964]P105(f326(f326(x99641,x99642),f558(x99643,x99642,x99644,x99641)))+~P105(f326(f326(f252(x99645,x99646,x99647,x99641,x99644),x99642),x99643))
% 157.55/157.22 [9988]P105(f326(f326(x99881,f558(x99882,x99883,x99881,x99884)),x99882))+~P105(f326(f326(f252(x99885,x99886,x99887,x99884,x99881),x99883),x99882))
% 157.55/157.22 [9089]~P19(x90896,x90891,x90893,x90897)+E(f326(f72(x90891,x90891,x90892,f326(x90893,x90894)),f326(f72(x90891,x90891,x90892,f326(x90893,x90894)),x90895)),f326(f72(x90891,x90891,x90892,f326(x90893,x90894)),x90895))
% 157.55/157.22 [9453]~P33(x94533,x94532,x94534,f326(f326(f154(x94531,x94533),x94535),x94536),x94537)+P33(x94531,x94532,f326(f326(f10(x94533,f917(x94532,a905),x94531),x94534),x94535),x94536,x94537)
% 157.55/157.22 [9476]P33(x94761,x94762,x94763,f326(f326(f154(x94764,x94761),x94765),x94766),x94767)+~P33(x94764,x94762,f326(f326(f10(x94761,f917(x94762,a905),x94764),x94763),x94765),x94766,x94767)
% 157.55/157.22 [9088]~P105(f326(f326(f328(x90881),x90882),f326(f326(x90885,x90886),x90887)))+P105(f326(f326(f328(x90881),x90882),f326(f326(f256(x90883,x90884,f917(x90881,a905)),x90885),f326(f326(f251(x90883,x90884),x90886),x90887))))
% 157.55/157.22 [9370]P105(f326(f326(f326(x93701,x93702),x93703),x93704))+~P105(f326(f326(f326(f256(x93705,x93706,f917(x93707,a905)),x93701),f326(f326(f251(x93705,x93706),x93702),x93703)),x93704))
% 157.55/157.22 [9515]P105(f326(f326(f328(x95151),f326(f326(x95152,x95153),x95154)),f326(f309(f916(x95155,x95156),x95151,f326(f256(x95155,x95156,x95151),x95152)),x95157)))+~P105(f326(f326(f328(f916(x95155,x95156)),f326(f326(f251(x95155,x95156),x95153),x95154)),x95157))
% 157.55/157.22 [9852]P105(f326(f326(f328(f916(f910(x98521),f910(x98521))),f326(f326(f251(f910(x98521),f910(x98521)),f326(f326(f134(x98521),x98522),f326(f326(f151(x98521),x98523),x98524))),f326(f326(f134(x98521),x98522),f326(f326(f151(x98521),x98525),x98526)))),f147(x98521,x98527)))+~P105(f326(f326(f328(f916(x98521,x98521)),f326(f326(f251(x98521,x98521),x98523),x98525)),x98527))
% 157.55/157.22 [9916]~P33(x99161,x99163,x99164,x99166,f326(f326(f154(x99162,x99163),x99165),x99167))+P33(x99161,x99162,f326(f326(f9(x99161,f917(x99162,x99163),f917(x99162,a905)),f326(f326(f10(f917(x99163,a905),f917(f917(x99162,x99163),f917(x99162,a905)),x99161),f10(x99163,a905,x99162)),x99164)),x99165),x99166,x99167)
% 157.55/157.22 [9992]P33(x99921,x99922,x99923,x99924,f326(f326(f154(x99925,x99922),x99926),x99927))+~P33(x99921,x99925,f326(f326(f9(x99921,f917(x99925,x99922),f917(x99925,a905)),f326(f326(f10(f917(x99922,a905),f917(f917(x99925,x99922),f917(x99925,a905)),x99921),f10(x99922,a905,x99925)),x99923)),x99926),x99924,x99927)
% 157.55/157.22 [10300]P105(f326(f326(f328(x103001),f429(x103002,x103003,x103004,x103005,x103006,x103007,x103001)),x103005))+P105(f326(f326(f326(f326(f39(x103001,f917(x103007,f917(x103006,a905))),x103005),x103004),x103003),x103002))
% 157.55/157.22 [10301]P105(f326(f326(f328(x103011),f779(x103012,x103013,x103014,x103015,x103016,x103017,x103011)),x103017))+P105(f326(f326(f326(f326(f39(x103011,f917(x103013,f917(x103012,a905))),x103017),x103016),x103015),x103014))
% 157.55/157.22 [10302]P105(f326(f326(f328(x103021),f472(x103022,x103023,x103024,x103025,x103026,x103027,x103021)),x103025))+~P105(f326(f326(f326(f326(f40(x103021,f917(x103027,f917(x103026,a905))),x103025),x103024),x103023),x103022))
% 157.55/157.22 [10303]P105(f326(f326(f328(x103031),f781(x103032,x103033,x103034,x103035,x103036,x103037,x103031)),x103035))+~P105(f326(f326(f326(f326(f40(x103031,f917(x103037,f917(x103036,a905))),x103035),x103034),x103033),x103032))
% 157.55/157.22 [10338]P105(f326(f326(f326(x103381,f472(x103382,x103383,x103381,x103384,x103385,x103386,x103387)),x103383),x103382))+~P105(f326(f326(f326(f326(f40(x103387,f917(x103386,f917(x103385,a905))),x103384),x103381),x103383),x103382))
% 157.55/157.22 [10339]P105(f326(f326(f326(x103391,f781(x103392,x103393,x103391,x103394,x103395,x103396,x103397)),x103393),x103392))+~P105(f326(f326(f326(f326(f40(x103397,f917(x103396,f917(x103395,a905))),x103394),x103391),x103393),x103392))
% 157.55/157.22 [10355]~P105(f326(f326(f326(x103555,f429(x103557,x103556,x103555,x103554,x103553,x103552,x103551)),x103556),x103557))+P105(f326(f326(f326(f326(f39(x103551,f917(x103552,f917(x103553,a905))),x103554),x103555),x103556),x103557))
% 157.55/157.22 [10356]~P105(f326(f326(f326(x103565,f779(x103563,x103562,x103567,x103566,x103565,x103564,x103561)),x103566),x103567))+P105(f326(f326(f326(f326(f39(x103561,f917(x103562,f917(x103563,a905))),x103564),x103565),x103566),x103567))
% 157.55/157.22 [10373]~P105(f326(f326(f328(f916(x103731,x103733)),f326(f326(f251(x103731,x103733),x103736),x103737)),f326(f326(f288(x103731,x103732,x103733),x103734),x103735)))+P105(f326(f326(f252(x103731,x103732,x103733,f326(f326(f9(x103731,f917(f916(x103731,x103732),a905),f917(x103732,a905)),f326(f326(f10(f917(x103732,f917(f917(f916(x103731,x103732),a905),a905)),f917(f917(f916(x103731,x103732),a905),f917(x103732,a905)),x103731),f9(x103732,f917(f916(x103731,x103732),a905),a905)),f326(f326(f10(f917(x103732,f916(x103731,x103732)),f917(x103732,f917(f917(f916(x103731,x103732),a905),a905)),x103731),f326(f10(f916(x103731,x103732),f917(f917(f916(x103731,x103732),a905),a905),x103732),f328(f916(x103731,x103732)))),f251(x103731,x103732)))),x103734),f326(f326(f9(x103732,f917(f916(x103732,x103733),a905),f917(x103733,a905)),f326(f326(f10(f917(x103733,f917(f917(f916(x103732,x103733),a905),a905)),f917(f917(f916(x103732,x103733),a905),f917(x103733,a905)),x103732),f9(x103733,f917(f916(x103732,x103733),a905),a905)),f326(f326(f10(f917(x103733,f916(x103732,x103733)),f917(x103733,f917(f917(f916(x103732,x103733),a905),a905)),x103732),f326(f10(f916(x103732,x103733),f917(f917(f916(x103732,x103733),a905),a905),x103733),f328(f916(x103732,x103733)))),f251(x103732,x103733)))),x103735)),x103736),x103737))
% 157.55/157.22 [10383]P105(f326(f326(f328(f916(x103831,x103832)),f326(f326(f251(x103831,x103832),x103833),x103834)),f326(f326(f288(x103831,x103835,x103832),x103836),x103837)))+~P105(f326(f326(f252(x103831,x103835,x103832,f326(f326(f9(x103831,f917(f916(x103831,x103835),a905),f917(x103835,a905)),f326(f326(f10(f917(x103835,f917(f917(f916(x103831,x103835),a905),a905)),f917(f917(f916(x103831,x103835),a905),f917(x103835,a905)),x103831),f9(x103835,f917(f916(x103831,x103835),a905),a905)),f326(f326(f10(f917(x103835,f916(x103831,x103835)),f917(x103835,f917(f917(f916(x103831,x103835),a905),a905)),x103831),f326(f10(f916(x103831,x103835),f917(f917(f916(x103831,x103835),a905),a905),x103835),f328(f916(x103831,x103835)))),f251(x103831,x103835)))),x103836),f326(f326(f9(x103835,f917(f916(x103835,x103832),a905),f917(x103832,a905)),f326(f326(f10(f917(x103832,f917(f917(f916(x103835,x103832),a905),a905)),f917(f917(f916(x103835,x103832),a905),f917(x103832,a905)),x103835),f9(x103832,f917(f916(x103835,x103832),a905),a905)),f326(f326(f10(f917(x103832,f916(x103835,x103832)),f917(x103832,f917(f917(f916(x103835,x103832),a905),a905)),x103835),f326(f10(f916(x103835,x103832),f917(f917(f916(x103835,x103832),a905),a905),x103832),f328(f916(x103835,x103832)))),f251(x103835,x103832)))),x103837)),x103833),x103834))
% 157.55/157.22 [10312]~P144(x103122)+E(f326(f326(f8(x103121,x103122),f326(f326(f9(x103121,f917(x103123,a905),x103122),f326(f326(f10(f917(x103123,x103122),f917(f917(x103123,a905),x103122),x103121),f8(x103123,x103122)),f326(f326(f9(x103121,f917(x103123,x103122),f917(x103123,x103122)),f326(f326(f10(f917(x103122,x103122),f917(f917(x103123,x103122),f917(x103123,x103122)),x103121),f10(x103122,x103122,x103123)),f326(f326(f10(x103122,f917(x103122,x103122),x103121),f80(x103122)),x103124))),x103125))),x103126)),x103127),f326(f326(f80(x103122),f326(f326(f8(x103121,x103122),x103124),x103127)),f326(f326(f8(x103123,x103122),x103125),x103126)))
% 157.55/157.22 [9402]~P18(x94027,x94021,x94023,x94028)+E(f326(f72(x94021,x94021,x94022,f326(x94023,x94024)),f326(f72(x94021,x94021,x94022,f326(x94023,x94025)),x94026)),f326(f72(x94021,x94021,x94022,f326(x94023,x94025)),f326(f72(x94021,x94021,x94022,f326(x94023,x94024)),x94026)))
% 157.55/157.22 [10378]E(f326(f326(f251(x103781,x103782),f326(x103783,f541(x103784,x103785,x103783,x103786,x103787,x103788,x103782,x103781))),f326(x103785,f542(x103784,x103785,x103783,x103786,x103787,x103788,x103782,x103781))),x103788)+~P105(f326(f326(f328(f916(x103781,x103782)),x103788),f326(f309(f916(x103787,x103786),f916(x103781,x103782),f257(x103787,x103781,x103786,x103782,x103783,x103785)),x103784)))
% 157.55/157.22 [10396]~P105(f326(f326(f328(f916(x103968,x103967)),x103966),f326(f309(f916(x103961,x103962),f916(x103968,x103967),f257(x103961,x103968,x103962,x103967,x103965,x103964)),x103963)))+P105(f326(f326(f328(f916(x103961,x103962)),f326(f326(f251(x103961,x103962),f541(x103963,x103964,x103965,x103962,x103961,x103966,x103967,x103968)),f542(x103963,x103964,x103965,x103962,x103961,x103966,x103967,x103968))),x103963))
% 157.55/157.22 [9842]P105(f326(f326(f328(f916(f916(x98421,x98422),f916(x98421,x98422))),f326(f326(f251(f916(x98421,x98422),f916(x98421,x98422)),f326(f326(f251(x98421,x98422),x98423),x98424)),f326(f326(f251(x98421,x98422),x98425),x98426))),f319(x98421,x98422,x98427,x98428)))+~P105(f326(f326(f328(f916(x98421,x98421)),f326(f326(f251(x98421,x98421),x98423),x98425)),x98427))
% 157.55/157.22 [10367]E(f326(f142(x103671,x103672,f326(f9(x103672,x103671,x103671),x103673),f326(x103674,x103675)),x103676),f326(x103674,f326(f142(x103677,x103672,f326(f9(x103672,x103677,x103677),x103678),x103675),x103676)))+P105(f326(f326(f328(x103672),f727(x103675,x103678,x103674,x103673,x103677,x103671,x103676,x103672)),f326(f172(x103672),x103676)))
% 157.55/157.22 [10386]~E(f326(f72(x103861,x103861,x103867,f326(x103863,f727(x103865,x103868,x103864,x103863,x103867,x103861,x103866,x103862))),x103864),f326(f72(x103867,x103861,x103867,x103864),f326(x103868,f727(x103865,x103868,x103864,x103863,x103867,x103861,x103866,x103862))))+E(f326(f142(x103861,x103862,f326(f9(x103862,x103861,x103861),x103863),f326(x103864,x103865)),x103866),f326(x103864,f326(f142(x103867,x103862,f326(f9(x103862,x103867,x103867),x103868),x103865),x103866)))
% 157.55/157.22 [8624]E(f326(x86241,f326(x86242,x86243)),f326(x86244,f326(x86245,x86243)))+~E(f326(f72(x86246,x86247,x86248,x86241),x86242),f326(f72(x86249,x86247,x86248,x86244),x86245))
% 157.55/157.22 [10226]P105(f326(f326(f328(f916(x102261,x102262)),f326(f326(f251(x102261,x102262),f326(x102263,x102264)),f326(x102265,x102266))),f326(f309(f916(x102267,x102268),f916(x102261,x102262),f257(x102267,x102261,x102268,x102262,x102263,x102265)),x102269)))+~P105(f326(f326(f328(f916(x102267,x102268)),f326(f326(f251(x102267,x102268),x102264),x102266)),x102269))
% 157.55/157.22 [8918]~E(f326(x89184,f326(x89185,x89186)),f326(x89189,f326(x891810,x891811)))+E(f326(f326(f72(x89181,x89182,x89183,x89184),x89185),x89186),f326(f326(f72(x89187,x89182,x89188,x89189),x891810),x891811))
% 157.55/157.22 [4723]~P108(x47231)+~P101(x47231)+E(f101(x47231),f232(x47231))
% 157.55/157.22 [4724]~P108(x47241)+~P100(x47241)+E(f110(x47241),f233(x47241))
% 157.55/157.22 [4973]~P118(x49731)+~P94(x49731)+E(f326(f75(x49731),f326(f103(x49731),a97)),f77(x49731))
% 157.55/157.22 [5266]E(x52661,f2(a1))+E(f81(a1,x52661),f326(f78(a1),f77(a1)))+P105(f326(f326(f235(a1),f2(a1)),x52661))
% 157.55/157.22 [5477]E(x54771,f2(a1))+E(f81(a1,x54771),f77(a1))+~P105(f326(f326(f235(a1),f2(a1)),x54771))
% 157.55/157.22 [7509]~P39(x75091)+P105(f326(f61(a1),x75091))+~P105(f326(f61(a909),f326(f309(a1,a909,a104),x75091)))
% 157.55/157.22 [9803]E(x98031,f188(f917(f916(a909,a909),a905)))+~P105(f326(f61(f916(a909,a909)),x98031))+P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),f188(f917(f916(a909,a909),a905))),x98031)),a34))
% 157.55/157.22 [9965]E(x99651,f2(a909))+E(x99651,f326(a112,f2(a909)))+~P105(f326(f326(f235(a909),x99651),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.55/157.22 [10256]E(x102561,f2(a99))+E(f326(f326(f79(a1),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(a24,f326(f326(f36(a99),x102561),f326(f103(a99),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))),f77(a1)),f326(a24,x102561))+E(f45(a99,x102561,f326(f103(a99),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f2(a99))
% 157.55/157.22 [10103]E(x101031,f2(a99))+~E(f45(a99,x101031,f326(f103(a99),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f2(a99))+E(f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(a24,f326(f326(f36(a99),x101031),f326(f103(a99),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))),f326(a24,x101031))
% 157.55/157.22 [4804]~P56(x48041,x48042)+P43(x48041,x48042)+~P44(a905)
% 157.55/157.22 [4733]~P143(x47331)+P27(x47331,x47332)+~E(x47332,f2(x47331))
% 157.55/157.22 [4734]~P108(x47341)+P12(x47341,x47342)+~E(x47342,f113(x47341))
% 157.55/157.22 [4743]~P118(x47431)+~E(x47432,f2(x47431))+E(f81(x47431,x47432),f2(x47431))
% 157.55/157.22 [4744]~P90(x47441)+~E(x47442,f2(x47441))+E(f81(x47441,x47442),f2(x47441))
% 157.55/157.22 [4752]~P143(x47522)+~P27(x47522,x47521)+E(x47521,f2(x47522))
% 157.55/157.22 [4797]~P118(x47972)+~E(f81(x47972,x47971),f2(x47972))+E(x47971,f2(x47972))
% 157.55/157.22 [4811]~P3(x48112)+~P3(x48111)+P3(f917(x48111,x48112))
% 157.55/157.22 [4812]~P3(x48122)+~P3(x48121)+P3(f915(x48121,x48122))
% 157.55/157.22 [4813]~P3(x48132)+~P3(x48131)+P3(f916(x48131,x48132))
% 157.55/157.22 [4814]~P5(x48142)+~P5(x48141)+P5(f194(x48141,x48142))
% 157.55/157.22 [4815]~P61(x48152)+~P61(x48151)+P61(f917(x48151,x48152))
% 157.55/157.22 [4816]~P61(x48162)+~P61(x48161)+P61(f915(x48161,x48162))
% 157.55/157.22 [4817]~P61(x48172)+~P61(x48171)+P61(f916(x48171,x48172))
% 157.55/157.22 [4818]~P103(x48182)+~P103(x48181)+P103(f916(x48181,x48182))
% 157.55/157.22 [4945]~P108(x49451)+~P12(x49451,x49452)+P12(x49451,f152(x49451,x49452))
% 157.55/157.22 [5193]~P5(x51932)+~P5(x51931)+P5(f45(a1,x51931,x51932))
% 157.55/157.22 [4754]~P75(x47541)+~E(x47542,f2(x47541))+E(f326(f78(x47541),x47542),x47542)
% 157.55/157.22 [4769]~P140(x47691)+~E(x47692,f2(a1))+E(f326(f102(x47691),x47692),f2(x47691))
% 157.55/157.22 [4770]~P92(x47701)+~E(x47702,f2(a1))+E(f326(f102(x47701),x47702),f2(x47701))
% 157.55/157.22 [4794]~P73(x47941)+~E(f2(x47941),x47942)+E(f326(f78(x47941),x47942),f2(x47941))
% 157.55/157.22 [4795]~P86(x47951)+~E(x47952,f2(x47951))+E(f326(f75(x47951),x47952),f2(x47951))
% 157.55/157.22 [4796]~P73(x47961)+~E(x47962,f2(x47961))+E(f326(f78(x47961),x47962),f2(x47961))
% 157.55/157.22 [4820]~P75(x48202)+E(x48201,f2(x48202))+~E(f326(f78(x48202),x48201),x48201)
% 157.55/157.22 [4826]E(x48261,f326(a104,x48262))+~E(x48261,f2(a909))+~E(x48262,f326(f100(a1),x48261))
% 157.55/157.22 [4827]E(f326(a104,x48271),x48272)+~E(x48272,f2(a909))+~E(x48271,f326(f100(a1),x48272))
% 157.55/157.22 [4831]~P92(x48312)+E(x48311,f2(a1))+~E(f326(f102(x48312),x48311),f2(x48312))
% 157.55/157.22 [4835]~P86(x48352)+E(x48351,f2(x48352))+~E(f326(f75(x48352),x48351),f2(x48352))
% 157.55/157.22 [4836]~P73(x48362)+E(x48361,f2(x48362))+~E(f326(f78(x48362),x48361),f2(x48362))
% 157.55/157.22 [4837]~P73(x48371)+E(f2(x48371),x48372)+~E(f326(f78(x48371),x48372),f2(x48371))
% 157.55/157.22 [5020]~P108(x50201)+~P12(x50201,x50202)+P12(x50201,f326(f171(x50201),x50202))
% 157.55/157.22 [5047]~P105(x50472)+~P105(x50471)+P105(f326(f326(a324,x50471),x50472))
% 157.55/157.22 [5085]~E(f77(a909),f2(a909))+E(f326(f35(x50851),x50852),f2(a909))+~P105(f326(f61(x50851),x50852))
% 157.55/157.22 [5121]~P115(x51211)+~P144(x51211)+E(f326(f326(f243(x51211),f2(x51211)),f326(a112,x51212)),f2(x51211))
% 157.55/157.22 [5161]~P108(x51611)+P12(x51611,f139(x51611,x51612))+~P105(f326(f61(x51611),x51612))
% 157.55/157.22 [5162]~P108(x51621)+P12(x51621,f719(x51622,x51621))+~P105(f326(f61(x51621),x51622))
% 157.55/157.22 [5185]~P108(x51851)+E(f326(f172(x51851),f139(x51851,x51852)),x51852)+~P105(f326(f61(x51851),x51852))
% 157.55/157.22 [5186]~P108(x51861)+E(f326(f172(x51861),f719(x51862,x51861)),x51862)+~P105(f326(f61(x51861),x51862))
% 157.55/157.22 [5215]P105(x52151)+P105(x52152)+~P105(f326(f326(a325,x52152),x52151))
% 157.55/157.22 [5228]E(x52281,f188(f917(x52282,a905)))+~E(f326(f35(x52282),x52281),f2(a909))+~P105(f326(f61(x52282),x52281))
% 157.55/157.22 [5233]P105(x52331)+~P105(x52332)+~P105(f326(f326(a329,x52332),x52331))
% 157.55/157.22 [5284]~P72(x52841)+E(f326(f75(x52841),x52842),x52842)+P105(f326(f326(f235(x52841),x52842),f2(x52841)))
% 157.55/157.22 [5344]~P61(x53442)+~P105(f326(f56(x53442),x53441))+P105(f326(x53441,f720(x53441,x53442)))
% 157.55/157.22 [5345]~P61(x53452)+~P105(f326(f56(x53452),x53451))+P105(f326(x53451,f728(x53451,x53452)))
% 157.55/157.22 [5387]E(x53871,f113(x53872))+P105(f326(f137(x53872),f114(x53872,x53871)))+~P105(f326(f137(x53872),x53871))
% 157.55/157.22 [5392]~P108(x53921)+~P105(f326(f61(x53921),x53922))+P105(f326(f137(x53921),f139(x53921,x53922)))
% 157.55/157.22 [5393]~P108(x53931)+~P105(f326(f61(x53931),x53932))+P105(f326(f137(x53931),f719(x53932,x53931)))
% 157.55/157.22 [5398]~P140(x53981)+E(f326(f100(x53981),f326(a104,x53982)),f326(f102(x53981),x53982))+P105(f326(f326(f235(a1),x53982),f2(a1)))
% 157.55/157.22 [5425]P6(x54252,x54251)+E(f326(x54251,f501(x54251)),f326(x54251,f504(x54251)))+P105(f326(f326(x54251,f501(x54251)),f504(x54251)))
% 157.55/157.22 [5438]E(f326(f100(a1),f370(x54381,x54382)),x54381)+P105(f326(x54382,f326(a104,x54381)))+~P105(f326(x54382,f2(a909)))
% 157.55/157.22 [5451]~P61(x54511)+~P105(f326(x54512,f734(x54512,x54511)))+P105(f326(f57(x54511),x54512))
% 157.55/157.22 [5452]~P61(x54521)+~P105(f326(x54522,f743(x54522,x54521)))+P105(f326(f57(x54521),x54522))
% 157.55/157.22 [5487]~P118(x54871)+~E(f81(x54871,x54872),f326(f78(x54871),f77(x54871)))+P105(f326(f326(f235(x54871),x54872),f2(x54871)))
% 157.55/157.22 [5562]~E(x55622,f2(a1))+E(f215(x55621,x55622),f326(f326(f251(a1,a1),f2(a1)),f77(a1)))+P105(f326(f326(f235(a1),x55622),f2(a1)))
% 157.55/157.22 [5563]~E(x55631,f2(a1))+E(f215(x55631,x55632),f326(f326(f251(a1,a1),f2(a1)),f77(a1)))+P105(f326(f326(f235(a1),x55632),f2(a1)))
% 157.55/157.22 [5616]E(f326(f100(a1),f370(x56161,x56162)),x56161)+P105(f326(x56162,f326(a104,x56161)))+P105(f326(f326(f235(a1),x56161),f2(a1)))
% 157.55/157.22 [5685]~P118(x56851)+E(f81(x56851,x56852),f326(f78(x56851),f77(x56851)))+~P105(f326(f326(f235(x56851),x56852),f2(x56851)))
% 157.55/157.22 [5686]~P86(x56861)+E(f326(f75(x56861),x56862),f326(f78(x56861),x56862))+~P105(f326(f326(f234(x56861),x56862),f2(x56861)))
% 157.55/157.22 [5687]~P86(x56871)+E(f326(f75(x56871),x56872),f326(f78(x56871),x56872))+~P105(f326(f326(f235(x56871),x56872),f2(x56871)))
% 157.55/157.22 [5688]~P72(x56881)+E(f326(f75(x56881),x56882),f326(f78(x56881),x56882))+~P105(f326(f326(f235(x56881),x56882),f2(x56881)))
% 157.55/157.22 [5789]~P105(f326(x57891,f370(x57892,x57891)))+P105(f326(x57891,f326(a104,x57892)))+~P105(f326(x57891,f2(a909)))
% 157.55/157.22 [5796]E(x57961,f2(a909))+E(f326(a112,f814(x57962,x57961)),x57961)+~P105(f326(f326(f235(a909),x57961),f326(a112,x57962)))
% 157.55/157.22 [5800]P6(x58001,x58002)+~E(f326(x58002,f501(x58002)),f326(x58002,f504(x58002)))+~P105(f326(f326(x58002,f501(x58002)),f504(x58002)))
% 157.55/157.22 [5818]~P108(x58181)+P12(x58181,x58182)+P105(f326(f326(f234(a909),f703(x58182,x58181)),f704(x58182,x58181)))
% 157.55/157.22 [5819]~P108(x58191)+P12(x58191,x58192)+P105(f326(f326(f234(a909),f711(x58192,x58191)),f715(x58192,x58191)))
% 157.55/157.22 [5905]~P86(x59051)+~E(x59052,f2(x59051))+P105(f326(f326(f234(x59051),f326(f75(x59051),x59052)),f2(x59051)))
% 157.55/157.22 [6002]~P105(f326(x60021,f370(x60022,x60021)))+P105(f326(x60021,f326(a104,x60022)))+P105(f326(f326(f235(a1),x60022),f2(a1)))
% 157.55/157.22 [6027]~P105(f326(x60271,f326(a104,x60272)))+P105(f326(x60271,f2(a909)))+~P105(f326(f326(f235(a1),x60272),f2(a1)))
% 157.55/157.22 [6370]~P118(x63701)+~P105(f326(f326(f235(x63701),x63702),f2(x63701)))+P105(f326(f326(f235(x63701),f81(x63701,x63702)),f2(x63701)))
% 157.55/157.22 [6485]~P118(x64851)+P105(f326(f326(f234(x64851),f326(f102(x64851),x64852)),f2(x64851)))+~P105(f326(f326(f234(a1),x64852),f2(a1)))
% 157.55/157.22 [6486]~P118(x64861)+P105(f326(f326(f235(x64861),f326(f102(x64861),x64862)),f2(x64861)))+~P105(f326(f326(f235(a1),x64862),f2(a1)))
% 157.55/157.22 [6495]~P86(x64952)+E(x64951,f2(x64952))+~P105(f326(f326(f234(x64952),f326(f75(x64952),x64951)),f2(x64952)))
% 157.55/157.22 [6571]~P140(x65711)+~P105(f326(f326(f328(x65711),x65712),f109(x65711)))+P105(f326(f326(f328(x65711),f326(f78(x65711),x65712)),f109(x65711)))
% 157.55/157.22 [6603]~P118(x66031)+~P105(f326(f326(f235(x66031),f81(x66031,x66032)),f2(x66031)))+P105(f326(f326(f235(x66031),x66032),f2(x66031)))
% 157.55/157.22 [6777]~P118(x67772)+~P105(f326(f326(f234(x67772),f326(f102(x67772),x67771)),f2(x67772)))+P105(f326(f326(f234(a1),x67771),f2(a1)))
% 157.55/157.22 [6778]~P118(x67782)+~P105(f326(f326(f235(x67782),f326(f102(x67782),x67781)),f2(x67782)))+P105(f326(f326(f235(a1),x67781),f2(a1)))
% 157.55/157.22 [7282]~P75(x72821)+~P105(f326(f326(f234(x72821),x72822),f2(x72821)))+P105(f326(f326(f234(x72821),f326(f326(f79(x72821),x72822),x72822)),f2(x72821)))
% 157.55/157.22 [7284]~P118(x72841)+~P105(f326(f326(f235(x72841),x72842),f2(x72841)))+P105(f326(f326(f235(x72841),f326(f326(f79(x72841),x72842),x72842)),f2(x72841)))
% 157.55/157.22 [7285]~P75(x72851)+~P105(f326(f326(f235(x72851),x72852),f2(x72851)))+P105(f326(f326(f235(x72851),f326(f326(f79(x72851),x72852),x72852)),f2(x72851)))
% 157.55/157.22 [7850]~P75(x78501)+~P105(f326(f326(f234(x78501),f326(f326(f79(x78501),x78502),x78502)),f2(x78501)))+P105(f326(f326(f234(x78501),x78502),f2(x78501)))
% 157.55/157.22 [7851]~P118(x78511)+~P105(f326(f326(f235(x78511),f326(f326(f79(x78511),x78512),x78512)),f2(x78511)))+P105(f326(f326(f235(x78511),x78512),f2(x78511)))
% 157.55/157.22 [7852]~P75(x78521)+~P105(f326(f326(f235(x78521),f326(f326(f79(x78521),x78522),x78522)),f2(x78521)))+P105(f326(f326(f235(x78521),x78522),f2(x78521)))
% 157.55/157.22 [4872]~E(x48722,f77(a909))+~E(x48721,f77(a909))+E(f326(f326(f80(a909),x48721),x48722),f77(a909))
% 157.55/157.22 [4873]~E(x48732,f77(a1))+~E(x48731,f77(a1))+E(f326(f326(f80(a1),x48731),x48732),f77(a1))
% 157.55/157.22 [4874]~E(x48742,f2(a909))+~E(x48741,f2(a909))+E(f326(f326(f79(a909),x48741),x48742),f2(a909))
% 157.55/157.22 [4929]~P121(x49292)+E(x49291,f2(x49292))+E(f326(f326(f290(x49292),x49291),x49291),f77(x49292))
% 157.55/157.22 [4930]~P59(x49302)+E(x49301,f2(x49302))+E(f326(f326(f36(x49302),x49301),x49301),f77(x49302))
% 157.55/157.22 [4931]~P122(x49312)+E(x49311,f2(x49312))+E(f326(f326(f290(x49312),x49311),x49311),f77(x49312))
% 157.55/157.22 [4951]~P141(x49511)+~E(x49512,f77(x49511))+E(f326(f326(f80(x49511),x49512),x49512),f77(x49511))
% 157.55/157.22 [4952]~P75(x49521)+~E(x49522,f2(x49521))+E(f326(f326(f79(x49521),x49522),x49522),f2(x49521))
% 157.55/157.22 [4953]~P122(x49531)+~E(x49532,f2(x49531))+E(f326(f326(f290(x49531),x49532),x49532),f2(x49531))
% 157.55/157.22 [4998]~E(x49982,f2(a909))+~E(x49981,f2(a909))+E(f326(f78(a1),f326(f100(a1),x49981)),f326(f100(a1),x49982))
% 157.55/157.22 [5017]E(x50171,f77(a909))+E(x50172,f2(a909))+~E(f326(f326(f80(a909),x50172),x50171),x50172)
% 157.55/157.22 [5029]E(x50291,f2(a909))+E(x50292,f2(a909))+~E(f326(f326(f80(a909),x50292),x50291),f2(a909))
% 157.55/157.22 [5056]~E(x50562,f2(a909))+~E(x50561,f326(a112,f2(a909)))+E(f326(f326(f79(a909),x50561),x50562),f326(a112,f2(a909)))
% 157.55/157.22 [5057]~E(x50571,f2(a909))+~E(x50572,f326(a112,f2(a909)))+E(f326(f326(f79(a909),x50571),x50572),f326(a112,f2(a909)))
% 157.55/157.22 [5064]E(x50641,f77(a1))+E(x50642,f326(f103(a1),a97))+~E(f326(f326(f80(a1),x50641),x50642),f77(a1))
% 157.55/157.22 [5065]E(x50651,f77(a1))+E(x50652,f326(f103(a1),a97))+~E(f326(f326(f80(a1),x50652),x50651),f77(a1))
% 157.55/157.22 [5066]E(x50661,f77(a1))+E(x50661,f326(f103(a1),a97))+~E(f326(f326(f80(a1),x50662),x50661),f77(a1))
% 157.55/157.22 [5068]E(x50681,f77(a1))+E(x50681,f326(f103(a1),a97))+~E(f326(f326(f80(a1),x50681),x50682),f77(a1))
% 157.55/157.22 [5093]~P75(x50932)+E(x50931,f2(x50932))+~E(f326(f326(f79(x50932),x50931),x50931),f2(x50932))
% 157.55/157.22 [5099]~E(x50991,f326(f103(a1),a97))+~E(x50992,f326(f103(a1),a97))+E(f326(f326(f80(a1),x50991),x50992),f77(a1))
% 157.55/157.22 [5110]E(x51101,f2(a909))+E(x51102,f2(a909))+~E(f326(f326(f79(a909),x51102),x51101),f326(a112,f2(a909)))
% 157.55/157.22 [5120]~P62(x51201)+~P94(x51201)+E(f326(f326(f290(x51201),x51202),f326(f103(x51201),a82)),f2(x51201))
% 157.55/157.22 [5127]~P141(x51271)+~E(x51272,f326(f78(x51271),f77(x51271)))+E(f326(f326(f80(x51271),x51272),x51272),f77(x51271))
% 157.55/157.22 [5132]~P5(x51322)+~P5(x51321)+P5(f326(f326(f80(a1),x51321),x51322))
% 157.55/157.22 [5133]~P5(x51332)+~P5(x51331)+P5(f326(f326(f79(a1),x51331),x51332))
% 157.55/157.22 [5134]~P5(x51342)+~P5(x51341)+P5(f326(f326(f36(a1),x51341),x51342))
% 157.55/157.22 [5136]~E(x51362,f2(a1))+E(x51361,f2(a1))+E(f46(x51361,x51362),f326(f326(f251(a1,a1),f2(a1)),x51361))
% 157.55/157.22 [5159]~E(x51592,f326(a112,f2(a909)))+~E(x51591,f326(a112,f2(a909)))+E(f326(f326(f80(a909),x51591),x51592),f326(a112,f2(a909)))
% 157.55/157.22 [5176]E(x51761,f2(a909))+E(x51762,f326(a112,f2(a909)))+~E(f326(f326(f243(a909),x51762),x51761),f326(a112,f2(a909)))
% 157.55/157.22 [5177]E(x51771,f2(a909))+E(x51771,f326(a112,f2(a909)))+~E(f326(f326(f79(a909),x51772),x51771),f326(a112,f2(a909)))
% 157.55/157.22 [5178]E(x51781,f2(a909))+E(x51781,f326(a112,f2(a909)))+~E(f326(f326(f79(a909),x51781),x51782),f326(a112,f2(a909)))
% 157.55/157.22 [5187]~P62(x51871)+~P94(x51871)+E(f326(f326(f290(x51871),x51872),f326(f103(x51871),a97)),f326(f78(x51871),x51872))
% 157.55/157.22 [5207]E(x52071,f326(a104,x52072))+~E(x52071,f2(a909))+P105(f326(f326(f234(a1),f2(a1)),x52072))
% 157.55/157.22 [5208]E(f326(a104,x52081),x52082)+~E(x52082,f2(a909))+P105(f326(f326(f234(a1),f2(a1)),x52081))
% 157.55/157.22 [5224]E(x52241,f326(a112,f2(a909)))+E(x52242,f326(a112,f2(a909)))+~E(f326(f326(f79(a909),x52241),x52242),f326(a112,f2(a909)))
% 157.55/157.22 [5235]~E(x52351,f326(a104,x52352))+E(x52351,f2(a909))+P105(f326(f326(f234(a1),f2(a1)),x52352))
% 157.55/157.22 [5236]~E(f326(a104,x52362),x52361)+E(x52361,f2(a909))+P105(f326(f326(f234(a1),f2(a1)),x52362))
% 157.55/157.22 [5259]~P77(x52591)+E(f326(f63(x52591,f110(x52591)),x52592),f12(x52591,x52592))+~P105(f326(f61(x52591),x52592))
% 157.55/157.22 [5260]~P77(x52601)+E(f326(f63(x52601,f101(x52601)),x52602),f13(x52601,x52602))+~P105(f326(f61(x52601),x52602))
% 157.55/157.22 [5261]~P108(x52611)+E(f326(f63(x52611,f232(x52611)),x52612),f16(x52611,x52612))+~P105(f326(f61(x52611),x52612))
% 157.55/157.22 [5262]~P108(x52621)+E(f326(f63(x52621,f233(x52621)),x52622),f17(x52621,x52622))+~P105(f326(f61(x52621),x52622))
% 157.55/157.22 [5339]E(x53391,x53392)+~E(f326(f326(f3(a909),x53392),x53391),f2(a909))+~E(f326(f326(f3(a909),x53391),x53392),f2(a909))
% 157.55/157.22 [5357]P5(x53571)+~P39(x53572)+~P105(f326(f326(f328(a1),x53571),x53572))
% 157.55/157.22 [5388]~P118(x53881)+~E(f81(x53881,x53882),f77(x53881))+P105(f326(f326(f235(x53881),f2(x53881)),x53882))
% 157.55/157.22 [5399]~P94(x53991)+E(f326(f100(x53991),f326(f103(a909),x53992)),f326(f103(x53991),x53992))+P105(f326(a193,f326(f103(a1),x53992)))
% 157.55/157.22 [5404]~P43(x54041,x54042)+P44(a905)+P105(f326(f61(f916(x54041,x54041)),x54042))
% 157.55/157.22 [5479]~P108(x54791)+E(f326(f63(x54791,f232(x54791)),x54792),f14(x54791,f232(x54791),x54792))+~P105(f326(f61(x54791),x54792))
% 157.55/157.22 [5480]~P108(x54801)+E(f326(f63(x54801,f233(x54801)),x54802),f15(x54801,f233(x54801),x54802))+~P105(f326(f61(x54801),x54802))
% 157.55/157.22 [5494]E(x54941,x54942)+P105(f326(f326(f235(a909),x54942),x54941))+P105(f326(f326(f235(a909),x54941),x54942))
% 157.55/157.22 [5495]E(x54951,x54952)+P105(f326(f326(f235(a1),x54952),x54951))+P105(f326(f326(f235(a1),x54951),x54952))
% 157.55/157.22 [5549]~P94(x55491)+E(f326(f100(x55491),f326(f103(a909),x55492)),f2(x55491))+~P105(f326(a193,f326(f103(a1),x55492)))
% 157.55/157.22 [5552]~E(x55522,f326(a104,x55521))+E(x55521,f326(f100(a1),x55522))+~P105(f326(f326(f234(a1),f2(a1)),x55521))
% 157.55/157.22 [5553]~E(f326(a104,x55531),x55532)+E(x55531,f326(f100(a1),x55532))+~P105(f326(f326(f234(a1),f2(a1)),x55531))
% 157.55/157.22 [5554]~E(x55541,f326(a104,x55542))+E(f326(f100(a1),x55541),x55542)+~P105(f326(f326(f234(a1),f2(a1)),x55542))
% 157.55/157.22 [5564]E(x55641,f326(a104,x55642))+~E(x55642,f326(f100(a1),x55641))+~P105(f326(f326(f234(a1),f2(a1)),x55642))
% 157.55/157.22 [5565]E(f326(a104,x55651),x55652)+~E(x55651,f326(f100(a1),x55652))+~P105(f326(f326(f234(a1),f2(a1)),x55651))
% 157.55/157.22 [5596]~P112(x55962)+E(x55961,f2(x55962))+~P105(f326(f326(f286(x55962),f2(x55962)),x55961))
% 157.55/157.22 [5607]~P86(x56072)+E(x56071,f2(x56072))+P105(f326(f326(f235(x56072),f2(x56072)),f326(f75(x56072),x56071)))
% 157.55/157.22 [5672]~P118(x56721)+E(f81(x56721,x56722),f77(x56721))+~P105(f326(f326(f235(x56721),f2(x56721)),x56722))
% 157.55/157.22 [5678]~P94(x56781)+E(f326(f100(x56781),f326(f103(a909),x56782)),f2(x56781))+P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x56782)))
% 157.55/157.22 [5689]~P86(x56891)+E(f326(f75(x56891),x56892),x56892)+~P105(f326(f326(f234(x56891),f2(x56891)),x56892))
% 157.55/157.22 [5690]~P86(x56901)+E(f326(f75(x56901),x56902),x56902)+~P105(f326(f326(f235(x56901),f2(x56901)),x56902))
% 157.55/157.22 [5699]E(x56991,f2(a909))+~E(f139(a909,f326(f301(a909,x56992),x56991)),f113(a909))+P105(f326(f326(f234(a909),x56991),x56992))
% 157.55/157.22 [5710]~P69(x57101)+E(f326(f326(f8(x57101,x57101),f7(x57101)),f326(f172(x57101),x57102)),f326(f165(x57101),x57102))+~P105(f326(f137(x57101),x57102))
% 157.55/157.22 [5713]~P140(x57131)+E(f326(f100(x57131),f326(a104,x57132)),f326(f102(x57131),x57132))+~P105(f326(f326(f234(a1),f2(a1)),x57132))
% 157.55/157.22 [5740]E(x57401,x57402)+P105(f326(f326(f235(a909),x57401),x57402))+~P105(f326(f326(f234(a909),x57401),x57402))
% 157.55/157.22 [5741]E(x57411,x57412)+P105(f326(f326(f235(a1),x57411),x57412))+~P105(f326(f326(f234(a1),x57411),x57412))
% 157.55/157.22 [5744]E(x57441,f77(a1))+~E(f326(f326(f80(a1),x57442),x57441),f77(a1))+~P105(f326(f326(f235(a1),f2(a1)),x57442))
% 157.55/157.22 [5745]E(x57451,f77(a1))+~E(f326(f326(f80(a1),x57451),x57452),f77(a1))+~P105(f326(f326(f235(a1),f2(a1)),x57451))
% 157.55/157.22 [5786]~P39(x57862)+P105(f326(f326(f234(a1),f2(a1)),x57861))+~P105(f326(f326(f328(a1),x57861),x57862))
% 157.55/157.22 [5805]~P56(x58051,x58052)+P36(x58051,x58052)+~P105(f326(f61(f916(x58051,x58051)),x58052))
% 157.55/157.22 [5807]~P56(x58071,x58072)+P43(x58071,x58072)+~P105(f326(f61(f916(x58071,x58071)),x58072))
% 157.55/157.22 [5849]E(x58491,f188(f917(x58492,a905)))+~P105(f326(f61(x58492),x58491))+P105(f326(f326(f235(a909),f2(a909)),f326(f35(x58492),x58491)))
% 157.55/157.22 [5876]~P105(f326(x58761,x58762))+P105(f326(x58761,f2(a909)))+P105(f326(f326(f235(a909),f883(x58762,x58761)),x58762))
% 157.55/157.22 [5899]E(x58991,f2(a909))+~E(f326(f165(a909),x58992),f2(a909))+~P105(f326(f326(f328(a909),x58991),f326(f172(a909),x58992)))
% 157.55/157.22 [5967]E(x59671,x59672)+~P105(f326(f326(f234(a909),x59672),x59671))+~P105(f326(f326(f234(a909),x59671),x59672))
% 157.55/157.22 [5968]E(x59681,x59682)+~P105(f326(f326(f234(a1),x59682),x59681))+~P105(f326(f326(f234(a1),x59681),x59682))
% 157.55/157.22 [5977]E(x59771,x59772)+~P105(f326(f326(f286(a909),x59772),x59771))+~P105(f326(f326(f286(a909),x59771),x59772))
% 157.55/157.22 [5979]E(f326(f35(x59791),x59792),f2(a909))+~P105(f326(f61(x59791),x59792))+P105(f326(f326(f328(x59791),f884(x59792,x59791)),x59792))
% 157.55/157.22 [5988]E(f50(x59881,x59882),f46(x59881,x59882))+P105(f326(f326(f234(a1),f2(a1)),x59881))+~P105(f326(f326(f235(a1),f2(a1)),x59882))
% 157.55/157.22 [6014]~P105(f326(x60141,f365(x60141)))+P105(f326(x60141,f326(a104,x60142)))+~P105(f326(f326(f234(a1),f2(a1)),x60142))
% 157.55/157.22 [6017]P105(f326(f326(f234(a909),x60171),f405(x60172)))+~P105(f326(f61(a909),x60172))+~P105(f326(f326(f328(a909),x60171),x60172))
% 157.55/157.22 [6018]P105(f326(f326(f235(a909),x60181),f402(x60182)))+~P105(f326(f61(a909),x60182))+~P105(f326(f326(f328(a909),x60181),x60182))
% 157.55/157.22 [6049]E(x60491,x60492)+~P105(f326(f326(f235(a909),x60491),f326(a112,x60492)))+P105(f326(f326(f235(a909),x60491),x60492))
% 157.55/157.22 [6081]E(x60811,f326(a112,x60812))+~P105(f326(f326(f234(a909),x60811),f326(a112,x60812)))+P105(f326(f326(f234(a909),x60811),x60812))
% 157.55/157.22 [6097]P105(f326(x60971,f366(x60971)))+~P105(f326(x60971,f326(a104,x60972)))+~P105(f326(f326(f234(a1),f2(a1)),x60972))
% 157.55/157.22 [6112]~P105(f326(x61121,x61122))+~P105(f326(f326(f234(a1),f2(a1)),x61122))+P105(f326(x61121,f326(f100(a1),f338(x61121))))
% 157.55/157.22 [6123]~P86(x61232)+~E(x61231,f2(x61232))+~P105(f326(f326(f235(x61232),f2(x61232)),f326(f75(x61232),x61231)))
% 157.55/157.22 [6148]~P56(x61481,x61482)+P36(x61481,f326(f285(x61481,x61481),x61482))+~P105(f326(f61(f916(x61481,x61481)),x61482))
% 157.55/157.22 [6157]~P94(x61571)+E(f326(f100(x61571),f326(f103(a909),x61572)),f326(f103(x61571),x61572))+~P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x61572)))
% 157.55/157.22 [6160]E(f326(a112,x61601),x61602)+~P105(f326(f326(f235(a909),x61601),x61602))+P105(f326(f326(f235(a909),f326(a112,x61601)),x61602))
% 157.55/157.22 [6176]E(f326(f326(f36(a1),x61761),x61762),f2(a1))+~P105(f326(f326(f234(a1),x61761),f2(a1)))+~P105(f326(f326(f235(a1),x61762),x61761))
% 157.55/157.22 [6187]E(f45(a1,x61871,x61872),x61871)+~P105(f326(f326(f234(a1),x61871),f2(a1)))+~P105(f326(f326(f235(a1),x61872),x61871))
% 157.55/157.22 [6201]E(f47(x62011,x62012),f46(x62011,x62012))+~P105(f326(f326(f234(a1),f2(a1)),x62011))+~P105(f326(f326(f234(a1),f2(a1)),x62012))
% 157.55/157.22 [6211]E(f326(f326(f36(a1),x62111),x62112),f2(a1))+~P105(f326(f326(f234(a1),f2(a1)),x62111))+~P105(f326(f326(f235(a1),x62111),x62112))
% 157.55/157.22 [6222]E(f45(a909,f326(f103(a909),x62221),f326(f103(a909),x62222)),f326(f103(a909),x62221))+P105(f326(a193,f326(f103(a1),x62221)))+~P105(f326(a193,f326(f103(a1),x62222)))
% 157.55/157.22 [6224]E(f45(a1,x62241,x62242),x62241)+~P105(f326(f326(f234(a1),f2(a1)),x62241))+~P105(f326(f326(f235(a1),x62241),x62242))
% 157.55/157.22 [6225]E(x62251,x62252)+~P105(f326(f326(f235(a909),x62251),f326(a112,x62252)))+~P105(f326(f326(f234(a909),x62252),x62251))
% 157.55/157.22 [6239]~P75(x62391)+~P105(f326(f326(f234(x62391),x62392),f2(x62391)))+P105(f326(f326(f234(x62391),x62392),f326(f78(x62391),x62392)))
% 157.55/157.22 [6240]~P118(x62401)+~P105(f326(f326(f235(x62401),x62402),f2(x62401)))+P105(f326(f326(f235(x62401),x62402),f326(f78(x62401),x62402)))
% 157.55/157.22 [6249]~P4(x62491)+E(f326(f326(f64(x62491,x62491,f110(x62491)),f188(x62491)),x62492),f37(x62491,x62492))+~P105(f326(f61(x62491),x62492))
% 157.55/157.22 [6250]~P4(x62501)+E(f326(f326(f64(x62501,x62501,f101(x62501)),f241(x62501)),x62502),f38(x62501,x62502))+~P105(f326(f61(x62501),x62502))
% 157.55/157.22 [6267]~P118(x62671)+~P105(f326(f326(f234(a1),f2(a1)),x62672))+P105(f326(f326(f234(x62671),f2(x62671)),f326(f102(x62671),x62672)))
% 157.55/157.22 [6268]~P124(x62681)+~P105(f326(f326(f235(a909),f2(a909)),x62682))+P105(f326(f326(f235(x62681),f2(x62681)),f326(f100(x62681),x62682)))
% 157.55/157.22 [6269]~P118(x62691)+~P105(f326(f326(f235(a1),f2(a1)),x62692))+P105(f326(f326(f235(x62691),f2(x62691)),f326(f102(x62691),x62692)))
% 157.55/157.22 [6272]~P5(x62722)+~P5(x62721)+E(f326(f309(a909,a1,f100(a1)),f302(a909,f326(a104,x62721),f326(a104,x62722))),f302(a1,x62721,x62722))
% 157.55/157.22 [6278]P105(f326(x62781,x62782))+~P105(f326(f326(f234(a1),f2(a1)),x62782))+~P105(f326(x62781,f326(f100(a1),f341(x62781))))
% 157.55/157.22 [6309]E(f326(f326(f79(a909),f326(f103(a909),x63091)),f326(f103(a909),x63092)),f326(f103(a909),x63091))+P105(f326(f326(f235(a1),x63091),a82))+~P105(f326(f326(f235(a1),x63092),a82))
% 157.55/157.22 [6313]~P118(x63131)+P105(f326(f326(f235(x63131),f2(x63131)),f81(x63131,x63132)))+~P105(f326(f326(f235(x63131),f2(x63131)),x63132))
% 157.55/157.22 [6326]~P79(x63261)+~P105(f326(f326(f234(x63261),x63262),f2(x63261)))+P105(f326(f326(f234(x63261),f2(x63261)),f326(f78(x63261),x63262)))
% 157.55/157.22 [6327]~P79(x63271)+~P105(f326(f326(f235(x63271),x63272),f2(x63271)))+P105(f326(f326(f235(x63271),f2(x63271)),f326(f78(x63271),x63272)))
% 157.55/157.22 [6330]E(x63301,f241(f917(x63302,a905)))+~E(f326(f35(x63302),x63301),f326(f35(x63302),f241(f917(x63302,a905))))+~P105(f326(f61(x63302),f241(f917(x63302,a905))))
% 157.55/157.22 [6362]~P75(x63621)+P105(f326(f326(f234(x63621),x63622),f2(x63621)))+~P105(f326(f326(f234(x63621),x63622),f326(f78(x63621),x63622)))
% 157.55/157.22 [6363]~P118(x63631)+P105(f326(f326(f235(x63631),x63632),f2(x63631)))+~P105(f326(f326(f235(x63631),x63632),f326(f78(x63631),x63632)))
% 157.55/157.22 [6372]~P94(x63721)+P105(f326(f326(f328(x63721),f326(f103(x63721),x63722)),f186(x63721)))+~P105(f326(f326(f234(a1),a82),x63722))
% 157.55/157.22 [6401]E(x64011,f2(a909))+~P105(f326(f326(f235(a909),x64011),f326(a112,x64012)))+P105(f326(f326(f235(a909),f814(x64012,x64011)),x64012))
% 157.55/157.22 [6424]~P118(x64241)+~P105(f326(f326(f235(x64241),f2(x64241)),f81(x64241,x64242)))+P105(f326(f326(f235(x64241),f2(x64241)),x64242))
% 157.55/157.22 [6426]~E(f326(f103(a909),x64262),f326(f103(a909),x64261))+P105(f326(f326(f234(a1),f326(f103(a1),x64261)),f2(a1)))+~P105(f326(a193,f326(f103(a1),x64262)))
% 157.55/157.22 [6455]E(f326(f250(a1,a1),f50(x64551,x64552)),f326(f326(f36(a1),x64551),x64552))+~P105(f326(f326(f235(a1),x64551),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x64552))
% 157.55/157.22 [6493]E(f326(f255(a1,a1),f50(x64931,x64932)),f45(a1,x64931,x64932))+~P105(f326(f326(f235(a1),x64931),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x64932))
% 157.55/157.22 [6496]~P118(x64962)+~P105(f326(f326(f234(x64962),f2(x64962)),f326(f102(x64962),x64961)))+P105(f326(f326(f234(a1),f2(a1)),x64961))
% 157.55/157.22 [6497]~P124(x64972)+~P105(f326(f326(f235(x64972),f2(x64972)),f326(f100(x64972),x64971)))+P105(f326(f326(f235(a909),f2(a909)),x64971))
% 157.55/157.22 [6498]~P118(x64982)+~P105(f326(f326(f235(x64982),f2(x64982)),f326(f102(x64982),x64981)))+P105(f326(f326(f235(a1),f2(a1)),x64981))
% 157.55/157.22 [6502]E(f326(f250(a1,a1),f47(x65021,x65022)),f326(f326(f36(a1),x65021),x65022))+~P105(f326(f326(f234(a1),f2(a1)),x65022))+~P105(f326(f326(f235(a1),f2(a1)),x65021))
% 157.55/157.22 [6516]E(f326(f255(a1,a1),f47(x65161,x65162)),f45(a1,x65161,x65162))+~P105(f326(f326(f234(a1),f2(a1)),x65162))+~P105(f326(f326(f235(a1),f2(a1)),x65161))
% 157.55/157.22 [6532]~P79(x65321)+P105(f326(f326(f234(x65321),x65322),f2(x65321)))+~P105(f326(f326(f234(x65321),f2(x65321)),f326(f78(x65321),x65322)))
% 157.55/157.22 [6533]~P79(x65331)+P105(f326(f326(f235(x65331),x65332),f2(x65331)))+~P105(f326(f326(f235(x65331),f2(x65331)),f326(f78(x65331),x65332)))
% 157.55/157.22 [6559]P105(f326(f49(x65591,x65592),f50(x65591,x65592)))+~P105(f326(f326(f235(a1),x65591),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x65592))
% 157.55/157.22 [6583]P105(f326(f49(x65831,x65832),f47(x65831,x65832)))+~P105(f326(f326(f234(a1),f2(a1)),x65831))+~P105(f326(f326(f235(a1),f2(a1)),x65832))
% 157.55/157.22 [6626]~P79(x66261)+P105(f326(f326(f234(x66261),f326(f78(x66261),x66262)),f2(x66261)))+~P105(f326(f326(f234(x66261),f2(x66261)),x66262))
% 157.55/157.22 [6627]~P79(x66271)+P105(f326(f326(f235(x66271),f326(f78(x66271),x66272)),f2(x66271)))+~P105(f326(f326(f235(x66271),f2(x66271)),x66272))
% 157.55/157.22 [6645]E(f326(f326(f3(a909),f326(a104,x66451)),f326(a104,x66452)),f326(a104,f194(x66451,x66452)))+~P105(f326(f326(f234(a1),f2(a1)),x66452))+~P105(f326(f326(f234(a1),f2(a1)),x66451))
% 157.55/157.22 [6663]P105(f326(f326(f234(a1),f2(a1)),f194(x66631,x66632)))+~P105(f326(f326(f234(a1),f2(a1)),x66632))+~P105(f326(f326(f234(a1),f2(a1)),x66631))
% 157.55/157.22 [6700]~P105(f326(x67001,x67002))+P105(f326(x67001,f2(a909)))+P105(f326(x67001,f326(f326(f79(a909),f883(x67002,x67001)),f77(a909))))
% 157.55/157.22 [6784]E(f326(f103(a909),x67841),f326(f103(a909),x67842))+~P105(f326(f326(f234(a1),f326(f103(a1),x67842)),f2(a1)))+~P105(f326(a193,f326(f103(a1),x67841)))
% 157.55/157.22 [6798]~E(x67981,f2(a909))+~E(f670(x67982,x67981),f2(a909))+E(f326(f142(a909,a909,f79(a909),x67981),x67982),f2(a909))
% 157.55/157.22 [6822]~P105(f326(f61(x68221),f753(x68222,x68221)))+~P105(f326(f61(f917(x68221,a905)),x68222))+P105(f326(f61(x68221),f37(f917(x68221,a905),x68222)))
% 157.55/157.22 [6828]E(x68281,x68282)+P105(f326(f326(f235(a1),x68281),x68282))+~P105(f326(f326(f235(a1),x68281),f326(f326(f79(a1),x68282),f77(a1))))
% 157.55/157.22 [6829]P105(f326(f326(f234(a909),f326(a104,x68291)),f326(a104,x68292)))+~P105(f326(f326(f234(a1),f2(a1)),x68292))+~P105(f326(f326(f234(a1),x68291),x68292))
% 157.55/157.22 [6830]P105(f326(f326(f234(a909),f326(a104,x68301)),f326(a104,x68302)))+~P105(f326(f326(f235(a1),f2(a1)),x68301))+~P105(f326(f326(f234(a1),x68301),x68302))
% 157.55/157.22 [6832]P105(f326(f326(f235(a909),f326(a104,x68321)),f326(a104,x68322)))+~P105(f326(f326(f234(a1),f2(a1)),x68321))+~P105(f326(f326(f235(a1),x68321),x68322))
% 157.55/157.22 [6833]P105(f326(f326(f235(a909),f326(a104,x68331)),f326(a104,x68332)))+~P105(f326(f326(f235(a1),f2(a1)),x68332))+~P105(f326(f326(f235(a1),x68331),x68332))
% 157.55/157.22 [6844]E(f45(a909,f326(a104,x68441),f326(a104,x68442)),f326(a104,f45(a1,x68441,x68442)))+~P105(f326(f326(f234(a1),f2(a1)),x68442))+~P105(f326(f326(f234(a1),f2(a1)),x68441))
% 157.55/157.22 [6868]~P79(x68681)+~P105(f326(f326(f234(x68681),f326(f78(x68681),x68682)),f2(x68681)))+P105(f326(f326(f234(x68681),f2(x68681)),x68682))
% 157.55/157.22 [6869]~P79(x68691)+~P105(f326(f326(f235(x68691),f326(f78(x68691),x68692)),f2(x68691)))+P105(f326(f326(f235(x68691),f2(x68691)),x68692))
% 157.55/157.22 [6883]~P105(f326(f326(f235(a1),a82),x68832))+~P105(f326(f326(f235(a1),x68831),x68832))+P105(f326(f326(f235(a909),f326(f103(a909),x68831)),f326(f103(a909),x68832)))
% 157.55/157.22 [6974]~P105(f326(f326(f234(a1),f2(a1)),x69741))+P105(f326(f326(f235(a909),f326(a104,x69741)),x69742))+~P105(f326(f326(f235(a1),x69741),f326(f100(a1),x69742)))
% 157.55/157.22 [6979]P105(f326(x69791,x69792))+~P105(f326(x69791,f326(a22,f803(x69791,x69792))))+~P105(f326(f326(f328(a909),x69792),f241(f917(a909,a905))))
% 157.55/157.22 [6990]E(x69901,f2(a1))+E(f45(a1,x69902,x69901),f2(a1))+E(f326(f326(f3(a1),f326(f78(a1),f326(f326(f36(a1),x69902),x69901))),f77(a1)),f326(f326(f36(a1),x69902),f326(f78(a1),x69901)))
% 157.55/157.22 [7004]~P105(f326(f326(f234(a1),f2(a1)),x70041))+~P105(f326(f326(f235(a909),f326(a104,x70041)),x70042))+P105(f326(f326(f235(a1),x70041),f326(f100(a1),x70042)))
% 157.55/157.22 [7038]~P105(f326(f326(f234(a909),f326(a104,x70381)),f326(a104,x70382)))+~P105(f326(f326(f234(a1),f2(a1)),x70382))+P105(f326(f326(f234(a1),x70381),x70382))
% 157.55/157.22 [7039]~P105(f326(f326(f234(a909),f326(a104,x70391)),f326(a104,x70392)))+~P105(f326(f326(f235(a1),f2(a1)),x70391))+P105(f326(f326(f234(a1),x70391),x70392))
% 157.55/157.22 [7068]P105(f326(f326(f234(a1),x70681),x70682))+~P105(f326(f326(f234(a909),f326(f103(a909),x70681)),f326(f103(a909),x70682)))+P105(f326(f326(f234(a1),x70681),a82))
% 157.55/157.22 [7093]P105(f326(f326(f234(a1),f2(a1)),f45(a1,x70931,x70932)))+~P105(f326(f326(f234(a1),f2(a1)),x70932))+~P105(f326(f326(f234(a1),f2(a1)),x70931))
% 157.55/157.22 [7192]P105(f326(f326(f235(a1),a82),x71921))+~P105(f326(f326(f235(a1),x71922),x71921))+~P105(f326(f326(f235(a909),f326(f103(a909),x71922)),f326(f103(a909),x71921)))
% 157.55/157.22 [7245]E(f326(f326(f251(a1,a1),f326(f326(f36(a1),x72451),x72452)),f45(a1,x72451,x72452)),f50(x72451,x72452))+~P105(f326(f326(f235(a1),x72451),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x72452))
% 157.55/157.22 [7265]E(f326(f326(f251(a1,a1),f326(f326(f36(a1),x72651),x72652)),f45(a1,x72651,x72652)),f47(x72651,x72652))+~P105(f326(f326(f234(a1),f2(a1)),x72652))+~P105(f326(f326(f234(a1),f2(a1)),x72651))
% 157.55/157.22 [7317]~P96(x73172)+E(x73171,f113(x73172))+E(f326(f142(x73172,x73172,f80(x73172),f326(f141(x73172),x73171)),f326(f171(x73172),x73171)),f326(f63(x73172,f80(x73172)),f326(f172(x73172),x73171)))
% 157.55/157.22 [7433]~E(x74331,f2(a909))+E(f326(f142(a909,a909,f79(a909),x74331),x74332),f2(a909))+P105(f326(f326(f328(a909),f670(x74332,x74331)),f326(f172(a909),x74332)))
% 157.55/157.22 [7488]~P105(f326(f326(f234(a1),x74881),f2(a1)))+P105(f326(f326(f234(a1),f326(f326(f36(a1),x74881),x74882)),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x74882))
% 157.55/157.22 [7489]~P105(f326(f326(f235(a1),x74892),f2(a1)))+P105(f326(f326(f234(a1),f326(f326(f36(a1),x74891),x74892)),f2(a1)))+~P105(f326(f326(f234(a1),f2(a1)),x74891))
% 157.55/157.22 [7490]~P105(f326(f326(f235(a1),x74902),f2(a1)))+P105(f326(f326(f235(a1),f326(f326(f36(a1),x74901),x74902)),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x74901))
% 157.55/157.22 [7492]~P105(f326(f326(f235(a1),x74921),f2(a1)))+P105(f326(f326(f235(a1),f326(f326(f36(a1),x74921),x74922)),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x74922))
% 157.55/157.22 [7499]P105(f326(f326(f328(f917(x74991,a905)),f753(x74992,x74991)),x74992))+~P105(f326(f61(f917(x74991,a905)),x74992))+P105(f326(f61(x74991),f37(f917(x74991,a905),x74992)))
% 157.55/157.22 [7588]P24(x75881,x75881,x75882,f241(f917(x75881,a905)))+~E(f326(f309(x75881,x75881,x75882),f241(f917(x75881,a905))),f241(f917(x75881,a905)))+~P105(f326(f61(x75881),f241(f917(x75881,a905))))
% 157.55/157.22 [7707]~P24(x77071,x77071,x77072,f241(f917(x77071,a905)))+E(f326(f309(x77071,x77071,x77072),f241(f917(x77071,a905))),f241(f917(x77071,a905)))+~P105(f326(f61(x77071),f241(f917(x77071,a905))))
% 157.55/157.22 [7844]E(f326(f326(f36(a1),x78441),x78442),f326(f103(a1),a97))+~P105(f326(f326(f234(a1),f326(f326(f79(a1),x78441),x78442)),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x78441))
% 157.55/157.22 [7901]~P105(f326(f326(f235(a1),x79012),f2(a1)))+~P105(f326(f326(f235(a1),f326(f326(f36(a1),x79011),x79012)),f2(a1)))+P105(f326(f326(f235(a1),f2(a1)),x79011))
% 157.55/157.22 [7906]E(f326(f326(f79(a1),x79061),x79062),f45(a1,x79061,x79062))+~P105(f326(f326(f234(a1),f326(f326(f79(a1),x79061),x79062)),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x79061))
% 157.55/157.22 [7909]P105(f326(f326(f235(a1),x79091),f2(a1)))+~P105(f326(f326(f235(a1),f326(f326(f36(a1),x79091),x79092)),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x79092))
% 157.55/157.22 [8593]~P108(x85931)+P12(x85931,x85932)+~P105(f326(f326(f234(x85931),f326(f326(f164(x85931),x85932),f703(x85932,x85931))),f326(f326(f164(x85931),x85932),f704(x85932,x85931))))
% 157.55/157.22 [8594]~P108(x85941)+P12(x85941,x85942)+~P105(f326(f326(f234(x85941),f326(f326(f164(x85941),x85942),f711(x85942,x85941))),f326(f326(f164(x85941),x85942),f715(x85942,x85941))))
% 157.55/157.22 [5842]E(x58421,f2(a1))+~E(f45(a1,x58422,x58421),f2(a1))+E(f326(f326(f36(a1),x58422),f326(f78(a1),x58421)),f326(f78(a1),f326(f326(f36(a1),x58422),x58421)))
% 157.55/157.22 [5860]~P39(x58602)+~P39(x58601)+P39(f326(f326(f110(f917(a1,a905)),x58601),x58602))
% 157.55/157.22 [5861]~P39(x58612)+~P39(x58611)+P39(f326(f326(f101(f917(a1,a905)),x58611),x58612))
% 157.55/157.22 [5879]~P62(x58791)+~P94(x58791)+E(f326(f78(x58791),f326(f326(f290(x58791),f77(x58791)),x58792)),f326(f326(f290(x58791),f326(f103(x58791),a97)),x58792))
% 157.55/157.22 [6006]E(x60061,f2(a1))+~E(f45(a1,x60062,x60061),f2(a1))+E(f326(f326(f36(a1),f326(f78(a1),x60062)),x60061),f326(f78(a1),f326(f326(f36(a1),x60062),x60061)))
% 157.55/157.22 [6142]~P108(x61421)+P12(x61421,x61422)+P105(f326(f326(f235(a909),f704(x61422,x61421)),f326(f189(f910(x61421)),x61422)))
% 157.55/157.22 [6143]~P108(x61431)+P12(x61431,x61432)+P105(f326(f326(f235(a909),f715(x61432,x61431)),f326(f189(f910(x61431)),x61432)))
% 157.55/157.22 [6303]~P94(x63031)+~E(f326(f103(x63031),x63032),f2(x63031))+P27(x63031,f326(f103(x63031),f326(f326(f79(a1),x63032),f326(f78(a1),a82))))
% 157.55/157.22 [6304]~P94(x63041)+~E(f326(f103(x63041),x63042),f2(x63041))+P27(x63041,f326(f103(x63041),f326(f326(f79(a1),a82),f326(f78(a1),x63042))))
% 157.55/157.22 [6306]E(f326(a51,f47(f326(f78(a1),x63061),f326(f78(a1),x63062))),f46(x63061,x63062))+P105(f326(f326(f234(a1),f2(a1)),x63061))+P105(f326(f326(f235(a1),f2(a1)),x63062))
% 157.55/157.22 [6432]~E(x64322,f2(a909))+~E(x64321,f2(a909))+P105(f326(f326(f234(a1),f326(f100(a1),x64321)),f326(f78(a1),f326(f100(a1),x64322))))
% 157.55/157.22 [6461]E(f326(f326(f79(a909),f326(f103(a909),x64611)),f326(f103(a909),x64612)),f326(f103(a909),f326(f326(f79(a1),x64611),x64612)))+P105(f326(f326(f235(a1),x64611),a82))+P105(f326(f326(f235(a1),x64612),a82))
% 157.55/157.22 [6592]~P75(x65921)+~P105(f326(f326(f234(x65921),f2(x65921)),x65922))+P105(f326(f326(f234(x65921),f326(f78(x65921),x65922)),x65922))
% 157.55/157.22 [6593]~P75(x65931)+~P105(f326(f326(f235(x65931),f2(x65931)),x65932))+P105(f326(f326(f235(x65931),f326(f78(x65931),x65932)),x65932))
% 157.55/157.22 [6770]E(f326(f326(f3(a909),f326(a104,x67701)),f326(a104,x67702)),f326(a104,f326(f326(f3(a1),x67701),x67702)))+~P105(f326(f326(f234(a1),f2(a1)),x67702))+~P105(f326(f326(f234(a1),x67702),x67701))
% 157.55/157.22 [6806]E(f326(a104,f45(a1,f326(f103(a1),x68061),f326(f103(a1),x68062))),f45(a909,f326(f103(a909),x68061),f326(f103(a909),x68062)))+P105(f326(a193,f326(f103(a1),x68061)))+P105(f326(a193,f326(f103(a1),x68062)))
% 157.55/157.22 [6823]~P75(x68231)+P105(f326(f326(f234(x68231),f2(x68231)),x68232))+~P105(f326(f326(f234(x68231),f326(f78(x68231),x68232)),x68232))
% 157.55/157.22 [6824]~P75(x68241)+P105(f326(f326(f235(x68241),f2(x68241)),x68242))+~P105(f326(f326(f235(x68241),f326(f78(x68241),x68242)),x68242))
% 157.55/157.22 [6836]~P75(x68361)+~P105(f326(f326(f234(x68361),f2(x68361)),x68362))+P105(f326(f326(f234(x68361),f2(x68361)),f326(f326(f79(x68361),x68362),x68362)))
% 157.55/157.22 [6838]~P75(x68381)+~P105(f326(f326(f235(x68381),f2(x68381)),x68382))+P105(f326(f326(f235(x68381),f2(x68381)),f326(f326(f79(x68381),x68382),x68382)))
% 157.55/157.22 [6850]E(f326(f326(f79(a909),f326(a104,x68501)),f326(a104,x68502)),f326(a104,f326(f326(f79(a1),x68501),x68502)))+~P105(f326(f326(f234(a1),f2(a1)),x68502))+~P105(f326(f326(f234(a1),f2(a1)),x68501))
% 157.55/157.22 [6861]E(x68611,f2(a909))+P105(f326(f326(f235(a909),f2(a909)),x68612))+~P105(f326(f326(f235(a909),f2(a909)),f326(f326(f243(a909),x68612),x68611)))
% 157.55/157.22 [6895]~P94(x68951)+E(f326(f103(x68951),x68952),f2(x68951))+~P27(x68951,f326(f103(x68951),f326(f326(f79(a1),a82),f326(f78(a1),x68952))))
% 157.55/157.22 [6896]~P94(x68961)+E(f326(f103(x68961),x68962),f2(x68961))+~P27(x68961,f326(f103(x68961),f326(f326(f79(a1),x68962),f326(f78(a1),a82))))
% 157.55/157.22 [6952]~P105(f326(f61(x69521),x69522))+~P105(f326(f61(x69521),f241(f917(x69521,a905))))+P105(f326(f61(x69521),f326(f78(f917(x69521,a905)),x69522)))
% 157.55/157.22 [6975]~P105(f326(f326(f235(a1),f2(a1)),x69752))+~P105(f326(f326(f234(a1),x69752),x69751))+P105(f326(f326(f235(a1),f2(a1)),f326(f326(f36(a1),x69751),x69752)))
% 157.55/157.22 [6976]~P105(f326(f326(f234(a1),x69761),f2(a1)))+~P105(f326(f326(f235(a1),x69762),f2(a1)))+P105(f326(f326(f234(a1),f2(a1)),f326(f326(f36(a1),x69761),x69762)))
% 157.55/157.22 [7012]~P105(f326(f326(f234(a1),f2(a1)),x70122))+~P105(f326(f326(f234(a1),f2(a1)),x70121))+P105(f326(f326(f234(a1),f2(a1)),f326(f326(f80(a1),x70121),x70122)))
% 157.55/157.22 [7013]~P105(f326(f326(f234(a1),f2(a1)),x70132))+~P105(f326(f326(f234(a1),f2(a1)),x70131))+P105(f326(f326(f234(a1),f2(a1)),f326(f326(f79(a1),x70131),x70132)))
% 157.55/157.22 [7014]~P105(f326(f326(f234(a1),f2(a1)),x70142))+~P105(f326(f326(f234(a1),f2(a1)),x70141))+P105(f326(f326(f234(a1),f2(a1)),f326(f326(f36(a1),x70141),x70142)))
% 157.55/157.22 [7015]~P105(f326(f326(f234(a1),f2(a1)),x70151))+~P105(f326(f326(f235(a1),f2(a1)),x70152))+P105(f326(f326(f234(a1),f2(a1)),f326(f326(f36(a1),x70151),x70152)))
% 157.55/157.22 [7016]~P105(f326(f326(f235(a909),f2(a909)),x70162))+~P105(f326(f326(f235(a909),f2(a909)),x70161))+P105(f326(f326(f235(a909),f2(a909)),f326(f326(f80(a909),x70161),x70162)))
% 157.55/157.22 [7080]E(x70801,f2(a1))+E(f45(a1,x70802,x70801),f2(a1))+E(f326(f326(f3(a1),f326(f78(a1),f326(f326(f36(a1),x70802),x70801))),f77(a1)),f326(f326(f36(a1),f326(f78(a1),x70802)),x70801))
% 157.55/157.22 [7137]P105(f326(f326(f235(a909),f2(a909)),x71371))+P105(f326(f326(f235(a909),f2(a909)),x71372))+~P105(f326(f326(f235(a909),f2(a909)),f326(f326(f79(a909),x71372),x71371)))
% 157.55/157.22 [7141]~P75(x71411)+P105(f326(f326(f234(x71411),f2(x71411)),x71412))+~P105(f326(f326(f234(x71411),f2(x71411)),f326(f326(f79(x71411),x71412),x71412)))
% 157.55/157.22 [7142]~P75(x71421)+P105(f326(f326(f235(x71421),f2(x71421)),x71422))+~P105(f326(f326(f235(x71421),f2(x71421)),f326(f326(f79(x71421),x71422),x71422)))
% 157.55/157.22 [7193]~P105(f326(f61(x71931),x71932))+P105(f326(f61(x71931),f241(f917(x71931,a905))))+~P105(f326(f61(x71931),f326(f78(f917(x71931,a905)),x71932)))
% 157.55/157.22 [7257]P105(f326(f326(f234(a1),x72571),f2(a1)))+~P105(f326(f326(f235(a1),x72572),f2(a1)))+~P105(f326(f326(f234(a1),f2(a1)),f326(f326(f36(a1),x72571),x72572)))
% 157.55/157.22 [7263]~P105(f326(f326(f235(a1),f2(a1)),x72631))+P105(f326(f326(f234(a1),x72631),x72632))+~P105(f326(f326(f235(a1),f2(a1)),f326(f326(f36(a1),x72632),x72631)))
% 157.55/157.22 [7264]~P105(f326(f326(f234(a1),f2(a1)),x72642))+P105(f326(f326(f234(a1),x72641),x72642))+~P105(f326(f326(f235(a1),f2(a1)),f326(f326(f36(a1),x72642),x72641)))
% 157.55/157.22 [7294]P105(f326(f326(f234(a1),f2(a1)),x72941))+~P105(f326(f326(f235(a1),f2(a1)),x72942))+~P105(f326(f326(f234(a1),f2(a1)),f326(f326(f36(a1),x72941),x72942)))
% 157.55/157.22 [7295]P105(f326(f326(f235(a1),f2(a1)),x72951))+~P105(f326(f326(f234(a1),f2(a1)),x72952))+~P105(f326(f326(f235(a1),f2(a1)),f326(f326(f36(a1),x72952),x72951)))
% 157.55/157.22 [7738]~P105(f326(f61(x77382),f241(f917(x77382,a905))))+~P105(f326(f61(x77381),f241(f917(x77381,a905))))+P105(f326(f61(f915(x77381,x77382)),f241(f917(f915(x77381,x77382),a905))))
% 157.55/157.22 [7739]~P105(f326(f61(x77392),f241(f917(x77392,a905))))+~P105(f326(f61(x77391),f241(f917(x77391,a905))))+P105(f326(f61(f916(x77391,x77392)),f241(f917(f916(x77391,x77392),a905))))
% 157.55/157.22 [7809]~P105(f326(f326(f235(a909),f326(a112,f2(a909))),x78091))+~P105(f326(f326(f235(a909),f326(a112,f2(a909))),x78092))+P105(f326(f326(f235(a909),x78091),f326(f326(f80(a909),x78092),x78091)))
% 157.55/157.22 [7810]~P105(f326(f326(f235(a909),f326(a112,f2(a909))),x78101))+~P105(f326(f326(f235(a909),f326(a112,f2(a909))),x78102))+P105(f326(f326(f235(a909),x78101),f326(f326(f80(a909),x78101),x78102)))
% 157.55/157.22 [7843]E(f326(f35(x78431),f241(f917(x78431,a905))),f326(a112,f2(a909)))+P105(f326(f61(x78432),f241(f917(x78432,a905))))+~P105(f326(f61(f917(x78432,x78431)),f241(f917(f917(x78432,x78431),a905))))
% 157.55/157.22 [7969]~P105(f326(f326(f234(a909),f326(a112,f2(a909))),x79691))+~P105(f326(f326(f234(a909),f326(a112,f2(a909))),x79692))+P105(f326(f326(f234(a909),f326(a112,f2(a909))),f326(f326(f80(a909),x79691),x79692)))
% 157.55/157.22 [7970]~P105(f326(f326(f235(a909),f326(a112,f2(a909))),x79702))+~P105(f326(f326(f235(a909),f326(a112,f2(a909))),x79701))+P105(f326(f326(f235(a909),f326(a112,f2(a909))),f326(f326(f80(a909),x79701),x79702)))
% 157.55/157.22 [8640]E(x86401,f113(x86402))+~P105(f326(f137(x86402),x86401))+E(f177(x86402,f326(f326(f10(a905,a905,x86402),a321),f326(f326(f9(x86402,x86402,a905),a323),f144(x86402,x86401))),x86401),f114(x86402,x86401))
% 157.55/157.22 [8734]~P39(x87342)+~P39(x87341)+E(f326(f309(a909,a1,f100(a1)),f326(f326(f110(f917(a909,a905)),f326(f309(a1,a909,a104),x87341)),f326(f309(a1,a909,a104),x87342))),f326(f326(f110(f917(a1,a905)),x87341),x87342))
% 157.55/157.22 [8735]~P39(x87352)+~P39(x87351)+E(f326(f309(a909,a1,f100(a1)),f326(f326(f101(f917(a909,a905)),f326(f309(a1,a909,a104),x87351)),f326(f309(a1,a909,a104),x87352))),f326(f326(f101(f917(a1,a905)),x87351),x87352))
% 157.55/157.22 [9396]~P94(x93961)+~E(f326(f103(x93961),x93962),f77(x93961))+P27(x93961,f326(f103(x93961),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f78(a1),x93962))))
% 157.55/157.22 [9635]~P94(x96351)+E(f326(f103(x96351),x96352),f77(x96351))+~P27(x96351,f326(f103(x96351),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f78(a1),x96352))))
% 157.55/157.22 [10393]E(x103931,f2(a1))+E(x103932,f2(a1))+E(f326(f257(a1,a1,a1,a1,f31(a1),f326(f80(a1),f81(a1,x103932))),f326(f326(f326(f96(f916(a1,a1)),f326(f326(a323,f81(a1,x103931)),f81(a1,x103932))),f53(x103931,x103932)),f326(f326(f256(a1,a1,f916(a1,a1)),f326(f326(f20(a1,f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),f326(f326(f10(f917(a1,f917(f916(a1,a1),f916(a1,a1))),f917(f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),a1),f20(a1,f916(a1,a1),f916(a1,a1))),f326(f326(f10(f916(a1,a1),f917(a1,f917(f916(a1,a1),f916(a1,a1))),a1),f326(f9(a1,f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),f326(f326(f10(a905,f917(f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),a1),f96(f916(a1,a1))),f326(f326(f9(a1,a1,a905),a323),f2(a1))))),f326(f326(f9(a1,a1,f916(a1,a1)),f326(f326(f10(a1,f917(a1,f916(a1,a1)),a1),f251(a1,a1)),f78(a1))),f2(a1))))),f326(f326(f9(a1,f917(a1,a1),f917(a1,f916(a1,a1))),f326(f326(f10(f917(a1,f916(a1,a1)),f917(f917(a1,a1),f917(a1,f916(a1,a1))),a1),f10(a1,f916(a1,a1),a1)),f326(f326(f10(a1,f917(a1,f916(a1,a1)),a1),f251(a1,a1)),f326(f326(f9(a1,a1,a1),f326(f326(f10(a1,f917(a1,a1),a1),f3(a1)),f78(a1))),f77(a1))))),f326(f3(a1),f326(f75(a1),x103932))))),f53(x103931,x103932)))),f46(x103931,x103932))
% 157.55/157.22 [10394]E(x103941,f2(a1))+E(x103942,f2(a1))+E(f326(f257(a1,a1,a1,a1,f31(a1),f326(f80(a1),f81(a1,x103942))),f326(f326(f326(f96(f916(a1,a1)),f326(f326(a325,f326(f326(a324,f326(f326(f235(a1),f2(a1)),x103942)),f326(f326(f234(a1),f2(a1)),x103941))),f326(f326(a324,f326(f326(f235(a1),x103942),f2(a1))),f326(f326(f235(a1),x103941),f2(a1))))),f53(x103941,x103942)),f326(f326(f256(a1,a1,f916(a1,a1)),f326(f326(f20(a1,f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),f326(f326(f10(f917(a1,f917(f916(a1,a1),f916(a1,a1))),f917(f917(a1,f916(a1,a1)),f917(a1,f916(a1,a1))),a1),f20(a1,f916(a1,a1),f916(a1,a1))),f326(f326(f10(f916(a1,a1),f917(a1,f917(f916(a1,a1),f916(a1,a1))),a1),f326(f9(a1,f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),f326(f326(f10(a905,f917(f916(a1,a1),f917(f916(a1,a1),f916(a1,a1))),a1),f96(f916(a1,a1))),f326(f326(f9(a1,a1,a905),a323),f2(a1))))),f326(f326(f9(a1,a1,f916(a1,a1)),f326(f326(f10(a1,f917(a1,f916(a1,a1)),a1),f251(a1,a1)),f78(a1))),f2(a1))))),f326(f326(f9(a1,f917(a1,a1),f917(a1,f916(a1,a1))),f326(f326(f10(f917(a1,f916(a1,a1)),f917(f917(a1,a1),f917(a1,f916(a1,a1))),a1),f10(a1,f916(a1,a1),a1)),f326(f326(f10(a1,f917(a1,f916(a1,a1)),a1),f251(a1,a1)),f326(f326(f9(a1,a1,a1),f326(f326(f10(a1,f917(a1,a1),a1),f3(a1)),f78(a1))),f77(a1))))),f326(f3(a1),f326(f75(a1),x103942))))),f53(x103941,x103942)))),f46(x103941,x103942))
% 157.55/157.22 [5868]~P118(x58681)+~P94(x58681)+E(f326(f75(x58681),f326(f326(f243(x58681),f326(f103(x58681),a97)),x58682)),f77(x58681))
% 157.55/157.22 [6373]~P140(x63731)+~P105(f326(f326(f235(a1),x63732),f2(a1)))+E(f326(f78(x63731),f326(f100(x63731),f326(a104,f326(f78(a1),x63732)))),f326(f102(x63731),x63732))
% 157.55/157.22 [6576]P105(f326(f326(f234(a99),x65761),f77(a99)))+E(f326(f326(f79(a99),f77(a99)),f271(x65761,f326(f326(f36(a99),x65762),x65761))),f271(x65761,x65762))+P105(f326(f326(f235(a99),x65762),x65761))
% 157.55/157.22 [7182]~P92(x71821)+~P105(f326(f326(f328(x71821),x71822),f109(x71821)))+~E(f326(f326(f79(x71821),f326(f326(f79(x71821),f77(x71821)),x71822)),x71822),f2(x71821))
% 157.55/157.22 [7296]~P105(f326(f326(f234(a1),x72962),f2(a1)))+~P105(f326(f326(f235(a1),x72961),f2(a1)))+E(f326(f250(a1,a1),f326(a51,f47(f326(f78(a1),x72961),f326(f78(a1),x72962)))),f326(f326(f36(a1),x72961),x72962))
% 157.55/157.22 [7313]~P105(f326(f326(f234(a1),x73132),f2(a1)))+~P105(f326(f326(f235(a1),x73131),f2(a1)))+E(f326(f255(a1,a1),f326(a51,f47(f326(f78(a1),x73131),f326(f78(a1),x73132)))),f45(a1,x73131,x73132))
% 157.55/157.22 [7319]~P105(f326(f326(f235(a1),x73192),f2(a1)))+E(f326(f250(a1,a1),f326(a51,f50(f326(f78(a1),x73191),f326(f78(a1),x73192)))),f326(f326(f36(a1),x73191),x73192))+~P105(f326(f326(f235(a1),f2(a1)),x73191))
% 157.55/157.22 [7337]~P105(f326(f326(f235(a1),x73372),f2(a1)))+E(f326(f255(a1,a1),f326(a51,f50(f326(f78(a1),x73371),f326(f78(a1),x73372)))),f45(a1,x73371,x73372))+~P105(f326(f326(f235(a1),f2(a1)),x73371))
% 157.55/157.22 [7389]E(f326(f326(f36(a1),f326(f326(f243(a1),x73891),x73892)),x73891),f326(f326(f243(a1),x73891),f326(f326(f3(a909),x73892),f326(a112,f2(a909)))))+~P105(f326(f326(f235(a909),f2(a909)),x73892))+~P105(f326(f326(f235(a1),f2(a1)),x73891))
% 157.55/157.22 [7495]~P105(f326(f326(f235(a909),f2(a909)),x74951))+~P105(f326(f326(f235(a909),f2(a909)),x74952))+P105(f326(f326(f235(a909),f326(f326(f3(a909),x74951),x74952)),x74951))
% 157.55/157.22 [7496]~P105(f326(f326(f235(a909),f2(a909)),x74961))+~P105(f326(f326(f235(a909),f77(a909)),x74962))+P105(f326(f326(f235(a909),f326(f326(f36(a909),x74961),x74962)),x74961))
% 157.55/157.22 [7497]~P105(f326(f326(f235(a1),f2(a1)),x74971))+~P105(f326(f326(f235(a1),f77(a1)),x74972))+P105(f326(f326(f235(a1),f326(f326(f36(a1),x74971),x74972)),x74971))
% 157.55/157.22 [7634]E(x76341,f2(a909))+~E(x76342,f2(a1))+~P105(f326(f326(f235(a1),f2(a1)),f326(f326(f243(a1),f326(f75(a1),x76342)),x76341)))
% 157.55/157.22 [8046]~E(x80462,f113(f910(x80461)))+E(f326(f189(f910(f910(x80461))),f179(x80461,x80462)),f2(a909))+~P12(a909,f326(f168(a909),f326(f326(f154(f910(x80461),a909),f189(f910(x80461))),x80462)))
% 157.55/157.22 [8293]P105(f326(x82931,x82932))+~P105(f326(x82931,f326(a107,f529(x82931,x82932))))+~P105(f326(f326(f328(f917(f916(a909,a909),a905)),x82932),a98))
% 157.55/157.22 [8309]E(x83091,f113(f910(x83092)))+E(f326(f189(f910(x83092)),f326(f326(f164(f910(x83092)),x83091),f2(a909))),f326(f189(f910(f910(x83092))),f179(x83092,x83091)))+~P12(a909,f326(f168(a909),f326(f326(f154(f910(x83092),a909),f189(f910(x83092))),x83091)))
% 157.55/157.22 [8449]~P37(x84491,x84492)+~P38(x84491,x84492)+P37(x84491,f326(f326(f3(f917(f916(x84491,x84491),a905)),x84492),f306(x84491,f188(f917(f916(x84491,x84491),a905)))))
% 157.55/157.22 [9019]~P105(f326(f61(x90191),f326(f261(x90191),x90192)))+~P105(f326(f61(x90191),f241(f917(x90191,a905))))+P105(f326(f61(x90191),f326(f261(x90191),f326(f326(f10(a905,a905,x90191),a321),x90192))))
% 157.55/157.22 [9083]E(f326(f326(f251(a909,a909),f326(a112,f326(f326(f36(a909),f326(f326(f3(a909),x90831),x90832)),x90832))),f45(a909,f326(f326(f3(a909),x90831),x90832),x90832)),f84(f916(a909,a909),f48(x90831,x90832)))+~P105(f326(f326(f235(a909),f2(a909)),x90832))+~P105(f326(f326(f234(a909),x90832),x90831))
% 157.55/157.22 [9362]~P105(f326(f61(x93621),f326(f261(x93621),x93622)))+P105(f326(f61(x93621),f241(f917(x93621,a905))))+~P105(f326(f61(x93621),f326(f261(x93621),f326(f326(f10(a905,a905,x93621),a321),x93622))))
% 157.55/157.22 [10075]P26(x100751,x100752)+~P36(x100751,f326(f250(f917(f916(x100751,x100751),a905),f917(f916(x100751,x100751),a905)),x100752))+~P105(f326(f326(f234(f917(f916(x100751,x100751),a905)),f326(f326(f288(x100751,x100751,x100751),f326(f250(f917(f916(x100751,x100751),a905),f917(f916(x100751,x100751),a905)),x100752)),f326(f255(f917(f916(x100751,x100751),a905),f917(f916(x100751,x100751),a905)),x100752))),f326(f250(f917(f916(x100751,x100751),a905),f917(f916(x100751,x100751),a905)),x100752)))
% 157.55/157.22 [10172]~E(f299(a909,f286(a909),f326(f326(f20(a909,f917(a909,a905),f917(a909,a905)),f326(f326(f10(f917(a909,f917(a905,a905)),f917(f917(a909,a905),f917(a909,a905)),a909),f20(a909,a905,a905)),f326(f326(f10(f917(a909,a905),f917(a909,f917(a905,a905)),a909),f326(f10(a905,f917(a905,a905),a909),a324)),f286(a909)))),f326(f326(f10(f917(a909,a905),f917(a909,a905),a909),f326(f10(a905,a905,a909),a321)),f326(f9(a909,a909,a905),f286(a909)))),x101722,x101721),f188(f917(a909,a905)))+~P105(f326(f326(f286(a909),x101722),x101721))+P105(f326(f326(f286(a909),x101721),x101722))
% 157.55/157.22 [10173]~E(f296(a909,f286(a909),f326(f326(f20(a909,f917(a909,a905),f917(a909,a905)),f326(f326(f10(f917(a909,f917(a905,a905)),f917(f917(a909,a905),f917(a909,a905)),a909),f20(a909,a905,a905)),f326(f326(f10(f917(a909,a905),f917(a909,f917(a905,a905)),a909),f326(f10(a905,f917(a905,a905),a909),a324)),f286(a909)))),f326(f326(f10(f917(a909,a905),f917(a909,a905),a909),f326(f10(a905,a905,a909),a321)),f326(f9(a909,a909,a905),f286(a909)))),x101732,x101731),f188(f917(a909,a905)))+~P105(f326(f326(f286(a909),x101732),x101731))+P105(f326(f326(f286(a909),x101731),x101732))
% 157.55/157.22 [7419]~P105(f326(f326(f235(a909),f2(a909)),x74192))+P105(f326(f326(f235(a909),x74191),x74192))+E(f326(a112,f326(f326(f36(a909),f326(f326(f3(a909),x74191),x74192)),x74192)),f326(f326(f36(a909),x74191),x74192))
% 157.55/157.22 [7560]~P105(f326(f326(f235(a909),f2(a909)),x75602))+~P105(f326(f326(f234(a909),x75602),x75601))+E(f326(a112,f326(f326(f36(a909),f326(f326(f3(a909),x75601),x75602)),x75602)),f326(f326(f36(a909),x75601),x75602))
% 157.55/157.22 [8512]~P94(x85121)+~P92(x85121)+~P27(x85121,f326(f103(x85121),f326(f326(f3(a1),f326(f326(f79(a1),x85122),x85122)),a97)))
% 157.55/157.22 [9272]E(x92721,f2(a909))+E(f326(f326(f256(a909,a909,f916(a909,a909)),f326(f326(f10(a909,f917(a909,f916(a909,a909)),a909),f251(a909,a909)),a112)),f84(f916(a909,a909),f48(f326(f326(f3(a909),x92722),x92721),x92721))),f84(f916(a909,a909),f48(x92722,x92721)))+P105(f326(f326(f235(a909),x92722),x92721))
% 157.55/157.22 [9448]~P37(x94481,x94482)+~P50(x94481,x94482)+P105(f326(f326(f234(f917(f916(x94481,x94481),a905)),f326(f326(f288(x94481,x94481,x94481),f326(f285(x94481,x94481),x94482)),x94482)),x94482))
% 157.55/157.22 [9699]P105(f326(x96992,f637(x96992,x96991)))+P105(f326(x96991,f637(x96992,x96991)))+E(f326(f261(a1),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),f2(a1)))),x96991)),f326(f261(a1),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),f2(a1)))),x96992)))
% 157.55/157.22 [9703]~P105(f326(x97032,f637(x97032,x97031)))+~P105(f326(x97031,f637(x97032,x97031)))+E(f326(f261(a1),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),f2(a1)))),x97031)),f326(f261(a1),f326(f326(f20(a1,a905,a905),f326(f326(f10(a905,f917(a905,a905),a1),a324),f326(f234(a1),f2(a1)))),x97032)))
% 157.55/157.22 [7767]~P63(x77671)+~P94(x77671)+E(f326(f326(f290(x77671),x77672),f326(f103(x77671),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))),x77672)
% 157.55/157.22 [9395]~P94(x93951)+~E(f326(f103(x93951),x93952),f77(x93951))+P27(x93951,f326(f103(x93951),f326(f326(f79(a1),x93952),f326(f78(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.55/157.22 [9577]~P141(x95771)+~E(x95772,f77(x95771))+E(f326(f326(f243(x95771),x95772),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f77(x95771))
% 157.55/157.22 [9578]~P141(x95781)+~E(x95782,f2(x95781))+E(f326(f326(f243(x95781),x95782),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f2(x95781))
% 157.55/157.22 [9593]~P141(x95931)+~E(x95932,f326(f78(x95931),f77(x95931)))+E(f326(f326(f243(x95931),x95932),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f77(x95931))
% 157.55/157.22 [9636]~P94(x96361)+E(f326(f103(x96361),x96362),f77(x96361))+~P27(x96361,f326(f103(x96361),f326(f326(f79(a1),x96362),f326(f78(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.55/157.22 [10018]~P118(x100182)+E(x100181,f2(x100182))+P105(f326(f326(f235(x100182),f2(x100182)),f326(f326(f243(x100182),x100181),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))
% 157.55/157.22 [10074]~P118(x100742)+~E(x100741,f2(x100742))+~P105(f326(f326(f235(x100742),f2(x100742)),f326(f326(f243(x100742),x100741),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))
% 157.55/157.22 [10111]P105(f326(f326(f234(a1),x101111),f2(a1)))+P105(f326(f326(f235(a1),x101112),x101111))+E(f326(f43(x101111),f47(x101112,f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x101111))),f47(x101112,x101111))
% 157.55/157.22 [10112]~P105(f326(f326(f235(a1),f2(a1)),x101121))+P105(f326(f326(f235(a1),x101122),x101121))+E(f326(f43(x101121),f47(x101122,f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x101121))),f47(x101122,x101121))
% 157.55/157.22 [10113]P105(f326(f326(f234(a1),x101131),f2(a1)))+P105(f326(f326(f234(a1),f2(a1)),f326(f326(f79(a1),x101132),x101131)))+E(f326(f43(x101131),f50(x101132,f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x101131))),f50(x101132,x101131))
% 157.55/157.22 [10114]~P105(f326(f326(f235(a1),f2(a1)),x101141))+P105(f326(f326(f234(a1),f2(a1)),f326(f326(f79(a1),x101142),x101141)))+E(f326(f43(x101141),f50(x101142,f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x101141))),f50(x101142,x101141))
% 157.55/157.22 [10115]~P143(x101151)+~P105(f326(f326(f234(a1),f2(a1)),x101152))+E(f326(f100(x101151),f326(a104,f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x101152))),f326(f326(f79(x101151),f326(f100(x101151),f326(a104,x101152))),f326(f100(x101151),f326(a104,x101152))))
% 157.55/157.22 [5194]~P145(x51941,x51943,x51942)+~E(x51943,f2(a1))+P105(f326(x51941,x51942))
% 157.55/157.22 [5318]~P108(x53181)+~P12(x53181,x53183)+P12(x53181,f170(x53181,x53182,x53183))
% 157.55/157.22 [5319]~P108(x53191)+~P12(x53191,x53193)+P12(x53191,f177(x53191,x53192,x53193))
% 157.55/157.22 [4882]~P73(x48822)+~E(x48823,f326(f78(x48822),x48821))+E(x48821,f326(f78(x48822),x48823))
% 157.55/157.22 [4884]~P73(x48841)+~E(f326(f78(x48841),x48843),x48842)+E(f326(f78(x48841),x48842),x48843)
% 157.55/157.22 [4963]~P102(x49633)+E(x49631,x49632)+~E(f326(f100(x49633),x49631),f326(f100(x49633),x49632))
% 157.55/157.22 [4964]~P73(x49643)+E(x49641,x49642)+~E(f326(f78(x49643),x49641),f326(f78(x49643),x49642))
% 157.55/157.22 [4965]~P95(x49653)+E(x49651,x49652)+~E(f326(f78(x49653),x49651),f326(f78(x49653),x49652))
% 157.55/157.22 [4966]~P92(x49663)+E(x49661,x49662)+~E(f326(f102(x49663),x49661),f326(f102(x49663),x49662))
% 157.55/157.22 [4967]~P108(x49673)+E(x49671,x49672)+~E(f326(f281(x49673),x49671),f326(f281(x49673),x49672))
% 157.55/157.22 [4968]~P108(x49683)+E(x49681,x49682)+~E(f326(f300(x49683),x49681),f326(f300(x49683),x49682))
% 157.55/157.22 [4969]~P108(x49693)+E(x49691,x49692)+~E(f326(f303(x49693),x49691),f326(f303(x49693),x49692))
% 157.55/157.22 [4970]~P108(x49703)+E(x49701,x49702)+~E(f326(f282(x49703),x49701),f326(f282(x49703),x49702))
% 157.55/157.22 [5072]~P61(x50721)+~P105(f326(x50722,x50723))+P105(f326(f56(x50721),x50722))
% 157.55/157.22 [5112]~P61(x51123)+P105(f326(x51121,x51122))+~P105(f326(f57(x51123),x51121))
% 157.55/157.22 [5214]~P146(x52141,x52142,x52143)+~E(x52142,f2(a1))+P105(f326(x52141,f2(a1)))
% 157.55/157.22 [5254]~E(x52541,f2(a909))+E(f812(x52541,x52542,x52543),f188(f917(x52543,a905)))+~E(f326(f35(x52543),x52542),f326(a112,x52541))
% 157.55/157.22 [5403]~E(x54032,f2(a909))+E(f326(f250(a909,a909),x54031),f2(a909))+~P105(f326(f48(x54033,x54032),x54031))
% 157.55/157.22 [5448]P105(f326(x54481,x54482))+~E(x54483,f326(f100(a1),x54482))+~P105(f326(x54481,f326(a104,x54483)))
% 157.55/157.22 [5932]~E(x59323,f2(a909))+~P105(f326(x59321,x59322))+P105(f326(x59321,f45(a909,x59322,x59323)))
% 157.55/157.22 [6171]~P103(x61712)+~P103(x61711)+E(f131(x61711,x61712,f132(x61711,x61713),f132(x61712,x61713)),f132(f916(x61711,x61712),x61713))
% 157.55/157.22 [6355]~E(x63553,f2(a909))+P105(f326(x63551,x63552))+~P105(f326(x63551,f45(a909,x63552,x63553)))
% 157.55/157.22 [7037]E(x70371,f2(a909))+~P105(f326(x70372,f377(x70371,x70373,x70372)))+P105(f326(x70372,f45(a909,x70373,x70371)))
% 157.55/157.22 [7147]~P4(x71471)+~P105(f326(f326(f234(x71471),x71472),f383(x71473,x71472,x71471)))+P105(f326(f326(f234(x71471),x71472),f38(x71471,x71473)))
% 157.55/157.22 [7149]~P105(f326(x71491,x71492))+~P105(f326(x71491,f377(x71493,x71492,x71491)))+P105(f326(x71491,f45(a909,x71492,x71493)))
% 157.55/157.22 [7251]E(x72511,f113(x72512))+E(f326(f326(f151(x72512),f684(x72513,x72511,x72512)),f687(x72513,x72511,x72512)),x72511)+~P105(f326(f326(f328(f910(x72512)),x72511),f161(x72512,x72513)))
% 157.55/157.22 [7283]~P140(x72831)+~P105(f326(f326(f328(x72831),x72832),f109(x72831)))+P105(f326(f326(f328(x72831),f326(f326(f243(x72831),x72832),x72833)),f109(x72831)))
% 157.55/157.22 [7606]P36(x76061,x76062)+~P105(f326(f326(f328(x76061),x76063),f612(x76062,x76061)))+P105(f326(f326(f328(x76061),f634(x76062,x76061,x76063)),f612(x76062,x76061)))
% 157.55/157.22 [7871]E(x78711,f113(x78712))+~P105(f326(f326(f328(f910(x78712)),x78711),f161(x78712,x78713)))+P105(f326(f326(f328(f910(x78712)),f687(x78713,x78711,x78712)),f161(x78712,x78713)))
% 157.55/157.22 [7923]E(x79231,f2(a909))+E(f326(f326(f79(a909),f326(f326(f80(a909),x79231),f378(x79231,x79232,x79233))),f377(x79231,x79232,x79233)),x79232)+P105(f326(x79233,f45(a909,x79232,x79231)))
% 157.55/157.22 [7964]~P105(f326(x79643,x79642))+E(f326(f326(f79(a909),f326(f326(f80(a909),x79641),f378(x79641,x79642,x79643))),f377(x79641,x79642,x79643)),x79642)+P105(f326(x79643,f45(a909,x79642,x79641)))
% 157.55/157.22 [8101]P105(f326(f326(f235(a1),x81011),f360(x81012,x81013,x81011)))+P105(f326(f326(x81013,f326(f326(f36(a1),x81012),x81011)),f45(a1,x81012,x81011)))+~P105(f326(f326(f235(a1),x81011),f2(a1)))
% 157.55/157.22 [8364]P105(f326(f326(x83642,f326(f326(f36(a1),x83641),x83643)),f45(a1,x83641,x83643)))+~P105(f326(f326(f235(a1),x83643),f2(a1)))+P105(f326(f326(f234(a1),f360(x83641,x83642,x83643)),f2(a1)))
% 157.55/157.22 [8546]E(f326(f326(f79(a1),f326(f326(f80(a1),x85461),f361(x85462,x85463,x85461))),f360(x85462,x85463,x85461)),x85462)+P105(f326(f326(x85463,f326(f326(f36(a1),x85462),x85461)),f45(a1,x85462,x85461)))+~P105(f326(f326(f235(a1),x85461),f2(a1)))
% 157.55/157.22 [8782]~P105(f326(f326(x87821,f361(x87822,x87821,x87823)),f360(x87822,x87821,x87823)))+P105(f326(f326(x87821,f326(f326(f36(a1),x87822),x87823)),f45(a1,x87822,x87823)))+~P105(f326(f326(f235(a1),x87823),f2(a1)))
% 157.55/157.22 [9032]~P108(x90321)+~P12(x90321,x90323)+P12(x90321,f149(x90321,x90321,f7(x90321),x90322,x90323))
% 157.55/157.22 [9525]~P125(x95252)+E(x95251,f2(x95252))+~P105(f326(f326(f234(x95252),f326(f326(f79(x95252),f326(f326(f80(x95252),x95253),x95253)),f326(f326(f80(x95252),x95251),x95251))),f2(x95252)))
% 157.55/157.22 [9526]~P125(x95262)+E(x95261,f2(x95262))+~P105(f326(f326(f234(x95262),f326(f326(f79(x95262),f326(f326(f80(x95262),x95261),x95261)),f326(f326(f80(x95262),x95263),x95263))),f2(x95262)))
% 157.55/157.22 [10326]~P118(x103261)+~P105(f326(f326(f235(x103261),x103262),f2(x103261)))+P105(f326(f326(f235(x103261),f326(f326(f243(x103261),x103262),f326(a112,f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x103263)))),f2(x103261)))
% 157.55/157.22 [10336]~P118(x103362)+E(x103361,f2(x103362))+~P105(f326(f326(f234(x103362),f326(f326(f79(x103362),f326(f326(f243(x103362),x103363),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x103362),x103361),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))),f2(x103362)))
% 157.55/157.22 [10337]~P118(x103372)+E(x103371,f2(x103372))+~P105(f326(f326(f234(x103372),f326(f326(f79(x103372),f326(f326(f243(x103372),x103371),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x103372),x103373),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))),f2(x103372)))
% 157.55/157.22 [4918]~E(x49182,x49183)+~P66(x49181)+E(f326(f326(f3(x49181),x49182),x49183),f2(x49181))
% 157.55/157.22 [4919]~E(x49192,x49193)+~P73(x49191)+E(f326(f326(f3(x49191),x49192),x49193),f2(x49191))
% 157.55/157.22 [4932]~P137(x49321)+~E(x49323,f2(x49321))+E(f326(f326(f79(x49321),x49322),x49323),x49322)
% 157.55/157.22 [4949]~P139(x49491)+~E(x49493,f2(x49491))+E(f326(f326(f80(x49491),x49492),x49493),f2(x49491))
% 157.55/157.22 [4950]~P139(x49501)+~E(x49502,f2(x49501))+E(f326(f326(f80(x49501),x49502),x49503),f2(x49501))
% 157.55/157.22 [4972]~E(x49723,f113(x49721))+~E(x49722,f113(x49721))+E(f326(f326(f134(x49721),x49722),x49723),f113(x49721))
% 157.55/157.22 [5062]~P137(x50622)+E(x50621,f2(x50622))+~E(f326(f326(f79(x50622),x50623),x50621),x50623)
% 157.55/157.22 [5063]~P73(x50631)+~E(x50632,f326(f78(x50631),x50633))+E(f326(f326(f79(x50631),x50632),x50633),f2(x50631))
% 157.55/157.22 [5070]E(x50701,f113(x50702))+E(x50703,f2(a909))+~E(f326(f326(f175(x50702),x50703),x50701),f113(x50702))
% 157.55/157.22 [5080]~P66(x50803)+E(x50801,x50802)+~E(f326(f326(f3(x50803),x50801),x50802),f2(x50803))
% 157.55/157.22 [5081]~P73(x50813)+E(x50811,x50812)+~E(f326(f326(f3(x50813),x50811),x50812),f2(x50813))
% 157.55/157.22 [5094]~P141(x50942)+E(x50941,f2(x50942))+~E(f326(f326(f243(x50942),x50941),x50943),f2(x50942))
% 157.55/157.22 [5095]~P78(x50952)+E(x50951,f188(x50952))+~E(f326(f326(f110(x50952),x50953),x50951),f188(x50952))
% 157.55/157.22 [5096]~P78(x50962)+E(x50961,f188(x50962))+~E(f326(f326(f110(x50962),x50961),x50963),f188(x50962))
% 157.55/157.22 [5097]~P99(x50972)+E(x50971,f241(x50972))+~E(f326(f326(f101(x50972),x50973),x50971),f241(x50972))
% 157.55/157.22 [5098]~P99(x50982)+E(x50981,f241(x50982))+~E(f326(f326(f101(x50982),x50981),x50983),f241(x50982))
% 157.55/157.22 [5168]~P73(x51682)+E(x51681,f326(f78(x51682),x51683))+~E(f326(f326(f79(x51682),x51681),x51683),f2(x51682))
% 157.55/157.22 [5169]~P73(x51691)+E(f326(f78(x51691),x51692),x51693)+~E(f326(f326(f79(x51691),x51692),x51693),f2(x51691))
% 157.55/157.22 [5171]~E(x51712,x51713)+~P106(x51711)+P105(f326(f326(f234(x51711),x51712),x51713))
% 157.55/157.22 [5173]~E(x51732,x51733)+~P109(x51731)+P105(f326(f326(f234(x51731),x51732),x51733))
% 157.55/157.22 [5271]~P120(x52711)+~E(x52712,f326(f78(x52711),x52713))+E(f326(f326(f80(x52711),x52712),x52712),f326(f326(f80(x52711),x52713),x52713))
% 157.55/157.22 [5279]~P108(x52791)+~P12(x52791,x52793)+P12(x52791,f326(f326(f175(x52791),x52792),x52793))
% 157.55/157.22 [5280]~P108(x52801)+~P12(x52801,x52803)+P12(x52801,f326(f326(f138(x52801),x52802),x52803))
% 157.55/157.22 [5316]E(x53161,x53162)+E(x53163,f2(a909))+~E(f326(f326(f80(a909),x53163),x53161),f326(f326(f80(a909),x53163),x53162))
% 157.55/157.22 [5317]E(x53171,x53172)+E(x53173,f2(a909))+~E(f326(f326(f80(a909),x53171),x53173),f326(f326(f80(a909),x53172),x53173))
% 157.55/157.22 [5396]~E(x53962,x53963)+~P109(x53961)+E(f302(x53961,x53962,x53963),f326(f326(f308(x53961),x53962),f188(f917(x53961,a905))))
% 157.55/157.22 [5437]~P118(x54371)+~E(f326(f75(x54371),x54372),f326(f75(x54371),x54373))+P105(f326(f326(f286(x54371),x54372),x54373))
% 157.55/157.22 [5445]~E(x54451,x54452)+~P108(x54453)+~P105(f326(f326(f235(x54453),x54451),x54452))
% 157.55/157.22 [5446]~E(x54461,x54462)+~P109(x54463)+~P105(f326(f326(f235(x54463),x54461),x54462))
% 157.55/157.22 [5459]~P109(x54591)+E(f326(f301(x54591,x54592),x54593),f188(f917(x54591,a905)))+P105(f326(f326(f235(x54591),x54592),x54593))
% 157.55/157.22 [5507]~P109(x55071)+E(f302(x55071,x55072,x55073),f188(f917(x55071,a905)))+P105(f326(f326(f234(x55071),x55072),x55073))
% 157.55/157.22 [5508]~P109(x55081)+E(f304(x55081,x55082,x55083),f188(f917(x55081,a905)))+P105(f326(f326(f235(x55081),x55082),x55083))
% 157.55/157.22 [5509]~P109(x55091)+E(f188(f917(x55091,a905)),f302(x55091,x55092,x55093))+P105(f326(f326(f234(x55091),x55092),x55093))
% 157.55/157.22 [5510]~P109(x55101)+E(f188(f917(x55101,a905)),f304(x55101,x55102,x55103))+P105(f326(f326(f235(x55101),x55102),x55103))
% 157.55/157.22 [5518]~P100(x55181)+~E(f326(f326(f110(x55181),x55182),x55183),x55183)+P105(f326(f326(f234(x55181),x55182),x55183))
% 157.55/157.22 [5519]~P101(x55191)+~E(f326(f326(f101(x55191),x55192),x55193),x55192)+P105(f326(f326(f234(x55191),x55192),x55193))
% 157.55/157.22 [5520]~P108(x55201)+~E(f326(f326(f232(x55201),x55202),x55203),x55202)+P105(f326(f326(f234(x55201),x55202),x55203))
% 157.55/157.22 [5521]~P108(x55211)+~E(f326(f326(f233(x55211),x55212),x55213),x55213)+P105(f326(f326(f234(x55211),x55212),x55213))
% 157.55/157.22 [5540]~P108(x55401)+P12(x55401,x55402)+~P12(x55401,f326(f326(f151(x55401),x55403),x55402))
% 157.55/157.22 [5541]~P108(x55411)+P12(x55411,x55412)+~P12(x55411,f326(f326(f134(x55411),x55413),x55412))
% 157.55/157.22 [5542]~P108(x55421)+P12(x55421,x55422)+~P12(x55421,f326(f326(f134(x55421),x55422),x55423))
% 157.55/157.22 [5547]~P59(x55471)+~E(f45(x55471,x55473,x55472),f2(x55471))+P105(f326(f326(f286(x55471),x55472),x55473))
% 157.55/157.22 [5609]~P108(x56091)+P105(f326(f326(f234(x56091),x56093),x56092))+P105(f326(f326(f234(x56091),x56092),x56093))
% 157.55/157.22 [5614]~P108(x56141)+P105(f326(f326(f235(x56141),x56143),x56142))+P105(f326(f326(f234(x56141),x56142),x56143))
% 157.55/157.22 [5652]~P100(x56521)+E(f326(f326(f110(x56521),x56522),x56523),x56522)+~P105(f326(f326(f234(x56521),x56523),x56522))
% 157.55/157.22 [5654]~P100(x56541)+E(f326(f326(f110(x56541),x56542),x56543),x56543)+~P105(f326(f326(f234(x56541),x56542),x56543))
% 157.55/157.22 [5655]~P101(x56551)+E(f326(f326(f101(x56551),x56552),x56553),x56553)+~P105(f326(f326(f234(x56551),x56553),x56552))
% 157.55/157.22 [5657]~P101(x56571)+E(f326(f326(f101(x56571),x56572),x56573),x56572)+~P105(f326(f326(f234(x56571),x56572),x56573))
% 157.55/157.22 [5658]~P108(x56581)+E(f326(f326(f232(x56581),x56582),x56583),x56583)+~P105(f326(f326(f234(x56581),x56583),x56582))
% 157.55/157.22 [5660]~P108(x56601)+E(f326(f326(f232(x56601),x56602),x56603),x56602)+~P105(f326(f326(f234(x56601),x56602),x56603))
% 157.55/157.22 [5661]~P108(x56611)+E(f326(f326(f233(x56611),x56612),x56613),x56612)+~P105(f326(f326(f234(x56611),x56613),x56612))
% 157.55/157.22 [5663]~P108(x56631)+E(f326(f326(f233(x56631),x56632),x56633),x56633)+~P105(f326(f326(f234(x56631),x56632),x56633))
% 157.55/157.22 [5670]~P121(x56702)+E(x56701,f2(x56702))+E(f326(f326(f290(x56702),f326(f78(x56702),x56703)),f326(f78(x56702),x56701)),f326(f326(f290(x56702),x56703),x56701))
% 157.55/157.22 [5677]~P59(x56771)+E(f45(x56771,x56772,x56773),f2(x56771))+~P105(f326(f326(f286(x56771),x56773),x56772))
% 157.55/157.22 [5724]~P109(x57241)+E(f326(f301(x57241,x57242),x57243),f188(f917(x57241,a905)))+~P105(f326(f326(f234(x57241),x57243),x57242))
% 157.55/157.22 [5757]~P109(x57571)+E(f302(x57571,x57572,x57573),f188(f917(x57571,a905)))+~P105(f326(f326(f235(x57571),x57573),x57572))
% 157.55/157.22 [5758]~P109(x57581)+E(f305(x57581,x57582,x57583),f188(f917(x57581,a905)))+~P105(f326(f326(f234(x57581),x57583),x57582))
% 157.55/157.22 [5759]~P109(x57591)+E(f304(x57591,x57592,x57593),f188(f917(x57591,a905)))+~P105(f326(f326(f234(x57591),x57593),x57592))
% 157.55/157.22 [5811]~E(f326(f326(f3(a909),x58111),x58113),x58112)+E(x58111,f326(f326(f79(a909),x58112),x58113))+~P105(f326(f326(f234(a909),x58113),x58111))
% 157.55/157.22 [5812]~E(x58121,f326(f326(f79(a909),x58123),x58122))+E(f326(f326(f3(a909),x58121),x58122),x58123)+~P105(f326(f326(f234(a909),x58122),x58121))
% 157.55/157.22 [5857]~P105(f326(x58571,x58573))+P105(f326(x58571,f422(x58571,x58572)))+~P105(f326(f326(f234(a909),x58573),x58572))
% 157.55/157.22 [5858]~P105(f326(x58581,x58583))+P105(f326(x58581,f444(x58581,x58582)))+~P105(f326(f326(f235(a909),x58583),x58582))
% 157.55/157.22 [5866]~P109(x58661)+~E(f326(f301(x58661,x58662),x58663),f188(f917(x58661,a905)))+~P105(f326(f326(f235(x58661),x58662),x58663))
% 157.55/157.22 [5871]~P106(x58711)+~P105(f326(f326(f235(x58711),x58712),x58713))+P105(f326(f326(f234(x58711),x58712),x58713))
% 157.55/157.22 [5873]~P109(x58731)+~P105(f326(f326(f235(x58731),x58732),x58733))+P105(f326(f326(f234(x58731),x58732),x58733))
% 157.55/157.22 [5991]~P109(x59911)+~E(f302(x59911,x59912,x59913),f188(f917(x59911,a905)))+~P105(f326(f326(f234(x59911),x59912),x59913))
% 157.55/157.22 [5992]~P109(x59921)+~E(f304(x59921,x59922,x59923),f188(f917(x59921,a905)))+~P105(f326(f326(f235(x59921),x59922),x59923))
% 157.55/157.22 [5993]~P109(x59931)+~E(f188(f917(x59931,a905)),f302(x59931,x59932,x59933))+~P105(f326(f326(f234(x59931),x59932),x59933))
% 157.55/157.22 [5994]~P109(x59941)+~E(f188(f917(x59941,a905)),f304(x59941,x59942,x59943))+~P105(f326(f326(f235(x59941),x59942),x59943))
% 157.55/157.22 [6004]P105(f326(x60041,x60042))+~P105(f326(x60041,f412(x60041,x60043)))+~P105(f326(f326(f234(a909),x60042),x60043))
% 157.55/157.22 [6005]P105(f326(x60051,x60052))+~P105(f326(x60051,f445(x60051,x60053)))+~P105(f326(f326(f235(a909),x60052),x60053))
% 157.55/157.22 [6013]~E(x60131,f326(a112,x60133))+P105(f326(f326(f235(a909),x60131),f326(a112,x60132)))+~P105(f326(f326(f235(a909),x60133),x60132))
% 157.55/157.22 [6032]E(x60321,x60322)+~E(f326(f326(f80(a909),x60323),x60321),f326(f326(f80(a909),x60323),x60322))+~P105(f326(f326(f235(a909),f2(a909)),x60323))
% 157.55/157.22 [6088]E(f326(x60881,f867(x60881,x60882,x60883)),f77(a909))+~E(f326(f326(f8(x60883,a909),x60881),x60882),f77(a909))+~P105(f326(f61(x60883),x60882))
% 157.55/157.22 [6104]~P4(x61041)+P105(f326(f326(f234(x61041),x61042),f37(x61041,x61043)))+~P105(f326(f326(f328(x61041),x61042),x61043))
% 157.55/157.22 [6127]~P106(x61271)+~P105(f326(f326(f235(x61271),x61273),x61272))+~P105(f326(f326(f234(x61271),x61272),x61273))
% 157.55/157.22 [6131]~P106(x61311)+~P105(f326(f326(f235(x61311),x61313),x61312))+~P105(f326(f326(f235(x61311),x61312),x61313))
% 157.55/157.22 [6134]~P108(x61341)+~P105(f326(f326(f235(x61341),x61343),x61342))+~P105(f326(f326(f234(x61341),x61342),x61343))
% 157.55/157.22 [6135]~P108(x61351)+~P105(f326(f326(f235(x61351),x61353),x61352))+~P105(f326(f326(f235(x61351),x61352),x61353))
% 157.55/157.22 [6136]~P109(x61361)+~P105(f326(f326(f235(x61361),x61363),x61362))+~P105(f326(f326(f235(x61361),x61362),x61363))
% 157.55/157.22 [6156]~E(x61562,x61563)+~E(x61561,x61562)+E(f289(a909,f286(a909),x61561,x61562),f326(f326(f308(a909),x61563),f188(f917(a909,a905))))
% 157.55/157.22 [6163]~E(f326(x61632,f868(x61632,x61633,x61631)),f2(a909))+E(f326(f326(f8(x61631,a909),x61632),x61633),f2(a909))+~P105(f326(f61(x61631),x61633))
% 157.55/157.22 [6164]~E(f326(x61642,f785(x61642,x61643,x61641)),f77(a909))+E(f326(f326(f11(x61641,a909),x61642),x61643),f77(a909))+~P105(f326(f61(x61641),x61643))
% 157.55/157.22 [6180]~P107(x61801)+~P105(f326(f326(f235(x61801),x61803),x61802))+P105(f326(f326(f328(x61801),x61802),f326(f303(x61801),x61803)))
% 157.55/157.22 [6181]~P107(x61811)+~P105(f326(f326(f234(x61811),x61813),x61812))+P105(f326(f326(f328(x61811),x61812),f326(f282(x61811),x61813)))
% 157.55/157.22 [6182]~P107(x61821)+~P105(f326(f326(f235(x61821),x61822),x61823))+P105(f326(f326(f328(x61821),x61822),f326(f281(x61821),x61823)))
% 157.55/157.22 [6183]~P107(x61831)+~P105(f326(f326(f234(x61831),x61832),x61833))+P105(f326(f326(f328(x61831),x61832),f326(f300(x61831),x61833)))
% 157.55/157.22 [6184]~P118(x61841)+~P105(f326(f326(f286(x61841),x61842),x61843))+P105(f326(f326(f286(x61841),x61842),f326(f75(x61841),x61843)))
% 157.55/157.22 [6196]E(f326(x61961,f869(x61961,x61962,x61963)),f326(a112,f2(a909)))+~E(f326(f326(f8(x61963,a909),x61961),x61962),f326(a112,f2(a909)))+~P105(f326(f61(x61963),x61962))
% 157.55/157.22 [6279]~P4(x62791)+~P105(f326(f326(f328(x62791),x62793),x62792))+P105(f326(f326(f234(x62791),f38(x62791,x62792)),x62793))
% 157.55/157.22 [6299]~P105(f326(f326(f234(a909),x62991),x62993))+P105(f326(f326(f234(a909),x62991),x62992))+~P105(f326(f326(f234(a909),x62993),x62992))
% 157.55/157.22 [6300]~P105(f326(f326(f234(a1),x63001),x63003))+P105(f326(f326(f234(a1),x63001),x63002))+~P105(f326(f326(f234(a1),x63003),x63002))
% 157.55/157.22 [6301]~P105(f326(f326(f286(a909),x63011),x63013))+P105(f326(f326(f286(a909),x63011),x63012))+~P105(f326(f326(f286(a909),x63013),x63012))
% 157.55/157.22 [6321]~P107(x63211)+~P105(f326(f326(f328(x63211),x63213),f326(f282(x63211),x63212)))+P105(f326(f326(f234(x63211),x63212),x63213))
% 157.55/157.22 [6322]~P107(x63221)+~P105(f326(f326(f328(x63221),x63222),f326(f300(x63221),x63223)))+P105(f326(f326(f234(x63221),x63222),x63223))
% 157.55/157.22 [6323]~P107(x63231)+~P105(f326(f326(f328(x63231),x63233),f326(f303(x63231),x63232)))+P105(f326(f326(f235(x63231),x63232),x63233))
% 157.55/157.22 [6324]~P107(x63241)+~P105(f326(f326(f328(x63241),x63242),f326(f281(x63241),x63243)))+P105(f326(f326(f235(x63241),x63242),x63243))
% 157.55/157.22 [6325]~P118(x63251)+~P105(f326(f326(f286(x63251),x63252),f326(f75(x63251),x63253)))+P105(f326(f326(f286(x63251),x63252),x63253))
% 157.55/157.22 [6398]~P105(f326(x63981,x63982))+P105(f326(x63981,f786(x63981)))+~P105(f326(f326(f328(x63983),x63982),f241(f917(x63983,a905))))
% 157.55/157.22 [6542]~P64(x65421)+P105(f326(f326(f235(x65421),f2(x65421)),f885(x65423,x65422,x65421)))+P105(f326(f326(f234(x65421),x65422),x65423))
% 157.55/157.22 [6543]~P65(x65431)+P105(f326(f326(f235(x65431),f2(x65431)),f891(x65433,x65432,x65431)))+P105(f326(f326(f234(x65431),x65432),x65433))
% 157.55/157.22 [6609]~P79(x66091)+~P105(f326(f326(f234(x66091),x66093),f326(f78(x66091),x66092)))+P105(f326(f326(f234(x66091),x66092),f326(f78(x66091),x66093)))
% 157.55/157.22 [6611]~P79(x66111)+~P105(f326(f326(f235(x66111),x66113),f326(f78(x66111),x66112)))+P105(f326(f326(f235(x66111),x66112),f326(f78(x66111),x66113)))
% 157.55/157.22 [6623]~P105(f326(f326(f235(a909),x66231),x66233))+~P105(f326(f326(f235(a909),x66233),x66232))+P105(f326(f326(f235(a909),f326(a112,x66231)),x66232))
% 157.55/157.22 [6651]~P124(x66511)+P105(f326(f326(f234(x66511),f326(f100(x66511),x66512)),f326(f100(x66511),x66513)))+~P105(f326(f326(f234(a909),x66512),x66513))
% 157.55/157.22 [6652]~P118(x66521)+P105(f326(f326(f234(x66521),f326(f102(x66521),x66522)),f326(f102(x66521),x66523)))+~P105(f326(f326(f234(a1),x66522),x66523))
% 157.55/157.22 [6654]~P118(x66541)+P105(f326(f326(f235(x66541),f326(f102(x66541),x66542)),f326(f102(x66541),x66543)))+~P105(f326(f326(f235(a1),x66542),x66543))
% 157.55/157.22 [6655]~P124(x66551)+P105(f326(f326(f235(x66551),f326(f100(x66551),x66552)),f326(f100(x66551),x66553)))+~P105(f326(f326(f235(a909),x66552),x66553))
% 157.55/157.22 [6661]~P108(x66611)+E(f326(f326(f110(f917(x66611,a905)),f326(f281(x66611),x66612)),f326(f301(x66611,x66612),x66613)),f326(f281(x66611),x66613))+~P105(f326(f326(f234(x66611),x66612),x66613))
% 157.55/157.22 [6691]~P79(x66911)+~P105(f326(f326(f234(x66911),x66913),x66912))+P105(f326(f326(f234(x66911),f326(f78(x66911),x66912)),f326(f78(x66911),x66913)))
% 157.55/157.22 [6693]~P95(x66931)+~P105(f326(f326(f234(x66931),x66933),x66932))+P105(f326(f326(f234(x66931),f326(f78(x66931),x66932)),f326(f78(x66931),x66933)))
% 157.55/157.22 [6694]~P79(x66941)+~P105(f326(f326(f235(x66941),x66943),x66942))+P105(f326(f326(f235(x66941),f326(f78(x66941),x66942)),f326(f78(x66941),x66943)))
% 157.55/157.22 [6729]~P108(x67291)+E(f326(f326(f110(f917(x67291,a905)),f326(f281(x67291),x67292)),f302(x67291,x67292,x67293)),f326(f300(x67291),x67293))+~P105(f326(f326(f234(x67291),x67292),x67293))
% 157.55/157.22 [6730]~P108(x67301)+E(f326(f326(f110(f917(x67301,a905)),f326(f300(x67301),x67302)),f305(x67301,x67302,x67303)),f326(f281(x67301),x67303))+~P105(f326(f326(f235(x67301),x67302),x67303))
% 157.55/157.22 [6731]~P108(x67311)+E(f326(f326(f110(f917(x67311,a905)),f326(f300(x67311),x67312)),f304(x67311,x67312,x67313)),f326(f300(x67311),x67313))+~P105(f326(f326(f234(x67311),x67312),x67313))
% 157.55/157.22 [6765]~P108(x67651)+E(f326(f326(f110(f917(x67651,a905)),f326(f301(x67651,x67652),x67653)),f326(f282(x67651),x67653)),f326(f282(x67651),x67652))+~P105(f326(f326(f234(x67651),x67652),x67653))
% 157.55/157.22 [6922]~P108(x69221)+E(f326(f326(f110(f917(x69221,a905)),f302(x69221,x69222,x69223)),f326(f303(x69221),x69223)),f326(f282(x69221),x69222))+~P105(f326(f326(f234(x69221),x69222),x69223))
% 157.55/157.22 [6923]~P108(x69231)+E(f326(f326(f110(f917(x69231,a905)),f305(x69231,x69232,x69233)),f326(f282(x69231),x69233)),f326(f303(x69231),x69232))+~P105(f326(f326(f235(x69231),x69232),x69233))
% 157.55/157.22 [6924]~P108(x69241)+E(f326(f326(f110(f917(x69241,a905)),f304(x69241,x69242,x69243)),f326(f303(x69241),x69243)),f326(f303(x69241),x69242))+~P105(f326(f326(f234(x69241),x69242),x69243))
% 157.55/157.22 [6943]P105(f326(x69431,x69432))+~P105(f326(f326(f234(a909),x69432),x69433))+P105(f326(f326(f328(a909),f412(x69431,x69433)),f302(a909,f2(a909),x69433)))
% 157.55/157.22 [6977]E(x69771,x69772)+~E(f326(f326(f164(x69773),x69771),f633(x69773,x69772,x69771)),f326(f326(f164(x69773),x69772),f633(x69773,x69772,x69771)))+~E(f326(f189(f910(x69773)),x69771),f326(f189(f910(x69773)),x69772))
% 157.55/157.22 [6982]~E(x69823,f326(f326(f36(a909),x69821),x69822))+~P105(f326(f326(f235(a909),f2(a909)),x69822))+P105(f326(f326(f235(a909),x69821),f326(f326(f80(a909),x69822),f326(a112,x69823))))
% 157.55/157.22 [6998]~P105(f326(x69981,x69983))+~P105(f326(f326(f234(a909),x69983),x69982))+P105(f326(f326(f328(a909),f422(x69981,x69982)),f302(a909,f2(a909),x69982)))
% 157.55/157.22 [7035]~P105(f326(x70351,x70353))+P105(f326(x70351,f423(x70351,x70352)))+~P105(f326(f326(f328(a909),x70353),f302(a909,f2(a909),x70352)))
% 157.55/157.22 [7053]~P124(x70533)+~P105(f326(f326(f234(x70533),f326(f100(x70533),x70531)),f326(f100(x70533),x70532)))+P105(f326(f326(f234(a909),x70531),x70532))
% 157.55/157.22 [7054]~P118(x70543)+~P105(f326(f326(f234(x70543),f326(f102(x70543),x70541)),f326(f102(x70543),x70542)))+P105(f326(f326(f234(a1),x70541),x70542))
% 157.55/157.22 [7056]~P124(x70563)+~P105(f326(f326(f235(x70563),f326(f100(x70563),x70561)),f326(f100(x70563),x70562)))+P105(f326(f326(f235(a909),x70561),x70562))
% 157.55/157.22 [7057]~P118(x70573)+~P105(f326(f326(f235(x70573),f326(f102(x70573),x70571)),f326(f102(x70573),x70572)))+P105(f326(f326(f235(a1),x70571),x70572))
% 157.55/157.22 [7074]~P124(x70741)+~P105(f326(f326(f235(x70741),f77(x70741)),x70742))+P105(f326(f326(f235(x70741),f77(x70741)),f326(f326(f243(x70741),x70742),f326(a112,x70743))))
% 157.55/157.22 [7076]~P79(x70761)+~P105(f326(f326(f234(x70761),f326(f78(x70761),x70763)),f326(f78(x70761),x70762)))+P105(f326(f326(f234(x70761),x70762),x70763))
% 157.55/157.22 [7077]~P95(x70771)+~P105(f326(f326(f234(x70771),f326(f78(x70771),x70773)),f326(f78(x70771),x70772)))+P105(f326(f326(f234(x70771),x70772),x70773))
% 157.55/157.22 [7078]~P79(x70781)+~P105(f326(f326(f235(x70781),f326(f78(x70781),x70783)),f326(f78(x70781),x70782)))+P105(f326(f326(f235(x70781),x70782),x70783))
% 157.55/157.22 [7102]P105(f326(x71021,x71022))+~P105(f326(x71021,f413(x71021,x71023)))+~P105(f326(f326(f328(a909),x71022),f302(a909,f2(a909),x71023)))
% 157.55/157.22 [7123]~P64(x71231)+P105(f326(f326(f235(x71231),f885(x71233,x71232,x71231)),f77(x71231)))+P105(f326(f326(f234(x71231),x71232),x71233))
% 157.55/157.22 [7144]~E(f45(a909,x71443,x71442),f45(a909,x71441,x71442))+E(f326(f326(f79(a909),x71441),f326(f326(f80(a909),x71442),f380(x71441,x71442,x71443))),x71443)+~P105(f326(f326(f234(a909),x71441),x71443))
% 157.55/157.22 [7199]E(f326(f326(f8(x71991,a909),x71992),x71993),f2(a909))+~P105(f326(f61(x71991),x71993))+P105(f326(f326(f328(x71991),f868(x71992,x71993,x71991)),x71993))
% 157.55/157.22 [7200]E(f326(f326(f11(x72001,a909),x72002),x72003),f77(a909))+~P105(f326(f61(x72001),x72003))+P105(f326(f326(f328(x72001),f785(x72002,x72003,x72001)),x72003))
% 157.55/157.22 [7222]~P108(x72221)+~P105(f326(f326(f234(x72221),x72222),x72223))+P105(f326(f326(f234(f917(x72221,a905)),f326(f281(x72221),x72222)),f326(f281(x72221),x72223)))
% 157.55/157.22 [7223]~P109(x72231)+~P105(f326(f326(f234(x72231),x72232),x72233))+P105(f326(f326(f234(f917(x72231,a905)),f326(f300(x72231),x72232)),f326(f300(x72231),x72233)))
% 157.55/157.22 [7224]~P108(x72241)+~P105(f326(f326(f234(x72241),x72243),x72242))+P105(f326(f326(f234(f917(x72241,a905)),f326(f303(x72241),x72242)),f326(f303(x72241),x72243)))
% 157.55/157.22 [7225]~P109(x72251)+~P105(f326(f326(f234(x72251),x72253),x72252))+P105(f326(f326(f234(f917(x72251,a905)),f326(f282(x72251),x72252)),f326(f282(x72251),x72253)))
% 157.55/157.22 [7226]~P108(x72261)+~P105(f326(f326(f235(x72261),x72262),x72263))+P105(f326(f326(f235(f917(x72261,a905)),f326(f281(x72261),x72262)),f326(f281(x72261),x72263)))
% 157.55/157.22 [7237]~P4(x72371)+P105(f326(f326(f234(x72371),x72372),f38(x72371,x72373)))+P105(f326(f326(f328(x72371),f383(x72373,x72372,x72371)),x72373))
% 157.55/157.22 [7243]~P79(x72431)+P105(f326(f326(f234(x72431),f326(f326(f3(x72431),x72432),x72433)),f2(x72431)))+~P105(f326(f326(f234(x72431),x72432),x72433))
% 157.55/157.22 [7244]~P79(x72441)+P105(f326(f326(f235(x72441),f326(f326(f3(x72441),x72442),x72443)),f2(x72441)))+~P105(f326(f326(f235(x72441),x72442),x72443))
% 157.55/157.22 [7286]P105(f326(x72861,x72862))+P105(f326(f326(f234(a909),f413(x72861,x72863)),x72863))+~P105(f326(f326(f328(a909),x72862),f302(a909,f2(a909),x72863)))
% 157.55/157.22 [7326]~E(f326(f326(f8(x73261,a909),x73262),x73263),f77(a909))+~P105(f326(f61(x73261),x73263))+P105(f326(f326(f328(x73261),f867(x73262,x73263,x73261)),x73263))
% 157.55/157.22 [7327]~P105(f326(x73271,x73273))+P105(f326(f326(f234(a909),f423(x73271,x73272)),x73272))+~P105(f326(f326(f328(a909),x73273),f302(a909,f2(a909),x73272)))
% 157.55/157.22 [7366]~P4(x73661)+P105(f326(f326(f328(x73661),f729(x73663,x73662,x73661)),x73662))+P105(f326(f326(f234(x73661),f37(x73661,x73662)),x73663))
% 157.55/157.22 [7400]~E(f326(f326(f8(x74001,a909),x74002),x74003),f326(a112,f2(a909)))+~P105(f326(f61(x74001),x74003))+P105(f326(f326(f328(x74001),f869(x74002,x74003,x74001)),x74003))
% 157.55/157.22 [7411]E(x74111,f2(a909))+P105(f326(x74112,f45(a909,x74113,x74111)))+P105(f326(f326(f235(a909),f377(x74111,x74113,x74112)),x74111))
% 157.55/157.22 [7525]~P105(f326(x75251,x75252))+P105(f326(x75251,f45(a909,x75252,x75253)))+P105(f326(f326(f235(a909),f377(x75253,x75252,x75251)),x75253))
% 157.55/157.22 [7638]E(x76381,f113(x76382))+~P105(f326(f326(f328(f910(x76382)),x76381),f161(x76382,x76383)))+P105(f326(f326(f328(x76382),f684(x76383,x76381,x76382)),x76383))
% 157.55/157.22 [7660]~P108(x76601)+E(f326(f326(f110(f917(x76601,a905)),f326(f326(f308(x76601),x76602),f188(f917(x76601,a905)))),f305(x76601,x76602,x76603)),f326(f301(x76601,x76602),x76603))+~P105(f326(f326(f235(x76601),x76602),x76603))
% 157.55/157.22 [7682]~P108(x76821)+E(f326(f326(f110(f917(x76821,a905)),f326(f326(f308(x76821),x76822),f188(f917(x76821,a905)))),f304(x76821,x76822,x76823)),f302(x76821,x76822,x76823))+~P105(f326(f326(f234(x76821),x76822),x76823))
% 157.55/157.22 [7789]~P108(x77891)+P105(f326(f326(f234(x77891),x77892),x77893))+~P105(f326(f326(f234(f917(x77891,a905)),f326(f303(x77891),x77893)),f326(f303(x77891),x77892)))
% 157.55/157.22 [7790]~P109(x77901)+P105(f326(f326(f234(x77901),x77902),x77903))+~P105(f326(f326(f234(f917(x77901,a905)),f326(f282(x77901),x77903)),f326(f282(x77901),x77902)))
% 157.55/157.22 [7791]~P108(x77911)+P105(f326(f326(f234(x77911),x77912),x77913))+~P105(f326(f326(f234(f917(x77911,a905)),f326(f281(x77911),x77912)),f326(f281(x77911),x77913)))
% 157.55/157.22 [7792]~P109(x77921)+P105(f326(f326(f234(x77921),x77922),x77923))+~P105(f326(f326(f234(f917(x77921,a905)),f326(f300(x77921),x77922)),f326(f300(x77921),x77923)))
% 157.55/157.22 [7793]~P108(x77931)+P105(f326(f326(f235(x77931),x77932),x77933))+~P105(f326(f326(f235(f917(x77931,a905)),f326(f281(x77931),x77932)),f326(f281(x77931),x77933)))
% 157.55/157.22 [7816]~P79(x78161)+~P105(f326(f326(f234(x78161),f326(f326(f3(x78161),x78162),x78163)),f2(x78161)))+P105(f326(f326(f234(x78161),x78162),x78163))
% 157.55/157.22 [7817]~P79(x78171)+~P105(f326(f326(f235(x78171),f326(f326(f3(x78171),x78172),x78173)),f2(x78171)))+P105(f326(f326(f235(x78171),x78172),x78173))
% 157.55/157.22 [7971]E(x79711,f2(a909))+~E(f326(f142(a909,a909,f79(a909),x79712),x79713),f2(a909))+~P105(f326(f326(f328(a909),x79711),f326(f172(a909),x79713)))
% 157.55/157.22 [7975]~P4(x79751)+~P105(f326(f326(f234(x79751),f729(x79753,x79752,x79751)),x79753))+P105(f326(f326(f234(x79751),f37(x79751,x79752)),x79753))
% 157.55/157.22 [8126]P105(f326(f326(f234(a1),f2(a1)),f362(x81261,x81262,x81263)))+P105(f326(f326(x81262,f326(f326(f36(a1),x81261),x81263)),f45(a1,x81261,x81263)))+~P105(f326(f326(f235(a1),f2(a1)),x81263))
% 157.55/157.22 [8214]E(x82141,x82142)+~E(f326(f189(f910(x82143)),x82141),f326(f189(f910(x82143)),x82142))+~P105(f326(f326(f256(x82143,x82143,a905),a323),f657(x82143,x82141,x82142)))
% 157.55/157.22 [8282]~P36(x82822,x82823)+E(x82821,f188(f917(x82822,a905)))+~P105(f326(f326(f234(f917(x82822,a905)),x82821),f326(f284(x82822,x82822,x82823),x82821)))
% 157.55/157.22 [8311]~P65(x83111)+~P105(f326(f326(f234(x83111),x83112),f326(f326(f79(x83111),x83113),f891(x83113,x83112,x83111))))+P105(f326(f326(f234(x83111),x83112),x83113))
% 157.55/157.22 [8346]P51(x83461,x83462,x83463)+P105(f326(f326(f328(x83461),f569(x83463,x83462,x83461)),x83462))+P105(f326(f326(f328(f916(x83461,x83461)),f570(x83463,x83462,x83461)),x83463))
% 157.55/157.22 [8367]P105(f326(f326(x83672,f326(f326(f36(a1),x83671),x83673)),f45(a1,x83671,x83673)))+~P105(f326(f326(f235(a1),f2(a1)),x83673))+P105(f326(f326(f235(a1),f362(x83671,x83672,x83673)),x83673))
% 157.55/157.22 [8391]E(f326(f309(a909,a909,f326(f326(f9(a909,a909,a909),f3(a909)),x83911)),f326(f301(a909,x83912),x83913)),f188(f917(a909,a905)))+P105(f326(f326(f235(a909),x83911),x83913))+P105(f326(f326(f235(a909),x83912),x83913))
% 157.55/157.22 [8501]E(f326(f309(a909,a909,f326(f326(f9(a909,a909,a909),f3(a909)),x85011)),f326(f301(a909,x85012),x85013)),f326(f326(f308(a909),f2(a909)),f188(f917(a909,a905))))+P105(f326(f326(f235(a909),x85011),x85013))+~P105(f326(f326(f235(a909),x85012),x85013))
% 157.55/157.22 [8515]~P108(x85151)+E(f149(x85151,x85151,f7(x85151),x85152,x85153),x85153)+~P105(f326(f326(f328(x85151),x85152),f326(f172(x85151),x85153)))
% 157.55/157.22 [8528]P24(x85281,x85281,x85282,x85283)+~P105(f326(f61(x85281),x85283))+~P105(f326(f326(f234(f917(x85281,a905)),x85283),f326(f309(x85281,x85281,x85282),x85283)))
% 157.55/157.22 [8553]E(f326(f326(f79(a1),f326(f326(f80(a1),x85531),f363(x85532,x85533,x85531))),f362(x85532,x85533,x85531)),x85532)+P105(f326(f326(x85533,f326(f326(f36(a1),x85532),x85531)),f45(a1,x85532,x85531)))+~P105(f326(f326(f235(a1),f2(a1)),x85531))
% 157.55/157.22 [8789]~P105(f326(f326(x87891,f363(x87892,x87891,x87893)),f362(x87892,x87891,x87893)))+P105(f326(f326(x87891,f326(f326(f36(a1),x87892),x87893)),f45(a1,x87892,x87893)))+~P105(f326(f326(f235(a1),f2(a1)),x87893))
% 157.55/157.22 [9667]~P105(f326(f61(x96671),x96672))+~P105(f326(f326(f328(x96671),x96673),x96672))+P105(f326(f326(f235(a909),f326(f35(x96671),f326(f326(f3(f917(x96671,a905)),x96672),f326(f326(f308(x96671),x96673),f188(f917(x96671,a905)))))),f326(f35(x96671),x96672)))
% 157.55/157.22 [10269]P51(x102691,x102692,x102693)+~P105(f326(f326(f256(x102691,x102691,a905),f326(f326(f9(x102691,f917(x102691,a905),f917(x102691,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x102691,a905),f917(x102691,a905)),x102691),f10(a905,a905,x102691)),f326(f326(f10(a905,f917(a905,a905),x102691),a324),f326(f326(f9(x102691,f917(x102691,a905),a905),f328(x102691)),x102692)))),f326(f326(f9(x102691,f917(x102691,a905),a905),f328(x102691)),x102692))),f570(x102693,x102692,x102691)))+P105(f326(f326(f328(x102691),f569(x102693,x102692,x102691)),x102692))
% 157.55/157.22 [5631]~P121(x56312)+E(x56311,f2(x56312))+E(f326(f326(f290(x56312),x56313),f326(f78(x56312),x56311)),f326(f78(x56312),f326(f326(f290(x56312),x56313),x56311)))
% 157.55/157.22 [5773]~E(x57733,f188(f917(x57731,a905)))+~E(x57732,f188(f917(x57731,a905)))+E(f326(f326(f110(f917(x57731,a905)),x57732),x57733),f188(f917(x57731,a905)))
% 157.55/157.22 [5831]~E(x58313,f2(a909))+~P105(f326(x58311,f2(a909)))+P105(f326(x58311,f326(f326(f36(a909),x58312),x58313)))
% 157.55/157.22 [5983]~P65(x59832)+E(x59831,f2(x59832))+E(f326(f326(f290(x59832),f326(f75(x59832),x59833)),f326(f75(x59832),x59831)),f326(f75(x59832),f326(f326(f290(x59832),x59833),x59831)))
% 157.55/157.22 [6152]~P105(f326(f61(x61521),x61523))+E(f326(f35(x61521),f326(f326(f308(x61521),x61522),x61523)),f326(a112,f326(f35(x61521),x61523)))+P105(f326(f326(f328(x61521),x61522),x61523))
% 157.55/157.22 [6228]~E(x62282,f2(a909))+P105(f326(x62281,f2(a909)))+~P105(f326(x62281,f326(f326(f36(a909),x62283),x62282)))
% 157.55/157.22 [6245]~P105(f326(f61(x62451),x62453))+E(f326(f35(x62451),f326(f326(f308(x62451),x62452),x62453)),f326(f35(x62451),x62453))+~P105(f326(f326(f328(x62451),x62452),x62453))
% 157.55/157.22 [6281]~P105(f326(f61(x62811),x62813))+E(f326(f35(x62811),f326(f326(f308(x62811),x62812),x62813)),f326(f326(f79(a909),f77(a909)),f326(f35(x62811),x62813)))+P105(f326(f326(f328(x62811),x62812),x62813))
% 157.55/157.22 [6399]E(f326(f326(f79(a909),x63991),f870(x63991,x63992,x63993)),x63992)+~P105(f326(x63993,f2(a909)))+P105(f326(x63993,f326(f326(f3(a909),x63992),x63991)))
% 157.55/157.22 [6400]E(f326(f326(f79(a909),x64001),f871(x64001,x64002,x64003)),x64002)+~P105(f326(x64003,f2(a909)))+P105(f326(x64003,f326(f326(f3(a909),x64002),x64001)))
% 157.55/157.22 [6447]~P4(x64471)+~P105(f326(f61(x64471),x64473))+E(f326(f326(f64(x64471,x64471,f110(x64471)),x64472),x64473),f326(f326(f110(x64471),x64472),f37(x64471,x64473)))
% 157.55/157.22 [6448]~P4(x64481)+~P105(f326(f61(x64481),x64483))+E(f326(f326(f64(x64481,x64481,f101(x64481)),x64482),x64483),f326(f326(f101(x64481),x64482),f38(x64481,x64483)))
% 157.55/157.22 [6454]~P94(x64541)+~E(f326(f103(x64541),x64542),f326(f103(x64541),x64543))+P27(x64541,f326(f103(x64541),f326(f326(f79(a1),x64542),f326(f78(a1),x64543))))
% 157.55/157.22 [6463]~P140(x64631)+E(f326(f326(f3(x64631),f326(f100(x64631),x64632)),f326(f100(x64631),x64633)),f326(f100(x64631),f326(f326(f3(a909),x64632),x64633)))+~P105(f326(f326(f234(a909),x64633),x64632))
% 157.55/157.22 [6469]~P118(x64691)+~P105(f326(f326(f286(x64691),x64692),x64693))+P105(f326(f326(f286(x64691),f326(f75(x64691),x64692)),x64693))
% 157.55/157.22 [6553]E(f326(f326(f79(a909),x65531),f870(x65531,x65532,x65533)),x65532)+P105(f326(f326(f235(a909),x65532),x65531))+P105(f326(x65533,f326(f326(f3(a909),x65532),x65531)))
% 157.55/157.22 [6554]E(f326(f326(f79(a909),x65541),f871(x65541,x65542,x65543)),x65542)+P105(f326(f326(f235(a909),x65542),x65541))+P105(f326(x65543,f326(f326(f3(a909),x65542),x65541)))
% 157.55/157.22 [6568]~P118(x65681)+E(f326(f326(f80(x65681),f326(f75(x65681),x65682)),x65683),f326(f75(x65681),f326(f326(f80(x65681),x65682),x65683)))+~P105(f326(f326(f234(x65681),f2(x65681)),x65683))
% 157.55/157.22 [6569]~P64(x65691)+E(f326(f326(f290(x65691),f326(f75(x65691),x65692)),x65693),f326(f75(x65691),f326(f326(f290(x65691),x65692),x65693)))+~P105(f326(f326(f235(x65691),f2(x65691)),x65693))
% 157.55/157.22 [6577]~P77(x65771)+~P105(f326(f61(x65771),x65773))+E(f326(f326(f64(x65771,x65771,f110(x65771)),x65772),x65773),f12(x65771,f326(f326(f308(x65771),x65772),x65773)))
% 157.55/157.22 [6578]~P77(x65781)+~P105(f326(f61(x65781),x65783))+E(f326(f326(f64(x65781,x65781,f101(x65781)),x65782),x65783),f13(x65781,f326(f326(f308(x65781),x65782),x65783)))
% 157.55/157.22 [6579]~P108(x65791)+~P105(f326(f61(x65791),x65793))+E(f326(f326(f64(x65791,x65791,f232(x65791)),x65792),x65793),f16(x65791,f326(f326(f308(x65791),x65792),x65793)))
% 157.55/157.22 [6580]~P108(x65801)+~P105(f326(f61(x65801),x65803))+E(f326(f326(f64(x65801,x65801,f233(x65801)),x65802),x65803),f17(x65801,f326(f326(f308(x65801),x65802),x65803)))
% 157.55/157.22 [6625]E(x66251,f113(x66252))+~E(f179(x66252,x66253),f113(f910(x66252)))+~P105(f326(f326(f328(f910(x66252)),x66251),f326(f172(f910(x66252)),x66253)))
% 157.55/157.22 [6669]~P105(f326(f137(x66691),x66693))+P105(f326(f326(f328(x66691),x66692),f326(f172(x66691),x66693)))+P105(f326(f137(x66691),f326(f326(f151(x66691),x66692),x66693)))
% 157.55/157.22 [6680]~P96(x66801)+~P105(f326(f61(x66801),x66803))+E(f326(f63(x66801,f80(x66801)),f326(f326(f308(x66801),x66802),x66803)),f326(f326(f64(x66801,x66801,f80(x66801)),x66802),x66803))
% 157.55/157.22 [6702]~P108(x67021)+~P105(f326(f61(x67021),x67023))+E(f14(x67021,f232(x67021),f326(f326(f308(x67021),x67022),x67023)),f326(f326(f64(x67021,x67021,f232(x67021)),x67022),x67023))
% 157.55/157.22 [6703]~P108(x67031)+~P105(f326(f61(x67031),x67033))+E(f15(x67031,f233(x67031),f326(f326(f308(x67031),x67032),x67033)),f326(f326(f64(x67031,x67031,f233(x67031)),x67032),x67033))
% 157.55/157.22 [6705]P105(f326(x67051,f2(a909)))+~P105(f326(f326(f235(a909),x67052),x67053))+~P105(f326(x67051,f326(f326(f3(a909),x67052),x67053)))
% 157.55/157.22 [6726]~P86(x67261)+P105(f326(f326(f234(x67261),x67262),x67263))+~P105(f326(f326(f234(x67261),f326(f75(x67261),x67262)),x67263))
% 157.55/157.22 [6727]~P118(x67271)+P105(f326(f326(f235(x67271),x67272),x67273))+~P105(f326(f326(f235(x67271),f326(f75(x67271),x67272)),x67273))
% 157.55/157.22 [6728]~P118(x67281)+P105(f326(f326(f286(x67281),x67282),x67283))+~P105(f326(f326(f286(x67281),f326(f75(x67281),x67282)),x67283))
% 157.55/157.22 [6745]E(x67451,f113(x67452))+E(f326(f141(x67452),f326(f326(f138(x67452),x67453),x67451)),f326(f326(f164(x67452),x67451),x67453))+~P105(f326(f326(f235(a909),x67453),f326(f189(f910(x67452)),x67451)))
% 157.55/157.22 [6800]~P105(f326(x68001,x68003))+P105(f326(x68001,f473(x68001,x68002)))+~P105(f326(f326(f328(a909),x68003),f326(f301(a909,f2(a909)),x68002)))
% 157.55/157.22 [6820]P105(f326(x68201,x68202))+~P105(f326(f326(f235(a909),x68202),x68203))+P105(f326(f326(f328(a909),f445(x68201,x68203)),f326(f301(a909,f2(a909)),x68203)))
% 157.55/157.22 [6835]~P124(x68351)+~P105(f326(f326(f234(x68351),f77(x68351)),x68352))+P105(f326(f326(f234(x68351),f77(x68351)),f326(f326(f243(x68351),x68352),x68353)))
% 157.55/157.22 [6837]~P124(x68371)+~P105(f326(f326(f234(x68371),f2(x68371)),x68372))+P105(f326(f326(f234(x68371),f2(x68371)),f326(f326(f243(x68371),x68372),x68373)))
% 157.55/157.22 [6839]~P124(x68391)+~P105(f326(f326(f235(x68391),f2(x68391)),x68392))+P105(f326(f326(f235(x68391),f2(x68391)),f326(f326(f243(x68391),x68392),x68393)))
% 157.55/157.22 [6864]~P105(f326(x68641,x68643))+~P105(f326(f326(f235(a909),x68643),x68642))+P105(f326(f326(f328(a909),f444(x68641,x68642)),f326(f301(a909,f2(a909)),x68642)))
% 157.55/157.22 [6872]P105(f326(f61(x68721),x68722))+~P105(f326(f61(x68721),x68723))+~P105(f326(f326(f234(f917(x68721,a905)),x68722),x68723))
% 157.55/157.22 [6879]P105(f326(x68791,x68792))+~P105(f326(x68791,f446(x68791,x68793)))+~P105(f326(f326(f328(a909),x68792),f326(f301(a909,f2(a909)),x68793)))
% 157.55/157.22 [6892]E(x68921,f2(a909))+P105(f326(x68922,f376(x68921,x68923,x68922)))+~P105(f326(x68922,f326(f326(f36(a909),x68923),x68921)))
% 157.55/157.22 [6900]~P125(x69002)+E(x69001,f2(x69002))+~E(f326(f326(f79(x69002),f326(f326(f80(x69002),x69003),x69003)),f326(f326(f80(x69002),x69001),x69001)),f2(x69002))
% 157.55/157.22 [6901]~P125(x69012)+E(x69011,f2(x69012))+~E(f326(f326(f79(x69012),f326(f326(f80(x69012),x69011),x69011)),f326(f326(f80(x69012),x69013),x69013)),f2(x69012))
% 157.55/157.22 [6944]E(x69441,f2(a909))+~P105(f326(x69442,f371(x69441,x69443,x69442)))+P105(f326(x69442,f326(f326(f36(a909),x69443),x69441)))
% 157.55/157.22 [6949]~P108(x69491)+~P12(x69491,x69493)+P12(x69491,f326(f326(f148(x69491,x69491,f7(x69491)),x69492),x69493))
% 157.55/157.22 [6991]P105(f326(x69911,f376(x69912,x69913,x69911)))+P105(f326(x69911,f2(a909)))+~P105(f326(x69911,f326(f326(f36(a909),x69913),x69912)))
% 157.55/157.22 [6997]~P94(x69971)+E(f326(f103(x69971),x69972),f326(f103(x69971),x69973))+~P27(x69971,f326(f103(x69971),f326(f326(f79(a1),x69972),f326(f78(a1),x69973))))
% 157.55/157.22 [7060]E(x70601,f2(a1))+E(x70602,f2(a1))+~P105(f326(f49(x70602,x70602),f326(f326(f251(a1,a1),x70603),x70601)))
% 157.55/157.22 [7061]E(x70611,f77(a1))+E(x70612,f2(a1))+~P105(f326(f49(x70612,x70612),f326(f326(f251(a1,a1),x70611),x70613)))
% 157.55/157.22 [7075]P105(f326(x70751,x70752))+P105(f326(f326(f235(a909),f446(x70751,x70753)),x70753))+~P105(f326(f326(f328(a909),x70752),f326(f301(a909,f2(a909)),x70753)))
% 157.55/157.22 [7098]~P105(f326(x70981,f870(x70983,x70982,x70981)))+~P105(f326(x70981,f2(a909)))+P105(f326(x70981,f326(f326(f3(a909),x70982),x70983)))
% 157.55/157.22 [7099]~P105(f326(x70991,f871(x70993,x70992,x70991)))+~P105(f326(x70991,f2(a909)))+P105(f326(x70991,f326(f326(f3(a909),x70992),x70993)))
% 157.55/157.22 [7100]~P105(f326(x71001,f371(x71003,x71002,x71001)))+~P105(f326(x71001,f2(a909)))+P105(f326(x71001,f326(f326(f36(a909),x71002),x71003)))
% 157.55/157.22 [7119]~P105(f326(x71191,x71193))+P105(f326(f326(f235(a909),f473(x71191,x71192)),x71192))+~P105(f326(f326(f328(a909),x71193),f326(f301(a909,f2(a909)),x71192)))
% 157.55/157.22 [7120]E(f326(f326(f3(a909),f326(f326(f3(a909),x71201),x71202)),f326(f326(f3(a909),x71203),x71202)),f326(f326(f3(a909),x71201),x71203))+~P105(f326(f326(f234(a909),x71202),x71201))+~P105(f326(f326(f234(a909),x71202),x71203))
% 157.55/157.22 [7157]~P79(x71571)+~P105(f326(f326(f234(x71571),f326(f78(x71571),x71573)),x71572))+P105(f326(f326(f234(x71571),f326(f78(x71571),x71572)),x71573))
% 157.55/157.22 [7159]~P86(x71591)+~P105(f326(f326(f234(x71591),f326(f75(x71591),x71592)),x71593))+P105(f326(f326(f234(x71591),f326(f78(x71591),x71592)),x71593))
% 157.55/157.22 [7161]~P79(x71611)+~P105(f326(f326(f235(x71611),f326(f78(x71611),x71613)),x71612))+P105(f326(f326(f235(x71611),f326(f78(x71611),x71612)),x71613))
% 157.55/157.22 [7162]~P118(x71621)+~P105(f326(f326(f235(x71621),f326(f75(x71621),x71622)),x71623))+P105(f326(f326(f235(x71621),f326(f78(x71621),x71622)),x71623))
% 157.55/157.22 [7194]~P105(f326(x71943,f870(x71942,x71941,x71943)))+P105(f326(f326(f235(a909),x71941),x71942))+P105(f326(x71943,f326(f326(f3(a909),x71941),x71942)))
% 157.55/157.22 [7195]~P105(f326(x71953,f871(x71952,x71951,x71953)))+P105(f326(f326(f235(a909),x71951),x71952))+P105(f326(x71953,f326(f326(f3(a909),x71951),x71952)))
% 157.55/157.22 [7247]~E(f777(x72473,x72472,x72471),f762(x72473,x72472,x72471))+E(f326(f326(f101(f917(x72471,a905)),x72472),f37(f917(x72471,a905),x72473)),f188(f917(x72471,a905)))+P105(f326(f326(f328(f917(x72471,a905)),x72472),x72473))
% 157.55/157.22 [7255]~P105(f326(f61(x72551),x72553))+P105(f326(f61(x72551),f38(f917(x72551,a905),x72552)))+~P105(f326(f326(f328(f917(x72551,a905)),x72553),x72552))
% 157.55/157.22 [7315]~P108(x73151)+E(f326(f326(f110(f917(x73151,a905)),f326(f301(x73151,x73152),x73153)),f326(f326(f308(x73151),x73153),f188(f917(x73151,a905)))),f302(x73151,x73152,x73153))+~P105(f326(f326(f234(x73151),x73152),x73153))
% 157.55/157.22 [7316]E(x73161,f2(a909))+P105(f326(f326(f235(a909),f372(x73161,x73163,x73162)),x73161))+P105(f326(x73162,f326(f326(f36(a909),x73163),x73161)))
% 157.55/157.22 [7345]P105(f326(f326(f235(a909),f326(f189(f910(x73451)),x73452)),f778(x73453,x73451)))+~P105(f326(f61(f910(x73451)),x73453))+~P105(f326(f326(f328(f910(x73451)),x73452),x73453))
% 157.55/157.22 [7351]E(x73511,x73512)+~P105(f326(f326(f234(f917(x73513,a905)),x73511),x73512))+P105(f326(f326(f235(f917(x73513,a905)),x73511),x73512))
% 157.55/157.22 [7363]E(x73631,x73632)+~E(f326(f189(f910(x73633)),x73631),f326(f189(f910(x73633)),x73632))+P105(f326(f326(f235(a909),f633(x73633,x73631,x73632)),f326(f189(f910(x73633)),x73632)))
% 157.55/157.22 [7412]P7(x74121,x74122,x74123)+~E(f326(f263(x74121,x74121),x74123),x74122)+~E(f326(f326(f288(x74121,x74121,x74121),f326(f285(x74121,x74121),x74123)),x74123),x74123)
% 157.55/157.22 [7494]~P105(f326(x74941,f2(a909)))+P105(f326(f326(f235(a909),f372(x74943,x74942,x74941)),x74943))+P105(f326(x74941,f326(f326(f36(a909),x74942),x74943)))
% 157.55/157.22 [7504]~P108(x75041)+E(f326(f326(f110(f917(x75041,a905)),f305(x75041,x75042,x75043)),f326(f326(f308(x75041),x75043),f188(f917(x75041,a905)))),f304(x75041,x75042,x75043))+~P105(f326(f326(f235(x75041),x75042),x75043))
% 157.55/157.22 [7595]~P105(f326(f61(x75951),x75953))+P105(f326(f326(f234(a909),f326(f35(x75951),x75952)),f326(f35(x75951),x75953)))+~P105(f326(f326(f234(f917(x75951,a905)),x75952),x75953))
% 157.55/157.22 [7596]~P105(f326(f61(x75961),x75963))+P105(f326(f326(f235(a909),f326(f35(x75961),x75962)),f326(f35(x75961),x75963)))+~P105(f326(f326(f235(f917(x75961,a905)),x75962),x75963))
% 157.55/157.22 [7726]E(x77261,x77262)+~P105(f326(f326(f234(f917(x77263,a905)),x77262),x77261))+~P105(f326(f326(f234(f917(x77263,a905)),x77261),x77262))
% 157.55/157.22 [7729]~P108(x77291)+P12(x77291,x77292)+~P12(x77291,f326(f326(f148(x77291,x77291,f7(x77291)),x77293),x77292))
% 157.55/157.22 [7798]~P105(f326(f326(f235(a909),x77983),x77982))+~P105(f326(f326(f235(a909),x77983),x77981))+P105(f326(f326(f235(a909),f326(f326(f3(a909),x77981),x77982)),f326(f326(f3(a909),x77981),x77983)))
% 157.55/157.22 [7799]~P105(f326(f326(f234(a909),x77992),x77991))+~P105(f326(f326(f235(a909),x77991),x77993))+P105(f326(f326(f235(a909),f326(f326(f3(a909),x77991),x77992)),f326(f326(f3(a909),x77993),x77992)))
% 157.55/157.22 [7814]~P105(f326(f326(f235(a1),x78142),f2(a1)))+~P105(f326(f326(f234(a1),x78143),x78141))+P105(f326(f326(f234(a1),f326(f326(f36(a1),x78141),x78142)),f326(f326(f36(a1),x78143),x78142)))
% 157.55/157.22 [7831]~P105(f326(f326(f235(a909),f2(a909)),x78313))+~P105(f326(f326(f234(a909),x78313),x78312))+P105(f326(f326(f234(a909),f326(f326(f36(a909),x78311),x78312)),f326(f326(f36(a909),x78311),x78313)))
% 157.55/157.22 [7832]~P105(f326(f326(f235(a1),f2(a1)),x78322))+~P105(f326(f326(f234(a1),x78321),x78323))+P105(f326(f326(f234(a1),f326(f326(f36(a1),x78321),x78322)),f326(f326(f36(a1),x78323),x78322)))
% 157.55/157.22 [7836]~P105(f326(f326(f235(a909),f2(a909)),x78362))+~P105(f326(f326(f235(a909),x78361),x78363))+P105(f326(f326(f235(a909),f326(f326(f80(a909),x78361),x78362)),f326(f326(f80(a909),x78363),x78362)))
% 157.55/157.22 [7837]~P105(f326(f326(f235(a909),f2(a909)),x78371))+~P105(f326(f326(f235(a909),x78372),x78373))+P105(f326(f326(f235(a909),f326(f326(f80(a909),x78371),x78372)),f326(f326(f80(a909),x78371),x78373)))
% 157.55/157.22 [7838]~P105(f326(f326(f235(a1),f2(a1)),x78381))+~P105(f326(f326(f235(a1),x78382),x78383))+P105(f326(f326(f235(a1),f326(f326(f80(a1),x78381),x78382)),f326(f326(f80(a1),x78381),x78383)))
% 157.55/157.22 [7886]E(x78861,f2(a909))+E(f326(f326(f79(a909),f326(f326(f80(a909),x78861),f371(x78861,x78862,x78863))),f372(x78861,x78862,x78863)),x78862)+P105(f326(x78863,f326(f326(f36(a909),x78862),x78861)))
% 157.55/157.22 [7945]E(f326(f326(f79(a909),f326(f326(f80(a909),x79451),f371(x79451,x79452,x79453))),f372(x79451,x79452,x79453)),x79452)+~P105(f326(x79453,f2(a909)))+P105(f326(x79453,f326(f326(f36(a909),x79452),x79451)))
% 157.55/157.22 [7962]~P105(f326(f61(x79621),x79623))+P105(f326(f326(f328(x79621),f876(x79622,x79623,x79621)),x79623))+P105(f326(f326(f235(a909),f2(a909)),f326(f326(f11(x79621,a909),x79622),x79623)))
% 157.55/157.22 [7963]~P105(f326(f61(x79631),x79633))+P105(f326(f326(f328(x79631),f889(x79632,x79633,x79631)),x79633))+P105(f326(f326(f235(a909),f2(a909)),f326(f326(f11(x79631,a909),x79632),x79633)))
% 157.55/157.22 [8250]E(x82501,f188(f917(x82502,a905)))+E(x82501,f326(f326(f308(x82502),x82503),f188(f917(x82502,a905))))+~P105(f326(f326(f234(f917(x82502,a905)),x82501),f326(f326(f308(x82502),x82503),f188(f917(x82502,a905)))))
% 157.55/157.22 [8283]~P105(f326(f326(f235(a909),f77(a909)),x82833))+P105(f326(f326(f234(a909),x82831),x82832))+~P105(f326(f326(f286(a909),f326(f326(f243(a909),x82833),x82831)),f326(f326(f243(a909),x82833),x82832)))
% 157.55/157.22 [8285]~P105(f326(f326(f235(a909),f2(a909)),x82853))+P105(f326(f326(f234(a909),x82851),x82852))+~P105(f326(f326(f234(a909),f326(f326(f80(a909),x82853),x82851)),f326(f326(f80(a909),x82853),x82852)))
% 157.55/157.22 [8286]~P105(f326(f326(f235(a909),f2(a909)),x82863))+P105(f326(f326(f234(a909),x82861),x82862))+~P105(f326(f326(f234(a909),f326(f326(f80(a909),x82861),x82863)),f326(f326(f80(a909),x82862),x82863)))
% 157.55/157.22 [8288]~P105(f326(f326(f235(a909),f2(a909)),x82883))+P105(f326(f326(f235(a909),x82881),x82882))+~P105(f326(f326(f235(a909),f326(f326(f243(a909),x82883),x82881)),f326(f326(f243(a909),x82883),x82882)))
% 157.55/157.22 [8327]~E(f326(f326(f101(f917(x83271,a905)),f762(x83273,x83272,x83271)),f777(x83273,x83272,x83271)),f188(f917(x83271,a905)))+E(f326(f326(f101(f917(x83271,a905)),x83272),f37(f917(x83271,a905),x83273)),f188(f917(x83271,a905)))+P105(f326(f326(f328(f917(x83271,a905)),x83272),x83273))
% 157.55/157.22 [8341]E(x83411,f113(x83412))+~E(f326(f142(f910(x83412),f910(x83412),f134(x83412),f113(x83412)),x83413),f113(x83412))+~P105(f326(f326(f328(f910(x83412)),x83411),f326(f172(f910(x83412)),x83413)))
% 157.55/157.22 [8396]E(x83961,f188(f917(f917(x83962,a905),a905)))+P105(f326(f326(f328(f917(x83962,a905)),f386(x83963,x83961,x83962)),x83961))+P105(f326(f326(f234(f917(x83962,a905)),f38(f917(x83962,a905),x83961)),x83963))
% 157.55/157.22 [8402]~P69(x84021)+~P74(x84021)+E(f326(f326(f8(a1,x84021),f326(f326(f10(a909,x84021,a1),x84022),a104)),f326(f309(a909,a1,f100(a1)),x84023)),f326(f326(f8(a909,x84021),x84022),x84023))
% 157.55/157.22 [8403]~P69(x84031)+~P74(x84031)+E(f326(f326(f11(a1,x84031),f326(f326(f10(a909,x84031,a1),x84032),a104)),f326(f309(a909,a1,f100(a1)),x84033)),f326(f326(f11(a909,x84031),x84032),x84033))
% 157.55/157.22 [8445]~P105(f326(f61(x84451),x84453))+~P105(f326(f326(f235(a909),f2(a909)),f326(x84452,f876(x84452,x84453,x84451))))+P105(f326(f326(f235(a909),f2(a909)),f326(f326(f11(x84451,a909),x84452),x84453)))
% 157.55/157.22 [8446]~P105(f326(f61(x84461),x84463))+~P105(f326(f326(f235(a909),f2(a909)),f326(x84462,f889(x84462,x84463,x84461))))+P105(f326(f326(f235(a909),f2(a909)),f326(f326(f11(x84461,a909),x84462),x84463)))
% 157.55/157.22 [8482]~P63(x84822)+E(x84821,f77(x84822))+E(f326(f326(f290(x84822),f326(f326(f3(x84822),f326(f326(f243(x84822),x84821),x84823)),f77(x84822))),f326(f326(f3(x84822),x84821),f77(x84822))),f326(f326(f8(a909,x84822),f326(f243(x84822),x84821)),f326(f301(a909,f2(a909)),x84823)))
% 157.55/157.22 [8539]E(x85391,f2(a909))+~P105(f326(x85393,f326(f326(f36(a909),x85392),x85391)))+P105(f326(f326(f235(a909),x85392),f326(f326(f80(a909),x85391),f326(a112,f376(x85391,x85392,x85393)))))
% 157.55/157.22 [8557]P105(f326(x85571,f2(a909)))+~P105(f326(x85571,f326(f326(f36(a909),x85572),x85573)))+P105(f326(f326(f235(a909),x85572),f326(f326(f80(a909),x85573),f326(a112,f376(x85573,x85572,x85571)))))
% 157.55/157.22 [8595]E(x85951,f2(a909))+~P105(f326(x85953,f326(f326(f36(a909),x85952),x85951)))+P105(f326(f326(f234(a909),f326(f326(f80(a909),x85951),f376(x85951,x85952,x85953))),x85952))
% 157.55/157.22 [8626]P105(f326(x86261,f2(a909)))+~P105(f326(x86261,f326(f326(f36(a909),x86263),x86262)))+P105(f326(f326(f234(a909),f326(f326(f80(a909),x86262),f376(x86262,x86263,x86261))),x86263))
% 157.55/157.22 [8634]~P108(x86341)+E(f326(f326(f148(x86341,x86341,f7(x86341)),x86342),x86343),f149(x86341,x86341,f7(x86341),x86342,x86343))+P105(f326(f326(f328(x86341),x86342),f326(f172(x86341),x86343)))
% 157.55/157.22 [8668]~E(f326(x86683,f580(x86682,x86683,x86681)),f326(x86683,f582(x86682,x86683,x86681)))+~P58(x86681,f326(x86683,f581(x86682,x86683,x86681)))+P58(x86681,f326(f326(f40(x86682,f917(x86681,f917(x86681,a905))),f241(f917(x86682,a905))),x86683))
% 157.55/157.22 [8677]E(x86771,f188(f917(f917(x86772,a905),a905)))+~P105(f326(f326(f234(f917(x86772,a905)),f386(x86773,x86771,x86772)),x86773))+P105(f326(f326(f234(f917(x86772,a905)),f38(f917(x86772,a905),x86771)),x86773))
% 157.55/157.22 [8737]~P65(x87371)+~P105(f326(f326(f235(x87371),x87372),x87373))+P105(f326(f326(f235(x87371),x87372),f326(f326(f290(x87371),f326(f326(f79(x87371),x87372),x87373)),f326(f326(f79(x87371),f77(x87371)),f77(x87371)))))
% 157.55/157.22 [8795]~P105(f326(f326(x87951,f392(x87951,x87953,x87952)),f394(x87951,x87953,x87952)))+P105(f326(f326(x87951,x87952),x87953))+~P105(f326(f314(f916(a1,a1),a52),f326(f326(f251(a1,a1),x87952),x87953)))
% 157.55/157.22 [8796]~P105(f326(f326(x87961,f395(x87961,x87963,x87962)),f396(x87961,x87963,x87962)))+P105(f326(f326(x87961,x87962),x87963))+~P105(f326(f314(f916(a1,a1),a58),f326(f326(f251(a1,a1),x87962),x87963)))
% 157.55/157.22 [8797]~P105(f326(f326(x87971,f397(x87971,x87973,x87972)),f400(x87971,x87973,x87972)))+P105(f326(f326(x87971,x87972),x87973))+~P105(f326(f314(f916(a1,a1),a221),f326(f326(f251(a1,a1),x87972),x87973)))
% 157.55/157.22 [8798]~P105(f326(f326(x87981,f401(x87981,x87983,x87982)),f403(x87981,x87983,x87982)))+P105(f326(f326(x87981,x87982),x87983))+~P105(f326(f314(f916(a909,a909),a219),f326(f326(f251(a909,a909),x87982),x87983)))
% 157.55/157.22 [8799]~P105(f326(f326(x87991,f671(x87991,x87993,x87992)),f673(x87991,x87993,x87992)))+P105(f326(f326(x87991,x87992),x87993))+~P105(f326(f314(f916(a1,a1),a182),f326(f326(f251(a1,a1),x87992),x87993)))
% 157.55/157.22 [8800]~P105(f326(f326(x88001,f766(x88001,x88003,x88002)),f767(x88001,x88003,x88002)))+P105(f326(f326(x88001,x88002),x88003))+~P105(f326(f314(f916(a1,a1),a133),f326(f326(f251(a1,a1),x88002),x88003)))
% 157.55/157.22 [9073]P105(f326(f326(x90731,x90732),x90733))+P105(f326(f314(f916(a909,a909),a219),f326(f326(f251(a909,a909),f401(x90731,x90733,x90732)),f403(x90731,x90733,x90732))))+~P105(f326(f314(f916(a909,a909),a219),f326(f326(f251(a909,a909),x90732),x90733)))
% 157.55/157.22 [9074]P105(f326(f326(x90741,x90742),x90743))+P105(f326(f314(f916(a1,a1),a52),f326(f326(f251(a1,a1),f392(x90741,x90743,x90742)),f394(x90741,x90743,x90742))))+~P105(f326(f314(f916(a1,a1),a52),f326(f326(f251(a1,a1),x90742),x90743)))
% 157.55/157.22 [9075]P105(f326(f326(x90751,x90752),x90753))+P105(f326(f314(f916(a1,a1),a58),f326(f326(f251(a1,a1),f395(x90751,x90753,x90752)),f396(x90751,x90753,x90752))))+~P105(f326(f314(f916(a1,a1),a58),f326(f326(f251(a1,a1),x90752),x90753)))
% 157.55/157.22 [9076]P105(f326(f326(x90761,x90762),x90763))+P105(f326(f314(f916(a1,a1),a221),f326(f326(f251(a1,a1),f397(x90761,x90763,x90762)),f400(x90761,x90763,x90762))))+~P105(f326(f314(f916(a1,a1),a221),f326(f326(f251(a1,a1),x90762),x90763)))
% 157.55/157.22 [9077]P105(f326(f326(x90771,x90772),x90773))+P105(f326(f314(f916(a1,a1),a182),f326(f326(f251(a1,a1),f671(x90771,x90773,x90772)),f673(x90771,x90773,x90772))))+~P105(f326(f314(f916(a1,a1),a182),f326(f326(f251(a1,a1),x90772),x90773)))
% 157.55/157.22 [9078]P105(f326(f326(x90781,x90782),x90783))+P105(f326(f314(f916(a1,a1),a133),f326(f326(f251(a1,a1),f766(x90781,x90783,x90782)),f767(x90781,x90783,x90782))))+~P105(f326(f314(f916(a1,a1),a133),f326(f326(f251(a1,a1),x90782),x90783)))
% 157.55/157.22 [9408]~P105(f326(f61(x94081),x94083))+P105(f326(f326(f328(f916(f917(x94081,a905),f917(x94081,a905))),f326(f326(f251(f917(x94081,a905),f917(x94081,a905)),x94082),x94083)),f313(x94081)))+~P105(f326(f326(f235(f917(x94081,a905)),x94082),x94083))
% 157.55/157.22 [9481]~P58(x94811,f326(x94813,f581(x94812,x94813,x94811)))+P58(x94811,f326(f326(f40(x94812,f917(x94811,f917(x94811,a905))),f241(f917(x94812,a905))),x94813))+~E(f326(f326(f101(f917(x94811,a905)),f248(x94811,x94811,f326(x94813,f580(x94812,x94813,x94811)))),f249(x94811,x94811,f326(x94813,f582(x94812,x94813,x94811)))),f188(f917(x94811,a905)))
% 157.55/157.22 [9680]P51(x96801,x96802,x96803)+P105(f326(f326(f328(f916(x96801,x96801)),f570(x96803,x96802,x96801)),x96803))+~P105(f326(f326(f328(f916(x96801,x96801)),f326(f326(f251(x96801,x96801),f569(x96803,x96802,x96801)),f569(x96803,x96802,x96801))),x96803))
% 157.55/157.22 [10272]P51(x102721,x102722,x102723)+~P105(f326(f326(f256(x102721,x102721,a905),f326(f326(f9(x102721,f917(x102721,a905),f917(x102721,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x102721,a905),f917(x102721,a905)),x102721),f10(a905,a905,x102721)),f326(f326(f10(a905,f917(a905,a905),x102721),a324),f326(f326(f9(x102721,f917(x102721,a905),a905),f328(x102721)),x102722)))),f326(f326(f9(x102721,f917(x102721,a905),a905),f328(x102721)),x102722))),f570(x102723,x102722,x102721)))+~P105(f326(f326(f328(f916(x102721,x102721)),f326(f326(f251(x102721,x102721),f569(x102723,x102722,x102721)),f569(x102723,x102722,x102721))),x102723))
% 157.55/157.22 [5813]~P59(x58132)+E(x58131,f2(x58132))+E(f326(f326(f36(x58132),f326(f326(f80(x58132),x58133),x58131)),x58131),x58133)
% 157.55/157.22 [5814]~P59(x58142)+E(x58141,f2(x58142))+E(f326(f326(f36(x58142),f326(f326(f80(x58142),x58141),x58143)),x58141),x58143)
% 157.55/157.22 [6624]~P69(x66241)+~E(f326(x66242,f2(a909)),f2(x66241))+E(f326(f326(f8(a909,x66241),x66242),f326(f301(a909,f326(a112,f2(a909))),x66243)),f326(f326(f8(a909,x66241),x66242),f326(f301(a909,f2(a909)),x66243)))
% 157.55/157.22 [6758]~P59(x67582)+E(x67581,f2(x67582))+E(f326(f326(f36(x67582),f326(f326(f79(x67582),x67583),x67581)),x67581),f326(f326(f79(x67582),f326(f326(f36(x67582),x67583),x67581)),f77(x67582)))
% 157.55/157.22 [6759]~P59(x67592)+E(x67591,f2(x67592))+E(f326(f326(f36(x67592),f326(f326(f79(x67592),x67591),x67593)),x67591),f326(f326(f79(x67592),f326(f326(f36(x67592),x67593),x67591)),f77(x67592)))
% 157.55/157.22 [6980]~P105(f326(x69803,f2(a1)))+P105(f326(f326(f234(a909),x69801),x69802))+P105(f326(x69803,f326(f100(a1),f326(f326(f3(a909),x69802),x69801))))
% 157.55/157.22 [7081]P105(f326(f326(f235(a909),x70812),x70811))+P105(f326(f326(f234(a909),x70811),x70812))+P105(f326(x70813,f326(f100(a1),f326(f326(f3(a909),x70812),x70811))))
% 157.55/157.22 [7155]E(f326(f326(f79(a909),f326(f103(a909),x71551)),f326(f326(f79(a909),f326(f103(a909),x71552)),x71553)),f326(f326(f79(a909),f326(f103(a909),x71551)),x71553))+P105(f326(a193,f326(f103(a1),x71551)))+~P105(f326(a193,f326(f103(a1),x71552)))
% 157.55/157.22 [7234]~E(x72342,f326(f326(f36(a909),x72343),x72341))+~P105(f326(f326(f235(a909),f2(a909)),x72341))+P105(f326(f326(f234(a909),f326(f326(f80(a909),x72341),x72342)),x72343))
% 157.55/157.22 [7348]~P105(f326(f61(x73481),x73483))+~P105(f326(f61(x73481),x73482))+P105(f326(f61(x73481),f326(f326(f110(f917(x73481,a905)),x73482),x73483)))
% 157.55/157.22 [7397]~P37(x73971,x73973)+~P37(x73971,x73972)+P37(x73971,f326(f326(f101(f917(f916(x73971,x73971),a905)),x73972),x73973))
% 157.55/157.22 [7398]~P50(x73981,x73983)+~P50(x73981,x73982)+P50(x73981,f326(f326(f110(f917(f916(x73981,x73981),a905)),x73982),x73983))
% 157.55/157.22 [7399]~P50(x73991,x73993)+~P50(x73991,x73992)+P50(x73991,f326(f326(f101(f917(f916(x73991,x73991),a905)),x73992),x73993))
% 157.55/157.22 [7644]~P108(x76441)+~P105(f326(f61(x76441),x76442))+E(f139(x76441,f326(f326(f3(f917(x76441,a905)),x76442),f326(f326(f308(x76441),x76443),f188(f917(x76441,a905))))),f170(x76441,x76443,f139(x76441,x76442)))
% 157.55/157.22 [7705]P105(f326(x77051,f2(a1)))+~P105(f326(f326(f235(a909),x77052),x77053))+~P105(f326(x77051,f326(f100(a1),f326(f326(f3(a909),x77052),x77053))))
% 157.55/157.22 [7723]~P105(f326(f61(x77231),x77232))+E(f326(f35(x77231),f326(f326(f3(f917(x77231,a905)),x77232),f326(f326(f308(x77231),x77233),f188(f917(x77231,a905))))),f326(f35(x77231),x77232))+P105(f326(f326(f328(x77231),x77233),x77232))
% 157.55/157.22 [7853]~P124(x78531)+~P105(f326(f326(f235(x78531),f77(x78531)),x78532))+P105(f326(f326(f235(x78531),f77(x78531)),f326(f326(f80(x78531),x78532),f326(f326(f243(x78531),x78532),x78533))))
% 157.55/157.22 [7896]~P105(f326(f61(x78961),x78963))+E(f326(f326(f3(a909),f326(f35(x78961),x78962)),f326(f35(x78961),x78963)),f326(f35(x78961),f326(f326(f3(f917(x78961,a905)),x78962),x78963)))+~P105(f326(f326(f234(f917(x78961,a905)),x78963),x78962))
% 157.55/157.22 [7953]~P105(f326(f326(f234(a909),x79532),x79533))+~P105(f326(f326(f234(a909),x79531),f326(f326(f3(a909),x79533),x79532)))+P105(f326(f326(f234(a909),f326(f326(f79(a909),x79531),x79532)),x79533))
% 157.55/157.22 [8004]P105(f326(f61(x80041),x80042))+~P105(f326(f61(x80041),x80043))+~P105(f326(f61(x80041),f326(f326(f3(f917(x80041,a905)),x80042),x80043)))
% 157.55/157.22 [8010]~P105(f326(f61(x80101),x80102))+E(f326(f35(x80101),f326(f326(f3(f917(x80101,a905)),x80102),f326(f326(f308(x80101),x80103),f188(f917(x80101,a905))))),f326(f326(f3(a909),f326(f35(x80101),x80102)),f77(a909)))+~P105(f326(f326(f328(x80101),x80103),x80102))
% 157.55/157.22 [8085]P58(x80851,x80852)+~P58(x80851,x80853)+~P105(f326(f326(f234(f917(x80851,f917(x80851,a905))),x80852),x80853))
% 157.55/157.22 [8125]~P105(f326(f326(f234(a909),x81253),x81252))+P105(f326(f326(f234(a909),x81251),f326(f326(f3(a909),x81252),x81253)))+~P105(f326(f326(f234(a909),f326(f326(f79(a909),x81251),x81253)),x81252))
% 157.55/157.22 [8143]P36(x81431,x81432)+~P36(x81431,x81433)+~P105(f326(f326(f234(f917(f916(x81431,x81431),a905)),x81432),x81433))
% 157.55/157.22 [8144]P56(x81441,x81442)+~P56(x81441,x81443)+~P105(f326(f326(f234(f917(f916(x81441,x81441),a905)),x81442),x81443))
% 157.55/157.22 [8145]P38(x81451,x81452)+~P38(x81451,x81453)+~P105(f326(f326(f234(f917(f916(x81451,x81451),a905)),x81452),x81453))
% 157.55/157.22 [8374]~P124(x83741)+~P105(f326(f326(f235(x83741),f77(x83741)),x83742))+P105(f326(f326(f235(x83741),f326(f326(f243(x83741),x83742),x83743)),f326(f326(f80(x83741),x83742),f326(f326(f243(x83741),x83742),x83743))))
% 157.55/157.22 [8464]~P105(f326(x84641,f2(a1)))+~P105(f326(x84641,f326(f326(f3(a1),f326(f100(a1),x84642)),f326(f100(a1),x84643))))+P105(f326(x84641,f326(f100(a1),f326(f326(f3(a909),x84642),x84643))))
% 157.55/157.23 [8479]~P105(f326(f326(f234(a909),x84793),x84792))+P105(f326(x84791,f326(f326(f3(a1),f326(f100(a1),x84792)),f326(f100(a1),x84793))))+~P105(f326(x84791,f326(f100(a1),f326(f326(f3(a909),x84792),x84793))))
% 157.55/157.23 [8498]P105(f326(f326(f235(a909),x84981),x84982))+~P105(f326(x84983,f326(f326(f3(a1),f326(f100(a1),x84981)),f326(f100(a1),x84982))))+P105(f326(x84983,f326(f100(a1),f326(f326(f3(a909),x84981),x84982))))
% 157.55/157.23 [8550]~P125(x85502)+E(x85501,f2(x85502))+P105(f326(f326(f235(x85502),f2(x85502)),f326(f326(f79(x85502),f326(f326(f80(x85502),x85503),x85503)),f326(f326(f80(x85502),x85501),x85501))))
% 157.55/157.23 [8551]~P125(x85512)+E(x85511,f2(x85512))+P105(f326(f326(f235(x85512),f2(x85512)),f326(f326(f79(x85512),f326(f326(f80(x85512),x85511),x85511)),f326(f326(f80(x85512),x85513),x85513))))
% 157.55/157.23 [8651]~P105(f326(f326(f235(a909),f2(a909)),x86511))+~P105(f326(f326(f235(a1),x86512),x86513))+P105(f326(f326(f235(a1),f326(f326(f80(a1),f326(f100(a1),x86511)),x86512)),f326(f326(f80(a1),f326(f100(a1),x86511)),x86513)))
% 157.55/157.23 [8706]E(f326(f326(f101(f917(x87061,a905)),x87062),f37(f917(x87061,a905),x87063)),f188(f917(x87061,a905)))+P105(f326(f326(f328(f917(x87061,a905)),x87062),x87063))+P105(f326(f326(f328(f917(x87061,a905)),f762(x87063,x87062,x87061)),f326(f326(f308(f917(x87061,a905)),x87062),x87063)))
% 157.55/157.23 [8707]E(f326(f326(f101(f917(x87071,a905)),x87072),f37(f917(x87071,a905),x87073)),f188(f917(x87071,a905)))+P105(f326(f326(f328(f917(x87071,a905)),x87072),x87073))+P105(f326(f326(f328(f917(x87071,a905)),f777(x87073,x87072,x87071)),f326(f326(f308(f917(x87071,a905)),x87072),x87073)))
% 157.55/157.23 [8736]E(x87361,x87362)+~E(f326(f189(f910(x87363)),x87361),f326(f189(f910(x87363)),x87362))+P105(f326(f326(f328(f916(x87363,x87363)),f657(x87363,x87361,x87362)),f326(f172(f916(x87363,x87363)),f326(f326(f181(x87363,x87363),x87362),x87361))))
% 157.55/157.23 [8986]E(f306(x89861,x89862),f306(x89861,x89863))+~P105(f326(f326(f234(f917(f916(x89861,x89861),a905)),x89863),f306(x89861,x89862)))+~P105(f326(f326(f234(f917(f916(x89861,x89861),a905)),x89862),x89863))
% 157.55/157.23 [9053]~P51(x90531,f241(f917(x90531,a905)),x90533)+P105(f326(f326(f234(f917(f916(f910(x90531),f910(x90531)),a905)),f157(x90531,x90532)),f158(x90531,x90533)))+~P105(f326(f326(f234(f917(f916(x90531,x90531),a905)),x90532),x90533))
% 157.55/157.23 [9248]P36(x92481,x92482)+~P105(f326(f326(f328(x92481),x92483),f612(x92482,x92481)))+P105(f326(f326(f328(f916(x92481,x92481)),f326(f326(f251(x92481,x92481),f634(x92482,x92481,x92483)),x92483)),x92482))
% 157.55/157.23 [9283]~P105(f326(f61(x92831),x92832))+P105(f326(f61(f917(x92831,a905)),f326(f326(f60(x92831),x92832),x92833)))+~P105(f326(f326(f234(f917(f916(x92831,x92831),a905)),x92833),f326(f326(f253(x92831,x92831),x92832),f326(f18(f917(x92831,a905),x92831),x92832))))
% 157.55/157.23 [9319]P51(x93191,x93192,x93193)+P105(f326(f326(f328(x93191),f534(x93193,x93192,x93191)),x93192))+~P105(f326(f326(f234(f917(f916(x93191,x93191),a905)),x93193),f326(f326(f253(x93191,x93191),x93192),f326(f18(f917(x93191,a905),x93191),x93192))))
% 157.55/157.23 [9320]P51(x93201,x93202,x93203)+P105(f326(f326(f328(x93201),f543(x93202,x93203,x93201)),x93202))+~P105(f326(f326(f234(f917(f916(x93201,x93201),a905)),x93203),f326(f326(f253(x93201,x93201),x93202),f326(f18(f917(x93201,a905),x93201),x93202))))
% 157.55/157.23 [9352]~P65(x93521)+~P105(f326(f326(f235(x93521),x93522),x93523))+P105(f326(f326(f235(x93521),f326(f326(f290(x93521),f326(f326(f79(x93521),x93522),x93523)),f326(f326(f79(x93521),f77(x93521)),f77(x93521)))),x93523))
% 157.55/157.23 [9381]~P64(x93811)+P105(f326(f326(f234(x93811),x93812),x93813))+~P105(f326(f326(f234(x93811),f326(f326(f80(x93811),f885(x93813,x93812,x93811)),x93812)),x93813))
% 157.55/157.23 [9516]E(f326(f189(f910(f910(x95161))),f326(f136(f910(x95161),f326(f326(f10(a909,a905,f910(x95161)),f326(f235(a909),x95162)),f189(f910(x95161)))),f179(x95161,x95163))),f326(f189(f910(x95161)),f326(f326(f164(f910(x95161)),x95163),x95162)))+~P12(a909,f326(f168(a909),f326(f326(f154(f910(x95161),a909),f189(f910(x95161))),x95163)))+~P105(f326(f326(f235(a909),x95162),f326(f189(f910(f910(x95161))),x95163)))
% 157.55/157.23 [9628]~P36(x96281,x96282)+P26(x96281,f326(f326(f251(f917(f916(x96281,x96281),a905),f917(f916(x96281,x96281),a905)),x96282),x96283))+~P105(f326(f326(f234(f917(f916(x96281,x96281),a905)),f326(f326(f288(x96281,x96281,x96281),x96282),x96283)),x96282))
% 157.55/157.23 [9633]E(f326(f326(f154(f910(x96331),x96331),f326(f326(f9(f910(x96331),a909,x96331),f164(x96331)),x96332)),f326(f136(f910(x96331),f326(f326(f10(a909,a905,f910(x96331)),f326(f235(a909),x96332)),f189(f910(x96331)))),f179(x96331,x96333))),f326(f326(f164(f910(x96331)),x96333),x96332))+~P12(a909,f326(f168(a909),f326(f326(f154(f910(x96331),a909),f189(f910(x96331))),x96333)))+~P105(f326(f326(f235(a909),x96332),f326(f189(f910(f910(x96331))),x96333)))
% 157.55/157.23 [9768]P51(x97681,x97682,x97683)+~P105(f326(f326(f328(f916(x97681,x97681)),f326(f326(f251(x97681,x97681),f534(x97683,x97682,x97681)),f534(x97683,x97682,x97681))),x97683))+~P105(f326(f326(f234(f917(f916(x97681,x97681),a905)),x97683),f326(f326(f253(x97681,x97681),x97682),f326(f18(f917(x97681,a905),x97681),x97682))))
% 157.55/157.23 [9769]P51(x97691,x97692,x97693)+~P105(f326(f326(f328(f916(x97691,x97691)),f326(f326(f251(x97691,x97691),f543(x97692,x97693,x97691)),f543(x97692,x97693,x97691))),x97693))+~P105(f326(f326(f234(f917(f916(x97691,x97691),a905)),x97693),f326(f326(f253(x97691,x97691),x97692),f326(f18(f917(x97691,a905),x97691),x97692))))
% 157.55/157.23 [9938]~P140(x99381)+~P123(x99381)+E(f326(f326(f290(x99381),f326(f102(x99381),f326(f326(f72(f916(a1,a1),a1,x99382,f250(a1,a1)),f212(x99382)),x99383))),f326(f102(x99381),f326(f326(f72(f916(a1,a1),a1,x99382,f255(a1,a1)),f212(x99382)),x99383))),f222(x99382,x99381,x99383))
% 157.55/157.23 [10143]~E(x101433,f2(a909))+~E(f326(f189(f910(x101431)),f326(f326(f164(f910(x101431)),x101432),f706(x101433,x101431,x101432))),x101433)+E(f326(f326(f154(a909,f910(x101431)),f326(f326(f9(a909,f910(a909),f910(x101431)),f326(f326(f10(f917(a909,x101431),f917(f910(a909),f910(x101431)),a909),f154(a909,x101431)),f326(f9(a909,a909,x101431),f326(f326(f10(f910(x101431),f917(a909,x101431),a909),f164(x101431)),f326(f164(f910(x101431)),x101432))))),f139(a909,f326(f301(a909,f2(a909)),f326(f189(f910(f910(x101431))),x101432))))),f139(a909,f326(f301(a909,f2(a909)),x101433))),f179(x101431,x101432))
% 157.55/157.23 [10144]E(x101441,f113(f910(x101442)))+~E(f326(f189(f910(x101442)),f326(f326(f164(f910(x101442)),x101441),f706(x101443,x101442,x101441))),x101443)+E(f326(f326(f154(a909,f910(x101442)),f326(f326(f9(a909,f910(a909),f910(x101442)),f326(f326(f10(f917(a909,x101442),f917(f910(a909),f910(x101442)),a909),f154(a909,x101442)),f326(f9(a909,a909,x101442),f326(f326(f10(f910(x101442),f917(a909,x101442),a909),f164(x101442)),f326(f164(f910(x101442)),x101441))))),f139(a909,f326(f301(a909,f2(a909)),f326(f189(f910(f910(x101442))),x101441))))),f139(a909,f326(f301(a909,f2(a909)),x101443))),f179(x101442,x101441))
% 157.55/157.23 [10145]~E(x101453,f2(a909))+E(f326(f326(f154(a909,f910(x101451)),f326(f326(f9(a909,f910(a909),f910(x101451)),f326(f326(f10(f917(a909,x101451),f917(f910(a909),f910(x101451)),a909),f154(a909,x101451)),f326(f9(a909,a909,x101451),f326(f326(f10(f910(x101451),f917(a909,x101451),a909),f164(x101451)),f326(f164(f910(x101451)),x101452))))),f139(a909,f326(f301(a909,f2(a909)),f326(f189(f910(f910(x101451))),x101452))))),f139(a909,f326(f301(a909,f2(a909)),x101453))),f179(x101451,x101452))+P105(f326(f326(f235(a909),f706(x101453,x101451,x101452)),f326(f189(f910(f910(x101451))),x101452)))
% 157.55/157.23 [10146]E(x101461,f113(f910(x101462)))+E(f326(f326(f154(a909,f910(x101462)),f326(f326(f9(a909,f910(a909),f910(x101462)),f326(f326(f10(f917(a909,x101462),f917(f910(a909),f910(x101462)),a909),f154(a909,x101462)),f326(f9(a909,a909,x101462),f326(f326(f10(f910(x101462),f917(a909,x101462),a909),f164(x101462)),f326(f164(f910(x101462)),x101461))))),f139(a909,f326(f301(a909,f2(a909)),f326(f189(f910(f910(x101462))),x101461))))),f139(a909,f326(f301(a909,f2(a909)),x101463))),f179(x101462,x101461))+P105(f326(f326(f235(a909),f706(x101463,x101462,x101461)),f326(f189(f910(f910(x101462))),x101461)))
% 157.55/157.23 [7893]E(f326(f326(f79(a909),f326(f103(a909),x78931)),f326(f326(f79(a909),f326(f103(a909),x78932)),x78933)),f326(f326(f79(a909),f326(f103(a909),f326(f326(f79(a1),x78931),x78932))),x78933))+P105(f326(a193,f326(f103(a1),x78931)))+P105(f326(a193,f326(f103(a1),x78932)))
% 157.55/157.23 [8643]~P105(f326(f61(x86431),x86432))+~P105(f326(f326(f328(x86431),x86433),x86432))+E(f326(a112,f326(f35(x86431),f326(f326(f3(f917(x86431,a905)),x86432),f326(f326(f308(x86431),x86433),f188(f917(x86431,a905)))))),f326(f35(x86431),x86432))
% 157.55/157.23 [8658]~P105(f326(f61(x86581),x86582))+~P105(f326(f326(f328(x86581),x86583),x86582))+E(f326(f326(f79(a909),f77(a909)),f326(f35(x86581),f326(f326(f3(f917(x86581,a905)),x86582),f326(f326(f308(x86581),x86583),f188(f917(x86581,a905)))))),f326(f35(x86581),x86582))
% 157.55/157.23 [8745]~P108(x87451)+~P105(f326(f61(x87451),x87453))+E(f326(f326(f148(x87451,x87451,f7(x87451)),x87452),f139(x87451,f326(f326(f3(f917(x87451,a905)),x87453),f326(f326(f308(x87451),x87452),f188(f917(x87451,a905)))))),f139(x87451,f326(f326(f308(x87451),x87452),x87453)))
% 157.55/157.23 [8911]~P105(f326(f61(x89111),x89113))+~P105(f326(f61(x89111),x89112))+E(f326(f326(f79(a909),f326(f35(x89111),f326(f326(f110(f917(x89111,a905)),x89112),x89113))),f326(f35(x89111),f326(f326(f101(f917(x89111,a905)),x89112),x89113))),f326(f326(f79(a909),f326(f35(x89111),x89112)),f326(f35(x89111),x89113)))
% 157.55/157.23 [10091]~P24(x100911,f917(f917(x100911,a905),a905),f326(f326(f9(x100911,f917(f916(x100911,x100911),a905),f917(f917(x100911,a905),a905)),f326(f326(f10(f917(x100911,a905),f917(f917(f916(x100911,x100911),a905),f917(f917(x100911,a905),a905)),x100911),f60(x100911)),f326(f326(f9(x100911,f917(x100911,a905),f917(x100911,a905)),f308(x100911)),f188(f917(x100911,a905))))),x100913),x100912)+~P105(f326(f61(x100911),x100912))+E(f326(f35(f917(x100911,a905)),f326(f326(f60(x100911),x100912),x100913)),f326(f35(x100911),x100912))
% 157.55/157.23 [8157]~P94(x81571)+P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x81573)))+E(f326(f326(f243(x81571),x81572),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),x81573),x81573)),a97))),f77(x81571))
% 157.55/157.23 [9613]~P94(x96131)+~P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),x96133)))+E(f326(f326(f243(x96131),x96132),f326(f103(a909),f326(f326(f3(a1),f326(f326(f79(a1),x96133),x96133)),a97))),f326(f326(f85(x96131,x96131),f326(f326(f243(x96131),x96132),f326(f103(a909),x96133))),f326(f326(f20(x96131,x96131,x96131),f326(f326(f10(x96131,f917(x96131,x96131),x96131),f80(x96131)),f326(f80(x96131),x96132))),f7(x96131))))
% 157.55/157.23 [10000]~P105(f326(f137(x100001),x100003))+~P105(f326(f326(f328(x100001),x100002),f326(f172(x100001),x100003)))+E(f326(f326(f138(x100001),f326(f189(f910(x100001)),f177(x100001,f326(f326(f10(a905,a905,x100001),a321),f326(f326(f9(x100001,x100001,a905),a323),x100002)),f326(f168(x100001),x100003)))),f326(f168(x100001),x100003)),f326(f326(f151(x100001),x100002),f326(f168(x100001),f177(x100001,f326(f326(f10(a905,a905,x100001),a321),f326(f326(f9(x100001,x100001,a905),a323),x100002)),x100003))))
% 157.55/157.23 [10061]P105(f326(f326(f234(f917(f916(x100611,x100611),a905)),f306(x100611,x100612)),x100613))+~P105(f326(f326(f234(f917(f916(x100611,x100611),a905)),f306(x100611,f188(f917(f916(x100611,x100611),a905)))),x100613))+~P105(f326(f326(f234(f917(f916(x100611,x100611),a905)),f326(f326(f288(x100611,x100611,x100611),f326(f326(f101(f917(f916(x100611,x100611),a905)),f306(x100611,x100612)),x100613)),x100612)),x100613))
% 157.55/157.23 [9918]~P105(f326(f61(x99181),f326(f261(x99181),x99183)))+~P105(f326(f61(x99181),f326(f261(x99181),x99182)))+P105(f326(f61(x99181),f326(f261(x99181),f326(f326(f20(x99181,a905,a905),f326(f326(f10(a905,f917(a905,a905),x99181),a325),x99182)),x99183))))
% 157.55/157.23 [10208]P105(f326(f326(f234(f917(f916(x102081,x102081),a905)),f326(f326(f288(x102081,x102081,x102081),x102082),f306(x102081,x102082))),x102083))+~P105(f326(f326(f234(f917(f916(x102081,x102081),a905)),x102082),x102083))+~P105(f326(f326(f234(f917(f916(x102081,x102081),a905)),f326(f326(f288(x102081,x102081,x102081),f326(f326(f101(f917(f916(x102081,x102081),a905)),f326(f326(f288(x102081,x102081,x102081),x102082),f306(x102081,x102082))),x102083)),x102082)),x102083))
% 157.55/157.23 [10159]~P118(x101592)+E(x101591,f2(x101592))+~E(f326(f326(f79(x101592),f326(f326(f243(x101592),x101593),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x101592),x101591),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f2(x101592))
% 157.55/157.23 [10160]~P118(x101602)+E(x101601,f2(x101602))+~E(f326(f326(f79(x101602),f326(f326(f243(x101602),x101601),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x101602),x101603),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f2(x101602))
% 157.55/157.23 [10165]~P105(f326(f137(x101651),x101653))+~P105(f326(f326(f328(x101651),x101652),f326(f172(x101651),x101653)))+E(f326(f168(x101651),f326(f171(x101651),f326(f326(f138(x101651),f326(f189(f910(x101651)),f177(x101651,f326(f326(f10(a905,a905,x101651),a321),f326(f326(f9(x101651,x101651,a905),a323),x101652)),x101653))),x101653))),f177(x101651,f326(f326(f10(a905,a905,x101651),a321),f326(f326(f9(x101651,x101651,a905),a323),x101652)),f326(f168(x101651),x101653)))
% 157.55/157.23 [10254]~P118(x102542)+E(x102541,f2(x102542))+P105(f326(f326(f235(x102542),f2(x102542)),f326(f326(f79(x102542),f326(f326(f243(x102542),x102543),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x102542),x102541),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))))
% 157.55/157.23 [10255]~P118(x102552)+E(x102551,f2(x102552))+P105(f326(f326(f235(x102552),f2(x102552)),f326(f326(f79(x102552),f326(f326(f243(x102552),x102551),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x102552),x102553),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))))
% 157.55/157.23 [10310]~P118(x103101)+P105(f326(f326(f234(x103101),f2(x103101)),x103102))+~P105(f326(f326(f234(x103101),f2(x103101)),f326(f326(f243(x103101),x103102),f326(a112,f326(f326(f80(a909),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),x103103)))))
% 157.55/157.23 [5644]~P23(x56441,x56444,x56443)+P23(x56441,x56442,x56443)+~P23(x56441,x56442,x56444)
% 157.55/157.23 [5104]~E(x51042,f89(x51043,x51041))+P105(f326(x51041,x51042))+~P105(f326(x51041,x51044))
% 157.55/157.23 [5350]E(f68(x53503,x53502,x53504),x53502)+E(x53501,f733(x53502,x53503,x53504))+~P105(f326(x53504,x53501))
% 157.55/157.23 [6681]E(f68(x66811,x66812,x66813),f84(x66811,x66813))+~E(f769(x66812,x66811,x66813,x66814),x66814)+~P105(f326(x66813,x66814))
% 157.55/157.23 [6893]~P36(x68932,x68934)+~P36(x68931,x68933)+P36(f916(x68931,x68932),f319(x68931,x68932,x68933,x68934))
% 157.55/157.23 [6894]~P37(x68942,x68944)+~P37(x68941,x68943)+P37(f916(x68941,x68942),f319(x68941,x68942,x68943,x68944))
% 157.55/157.23 [5290]~P6(x52904,x52901)+~E(f326(x52901,x52902),f326(x52901,x52903))+P105(f326(f326(x52901,x52902),x52903))
% 157.55/157.23 [5456]~P6(x54564,x54561)+E(f326(x54561,x54562),f326(x54561,x54563))+~P105(f326(f326(x54561,x54562),x54563))
% 157.55/157.23 [5457]~P14(x54574,x54571)+E(f326(x54571,x54572),f326(x54571,x54573))+~P105(f326(f326(x54571,x54572),x54573))
% 157.55/157.23 [5550]~P17(x55503,x55504,x55501)+E(f326(x55501,x55502),f326(f63(x55503,x55504),x55502))+~P105(f326(f61(x55503),x55502))
% 157.55/157.23 [5551]~P8(x55513,x55514,x55511)+E(f326(x55511,x55512),f326(f63(x55513,x55514),x55512))+~P105(f326(f61(x55513),x55512))
% 157.55/157.23 [5679]~P6(x56794,x56791)+~P105(f326(f326(x56791,x56793),x56792))+P105(f326(f326(x56791,x56792),x56793))
% 157.55/157.23 [5680]~P49(x56804,x56801)+~P105(f326(f326(x56801,x56803),x56802))+P105(f326(f326(x56801,x56802),x56803))
% 157.55/157.23 [5681]~P14(x56814,x56811)+~P105(f326(f326(x56811,x56813),x56812))+P105(f326(f326(x56811,x56812),x56813))
% 157.55/157.23 [5682]~P14(x56823,x56821)+P105(f326(f326(x56821,x56822),x56822))+~P105(f326(f326(x56821,x56824),x56822))
% 157.55/157.23 [5683]~P14(x56833,x56831)+P105(f326(f326(x56831,x56832),x56832))+~P105(f326(f326(x56831,x56832),x56834))
% 157.55/157.23 [5754]E(x57541,x57542)+~E(f326(f250(x57543,x57544),x57541),f326(f250(x57543,x57544),x57542))+~E(f326(f255(x57543,x57544),x57541),f326(f255(x57543,x57544),x57542))
% 157.55/157.23 [5782]E(x57821,x57822)+~P105(f326(f48(x57823,x57824),x57822))+~P105(f326(f48(x57823,x57824),x57821))
% 157.55/157.23 [5982]~P69(x59822)+E(f231(x59821,x59822,x59823,x59824),f2(x59822))+P105(f326(f61(x59821),x59824))
% 157.55/157.23 [6030]~P6(x60303,x60302)+~P105(f326(x60301,x60304))+P105(f326(x60301,f815(x60301,x60302,x60303)))
% 157.55/157.23 [6122]~P105(f326(f314(x61221,x61222),x61224))+P105(f326(f314(x61221,x61222),x61223))+~P105(f326(f326(x61222,x61223),x61224))
% 157.55/157.23 [6927]~P28(x69271,x69273,x69274)+P105(f326(x69271,x69272))+~P105(f326(f326(f328(a1),x69272),f302(a1,x69273,x69274)))
% 157.55/157.23 [7116]~P6(x71161,x71163)+~P105(f326(x71162,x71164))+P105(f326(f326(f328(x71161),f815(x71162,x71163,x71161)),f269(x71161,x71163)))
% 157.55/157.23 [7999]E(x79991,f2(a909))+~P105(f326(x79992,x79993))+P105(f326(x79992,f764(x79992,x79993,x79991,x79994)))
% 157.55/157.23 [8080]~P108(x80802)+~P105(f326(f137(x80801),x80804))+P105(f326(f137(x80801),f150(x80801,x80802,x80803,x80804)))
% 157.55/157.23 [8124]E(f68(x81241,x81242,x81243),f84(x81241,x81243))+~P105(f326(x81243,x81244))+P105(f326(x81243,f769(x81242,x81241,x81243,x81244)))
% 157.55/157.23 [8301]~P105(f326(f61(x83012),x83014))+~P105(f326(f61(x83011),x83013))+P105(f326(f61(f915(x83011,x83012)),f312(x83011,x83012,x83013,x83014)))
% 157.55/157.23 [8302]~P105(f326(f137(x83022),x83024))+~P105(f326(f137(x83021),x83023))+P105(f326(f137(f916(x83021,x83022)),f59(x83021,x83022,x83023,x83024)))
% 157.55/157.23 [8305]P105(f326(f326(f328(f910(x83051)),f326(f326(f134(x83051),x83052),x83053)),f161(x83051,x83054)))+~P105(f326(f326(f328(f910(x83051)),x83053),f161(x83051,x83054)))+~P105(f326(f326(f328(f910(x83051)),x83052),f161(x83051,x83054)))
% 157.55/157.23 [8581]E(x85811,f2(a909))+P105(f326(x85812,x85813))+~P105(f326(x85812,f765(x85812,x85813,x85811,x85814)))
% 157.55/157.23 [8618]~P108(x86183)+~P105(f326(f137(x86181),f150(x86181,x86183,x86184,x86182)))+P105(f326(f137(x86181),x86182))
% 157.55/157.23 [8900]~P105(f326(f326(f328(f916(x89001,x89001)),f326(f326(f251(x89001,x89001),x89002),x89004)),f306(x89001,x89003)))+P105(f326(f326(f328(x89001),x89002),f315(x89001,x89003)))+~P105(f326(f326(f328(x89001),x89004),f315(x89001,x89003)))
% 157.55/157.23 [5274]~P69(x52742)+E(f326(f326(f8(x52741,x52742),x52743),x52744),f2(x52742))+P105(f326(f61(x52741),x52744))
% 157.55/157.23 [5277]~P74(x52772)+E(f326(f326(f11(x52771,x52772),x52773),x52774),f77(x52772))+P105(f326(f61(x52771),x52774))
% 157.55/157.23 [5419]~P70(x54193)+E(x54191,x54192)+~E(f326(f326(f79(x54193),x54194),x54191),f326(f326(f79(x54193),x54194),x54192))
% 157.55/157.23 [5420]~P71(x54203)+E(x54201,x54202)+~E(f326(f326(f79(x54203),x54204),x54201),f326(f326(f79(x54203),x54204),x54202))
% 157.55/157.23 [5422]~P70(x54223)+E(x54221,x54222)+~E(f326(f326(f79(x54223),x54221),x54224),f326(f326(f79(x54223),x54222),x54224))
% 157.55/157.23 [5545]~P4(x55453)+E(x55451,f188(f917(x55452,a905)))+E(f326(f326(f39(x55452,x55453),x55451),f326(f18(x55453,x55452),x55454)),x55454)
% 157.55/157.23 [5546]~P4(x55463)+E(x55461,f188(f917(x55462,a905)))+E(f326(f326(f40(x55462,x55463),x55461),f326(f18(x55463,x55462),x55464)),x55464)
% 157.55/157.23 [5700]~E(x57004,f188(f917(x57001,a905)))+~E(x57004,f326(f326(f308(x57001),x57002),x57003))+P105(f326(f326(f328(x57001),x57002),x57003))
% 157.55/157.23 [5768]~P109(x57683)+E(x57681,x57682)+~E(f302(x57683,x57684,x57681),f326(f326(f308(x57683),x57682),f188(f917(x57683,a905))))
% 157.55/157.23 [5769]~P109(x57693)+E(x57691,x57692)+~E(f302(x57693,x57691,x57692),f326(f326(f308(x57693),x57694),f188(f917(x57693,a905))))
% 157.55/157.23 [5829]~P34(x58293,x58291,x58294)+P34(x58293,x58291,f326(f326(f151(x58293),x58292),x58294))+P105(f326(x58291,x58292))
% 157.55/157.23 [5931]~P30(x59311,x59312,x59314)+~P105(f326(x59312,x59313))+P30(x59311,x59312,f326(f326(f151(x59311),x59313),x59314))
% 157.55/157.23 [6078]P105(f326(x60781,x60782))+~P105(f326(f247(x60783,x60781),x60784))+~P105(f326(f326(f328(x60783),x60782),x60784))
% 157.55/157.23 [6087]~P30(x60871,x60872,x60874)+~P30(x60871,x60872,x60873)+P30(x60871,x60872,f326(f326(f134(x60871),x60873),x60874))
% 157.55/157.23 [6101]P32(x61011,x61012,x61013)+~P32(x61011,x61012,f326(f326(f151(x61011),x61014),x61013))+P105(f326(x61012,x61014))
% 157.55/157.23 [6102]P34(x61021,x61022,x61023)+~P34(x61021,x61022,f326(f326(f151(x61021),x61024),x61023))+P105(f326(x61022,x61024))
% 157.55/157.23 [6177]P32(x61771,x61772,x61773)+P32(x61771,x61772,x61774)+~P32(x61771,x61772,f326(f326(f134(x61771),x61774),x61773))
% 157.55/157.23 [6197]~P69(x61971)+E(f326(f326(f8(a909,x61971),x61972),f326(f301(a909,x61973),f326(a112,x61974))),f2(x61971))+~P105(f326(f326(f235(a909),x61974),x61973))
% 157.55/157.23 [6202]~P60(x62021)+~E(f45(x62021,x62022,x62023),f45(x62021,x62024,x62023))+E(f45(x62021,f326(f78(x62021),x62022),x62023),f45(x62021,f326(f78(x62021),x62024),x62023))
% 157.55/157.23 [6270]P105(f326(x62701,x62702))+~E(f326(f136(x62703,x62701),x62704),x62704)+~P105(f326(f326(f328(x62703),x62702),f326(f172(x62703),x62704)))
% 157.55/157.23 [6289]~E(f326(f326(f79(a909),x62893),x62892),f326(f326(f79(a909),x62891),x62894))+~P105(f326(f326(f235(a909),x62893),x62894))+P105(f326(f326(f235(a909),x62891),x62892))
% 157.55/157.23 [6295]P32(x62951,x62952,x62953)+~P105(f326(x62952,x62954))+~P105(f326(f326(f328(x62951),x62954),f326(f172(x62951),x62953)))
% 157.55/157.23 [6298]~P59(x62981)+E(f45(x62981,f45(x62981,x62982,x62983),x62984),f45(x62981,x62982,x62984))+~P105(f326(f326(f286(x62981),x62984),x62983))
% 157.55/157.23 [6337]~P30(x63373,x63371,x63374)+P105(f326(x63371,x63372))+~P105(f326(f326(f328(x63373),x63372),f326(f172(x63373),x63374)))
% 157.55/157.23 [6339]~E(f326(f136(x63391,x63392),x63393),f113(x63391))+~P105(f326(x63392,x63394))+~P105(f326(f326(f328(x63391),x63394),f326(f172(x63391),x63393)))
% 157.55/157.23 [6340]~E(f177(x63403,x63401,x63404),x63404)+P105(f326(x63401,x63402))+~P105(f326(f326(f328(x63403),x63402),f326(f172(x63403),x63404)))
% 157.55/157.23 [6366]~E(x63664,f188(f917(x63662,a905)))+~E(x63663,f188(f917(x63661,a905)))+E(f312(x63661,x63662,x63663,x63664),f188(f917(f915(x63661,x63662),a905)))
% 157.55/157.23 [6514]P105(f326(x65141,x65142))+~P105(f326(f160(x65143,x65141),x65144))+~P105(f326(f326(f328(x65143),x65142),f326(f172(x65143),x65144)))
% 157.55/157.23 [6650]~P29(x66501,x66503,x66504)+P105(f326(x66501,x66502))+~P105(f326(f326(f328(a909),x66502),f326(f301(a909,x66503),x66504)))
% 157.55/157.23 [6788]~P69(x67881)+E(f326(f326(f8(a909,x67881),x67882),f302(a909,x67883,f326(a112,x67884))),f2(x67881))+~P105(f326(f326(f235(a909),f326(a112,x67884)),x67883))
% 157.55/157.23 [6930]~P108(x69301)+E(f326(f326(f3(f917(x69301,a905)),f326(f301(x69301,x69302),x69303)),f326(f301(x69301,x69302),x69304)),f326(f301(x69301,x69304),x69303))+~P105(f326(f326(f234(x69301),x69302),x69304))
% 157.55/157.23 [7001]~E(x70013,x70014)+E(x70011,f2(a909))+P105(f326(f326(f328(x70012),x70013),f326(f172(x70012),f169(x70012,x70011,x70014))))
% 157.55/157.23 [7280]~P105(f326(f326(f328(f910(x72801)),x72804),f161(x72801,x72803)))+P105(f326(f326(f328(x72801),x72802),x72803))+~P105(f326(f326(f328(x72801),x72802),f326(f172(x72801),x72804)))
% 157.55/157.23 [7287]~P36(x72871,x72872)+P105(f326(f326(f328(x72871),f613(x72872,x72871,x72873)),x72873))+~P105(f326(f326(f328(x72871),x72874),x72873))
% 157.55/157.23 [7342]~P69(x73421)+E(f326(f326(f326(f65(x73421,x73422,f79(x73421)),x73423),f2(x73421)),x73424),f326(f326(f8(x73422,x73421),x73423),x73424))+~P105(f326(f61(x73422),x73424))
% 157.55/157.23 [7344]~P74(x73441)+E(f326(f326(f326(f65(x73441,x73442,f80(x73441)),x73443),f77(x73441)),x73444),f326(f326(f11(x73442,x73441),x73443),x73444))+~P105(f326(f61(x73442),x73444))
% 157.55/157.23 [7372]P24(x73721,x73722,x73723,x73724)+~E(f326(f35(x73722),f326(f309(x73721,x73722,x73723),x73724)),f326(f35(x73721),x73724))+~P105(f326(f61(x73721),x73724))
% 157.55/157.23 [7566]~P69(x75661)+E(f326(f326(f79(x75661),f326(x75662,x75663)),f326(f326(f8(a909,x75661),x75662),f304(a909,x75663,x75664))),f326(f326(f8(a909,x75661),x75662),f302(a909,x75663,x75664)))+~P105(f326(f326(f234(a909),x75663),x75664))
% 157.55/157.23 [7576]~P69(x75761)+~P24(x75762,x75761,x75763,x75764)+E(f326(f326(f8(x75761,x75761),f31(x75761)),f326(f309(x75762,x75761,x75763),x75764)),f326(f326(f8(x75762,x75761),x75763),x75764))
% 157.55/157.23 [7577]~P74(x75771)+~P24(x75772,x75771,x75773,x75774)+E(f326(f326(f11(x75771,x75771),f31(x75771)),f326(f309(x75772,x75771,x75773),x75774)),f326(f326(f11(x75772,x75771),x75773),x75774))
% 157.55/157.23 [7626]E(f326(f35(f915(x76261,x76262)),f312(x76261,x76262,x76263,x76264)),f326(f326(f79(a909),f326(f35(x76261),x76263)),f326(f35(x76262),x76264)))+~P105(f326(f61(x76262),x76264))+~P105(f326(f61(x76261),x76263))
% 157.55/157.23 [7706]E(x77061,x77062)+P105(f326(f326(f328(x77063),x77061),f326(f172(x77063),f170(x77063,x77062,x77064))))+~P105(f326(f326(f328(x77063),x77061),f326(f172(x77063),x77064)))
% 157.55/157.23 [7932]~P69(x79321)+E(f326(f326(f79(x79321),f326(f326(f8(a909,x79321),x79322),f326(f301(a909,x79323),x79324))),f326(x79322,x79324)),f326(f326(f8(a909,x79321),x79322),f326(f301(a909,x79323),f326(a112,x79324))))+P105(f326(f326(f235(a909),x79324),x79323))
% 157.55/157.23 [7981]~P24(x79811,x79812,x79813,f241(f917(x79811,a905)))+~P105(f326(f61(x79812),x79814))+P105(f326(f61(x79811),f326(f310(x79811,x79812,x79813),x79814)))
% 157.55/157.23 [8095]P105(f326(f326(f328(f910(x80951)),f326(f326(f151(x80951),x80952),x80953)),f161(x80951,x80954)))+~P105(f326(f326(f328(f910(x80951)),x80953),f161(x80951,x80954)))+~P105(f326(f326(f328(x80951),x80952),x80954))
% 157.55/157.23 [8181]~E(f326(f309(x81813,x81811,x81814),f241(f917(x81813,a905))),f241(f917(x81811,a905)))+P105(f326(f61(x81811),x81812))+~P105(f326(f61(x81813),f326(f310(x81813,x81811,x81814),x81812)))
% 157.55/157.23 [8273]~P24(x82731,x82733,x82734,x82732)+P105(f326(f61(x82731),x82732))+~P105(f326(f61(x82733),f326(f309(x82731,x82733,x82734),x82732)))
% 157.55/157.23 [8295]~E(x82952,x82953)+P105(f326(f326(f328(f916(x82951,x82951)),f326(f326(f251(x82951,x82951),x82952),x82953)),f262(x82951,x82954)))+~P105(f326(f326(f328(x82951),x82952),x82954))
% 157.55/157.23 [8328]~P69(x83281)+E(f326(f326(f79(x83281),f326(f326(f8(a909,x83281),x83282),f302(a909,x83283,x83284))),f326(x83282,f326(a112,x83284))),f326(f326(f8(a909,x83281),x83282),f302(a909,x83283,f326(a112,x83284))))+P105(f326(f326(f235(a909),f326(a112,x83284)),x83283))
% 157.55/157.23 [8388]P105(f326(x83881,x83882))+~P105(f326(x83881,f326(f326(f164(x83883),x83884),f656(x83881,x83884,x83883))))+~P105(f326(f326(f328(x83883),x83882),f326(f172(x83883),x83884)))
% 157.55/157.23 [8527]~P105(f326(f326(f328(x85271),x85272),f315(x85271,x85274)))+P105(f326(f326(f328(f910(x85271)),f326(f326(f151(x85271),x85272),x85273)),f315(f910(x85271),f157(x85271,x85274))))+~P105(f326(f326(f328(f910(x85271)),x85273),f315(f910(x85271),f157(x85271,x85274))))
% 157.55/157.23 [8542]~P24(x85422,x85423,x85424,f526(x85424,x85423,x85422,x85421))+P24(x85422,x85423,x85424,f38(f917(x85422,a905),x85421))+E(x85421,f188(f917(f917(x85422,a905),a905)))
% 157.55/157.23 [8809]E(x88091,x88092)+~P105(f326(f326(f328(f916(x88093,x88093)),f326(f326(f251(x88093,x88093),x88091),x88092)),f306(x88093,x88094)))+P105(f326(f326(f328(x88093),x88091),f326(f263(x88093,x88093),x88094)))
% 157.55/157.23 [9087]E(x90871,f2(a909))+P105(f326(x90872,x90873))+P105(f326(f326(f328(x90874),f765(x90872,x90873,x90871,x90874)),f326(f172(x90874),f169(x90874,x90871,x90873))))
% 157.55/157.23 [9099]E(x90991,f2(a909))+~P105(f326(x90993,x90994))+P105(f326(f326(f328(x90992),f764(x90993,x90994,x90991,x90992)),f326(f172(x90992),f169(x90992,x90991,x90994))))
% 157.55/157.23 [9101]~P25(x91011,x91012,x91013,f241(f917(x91011,a905)),f241(f917(x91012,a905)))+~P105(f326(f61(x91012),x91014))+P105(f326(f61(x91011),f326(f310(x91011,x91012,x91013),x91014)))
% 157.55/157.23 [9104]P24(x91042,x91043,x91044,f38(f917(x91042,a905),x91041))+E(x91041,f188(f917(f917(x91042,a905),a905)))+P105(f326(f326(f328(f917(x91042,a905)),f526(x91044,x91043,x91042,x91041)),x91041))
% 157.55/157.23 [9219]~P25(x92193,x92191,x92194,f241(f917(x92193,a905)),f241(f917(x92191,a905)))+P105(f326(f61(x92191),x92192))+~P105(f326(f61(x92193),f326(f310(x92193,x92191,x92194),x92192)))
% 157.55/157.23 [9236]P105(f326(f61(x92361),x92362))+~P105(f326(f61(x92364),f326(f309(x92361,x92364,x92363),x92362)))+P105(f326(f326(f328(x92361),f571(x92363,x92364,x92362,x92361)),x92362))
% 157.55/157.23 [9330]~P4(x93302)+E(f326(f326(f64(x93301,x93302,f326(f326(f10(x93302,f917(x93302,x93302),x93301),f101(x93302)),x93303)),f241(x93302)),x93304),f326(f326(f39(x93301,x93302),x93304),x93303))+~P105(f326(f61(x93301),x93304))
% 157.55/157.23 [9331]~P4(x93312)+E(f326(f326(f64(x93311,x93312,f326(f326(f10(x93312,f917(x93312,x93312),x93311),f110(x93312)),x93313)),f188(x93312)),x93314),f326(f326(f40(x93311,x93312),x93314),x93313))+~P105(f326(f61(x93311),x93314))
% 157.55/157.23 [9411]P105(f326(x94111,x94112))+~P105(f326(x94111,f326(f326(f164(x94113),x94114),f693(x94112,x94111,x94114,x94113))))+~P105(f326(f326(f328(x94113),x94112),f326(f172(x94113),x94114)))
% 157.55/157.23 [9432]E(x94321,x94322)+~P105(f326(f326(f328(f916(x94323,x94323)),f326(f326(f251(x94323,x94323),x94321),x94322)),f306(x94323,x94324)))+P105(f326(f326(f328(f916(x94323,x94323)),f326(f326(f251(x94323,x94323),x94321),x94322)),f326(f326(f288(x94323,x94323,x94323),x94324),f306(x94323,x94324))))
% 157.55/157.23 [9482]~E(f326(f189(f910(x94821)),x94822),f326(f189(f910(x94821)),x94823))+~P105(f326(f326(f328(f916(f910(x94821),f910(x94821))),f326(f326(f251(f910(x94821),f910(x94821)),x94822),x94823)),f147(x94821,x94824)))+P105(f326(f326(f328(f916(f910(x94821),f910(x94821))),f326(f326(f251(f910(x94821),f910(x94821)),x94822),x94823)),f145(x94821,x94824)))
% 157.55/157.23 [9716]P30(x97161,f326(f326(f20(x97161,a905,a905),f326(f326(f10(a905,f917(a905,a905),x97161),a325),f326(f326(f10(a905,a905,x97161),a321),x97162))),f326(a323,x97163)),x97164)+~P105(f326(x97162,x97163))+~P34(x97161,x97162,f326(f326(f151(x97161),x97163),x97164))
% 157.55/157.23 [9882]~P30(x98821,f326(f326(f20(x98821,a905,a905),f326(f326(f10(a905,f917(a905,a905),x98821),a325),f326(f326(f10(a905,a905,x98821),a321),x98822))),f326(a323,x98823)),x98824)+~P105(f326(x98822,x98823))+P34(x98821,x98822,f326(f326(f151(x98821),x98823),x98824))
% 157.55/157.23 [9886]~P34(x98861,x98862,x98864)+~P30(x98861,f326(f326(f20(x98861,a905,a905),f326(f326(f10(a905,f917(a905,a905),x98861),a325),f326(f326(f10(a905,a905,x98861),a321),x98862))),f326(a323,x98863)),x98864)+P34(x98861,x98862,f326(f326(f151(x98861),x98863),x98864))
% 157.55/157.23 [9919]~P66(x99191)+E(f326(f326(f8(a909,x99191),f326(f326(f20(a909,x99191,x99191),f326(f326(f10(x99191,f917(x99191,x99191),a909),f3(x99191)),x99192)),f326(f326(f10(a909,x99191,a909),x99192),f326(f326(f9(a909,a909,a909),f79(a909)),f77(a909))))),f302(a909,x99193,x99194)),f2(x99191))+P105(f326(f326(f234(a909),x99193),x99194))
% 157.55/157.23 [10158]~P36(x101582,x101584)+~P24(x101582,x101581,x101583,f241(f917(x101582,a905)))+P36(x101581,f326(f309(f916(x101582,x101582),f916(x101581,x101581),f257(x101582,x101581,x101582,x101581,x101583,x101583)),x101584))
% 157.55/157.23 [10348]~E(f326(f189(f910(x103481)),x103483),f326(f189(f910(x103481)),x103482))+P105(f326(f326(f328(f916(f910(x103481),f910(x103481))),f326(f326(f251(f910(x103481),f910(x103481)),x103482),x103483)),f158(x103481,x103484)))+~P105(f326(f326(f256(x103481,x103481,a905),f326(f326(f9(x103481,f917(f916(x103481,x103481),a905),f917(x103481,a905)),f326(f326(f10(f917(x103481,f917(f917(f916(x103481,x103481),a905),a905)),f917(f917(f916(x103481,x103481),a905),f917(x103481,a905)),x103481),f9(x103481,f917(f916(x103481,x103481),a905),a905)),f326(f326(f10(f917(x103481,f916(x103481,x103481)),f917(x103481,f917(f917(f916(x103481,x103481),a905),a905)),x103481),f326(f10(f916(x103481,x103481),f917(f917(f916(x103481,x103481),a905),a905),x103481),f328(f916(x103481,x103481)))),f251(x103481,x103481)))),x103484)),f658(x103484,x103483,x103482,x103481)))
% 157.55/157.23 [6251]~P59(x62511)+~E(x62512,f2(x62511))+E(f326(f326(f36(x62511),f326(f326(f80(x62511),x62512),x62513)),f326(f326(f80(x62511),x62512),x62514)),f2(x62511))
% 157.55/157.23 [6292]E(x62921,f113(x62922))+E(x62923,f326(f326(f3(a909),f326(f189(f910(x62922)),x62921)),f77(a909)))+E(f144(x62922,f326(f326(f159(x62922,x62921),x62923),x62924)),f144(x62922,x62921))
% 157.55/157.23 [6328]E(x63281,x63282)+P105(f326(x63283,x63282))+~P105(f326(f326(f326(f308(x63284),x63281),x63283),x63282))
% 157.55/157.23 [6344]~P69(x63441)+~P105(f326(f137(x63442),x63444))+E(f326(f165(x63441),f326(f326(f154(x63442,x63441),x63443),x63444)),f326(f326(f8(x63442,x63441),x63443),f326(f172(x63442),x63444)))
% 157.55/157.23 [6359]~P74(x63592)+~P105(f326(f61(x63591),x63594))+E(f326(f326(f11(x63591,x63592),f326(f18(x63592,x63591),x63593)),x63594),f326(f326(f243(x63592),x63593),f326(f35(x63591),x63594)))
% 157.55/157.23 [6413]~P62(x64132)+E(x64131,f2(x64132))+E(f326(f326(f290(x64132),f326(f326(f80(x64132),x64133),x64131)),f326(f326(f80(x64132),x64134),x64131)),f326(f326(f290(x64132),x64133),x64134))
% 157.55/157.23 [6414]~P62(x64142)+E(x64141,f2(x64142))+E(f326(f326(f290(x64142),f326(f326(f80(x64142),x64141),x64143)),f326(f326(f80(x64142),x64141),x64144)),f326(f326(f290(x64142),x64143),x64144))
% 157.55/157.23 [6415]~P59(x64152)+E(x64151,f2(x64152))+E(f326(f326(f36(x64152),f326(f326(f80(x64152),x64153),x64151)),f326(f326(f80(x64152),x64154),x64151)),f326(f326(f36(x64152),x64153),x64154))
% 157.55/157.23 [6417]~P59(x64172)+E(x64171,f2(x64172))+E(f326(f326(f36(x64172),f326(f326(f80(x64172),x64171),x64173)),f326(f326(f80(x64172),x64171),x64174)),f326(f326(f36(x64172),x64173),x64174))
% 157.55/157.23 [6482]P105(f326(x64821,x64822))+~E(x64823,f326(f326(f79(a909),x64824),x64822))+~P105(f326(x64821,f326(f326(f3(a909),x64823),x64824)))
% 157.55/157.23 [6567]~P105(f326(x65672,x65673))+~P105(f326(f160(x65671,x65672),x65674))+P105(f326(f160(x65671,x65672),f326(f326(f151(x65671),x65673),x65674)))
% 157.55/157.23 [6607]E(x66071,f113(x66072))+~E(x66073,f326(f326(f3(a909),f326(f189(f910(x66072)),x66071)),f77(a909)))+E(f144(x66072,f326(f326(f159(x66072,x66071),x66073),x66074)),x66074)
% 157.55/157.23 [6630]~P100(x66301)+~P105(f326(f326(f234(x66301),x66302),x66304))+P105(f326(f326(f234(x66301),x66302),f326(f326(f110(x66301),x66303),x66304)))
% 157.55/157.23 [6631]~P100(x66311)+~P105(f326(f326(f234(x66311),x66312),x66313))+P105(f326(f326(f234(x66311),x66312),f326(f326(f110(x66311),x66313),x66314)))
% 157.55/157.23 [6633]~P108(x66331)+~P105(f326(f326(f234(x66331),x66332),x66334))+P105(f326(f326(f234(x66331),x66332),f326(f326(f233(x66331),x66333),x66334)))
% 157.55/157.23 [6635]~P108(x66351)+~P105(f326(f326(f234(x66351),x66352),x66353))+P105(f326(f326(f234(x66351),x66352),f326(f326(f233(x66351),x66353),x66354)))
% 157.55/157.23 [6636]~P100(x66361)+~P105(f326(f326(f235(x66361),x66362),x66364))+P105(f326(f326(f235(x66361),x66362),f326(f326(f110(x66361),x66363),x66364)))
% 157.55/157.23 [6637]~P100(x66371)+~P105(f326(f326(f235(x66371),x66372),x66373))+P105(f326(f326(f235(x66371),x66372),f326(f326(f110(x66371),x66373),x66374)))
% 157.55/157.23 [6639]~P108(x66391)+~P105(f326(f326(f235(x66391),x66392),x66394))+P105(f326(f326(f235(x66391),x66392),f326(f326(f233(x66391),x66393),x66394)))
% 157.55/157.23 [6641]~P108(x66411)+~P105(f326(f326(f235(x66411),x66412),x66413))+P105(f326(f326(f235(x66411),x66412),f326(f326(f233(x66411),x66413),x66414)))
% 157.55/157.23 [6732]~E(f326(f326(f164(x67321),x67322),x67323),x67324)+E(f326(f326(f159(x67321,x67322),x67323),x67324),x67322)+~P105(f326(f326(f235(a909),x67323),f326(f189(f910(x67321)),x67322)))
% 157.55/157.23 [6772]P105(f326(x67721,x67722))+~P105(f326(x67723,x67722))+~P105(f326(f326(f234(f917(x67724,a905)),x67723),x67721))
% 157.55/157.23 [6807]~E(f326(f326(f159(x68071,x68072),x68073),x68074),x68072)+E(f326(f326(f164(x68071),x68072),x68073),x68074)+~P105(f326(f326(f235(a909),x68073),f326(f189(f910(x68071)),x68072)))
% 157.55/157.23 [6821]~P105(f326(f160(x68211,x68212),x68214))+~P105(f326(f160(x68211,x68212),x68213))+P105(f326(f160(x68211,x68212),f326(f326(f134(x68211),x68213),x68214)))
% 157.55/157.23 [6926]E(x69261,f188(f917(x69262,a905)))+E(x69263,f188(f917(x69264,a905)))+~E(f326(f326(f253(x69264,x69262),x69263),f326(f18(f917(x69262,a905),x69264),x69261)),f188(f917(f916(x69264,x69262),a905)))
% 157.55/157.23 [6946]E(x69461,x69462)+P105(f326(f326(f328(x69463),x69461),x69464))+~P105(f326(f326(f328(x69463),x69461),f326(f326(f308(x69463),x69462),x69464)))
% 157.55/157.23 [6963]~P108(x69631)+P105(f326(f326(f234(x69631),x69632),x69633))+~P105(f326(f326(f234(x69631),x69632),f326(f326(f232(x69631),x69634),x69633)))
% 157.55/157.23 [6965]~P108(x69651)+P105(f326(f326(f234(x69651),x69652),x69653))+~P105(f326(f326(f234(x69651),x69652),f326(f326(f232(x69651),x69653),x69654)))
% 157.55/157.23 [6967]~P101(x69671)+P105(f326(f326(f234(x69671),x69672),x69673))+~P105(f326(f326(f234(x69671),x69672),f326(f326(f101(x69671),x69674),x69673)))
% 157.55/157.23 [6969]~P101(x69691)+P105(f326(f326(f234(x69691),x69692),x69693))+~P105(f326(f326(f234(x69691),x69692),f326(f326(f101(x69691),x69693),x69694)))
% 157.55/157.23 [6970]~P108(x69701)+P105(f326(f326(f235(x69701),x69702),x69703))+~P105(f326(f326(f235(x69701),x69702),f326(f326(f232(x69701),x69704),x69703)))
% 157.55/157.23 [6971]~P108(x69711)+P105(f326(f326(f235(x69711),x69712),x69713))+~P105(f326(f326(f235(x69711),x69712),f326(f326(f232(x69711),x69713),x69714)))
% 157.55/157.23 [6992]~E(f326(f326(f164(x69921),x69923),x69924),x69922)+P105(f326(f326(f328(x69921),x69922),f326(f172(x69921),x69923)))+~P105(f326(f326(f235(a909),x69924),f326(f189(f910(x69921)),x69923)))
% 157.55/157.23 [7002]~P108(x70021)+~P12(x70021,f326(f326(f151(x70021),x70022),f326(f326(f151(x70021),x70023),x70024)))+P105(f326(f326(f234(x70021),x70022),x70023))
% 157.55/157.23 [7145]~P30(x71452,x71451,x71453)+P105(f326(x71451,f326(f326(f164(x71452),x71453),x71454)))+~P105(f326(f326(f235(a909),x71454),f326(f189(f910(x71452)),x71453)))
% 157.55/157.23 [7163]E(x71631,f2(a1))+E(f326(f326(f36(a1),x71632),x71631),x71633)+~P105(f326(f49(x71632,x71631),f326(f326(f251(a1,a1),x71633),x71634)))
% 157.55/157.23 [7185]E(f45(a1,x71852,x71851),x71853)+E(x71851,f2(a1))+~P105(f326(f49(x71852,x71851),f326(f326(f251(a1,a1),x71854),x71853)))
% 157.55/157.23 [7304]P105(f326(f326(f328(x73041),x73042),x73043))+~P105(f326(f326(f328(x73041),x73042),x73044))+~P105(f326(f326(f235(f917(x73041,a905)),x73044),x73043))
% 157.55/157.23 [7305]P105(f326(f326(f328(x73051),x73052),x73053))+~P105(f326(f326(f328(x73051),x73052),x73054))+~P105(f326(f326(f234(f917(x73051,a905)),x73054),x73053))
% 157.55/157.23 [7416]P32(x74161,x74162,x74163)+~P105(f326(x74162,f326(f326(f164(x74161),x74163),x74164)))+~P105(f326(f326(f235(a909),x74164),f326(f189(f910(x74161)),x74163)))
% 157.55/157.23 [7533]~P107(x75332)+~P105(f326(f326(f235(f917(x75331,x75332)),x75333),x75334))+P105(f326(f326(f234(f917(x75331,x75332)),x75333),x75334))
% 157.55/157.23 [7615]~P23(x76151,x76152,x76154)+P23(x76151,x76152,f326(f326(f308(f908(x76151)),x76153),x76154))+~P23(x76151,x76152,f326(f326(f308(f908(x76151)),x76153),f188(f917(f908(x76151),a905))))
% 157.55/157.23 [7657]~P105(f326(f326(f328(x76571),x76572),x76574))+P105(f326(f326(f328(x76571),x76572),f37(f917(x76571,a905),x76573)))+~P105(f326(f326(f328(f917(x76571,a905)),x76574),x76573))
% 157.55/157.23 [7685]~P84(x76851)+~P105(f326(f326(f234(x76851),x76853),x76854))+P105(f326(f326(f234(x76851),f326(f326(f79(x76851),x76852),x76853)),f326(f326(f79(x76851),x76852),x76854)))
% 157.55/157.23 [7686]~P85(x76861)+~P105(f326(f326(f234(x76861),x76863),x76864))+P105(f326(f326(f234(x76861),f326(f326(f79(x76861),x76862),x76863)),f326(f326(f79(x76861),x76862),x76864)))
% 157.55/157.23 [7687]~P84(x76871)+~P105(f326(f326(f234(x76871),x76872),x76874))+P105(f326(f326(f234(x76871),f326(f326(f79(x76871),x76872),x76873)),f326(f326(f79(x76871),x76874),x76873)))
% 157.55/157.23 [7688]~P85(x76881)+~P105(f326(f326(f234(x76881),x76882),x76884))+P105(f326(f326(f234(x76881),f326(f326(f79(x76881),x76882),x76883)),f326(f326(f79(x76881),x76884),x76883)))
% 157.55/157.23 [7689]~P83(x76891)+~P105(f326(f326(f235(x76891),x76893),x76894))+P105(f326(f326(f235(x76891),f326(f326(f79(x76891),x76892),x76893)),f326(f326(f79(x76891),x76892),x76894)))
% 157.55/157.23 [7690]~P84(x76901)+~P105(f326(f326(f235(x76901),x76903),x76904))+P105(f326(f326(f235(x76901),f326(f326(f79(x76901),x76902),x76903)),f326(f326(f79(x76901),x76902),x76904)))
% 157.55/157.23 [7691]~P83(x76911)+~P105(f326(f326(f235(x76911),x76912),x76914))+P105(f326(f326(f235(x76911),f326(f326(f79(x76911),x76912),x76913)),f326(f326(f79(x76911),x76914),x76913)))
% 157.55/157.23 [7692]~P84(x76921)+~P105(f326(f326(f235(x76921),x76922),x76924))+P105(f326(f326(f235(x76921),f326(f326(f79(x76921),x76922),x76923)),f326(f326(f79(x76921),x76924),x76923)))
% 157.55/157.23 [7693]~P112(x76931)+~P105(f326(f326(f286(x76931),x76932),x76934))+P105(f326(f326(f286(x76931),f326(f326(f243(x76931),x76932),x76933)),f326(f326(f243(x76931),x76934),x76933)))
% 157.55/157.23 [7700]~P110(x77001)+~P93(x77001)+E(f326(f326(f3(x77001),f326(f326(f80(x77001),x77002),f326(f103(x77001),x77003))),f326(f326(f80(x77001),x77004),f326(f103(x77001),x77003))),f326(f326(f80(x77001),f326(f326(f3(x77001),x77002),x77004)),f326(f103(x77001),x77003)))
% 157.55/157.23 [7701]~P138(x77011)+~P93(x77011)+E(f326(f326(f79(x77011),f326(f326(f80(x77011),x77012),f326(f103(x77011),x77013))),f326(f326(f80(x77011),x77014),f326(f103(x77011),x77013))),f326(f326(f80(x77011),f326(f326(f79(x77011),x77012),x77014)),f326(f103(x77011),x77013)))
% 157.55/157.23 [7737]~P69(x77371)+E(f326(f326(f79(x77371),f326(x77372,x77373)),f326(f326(f8(a909,x77371),x77372),f302(a909,f326(a112,x77373),x77374))),f326(f326(f8(a909,x77371),x77372),f302(a909,x77373,x77374)))+~P105(f326(f326(f234(a909),x77373),x77374))
% 157.55/157.23 [7749]~P24(x77492,x77491,x77493,f326(f172(x77492),x77494))+~P105(f326(f137(x77492),x77494))+P105(f326(f137(x77491),f326(f326(f154(x77492,x77491),x77493),x77494)))
% 157.55/157.23 [7796]~P105(f326(f326(f234(a909),x77962),x77964))+~P105(f326(f326(f234(a909),x77961),x77963))+P105(f326(f326(f234(a909),f326(f326(f80(a909),x77961),x77962)),f326(f326(f80(a909),x77963),x77964)))
% 157.55/157.23 [7797]~P105(f326(f326(f234(a909),x77972),x77974))+~P105(f326(f326(f234(a909),x77971),x77973))+P105(f326(f326(f234(a909),f326(f326(f79(a909),x77971),x77972)),f326(f326(f79(a909),x77973),x77974)))
% 157.55/157.23 [7800]~P105(f326(f326(f235(a909),x78002),x78004))+~P105(f326(f326(f235(a909),x78001),x78003))+P105(f326(f326(f235(a909),f326(f326(f79(a909),x78001),x78002)),f326(f326(f79(a909),x78003),x78004)))
% 157.55/157.23 [7801]~P105(f326(f326(f234(a1),x78012),x78014))+~P105(f326(f326(f235(a1),x78011),x78013))+P105(f326(f326(f235(a1),f326(f326(f79(a1),x78011),x78012)),f326(f326(f79(a1),x78013),x78014)))
% 157.55/157.23 [7848]P105(f326(f326(f328(x78481),x78482),x78483))+~P105(f326(f326(f328(x78481),x78482),f38(f917(x78481,a905),x78484)))+~P105(f326(f326(f328(f917(x78481,a905)),x78483),x78484))
% 157.55/157.23 [7865]~P105(f326(x78651,f654(x78651,x78653,x78652)))+P105(f326(x78651,f326(f326(f164(x78652),x78653),x78654)))+~P105(f326(f326(f235(a909),x78654),f326(f189(f910(x78652)),x78653)))
% 157.55/157.23 [7870]P105(f326(x78701,x78702))+~P105(f326(f326(f328(x78704),x78702),f326(f172(x78704),x78703)))+P105(f326(f326(f235(a909),f656(x78701,x78703,x78704)),f326(f189(f910(x78704)),x78703)))
% 157.55/157.23 [7917]~P107(x79171)+~P105(f326(f326(f235(f917(x79172,x79171)),x79174),x79173))+~P105(f326(f326(f234(f917(x79172,x79171)),x79173),x79174))
% 157.55/157.23 [7960]~P105(f326(x79604,x79602))+~P105(f326(f326(f328(x79601),x79602),x79603))+P105(f326(f326(f328(x79601),x79602),f326(f326(f101(f917(x79601,a905)),x79603),f326(f261(x79601),x79604))))
% 157.55/157.23 [8102]~P105(f326(f326(f328(x81021),x81023),x81024))+~P105(f326(f326(f235(f917(x81021,a905)),x81022),x81024))+P105(f326(f326(f235(f917(x81021,a905)),x81022),f326(f326(f308(x81021),x81023),x81024)))
% 157.55/157.23 [8104]E(f326(f326(f101(f917(x81041,a905)),x81042),x81043),f188(f917(x81041,a905)))+~E(f326(f326(f101(f917(x81041,a905)),f37(f917(x81041,a905),x81044)),x81043),f188(f917(x81041,a905)))+~P105(f326(f326(f328(f917(x81041,a905)),x81042),x81044))
% 157.55/157.23 [8177]P105(f326(f326(f328(x81771),x81772),x81773))+~P105(f326(f326(f234(f917(x81771,a905)),x81773),f326(f326(f308(x81771),x81772),x81774)))+P105(f326(f326(f234(f917(x81771,a905)),x81773),x81774))
% 157.55/157.23 [8194]P105(f326(f326(f328(x81942),f654(x81941,x81943,x81942)),f326(f172(x81942),x81943)))+P105(f326(x81941,f326(f326(f164(x81942),x81943),x81944)))+~P105(f326(f326(f235(a909),x81944),f326(f189(f910(x81942)),x81943)))
% 157.55/157.23 [8202]~P105(f326(f326(f234(f917(x82021,a905)),x82022),x82024))+P105(f326(f326(f234(f917(x82021,a905)),x82022),x82023))+~P105(f326(f326(f234(f917(x82021,a905)),x82024),x82023))
% 157.55/157.23 [8203]~P105(f326(f326(f235(f917(x82031,a905)),x82032),x82034))+~P105(f326(f326(f234(f917(x82031,a905)),x82034),x82033))+P105(f326(f326(f235(f917(x82031,a905)),x82032),x82033))
% 157.55/157.23 [8204]~P105(f326(f326(f234(f917(x82041,a905)),x82042),x82044))+~P105(f326(f326(f235(f917(x82041,a905)),x82044),x82043))+P105(f326(f326(f235(f917(x82041,a905)),x82042),x82043))
% 157.55/157.23 [8205]~P105(f326(f326(f235(f917(x82051,a905)),x82052),x82054))+P105(f326(f326(f235(f917(x82051,a905)),x82052),x82053))+~P105(f326(f326(f235(f917(x82051,a905)),x82054),x82053))
% 157.55/157.23 [8249]~P105(f326(f326(f328(x82491),x82494),x82493))+~P105(f326(f326(f235(f917(x82491,a905)),x82492),f326(f326(f308(x82491),x82494),x82493)))+P105(f326(f326(f235(f917(x82491,a905)),x82492),x82493))
% 157.55/157.23 [8260]~P84(x82601)+P105(f326(f326(f234(x82601),x82602),x82603))+~P105(f326(f326(f234(x82601),f326(f326(f79(x82601),x82604),x82602)),f326(f326(f79(x82601),x82604),x82603)))
% 157.55/157.23 [8262]~P84(x82621)+P105(f326(f326(f234(x82621),x82622),x82623))+~P105(f326(f326(f234(x82621),f326(f326(f79(x82621),x82622),x82624)),f326(f326(f79(x82621),x82623),x82624)))
% 157.55/157.23 [8264]~P84(x82641)+P105(f326(f326(f235(x82641),x82642),x82643))+~P105(f326(f326(f235(x82641),f326(f326(f79(x82641),x82644),x82642)),f326(f326(f79(x82641),x82644),x82643)))
% 157.55/157.23 [8266]~P84(x82661)+P105(f326(f326(f235(x82661),x82662),x82663))+~P105(f326(f326(f235(x82661),f326(f326(f79(x82661),x82662),x82664)),f326(f326(f79(x82661),x82663),x82664)))
% 157.55/157.23 [8312]P105(f326(x83121,x83122))+~E(f326(f326(f138(x83123),f326(f189(f910(x83123)),f177(x83123,x83121,x83124))),x83124),f113(x83123))+~P105(f326(f326(f328(x83123),x83122),f326(f172(x83123),x83124)))
% 157.55/157.23 [8430]P105(f326(x84301,x84302))+~P105(f326(f326(f328(x84303),x84302),f326(f172(x84303),x84304)))+P105(f326(f326(f235(a909),f326(f189(f910(x84303)),f326(f136(x84303,x84301),x84304))),f326(f189(f910(x84303)),x84304)))
% 157.55/157.23 [8916]~P105(f326(x89161,f747(x89161,x89163,x89162,x89164)))+P105(f326(x89161,f326(f326(f164(x89162),x89163),x89164)))+~P105(f326(f326(f235(a909),x89164),f326(f189(f910(x89162)),x89163)))
% 157.55/157.23 [8940]~P24(x89404,x89403,x89401,f241(f917(x89404,a905)))+E(f326(x89401,f515(x89402,x89401,x89403,x89404)),x89402)+~P105(f326(f326(f328(x89403),x89402),f326(f309(x89404,x89403,x89401),f241(f917(x89404,a905)))))
% 157.55/157.23 [9008]E(f177(x90081,x90082,x90083),f326(f326(f175(x90081),x90084),x90083))+P105(f326(f326(f235(a909),f717(x90082,x90083,x90081,x90084)),x90084))+P105(f326(f326(f235(a909),x90084),f326(f189(f910(x90081)),x90083)))
% 157.55/157.23 [9011]E(f177(x90111,x90112,x90113),f326(f326(f175(x90111),x90114),x90113))+P105(f326(f326(f235(a909),f717(x90112,x90113,x90111,x90114)),x90114))+P105(f326(x90112,f326(f326(f164(x90111),x90113),x90114)))
% 157.55/157.23 [9046]P105(f326(x90461,x90462))+~P105(f326(f326(f328(x90464),x90462),f326(f172(x90464),x90463)))+P105(f326(f326(f235(a909),f693(x90462,x90461,x90463,x90464)),f326(f189(f910(x90464)),x90463)))
% 157.55/157.23 [9048]E(f177(x90481,x90482,x90483),f326(f326(f175(x90481),x90484),x90483))+P105(f326(f326(f235(a909),x90484),f326(f189(f910(x90481)),x90483)))+P105(f326(f326(f235(a909),f717(x90482,x90483,x90481,x90484)),f326(f189(f910(x90481)),x90483)))
% 157.55/157.23 [9055]E(f177(x90551,x90552,x90553),f326(f326(f175(x90551),x90554),x90553))+P105(f326(x90552,f326(f326(f164(x90551),x90553),x90554)))+P105(f326(f326(f235(a909),f717(x90552,x90553,x90551,x90554)),f326(f189(f910(x90551)),x90553)))
% 157.55/157.23 [9080]~P124(x90804)+P105(f326(f326(f328(x90801),f897(x90802,x90803,x90801,x90804)),x90803))+P105(f326(f326(f235(x90804),f2(x90804)),f326(f326(f11(x90801,x90804),x90802),x90803)))
% 157.55/157.23 [9081]~P124(x90814)+P105(f326(f326(f328(x90811),f898(x90812,x90813,x90811,x90814)),x90813))+P105(f326(f326(f234(x90814),f2(x90814)),f326(f326(f11(x90811,x90814),x90812),x90813)))
% 157.55/157.23 [9106]~P105(f326(f61(x91061),x91064))+P105(f326(f326(f328(x91061),f532(x91062,x91063,x91064,x91061)),x91064))+P105(f326(f61(f916(x91061,x91063)),f326(f326(f253(x91061,x91063),x91064),x91062)))
% 157.55/157.23 [9138]P105(f326(f326(f328(x91382),f747(x91381,x91383,x91382,x91384)),f326(f172(x91382),x91383)))+P105(f326(x91381,f326(f326(f164(x91382),x91383),x91384)))+~P105(f326(f326(f235(a909),x91384),f326(f189(f910(x91382)),x91383)))
% 157.55/157.23 [9267]P105(f326(f326(f234(a909),x92674),f326(f189(f910(x92672)),f177(x92672,x92673,x92671))))+P105(f326(f326(f235(a909),f718(x92671,x92672,x92673,x92674)),x92674))+~P105(f326(f326(f234(a909),x92674),f326(f189(f910(x92672)),x92671)))
% 157.55/157.23 [9415]E(f177(x94151,x94152,x94153),f326(f326(f175(x94151),x94154),x94153))+~P105(f326(x94152,f326(f326(f164(x94151),x94153),f717(x94152,x94153,x94151,x94154))))+P105(f326(f326(f235(a909),x94154),f326(f189(f910(x94151)),x94153)))
% 157.55/157.23 [9422]E(f177(x94221,x94222,x94223),f326(f326(f175(x94221),x94224),x94223))+~P105(f326(x94222,f326(f326(f164(x94221),x94223),f717(x94222,x94223,x94221,x94224))))+P105(f326(x94222,f326(f326(f164(x94221),x94223),x94224)))
% 157.55/157.23 [9426]~P105(f326(f61(x94261),x94263))+~P105(f326(f61(x94262),f326(x94264,f532(x94264,x94262,x94263,x94261))))+P105(f326(f61(f916(x94261,x94262)),f326(f326(f253(x94261,x94262),x94263),x94264)))
% 157.55/157.23 [9434]~P124(x94341)+~P105(f326(f326(f234(x94341),f2(x94341)),f326(x94343,f898(x94343,x94344,x94342,x94341))))+P105(f326(f326(f234(x94341),f2(x94341)),f326(f326(f11(x94342,x94341),x94343),x94344)))
% 157.55/157.23 [9435]~P124(x94351)+~P105(f326(f326(f235(x94351),f2(x94351)),f326(x94353,f897(x94353,x94354,x94352,x94351))))+P105(f326(f326(f235(x94351),f2(x94351)),f326(f326(f11(x94352,x94351),x94353),x94354)))
% 157.55/157.23 [9443]~E(f326(f189(f910(x94434)),x94432),f326(f189(f910(x94434)),x94433))+P105(f326(f326(f328(f916(f910(x94434),f910(x94434))),f326(f326(f251(f910(x94434),f910(x94434)),x94433),x94432)),f158(x94434,x94431)))+P105(f326(f326(f235(a909),f642(x94431,x94432,x94433,x94434)),f326(f189(f910(x94434)),x94433)))
% 157.55/157.23 [9495]~P105(f326(x94953,f326(f326(f164(x94952),x94954),f718(x94954,x94952,x94953,x94951))))+P105(f326(f326(f234(a909),x94951),f326(f189(f910(x94952)),f177(x94952,x94953,x94954))))+~P105(f326(f326(f234(a909),x94951),f326(f189(f910(x94952)),x94954)))
% 157.55/157.23 [9574]E(f326(f326(f175(x95741),f655(x95742,x95743,x95744,x95741)),x95743),f326(f326(f175(x95741),f655(x95742,x95743,x95744,x95741)),x95744))+~P105(f326(f326(f328(f916(f910(x95741),f910(x95741))),f326(f326(f251(f910(x95741),f910(x95741)),x95744),x95743)),f147(x95741,x95742)))+P105(f326(f326(f235(a909),f326(f189(f910(x95741)),x95744)),f326(f189(f910(x95741)),x95743)))
% 157.55/157.23 [9630]~P105(f326(f326(f235(a909),f2(a909)),x96303))+~P105(f326(f326(f235(a909),x96304),x96301))+P105(f326(f326(f235(a909),f326(f326(f79(a909),f326(f326(f80(a909),x96301),f45(a909,x96302,x96303))),x96304)),f326(f326(f80(a909),x96301),x96303)))
% 157.55/157.23 [9822]~P107(x98222)+~P105(f326(f326(f234(x98222),f326(x98223,f882(x98224,x98223,x98221,x98222))),f326(x98224,f882(x98224,x98223,x98221,x98222))))+P105(f326(f326(f234(f917(x98221,x98222)),x98223),x98224))
% 157.55/157.23 [9924]~P66(x99241)+E(f326(f326(f8(a909,x99241),f326(f326(f20(a909,x99241,x99241),f326(f326(f10(x99241,f917(x99241,x99241),a909),f3(x99241)),x99242)),f326(f326(f10(a909,x99241,a909),x99242),f326(f326(f9(a909,a909,a909),f79(a909)),f77(a909))))),f302(a909,x99243,x99244)),f326(f326(f3(x99241),f326(x99242,x99243)),f326(x99242,f326(f326(f79(a909),x99244),f77(a909)))))+~P105(f326(f326(f234(a909),x99243),x99244))
% 157.55/157.23 [9999]~P36(x99993,f326(f326(f288(x99993,x99993,x99993),x99992),f306(x99993,x99992)))+~P105(f326(f326(f328(f916(x99993,x99993)),f326(f326(f251(x99993,x99993),f326(x99991,f326(a112,f832(x99992,x99991,x99993)))),f326(x99991,f832(x99992,x99991,x99993)))),f306(x99993,x99992)))+E(f326(x99991,f326(f326(f79(a909),f831(x99992,x99991,x99993)),x99994)),f326(x99991,f831(x99992,x99991,x99993)))
% 157.55/157.23 [6996]E(f326(f326(f134(x69961),x69962),x69963),x69964)+~E(x69963,f326(f326(f138(x69961),f326(f189(f910(x69961)),x69962)),x69964))+~E(f326(f326(f175(x69961),f326(f189(f910(x69961)),x69962)),x69964),x69962)
% 157.55/157.23 [7049]~P63(x70492)+E(x70491,f2(x70492))+E(f326(f326(f290(x70492),f326(f326(f243(x70492),x70493),x70494)),f326(f326(f243(x70492),x70491),x70494)),f326(f326(f243(x70492),f326(f326(f290(x70492),x70493),x70491)),x70494))
% 157.55/157.23 [7201]~P101(x72011)+~P105(f326(f326(f234(x72011),x72013),x72014))+P105(f326(f326(f234(x72011),f326(f326(f101(x72011),x72012),x72013)),x72014))
% 157.55/157.23 [7202]~P101(x72021)+~P105(f326(f326(f234(x72021),x72022),x72024))+P105(f326(f326(f234(x72021),f326(f326(f101(x72021),x72022),x72023)),x72024))
% 157.55/157.23 [7204]~P108(x72041)+~P105(f326(f326(f234(x72041),x72043),x72044))+P105(f326(f326(f234(x72041),f326(f326(f232(x72041),x72042),x72043)),x72044))
% 157.55/157.23 [7206]~P108(x72061)+~P105(f326(f326(f234(x72061),x72062),x72064))+P105(f326(f326(f234(x72061),f326(f326(f232(x72061),x72062),x72063)),x72064))
% 157.55/157.23 [7207]~P101(x72071)+~P105(f326(f326(f235(x72071),x72073),x72074))+P105(f326(f326(f235(x72071),f326(f326(f101(x72071),x72072),x72073)),x72074))
% 157.55/157.23 [7208]~P101(x72081)+~P105(f326(f326(f235(x72081),x72082),x72084))+P105(f326(f326(f235(x72081),f326(f326(f101(x72081),x72082),x72083)),x72084))
% 157.55/157.23 [7210]~P108(x72101)+~P105(f326(f326(f235(x72101),x72103),x72104))+P105(f326(f326(f235(x72101),f326(f326(f232(x72101),x72102),x72103)),x72104))
% 157.55/157.23 [7212]~P108(x72121)+~P105(f326(f326(f235(x72121),x72122),x72124))+P105(f326(f326(f235(x72121),f326(f326(f232(x72121),x72122),x72123)),x72124))
% 157.55/157.23 [7235]~P105(f326(x72353,x72354))+~P105(f326(x72352,x72354))+P105(f326(f326(f326(f101(f917(x72351,a905)),x72352),x72353),x72354))
% 157.55/157.23 [7359]P23(x73591,x73592,x73593)+~P23(x73591,x73592,x73594)+~P105(f326(f326(f234(f917(f908(x73591),a905)),x73593),x73594))
% 157.55/157.23 [7498]~P59(x74981)+E(f326(f326(f36(x74981),f326(f326(f243(x74981),x74982),x74983)),f326(f326(f243(x74981),x74984),x74983)),f326(f326(f243(x74981),f326(f326(f36(x74981),x74982),x74984)),x74983))+~P105(f326(f326(f286(x74981),x74984),x74982))
% 157.55/157.23 [7727]~P69(x77271)+E(f326(f326(f79(x77271),f326(x77272,x77273)),f326(f326(f8(a909,x77271),x77272),f326(f301(a909,f326(a112,x77273)),x77274))),f326(f326(f8(a909,x77271),x77272),f326(f301(a909,x77273),x77274)))+~P105(f326(f326(f235(a909),x77273),x77274))
% 157.55/157.23 [7745]E(x77451,x77452)+P105(f326(f326(f172(x77453),x77454),x77452))+~P105(f326(f326(f172(x77453),f326(f326(f151(x77453),x77451),x77454)),x77452))
% 157.55/157.23 [7757]~P108(x77571)+P105(f326(f326(f234(x77571),x77572),x77573))+~P105(f326(f326(f234(x77571),f326(f326(f233(x77571),x77574),x77572)),x77573))
% 157.55/157.23 [7759]~P108(x77591)+P105(f326(f326(f234(x77591),x77592),x77593))+~P105(f326(f326(f234(x77591),f326(f326(f233(x77591),x77592),x77594)),x77593))
% 157.55/157.23 [7761]~P100(x77611)+P105(f326(f326(f234(x77611),x77612),x77613))+~P105(f326(f326(f234(x77611),f326(f326(f110(x77611),x77614),x77612)),x77613))
% 157.55/157.23 [7763]~P100(x77631)+P105(f326(f326(f234(x77631),x77632),x77633))+~P105(f326(f326(f234(x77631),f326(f326(f110(x77631),x77632),x77634)),x77633))
% 157.55/157.23 [7764]~P108(x77641)+P105(f326(f326(f235(x77641),x77642),x77643))+~P105(f326(f326(f235(x77641),f326(f326(f233(x77641),x77644),x77642)),x77643))
% 157.55/157.23 [7765]~P108(x77651)+P105(f326(f326(f235(x77651),x77652),x77653))+~P105(f326(f326(f235(x77651),f326(f326(f233(x77651),x77652),x77654)),x77653))
% 157.55/157.23 [7840]~P105(f326(f326(f328(x78401),x78402),x78404))+P105(f326(f326(f328(x78401),x78402),x78403))+P105(f326(f326(f328(x78401),x78402),f326(f326(f3(f917(x78401,a905)),x78404),x78403)))
% 157.55/157.23 [7924]P105(f326(x79241,x79242))+P105(f326(x79243,x79242))+~P105(f326(f326(f326(f110(f917(x79244,a905)),x79243),x79241),x79242))
% 157.55/157.23 [7935]~P105(f326(f326(f328(x79351),x79352),x79354))+~P105(f326(f326(f328(x79351),x79352),x79353))+P105(f326(f326(f328(x79351),x79352),f326(f326(f101(f917(x79351,a905)),x79353),x79354)))
% 157.55/157.23 [7982]~P100(x79821)+~P105(f326(f61(x79821),x79824))+E(f326(f326(f64(x79821,x79821,f110(x79821)),x79822),f326(f326(f308(x79821),x79823),x79824)),f326(f326(f110(x79821),x79823),f326(f326(f64(x79821,x79821,f110(x79821)),x79822),x79824)))
% 157.55/157.23 [7983]~P101(x79831)+~P105(f326(f61(x79831),x79834))+E(f326(f326(f64(x79831,x79831,f101(x79831)),x79832),f326(f326(f308(x79831),x79833),x79834)),f326(f326(f101(x79831),x79833),f326(f326(f64(x79831,x79831,f101(x79831)),x79832),x79834)))
% 157.55/157.23 [7984]~P108(x79841)+~P105(f326(f61(x79841),x79844))+E(f326(f326(f64(x79841,x79841,f232(x79841)),x79842),f326(f326(f308(x79841),x79843),x79844)),f326(f326(f232(x79841),x79843),f326(f326(f64(x79841,x79841,f232(x79841)),x79842),x79844)))
% 157.55/157.23 [7985]~P108(x79851)+~P105(f326(f61(x79851),x79854))+E(f326(f326(f64(x79851,x79851,f233(x79851)),x79852),f326(f326(f308(x79851),x79853),x79854)),f326(f326(f233(x79851),x79853),f326(f326(f64(x79851,x79851,f233(x79851)),x79852),x79854)))
% 157.55/157.23 [7986]~P110(x79861)+~P93(x79861)+E(f326(f326(f3(x79861),f326(f326(f80(x79861),f326(f103(x79861),x79862)),x79863)),f326(f326(f80(x79861),f326(f103(x79861),x79862)),x79864)),f326(f326(f80(x79861),f326(f103(x79861),x79862)),f326(f326(f3(x79861),x79863),x79864)))
% 157.55/157.23 [7987]~P138(x79871)+~P93(x79871)+E(f326(f326(f79(x79871),f326(f326(f80(x79871),f326(f103(x79871),x79872)),x79873)),f326(f326(f80(x79871),f326(f103(x79871),x79872)),x79874)),f326(f326(f80(x79871),f326(f103(x79871),x79872)),f326(f326(f79(x79871),x79873),x79874)))
% 157.55/157.23 [8100]E(x81001,x81002)+P105(f326(f326(f328(x81003),x81001),f326(f172(x81003),x81004)))+~P105(f326(f326(f328(x81003),x81001),f326(f172(x81003),f326(f326(f151(x81003),x81002),x81004))))
% 157.55/157.23 [8271]P53(x82711,x82712,x82713)+~P53(x82711,x82712,x82714)+~P105(f326(f326(f234(f917(f916(x82711,x82712),a905)),x82713),x82714))
% 157.55/157.23 [8314]P105(f326(f326(f328(x83141),x83142),x83143))+P105(f326(f326(f328(x83141),x83142),x83144))+~P105(f326(f326(f328(x83141),x83142),f326(f326(f110(f917(x83141,a905)),x83144),x83143)))
% 157.55/157.23 [8324]~P51(x83241,x83244,x83243)+~P105(f326(f326(f328(x83241),x83242),x83244))+P105(f326(f326(f328(f916(x83241,x83241)),f326(f326(f251(x83241,x83241),x83242),x83242)),x83243))
% 157.55/157.23 [8336]~P105(f326(f61(x83362),x83364))+~P105(f326(f61(x83361),x83363))+P105(f326(f61(f916(x83361,x83362)),f326(f326(f253(x83361,x83362),x83363),f326(f18(f917(x83362,a905),x83361),x83364))))
% 157.55/157.23 [8337]~P105(f326(f326(f328(x83371),x83372),x83374))+~P105(f326(f326(f234(f917(x83371,a905)),x83373),x83374))+P105(f326(f326(f234(f917(x83371,a905)),f326(f326(f308(x83371),x83372),x83373)),x83374))
% 157.55/157.23 [8344]~P74(x83442)+~P143(x83442)+E(f326(f326(f11(x83441,x83442),f326(f326(f10(a909,x83442,x83441),f100(x83442)),x83443)),x83444),f326(f100(x83442),f326(f326(f11(x83441,a909),x83443),x83444)))
% 157.55/157.23 [8345]~P74(x83452)+~P140(x83452)+E(f326(f326(f11(x83451,x83452),f326(f326(f10(a1,x83452,x83451),f102(x83452)),x83453)),x83454),f326(f102(x83452),f326(f326(f11(x83451,a1),x83453),x83454)))
% 157.55/157.23 [8369]E(f326(f326(f3(f917(x83691,a905)),x83692),f326(f326(f3(f917(x83691,a905)),x83693),x83694)),x83694)+~P105(f326(f326(f234(f917(x83691,a905)),x83692),x83693))+~P105(f326(f326(f234(f917(x83691,a905)),x83694),x83692))
% 157.55/157.23 [8465]~P105(f326(f61(x84651),x84654))+E(f326(f326(f3(a909),f326(f326(f8(x84651,a909),x84652),x84653)),f326(f326(f8(x84651,a909),x84652),x84654)),f326(f326(f8(x84651,a909),x84652),f326(f326(f3(f917(x84651,a905)),x84653),x84654)))+~P105(f326(f326(f234(f917(x84651,a905)),x84654),x84653))
% 157.55/157.23 [8615]~P7(x86151,x86154,x86153)+~P105(f326(f326(f328(x86151),x86152),x86154))+P105(f326(f326(f328(x86151),x86152),f326(f284(x86151,x86151,x86153),f326(f326(f308(x86151),x86152),f188(f917(x86151,a905))))))
% 157.55/157.23 [8675]~P105(f326(f326(f234(f917(x86751,a905)),x86752),x86753))+~P105(f326(f326(f234(f917(x86751,a905)),x86752),x86754))+P105(f326(f326(f234(f917(x86751,a905)),x86752),f326(f326(f101(f917(x86751,a905)),x86753),x86754)))
% 157.55/157.23 [8777]E(x87771,f188(f917(x87772,a905)))+P105(f326(f61(x87773),x87774))+~P105(f326(f61(f916(x87773,x87772)),f326(f326(f253(x87773,x87772),x87774),f326(f18(f917(x87772,a905),x87773),x87771))))
% 157.55/157.23 [8778]E(x87781,f188(f917(x87782,a905)))+P105(f326(f61(x87783),x87784))+~P105(f326(f61(f916(x87782,x87783)),f326(f326(f253(x87782,x87783),x87781),f326(f18(f917(x87783,a905),x87782),x87784))))
% 157.55/157.23 [8851]P105(f326(f326(f328(x88511),x88512),f315(x88511,x88513)))+~P105(f326(f326(f328(x88511),x88514),f315(x88511,x88513)))+~P105(f326(f326(f328(f916(x88511,x88511)),f326(f326(f251(x88511,x88511),x88512),x88514)),x88513))
% 157.55/157.23 [8908]~P36(x89081,x89084)+P105(f326(f326(f328(f916(x89081,x89081)),f326(f326(f251(x89081,x89081),x89083),x89082)),f306(x89081,x89084)))+P36(x89081,f326(f326(f308(f916(x89081,x89081)),f326(f326(f251(x89081,x89081),x89082),x89083)),x89084))
% 157.55/157.23 [8909]~P56(x89091,x89094)+P105(f326(f326(f328(f916(x89091,x89091)),f326(f326(f251(x89091,x89091),x89093),x89092)),f306(x89091,x89094)))+P56(x89091,f326(f326(f308(f916(x89091,x89091)),f326(f326(f251(x89091,x89091),x89092),x89093)),x89094))
% 157.55/157.23 [8991]~E(x89912,x89913)+~P105(f326(f326(f328(x89911),x89912),f326(f172(x89911),x89914)))+P105(f326(f326(f328(f916(x89911,x89911)),f326(f326(f251(x89911,x89911),x89912),x89913)),f326(f172(f916(x89911,x89911)),f326(f326(f181(x89911,x89911),x89914),x89914))))
% 157.55/157.23 [9079]~E(x90793,x90794)+P105(f326(f326(f256(x90791,x90791,a905),a323),x90792))+~P105(f326(f326(f328(f916(x90791,x90791)),x90792),f326(f172(f916(x90791,x90791)),f326(f326(f181(x90791,x90791),x90793),x90794))))
% 157.55/157.23 [9123]P105(f326(f326(f328(f916(f910(x91231),f910(x91231))),f326(f326(f251(f910(x91231),f910(x91231)),x91232),x91233)),f147(x91231,x91234)))+~E(f326(f326(f175(x91231),f326(f189(f910(x91231)),x91232)),x91233),x91232)+~P105(f326(f326(f235(a909),f326(f189(f910(x91231)),x91232)),f326(f189(f910(x91231)),x91233)))
% 157.55/157.23 [9126]~P50(x91261,x91264)+~P105(f326(f326(f328(f916(x91261,x91261)),f326(f326(f251(x91261,x91261),x91263),x91262)),x91264))+P105(f326(f326(f328(f916(x91261,x91261)),f326(f326(f251(x91261,x91261),x91262),x91263)),x91264))
% 157.55/157.23 [9217]~P105(f326(f61(x92171),x92174))+P105(f326(f326(f328(x92171),f462(x92172,x92173,x92174,x92171)),x92174))+P105(f326(f61(x92173),f326(f326(f40(x92171,f917(x92173,a905)),x92174),x92172)))
% 157.55/157.23 [9218]~P105(f326(f61(x92181),x92184))+P105(f326(f326(f328(x92181),f579(x92182,x92183,x92184,x92181)),x92184))+P105(f326(f61(x92183),f326(f326(f40(x92181,f917(x92183,a905)),x92184),x92182)))
% 157.55/157.23 [9303]P105(f326(f326(f328(f916(x93031,x93031)),x93032),f326(f326(f288(x93031,x93031,x93031),x93033),f306(x93031,x93033))))+~P105(f326(f326(f235(a909),f2(a909)),x93034))+~P105(f326(f326(f328(f916(x93031,x93031)),x93032),f326(f326(f183(f916(x93031,x93031),a905),x93034),x93033)))
% 157.55/157.23 [9311]~P36(x93111,x93112)+~P105(f326(f326(f328(f916(x93111,x93111)),f326(f326(f251(x93111,x93111),x93114),x93113)),x93112))+~P105(f326(f326(f328(f916(x93111,x93111)),f326(f326(f251(x93111,x93111),x93113),x93114)),x93112))
% 157.55/157.23 [9433]~P105(f326(f61(x94331),x94334))+E(f326(f326(f8(x94331,a909),f326(f326(f10(f917(x94332,a905),a909,x94331),f35(x94332)),x94333)),x94334),f326(f35(f916(x94331,x94332)),f326(f326(f253(x94331,x94332),x94334),x94333)))+P105(f326(f326(f328(x94331),f535(x94333,x94332,x94334,x94331)),x94334))
% 157.55/157.23 [9437]~P105(f326(f137(x94371),x94372))+P105(f326(f137(x94371),f326(f326(f159(x94371,x94372),x94373),x94374)))+P105(f326(f326(f328(x94371),x94374),f326(f326(f3(f917(x94371,a905)),f326(f172(x94371),x94372)),f326(f326(f308(x94371),f326(f326(f164(x94371),x94372),x94373)),f188(f917(x94371,a905))))))
% 157.55/157.23 [9454]~P105(f326(f61(x94542),x94543))+~P105(f326(f61(x94541),f326(x94544,f462(x94544,x94541,x94543,x94542))))+P105(f326(f61(x94541),f326(f326(f40(x94542,f917(x94541,a905)),x94543),x94544)))
% 157.55/157.23 [9455]~P105(f326(f61(x94552),x94553))+~P105(f326(f61(x94551),f326(x94554,f579(x94554,x94551,x94553,x94552))))+P105(f326(f61(x94551),f326(f326(f40(x94552,f917(x94551,a905)),x94553),x94554)))
% 157.55/157.23 [9533]~P105(f326(f326(f328(f916(x95331,x95331)),x95332),f326(f326(f288(x95331,x95331,x95331),x95334),f306(x95331,x95334))))+P105(f326(f326(f328(f916(x95331,x95331)),x95332),f326(f326(f288(x95331,x95331,x95331),x95333),f306(x95331,x95333))))+~P105(f326(f326(f234(f917(f916(x95331,x95331),a905)),x95334),x95333))
% 157.55/157.23 [9541]E(f326(f326(f175(x95411),f655(x95414,x95413,x95412,x95411)),x95413),f326(f326(f175(x95411),f655(x95414,x95413,x95412,x95411)),x95412))+~P105(f326(f326(f328(f916(f910(x95411),f910(x95411))),f326(f326(f251(f910(x95411),f910(x95411)),x95412),x95413)),f147(x95411,x95414)))+E(f326(f326(f175(x95411),f326(f189(f910(x95411)),x95412)),x95413),x95412)
% 157.55/157.23 [9557]~P105(f326(f61(x95571),x95574))+E(f326(f326(f8(x95571,a909),f326(f326(f10(f917(x95572,a905),a909,x95571),f35(x95572)),x95573)),x95574),f326(f35(f916(x95571,x95572)),f326(f326(f253(x95571,x95572),x95574),x95573)))+~P105(f326(f61(x95572),f326(x95573,f535(x95573,x95572,x95574,x95571))))
% 157.55/157.23 [9561]~E(f326(f189(f910(x95611)),x95613),f326(f189(f910(x95611)),x95612))+P105(f326(f326(f328(f916(f910(x95611),f910(x95611))),f326(f326(f251(f910(x95611),f910(x95611)),x95612),x95613)),f158(x95611,x95614)))+P105(f326(f326(f328(f916(x95611,x95611)),f658(x95614,x95613,x95612,x95611)),f326(f172(f916(x95611,x95611)),f326(f326(f181(x95611,x95611),x95612),x95613))))
% 157.55/157.23 [9641]~P105(f326(f326(f328(f916(f910(x96411),f910(x96411))),f326(f326(f251(f910(x96411),f910(x96411)),x96412),x96413)),f147(x96411,x96414)))+E(f326(f326(f175(x96411),f326(f189(f910(x96411)),x96412)),x96413),x96412)+P105(f326(f326(f235(a909),f655(x96414,x96413,x96412,x96411)),f326(f326(f232(a909),f326(f189(f910(x96411)),x96412)),f326(f189(f910(x96411)),x96413))))
% 157.55/157.23 [9665]~P105(f326(f326(f328(f916(f910(x96651),f910(x96651))),f326(f326(f251(f910(x96651),f910(x96651)),x96652),x96653)),f147(x96651,x96654)))+P105(f326(f326(f235(a909),f326(f189(f910(x96651)),x96652)),f326(f189(f910(x96651)),x96653)))+P105(f326(f326(f235(a909),f655(x96654,x96653,x96652,x96651)),f326(f326(f232(a909),f326(f189(f910(x96651)),x96652)),f326(f189(f910(x96651)),x96653))))
% 157.55/157.23 [10067]~P105(f326(f326(f328(f916(f910(x100671),f910(x100671))),f326(f326(f251(f910(x100671),f910(x100671)),x100672),x100673)),f147(x100671,x100674)))+E(f326(f326(f175(x100671),f326(f189(f910(x100671)),x100672)),x100673),x100672)+P105(f326(f326(f328(f916(x100671,x100671)),f326(f326(f251(x100671,x100671),f326(f326(f164(x100671),x100672),f655(x100674,x100673,x100672,x100671))),f326(f326(f164(x100671),x100673),f655(x100674,x100673,x100672,x100671)))),x100674))
% 157.55/157.23 [10068]~P105(f326(f326(f328(f916(f910(x100681),f910(x100681))),f326(f326(f251(f910(x100681),f910(x100681)),x100682),x100683)),f147(x100681,x100684)))+P105(f326(f326(f235(a909),f326(f189(f910(x100681)),x100682)),f326(f189(f910(x100681)),x100683)))+P105(f326(f326(f328(f916(x100681,x100681)),f326(f326(f251(x100681,x100681),f326(f326(f164(x100681),x100682),f655(x100684,x100683,x100682,x100681))),f326(f326(f164(x100681),x100683),f655(x100684,x100683,x100682,x100681)))),x100684))
% 157.55/157.23 [10136]~E(f326(f189(f910(x101361)),x101362),f326(f189(f910(x101361)),x101363))+P105(f326(f326(f328(f916(f910(x101361),f910(x101361))),f326(f326(f251(f910(x101361),f910(x101361)),x101362),x101363)),f158(x101361,x101364)))+~P105(f326(f326(f328(f916(x101361,x101361)),f326(f326(f251(x101361,x101361),f326(f326(f164(x101361),x101362),f642(x101364,x101363,x101362,x101361))),f326(f326(f164(x101361),x101363),f642(x101364,x101363,x101362,x101361)))),x101364))
% 157.55/157.23 [10283]~P69(x102831)+~P105(f326(f61(x102832),x102834))+E(f326(f165(x102831),f326(f326(f154(x102832,x102831),x102833),f89(f910(x102832),f326(f326(f20(f910(x102832),a905,a905),f326(f326(f10(a905,f917(a905,a905),f910(x102832)),a324),f326(f326(f9(f910(x102832),f917(x102832,a905),a905),f326(f326(f10(f917(x102832,a905),f917(f917(x102832,a905),a905),f910(x102832)),a323),f172(x102832))),x102834))),f137(x102832))))),f231(x102832,x102831,x102833,x102834))
% 157.55/157.23 [7578]~P62(x75782)+E(x75781,f2(x75782))+E(f326(f326(f290(x75782),f326(f326(f79(x75782),x75783),f326(f326(f80(x75782),x75784),x75781))),x75781),f326(f326(f79(x75782),x75784),f326(f326(f290(x75782),x75783),x75781)))
% 157.55/157.23 [7579]~P59(x75792)+E(x75791,f2(x75792))+E(f326(f326(f36(x75792),f326(f326(f79(x75792),x75793),f326(f326(f80(x75792),x75794),x75791))),x75791),f326(f326(f79(x75792),x75794),f326(f326(f36(x75792),x75793),x75791)))
% 157.55/157.23 [7580]~P59(x75802)+E(x75801,f2(x75802))+E(f326(f326(f36(x75802),f326(f326(f79(x75802),x75803),f326(f326(f80(x75802),x75801),x75804))),x75801),f326(f326(f79(x75802),x75804),f326(f326(f36(x75802),x75803),x75801)))
% 157.55/157.23 [7804]~P63(x78042)+E(x78041,f2(x78042))+E(f326(f326(f290(x78042),f326(f326(f3(x78042),x78043),f326(f326(f80(x78042),x78041),x78044))),x78041),f326(f326(f3(x78042),f326(f326(f290(x78042),x78043),x78041)),x78044))
% 157.55/157.23 [7805]~P62(x78052)+E(x78051,f2(x78052))+E(f326(f326(f290(x78052),f326(f326(f79(x78052),x78053),f326(f326(f80(x78052),x78054),x78051))),x78051),f326(f326(f79(x78052),f326(f326(f290(x78052),x78053),x78051)),x78054))
% 157.55/157.23 [7806]~P63(x78062)+E(x78061,f2(x78062))+E(f326(f326(f290(x78062),f326(f326(f79(x78062),x78063),f326(f326(f80(x78062),x78061),x78064))),x78061),f326(f326(f79(x78062),f326(f326(f290(x78062),x78063),x78061)),x78064))
% 157.55/157.23 [8496]~P105(f326(f160(x84961,x84963),x84964))+~P105(f326(f160(x84961,x84962),x84964))+P105(f326(f160(x84961,f326(f326(f101(f917(x84961,a905)),x84962),x84963)),x84964))
% 157.55/157.23 [8866]~E(f326(f326(f288(x88661,x88661,x88661),x88662),x88664),f188(f917(f916(x88661,x88661),a905)))+~E(f326(f326(f288(x88661,x88661,x88661),x88662),x88663),f188(f917(f916(x88661,x88661),a905)))+E(f326(f326(f288(x88661,x88661,x88661),x88662),f326(f326(f110(f917(f916(x88661,x88661),a905)),x88663),x88664)),f188(f917(f916(x88661,x88661),a905)))
% 157.55/157.23 [8992]~P105(f326(f326(f234(f917(x89921,a905)),x89923),x89924))+~P105(f326(f326(f234(f917(x89921,a905)),x89922),x89924))+P105(f326(f326(f234(f917(x89921,a905)),f326(f326(f110(f917(x89921,a905)),x89922),x89923)),x89924))
% 157.55/157.23 [9363]~P105(f326(f61(x93631),x93634))+~P105(f326(f61(x93631),x93633))+E(f326(f326(f3(a909),f326(f326(f79(a909),f326(f326(f8(x93631,a909),x93632),x93633)),f326(f326(f8(x93631,a909),x93632),x93634))),f326(f326(f8(x93631,a909),x93632),f326(f326(f101(f917(x93631,a905)),x93633),x93634))),f326(f326(f8(x93631,a909),x93632),f326(f326(f110(f917(x93631,a905)),x93633),x93634)))
% 157.55/157.23 [9451]~P105(f326(f326(f328(x94511),x94513),x94512))+~P105(f326(f326(f234(f917(x94511,a905)),x94512),f326(f326(f308(x94511),x94513),x94514)))+P105(f326(f326(f234(f917(x94511,a905)),f326(f326(f3(f917(x94511,a905)),x94512),f326(f326(f308(x94511),x94513),f188(f917(x94511,a905))))),x94514))
% 157.55/157.23 [9617]~P105(f326(f326(f328(x96171),x96173),x96172))+P105(f326(f326(f234(f917(x96171,a905)),x96172),f326(f326(f308(x96171),x96173),x96174)))+~P105(f326(f326(f234(f917(x96171,a905)),f326(f326(f3(f917(x96171,a905)),x96172),f326(f326(f308(x96171),x96173),f188(f917(x96171,a905))))),x96174))
% 157.55/157.23 [9705]~P105(f326(f326(f234(a909),x97051),x97053))+~P105(f326(f326(f235(a909),x97052),x97054))+P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),f326(f326(f251(a909,a909),x97051),x97052)),f326(f326(f251(a909,a909),x97053),x97054))),a32))
% 157.55/157.23 [9706]~P105(f326(f326(f234(a909),x97062),x97064))+~P105(f326(f326(f234(a909),x97061),x97063))+P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),f326(f326(f251(a909,a909),x97061),x97062)),f326(f326(f251(a909,a909),x97063),x97064))),a70))
% 157.55/157.23 [9997]~P105(f326(f326(f328(f910(x99971)),x99974),f161(x99971,x99973)))+~P105(f326(f326(f328(f910(x99971)),x99974),f161(x99971,x99972)))+P105(f326(f160(x99971,f326(f326(f101(f917(x99971,a905)),f326(f326(f9(x99971,f917(x99971,a905),a905),f328(x99971)),x99972)),f326(f326(f9(x99971,f917(x99971,a905),a905),f328(x99971)),x99973))),x99974))
% 157.55/157.23 [10102]~P24(x101021,f917(f917(x101021,a905),a905),f326(f326(f9(x101021,f917(f916(x101021,x101021),a905),f917(f917(x101021,a905),a905)),f326(f326(f10(f917(x101021,a905),f917(f917(f916(x101021,x101021),a905),f917(f917(x101021,a905),a905)),x101021),f60(x101021)),f326(f326(f9(x101021,f917(x101021,a905),f917(x101021,a905)),f308(x101021)),f188(f917(x101021,a905))))),x101023),x101022)+~P105(f326(f326(f328(x101021),x101024),x101022))+E(f326(f326(f3(f917(f917(x101021,a905),a905)),f326(f326(f60(x101021),x101022),x101023)),f326(f326(f60(x101021),f326(f326(f308(x101021),x101024),f188(f917(x101021,a905)))),x101023)),f326(f326(f60(x101021),f326(f326(f3(f917(x101021,a905)),x101022),f326(f326(f308(x101021),x101024),f188(f917(x101021,a905))))),x101023))
% 157.55/157.23 [10238]~P51(x102381,x102382,x102384)+~P105(f326(f326(f328(f916(x102381,x102381)),x102383),x102384))+P105(f326(f326(f256(x102381,x102381,a905),f326(f326(f9(x102381,f917(x102381,a905),f917(x102381,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x102381,a905),f917(x102381,a905)),x102381),f10(a905,a905,x102381)),f326(f326(f10(a905,f917(a905,a905),x102381),a324),f326(f326(f9(x102381,f917(x102381,a905),a905),f328(x102381)),x102382)))),f326(f326(f9(x102381,f917(x102381,a905),a905),f328(x102381)),x102382))),x102383))
% 157.55/157.23 [10251]P105(f326(f61(x102511),x102512))+~P105(f326(f61(x102513),f326(f309(x102511,x102513,x102514),x102512)))+~P105(f326(f61(x102511),f326(f261(x102511),f326(f326(f20(x102511,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102511),a324),f326(f326(f9(x102511,f917(x102511,a905),a905),f328(x102511)),x102512))),f326(f326(f9(x102511,x102513,a905),f326(f326(f10(x102513,f917(x102513,a905),x102511),a323),x102514)),f326(x102514,f571(x102514,x102513,x102512,x102511)))))))
% 157.55/157.23 [8255]~P63(x82552)+E(x82551,f2(x82552))+E(f326(f326(f290(x82552),f326(f326(f3(x82552),f326(f326(f80(x82552),x82551),x82553)),x82554)),x82551),f326(f326(f3(x82552),x82553),f326(f326(f290(x82552),x82554),x82551)))
% 157.55/157.23 [8256]~P63(x82562)+E(x82561,f2(x82562))+E(f326(f326(f290(x82562),f326(f326(f79(x82562),f326(f326(f80(x82562),x82561),x82563)),x82564)),x82561),f326(f326(f79(x82562),x82563),f326(f326(f290(x82562),x82564),x82561)))
% 157.55/157.23 [9152]~E(f326(f326(f288(x91521,x91521,x91521),x91523),x91524),f188(f917(f916(x91521,x91521),a905)))+~E(f326(f326(f288(x91521,x91521,x91521),x91522),x91524),f188(f917(f916(x91521,x91521),a905)))+E(f326(f326(f288(x91521,x91521,x91521),f326(f326(f110(f917(f916(x91521,x91521),a905)),x91522),x91523)),x91524),f188(f917(f916(x91521,x91521),a905)))
% 157.55/157.23 [9914]~P105(f326(f160(x99141,x99143),x99144))+~P105(f326(f160(x99141,x99142),x99144))+P105(f326(f160(x99141,f326(f326(f20(x99141,a905,a905),f326(f326(f10(a905,f917(a905,a905),x99141),a324),x99142)),x99143)),x99144))
% 157.55/157.23 [10175]P105(f326(x101751,f551(x101752,x101753,x101751,x101754)))+~P105(f326(f61(x101754),f326(f261(x101754),x101751)))+P105(f326(f61(x101753),f326(f261(x101753),f326(f326(f10(f917(x101754,a905),a905,x101753),f86(x101754)),f326(f326(f10(f917(x101754,a905),f917(x101754,a905),x101753),f326(f20(x101754,a905,a905),f326(f326(f10(a905,f917(a905,a905),x101754),a324),x101751))),x101752)))))
% 157.55/157.23 [10193]~P105(f326(f61(x101932),f326(f261(x101932),x101933)))+~P105(f326(f61(x101931),f326(f261(x101931),f326(f326(f9(x101931,x101932,a905),x101934),f551(x101934,x101931,x101933,x101932)))))+P105(f326(f61(x101931),f326(f261(x101931),f326(f326(f10(f917(x101932,a905),a905,x101931),f86(x101932)),f326(f326(f10(f917(x101932,a905),f917(x101932,a905),x101931),f326(f20(x101932,a905,a905),f326(f326(f10(a905,f917(a905,a905),x101932),a324),x101933))),x101934)))))
% 157.55/157.23 [10262]~P105(f326(f61(x102621),x102624))+P105(f326(f326(f328(x102621),f787(x102622,x102623,x102624,x102621)),x102624))+P105(f326(f61(x102623),f326(f261(x102623),f326(f326(f10(f917(x102621,a905),a905,x102623),f86(x102621)),f326(f326(f10(f917(x102621,a905),f917(x102621,a905),x102623),f326(f20(x102621,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102621),a324),f326(f326(f9(x102621,f917(x102621,a905),a905),f328(x102621)),x102624)))),x102622)))))
% 157.55/157.23 [10268]~P105(f326(f61(x102682),x102683))+~P105(f326(f61(x102681),f326(f261(x102681),f326(f326(f9(x102681,x102682,a905),x102684),f787(x102684,x102681,x102683,x102682)))))+P105(f326(f61(x102681),f326(f261(x102681),f326(f326(f10(f917(x102682,a905),a905,x102681),f86(x102682)),f326(f326(f10(f917(x102682,a905),f917(x102682,a905),x102681),f326(f20(x102682,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102682),a324),f326(f326(f9(x102682,f917(x102682,a905),a905),f328(x102682)),x102683)))),x102684)))))
% 157.55/157.23 [5182]~E(x51822,x51824)+E(f169(x51821,x51822,x51823),f169(x51821,x51824,x51825))+~E(x51822,f2(a909))
% 157.55/157.23 [5436]E(x54361,x54362)+~E(f169(x54364,x54363,x54361),f169(x54364,x54365,x54362))+E(x54363,f2(a909))
% 157.55/157.23 [6711]E(x67111,x67112)+~E(f326(x67113,x67111),f326(x67113,x67112))+~P24(x67114,x67115,x67113,f241(f917(x67114,a905)))
% 157.55/157.23 [7610]E(x76101,x76102)+~P24(x76103,x76104,x76105,f241(f917(x76103,a905)))+~E(f326(f309(x76103,x76104,x76105),x76101),f326(f309(x76103,x76104,x76105),x76102))
% 157.55/157.23 [7858]P24(x78582,x78583,f505(x78584,x78583,x78582,x78581),x78581)+~E(f326(f309(x78583,x78582,x78585),x78584),x78581)+E(x78581,f188(f917(x78582,a905)))
% 157.55/157.23 [8380]~P105(f326(f326(x83803,x83802),x83805))+~P105(f326(f326(x83803,x83804),x83802))+P105(f326(f326(f328(x83801),x83802),f298(x83801,x83803,x83804,x83805)))
% 157.55/157.23 [8381]~P105(f326(f326(x83813,x83812),x83815))+~P105(f326(f326(x83813,x83814),x83812))+P105(f326(f326(f328(x83811),x83812),f289(x83811,x83813,x83814,x83815)))
% 157.55/157.23 [8683]~P24(x86831,x86832,x86833,x86834)+P25(x86831,x86832,x86833,x86834,x86835)+~E(f326(f309(x86831,x86832,x86833),x86834),x86835)
% 157.55/157.23 [8816]~P25(x88161,x88163,x88164,x88162,x88165)+~P105(f326(f61(x88163),x88165))+P105(f326(f61(x88161),x88162))
% 157.55/157.23 [8817]~P25(x88173,x88171,x88174,x88175,x88172)+~P105(f326(f61(x88173),x88175))+P105(f326(f61(x88171),x88172))
% 157.55/157.23 [8949]~P24(x89491,x89493,x89495,f241(f917(x89491,a905)))+~P24(x89493,x89492,x89494,f241(f917(x89493,a905)))+P24(x89491,x89492,f326(f72(x89493,x89492,x89491,x89494),x89495),f241(f917(x89491,a905)))
% 157.55/157.23 [9510]P105(f326(f326(f328(f916(x95101,x95101)),f326(f326(f251(x95101,x95101),x95102),x95103)),f306(x95101,x95104)))+~P105(f326(f326(f328(f916(x95101,x95101)),f326(f326(f251(x95101,x95101),x95102),x95105)),f306(x95101,x95104)))+~P105(f326(f326(f328(f916(x95101,x95101)),f326(f326(f251(x95101,x95101),x95105),x95103)),f306(x95101,x95104)))
% 157.55/157.23 [9548]~P108(x95482)+~P105(f326(f137(x95481),x95485))+P105(f326(f137(x95481),f149(x95481,x95482,x95483,x95484,x95485)))
% 157.55/157.23 [5513]~E(x55132,f113(x55131))+E(f326(f326(f134(x55131),x55132),x55133),f326(f326(f151(x55131),x55134),x55135))+~E(x55133,f326(f326(f151(x55131),x55134),x55135))
% 157.55/157.23 [5514]~E(x55142,f113(x55141))+E(f326(f326(f134(x55141),x55142),x55143),f326(f326(f151(x55141),x55144),x55145))+~E(f326(f326(f151(x55141),x55144),x55145),x55143)
% 157.55/157.23 [6667]~E(f326(f189(f910(x66671)),x66675),f326(f189(f910(x66672)),x66674))+E(f326(f326(f154(f916(x66671,x66672),x66672),f255(x66671,x66672)),x66673),x66674)+~E(f326(f326(f181(x66671,x66672),x66675),x66674),x66673)
% 157.55/157.23 [6668]~E(f326(f189(f910(x66681)),x66684),f326(f189(f910(x66682)),x66685))+E(f326(f326(f154(f916(x66681,x66682),x66681),f250(x66681,x66682)),x66683),x66684)+~E(f326(f326(f181(x66681,x66682),x66684),x66685),x66683)
% 157.55/157.23 [7146]~P108(x71461)+~P12(x71461,f326(f326(f154(x71462,x71461),x71463),x71465))+P12(x71461,f326(f326(f154(x71462,x71461),x71463),f326(f136(x71462,x71464),x71465)))
% 157.55/157.23 [7189]~P105(f326(x71893,x71895))+~P105(f326(f326(x71892,x71894),x71895))+P105(f326(f326(f92(x71891,x71892,x71893),x71894),x71895))
% 157.55/157.23 [7288]~P108(x72881)+P12(x72881,f326(f326(f154(x72882,x72881),x72883),f170(x72882,x72884,x72885)))+~P12(x72881,f326(f326(f154(x72882,x72881),x72883),x72885))
% 157.55/157.23 [7311]~P53(x73113,x73112,x73115)+~P53(x73111,x73113,x73114)+P53(x73111,x73112,f326(f326(f288(x73111,x73113,x73112),x73114),x73115))
% 157.55/157.23 [7405]E(x74051,x74052)+~P24(x74053,x74054,x74055,f241(f917(x74053,a905)))+~E(f326(f326(f154(x74053,x74054),x74055),x74051),f326(f326(f154(x74053,x74054),x74055),x74052))
% 157.55/157.23 [7564]~P105(f326(f326(f234(a909),x75641),f326(x75643,x75645)))+P105(f326(f326(f234(a909),x75641),f155(x75642,x75643,x75644)))+~P105(f326(f326(f328(x75642),x75645),f326(f172(x75642),x75644)))
% 157.55/157.23 [7565]~P105(f326(f326(f235(a909),x75651),f326(x75653,x75655)))+P105(f326(f326(f235(a909),x75651),f155(x75652,x75653,x75654)))+~P105(f326(f326(f328(x75652),x75655),f326(f172(x75652),x75654)))
% 157.55/157.23 [7954]P105(f326(x79541,x79542))+~P105(f326(x79541,x79543))+~P105(f326(f326(f328(x79544),x79542),f326(f172(x79544),f169(x79544,x79545,x79543))))
% 157.55/157.23 [7955]P105(f326(x79551,x79552))+~P105(f326(x79551,x79553))+~P105(f326(f326(f328(x79554),x79553),f326(f172(x79554),f169(x79554,x79555,x79552))))
% 157.55/157.23 [7959]~P109(x79591)+P105(f326(f326(f234(f917(x79591,a905)),f302(x79591,x79592,x79593)),f302(x79591,x79594,x79595)))+P105(f326(f326(f234(x79591),x79592),x79593))
% 157.55/157.23 [7980]~P4(x79801)+P105(f326(f326(f234(x79801),f326(f326(f39(x79802,x79801),x79803),x79804)),f326(x79804,x79805)))+~P105(f326(f326(f328(x79802),x79805),x79803))
% 157.55/157.23 [8047]~P24(x80471,x80472,x80474,x80473)+E(f326(f76(x80471,x80472,x80473,x80474),f326(x80474,x80475)),x80475)+~P105(f326(f326(f328(x80471),x80475),x80473))
% 157.55/157.23 [8048]~P24(x80481,x80482,x80484,x80483)+E(f326(f90(x80481,x80482,x80483,x80484),f326(x80484,x80485)),x80485)+~P105(f326(f326(f328(x80481),x80485),x80483))
% 157.55/157.23 [8244]~P105(f326(x82441,x82445))+P105(f326(x82441,f344(x82441,x82442,x82443,x82444)))+~P105(f326(f326(f328(x82444),x82445),x82443))
% 157.55/157.23 [8245]~P105(f326(x82451,x82455))+P105(f326(x82451,f344(x82451,x82452,x82453,x82454)))+~P105(f326(f326(f328(x82454),x82455),x82452))
% 157.55/157.23 [8334]P105(f326(f61(x83341),x83342))+~P105(f326(f61(x83343),x83344))+~P105(f326(f326(f234(f917(x83341,a905)),x83342),f326(f309(x83343,x83341,x83345),x83344)))
% 157.55/157.23 [8500]E(x85001,x85002)+~P24(x85003,x85004,x85005,f326(f326(f110(f917(x85003,a905)),f326(f172(x85003),x85001)),f326(f172(x85003),x85002)))+~E(f326(f326(f154(x85003,x85004),x85005),x85001),f326(f326(f154(x85003,x85004),x85005),x85002))
% 157.55/157.23 [8552]~P109(x85521)+~P105(f326(f326(f235(f917(x85521,a905)),f302(x85521,x85524,x85525)),f302(x85521,x85522,x85523)))+P105(f326(f326(f234(x85521),x85522),x85523))
% 157.55/157.23 [8614]~P24(x86141,x86144,x86145,f241(f917(x86141,a905)))+~P105(f326(f326(f328(x86144),f326(x86145,x86142)),f326(f309(x86141,x86144,x86145),x86143)))+P105(f326(f326(f328(x86141),x86142),x86143))
% 157.55/157.23 [8689]P105(f326(x86891,x86892))+~P105(f326(x86891,f357(x86891,x86893,x86894,x86895)))+~P105(f326(f326(f328(x86895),x86892),x86894))
% 157.55/157.23 [8690]P105(f326(x86901,x86902))+~P105(f326(x86901,f357(x86901,x86903,x86904,x86905)))+~P105(f326(f326(f328(x86905),x86902),x86903))
% 157.55/157.23 [8989]~P24(x89892,x89893,x89891,x89894)+E(f326(x89891,f326(f76(x89892,x89893,x89894,x89891),x89895)),x89895)+~P105(f326(f326(f328(x89893),x89895),f326(f309(x89892,x89893,x89891),x89894)))
% 157.55/157.23 [9092]E(x90921,f113(x90922))+E(f326(f326(f151(x90922),x90923),f674(x90924,x90923,x90925,x90921,x90922)),x90921)+~E(f326(f326(f134(x90922),x90921),x90925),f326(f326(f151(x90922),x90923),x90924))
% 157.55/157.23 [9093]E(x90931,f113(x90932))+E(f326(f326(f151(x90932),x90933),f675(x90934,x90931,x90935,x90933,x90932)),x90931)+~E(f326(f326(f134(x90932),x90931),x90934),f326(f326(f151(x90932),x90933),x90935))
% 157.55/157.23 [9111]E(f326(f326(f151(x91112),x91113),f674(x91114,x91113,x91111,x91115,x91112)),x91115)+~E(f326(f326(f134(x91112),x91115),x91111),f326(f326(f151(x91112),x91113),x91114))+E(x91111,f326(f326(f151(x91112),x91113),x91114))
% 157.55/157.23 [9112]E(f326(f326(f151(x91121),x91122),f675(x91124,x91125,x91123,x91122,x91121)),x91125)+~E(f326(f326(f134(x91121),x91125),x91124),f326(f326(f151(x91121),x91122),x91123))+E(f326(f326(f151(x91121),x91122),x91123),x91124)
% 157.55/157.23 [9188]~E(f326(f309(x91883,x91882,x91884),f241(f917(x91883,a905))),f241(f917(x91882,a905)))+~E(f326(f309(x91881,x91883,x91885),f241(f917(x91881,a905))),f241(f917(x91883,a905)))+E(f326(f309(x91881,x91882,f326(f72(x91883,x91882,x91881,x91884),x91885)),f241(f917(x91881,a905))),f241(f917(x91882,a905)))
% 157.55/157.23 [9554]E(x95541,f113(x95542))+~E(f326(f326(f134(x95542),x95541),x95543),f326(f326(f151(x95542),x95545),x95544))+E(f326(f326(f134(x95542),f675(x95543,x95541,x95544,x95545,x95542)),x95543),x95544)
% 157.55/157.23 [9555]E(x95551,f113(x95552))+~E(f326(f326(f134(x95552),x95551),x95555),f326(f326(f151(x95552),x95554),x95553))+E(f326(f326(f134(x95552),f674(x95553,x95554,x95555,x95551,x95552)),x95555),x95553)
% 157.55/157.23 [9562]E(f326(f326(f134(x95622),f674(x95624,x95623,x95621,x95625,x95622)),x95621),x95624)+~E(f326(f326(f134(x95622),x95625),x95621),f326(f326(f151(x95622),x95623),x95624))+E(x95621,f326(f326(f151(x95622),x95623),x95624))
% 157.55/157.23 [9563]~E(f326(f326(f134(x95631),x95635),x95634),f326(f326(f151(x95631),x95632),x95633))+E(f326(f326(f134(x95631),f675(x95634,x95635,x95633,x95632,x95631)),x95634),x95633)+E(f326(f326(f151(x95631),x95632),x95633),x95634)
% 157.55/157.23 [9564]E(f326(f326(f134(x95641),x95645),f677(x95643,x95642,x95644,x95645,x95641)),x95642)+E(f326(f326(f134(x95641),x95642),f676(x95643,x95642,x95644,x95645,x95641)),x95645)+~E(f326(f326(f134(x95641),x95645),x95644),f326(f326(f134(x95641),x95642),x95643))
% 157.55/157.23 [9600]~P108(x96001)+P12(x96001,f326(f326(f154(x96002,x96001),x96003),f149(x96002,x96001,x96003,x96004,x96005)))+~P12(x96001,f326(f326(f154(x96002,x96001),x96003),x96005))
% 157.55/157.23 [9614]~P57(x96145,x96141,x96144,x96143)+P105(f326(f326(x96141,x96142),f523(x96143,x96144,x96141,x96145,x96142)))+~P105(f326(f326(f328(x96145),x96142),x96144))
% 157.55/157.23 [9615]~P57(x96155,x96151,x96154,x96153)+P105(f326(f326(x96151,x96152),f791(x96153,x96154,x96151,x96155,x96152)))+~P105(f326(f326(f328(x96155),x96152),x96154))
% 157.55/157.23 [9717]~P105(f326(f326(f328(f916(x97171,x97171)),f326(f326(f251(x97171,x97171),x97175),x97173)),f306(x97171,x97174)))+P105(f326(f326(f328(f916(x97171,x97171)),f326(f326(f251(x97171,x97171),x97172),x97173)),f326(f326(f288(x97171,x97171,x97171),x97174),f306(x97171,x97174))))+~P105(f326(f326(f328(f916(x97171,x97171)),f326(f326(f251(x97171,x97171),x97172),x97175)),f326(f326(f288(x97171,x97171,x97171),x97174),f306(x97171,x97174))))
% 157.55/157.23 [9718]~P105(f326(f326(f328(f916(x97181,x97181)),f326(f326(f251(x97181,x97181),x97182),x97185)),f306(x97181,x97184)))+P105(f326(f326(f328(f916(x97181,x97181)),f326(f326(f251(x97181,x97181),x97182),x97183)),f326(f326(f288(x97181,x97181,x97181),x97184),f306(x97181,x97184))))+~P105(f326(f326(f328(f916(x97181,x97181)),f326(f326(f251(x97181,x97181),x97185),x97183)),f326(f326(f288(x97181,x97181,x97181),x97184),f306(x97181,x97184))))
% 157.55/157.23 [9720]P105(f326(f326(f328(f916(f910(x97201),f910(x97201))),f326(f326(f251(f910(x97201),f910(x97201)),x97202),x97203)),f158(x97201,f306(x97201,x97204))))+~P105(f326(f326(f328(f916(f910(x97201),f910(x97201))),f326(f326(f251(f910(x97201),f910(x97201)),x97202),x97205)),f158(x97201,f306(x97201,x97204))))+~P105(f326(f326(f328(f916(f910(x97201),f910(x97201))),f326(f326(f251(f910(x97201),f910(x97201)),x97205),x97203)),f158(x97201,f306(x97201,x97204))))
% 157.55/157.23 [9724]E(f326(f326(f134(x97241),x97242),f676(x97243,x97242,x97244,x97245,x97241)),x97245)+E(f326(f326(f134(x97241),f677(x97243,x97242,x97244,x97245,x97241)),x97243),x97244)+~E(f326(f326(f134(x97241),x97242),x97243),f326(f326(f134(x97241),x97245),x97244))
% 157.55/157.23 [9725]E(f326(f326(f134(x97251),x97252),f677(x97253,x97254,x97255,x97252,x97251)),x97254)+E(f326(f326(f134(x97251),f676(x97253,x97254,x97255,x97252,x97251)),x97255),x97253)+~E(f326(f326(f134(x97251),x97252),x97255),f326(f326(f134(x97251),x97254),x97253))
% 157.55/157.23 [9779]P105(f326(f326(f328(f916(x97791,x97791)),f326(f326(f251(x97791,x97791),x97792),x97793)),f326(f326(f288(x97791,x97791,x97791),x97794),f306(x97791,x97794))))+~P105(f326(f326(f328(f916(x97791,x97791)),f326(f326(f251(x97791,x97791),x97792),x97795)),f326(f326(f288(x97791,x97791,x97791),x97794),f306(x97791,x97794))))+~P105(f326(f326(f328(f916(x97791,x97791)),f326(f326(f251(x97791,x97791),x97795),x97793)),f326(f326(f288(x97791,x97791,x97791),x97794),f306(x97791,x97794))))
% 157.55/157.23 [9806]P33(x98061,x98062,x98063,x98064,x98065)+~E(f326(f189(f910(x98061)),x98064),f326(f189(f910(x98062)),x98065))+~P105(f326(f326(f256(x98061,x98062,a905),x98063),f694(x98065,x98064,x98063,x98062,x98061)))
% 157.55/157.23 [9807]P33(x98071,x98072,x98073,x98074,x98075)+~E(f326(f189(f910(x98071)),x98074),f326(f189(f910(x98072)),x98075))+~P105(f326(f326(f256(x98071,x98072,a905),x98073),f695(x98073,x98075,x98074,x98072,x98071)))
% 157.55/157.23 [9813]E(f326(f326(f134(x98131),f676(x98132,x98133,x98134,x98135,x98131)),x98134),x98132)+~E(f326(f326(f134(x98131),x98133),x98132),f326(f326(f134(x98131),x98135),x98134))+E(f326(f326(f134(x98131),f677(x98132,x98133,x98134,x98135,x98131)),x98132),x98134)
% 157.55/157.23 [9828]~P108(x98282)+E(f326(f326(f148(x98281,x98282,x98283),x98284),x98285),f326(f326(f151(x98281),x98284),x98285))+P105(f326(f326(f328(x98281),f739(x98284,x98283,x98285,x98281,x98282)),f326(f172(x98281),x98285)))
% 157.55/157.23 [9832]~P57(x98321,x98324,x98323,x98322)+~P105(f326(f326(f328(x98321),x98325),x98323))+P105(f326(f326(f328(x98321),f523(x98322,x98323,x98324,x98321,x98325)),x98322))
% 157.55/157.23 [9833]~P57(x98331,x98334,x98333,x98332)+~P105(f326(f326(f328(x98331),x98335),x98333))+P105(f326(f326(f328(x98331),f791(x98332,x98333,x98334,x98331,x98335)),x98332))
% 157.55/157.23 [9947]~P105(f326(f326(f328(f916(f917(x99471,a905),f917(x99471,a905))),f326(f326(f251(f917(x99471,a905),f917(x99471,a905)),x99474),x99473)),f318(x99471,x99472)))+~P105(f326(f326(f328(x99471),x99475),x99474))+P105(f326(f326(f328(x99471),f599(x99472,x99473,x99474,x99471,x99475)),x99473))
% 157.55/157.23 [9957]~P108(x99572)+E(f326(f326(f148(x99571,x99572,x99573),x99574),x99575),f326(f326(f151(x99571),x99574),x99575))+~P105(f326(f326(f234(x99572),f326(x99573,x99574)),f326(x99573,f739(x99574,x99573,x99575,x99571,x99572))))
% 157.55/157.23 [10006]~P24(x100063,x100064,x100065,f241(f917(x100063,a905)))+P105(f326(x100061,x100062))+~P105(f326(x100061,f326(f90(x100063,x100064,f241(f917(x100063,a905)),x100065),f807(x100062,x100061,x100065,x100064,x100063))))
% 157.55/157.23 [10153]P33(x101531,x101532,x101533,x101534,x101535)+~E(f326(f189(f910(x101531)),x101534),f326(f189(f910(x101532)),x101535))+~P105(f326(f326(x101533,f326(f326(f164(x101531),x101534),f696(x101535,x101534,x101533,x101532,x101531))),f326(f326(f164(x101532),x101535),f696(x101535,x101534,x101533,x101532,x101531))))
% 157.55/157.23 [10154]P33(x101541,x101542,x101543,x101544,x101545)+~E(f326(f189(f910(x101541)),x101544),f326(f189(f910(x101542)),x101545))+~P105(f326(f326(x101543,f326(f326(f164(x101541),x101544),f731(x101543,x101545,x101542,x101544,x101541))),f326(f326(f164(x101542),x101545),f731(x101543,x101545,x101542,x101544,x101541))))
% 157.55/157.23 [6741]~P16(x67412,x67415,x67411)+~P105(f326(f61(x67412),x67414))+E(f326(x67411,f326(f326(f308(x67412),x67413),x67414)),f326(f326(f64(x67412,x67412,x67415),x67413),x67414))
% 157.55/157.23 [6742]~E(x67423,x67424)+~E(x67422,x67425)+E(f326(f326(f308(x67421),x67422),f326(f326(f308(x67421),x67423),f188(f917(x67421,a905)))),f326(f326(f308(x67421),x67424),f326(f326(f308(x67421),x67425),f188(f917(x67421,a905)))))
% 157.55/157.23 [6753]P105(f326(x67532,x67535))+E(f177(x67531,x67532,f326(f326(f134(x67531),x67533),x67534)),f177(x67531,x67532,x67533))+~P105(f326(f326(f328(x67531),x67535),f326(f172(x67531),x67533)))
% 157.55/157.23 [6791]E(f326(x67911,x67912),f188(f917(x67913,a905)))+~E(f326(f326(f40(x67914,f917(x67913,a905)),x67915),x67911),f188(f917(x67913,a905)))+~P105(f326(f326(f328(x67914),x67912),x67915))
% 157.55/157.23 [6792]E(f326(x67921,x67922),f241(f917(x67923,a905)))+~E(f326(f326(f39(x67924,f917(x67923,a905)),x67925),x67921),f241(f917(x67923,a905)))+~P105(f326(f326(f328(x67924),x67922),x67925))
% 157.55/157.23 [7298]~E(x72982,x72984)+~P137(x72981)+E(f326(f326(f79(x72981),f326(f326(f80(x72981),x72982),x72983)),f326(f326(f80(x72981),x72984),x72985)),f326(f326(f79(x72981),f326(f326(f80(x72981),x72982),x72985)),f326(f326(f80(x72981),x72984),x72983)))
% 157.55/157.23 [7358]~P4(x73581)+~P105(f326(f326(f328(x73584),x73583),x73585))+P105(f326(f326(f234(x73581),f326(x73582,x73583)),f326(f326(f40(x73584,x73581),x73585),x73582)))
% 157.55/157.23 [7410]~P107(x74101)+P105(f326(f326(f234(x74101),f326(x74102,x74103)),f326(x74104,x74103)))+~P105(f326(f326(f234(f917(x74105,x74101)),x74102),x74104))
% 157.55/157.23 [7535]E(x75351,x75352)+E(x75353,x75351)+~E(f326(f326(f308(x75354),x75351),f326(f326(f308(x75354),x75355),f188(f917(x75354,a905)))),f326(f326(f308(x75354),x75352),f326(f326(f308(x75354),x75353),f188(f917(x75354,a905)))))
% 157.55/157.23 [7536]E(x75361,x75362)+E(x75363,x75361)+~E(f326(f326(f308(x75364),x75363),f326(f326(f308(x75364),x75362),f188(f917(x75364,a905)))),f326(f326(f308(x75364),x75365),f326(f326(f308(x75364),x75361),f188(f917(x75364,a905)))))
% 157.55/157.23 [7537]E(x75371,x75372)+E(x75371,x75373)+~E(f326(f326(f308(x75374),x75373),f326(f326(f308(x75374),x75372),f188(f917(x75374,a905)))),f326(f326(f308(x75374),x75375),f326(f326(f308(x75374),x75371),f188(f917(x75374,a905)))))
% 157.55/157.23 [7538]E(x75381,x75382)+E(x75381,x75383)+~E(f326(f326(f308(x75384),x75381),f326(f326(f308(x75384),x75385),f188(f917(x75384,a905)))),f326(f326(f308(x75384),x75382),f326(f326(f308(x75384),x75383),f188(f917(x75384,a905)))))
% 157.55/157.23 [8057]P24(x80571,x80572,x80573,x80574)+~P24(x80571,x80572,x80573,x80575)+~P105(f326(f326(f234(f917(x80571,a905)),x80574),x80575))
% 157.55/157.23 [8086]~E(f326(x80863,x80865),x80864)+~P24(x80861,x80862,x80863,f241(f917(x80861,a905)))+E(f326(f90(x80861,x80862,f241(f917(x80861,a905)),x80863),x80864),x80865)
% 157.55/157.23 [8232]E(x82321,x82322)+~E(f326(f309(x82323,x82324,x82325),x82321),f326(f309(x82323,x82324,x82325),x82322))+~P24(x82323,x82324,x82325,f326(f326(f110(f917(x82323,a905)),x82321),x82322))
% 157.55/157.23 [8304]P105(f326(x83042,x83044))+E(f326(f326(f138(x83041),f326(f189(f910(x83041)),f177(x83041,x83042,x83043))),x83043),f326(f326(f151(x83041),x83044),x83045))+~E(f326(f326(f134(x83041),f177(x83041,x83042,x83043)),f326(f326(f151(x83041),x83044),x83045)),x83043)
% 157.55/157.23 [8332]~P24(x83321,x83322,x83323,x83325)+~P24(x83321,x83322,x83323,x83324)+P24(x83321,x83322,x83323,f326(f326(f101(f917(x83321,a905)),x83324),x83325))
% 157.55/157.23 [8439]~P69(x84391)+E(f326(f326(f79(x84391),f326(x84392,x84393)),f326(f165(x84391),f326(f326(f154(x84394,x84391),x84392),f170(x84394,x84393,x84395)))),f326(f165(x84391),f326(f326(f154(x84394,x84391),x84392),x84395)))+~P105(f326(f326(f328(x84394),x84393),f326(f172(x84394),x84395)))
% 157.55/157.23 [8526]~P108(x85261)+~P12(x85261,f326(f326(f154(x85262,x85261),x85263),x85265))+P12(x85261,f326(f326(f154(x85262,x85261),x85263),f326(f326(f148(x85262,x85261,x85263),x85264),x85265)))
% 157.55/157.23 [8610]~P4(x86101)+P105(f326(f326(f234(x86101),f326(f326(f39(x86102,x86101),x86103),x86104)),f326(f326(f39(x86102,x86101),x86105),x86104)))+~P105(f326(f326(f234(f917(x86102,a905)),x86105),x86103))
% 157.55/157.23 [8611]~P4(x86111)+P105(f326(f326(f234(x86111),f326(f326(f40(x86112,x86111),x86113),x86114)),f326(f326(f40(x86112,x86111),x86115),x86114)))+~P105(f326(f326(f234(f917(x86112,a905)),x86113),x86115))
% 157.55/157.23 [8644]~P108(x86443)+P105(f326(f137(x86441),x86442))+~P105(f326(f137(x86441),f326(f326(f148(x86441,x86443,x86444),x86445),x86442)))
% 157.55/157.23 [8788]~P108(x87881)+~P105(f326(f326(f328(x87882),x87883),f326(f172(x87882),x87884)))+~P105(f326(f137(x87882),f326(f326(f148(x87882,x87881,x87885),x87883),x87884)))
% 157.55/157.23 [8878]~P108(x88781)+P12(x88781,f326(f326(f154(x88782,x88781),x88783),x88784))+~P12(x88781,f326(f326(f154(x88782,x88781),x88783),f326(f326(f148(x88782,x88781,x88783),x88785),x88784)))
% 157.55/157.23 [8924]~P24(x89242,x89241,x89244,x89243)+E(f326(f309(x89241,x89242,f90(x89242,x89241,x89243,x89244)),f326(f309(x89242,x89241,x89244),x89245)),x89245)+~P105(f326(f326(f234(f917(x89242,a905)),x89245),x89243))
% 157.55/157.23 [8977]~P108(x89772)+E(f326(f326(f148(x89771,x89772,x89773),x89774),x89775),f149(x89771,x89772,x89773,x89774,x89775))+P105(f326(f326(f328(x89772),f326(x89773,x89774)),f326(f309(x89771,x89772,x89773),f326(f172(x89771),x89775))))
% 157.55/157.23 [9058]~P108(x90582)+E(f149(x90581,x90582,x90583,x90584,x90585),x90585)+~P105(f326(f326(f328(x90582),f326(x90583,x90584)),f326(f309(x90581,x90582,x90583),f326(f172(x90581),x90585))))
% 157.55/157.23 [9072]~P24(x90722,x90721,x90723,x90725)+P105(f326(f326(f235(f917(x90721,a905)),f326(f309(x90722,x90721,x90723),x90724)),f326(f309(x90722,x90721,x90723),x90725)))+~P105(f326(f326(f235(f917(x90722,a905)),x90724),x90725))
% 157.55/157.23 [9229]~P24(x92291,x92292,x92293,f241(f917(x92291,a905)))+~P105(f326(f326(f234(f917(x92292,a905)),x92294),f326(f309(x92291,x92292,x92293),x92295)))+P105(f326(f326(f234(f917(x92291,a905)),f326(f310(x92291,x92292,x92293),x92294)),x92295))
% 157.55/157.23 [9252]~E(f326(f309(x92523,x92521,x92524),f241(f917(x92523,a905))),f241(f917(x92521,a905)))+P105(f326(f326(f234(f917(x92521,a905)),x92522),f326(f309(x92523,x92521,x92524),x92525)))+~P105(f326(f326(f234(f917(x92523,a905)),f326(f310(x92523,x92521,x92524),x92522)),x92525))
% 157.55/157.23 [9356]~P24(x93561,x93564,x93565,f241(f917(x93561,a905)))+~P105(f326(f326(f234(f917(x93564,a905)),f326(f309(x93561,x93564,x93565),x93562)),f326(f309(x93561,x93564,x93565),x93563)))+P105(f326(f326(f234(f917(x93561,a905)),x93562),x93563))
% 157.55/157.23 [9478]~P82(x94781)+~E(f326(x94783,f714(x94783,x94784,x94785,x94782,x94781)),f2(x94781))+E(f326(f165(x94781),f326(f326(f154(x94782,x94781),x94783),f326(f136(x94782,x94784),x94785))),f326(f165(x94781),f326(f326(f154(x94782,x94781),x94783),x94785)))
% 157.55/157.23 [9505]~P25(x95051,x95052,x95053,f241(f917(x95051,a905)),f241(f917(x95052,a905)))+~P105(f326(f326(f234(f917(x95052,a905)),x95054),f326(f309(x95051,x95052,x95053),x95055)))+P105(f326(f326(f234(f917(x95051,a905)),f326(f310(x95051,x95052,x95053),x95054)),x95055))
% 157.55/157.23 [9534]~P25(x95343,x95341,x95344,f241(f917(x95343,a905)),f241(f917(x95341,a905)))+P105(f326(f326(f234(f917(x95341,a905)),x95342),f326(f309(x95343,x95341,x95344),x95345)))+~P105(f326(f326(f234(f917(x95343,a905)),f326(f310(x95343,x95341,x95344),x95342)),x95345))
% 157.55/157.23 [9658]~P15(x96581,x96582,x96583)+~P105(f326(f61(x96581),x96585))+P105(f326(f66(x96581,x96582,x96583,x96584,x96585),f326(f326(f64(x96581,x96582,x96583),x96584),x96585)))
% 157.55/157.23 [9737]~P25(x97372,x97371,x97374,f241(f917(x97372,a905)),f241(f917(x97371,a905)))+~P25(x97371,x97373,x97375,f241(f917(x97371,a905)),f241(f917(x97373,a905)))+E(f326(f72(x97371,x97372,x97373,f90(x97372,x97371,f241(f917(x97372,a905)),x97374)),f90(x97371,x97373,f241(f917(x97371,a905)),x97375)),f90(x97372,x97373,f241(f917(x97372,a905)),f326(f72(x97371,x97373,x97372,x97375),x97374)))
% 157.55/157.23 [9738]P105(f326(x97381,f638(x97382,x97381,x97383,x97384,x97385)))+~P105(f326(f326(f234(f917(x97385,a905)),x97384),x97383))+P105(f326(f326(f234(f917(x97385,a905)),f326(f326(f101(f917(x97385,a905)),x97384),f326(f261(x97385),x97381))),f326(f326(f101(f917(x97385,a905)),x97383),f326(f261(x97385),x97382))))
% 157.55/157.23 [9752]~P82(x97521)+~P105(f326(x97524,f714(x97523,x97524,x97525,x97522,x97521)))+E(f326(f165(x97521),f326(f326(f154(x97522,x97521),x97523),f326(f136(x97522,x97524),x97525))),f326(f165(x97521),f326(f326(f154(x97522,x97521),x97523),x97525)))
% 157.55/157.23 [9830]~P4(x98305)+P105(f326(f326(f328(x98301),f418(x98302,x98303,x98301,x98304,x98305)),x98303))+P105(f326(f326(f234(x98305),x98304),f326(f326(f39(x98301,x98305),x98303),x98302)))
% 157.55/157.23 [9834]~P82(x98341)+E(f326(f165(x98341),f326(f326(f154(x98342,x98341),x98343),f326(f136(x98342,x98344),x98345))),f326(f165(x98341),f326(f326(f154(x98342,x98341),x98343),x98345)))+P105(f326(f326(f328(x98342),f714(x98343,x98344,x98345,x98342,x98341)),f326(f172(x98342),x98345)))
% 157.55/157.23 [9844]~P105(f326(x98445,f638(x98445,x98443,x98444,x98442,x98441)))+~P105(f326(f326(f234(f917(x98441,a905)),x98442),x98444))+P105(f326(f326(f234(f917(x98441,a905)),f326(f326(f101(f917(x98441,a905)),x98442),f326(f261(x98441),x98443))),f326(f326(f101(f917(x98441,a905)),x98444),f326(f261(x98441),x98445))))
% 157.55/157.23 [9860]~P24(x98605,x98603,x98604,f241(f917(x98605,a905)))+P105(f326(x98601,x98602))+P105(f326(f326(f328(x98603),f807(x98602,x98601,x98604,x98603,x98605)),f326(f309(x98605,x98603,x98604),f241(f917(x98605,a905)))))
% 157.55/157.23 [9883]P33(x98831,x98832,x98833,x98834,x98835)+~E(f326(f189(f910(x98832)),x98835),f326(f189(f910(x98831)),x98834))+P105(f326(f326(f235(a909),f696(x98835,x98834,x98833,x98832,x98831)),f326(f189(f910(x98831)),x98834)))
% 157.55/157.23 [9884]P33(x98841,x98842,x98843,x98844,x98845)+~E(f326(f189(f910(x98842)),x98845),f326(f189(f910(x98841)),x98844))+P105(f326(f326(f235(a909),f731(x98843,x98845,x98842,x98844,x98841)),f326(f189(f910(x98841)),x98844)))
% 157.55/157.23 [9915]P105(f326(f326(f328(x99151),f638(x99152,x99153,x99154,x99155,x99151)),x99155))+~P105(f326(f326(f234(f917(x99151,a905)),x99155),x99154))+P105(f326(f326(f234(f917(x99151,a905)),f326(f326(f101(f917(x99151,a905)),x99155),f326(f261(x99151),x99153))),f326(f326(f101(f917(x99151,a905)),x99154),f326(f261(x99151),x99152))))
% 157.55/157.23 [9958]~P4(x99581)+~P105(f326(f326(f234(x99581),x99582),f326(x99585,f418(x99585,x99584,x99583,x99582,x99581))))+P105(f326(f326(f234(x99581),x99582),f326(f326(f39(x99583,x99581),x99584),x99585)))
% 157.55/157.23 [9995]~P74(x99951)+~P105(f326(f61(x99952),x99955))+E(f326(f326(f326(f65(x99951,x99952,f80(x99951)),f326(f326(f20(x99952,x99951,x99951),f326(f326(f10(x99951,f917(x99951,x99951),x99952),f80(x99951)),x99953)),x99954)),f77(x99951)),x99955),f326(f326(f80(x99951),f326(f326(f326(f65(x99951,x99952,f80(x99951)),x99953),f77(x99951)),x99955)),f326(f326(f326(f65(x99951,x99952,f80(x99951)),x99954),f77(x99951)),x99955)))
% 157.55/157.23 [10051]~P105(f326(f326(f328(f916(f917(x100511,a905),f917(x100511,a905))),f326(f326(f251(f917(x100511,a905),f917(x100511,a905)),x100515),x100514)),f318(x100511,x100513)))+~P105(f326(f326(f328(x100511),x100512),x100515))+P105(f326(f326(f328(f916(x100511,x100511)),f326(f326(f251(x100511,x100511),x100512),f599(x100513,x100514,x100515,x100511,x100512))),x100513))
% 157.55/157.23 [10190]~P105(f326(f326(f328(f916(f910(x101901),f910(x101901))),f326(f326(f251(f910(x101901),f910(x101901)),f326(f326(f134(x101901),x101905),x101902)),f326(f326(f134(x101901),x101905),x101903))),f147(x101901,x101904)))+P105(f326(f326(f328(f916(f910(x101901),f910(x101901))),f326(f326(f251(f910(x101901),f910(x101901)),x101902),x101903)),f147(x101901,x101904)))+P105(f326(f326(f328(f916(x101901,x101901)),f326(f326(f251(x101901,x101901),f683(x101904,x101903,x101902,x101905,x101901)),f683(x101904,x101903,x101902,x101905,x101901))),x101904))
% 157.55/157.23 [7413]~E(x74133,x74135)+E(f326(f326(f164(x74131),f326(f326(f159(x74131,x74132),x74133),x74134)),x74135),x74134)+~P105(f326(f326(f235(a909),x74133),f326(f189(f910(x74131)),x74132)))
% 157.55/157.23 [7531]~E(f326(f326(f134(x75311),x75312),x75314),f326(f326(f134(x75311),x75313),x75315))+E(f326(f326(f175(x75311),f326(f189(f910(x75311)),x75312)),x75313),x75312)+P105(f326(f326(f234(a909),f326(f189(f910(x75311)),x75313)),f326(f189(f910(x75311)),x75312)))
% 157.55/157.23 [8018]~E(f326(f326(f134(x80181),x80182),x80184),f326(f326(f134(x80181),x80183),x80185))+E(f326(f326(f175(x80181),f326(f189(f910(x80181)),x80182)),x80183),x80182)+~P105(f326(f326(f234(a909),f326(f189(f910(x80181)),x80182)),f326(f189(f910(x80181)),x80183)))
% 157.55/157.23 [8042]~P105(f326(f61(x80421),f326(x80424,x80425)))+~P105(f326(f326(f328(x80422),x80425),x80423))+P105(f326(f61(x80421),f326(f326(f39(x80422,f917(x80421,a905)),x80423),x80424)))
% 157.55/157.23 [8216]~P51(x82161,x82163,x82165)+~P51(x82161,x82162,x82164)+P51(x82161,f326(f326(f110(f917(x82161,a905)),x82162),x82163),f326(f326(f110(f917(f916(x82161,x82161),a905)),x82164),x82165))
% 157.55/157.23 [8217]~P51(x82171,x82173,x82175)+~P51(x82171,x82172,x82174)+P51(x82171,f326(f326(f101(f917(x82171,a905)),x82172),x82173),f326(f326(f101(f917(f916(x82171,x82171),a905)),x82174),x82175))
% 157.55/157.23 [8565]E(f326(f326(f251(x85651,x85652),f326(f326(f164(x85651),x85653),x85654)),f326(f326(f164(x85652),x85655),x85654)),f326(f326(f164(f916(x85651,x85652)),f326(f326(f181(x85651,x85652),x85653),x85655)),x85654))+~P105(f326(f326(f235(a909),x85654),f326(f189(f910(x85651)),x85653)))+~P105(f326(f326(f235(a909),x85654),f326(f189(f910(x85652)),x85655)))
% 157.55/157.23 [8717]~P51(x87171,x87173,x87174)+P105(f326(f326(f328(x87171),x87172),x87173))+~P105(f326(f326(f328(f916(x87171,x87171)),f326(f326(f251(x87171,x87171),x87175),x87172)),x87174))
% 157.55/157.23 [8718]~P51(x87181,x87183,x87184)+P105(f326(f326(f328(x87181),x87182),x87183))+~P105(f326(f326(f328(f916(x87181,x87181)),f326(f326(f251(x87181,x87181),x87182),x87185)),x87184))
% 157.55/157.23 [8719]~P7(x87191,x87193,x87194)+P105(f326(f326(f328(x87191),x87192),x87193))+~P105(f326(f326(f328(f916(x87191,x87191)),f326(f326(f251(x87191,x87191),x87195),x87192)),x87194))
% 157.55/157.23 [8720]~P7(x87201,x87203,x87204)+P105(f326(f326(f328(x87201),x87202),x87203))+~P105(f326(f326(f328(f916(x87201,x87201)),f326(f326(f251(x87201,x87201),x87202),x87205)),x87204))
% 157.55/157.23 [9001]~P7(x90011,x90015,x90012)+E(f326(f284(x90011,x90011,x90012),f326(f326(f308(x90011),x90013),f188(f917(x90011,a905)))),f326(f284(x90011,x90011,x90012),f326(f326(f308(x90011),x90014),f188(f917(x90011,a905)))))+~P105(f326(f326(f328(f916(x90011,x90011)),f326(f326(f251(x90011,x90011),x90013),x90014)),x90012))
% 157.55/157.23 [9185]P105(f326(x91851,x91852))+~P105(f326(f326(f328(x91853),x91852),x91855))+P105(f326(f326(f328(x91853),f357(x91851,x91854,x91855,x91853)),f326(f326(f110(f917(x91853,a905)),x91855),x91854)))
% 157.55/157.23 [9186]P105(f326(x91861,x91862))+~P105(f326(f326(f328(x91863),x91862),x91864))+P105(f326(f326(f328(x91863),f357(x91861,x91864,x91865,x91863)),f326(f326(f110(f917(x91863,a905)),x91865),x91864)))
% 157.55/157.23 [9194]~P105(f326(x91942,x91945))+~P105(f326(f326(f328(x91941),x91945),x91944))+P105(f326(f326(f328(x91941),f344(x91942,x91943,x91944,x91941)),f326(f326(f110(f917(x91941,a905)),x91944),x91943)))
% 157.55/157.23 [9195]~P105(f326(x91952,x91955))+~P105(f326(f326(f328(x91951),x91955),x91953))+P105(f326(f326(f328(x91951),f344(x91952,x91953,x91954,x91951)),f326(f326(f110(f917(x91951,a905)),x91954),x91953)))
% 157.55/157.23 [9210]~P105(f326(f326(f234(f917(x92101,a905)),x92103),x92105))+~P105(f326(f326(f234(f917(x92101,a905)),x92102),x92104))+P105(f326(f326(f234(f917(x92101,a905)),f326(f326(f110(f917(x92101,a905)),x92102),x92103)),f326(f326(f110(f917(x92101,a905)),x92104),x92105)))
% 157.55/157.23 [9211]~P105(f326(f326(f234(f917(x92111,a905)),x92115),x92113))+~P105(f326(f326(f234(f917(x92111,a905)),x92112),x92114))+P105(f326(f326(f234(f917(x92111,a905)),f326(f326(f3(f917(x92111,a905)),x92112),x92113)),f326(f326(f3(f917(x92111,a905)),x92114),x92115)))
% 157.55/157.23 [9212]~P105(f326(f326(f234(f917(x92121,a905)),x92123),x92125))+~P105(f326(f326(f234(f917(x92121,a905)),x92122),x92124))+P105(f326(f326(f234(f917(x92121,a905)),f326(f326(f101(f917(x92121,a905)),x92122),x92123)),f326(f326(f101(f917(x92121,a905)),x92124),x92125)))
% 157.55/157.23 [9306]P105(f326(f326(f328(f916(x93061,x93061)),f326(f326(f251(x93061,x93061),x93062),x93063)),f320(x93061,x93064,x93065)))+~P105(f326(f326(f234(a909),f326(x93064,x93062)),f326(x93064,x93063)))+~P105(f326(f326(f328(f916(x93061,x93061)),f326(f326(f251(x93061,x93061),x93062),x93063)),x93065))
% 157.55/157.23 [9488]P105(f326(f326(f328(f916(x94881,x94881)),f326(f326(f251(x94881,x94881),x94882),x94883)),f306(x94881,x94884)))+~P105(f326(f326(f328(f916(x94881,x94881)),f326(f326(f251(x94881,x94881),x94882),x94885)),f306(x94881,x94884)))+~P105(f326(f326(f328(f916(x94881,x94881)),f326(f326(f251(x94881,x94881),x94885),x94883)),x94884))
% 157.55/157.23 [9489]P105(f326(f326(f328(f916(x94891,x94891)),f326(f326(f251(x94891,x94891),x94892),x94893)),f306(x94891,x94894)))+~P105(f326(f326(f328(f916(x94891,x94891)),f326(f326(f251(x94891,x94891),x94895),x94893)),f306(x94891,x94894)))+~P105(f326(f326(f328(f916(x94891,x94891)),f326(f326(f251(x94891,x94891),x94892),x94895)),x94894))
% 157.55/157.23 [9587]E(x95871,x95872)+E(f326(a112,f618(x95873,x95874,x95871,x95872,x95875)),x95874)+~P105(f326(f326(f328(f916(x95875,x95875)),f326(f326(f251(x95875,x95875),x95872),x95871)),f326(f326(f183(f916(x95875,x95875),a905),x95874),x95873)))
% 157.55/157.23 [9588]E(x95881,x95882)+E(f326(a112,f620(x95883,x95884,x95881,x95882,x95885)),x95884)+~P105(f326(f326(f328(f916(x95885,x95885)),f326(f326(f251(x95885,x95885),x95882),x95881)),f326(f326(f183(f916(x95885,x95885),a905),x95884),x95883)))
% 157.55/157.23 [9589]E(x95891,f2(a909))+E(f326(a112,f618(x95892,x95891,x95893,x95894,x95895)),x95891)+~P105(f326(f326(f328(f916(x95895,x95895)),f326(f326(f251(x95895,x95895),x95894),x95893)),f326(f326(f183(f916(x95895,x95895),a905),x95891),x95892)))
% 157.55/157.23 [9590]E(x95901,f2(a909))+E(f326(a112,f620(x95902,x95901,x95903,x95904,x95905)),x95901)+~P105(f326(f326(f328(f916(x95905,x95905)),f326(f326(f251(x95905,x95905),x95904),x95903)),f326(f326(f183(f916(x95905,x95905),a905),x95901),x95902)))
% 157.55/157.23 [9611]P105(f326(f326(f328(f916(x96111,x96111)),f326(f326(f251(x96111,x96111),x96112),x96113)),f326(f326(f288(x96111,x96111,x96111),x96114),f306(x96111,x96114))))+~P105(f326(f326(f328(f916(x96111,x96111)),f326(f326(f251(x96111,x96111),x96112),x96115)),x96114))+~P105(f326(f326(f328(f916(x96111,x96111)),f326(f326(f251(x96111,x96111),x96115),x96113)),x96114))
% 157.55/157.23 [9618]~P105(f326(f326(f328(f916(x96181,x96181)),f326(f326(f251(x96181,x96181),x96182),x96185)),f306(x96181,x96184)))+P105(f326(f326(f328(f916(x96181,x96181)),f326(f326(f251(x96181,x96181),x96182),x96183)),f326(f326(f288(x96181,x96181,x96181),x96184),f306(x96181,x96184))))+~P105(f326(f326(f328(f916(x96181,x96181)),f326(f326(f251(x96181,x96181),x96185),x96183)),x96184))
% 157.55/157.23 [9652]~P7(x96521,x96525,x96522)+~P105(f326(f326(f328(f916(x96521,x96521)),f326(f326(f251(x96521,x96521),x96523),x96524)),x96522))+P105(f326(f326(f234(f917(x96521,a905)),f326(f284(x96521,x96521,x96522),f326(f326(f308(x96521),x96523),f188(f917(x96521,a905))))),f326(f284(x96521,x96521,x96522),f326(f326(f308(x96521),x96524),f188(f917(x96521,a905))))))
% 157.55/157.23 [9710]P105(f326(f326(f328(f916(x97101,x97101)),f326(f326(f251(x97101,x97101),x97102),x97103)),f326(f326(f288(x97101,x97101,x97101),x97104),f306(x97101,x97104))))+~P105(f326(f326(f328(f916(x97101,x97101)),f326(f326(f251(x97101,x97101),x97102),x97105)),f326(f326(f288(x97101,x97101,x97101),x97104),f306(x97101,x97104))))+~P105(f326(f326(f328(f916(x97101,x97101)),f326(f326(f251(x97101,x97101),x97105),x97103)),x97104))
% 157.55/157.23 [9711]P105(f326(f326(f328(f916(x97111,x97111)),f326(f326(f251(x97111,x97111),x97112),x97113)),f326(f326(f288(x97111,x97111,x97111),x97114),f306(x97111,x97114))))+~P105(f326(f326(f328(f916(x97111,x97111)),f326(f326(f251(x97111,x97111),x97115),x97113)),f326(f326(f288(x97111,x97111,x97111),x97114),f306(x97111,x97114))))+~P105(f326(f326(f328(f916(x97111,x97111)),f326(f326(f251(x97111,x97111),x97112),x97115)),x97114))
% 157.55/157.23 [9761]~P105(f326(f66(x97611,x97611,x97614,x97612,x97613),x97615))+P105(f326(f326(f328(x97611),x97612),x97613))+P105(f326(f62(x97611,x97614,f326(f326(f308(x97611),x97612),x97613)),x97615))
% 157.55/157.23 [9799]~E(f326(f309(x97993,x97992,x97995),x97994),x97991)+E(x97991,f188(f917(x97992,a905)))+P105(f326(f326(f234(f917(x97993,a905)),f326(f309(x97992,x97993,f505(x97994,x97993,x97992,x97991)),x97991)),x97994))
% 157.55/157.23 [9847]~P4(x98475)+P105(f326(f326(f328(x98471),f465(x98472,x98473,x98474,x98471,x98475)),x98474))+P105(f326(f326(f234(x98475),f326(f326(f40(x98471,x98475),x98474),x98473)),x98472))
% 157.55/157.23 [9902]P33(x99021,x99022,x99023,x99024,x99025)+~E(f326(f189(f910(x99021)),x99024),f326(f189(f910(x99022)),x99025))+P105(f326(f326(f328(f916(x99021,x99022)),f694(x99025,x99024,x99023,x99022,x99021)),f326(f172(f916(x99021,x99022)),f326(f326(f181(x99021,x99022),x99024),x99025))))
% 157.55/157.23 [9903]P33(x99031,x99032,x99033,x99034,x99035)+~E(f326(f189(f910(x99031)),x99034),f326(f189(f910(x99032)),x99035))+P105(f326(f326(f328(f916(x99031,x99032)),f695(x99033,x99035,x99034,x99032,x99031)),f326(f172(f916(x99031,x99032)),f326(f326(f181(x99031,x99032),x99034),x99035))))
% 157.55/157.23 [10029]E(x100291,x100292)+P105(f326(f326(f328(f916(x100293,x100293)),f326(f326(f251(x100293,x100293),x100291),f619(x100294,x100295,x100292,x100291,x100293))),x100294))+~P105(f326(f326(f328(f916(x100293,x100293)),f326(f326(f251(x100293,x100293),x100291),x100292)),f326(f326(f183(f916(x100293,x100293),a905),x100295),x100294)))
% 157.55/157.23 [10030]E(x100301,f2(a909))+P105(f326(f326(f328(f916(x100302,x100302)),f326(f326(f251(x100302,x100302),x100303),f619(x100304,x100301,x100305,x100303,x100302))),x100304))+~P105(f326(f326(f328(f916(x100302,x100302)),f326(f326(f251(x100302,x100302),x100303),x100305)),f326(f326(f183(f916(x100302,x100302),a905),x100301),x100304)))
% 157.55/157.23 [10070]~P4(x100701)+~P105(f326(f326(f234(x100701),f326(x100704,f465(x100705,x100704,x100703,x100702,x100701))),x100705))+P105(f326(f326(f234(x100701),f326(f326(f40(x100702,x100701),x100703),x100704)),x100705))
% 157.55/157.23 [10123]E(x101231,x101232)+P105(f326(f326(f328(f916(x101233,x101233)),f326(f326(f251(x101233,x101233),f621(x101234,x101235,x101231,x101232,x101233)),x101231)),x101234))+~P105(f326(f326(f328(f916(x101233,x101233)),f326(f326(f251(x101233,x101233),x101232),x101231)),f326(f326(f183(f916(x101233,x101233),a905),x101235),x101234)))
% 157.55/157.23 [10124]E(x101241,f2(a909))+P105(f326(f326(f328(f916(x101242,x101242)),f326(f326(f251(x101242,x101242),f621(x101243,x101241,x101244,x101245,x101242)),x101244)),x101243))+~P105(f326(f326(f328(f916(x101242,x101242)),f326(f326(f251(x101242,x101242),x101245),x101244)),f326(f326(f183(f916(x101242,x101242),a905),x101241),x101243)))
% 157.55/157.23 [10128]E(x101281,x101282)+P105(f326(f326(f328(f916(x101283,x101283)),f326(f326(f251(x101283,x101283),x101281),f621(x101284,x101285,x101282,x101281,x101283))),f326(f326(f183(f916(x101283,x101283),a905),f620(x101284,x101285,x101282,x101281,x101283)),x101284)))+~P105(f326(f326(f328(f916(x101283,x101283)),f326(f326(f251(x101283,x101283),x101281),x101282)),f326(f326(f183(f916(x101283,x101283),a905),x101285),x101284)))
% 157.55/157.23 [10129]E(x101291,f2(a909))+P105(f326(f326(f328(f916(x101292,x101292)),f326(f326(f251(x101292,x101292),x101293),f621(x101294,x101291,x101295,x101293,x101292))),f326(f326(f183(f916(x101292,x101292),a905),f620(x101294,x101291,x101295,x101293,x101292)),x101294)))+~P105(f326(f326(f328(f916(x101292,x101292)),f326(f326(f251(x101292,x101292),x101293),x101295)),f326(f326(f183(f916(x101292,x101292),a905),x101291),x101294)))
% 157.55/157.23 [10181]E(x101811,x101812)+P105(f326(f326(f328(f916(x101813,x101813)),f326(f326(f251(x101813,x101813),f619(x101814,x101815,x101811,x101812,x101813)),x101811)),f326(f326(f183(f916(x101813,x101813),a905),f618(x101814,x101815,x101811,x101812,x101813)),x101814)))+~P105(f326(f326(f328(f916(x101813,x101813)),f326(f326(f251(x101813,x101813),x101812),x101811)),f326(f326(f183(f916(x101813,x101813),a905),x101815),x101814)))
% 157.55/157.23 [10182]E(x101821,f2(a909))+P105(f326(f326(f328(f916(x101822,x101822)),f326(f326(f251(x101822,x101822),f619(x101823,x101821,x101824,x101825,x101822)),x101824)),f326(f326(f183(f916(x101822,x101822),a905),f618(x101823,x101821,x101824,x101825,x101822)),x101823)))+~P105(f326(f326(f328(f916(x101822,x101822)),f326(f326(f251(x101822,x101822),x101825),x101824)),f326(f326(f183(f916(x101822,x101822),a905),x101821),x101823)))
% 157.55/157.23 [10216]~P69(x102162)+~P105(f326(f61(x102161),x102165))+E(f326(f326(f8(x102161,x102162),f326(f326(f9(x102161,x102162,x102162),f326(f326(f20(x102161,x102162,f917(x102162,x102162)),f326(f326(f10(a905,f917(x102162,f917(x102162,x102162)),x102161),f96(x102162)),f326(f326(f9(x102161,f917(x102161,a905),a905),f328(x102161)),x102163))),x102164)),f2(x102162))),x102165),f326(f326(f8(x102161,x102162),x102164),f326(f326(f101(f917(x102161,a905)),x102165),x102163)))
% 157.55/157.23 [8785]~P69(x87851)+~P105(f326(f61(x87854),x87855))+E(f326(f326(f79(x87851),f326(x87852,x87853)),f326(f326(f8(x87854,x87851),x87852),f326(f326(f3(f917(x87854,a905)),x87855),f326(f326(f308(x87854),x87853),f188(f917(x87854,a905)))))),f326(f326(f8(x87854,x87851),x87852),f326(f326(f308(x87854),x87853),x87855)))
% 157.55/157.23 [8786]~P74(x87861)+~P105(f326(f61(x87864),x87865))+E(f326(f326(f80(x87861),f326(x87862,x87863)),f326(f326(f11(x87864,x87861),x87862),f326(f326(f3(f917(x87864,a905)),x87865),f326(f326(f308(x87864),x87863),f188(f917(x87864,a905)))))),f326(f326(f11(x87864,x87861),x87862),f326(f326(f308(x87864),x87863),x87865)))
% 157.55/157.23 [9118]~P108(x91182)+~P12(x91182,f326(f168(x91182),f326(f326(f154(x91181,x91182),x91184),x91185)))+E(f326(f136(x91181,f326(f326(f10(x91182,a905,x91181),f326(f235(x91182),x91183)),x91184)),x91185),f177(x91181,f326(f326(f10(x91182,a905,x91181),f326(f235(x91182),x91183)),x91184),x91185))
% 157.55/157.23 [9142]~P69(x91421)+E(f326(f326(f79(x91421),f326(f326(f8(a909,x91421),x91422),f302(a909,x91423,x91424))),f326(f326(f8(a909,x91421),x91422),f302(a909,f326(f326(f79(a909),x91424),f77(a909)),f326(f326(f79(a909),x91424),x91425)))),f326(f326(f8(a909,x91421),x91422),f302(a909,x91423,f326(f326(f79(a909),x91424),x91425))))+~P105(f326(f326(f234(a909),x91423),f326(f326(f79(a909),x91424),f77(a909))))
% 157.55/157.23 [9143]~P105(f326(f326(f328(x91431),x91434),x91435))+~P105(f326(f326(f234(f917(x91431,a905)),f326(f172(x91431),x91432)),x91435))+P105(f326(f326(f234(f917(x91431,a905)),f326(f172(x91431),f326(f326(f159(x91431,x91432),x91433),x91434))),x91435))
% 157.55/157.23 [9364]~P4(x93642)+~P105(f326(f61(x93641),x93645))+E(f326(f326(f64(x93641,x93642,f326(f326(f10(x93642,f917(x93642,x93642),x93641),f110(x93642)),x93643)),x93644),x93645),f326(f326(f110(x93642),x93644),f326(f326(f40(x93641,x93642),x93645),x93643)))
% 157.55/157.23 [9365]~P4(x93652)+~P105(f326(f61(x93651),x93655))+E(f326(f326(f64(x93651,x93652,f326(f326(f10(x93652,f917(x93652,x93652),x93651),f101(x93652)),x93653)),x93654),x93655),f326(f326(f101(x93652),x93654),f326(f326(f39(x93651,x93652),x93655),x93653)))
% 157.55/157.23 [9413]E(f326(x94131,x94132),f326(x94131,x94133))+P105(f326(f326(f235(a909),f326(x94131,x94132)),f326(x94131,x94133)))+~P105(f326(f326(f328(f916(x94134,x94134)),f326(f326(f251(x94134,x94134),x94132),x94133)),f153(x94134,f326(f326(f151(f917(x94134,a909)),x94131),x94135))))
% 157.55/157.23 [9446]~E(f326(x94464,x94462),f326(x94464,x94463))+~P105(f326(f326(f328(f916(x94461,x94461)),f326(f326(f251(x94461,x94461),x94462),x94463)),f153(x94461,x94465)))+P105(f326(f326(f328(f916(x94461,x94461)),f326(f326(f251(x94461,x94461),x94462),x94463)),f153(x94461,f326(f326(f151(f917(x94461,a909)),x94464),x94465))))
% 157.55/157.23 [9466]~P24(x94661,x94662,x94663,x94665)+P24(x94661,x94662,x94663,f326(f326(f308(x94661),x94664),x94665))+P105(f326(f326(f328(x94662),f326(x94663,x94664)),f326(f309(x94661,x94662,x94663),f326(f326(f3(f917(x94661,a905)),x94665),f326(f326(f308(x94661),x94664),f188(f917(x94661,a905)))))))
% 157.55/157.23 [9469]P105(f326(x94692,x94695))+~P105(f326(f326(f328(x94691),x94695),f326(f172(x94691),x94693)))+E(f326(f326(f138(x94691),f326(f189(f910(x94691)),f177(x94691,x94692,f326(f326(f134(x94691),x94693),x94694)))),f326(f326(f134(x94691),x94693),x94694)),f326(f326(f134(x94691),f326(f326(f138(x94691),f326(f189(f910(x94691)),f177(x94691,x94692,x94693))),x94693)),x94694))
% 157.55/157.23 [9474]~P105(f326(f326(f328(f916(x94741,x94741)),f326(f326(f251(x94741,x94741),x94742),x94743)),f153(x94741,x94745)))+~P105(f326(f326(f234(a909),f326(x94744,x94742)),f326(x94744,x94743)))+P105(f326(f326(f328(f916(x94741,x94741)),f326(f326(f251(x94741,x94741),x94742),x94743)),f153(x94741,f326(f326(f151(f917(x94741,a909)),x94744),x94745))))
% 157.55/157.23 [9539]P105(f326(f326(f328(f916(x95394,x95394)),f326(f326(f251(x95394,x95394),x95392),x95393)),f153(x95394,x95395)))+P105(f326(f326(f235(a909),f326(x95391,x95392)),f326(x95391,x95393)))+~P105(f326(f326(f328(f916(x95394,x95394)),f326(f326(f251(x95394,x95394),x95392),x95393)),f153(x95394,f326(f326(f151(f917(x95394,a909)),x95391),x95395))))
% 157.55/157.23 [9682]~P105(f326(f326(f328(f916(f910(x96821),f910(x96821))),f326(f326(f251(f910(x96821),f910(x96821)),x96822),x96824)),f158(x96821,x96825)))+~P105(f326(f326(f235(a909),x96823),f326(f189(f910(x96821)),x96822)))+P105(f326(f326(f328(f916(x96821,x96821)),f326(f326(f251(x96821,x96821),f326(f326(f164(x96821),x96822),x96823)),f326(f326(f164(x96821),x96824),x96823))),x96825))
% 157.55/157.23 [9925]E(x99251,f2(a1))+~P105(f326(f49(x99253,x99251),f326(f326(f251(a1,a1),x99254),x99255)))+P105(f326(f49(f326(f326(f80(a1),x99252),x99253),x99251),f326(f326(f251(a1,a1),f326(f326(f79(a1),f326(f326(f80(a1),x99252),x99254)),f326(f326(f36(a1),f326(f326(f80(a1),x99252),x99255)),x99251))),f45(a1,f326(f326(f80(a1),x99252),x99255),x99251))))
% 157.55/157.23 [9926]~P105(f326(f326(f235(a909),f2(a909)),x99263))+~P105(f326(f48(x99262,x99263),f326(f326(f251(a909,a909),x99264),x99265)))+P105(f326(f48(f326(f326(f80(a909),x99261),x99262),x99263),f326(f326(f251(a909,a909),f326(f326(f79(a909),f326(f326(f80(a909),x99261),x99264)),f326(f326(f36(a909),f326(f326(f80(a909),x99261),x99265)),x99263))),f45(a909,f326(f326(f80(a909),x99261),x99265),x99263))))
% 157.55/157.23 [10239]~P69(x102392)+~P105(f326(f61(x102391),x102394))+E(f326(f326(f8(x102391,x102392),x102393),f326(f261(x102391),f326(f326(f20(x102391,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102391),a324),f326(f326(f9(x102391,f917(x102391,a905),a905),f328(x102391)),x102394))),f326(f326(f9(x102391,f917(x102391,a905),a905),f328(x102391)),x102395)))),f326(f326(f8(x102391,x102392),f326(f326(f9(x102391,x102392,x102392),f326(f326(f20(x102391,x102392,f917(x102392,x102392)),f326(f326(f10(a905,f917(x102392,f917(x102392,x102392)),x102391),f96(x102392)),f326(f326(f9(x102391,f917(x102391,a905),a905),f328(x102391)),x102395))),x102393)),f2(x102392))),x102394))
% 157.55/157.23 [8418]~E(f326(f326(f134(x84181),x84182),x84185),f326(f326(f134(x84181),x84183),x84184))+E(f326(f326(f134(x84181),f326(f326(f138(x84181),f326(f189(f910(x84181)),x84182)),x84183)),x84184),x84185)+P105(f326(f326(f234(a909),f326(f189(f910(x84181)),x84183)),f326(f189(f910(x84181)),x84182)))
% 157.55/157.23 [8613]~E(f326(f326(f134(x86132),x86133),x86131),f326(f326(f134(x86132),x86134),x86135))+E(x86131,f326(f326(f134(x86132),f326(f326(f138(x86132),f326(f189(f910(x86132)),x86133)),x86134)),x86135))+~P105(f326(f326(f234(a909),f326(f189(f910(x86132)),x86133)),f326(f189(f910(x86132)),x86134)))
% 157.55/157.23 [8700]~E(f326(f326(f79(a909),f326(f326(f80(a909),x87003),x87004)),x87001),f326(f326(f79(a909),f326(f326(f80(a909),x87002),x87004)),x87005))+~P105(f326(f326(f234(a909),x87003),x87002))+E(x87001,f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x87002),x87003)),x87004)),x87005))
% 157.55/157.23 [8701]~E(f326(f326(f79(a909),f326(f326(f80(a909),x87011),x87013)),x87014),f326(f326(f79(a909),f326(f326(f80(a909),x87012),x87013)),x87015))+~P105(f326(f326(f234(a909),x87012),x87011))+E(f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x87011),x87012)),x87013)),x87014),x87015)
% 157.55/157.23 [8869]E(f326(f326(f79(a909),f326(f326(f80(a909),x88691),x88692)),x88693),f326(f326(f79(a909),f326(f326(f80(a909),x88694),x88692)),x88695))+~P105(f326(f326(f234(a909),x88694),x88691))+~E(x88695,f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x88691),x88694)),x88692)),x88693))
% 157.55/157.23 [8870]E(f326(f326(f79(a909),f326(f326(f80(a909),x88701),x88702)),x88703),f326(f326(f79(a909),f326(f326(f80(a909),x88704),x88702)),x88705))+~P105(f326(f326(f234(a909),x88704),x88701))+~E(f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x88701),x88704)),x88702)),x88703),x88705)
% 157.55/157.23 [9736]~P62(x97362)+~P105(f326(f61(x97361),x97365))+E(f326(f326(f11(x97361,x97362),f326(f326(f20(x97361,x97362,x97362),f326(f326(f10(x97362,f917(x97362,x97362),x97361),f290(x97362)),x97363)),x97364)),x97365),f326(f326(f290(x97362),f326(f326(f11(x97361,x97362),x97363),x97365)),f326(f326(f11(x97361,x97362),x97364),x97365)))
% 157.55/157.23 [9866]~E(f623(x98665,x98664,x98663,x98662,x98661),f624(x98665,x98664,x98663,x98662,x98661))+P105(f326(f326(f328(f916(x98661,x98661)),f326(f326(f251(x98661,x98661),x98662),x98663)),f306(x98661,x98664)))+~P105(f326(f326(f328(f916(x98661,x98661)),f326(f326(f251(x98661,x98661),x98662),x98663)),f306(x98661,f326(f326(f110(f917(f916(x98661,x98661),a905)),x98664),x98665))))
% 157.55/157.23 [9867]~E(f626(x98675,x98674,x98673,x98672,x98671),f627(x98675,x98674,x98673,x98672,x98671))+P105(f326(f326(f328(f916(x98671,x98671)),f326(f326(f251(x98671,x98671),x98672),x98673)),f306(x98671,x98674)))+~P105(f326(f326(f328(f916(x98671,x98671)),f326(f326(f251(x98671,x98671),x98672),x98673)),f306(x98671,f326(f326(f110(f917(f916(x98671,x98671),a905)),x98674),x98675))))
% 157.55/157.23 [10060]P105(f326(f326(f328(f916(x100601,x100601)),f326(f326(f251(x100601,x100601),x100602),f627(x100605,x100604,x100603,x100602,x100601))),f306(x100601,x100604)))+P105(f326(f326(f328(f916(x100601,x100601)),f326(f326(f251(x100601,x100601),x100602),x100603)),f306(x100601,x100604)))+~P105(f326(f326(f328(f916(x100601,x100601)),f326(f326(f251(x100601,x100601),x100602),x100603)),f306(x100601,f326(f326(f110(f917(f916(x100601,x100601),a905)),x100604),x100605))))
% 157.55/157.23 [10150]P105(f326(f326(f328(f916(x101501,x101501)),f326(f326(f251(x101501,x101501),f624(x101505,x101504,x101503,x101502,x101501)),x101503)),f306(x101501,x101504)))+P105(f326(f326(f328(f916(x101501,x101501)),f326(f326(f251(x101501,x101501),x101502),x101503)),f306(x101501,x101504)))+~P105(f326(f326(f328(f916(x101501,x101501)),f326(f326(f251(x101501,x101501),x101502),x101503)),f306(x101501,f326(f326(f110(f917(f916(x101501,x101501),a905)),x101504),x101505))))
% 157.55/157.23 [10188]P105(f326(f326(f328(f916(x101881,x101881)),f326(f326(f251(x101881,x101881),x101882),x101883)),f306(x101881,x101884)))+P105(f326(f326(f328(f916(x101881,x101881)),f326(f326(f251(x101881,x101881),f623(x101885,x101884,x101883,x101882,x101881)),f624(x101885,x101884,x101883,x101882,x101881))),x101885))+~P105(f326(f326(f328(f916(x101881,x101881)),f326(f326(f251(x101881,x101881),x101882),x101883)),f306(x101881,f326(f326(f110(f917(f916(x101881,x101881),a905)),x101884),x101885))))
% 157.55/157.23 [10189]P105(f326(f326(f328(f916(x101891,x101891)),f326(f326(f251(x101891,x101891),x101892),x101893)),f306(x101891,x101894)))+P105(f326(f326(f328(f916(x101891,x101891)),f326(f326(f251(x101891,x101891),f627(x101895,x101894,x101893,x101892,x101891)),f626(x101895,x101894,x101893,x101892,x101891))),x101895))+~P105(f326(f326(f328(f916(x101891,x101891)),f326(f326(f251(x101891,x101891),x101892),x101893)),f306(x101891,f326(f326(f110(f917(f916(x101891,x101891),a905)),x101894),x101895))))
% 157.55/157.23 [10334]~P105(f326(f326(f328(f916(f910(x103341),f910(x103341))),f326(f326(f251(f910(x103341),f910(x103341)),x103344),x103345)),f158(x103341,x103342)))+~P105(f326(f326(f328(f916(x103341,x103341)),x103343),f326(f172(f916(x103341,x103341)),f326(f326(f181(x103341,x103341),x103344),x103345))))+P105(f326(f326(f256(x103341,x103341,a905),f326(f326(f9(x103341,f917(f916(x103341,x103341),a905),f917(x103341,a905)),f326(f326(f10(f917(x103341,f917(f917(f916(x103341,x103341),a905),a905)),f917(f917(f916(x103341,x103341),a905),f917(x103341,a905)),x103341),f9(x103341,f917(f916(x103341,x103341),a905),a905)),f326(f326(f10(f917(x103341,f916(x103341,x103341)),f917(x103341,f917(f917(f916(x103341,x103341),a905),a905)),x103341),f326(f10(f916(x103341,x103341),f917(f917(f916(x103341,x103341),a905),a905),x103341),f328(f916(x103341,x103341)))),f251(x103341,x103341)))),x103342)),x103343))
% 157.55/157.23 [9765]~P105(f326(f326(f234(a909),x97653),x97652))+~P105(f326(f326(f234(a909),f326(f326(f79(a909),f326(f326(f80(a909),x97653),x97654)),x97651)),f326(f326(f79(a909),f326(f326(f80(a909),x97652),x97654)),x97655)))+P105(f326(f326(f234(a909),x97651),f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x97652),x97653)),x97654)),x97655)))
% 157.55/157.23 [9766]~P105(f326(f326(f234(a909),x97663),x97662))+~P105(f326(f326(f235(a909),f326(f326(f79(a909),f326(f326(f80(a909),x97663),x97664)),x97661)),f326(f326(f79(a909),f326(f326(f80(a909),x97662),x97664)),x97665)))+P105(f326(f326(f235(a909),x97661),f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x97662),x97663)),x97664)),x97665)))
% 157.55/157.23 [9783]~P105(f326(f326(f234(a909),x97831),x97834))+P105(f326(f326(f234(a909),f326(f326(f79(a909),f326(f326(f80(a909),x97831),x97832)),x97833)),f326(f326(f79(a909),f326(f326(f80(a909),x97834),x97832)),x97835)))+~P105(f326(f326(f234(a909),x97833),f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x97834),x97831)),x97832)),x97835)))
% 157.55/157.23 [9784]~P105(f326(f326(f234(a909),x97841),x97844))+P105(f326(f326(f235(a909),f326(f326(f79(a909),f326(f326(f80(a909),x97841),x97842)),x97843)),f326(f326(f79(a909),f326(f326(f80(a909),x97844),x97842)),x97845)))+~P105(f326(f326(f235(a909),x97843),f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x97844),x97841)),x97842)),x97845)))
% 157.55/157.23 [9900]~P105(f326(f326(f234(a909),x99002),x99001))+~P105(f326(f326(f234(a909),f326(f326(f79(a909),f326(f326(f80(a909),x99001),x99003)),x99004)),f326(f326(f79(a909),f326(f326(f80(a909),x99002),x99003)),x99005)))+P105(f326(f326(f234(a909),f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x99001),x99002)),x99003)),x99004)),x99005))
% 157.55/157.23 [9901]~P105(f326(f326(f234(a909),x99012),x99011))+~P105(f326(f326(f235(a909),f326(f326(f79(a909),f326(f326(f80(a909),x99011),x99013)),x99014)),f326(f326(f79(a909),f326(f326(f80(a909),x99012),x99013)),x99015)))+P105(f326(f326(f235(a909),f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x99011),x99012)),x99013)),x99014)),x99015))
% 157.55/157.23 [9944]~P105(f326(f326(f234(a909),x99444),x99441))+P105(f326(f326(f234(a909),f326(f326(f79(a909),f326(f326(f80(a909),x99441),x99442)),x99443)),f326(f326(f79(a909),f326(f326(f80(a909),x99444),x99442)),x99445)))+~P105(f326(f326(f234(a909),f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x99441),x99444)),x99442)),x99443)),x99445))
% 157.55/157.23 [9945]~P105(f326(f326(f234(a909),x99454),x99451))+P105(f326(f326(f235(a909),f326(f326(f79(a909),f326(f326(f80(a909),x99451),x99452)),x99453)),f326(f326(f79(a909),f326(f326(f80(a909),x99454),x99452)),x99455)))+~P105(f326(f326(f235(a909),f326(f326(f79(a909),f326(f326(f80(a909),f326(f326(f3(a909),x99451),x99454)),x99452)),x99453)),x99455))
% 157.55/157.23 [10176]~P10(x101761,x101762,x101765,x101763)+~P105(f326(f326(f328(f916(x101761,x101761)),x101764),x101765))+P105(f326(f326(f256(x101761,x101761,a905),f326(f326(f9(x101761,f917(x101761,x101762),f917(x101761,a905)),f326(f326(f10(f917(x101762,a905),f917(f917(x101761,x101762),f917(x101761,a905)),x101761),f10(x101762,a905,x101761)),f326(f326(f10(x101762,f917(x101762,a905),x101761),a323),x101763))),x101763)),x101764))
% 157.55/157.23 [8577]~P18(x85776,x85771,x85772,x85774)+E(f326(f72(x85771,x85771,x85771,f326(x85772,x85773)),f326(x85774,x85775)),f326(f72(x85771,x85771,x85771,f326(x85774,x85775)),f326(x85772,x85773)))+~P105(f326(f61(x85776),x85775))
% 157.55/157.23 [9013]~P24(x90131,x90133,x90135,x90136)+~P24(x90133,x90132,x90134,f326(f309(x90131,x90133,x90135),x90136))+P24(x90131,x90132,f326(f72(x90133,x90132,x90131,x90134),x90135),x90136)
% 157.55/157.23 [9571]~P105(f326(f326(x95713,x95712),x95716))+~P105(f326(f326(x95714,x95715),x95712))+P105(f326(f326(f328(x95711),x95712),f299(x95711,x95713,x95714,x95715,x95716)))
% 157.55/157.23 [9572]~P105(f326(f326(x95724,x95722),x95726))+~P105(f326(f326(x95723,x95725),x95722))+P105(f326(f326(f328(x95721),x95722),f296(x95721,x95723,x95724,x95725,x95726)))
% 157.55/157.23 [9683]E(x96831,x96832)+E(x96833,x96834)+~P105(f326(f326(f328(f916(f910(x96835),f910(x96835))),f326(f326(f251(f910(x96835),f910(x96835)),f326(f326(f151(x96835),x96833),x96831)),f326(f326(f151(x96835),x96834),x96832))),f157(x96835,x96836)))
% 157.55/157.23 [9692]~E(x96922,x96924)+P105(f326(f326(f328(f916(f910(x96921),f910(x96921))),f326(f326(f251(f910(x96921),f910(x96921)),f326(f326(f151(x96921),x96922),x96923)),f326(f326(f151(x96921),x96924),x96925))),f145(x96921,x96926)))+~P105(f326(f326(f328(f916(f910(x96921),f910(x96921))),f326(f326(f251(f910(x96921),f910(x96921)),x96923),x96925)),f145(x96921,x96926)))
% 157.55/157.23 [9693]~E(x96932,x96934)+P105(f326(f326(f328(f916(f910(x96931),f910(x96931))),f326(f326(f251(f910(x96931),f910(x96931)),f326(f326(f151(x96931),x96932),x96933)),f326(f326(f151(x96931),x96934),x96935))),f147(x96931,x96936)))+~P105(f326(f326(f328(f916(f910(x96931),f910(x96931))),f326(f326(f251(f910(x96931),f910(x96931)),x96933),x96935)),f147(x96931,x96936)))
% 157.55/157.23 [9694]~E(x96942,x96944)+P105(f326(f326(f328(f916(f910(x96941),f910(x96941))),f326(f326(f251(f910(x96941),f910(x96941)),f326(f326(f151(x96941),x96942),x96943)),f326(f326(f151(x96941),x96944),x96945))),f157(x96941,x96946)))+~P105(f326(f326(f328(f916(f910(x96941),f910(x96941))),f326(f326(f251(f910(x96941),f910(x96941)),x96943),x96945)),f157(x96941,x96946)))
% 157.55/157.23 [9695]~E(x96952,x96954)+P105(f326(f326(f328(f916(f910(x96951),f910(x96951))),f326(f326(f251(f910(x96951),f910(x96951)),f326(f326(f134(x96951),x96952),x96953)),f326(f326(f134(x96951),x96954),x96955))),f157(x96951,x96956)))+~P105(f326(f326(f328(f916(f910(x96951),f910(x96951))),f326(f326(f251(f910(x96951),f910(x96951)),x96953),x96955)),f157(x96951,x96956)))
% 157.55/157.23 [9696]~E(x96963,x96965)+P105(f326(f326(f328(f916(f910(x96961),f910(x96961))),f326(f326(f251(f910(x96961),f910(x96961)),f326(f326(f134(x96961),x96962),x96963)),f326(f326(f134(x96961),x96964),x96965))),f157(x96961,x96966)))+~P105(f326(f326(f328(f916(f910(x96961),f910(x96961))),f326(f326(f251(f910(x96961),f910(x96961)),x96962),x96964)),f157(x96961,x96966)))
% 157.55/157.23 [9753]E(x97531,x97532)+P105(f326(f326(f328(f916(f910(x97533),f910(x97533))),f326(f326(f251(f910(x97533),f910(x97533)),x97531),x97532)),f157(x97533,x97534)))+~P105(f326(f326(f328(f916(f910(x97533),f910(x97533))),f326(f326(f251(f910(x97533),f910(x97533)),f326(f326(f151(x97533),x97535),x97531)),f326(f326(f151(x97533),x97536),x97532))),f157(x97533,x97534)))
% 157.55/157.23 [9904]~E(x99043,x99045)+P105(f326(f326(f328(f916(f910(x99041),f910(x99041))),f326(f326(f251(f910(x99041),f910(x99041)),f326(f326(f134(x99041),x99042),f326(f326(f151(x99041),x99043),f113(x99041)))),f326(f326(f134(x99041),x99044),f326(f326(f151(x99041),x99045),f113(x99041))))),f157(x99041,x99046)))+~P105(f326(f326(f328(f916(f910(x99041),f910(x99041))),f326(f326(f251(f910(x99041),f910(x99041)),x99042),x99044)),f157(x99041,x99046)))
% 157.55/157.23 [9948]E(x99481,x99482)+E(x99483,x99484)+~P105(f326(f326(f328(f916(f910(x99485),f910(x99485))),f326(f326(f251(f910(x99485),f910(x99485)),f326(f326(f134(x99485),x99483),f326(f326(f151(x99485),x99481),f113(x99485)))),f326(f326(f134(x99485),x99484),f326(f326(f151(x99485),x99482),f113(x99485))))),f157(x99485,x99486)))
% 157.55/157.23 [9974]E(x99741,x99742)+~P105(f326(f326(f328(f916(f910(x99743),f910(x99743))),f326(f326(f251(f910(x99743),f910(x99743)),f326(f326(f134(x99743),x99741),f326(f326(f151(x99743),x99745),f113(x99743)))),f326(f326(f134(x99743),x99742),f326(f326(f151(x99743),x99746),f113(x99743))))),f157(x99743,x99744)))+P105(f326(f326(f328(f916(f910(x99743),f910(x99743))),f326(f326(f251(f910(x99743),f910(x99743)),x99741),x99742)),f157(x99743,x99744)))
% 157.55/157.23 [10012]~P105(f326(f326(f328(f916(f917(x100121,a905),f917(x100121,a905))),f326(f326(f251(f917(x100121,a905),f917(x100121,a905)),x100122),x100124)),f318(x100121,x100126)))+~P105(f326(f326(f328(f916(f917(x100121,a905),f917(x100121,a905))),f326(f326(f251(f917(x100121,a905),f917(x100121,a905)),x100123),x100125)),f318(x100121,x100126)))+P105(f326(f326(f328(f916(f917(x100121,a905),f917(x100121,a905))),f326(f326(f251(f917(x100121,a905),f917(x100121,a905)),f326(f326(f110(f917(x100121,a905)),x100122),x100123)),f326(f326(f110(f917(x100121,a905)),x100124),x100125))),f318(x100121,x100126)))
% 157.55/157.23 [5821]~E(f326(f326(f134(x58211),x58216),x58213),x58215)+E(f326(f326(f134(x58211),x58212),x58213),f326(f326(f151(x58211),x58214),x58215))+~E(x58212,f326(f326(f151(x58211),x58214),x58216))
% 157.55/157.23 [5822]~E(f326(f326(f134(x58221),x58226),x58223),x58225)+E(f326(f326(f134(x58221),x58222),x58223),f326(f326(f134(x58221),x58224),x58225))+~E(x58222,f326(f326(f134(x58221),x58224),x58226))
% 157.55/157.23 [5824]E(f326(f326(f134(x58241),x58242),x58243),f326(f326(f151(x58241),x58244),x58245))+~E(f326(f326(f151(x58241),x58244),x58246),x58242)+~E(x58245,f326(f326(f134(x58241),x58246),x58243))
% 157.55/157.23 [5826]~E(f326(f326(f134(x58261),x58262),x58266),x58264)+E(f326(f326(f134(x58261),x58262),x58263),f326(f326(f134(x58261),x58264),x58265))+~E(x58263,f326(f326(f134(x58261),x58266),x58265))
% 157.55/157.23 [6978]E(f326(x69781,x69782),f326(x69783,x69782))+~E(f326(f326(f154(x69784,x69785),x69781),x69786),f326(f326(f154(x69784,x69785),x69783),x69786))+~P105(f326(f326(f328(x69784),x69782),f326(f172(x69784),x69786)))
% 157.55/157.23 [7360]~P18(x73604,x73605,x73606,x73601)+E(f326(f326(x73601,x73602),x73603),f326(f326(f64(x73604,x73605,x73606),x73603),x73602))+~P105(f326(f61(x73604),x73602))
% 157.55/157.23 [7431]~E(x74312,f326(x74314,x74316))+~P105(f326(f326(f328(x74313),x74316),x74315))+P105(f326(f326(f328(x74311),x74312),f326(f309(x74313,x74311,x74314),x74315)))
% 157.55/157.23 [7432]~E(f326(x74324,x74322),x74326)+~P105(f326(f326(f328(x74323),x74326),x74325))+P105(f326(f326(f328(x74321),x74322),f326(f310(x74321,x74323,x74324),x74325)))
% 157.55/157.23 [7879]~P31(x78791,x78792,x78794,x78796)+P31(x78791,x78792,f326(f326(f151(x78791),x78793),x78794),f326(f326(f151(x78791),x78795),x78796))+~P105(f326(f326(x78792,x78793),x78795))
% 157.55/157.23 [8879]~P55(x88794,x88795,x88791,x88792,x88796)+E(f326(x88791,f326(x88792,x88793)),x88793)+~P105(f326(f326(f328(x88795),x88793),x88796))
% 157.55/157.23 [9373]~P25(x93732,x93731,x93735,x93734,x93733)+E(f326(f90(x93731,x93732,x93733,f90(x93732,x93731,x93734,x93735)),x93736),f326(x93735,x93736))+~P105(f326(f326(f328(x93732),x93736),x93734))
% 157.55/157.23 [9384]~P24(x93841,x93842,x93843,x93846)+P24(x93841,x93842,f74(x93841,x93842,x93843,x93844,x93845),x93846)+P105(f326(f326(f328(x93842),x93845),f326(f309(x93841,x93842,x93843),x93846)))
% 157.55/157.23 [9685]E(x96851,x96852)+E(f326(f189(f910(x96853)),x96854),f326(f189(f910(x96853)),x96855))+~P105(f326(f326(f328(f916(f910(x96853),f910(x96853))),f326(f326(f251(f910(x96853),f910(x96853)),f326(f326(f151(x96853),x96851),x96854)),f326(f326(f151(x96853),x96852),x96855))),f145(x96853,x96856)))
% 157.55/157.23 [9748]~P15(x97481,x97482,x97483)+E(f326(f326(f64(x97481,x97482,x97483),x97484),x97485),x97486)+~P105(f326(f66(x97481,x97482,x97483,x97484,x97485),x97486))
% 157.55/157.23 [9756]E(f326(f189(f910(x97561)),x97562),f326(f189(f910(x97561)),x97563))+P105(f326(f326(f328(f916(f910(x97561),f910(x97561))),f326(f326(f251(f910(x97561),f910(x97561)),x97562),x97563)),f145(x97561,x97564)))+~P105(f326(f326(f328(f916(f910(x97561),f910(x97561))),f326(f326(f251(f910(x97561),f910(x97561)),f326(f326(f151(x97561),x97565),x97562)),f326(f326(f151(x97561),x97566),x97563))),f145(x97561,x97564)))
% 157.55/157.23 [9777]~P105(f326(f326(f328(f916(x97771,x97771)),f326(f326(f251(x97771,x97771),x97772),x97774)),f306(x97771,x97776)))+P105(f326(f326(f328(f916(f910(x97771),f910(x97771))),f326(f326(f251(f910(x97771),f910(x97771)),f326(f326(f151(x97771),x97772),x97773)),f326(f326(f151(x97771),x97774),x97775))),f306(f910(x97771),f157(x97771,x97776))))+~P105(f326(f326(f328(f916(f910(x97771),f910(x97771))),f326(f326(f251(f910(x97771),f910(x97771)),x97773),x97775)),f306(f910(x97771),f157(x97771,x97776))))
% 157.55/157.23 [9954]~P105(f326(x99542,x99546))+~E(f326(f136(x99541,x99542),x99543),f326(f326(f151(x99541),x99544),x99545))+~P105(f326(f326(f328(x99541),x99546),f326(f172(x99541),f740(x99545,x99544,x99543,x99542,x99541))))
% 157.55/157.23 [9955]~P105(f326(x99554,x99556))+~E(f326(f326(f151(x99551),x99552),x99553),f326(f136(x99551,x99554),x99555))+~P105(f326(f326(f328(x99551),x99556),f326(f172(x99551),f738(x99555,x99554,x99553,x99552,x99551))))
% 157.55/157.23 [10273]~P69(x102732)+E(f326(f326(f8(x102731,x102732),f326(f326(f10(f917(x102733,a905),x102732,x102731),f326(f8(x102733,x102732),x102734)),f326(f326(f10(f917(x102733,a905),f917(x102733,a905),x102731),f261(x102733)),f326(f326(f10(f917(x102733,a905),f917(x102733,a905),x102731),f326(f20(x102733,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102733),a324),f326(f326(f9(x102733,f917(x102733,a905),a905),f328(x102733)),x102735)))),f326(f9(x102733,x102731,a905),f326(f326(f10(x102731,f917(x102731,a905),x102733),a323),x102736)))))),f326(f309(x102733,x102731,x102736),x102735)),f326(f326(f8(x102733,x102732),x102734),x102735))+~P105(f326(f61(x102733),x102735))
% 157.55/157.23 [7034]~P108(x70343)+P105(f326(x70342,x70345))+E(f326(f136(x70341,x70342),f326(f326(f148(x70341,x70343,x70344),x70345),x70346)),f326(f136(x70341,x70342),x70346))
% 157.55/157.23 [7036]P105(f326(x70361,x70362))+~E(f166(x70363,x70361,x70364),f326(f326(f251(f910(x70363),f910(x70363)),x70365),x70366))+~P105(f326(f326(f328(x70363),x70362),f326(f172(x70363),x70365)))
% 157.55/157.23 [7079]~P105(f326(x70792,x70796))+~E(f166(x70791,x70792,x70793),f326(f326(f251(f910(x70791),f910(x70791)),x70794),x70795))+~P105(f326(f326(f328(x70791),x70796),f326(f172(x70791),x70795)))
% 157.55/157.23 [7744]~P13(x77441,x77442,x77443)+~P105(f326(f61(x77441),x77446))+E(f326(f326(f64(x77441,x77442,x77443),x77444),f326(f326(f308(x77441),x77445),x77446)),f326(f326(f64(x77441,x77442,x77443),f326(f326(x77443,x77445),x77444)),x77446))
% 157.55/157.23 [7795]~P108(x77952)+~P105(f326(f326(f234(x77952),f326(x77953,x77954)),f326(x77953,x77955)))+E(f326(f326(f148(x77951,x77952,x77953),x77954),f326(f326(f151(x77951),x77955),x77956)),f326(f326(f151(x77951),x77954),f326(f326(f151(x77951),x77955),x77956)))
% 157.55/157.23 [7907]E(x79071,x79072)+~E(f326(f326(f253(x79073,x79074),x79071),f326(f18(f917(x79074,a905),x79073),x79075)),f326(f326(f253(x79073,x79074),x79072),f326(f18(f917(x79074,a905),x79073),x79075)))+~P105(f326(f326(f328(x79074),x79076),x79075))
% 157.55/157.23 [7972]~P13(x79721,x79722,x79723)+~P105(f326(f61(x79721),x79726))+E(f326(f326(f64(x79721,x79722,x79723),x79724),f326(f326(f308(x79721),x79725),x79726)),f326(f326(x79723,x79725),f326(f326(f64(x79721,x79722,x79723),x79724),x79726)))
% 157.55/157.23 [8087]~P15(x80871,x80872,x80873)+~P105(f326(f61(x80871),x80876))+E(f326(f326(f64(x80871,x80872,x80873),f326(f326(x80873,x80874),x80875)),x80876),f326(f326(x80873,x80874),f326(f326(f64(x80871,x80872,x80873),x80875),x80876)))
% 157.55/157.23 [8155]~P19(x81552,x81555,x81556,x81551)+~P105(f326(f61(x81552),x81554))+E(f326(x81551,f326(f326(f308(x81552),x81553),x81554)),f326(f72(x81555,x81555,x81555,f326(x81551,x81554)),f326(x81556,x81553)))
% 157.55/157.23 [8187]~P108(x81872)+P105(f326(f326(f234(x81872),f326(x81873,x81874)),f326(x81873,x81875)))+E(f326(f326(f148(x81871,x81872,x81873),x81874),f326(f326(f151(x81871),x81875),x81876)),f326(f326(f151(x81871),x81875),f326(f326(f148(x81871,x81872,x81873),x81874),x81876)))
% 157.55/157.23 [8325]~E(f326(f189(f910(x83251)),x83255),f326(f189(f910(x83252)),x83256))+~E(f326(f189(f910(x83251)),x83253),f326(f189(f910(x83252)),x83254))+E(f326(f326(f134(f916(x83251,x83252)),f326(f326(f181(x83251,x83252),x83253),x83254)),f326(f326(f181(x83251,x83252),x83255),x83256)),f326(f326(f181(x83251,x83252),f326(f326(f134(x83251),x83253),x83255)),f326(f326(f134(x83252),x83254),x83256)))
% 157.55/157.23 [8436]~E(x84362,f326(f309(x84363,x84361,x84364),x84366))+P105(f326(f326(f234(f917(x84361,a905)),x84362),f326(f309(x84363,x84361,x84364),x84365)))+~P105(f326(f326(f234(f917(x84363,a905)),x84366),x84365))
% 157.55/157.23 [8537]~P108(x85375)+E(f326(x85371,x85372),f326(x85371,x85373))+E(f326(f326(f148(x85374,x85375,x85371),x85372),f326(f326(f148(x85374,x85375,x85371),x85373),x85376)),f326(f326(f148(x85374,x85375,x85371),x85373),f326(f326(f148(x85374,x85375,x85371),x85372),x85376)))
% 157.55/157.23 [8709]~P105(f326(f326(f328(x87092),x87094),f326(x87096,x87093)))+~P105(f326(f326(f328(x87091),x87093),x87095))+P105(f326(f326(f328(f916(x87091,x87092)),f326(f326(f251(x87091,x87092),x87093),x87094)),f326(f326(f253(x87091,x87092),x87095),x87096)))
% 157.55/157.23 [9183]~P69(x91832)+~P24(x91834,x91831,x91835,x91836)+E(f326(f326(f8(x91831,x91832),x91833),f326(f309(x91834,x91831,x91835),x91836)),f326(f326(f8(x91834,x91832),f326(f72(x91831,x91832,x91834,x91833),x91835)),x91836))
% 157.55/157.23 [9184]~P74(x91842)+~P24(x91844,x91841,x91845,x91846)+E(f326(f326(f11(x91841,x91842),x91843),f326(f309(x91844,x91841,x91845),x91846)),f326(f326(f11(x91844,x91842),f326(f72(x91841,x91842,x91844,x91843),x91845)),x91846))
% 157.55/157.23 [9231]~P33(x92312,x92315,x92311,x92313,x92316)+P105(f326(f326(x92311,f326(f326(f164(x92312),x92313),x92314)),f326(f326(f164(x92315),x92316),x92314)))+~P105(f326(f326(f235(a909),x92314),f326(f189(f910(x92315)),x92316)))
% 157.55/157.23 [9232]~P33(x92322,x92325,x92321,x92323,x92326)+P105(f326(f326(x92321,f326(f326(f164(x92322),x92323),x92324)),f326(f326(f164(x92325),x92326),x92324)))+~P105(f326(f326(f235(a909),x92324),f326(f189(f910(x92322)),x92323)))
% 157.55/157.23 [9243]~E(f326(f309(x92431,x92432,x92433),x92434),x92436)+E(f326(f309(x92431,x92432,x92433),f326(f309(x92432,x92431,f90(x92431,x92432,x92434,x92433)),x92435)),x92435)+~P105(f326(f326(f234(f917(x92432,a905)),x92435),x92436))
% 157.55/157.23 [9441]~P18(x94413,x94411,x94416,x94412)+~P105(f326(f61(x94413),x94414))+E(f326(f72(x94411,x94411,x94411,f326(x94412,f326(f326(f3(f917(x94413,a905)),x94414),f326(f326(f308(x94413),x94415),f188(f917(x94413,a905)))))),f326(x94416,x94415)),f326(x94412,f326(f326(f308(x94413),x94415),x94414)))
% 157.55/157.23 [10042]~E(f326(f309(x100422,x100424,x100426),f241(f917(x100422,a905))),f241(f917(x100424,a905)))+~E(f326(f309(x100421,x100423,x100425),f241(f917(x100421,a905))),f241(f917(x100423,a905)))+E(f326(f309(f916(x100421,x100422),f916(x100423,x100424),f257(x100421,x100423,x100422,x100424,x100425,x100426)),f241(f917(f916(x100421,x100422),a905))),f241(f917(f916(x100423,x100424),a905)))
% 157.55/157.23 [10100]~P24(x101003,x101004,x101005,f326(x101006,f544(x101006,x101005,x101004,x101003,x101002,x101001)))+P24(x101003,x101004,x101005,f326(f326(f39(x101002,f917(x101003,a905)),x101001),x101006))+E(x101001,f188(f917(x101002,a905)))
% 157.55/157.23 [10157]P24(x101576,x101575,x101574,f326(f326(f39(x101572,f917(x101576,a905)),x101571),x101573))+E(x101571,f188(f917(x101572,a905)))+P105(f326(f326(f328(x101572),f544(x101573,x101574,x101575,x101576,x101572,x101571)),x101571))
% 157.55/157.23 [10162]P105(f326(f326(f328(x101621),f596(x101622,x101623,x101624,x101625,x101626,x101621)),x101626))+P105(f326(f326(f234(f917(f916(x101621,x101624),a905)),f326(f326(f253(x101621,x101624),x101626),x101623)),f326(f326(f253(x101621,x101624),x101625),x101622)))+~P105(f326(f326(f234(f917(x101621,a905)),x101626),x101625))
% 157.55/157.23 [10205]P23(x102056,x102055,f326(f326(f308(f908(x102056)),f91(x102056,x102051,x102053,x102052)),f188(f917(f908(x102056),a905))))+~P23(x102056,x102055,f326(f326(f308(f908(x102056)),f91(x102056,x102054,x102053,x102052)),f188(f917(f908(x102056),a905))))+P105(f326(f326(x102051,f555(x102051,x102052,x102053,x102054,x102055,x102056)),f664(x102051,x102052,x102053,x102054,x102055,x102056)))
% 157.55/157.23 [10248]~P23(x102481,x102482,f326(f326(f308(f908(x102481)),f91(x102481,x102486,x102484,x102485)),f188(f917(f908(x102481),a905))))+P23(x102481,x102482,f326(f326(f308(f908(x102481)),f91(x102481,x102483,x102484,x102485)),f188(f917(f908(x102481),a905))))+~P105(f326(f326(x102486,f555(x102483,x102485,x102484,x102486,x102482,x102481)),f664(x102483,x102485,x102484,x102486,x102482,x102481)))
% 157.55/157.23 [10287]~P105(f326(f326(f234(f917(x102872,a905)),f326(x102874,f596(x102876,x102874,x102872,x102875,x102873,x102871))),f326(x102876,f596(x102876,x102874,x102872,x102875,x102873,x102871))))+~P105(f326(f326(f234(f917(x102871,a905)),x102873),x102875))+P105(f326(f326(f234(f917(f916(x102871,x102872),a905)),f326(f326(f253(x102871,x102872),x102873),x102874)),f326(f326(f253(x102871,x102872),x102875),x102876)))
% 157.55/157.23 [7929]~P105(f326(x79291,x79295))+~P105(f326(x79296,x79294))+P105(f326(x79291,f326(f255(x79292,x79293),f326(f326(f251(x79292,x79293),x79294),x79295))))
% 157.55/157.23 [7930]~P105(f326(x79301,x79304))+~P105(f326(x79306,x79305))+P105(f326(x79301,f326(f250(x79302,x79303),f326(f326(f251(x79302,x79303),x79304),x79305))))
% 157.55/157.23 [7977]~P105(f326(f326(x79774,x79776),x79775))+~P105(f326(f326(f328(x79771),x79776),x79773))+P105(f326(f326(f326(f40(x79771,f917(x79772,a905)),x79773),x79774),x79775))
% 157.55/157.23 [8277]~P105(f326(f326(f328(x82771),x82772),f326(x82775,x82776)))+~P105(f326(f326(f328(x82773),x82776),x82774))+P105(f326(f326(f328(x82771),x82772),f326(f326(f40(x82773,f917(x82771,a905)),x82774),x82775)))
% 157.55/157.23 [8319]P105(f326(f326(x83191,x83192),x83193))+~P105(f326(f326(x83194,x83192),x83193))+~P105(f326(f326(f234(f917(x83195,f917(x83196,a905))),x83194),x83191))
% 157.55/157.23 [8459]P105(f326(f326(x84591,x84592),x84593))+~P105(f326(f326(f328(x84594),x84592),x84595))+~P105(f326(f326(f326(f39(x84594,f917(x84596,a905)),x84595),x84591),x84593))
% 157.55/157.23 [8592]P105(f326(f326(f328(x85921),x85922),f326(x85923,x85924)))+~P105(f326(f326(f328(x85925),x85924),x85926))+~P105(f326(f326(f328(x85921),x85922),f326(f326(f39(x85925,f917(x85921,a905)),x85926),x85923)))
% 157.55/157.23 [8858]~P10(x88584,x88585,x88586,x88581)+E(f326(x88581,x88582),f326(x88581,x88583))+~P105(f326(f326(f328(f916(x88584,x88584)),f326(f326(f251(x88584,x88584),x88582),x88583)),x88586))
% 157.55/157.23 [8893]P105(f326(f326(f234(f917(x88931,a905)),x88932),f326(x88933,x88934)))+~P105(f326(f326(f328(x88935),x88934),x88936))+~P105(f326(f326(f234(f917(x88931,a905)),x88932),f326(f326(f39(x88935,f917(x88931,a905)),x88936),x88933)))
% 157.55/157.23 [8926]~P53(x89263,x89264,f326(f285(x89264,x89263),x89265))+E(x89261,f188(f917(x89262,a905)))+E(f326(f326(f39(x89262,f917(x89263,a905)),x89261),f326(f326(f10(f917(x89264,a905),f917(x89263,a905),x89262),f284(x89264,x89263,x89265)),x89266)),f326(f284(x89264,x89263,x89265),f326(f326(f39(x89262,f917(x89264,a905)),x89261),x89266)))
% 157.55/157.23 [9004]P105(f326(f326(f328(x90041),x90042),f326(f284(x90043,x90041,x90044),x90045)))+~P105(f326(f326(f328(x90043),x90046),x90045))+~P105(f326(f326(f328(f916(x90043,x90041)),f326(f326(f251(x90043,x90041),x90046),x90042)),x90044))
% 157.55/157.23 [9308]P105(f326(f326(f234(f917(x93081,a905)),f326(f284(x93082,x93081,x93083),x93084)),f326(f284(x93082,x93081,x93085),x93086)))+~P105(f326(f326(f234(f917(x93082,a905)),x93084),x93086))+~P105(f326(f326(f234(f917(f916(x93082,x93081),a905)),x93083),x93085))
% 157.55/157.23 [9490]~P105(f326(f326(f328(x94902),x94906),x94904))+~P105(f326(f326(f234(f917(x94901,a905)),x94903),x94905))+P105(f326(f326(f234(f917(f916(x94901,x94902),a905)),f326(f326(f253(x94901,x94902),x94903),f326(f18(f917(x94902,a905),x94901),x94904))),f326(f326(f253(x94901,x94902),x94905),f326(f18(f917(x94902,a905),x94901),x94904))))
% 157.55/157.23 [9502]~P33(x95021,x95022,x95023,x95025,x95026)+P105(f326(f326(f256(x95021,x95022,a905),x95023),x95024))+~P105(f326(f326(f328(f916(x95021,x95022)),x95024),f326(f172(f916(x95021,x95022)),f326(f326(f181(x95021,x95022),x95025),x95026))))
% 157.55/157.23 [9639]~E(x96393,x96395)+P105(f326(f326(f328(f916(f910(x96391),f910(x96391))),f326(f326(f251(f910(x96391),f910(x96391)),f326(f326(f151(x96391),x96392),x96393)),f326(f326(f151(x96391),x96394),x96395))),f157(x96391,x96396)))+~P105(f326(f326(f328(f916(x96391,x96391)),f326(f326(f251(x96391,x96391),x96392),x96394)),x96396))
% 157.55/157.23 [9645]~E(f326(f189(f910(x96451)),x96453),f326(f189(f910(x96451)),x96455))+P105(f326(f326(f328(f916(f910(x96451),f910(x96451))),f326(f326(f251(f910(x96451),f910(x96451)),f326(f326(f151(x96451),x96452),x96453)),f326(f326(f151(x96451),x96454),x96455))),f145(x96451,x96456)))+~P105(f326(f326(f328(f916(x96451,x96451)),f326(f326(f251(x96451,x96451),x96452),x96454)),x96456))
% 157.55/157.23 [9677]P105(f326(f326(f328(f916(x96771,x96771)),f326(f326(f251(x96771,x96771),x96772),x96773)),f326(f326(f183(f916(x96771,x96771),a905),f326(a112,x96774)),x96775)))+~P105(f326(f326(f328(f916(x96771,x96771)),f326(f326(f251(x96771,x96771),x96776),x96773)),x96775))+~P105(f326(f326(f328(f916(x96771,x96771)),f326(f326(f251(x96771,x96771),x96772),x96776)),f326(f326(f183(f916(x96771,x96771),a905),x96774),x96775)))
% 157.55/157.23 [9678]P105(f326(f326(f328(f916(x96781,x96781)),f326(f326(f251(x96781,x96781),x96782),x96783)),f326(f326(f183(f916(x96781,x96781),a905),f326(a112,x96784)),x96785)))+~P105(f326(f326(f328(f916(x96781,x96781)),f326(f326(f251(x96781,x96781),x96782),x96786)),x96785))+~P105(f326(f326(f328(f916(x96781,x96781)),f326(f326(f251(x96781,x96781),x96786),x96783)),f326(f326(f183(f916(x96781,x96781),a905),x96784),x96785)))
% 157.55/157.23 [9681]~P105(f326(f326(f328(x96814),x96815),x96816))+P105(f326(f326(f234(f917(x96811,a905)),x96812),x96813))+~P105(f326(f326(f234(f917(f916(x96811,x96814),a905)),f326(f326(f253(x96811,x96814),x96812),f326(f18(f917(x96814,a905),x96811),x96816))),f326(f326(f253(x96811,x96814),x96813),f326(f18(f917(x96814,a905),x96811),x96816))))
% 157.55/157.23 [9726]E(x97261,x97262)+~P105(f326(f326(f328(f916(f910(x97263),f910(x97263))),f326(f326(f251(f910(x97263),f910(x97263)),f326(f326(f151(x97263),x97261),x97265)),f326(f326(f151(x97263),x97262),x97266))),f145(x97263,x97264)))+P105(f326(f326(f328(f916(x97263,x97263)),f326(f326(f251(x97263,x97263),x97261),x97262)),x97264))
% 157.55/157.23 [9727]E(x97271,x97272)+~P105(f326(f326(f328(f916(f910(x97273),f910(x97273))),f326(f326(f251(f910(x97273),f910(x97273)),f326(f326(f151(x97273),x97271),x97275)),f326(f326(f151(x97273),x97272),x97276))),f147(x97273,x97274)))+P105(f326(f326(f328(f916(x97273,x97273)),f326(f326(f251(x97273,x97273),x97271),x97272)),x97274))
% 157.55/157.23 [9728]E(x97281,x97282)+~P105(f326(f326(f328(f916(f910(x97283),f910(x97283))),f326(f326(f251(f910(x97283),f910(x97283)),f326(f326(f151(x97283),x97281),x97285)),f326(f326(f151(x97283),x97282),x97286))),f157(x97283,x97284)))+P105(f326(f326(f328(f916(x97283,x97283)),f326(f326(f251(x97283,x97283),x97281),x97282)),x97284))
% 157.55/157.23 [9764]P105(f326(f326(f328(f916(f910(x97641),f910(x97641))),f326(f326(f251(f910(x97641),f910(x97641)),f326(f326(f151(x97641),x97642),x97643)),f326(f326(f151(x97641),x97644),x97645))),f158(x97641,x97646)))+~P105(f326(f326(f328(f916(f910(x97641),f910(x97641))),f326(f326(f251(f910(x97641),f910(x97641)),x97643),x97645)),f158(x97641,x97646)))+~P105(f326(f326(f328(f916(x97641,x97641)),f326(f326(f251(x97641,x97641),x97642),x97644)),x97646))
% 157.55/157.23 [9781]P105(f326(x97811,x97812))+~P105(f326(x97811,f468(x97811,x97813,x97814,x97815,x97816)))+~P105(f326(f326(f328(x97816),x97812),f326(f326(f40(x97815,f917(x97816,a905)),x97814),x97813)))
% 157.55/157.23 [9786]~P105(f326(f326(f328(f916(f910(x97861),f910(x97861))),f326(f326(f251(f910(x97861),f910(x97861)),f326(f326(f151(x97861),x97862),x97865)),f326(f326(f151(x97861),x97863),x97866))),f145(x97861,x97864)))+P105(f326(f326(f328(f916(f910(x97861),f910(x97861))),f326(f326(f251(f910(x97861),f910(x97861)),x97865),x97866)),f145(x97861,x97864)))+P105(f326(f326(f328(f916(x97861,x97861)),f326(f326(f251(x97861,x97861),x97862),x97863)),x97864))
% 157.55/157.23 [9787]~P105(f326(f326(f328(f916(f910(x97871),f910(x97871))),f326(f326(f251(f910(x97871),f910(x97871)),f326(f326(f151(x97871),x97872),x97875)),f326(f326(f151(x97871),x97873),x97876))),f147(x97871,x97874)))+P105(f326(f326(f328(f916(f910(x97871),f910(x97871))),f326(f326(f251(f910(x97871),f910(x97871)),x97875),x97876)),f147(x97871,x97874)))+P105(f326(f326(f328(f916(x97871,x97871)),f326(f326(f251(x97871,x97871),x97872),x97873)),x97874))
% 157.55/157.23 [9788]~P105(f326(f326(f328(f916(f910(x97881),f910(x97881))),f326(f326(f251(f910(x97881),f910(x97881)),f326(f326(f151(x97881),x97882),x97885)),f326(f326(f151(x97881),x97883),x97886))),f157(x97881,x97884)))+P105(f326(f326(f328(f916(f910(x97881),f910(x97881))),f326(f326(f251(f910(x97881),f910(x97881)),x97885),x97886)),f157(x97881,x97884)))+P105(f326(f326(f328(f916(x97881,x97881)),f326(f326(f251(x97881,x97881),x97882),x97883)),x97884))
% 157.55/157.23 [9877]P105(f326(x98771,x98772))+P105(f326(f326(f328(x98773),f469(x98771,x98774,x98775,x98773,x98776)),x98775))+~P105(f326(f326(f328(x98776),x98772),f326(f326(f40(x98773,f917(x98776,a905)),x98775),x98774)))
% 157.55/157.23 [9888]~E(x98882,x98884)+P105(f326(f326(f328(f916(f910(x98881),f910(x98881))),f326(f326(f251(f910(x98881),f910(x98881)),f326(f326(f134(x98881),x98882),f326(f326(f151(x98881),x98883),f113(x98881)))),f326(f326(f134(x98881),x98884),f326(f326(f151(x98881),x98885),f113(x98881))))),f157(x98881,x98886)))+~P105(f326(f326(f328(f916(x98881,x98881)),f326(f326(f251(x98881,x98881),x98883),x98885)),x98886))
% 157.55/157.23 [9962]E(x99621,x99622)+~P105(f326(f326(f328(f916(f910(x99623),f910(x99623))),f326(f326(f251(f910(x99623),f910(x99623)),f326(f326(f134(x99623),x99625),f326(f326(f151(x99623),x99621),f113(x99623)))),f326(f326(f134(x99623),x99626),f326(f326(f151(x99623),x99622),f113(x99623))))),f157(x99623,x99624)))+P105(f326(f326(f328(f916(x99623,x99623)),f326(f326(f251(x99623,x99623),x99621),x99622)),x99624))
% 157.55/157.23 [9993]~P105(f326(f326(f328(f916(f910(x99931),f910(x99931))),f326(f326(f251(f910(x99931),f910(x99931)),f326(f326(f134(x99931),x99935),f326(f326(f151(x99931),x99932),f113(x99931)))),f326(f326(f134(x99931),x99936),f326(f326(f151(x99931),x99933),f113(x99931))))),f157(x99931,x99934)))+P105(f326(f326(f328(f916(f910(x99931),f910(x99931))),f326(f326(f251(f910(x99931),f910(x99931)),x99935),x99936)),f157(x99931,x99934)))+P105(f326(f326(f328(f916(x99931,x99931)),f326(f326(f251(x99931,x99931),x99932),x99933)),x99934))
% 157.55/157.23 [10013]P105(f326(x100131,x100132))+P105(f326(f326(f328(x100133),f468(x100131,x100134,x100135,x100136,x100133)),f326(x100134,f469(x100131,x100134,x100135,x100136,x100133))))+~P105(f326(f326(f328(x100133),x100132),f326(f326(f40(x100136,f917(x100133,a905)),x100135),x100134)))
% 157.55/157.23 [10166]P105(f326(f326(f328(x101661),f833(x101662,x101663,x101664,x101665,x101666,x101661)),x101665))+~P105(f326(f326(f234(f917(x101661,a905)),x101666),x101665))+P105(f326(f326(f234(f917(x101664,a905)),f326(f326(f39(x101661,f917(x101664,a905)),x101665),x101663)),f326(f326(f39(x101661,f917(x101664,a905)),x101665),x101662)))
% 157.55/157.23 [10288]~P105(f326(f326(f234(f917(x102881,a905)),f326(x102884,f833(x102885,x102884,x102881,x102883,x102886,x102882))),f326(x102885,f833(x102885,x102884,x102881,x102883,x102886,x102882))))+~P105(f326(f326(f234(f917(x102882,a905)),x102886),x102883))+P105(f326(f326(f234(f917(x102881,a905)),f326(f326(f39(x102882,f917(x102881,a905)),x102883),x102884)),f326(f326(f39(x102882,f917(x102881,a905)),x102883),x102885)))
% 157.55/157.23 [9024]~P15(x90243,x90244,x90241)+~P105(f326(f61(x90243),x90246))+E(f326(f326(x90241,x90242),f326(f326(f64(x90243,x90244,x90241),x90245),f326(f326(f3(f917(x90243,a905)),x90246),f326(f326(f308(x90243),x90242),f188(f917(x90243,a905)))))),f326(f326(f64(x90243,x90244,x90241),x90245),f326(f326(f308(x90243),x90242),x90246)))
% 157.55/157.23 [9317]~P105(f326(f326(f328(x93175),x93173),x93176))+P105(f326(f326(f234(f917(x93171,a905)),f326(x93172,x93173)),x93174))+~P105(f326(f326(f234(f917(x93171,a905)),f326(f326(f40(x93175,f917(x93171,a905)),x93176),x93172)),x93174))
% 157.55/157.23 [9937]~P7(x99371,x99375,x99374)+P105(f326(f326(f328(f916(x99371,x99371)),f326(f326(f251(x99371,x99371),x99372),x99373)),x99374))+~P105(f326(f326(f328(x99371),x99376),f326(f326(f101(f917(x99371,a905)),f326(f284(x99371,x99371,x99374),f326(f326(f308(x99371),x99372),f188(f917(x99371,a905))))),f326(f284(x99371,x99371,x99374),f326(f326(f308(x99371),x99373),f188(f917(x99371,a905)))))))
% 157.55/157.23 [8746]~P110(x87462)+~E(f326(f326(f79(x87462),f326(f326(f80(x87462),x87464),x87465)),x87461),f326(f326(f79(x87462),f326(f326(f80(x87462),x87463),x87465)),x87466))+E(x87461,f326(f326(f79(x87462),f326(f326(f80(x87462),f326(f326(f3(x87462),x87463),x87464)),x87465)),x87466))
% 157.55/157.23 [8747]~P110(x87471)+~E(f326(f326(f79(x87471),f326(f326(f80(x87471),x87472),x87474)),x87475),f326(f326(f79(x87471),f326(f326(f80(x87471),x87473),x87474)),x87476))+E(f326(f326(f79(x87471),f326(f326(f80(x87471),f326(f326(f3(x87471),x87472),x87473)),x87474)),x87475),x87476)
% 157.55/157.23 [8929]~P110(x89291)+E(f326(f326(f79(x89291),f326(f326(f80(x89291),x89292),x89293)),x89294),f326(f326(f79(x89291),f326(f326(f80(x89291),x89295),x89293)),x89296))+~E(x89296,f326(f326(f79(x89291),f326(f326(f80(x89291),f326(f326(f3(x89291),x89292),x89295)),x89293)),x89294))
% 157.55/157.23 [8930]~P110(x89301)+E(f326(f326(f79(x89301),f326(f326(f80(x89301),x89302),x89303)),x89304),f326(f326(f79(x89301),f326(f326(f80(x89301),x89305),x89303)),x89306))+~E(f326(f326(f79(x89301),f326(f326(f80(x89301),f326(f326(f3(x89301),x89302),x89305)),x89303)),x89304),x89306)
% 157.55/157.23 [9254]~P105(f326(f326(x92544,x92545),x92546))+~P105(f326(f326(x92543,x92545),x92546))+P105(f326(f326(f326(f326(f101(f917(x92541,f917(x92542,a905))),x92543),x92544),x92545),x92546))
% 157.55/157.23 [9511]P105(f326(f326(x95111,x95112),x95113))+P105(f326(f326(x95114,x95112),x95113))+~P105(f326(f326(f326(f326(f110(f917(x95115,f917(x95116,a905))),x95114),x95111),x95112),x95113))
% 157.55/157.23 [9801]~P111(x98011)+~P105(f326(f326(f234(x98011),f326(f326(f79(x98011),f326(f326(f80(x98011),x98014),x98015)),x98012)),f326(f326(f79(x98011),f326(f326(f80(x98011),x98013),x98015)),x98016)))+P105(f326(f326(f234(x98011),x98012),f326(f326(f79(x98011),f326(f326(f80(x98011),f326(f326(f3(x98011),x98013),x98014)),x98015)),x98016)))
% 157.55/157.23 [9802]~P111(x98021)+~P105(f326(f326(f235(x98021),f326(f326(f79(x98021),f326(f326(f80(x98021),x98024),x98025)),x98022)),f326(f326(f79(x98021),f326(f326(f80(x98021),x98023),x98025)),x98026)))+P105(f326(f326(f235(x98021),x98022),f326(f326(f79(x98021),f326(f326(f80(x98021),f326(f326(f3(x98021),x98023),x98024)),x98025)),x98026)))
% 157.55/157.23 [9826]~P111(x98261)+P105(f326(f326(f234(x98261),f326(f326(f79(x98261),f326(f326(f80(x98261),x98262),x98263)),x98264)),f326(f326(f79(x98261),f326(f326(f80(x98261),x98265),x98263)),x98266)))+~P105(f326(f326(f234(x98261),x98264),f326(f326(f79(x98261),f326(f326(f80(x98261),f326(f326(f3(x98261),x98265),x98262)),x98263)),x98266)))
% 157.55/157.23 [9827]~P111(x98271)+P105(f326(f326(f235(x98271),f326(f326(f79(x98271),f326(f326(f80(x98271),x98272),x98273)),x98274)),f326(f326(f79(x98271),f326(f326(f80(x98271),x98275),x98273)),x98276)))+~P105(f326(f326(f235(x98271),x98274),f326(f326(f79(x98271),f326(f326(f80(x98271),f326(f326(f3(x98271),x98275),x98272)),x98273)),x98276)))
% 157.55/157.23 [9929]~P111(x99291)+~P105(f326(f326(f234(x99291),f326(f326(f79(x99291),f326(f326(f80(x99291),x99292),x99294)),x99295)),f326(f326(f79(x99291),f326(f326(f80(x99291),x99293),x99294)),x99296)))+P105(f326(f326(f234(x99291),f326(f326(f79(x99291),f326(f326(f80(x99291),f326(f326(f3(x99291),x99292),x99293)),x99294)),x99295)),x99296))
% 157.55/157.23 [9930]~P111(x99301)+~P105(f326(f326(f235(x99301),f326(f326(f79(x99301),f326(f326(f80(x99301),x99302),x99304)),x99305)),f326(f326(f79(x99301),f326(f326(f80(x99301),x99303),x99304)),x99306)))+P105(f326(f326(f235(x99301),f326(f326(f79(x99301),f326(f326(f80(x99301),f326(f326(f3(x99301),x99302),x99303)),x99304)),x99305)),x99306))
% 157.55/157.23 [9976]~P111(x99761)+P105(f326(f326(f234(x99761),f326(f326(f79(x99761),f326(f326(f80(x99761),x99762),x99763)),x99764)),f326(f326(f79(x99761),f326(f326(f80(x99761),x99765),x99763)),x99766)))+~P105(f326(f326(f234(x99761),f326(f326(f79(x99761),f326(f326(f80(x99761),f326(f326(f3(x99761),x99762),x99765)),x99763)),x99764)),x99766))
% 157.55/157.23 [9977]~P111(x99771)+P105(f326(f326(f235(x99771),f326(f326(f79(x99771),f326(f326(f80(x99771),x99772),x99773)),x99774)),f326(f326(f79(x99771),f326(f326(f80(x99771),x99775),x99773)),x99776)))+~P105(f326(f326(f235(x99771),f326(f326(f79(x99771),f326(f326(f80(x99771),f326(f326(f3(x99771),x99772),x99775)),x99773)),x99774)),x99776))
% 157.55/157.23 [10151]~P69(x101512)+~P105(f326(f61(x101511),x101516))+E(f326(f326(f8(x101511,x101512),f326(f326(f20(x101511,x101512,x101512),f326(f326(f20(x101511,x101512,f917(x101512,x101512)),f326(f326(f10(a905,f917(x101512,f917(x101512,x101512)),x101511),f96(x101512)),x101513)),x101514)),x101515)),x101516),f326(f326(f79(x101512),f326(f326(f8(x101511,x101512),x101514),f326(f326(f101(f917(x101511,a905)),x101516),f326(f261(x101511),x101513)))),f326(f326(f8(x101511,x101512),x101515),f326(f326(f101(f917(x101511,a905)),x101516),f326(f78(f917(x101511,a905)),f326(f261(x101511),x101513))))))
% 157.55/157.23 [10212]P105(f326(f326(f328(x102122),x102124),x102126))+P105(f326(f326(f328(x102122),x102125),x102126))+E(f326(f310(x102121,x102122,f326(f326(f9(x102121,x102122,x102122),f326(f326(f9(x102121,x102122,f917(x102122,x102122)),f326(f326(f10(a905,f917(x102122,f917(x102122,x102122)),x102121),f96(x102122)),f326(f326(f9(x102121,f917(x102121,a905),a905),f328(x102121)),x102123))),x102124)),x102125)),x102126),f188(f917(x102121,a905)))
% 157.55/157.23 [10213]P105(f326(f326(f328(x102132),x102135),x102136))+~P105(f326(f326(f328(x102132),x102134),x102136))+E(f326(f310(x102131,x102132,f326(f326(f9(x102131,x102132,x102132),f326(f326(f9(x102131,x102132,f917(x102132,x102132)),f326(f326(f10(a905,f917(x102132,f917(x102132,x102132)),x102131),f96(x102132)),f326(f326(f9(x102131,f917(x102131,a905),a905),f328(x102131)),x102133))),x102134)),x102135)),x102136),x102133)
% 157.55/157.23 [10214]P105(f326(f326(f328(x102142),x102144),x102146))+~P105(f326(f326(f328(x102142),x102145),x102146))+E(f326(f310(x102141,x102142,f326(f326(f9(x102141,x102142,x102142),f326(f326(f9(x102141,x102142,f917(x102142,x102142)),f326(f326(f10(a905,f917(x102142,f917(x102142,x102142)),x102141),f96(x102142)),f326(f326(f9(x102141,f917(x102141,a905),a905),f328(x102141)),x102143))),x102144)),x102145)),x102146),f326(f78(f917(x102141,a905)),x102143))
% 157.55/157.23 [10215]~P105(f326(f326(f328(x102152),x102154),x102156))+~P105(f326(f326(f328(x102152),x102155),x102156))+E(f326(f310(x102151,x102152,f326(f326(f9(x102151,x102152,x102152),f326(f326(f9(x102151,x102152,f917(x102152,x102152)),f326(f326(f10(a905,f917(x102152,f917(x102152,x102152)),x102151),f96(x102152)),f326(f326(f9(x102151,f917(x102151,a905),a905),f328(x102151)),x102153))),x102154)),x102155)),x102156),f241(f917(x102151,a905)))
% 157.55/157.23 [8779]E(x87791,x87792)+~P55(x87794,x87795,x87793,x87796,x87797)+~E(f326(x87793,x87791),f326(x87793,x87792))
% 157.55/157.23 [8808]~P9(x88086,x88085,x88087,x88084,x88081)+E(f326(f326(x88081,x88082),x88083),x88084)+P105(f326(f61(x88085),x88083))
% 157.55/157.23 [9668]P41(x96681,x96682,x96683,x96684,x96685,f326(f326(x96683,x96686),x96687))+~E(f326(f326(x96683,x96686),x96687),x96684)+~E(x96685,f188(f917(x96681,a905)))
% 157.55/157.23 [9848]~P105(f326(x98486,x98483))+~P105(f326(f326(f328(f916(x98482,x98482)),f326(f326(f251(x98482,x98482),x98484),x98485)),f326(x98487,x98483)))+P105(f326(f326(f328(f916(f916(x98481,x98482),f916(x98481,x98482))),f326(f326(f251(f916(x98481,x98482),f916(x98481,x98482)),f326(f326(f251(x98481,x98482),x98483),x98484)),f326(f326(f251(x98481,x98482),x98483),x98485))),f279(x98481,x98482,x98486,x98487)))
% 157.55/157.23 [10276]~P41(x102762,x102767,x102763,x102766,x102761,f326(f326(x102763,x102765),x102764))+E(f326(f326(x102763,f436(x102764,x102765,x102761,x102766,x102763,x102767,x102762)),f443(x102764,x102765,x102761,x102766,x102763,x102767,x102762)),f326(f326(x102763,x102765),x102764))+E(x102761,f188(f917(x102762,a905)))
% 157.55/157.23 [10277]~P41(x102777,x102776,x102771,x102774,x102775,f326(f326(x102771,x102772),x102773))+E(f326(f326(x102771,f436(x102773,x102772,x102775,x102774,x102771,x102776,x102777)),f443(x102773,x102772,x102775,x102774,x102771,x102776,x102777)),f326(f326(x102771,x102772),x102773))+E(f326(f326(x102771,x102772),x102773),x102774)
% 157.55/157.23 [9350]~P33(x93501,x93502,x93503,x93505,x93507)+P33(x93501,x93502,x93503,f326(f326(f151(x93501),x93504),x93505),f326(f326(f151(x93502),x93506),x93507))+~P105(f326(f326(x93503,x93504),x93506))
% 157.55/157.23 [9366]P33(x93661,x93662,x93663,x93664,x93665)+~P33(x93661,x93662,x93663,f326(f326(f134(x93661),x93666),x93664),f326(f326(f134(x93662),x93667),x93665))+~E(f326(f189(f910(x93661)),x93666),f326(f189(f910(x93662)),x93667))
% 157.55/157.23 [9367]P33(x93671,x93672,x93673,x93674,x93675)+~P33(x93671,x93672,x93673,f326(f326(f134(x93671),x93674),x93676),f326(f326(f134(x93672),x93675),x93677))+~E(f326(f189(f910(x93671)),x93674),f326(f189(f910(x93672)),x93675))
% 157.55/157.23 [9575]~P33(x95751,x95752,x95753,x95755,x95757)+~P33(x95751,x95752,x95753,x95754,x95756)+P33(x95751,x95752,x95753,f326(f326(f134(x95751),x95754),x95755),f326(f326(f134(x95752),x95756),x95757))
% 157.55/157.23 [9922]~P105(f326(f66(x99221,x99224,x99225,x99226,x99223),x99227))+P105(f326(f66(x99221,x99224,x99225,x99226,f326(f326(f308(x99221),x99222),x99223)),f326(f326(x99225,x99222),x99227)))+P105(f326(f326(f328(x99221),x99222),x99223))
% 157.55/157.23 [10304]~P41(x103042,x103047,x103046,x103045,x103041,f326(f326(x103046,x103044),x103043))+E(x103041,f188(f917(x103042,a905)))+P105(f326(f326(f328(x103042),f436(x103043,x103044,x103041,x103045,x103046,x103047,x103042)),x103041))
% 157.55/157.23 [10305]~P41(x103055,x103057,x103051,x103054,x103056,f326(f326(x103051,x103052),x103053))+E(f326(f326(x103051,x103052),x103053),x103054)+P105(f326(f326(f328(x103055),f436(x103053,x103052,x103056,x103054,x103051,x103057,x103055)),x103056))
% 157.55/157.23 [10395]E(f326(f326(f251(x103951,x103952),x103953),x103954),f326(f326(f251(x103951,x103952),x103955),x103956))+P105(f326(f326(f328(f916(f916(x103951,x103952),f916(x103951,x103952))),f326(f326(f251(f916(x103951,x103952),f916(x103951,x103952)),f326(f326(f251(x103951,x103952),f841(x103957,x103954,x103953,x103956,x103955,x103952,x103951)),f842(x103957,x103954,x103953,x103956,x103955,x103952,x103951))),f326(f326(f251(x103951,x103952),x103953),x103954))),f306(f916(x103951,x103952),x103957)))+~P105(f326(f326(f328(f916(f916(x103951,x103952),f916(x103951,x103952))),f326(f326(f251(f916(x103951,x103952),f916(x103951,x103952)),f326(f326(f251(x103951,x103952),x103955),x103956)),f326(f326(f251(x103951,x103952),x103953),x103954))),f306(f916(x103951,x103952),x103957)))
% 157.55/157.23 [9049]~P20(x90494,x90495,x90496,x90497,x90491)+~P105(f326(f61(x90495),x90493))+E(f326(f326(x90491,x90492),x90493),f326(f326(f326(f65(x90494,x90495,x90496),x90492),x90497),x90493))
% 157.55/157.23 [9050]~P9(x90504,x90505,x90506,x90507,x90501)+~P105(f326(f61(x90505),x90503))+E(f326(f326(x90501,x90502),x90503),f326(f326(f326(f65(x90504,x90505,x90506),x90502),x90507),x90503))
% 157.55/157.23 [9812]~P23(x98121,x98122,f326(f326(f308(f908(x98121)),f91(x98121,x98123,x98124,x98127)),f188(f917(f908(x98121),a905))))+P23(x98121,x98122,f326(f326(f308(f908(x98121)),f91(x98121,x98123,f30(x98124,x98125),x98126)),f188(f917(f908(x98121),a905))))+~P23(x98121,x98122,f326(f326(f308(f908(x98121)),f91(x98121,x98127,x98125,x98126)),f188(f917(f908(x98121),a905))))
% 157.55/157.23 [9821]~P22(x98213,x98214,x98215,x98217,x98216,x98211)+~P105(f326(f61(x98214),x98212))+E(f326(x98211,x98212),f326(f326(f326(f65(x98213,x98214,x98215),x98216),x98217),x98212))
% 157.55/157.23 [9971]P41(x99711,x99712,x99713,x99714,x99715,f326(f326(x99713,x99716),x99717))+~P41(x99711,x99712,x99713,x99714,f326(f326(f3(f917(x99711,a905)),x99715),f326(f326(f308(x99711),x99716),f188(f917(x99711,a905)))),x99717)+~P105(f326(f326(f328(x99711),x99716),x99715))
% 157.55/157.23 [10097]~P23(x100971,x100972,f326(f326(f308(f908(x100971)),f91(x100971,f92(x100971,x100973,x100974),x100975,x100977)),f188(f917(f908(x100971),a905))))+P23(x100971,x100972,f326(f326(f308(f908(x100971)),f91(x100971,x100973,f27(x100974,x100975,x100976),x100977)),f188(f917(f908(x100971),a905))))+~P23(x100971,x100972,f326(f326(f308(f908(x100971)),f91(x100971,f92(x100971,x100973,f326(f72(a905,a905,a907,a321),x100974)),x100976,x100977)),f188(f917(f908(x100971),a905))))
% 157.55/157.23 [10329]P105(f326(f326(x103297,f782(x103294,x103295,x103291,x103296,x103293,x103292,x103297)),f783(x103294,x103295,x103291,x103296,x103293,x103292,x103297)))+~P105(f326(f326(x103297,f326(f255(x103292,x103293),x103296)),f326(f250(x103292,x103293),x103296)))+P105(f326(x103291,f326(f326(f256(x103292,x103293,x103294),x103295),x103296)))
% 157.55/157.23 [10330]P23(x103307,x103306,f326(f326(f308(f908(x103307)),f91(x103307,x103301,x103304,x103302)),f188(f917(f908(x103307),a905))))+~P23(x103307,x103306,f326(f326(f308(f908(x103307)),f91(x103307,x103305,x103304,x103303)),f188(f917(f908(x103307),a905))))+P105(f326(f326(x103301,f780(x103302,x103301,x103303,x103304,x103305,x103306,x103307)),f864(x103302,x103301,x103303,x103304,x103305,x103306,x103307)))
% 157.55/157.23 [10340]~P41(x103402,x103403,x103404,x103405,x103401,f326(f326(x103404,x103407),x103406))+P41(x103402,x103403,x103404,x103405,f326(f326(f3(f917(x103402,a905)),x103401),f326(f326(f308(x103402),f436(x103406,x103407,x103401,x103405,x103404,x103403,x103402)),f188(f917(x103402,a905)))),f443(x103406,x103407,x103401,x103405,x103404,x103403,x103402))+E(x103401,f188(f917(x103402,a905)))
% 157.55/157.23 [10341]~P41(x103415,x103416,x103411,x103414,x103417,f326(f326(x103411,x103412),x103413))+P41(x103415,x103416,x103411,x103414,f326(f326(f3(f917(x103415,a905)),x103417),f326(f326(f308(x103415),f436(x103413,x103412,x103417,x103414,x103411,x103416,x103415)),f188(f917(x103415,a905)))),f443(x103413,x103412,x103417,x103414,x103411,x103416,x103415))+E(f326(f326(x103411,x103412),x103413),x103414)
% 157.55/157.23 [10342]~P23(x103421,x103422,f326(f326(f308(f908(x103421)),f91(x103421,x103427,x103424,x103426)),f188(f917(f908(x103421),a905))))+P23(x103421,x103422,f326(f326(f308(f908(x103421)),f91(x103421,x103423,x103424,x103425)),f188(f917(f908(x103421),a905))))+~P105(f326(f326(x103425,f780(x103425,x103423,x103426,x103424,x103427,x103422,x103421)),f873(x103425,x103423,x103426,x103424,x103427,x103422,x103421)))
% 157.55/157.23 [10362]~P105(f326(x103621,f326(f326(x103625,f783(x103624,x103625,x103621,x103626,x103623,x103622,x103627)),f782(x103624,x103625,x103621,x103626,x103623,x103622,x103627))))+~P105(f326(f326(x103627,f326(f255(x103622,x103623),x103626)),f326(f250(x103622,x103623),x103626)))+P105(f326(x103621,f326(f326(f256(x103622,x103623,x103624),x103625),x103626)))
% 157.55/157.23 [9653]P105(f326(f326(f234(f917(f916(x96531,x96532),a905)),f326(f326(f288(x96531,x96533,x96532),x96534),x96535)),f326(f326(f288(x96531,x96533,x96532),x96536),x96537)))+~P105(f326(f326(f234(f917(f916(x96533,x96532),a905)),x96535),x96537))+~P105(f326(f326(f234(f917(f916(x96531,x96533),a905)),x96534),x96536))
% 157.55/157.23 [10389]E(f326(f326(f251(x103891,x103892),x103893),x103894),f326(f326(f251(x103891,x103892),x103895),x103896))+~P105(f326(f326(f328(f916(f916(x103891,x103892),f916(x103891,x103892))),f326(f326(f251(f916(x103891,x103892),f916(x103891,x103892)),f326(f326(f251(x103891,x103892),x103893),x103894)),f326(f326(f251(x103891,x103892),x103895),x103896))),f306(f916(x103891,x103892),x103897)))+P105(f326(f326(f328(f916(f916(x103891,x103892),f916(x103891,x103892))),f326(f326(f251(f916(x103891,x103892),f916(x103891,x103892)),f326(f326(f251(x103891,x103892),x103893),x103894)),f326(f326(f251(x103891,x103892),f841(x103897,x103896,x103895,x103894,x103893,x103892,x103891)),f842(x103897,x103896,x103895,x103894,x103893,x103892,x103891)))),x103897))
% 157.55/157.23 [9982]~P105(f326(f326(f328(x99821),x99826),x99825))+P105(f326(f66(x99821,x99822,x99823,x99824,x99825),f326(f326(x99823,x99826),x99827)))+~P105(f326(f66(x99821,x99822,x99823,x99824,f326(f326(f3(f917(x99821,a905)),x99825),f326(f326(f308(x99821),x99826),f188(f917(x99821,a905))))),x99827))
% 157.55/157.23 [10402]~P144(x104021)+~P24(f916(x104022,x104023),x104021,f326(f256(x104022,x104023,x104021),f326(f326(f9(x104022,f917(x104023,x104021),f917(x104023,x104021)),f326(f326(f10(f917(x104021,x104021),f917(f917(x104023,x104021),f917(x104023,x104021)),x104022),f10(x104021,x104021,x104023)),f326(f326(f10(x104021,f917(x104021,x104021),x104022),f80(x104021)),x104024))),x104025)),f326(f326(f253(x104022,x104023),x104026),f326(f18(f917(x104023,a905),x104022),x104027)))+E(f326(f326(f8(x104021,x104021),f31(x104021)),f326(f261(x104021),f326(f326(f10(f917(x104022,a905),a905,x104021),f86(x104022)),f326(f326(f10(f917(x104022,f917(x104023,a905)),f917(x104022,a905),x104021),f326(f10(f917(x104023,a905),a905,x104022),f86(x104023))),f326(f326(f9(x104021,f917(x104022,f917(x104023,a905)),f917(x104022,f917(x104023,a905))),f326(f326(f10(f917(x104022,f917(f917(x104023,a905),f917(x104023,a905))),f917(f917(x104022,f917(x104023,a905)),f917(x104022,f917(x104023,a905))),x104021),f20(x104022,f917(x104023,a905),f917(x104023,a905))),f326(f326(f10(f917(x104022,f917(x104023,f917(a905,a905))),f917(x104022,f917(f917(x104023,a905),f917(x104023,a905))),x104021),f326(f10(f917(x104023,f917(a905,a905)),f917(f917(x104023,a905),f917(x104023,a905)),x104022),f20(x104023,a905,a905))),f326(f326(f10(f917(x104022,f917(x104023,a905)),f917(x104022,f917(x104023,f917(a905,a905))),x104021),f326(f10(f917(x104023,a905),f917(x104023,f917(a905,a905)),x104022),f326(f10(a905,f917(a905,a905),x104023),a324))),f326(f326(f9(x104021,f917(x104022,f917(x104023,x104021)),f917(x104022,f917(x104023,a905))),f326(f326(f10(f917(f917(x104023,x104021),f917(x104023,a905)),f917(f917(x104022,f917(x104023,x104021)),f917(x104022,f917(x104023,a905))),x104021),f10(f917(x104023,x104021),f917(x104023,a905),x104022)),f326(f326(f10(f917(x104021,a905),f917(f917(x104023,x104021),f917(x104023,a905)),x104021),f10(x104021,a905,x104023)),a323))),f326(f326(f9(x104022,f917(x104023,x104021),f917(x104023,x104021)),f326(f326(f10(f917(x104021,x104021),f917(f917(x104023,x104021),f917(x104023,x104021)),x104022),f10(x104021,x104021,x104023)),f326(f326(f10(x104021,f917(x104021,x104021),x104022),f80(x104021)),x104024))),x104025)))))),f326(f326(f9(x104022,f917(x104023,a905),f917(x104023,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x104023,a905),f917(x104023,a905)),x104022),f10(a905,a905,x104023)),f326(f326(f10(a905,f917(a905,a905),x104022),a324),f326(f326(f9(x104022,f917(x104022,a905),a905),f328(x104022)),x104026)))),f326(f326(f9(x104023,f917(x104023,a905),a905),f328(x104023)),x104027))))))),f326(f326(f80(x104021),f326(f326(f8(x104022,x104021),x104024),x104026)),f326(f326(f8(x104023,x104021),x104025),x104027)))
% 157.55/157.23 [9657]~P25(x96571,x96573,x96575,x96576,x96578)+~P25(x96573,x96572,x96574,x96578,x96577)+P25(x96571,x96572,f326(f72(x96573,x96572,x96571,x96574),x96575),x96576,x96577)
% 157.55/157.23 [9686]P25(x96861,x96862,x96863,x96864,x96865)+~P25(x96866,x96861,x96867,x96868,x96864)+~P25(x96866,x96862,f326(f72(x96861,x96862,x96866,x96863),x96867),x96868,x96865)
% 157.55/157.23 [9819]~P105(f326(f326(x98194,x98196),x98198))+~P105(f326(f326(x98195,x98198),x98197))+P105(f326(f326(f252(x98191,x98192,x98193,x98194,x98195),x98196),x98197))
% 157.55/157.23 [9418]~P18(x94188,x94181,x94183,x94185)+~P105(f326(f61(x94188),x94186))+E(f326(f72(x94181,x94181,x94182,f326(x94183,x94184)),f326(f72(x94181,x94181,x94182,f326(x94185,x94186)),x94187)),f326(f72(x94181,x94181,x94182,f326(x94185,x94186)),f326(f72(x94181,x94181,x94182,f326(x94183,x94184)),x94187)))
% 157.55/157.23 [9808]~P21(x98087,x98082,x98085,x98088,x98086,x98081)+~P105(f326(f61(x98082),x98084))+E(f326(x98081,f326(f326(f308(x98082),x98083),x98084)),f326(f326(x98085,f326(x98086,x98083)),f326(x98081,x98084)))
% 157.55/157.23 [9927]~P24(x99272,x99274,x99276,x99278)+~P24(x99271,x99273,x99275,x99277)+P24(f916(x99271,x99272),f916(x99273,x99274),f257(x99271,x99273,x99272,x99274,x99275,x99276),f326(f326(f253(x99271,x99272),x99277),f326(f18(f917(x99272,a905),x99271),x99278)))
% 157.55/157.23 [9601]P105(f326(f326(f328(f916(x96011,x96012)),f326(f326(f251(x96011,x96012),x96013),x96014)),f326(f326(f288(x96011,x96015,x96012),x96016),x96017)))+~P105(f326(f326(f328(f916(x96011,x96015)),f326(f326(f251(x96011,x96015),x96013),x96018)),x96016))+~P105(f326(f326(f328(f916(x96015,x96012)),f326(f326(f251(x96015,x96012),x96018),x96014)),x96017))
% 157.55/157.23 [9789]~P105(f326(f326(f234(f917(f916(x97893,x97892),a905)),x97895),f326(f326(f253(x97893,x97892),x97898),f326(f18(f917(x97892,a905),x97893),x97897))))+~P105(f326(f326(f234(f917(f916(x97891,x97893),a905)),x97894),f326(f326(f253(x97891,x97893),x97896),f326(f18(f917(x97893,a905),x97891),x97898))))+P105(f326(f326(f234(f917(f916(x97891,x97892),a905)),f326(f326(f288(x97891,x97893,x97892),x97894),x97895)),f326(f326(f253(x97891,x97892),x97896),f326(f18(f917(x97892,a905),x97891),x97897))))
% 157.55/157.23 [9843]~E(x98433,x98435)+P105(f326(f326(f328(f916(f916(x98431,x98432),f916(x98431,x98432))),f326(f326(f251(f916(x98431,x98432),f916(x98431,x98432)),f326(f326(f251(x98431,x98432),x98433),x98434)),f326(f326(f251(x98431,x98432),x98435),x98436))),f319(x98431,x98432,x98437,x98438)))+~P105(f326(f326(f328(f916(x98432,x98432)),f326(f326(f251(x98432,x98432),x98434),x98436)),x98438))
% 157.55/157.23 [9946]E(x99461,x99462)+~P105(f326(f326(f328(f916(f916(x99463,x99465),f916(x99463,x99465))),f326(f326(f251(f916(x99463,x99465),f916(x99463,x99465)),f326(f326(f251(x99463,x99465),x99461),x99466)),f326(f326(f251(x99463,x99465),x99462),x99467))),f319(x99463,x99465,x99464,x99468)))+P105(f326(f326(f328(f916(x99463,x99463)),f326(f326(f251(x99463,x99463),x99461),x99462)),x99464))
% 157.55/157.23 [9961]~P105(f326(f326(f328(f916(f916(x99611,x99615),f916(x99611,x99615))),f326(f326(f251(f916(x99611,x99615),f916(x99611,x99615)),f326(f326(f251(x99611,x99615),x99612),x99616)),f326(f326(f251(x99611,x99615),x99613),x99617))),f319(x99611,x99615,x99614,x99618)))+P105(f326(f326(f328(f916(x99611,x99611)),f326(f326(f251(x99611,x99611),x99612),x99613)),x99614))+P105(f326(f326(f328(f916(x99615,x99615)),f326(f326(f251(x99615,x99615),x99616),x99617)),x99618))
% 157.55/157.23 [9878]~P22(x98787,x98785,x98781,x98788,x98782,x98784)+~P105(f326(f61(x98785),x98786))+E(f326(f326(x98781,f326(x98782,x98783)),f326(x98784,f326(f326(f3(f917(x98785,a905)),x98786),f326(f326(f308(x98785),x98783),f188(f917(x98785,a905)))))),f326(x98784,f326(f326(f308(x98785),x98783),x98786)))
% 157.55/157.23 [9372]~P105(f326(f326(f326(x93725,x93728),x93726),x93727))+~P105(f326(f326(f328(x93721),x93728),x93724))+P105(f326(f326(f326(f326(f40(x93721,f917(x93722,f917(x93723,a905))),x93724),x93725),x93726),x93727))
% 157.55/157.23 [9586]P105(f326(f326(f326(x95861,x95862),x95863),x95864))+~P105(f326(f326(f328(x95865),x95862),x95866))+~P105(f326(f326(f326(f326(f39(x95865,f917(x95867,f917(x95868,a905))),x95866),x95861),x95863),x95864))
% 157.55/157.23 [9782]~P20(x97823,x97822,x97824,x97828,x97821)+~P105(f326(f61(x97822),x97827))+E(f326(f326(x97821,f326(f326(f20(x97822,x97823,x97823),f326(f326(f10(x97823,f917(x97823,x97823),x97822),x97824),x97825)),x97826)),x97827),f326(f326(x97824,f326(f326(x97821,x97825),x97827)),f326(f326(x97821,x97826),x97827)))
% 157.55/157.23 [10048]~E(f326(f309(x100482,x100484,x100486),x100488),x1004810)+~E(f326(f309(x100481,x100483,x100485),x100487),x100489)+E(f326(f309(f916(x100481,x100482),f916(x100483,x100484),f257(x100481,x100483,x100482,x100484,x100485,x100486)),f326(f326(f253(x100481,x100482),x100487),f326(f18(f917(x100482,a905),x100481),x100488))),f326(f326(f253(x100483,x100484),x100489),f326(f18(f917(x100484,a905),x100483),x1004810)))
% 157.55/157.23 [5022]~P42(x50221,x50222)+~P48(x50221,x50222)+~P49(x50221,x50222)+P6(x50221,x50222)
% 157.55/157.23 [4978]~P108(x49782)+~P12(x49782,x49781)+P12(x49782,f114(x49782,x49781))+E(x49781,f113(x49782))
% 157.55/157.23 [4979]~P108(x49792)+~P12(x49792,x49791)+P12(x49792,f702(x49791,x49792))+E(x49791,f113(x49792))
% 157.55/157.23 [5226]~P4(x52262)+E(f12(x52262,x52261),f37(x52262,x52261))+E(x52261,f188(f917(x52262,a905)))+~P105(f326(f61(x52262),x52261))
% 157.55/157.23 [5227]~P4(x52272)+E(f13(x52272,x52271),f38(x52272,x52271))+E(x52271,f188(f917(x52272,a905)))+~P105(f326(f61(x52272),x52271))
% 157.55/157.23 [5385]~P108(x53852)+~P12(x53852,x53851)+E(x53851,f113(x53852))+E(f326(f326(f151(x53852),f721(x53851,x53852)),f702(x53851,x53852)),x53851)
% 157.55/157.23 [6208]~P77(x62082)+E(x62081,f188(f917(x62082,a905)))+P105(f326(f326(f234(x62082),f13(x62082,x62081)),f12(x62082,x62081)))+~P105(f326(f61(x62082),x62081))
% 157.55/157.23 [6219]~P39(x62192)+~P39(x62191)+E(x62191,x62192)+~E(f326(f309(a1,a909,a104),x62191),f326(f309(a1,a909,a104),x62192))
% 157.55/157.23 [9233]~P118(x92331)+~P105(f326(f326(f328(x92331),x92332),f109(x92331)))+P105(f326(f326(f235(x92331),f326(f326(f79(x92331),f326(f326(f79(x92331),f77(x92331)),x92332)),x92332)),f2(x92331)))+~P105(f326(f326(f235(x92331),x92332),f2(x92331)))
% 157.55/157.23 [9471]~P118(x94711)+~P105(f326(f326(f328(x94711),x94712),f109(x94711)))+~P105(f326(f326(f235(x94711),f326(f326(f79(x94711),f326(f326(f79(x94711),f77(x94711)),x94712)),x94712)),f2(x94711)))+P105(f326(f326(f235(x94711),x94712),f2(x94711)))
% 157.55/157.23 [5037]~P115(x50372)+~P144(x50372)+E(x50371,f2(a909))+E(f326(f326(f243(x50372),f2(x50372)),x50371),f2(x50372))
% 157.55/157.23 [5040]~P115(x50401)+~P144(x50401)+~E(x50402,f2(a909))+E(f326(f326(f243(x50401),f2(x50401)),x50402),f77(x50401))
% 157.55/157.23 [5212]~P141(x52122)+E(x52121,f77(x52122))+E(x52121,f326(f78(x52122),f77(x52122)))+~E(f326(f326(f80(x52122),x52121),x52121),f77(x52122))
% 157.55/157.23 [5467]~P90(x54672)+E(x54671,f2(x54672))+E(f81(x54672,x54671),f326(f78(x54672),f77(x54672)))+P105(f326(f326(f235(x54672),f2(x54672)),x54671))
% 157.55/157.23 [5711]~P90(x57112)+E(f81(x57112,x57111),f77(x57112))+E(x57111,f2(x57112))+~P105(f326(f326(f235(x57112),f2(x57112)),x57111))
% 157.55/157.23 [5720]E(x57201,x57202)+~E(f326(f103(a909),x57201),f326(f103(a909),x57202))+P105(f326(a193,f326(f103(a1),x57202)))+P105(f326(a193,f326(f103(a1),x57201)))
% 157.55/157.23 [5771]~P92(x57711)+~E(x57712,f2(x57711))+E(f326(f326(f79(x57711),x57712),x57712),f2(x57711))+~P105(f326(f326(f328(x57711),x57712),f109(x57711)))
% 157.55/157.23 [5810]E(x58101,f2(a1))+~E(f326(f326(f36(a1),x58102),x58101),f2(a1))+P105(f326(f326(f235(a1),x58101),x58102))+P105(f326(f326(f235(a1),x58102),x58101))
% 157.55/157.23 [5840]E(x58401,f2(a1))+~E(f326(f326(f36(a1),x58402),x58401),f2(a1))+P105(f326(f326(f234(a1),x58402),f2(a1)))+P105(f326(f326(f235(a1),x58402),x58401))
% 157.55/157.23 [5874]E(x58741,f2(a1))+~E(f326(f326(f36(a1),x58742),x58741),f2(a1))+P105(f326(f326(f234(a1),f2(a1)),x58742))+P105(f326(f326(f235(a1),x58741),x58742))
% 157.55/157.23 [5909]~P92(x59092)+E(x59091,f2(x59092))+~E(f326(f326(f79(x59092),x59091),x59091),f2(x59092))+~P105(f326(f326(f328(x59092),x59091),f109(x59092)))
% 157.55/157.23 [5980]E(f326(f103(a909),x59801),f326(f103(a909),x59802))+~E(f326(f103(a1),x59802),f2(a1))+P105(f326(a193,f326(f103(a1),x59802)))+~P105(f326(a193,f326(f103(a1),x59801)))
% 157.55/157.23 [6009]~E(f326(f103(a909),x60092),f326(f103(a909),x60091))+E(f326(f103(a1),x60091),f2(a1))+P105(f326(a193,f326(f103(a1),x60091)))+~P105(f326(a193,f326(f103(a1),x60092)))
% 157.55/157.23 [6019]~P108(x60192)+E(x60191,f188(f917(x60192,a905)))+~P105(f326(f61(x60192),x60191))+P105(f326(f326(f328(x60192),f16(x60192,x60191)),x60191))
% 157.55/157.23 [6020]~P108(x60202)+E(x60201,f188(f917(x60202,a905)))+~P105(f326(f61(x60202),x60201))+P105(f326(f326(f328(x60202),f17(x60202,x60201)),x60201))
% 157.55/157.23 [6185]~P118(x61851)+~P94(x61851)+P105(f326(f326(f234(x61851),f2(x61851)),f326(f103(x61851),x61852)))+~P105(f326(f326(f234(a1),a82),x61852))
% 157.55/157.23 [6186]~P118(x61861)+~P94(x61861)+P105(f326(f326(f235(x61861),f2(x61861)),f326(f103(x61861),x61862)))+~P105(f326(f326(f235(a1),a82),x61862))
% 157.55/157.23 [6207]~P118(x62071)+~P94(x62071)+E(f326(f75(x62071),f326(f103(x62071),x62072)),f326(f103(x62071),x62072))+P105(f326(f326(f235(x62071),f326(f103(x62071),x62072)),f2(x62071)))
% 157.55/157.23 [6243]E(x62431,x62432)+~E(f326(a104,x62431),f326(a104,x62432))+~P105(f326(f326(f234(a1),f2(a1)),x62432))+~P105(f326(f326(f234(a1),f2(a1)),x62431))
% 157.55/157.23 [6439]~P94(x64392)+~P118(x64392)+~P105(f326(f326(f234(x64392),f2(x64392)),f326(f103(x64392),x64391)))+P105(f326(f326(f234(a1),a82),x64391))
% 157.55/157.23 [6440]~P94(x64402)+~P118(x64402)+~P105(f326(f326(f235(x64402),f2(x64402)),f326(f103(x64402),x64401)))+P105(f326(f326(f235(a1),a82),x64401))
% 157.55/157.23 [6445]~P118(x64451)+~P94(x64451)+P105(f326(f326(f234(x64451),f326(f103(x64451),x64452)),f2(x64451)))+~P105(f326(f326(f234(a1),x64452),a82))
% 157.55/157.23 [6446]~P118(x64461)+~P94(x64461)+P105(f326(f326(f235(x64461),f326(f103(x64461),x64462)),f2(x64461)))+~P105(f326(f326(f235(a1),x64462),a82))
% 157.55/157.23 [6763]~P94(x67632)+~P118(x67632)+~P105(f326(f326(f234(x67632),f326(f103(x67632),x67631)),f2(x67632)))+P105(f326(f326(f234(a1),x67631),a82))
% 157.55/157.23 [6764]~P94(x67642)+~P118(x67642)+~P105(f326(f326(f235(x67642),f326(f103(x67642),x67641)),f2(x67642)))+P105(f326(f326(f235(a1),x67641),a82))
% 157.55/157.23 [6857]~P118(x68571)+~P94(x68571)+E(f326(f75(x68571),f326(f103(x68571),x68572)),f326(f78(x68571),f326(f103(x68571),x68572)))+~P105(f326(f326(f235(x68571),f326(f103(x68571),x68572)),f2(x68571)))
% 157.55/157.23 [6876]E(f326(f103(a909),x68761),f326(f103(a909),x68762))+~E(f326(f103(a1),x68762),f2(a1))+~P105(f326(f326(f234(a1),f326(f103(a1),x68761)),f2(a1)))+~P105(f326(a193,f326(f103(a1),x68761)))
% 157.55/157.23 [7751]~P108(x77512)+E(x77511,f188(f917(x77512,a905)))+~P105(f326(f61(x77512),x77511))+P105(f326(f326(f234(x77512),f14(x77512,f232(x77512),x77511)),f15(x77512,f233(x77512),x77511)))
% 157.55/157.23 [8063]~P5(x80631)+~P39(x80632)+P105(f326(f326(f328(a1),x80631),x80632))+~P105(f326(f326(f328(a909),f326(a104,x80631)),f326(f309(a1,a909,a104),x80632)))
% 157.55/157.23 [6015]~P140(x60152)+E(x60151,f2(a1))+E(f326(f78(x60152),f326(f102(x60152),f326(f78(a1),x60151))),f326(f102(x60152),x60151))+~P105(f326(f326(f235(a1),x60151),f2(a1)))
% 157.55/157.23 [6089]~P92(x60891)+~P94(x60891)+~P27(x60891,f326(f103(x60891),x60892))+P27(x60891,f326(f103(x60891),f326(f326(f79(a1),x60892),x60892)))
% 157.55/157.23 [6428]~P75(x64282)+E(x64281,f188(f917(x64282,a905)))+E(f17(x64282,f326(f309(x64282,x64282,f78(x64282)),x64281)),f326(f78(x64282),f16(x64282,x64281)))+~P105(f326(f61(x64282),x64281))
% 157.55/157.23 [6429]~P75(x64292)+E(x64291,f188(f917(x64292,a905)))+E(f16(x64292,f326(f309(x64292,x64292,f78(x64292)),x64291)),f326(f78(x64292),f17(x64292,x64291)))+~P105(f326(f61(x64292),x64291))
% 157.55/157.23 [6462]~P92(x64621)+~P94(x64621)+P27(x64621,f326(f103(x64621),x64622))+~P27(x64621,f326(f103(x64621),f326(f326(f79(a1),x64622),x64622)))
% 157.55/157.23 [6555]E(x65551,f2(a1))+E(f326(a51,f50(f326(f78(a1),x65551),f326(f78(a1),x65552))),f46(x65551,x65552))+P105(f326(f326(f234(a1),f2(a1)),x65552))+~P105(f326(f326(f234(a1),f2(a1)),x65551))
% 157.55/157.23 [8836]~P39(x88362)+~P39(x88361)+P105(f326(f326(f235(f917(a909,a905)),f326(f309(a1,a909,a104),x88361)),f326(f309(a1,a909,a104),x88362)))+~P105(f326(f326(f235(f917(a1,a905)),x88361),x88362))
% 157.55/157.23 [9067]~E(f724(x90672,x90671),f725(x90672,x90671))+~P105(f326(f137(x90671),f726(x90672,x90671)))+~P105(f326(f137(f910(x90671)),x90672))+P105(f326(f137(x90671),f326(f142(f910(x90671),f910(x90671),f134(x90671),f113(x90671)),x90672)))
% 157.55/157.23 [9153]~P39(x91532)+~P39(x91531)+~P105(f326(f326(f234(f917(a909,a905)),f326(f309(a1,a909,a104),x91531)),f326(f309(a1,a909,a104),x91532)))+P105(f326(f326(f234(f917(a1,a905)),x91531),x91532))
% 157.55/157.23 [9154]~P39(x91542)+~P39(x91541)+~P105(f326(f326(f235(f917(a909,a905)),f326(f309(a1,a909,a104),x91541)),f326(f309(a1,a909,a104),x91542)))+P105(f326(f326(f235(f917(a1,a905)),x91541),x91542))
% 157.55/157.23 [9160]~E(f724(x91602,x91601),f725(x91602,x91601))+~P105(f326(f137(f910(x91601)),x91602))+P105(f326(f137(x91601),f326(f142(f910(x91601),f910(x91601),f134(x91601),f113(x91601)),x91602)))+P105(f326(f326(f328(f910(x91601)),f726(x91602,x91601)),f326(f172(f910(x91601)),x91602)))
% 157.55/157.23 [9201]~P105(f326(f137(x92011),f726(x92012,x92011)))+~P105(f326(f137(f910(x92011)),x92012))+P105(f326(f137(x92011),f326(f142(f910(x92011),f910(x92011),f134(x92011),f113(x92011)),x92012)))+P105(f326(f326(f328(f910(x92011)),f725(x92012,x92011)),f326(f172(f910(x92011)),x92012)))
% 157.55/157.23 [9202]~P105(f326(f137(x92021),f726(x92022,x92021)))+~P105(f326(f137(f910(x92021)),x92022))+P105(f326(f137(x92021),f326(f142(f910(x92021),f910(x92021),f134(x92021),f113(x92021)),x92022)))+P105(f326(f326(f328(f910(x92021)),f724(x92022,x92021)),f326(f172(f910(x92021)),x92022)))
% 157.55/157.23 [9279]~P105(f326(f137(f910(x92791)),x92792))+P105(f326(f137(x92791),f326(f142(f910(x92791),f910(x92791),f134(x92791),f113(x92791)),x92792)))+P105(f326(f326(f328(f910(x92791)),f725(x92792,x92791)),f326(f172(f910(x92791)),x92792)))+P105(f326(f326(f328(f910(x92791)),f726(x92792,x92791)),f326(f172(f910(x92791)),x92792)))
% 157.55/157.23 [9280]~P105(f326(f137(f910(x92801)),x92802))+P105(f326(f137(x92801),f326(f142(f910(x92801),f910(x92801),f134(x92801),f113(x92801)),x92802)))+P105(f326(f326(f328(f910(x92801)),f724(x92802,x92801)),f326(f172(f910(x92801)),x92802)))+P105(f326(f326(f328(f910(x92801)),f726(x92802,x92801)),f326(f172(f910(x92801)),x92802)))
% 157.55/157.23 [9294]~E(f326(f326(f101(f917(x92941,a905)),f326(f172(x92941),f725(x92942,x92941))),f326(f172(x92941),f724(x92942,x92941))),f188(f917(x92941,a905)))+~P105(f326(f137(x92941),f726(x92942,x92941)))+~P105(f326(f137(f910(x92941)),x92942))+P105(f326(f137(x92941),f326(f142(f910(x92941),f910(x92941),f134(x92941),f113(x92941)),x92942)))
% 157.55/157.23 [9354]~E(f326(f326(f101(f917(x93541,a905)),f326(f172(x93541),f725(x93542,x93541))),f326(f172(x93541),f724(x93542,x93541))),f188(f917(x93541,a905)))+~P105(f326(f137(f910(x93541)),x93542))+P105(f326(f137(x93541),f326(f142(f910(x93541),f910(x93541),f134(x93541),f113(x93541)),x93542)))+P105(f326(f326(f328(f910(x93541)),f726(x93542,x93541)),f326(f172(f910(x93541)),x93542)))
% 157.55/157.23 [9626]E(x96261,f2(a1))+E(x96262,f2(a1))+E(f326(f326(f85(a1,f916(a1,a1)),f326(f326(a217,x96262),x96261)),f326(f326(f20(a1,a1,f916(a1,a1)),f326(f326(f10(a1,f917(a1,f916(a1,a1)),a1),f251(a1,a1)),f326(f36(a1),x96262))),f326(f36(a1),x96261))),f215(x96262,x96261))+P105(f326(f326(f235(a1),x96261),f2(a1)))
% 157.55/157.23 [8384]~P94(x83842)+~P118(x83842)+~P105(f326(f326(f234(x83842),f326(f103(x83842),x83841)),f77(x83842)))+P105(f326(f326(f234(a1),x83841),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))
% 157.55/157.23 [8385]~P94(x83852)+~P118(x83852)+~P105(f326(f326(f235(x83852),f326(f103(x83852),x83851)),f77(x83852)))+P105(f326(f326(f235(a1),x83851),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))
% 157.55/157.23 [8653]~P118(x86531)+~P94(x86531)+P105(f326(f326(f234(x86531),f326(f103(x86531),x86532)),f77(x86531)))+~P105(f326(f326(f234(a1),x86532),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))
% 157.55/157.23 [8654]~P118(x86541)+~P94(x86541)+P105(f326(f326(f235(x86541),f326(f103(x86541),x86542)),f77(x86541)))+~P105(f326(f326(f235(a1),x86542),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))
% 157.55/157.23 [8864]~P94(x88642)+~P118(x88642)+~P105(f326(f326(f234(x88642),f77(x88642)),f326(f103(x88642),x88641)))+P105(f326(f326(f234(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),x88641))
% 157.55/157.23 [8865]~P94(x88652)+~P118(x88652)+~P105(f326(f326(f235(x88652),f77(x88652)),f326(f103(x88652),x88651)))+P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),x88651))
% 157.55/157.23 [9239]~P118(x92391)+~P94(x92391)+P105(f326(f326(f234(x92391),f77(x92391)),f326(f103(x92391),x92392)))+~P105(f326(f326(f234(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),x92392))
% 157.55/157.23 [9240]~P118(x92401)+~P94(x92401)+P105(f326(f326(f235(x92401),f77(x92401)),f326(f103(x92401),x92402)))+~P105(f326(f326(f235(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),x92402))
% 157.55/157.23 [9755]~P141(x97552)+E(x97551,f77(x97552))+E(x97551,f326(f78(x97552),f77(x97552)))+~E(f326(f326(f243(x97552),x97551),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f77(x97552))
% 157.55/157.23 [10023]~P64(x100231)+~P94(x100231)+~P105(f326(f326(f235(x100231),f2(x100231)),x100232))+P105(f326(f326(f235(x100231),f2(x100231)),f326(f326(f290(x100231),x100232),f326(f103(x100231),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))
% 157.55/157.23 [10076]~P64(x100761)+~P94(x100761)+P105(f326(f326(f235(x100761),f2(x100761)),x100762))+~P105(f326(f326(f235(x100761),f2(x100761)),f326(f326(f290(x100761),x100762),f326(f103(x100761),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))
% 157.55/157.23 [10369]~P140(x103692)+E(x103691,f2(a1))+P105(f326(f326(f235(a1),x103691),f2(a1)))+E(f326(f326(f256(a1,a1,x103692),f326(f326(f9(a1,f917(a1,f917(x103692,x103692)),f917(a1,x103692)),f326(f326(f10(f917(f917(x103692,x103692),x103692),f917(f917(a1,f917(x103692,x103692)),f917(a1,x103692)),a1),f10(f917(x103692,x103692),x103692,a1)),f326(f326(f10(x103692,f917(f917(x103692,x103692),x103692),a1),f85(x103692,x103692)),f102(x103692)))),f326(f326(f9(a1,f917(x103692,x103692),f917(x103692,x103692)),f326(f326(f10(f917(x103692,f917(x103692,x103692)),f917(f917(x103692,x103692),f917(x103692,x103692)),a1),f20(x103692,x103692,x103692)),f326(f326(f9(a1,f917(x103692,x103692),f917(x103692,f917(x103692,x103692))),f326(f326(f10(f917(x103692,f917(x103692,x103692)),f917(f917(x103692,x103692),f917(x103692,f917(x103692,x103692))),a1),f10(x103692,f917(x103692,x103692),x103692)),f326(f326(f10(a905,f917(x103692,f917(x103692,x103692)),a1),f96(x103692)),f326(f326(f9(a1,a1,a905),a323),f2(a1))))),f326(f326(f20(x103692,x103692,x103692),f79(x103692)),f7(x103692))))),f326(f326(f9(x103692,x103692,x103692),f326(f326(f10(x103692,f917(x103692,x103692),x103692),f79(x103692)),f326(f326(f20(x103692,x103692,x103692),f79(x103692)),f7(x103692)))),f77(x103692))))),f46(x103691,f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f102(x103692),x103691))
% 157.55/157.23 [5476]~P37(x54761,x54763)+~P50(x54761,x54763)+~P51(x54761,x54762,x54763)+P7(x54761,x54762,x54763)
% 157.55/157.23 [5006]~P92(x50063)+~P94(x50063)+E(x50061,x50062)+~E(f326(f103(x50063),x50061),f326(f103(x50063),x50062))
% 157.55/157.23 [5486]~P48(x54861,x54862)+~P49(x54861,x54862)+P14(x54861,x54862)+~P105(f326(f326(x54862,x54863),x54863))
% 157.55/157.23 [5995]P14(x59952,x59951)+E(f326(x59951,f800(x59951)),f326(x59951,f801(x59951)))+P105(f326(f326(x59951,f800(x59951)),f801(x59951)))+~P105(f326(f326(x59951,x59953),x59953))
% 157.55/157.23 [6195]~P105(f326(x61951,x61952))+~P105(f326(x61951,x61953))+~P105(f326(f326(f234(a909),x61953),f883(x61952,x61951)))+P105(f326(x61951,f2(a909)))
% 157.55/157.23 [6262]P14(x62621,x62622)+P105(f326(f326(x62622,f800(x62622)),f800(x62622)))+P105(f326(f326(x62622,f800(x62622)),f801(x62622)))+~P105(f326(f326(x62622,x62623),x62623))
% 157.55/157.23 [6263]P14(x62631,x62632)+P105(f326(f326(x62632,f800(x62632)),f801(x62632)))+P105(f326(f326(x62632,f801(x62632)),f801(x62632)))+~P105(f326(f326(x62632,x62633),x62633))
% 157.55/157.23 [6617]P146(x66172,x66171,x66173)+E(x66171,f2(a1))+P105(f326(f326(f234(a1),f2(a1)),f850(x66173,x66171,x66172)))+P105(f326(f326(f235(a1),x66171),f2(a1)))
% 157.55/157.23 [6618]P145(x66182,x66181,x66183)+E(x66181,f2(a1))+P105(f326(f326(f234(a1),f2(a1)),f856(x66183,x66181,x66182)))+P105(f326(f326(f235(a1),x66181),f2(a1)))
% 157.55/157.23 [6743]P145(x67431,x67432,x67433)+~P105(f326(x67431,x67433))+P105(f326(f326(f234(a1),f2(a1)),f856(x67433,x67432,x67431)))+P105(f326(f326(f235(a1),x67432),f2(a1)))
% 157.55/157.23 [6769]P146(x67691,x67692,x67693)+P105(f326(f326(f234(a1),f2(a1)),f850(x67693,x67692,x67691)))+~P105(f326(x67691,f2(a1)))+P105(f326(f326(f235(a1),x67692),f2(a1)))
% 157.55/157.23 [6801]P146(x68012,x68011,x68013)+E(x68011,f2(a1))+~P105(f326(x68012,f851(x68013,x68011,x68012)))+P105(f326(f326(f235(a1),x68011),f2(a1)))
% 157.55/157.23 [6802]P145(x68022,x68021,x68023)+E(x68021,f2(a1))+~P105(f326(x68022,f856(x68023,x68021,x68022)))+P105(f326(f326(f235(a1),x68021),f2(a1)))
% 157.55/157.23 [6903]~P108(x69031)+~P4(x69031)+~P105(f326(f326(f235(x69031),x69032),f37(x69031,x69033)))+P105(f326(f326(f235(x69031),x69032),f744(x69033,x69032,x69031)))
% 157.55/157.23 [6912]P145(x69121,x69122,x69123)+~P105(f326(x69121,x69123))+~P105(f326(x69121,f856(x69123,x69122,x69121)))+P105(f326(f326(f235(a1),x69122),f2(a1)))
% 157.55/157.23 [6942]P146(x69421,x69422,x69423)+~P105(f326(x69421,f851(x69423,x69422,x69421)))+~P105(f326(x69421,f2(a1)))+P105(f326(f326(f235(a1),x69422),f2(a1)))
% 157.55/157.23 [7190]P146(x71902,x71901,x71903)+E(x71901,f2(a1))+P105(f326(f326(f234(a1),f2(a1)),f850(x71903,x71901,x71902)))+P105(f326(f326(f235(a1),x71901),f849(x71903,x71901,x71902)))
% 157.55/157.23 [7191]P145(x71912,x71911,x71913)+E(x71911,f2(a1))+P105(f326(f326(f234(a1),f2(a1)),f856(x71913,x71911,x71912)))+P105(f326(f326(f235(a1),x71911),f855(x71913,x71911,x71912)))
% 157.55/157.23 [7310]P145(x73101,x73102,x73103)+~P105(f326(x73101,x73103))+P105(f326(f326(f234(a1),f2(a1)),f856(x73103,x73102,x73101)))+P105(f326(f326(f235(a1),x73102),f855(x73103,x73102,x73101)))
% 157.55/157.23 [7329]P146(x73291,x73292,x73293)+P105(f326(f326(f234(a1),f2(a1)),f850(x73293,x73292,x73291)))+P105(f326(f326(f235(a1),x73292),f849(x73293,x73292,x73291)))+~P105(f326(x73291,f2(a1)))
% 157.55/157.23 [7361]P146(x73612,x73611,x73613)+E(x73611,f2(a1))+~P105(f326(x73612,f851(x73613,x73611,x73612)))+P105(f326(f326(f235(a1),x73611),f849(x73613,x73611,x73612)))
% 157.55/157.23 [7362]P145(x73622,x73621,x73623)+E(x73621,f2(a1))+~P105(f326(x73622,f856(x73623,x73621,x73622)))+P105(f326(f326(f235(a1),x73621),f855(x73623,x73621,x73622)))
% 157.55/157.23 [7406]P146(x74062,x74061,x74063)+E(x74061,f2(a1))+P105(f326(f326(f234(a1),f2(a1)),f850(x74063,x74061,x74062)))+~P105(f326(x74062,f853(x74063,x74061,x74062)))
% 157.55/157.23 [7407]P145(x74072,x74071,x74073)+E(x74071,f2(a1))+P105(f326(f326(f234(a1),f2(a1)),f856(x74073,x74071,x74072)))+~P105(f326(x74072,f855(x74073,x74071,x74072)))
% 157.55/157.23 [7506]P145(x75061,x75062,x75063)+~P105(f326(x75061,x75063))+~P105(f326(x75061,f856(x75063,x75062,x75061)))+P105(f326(f326(f235(a1),x75062),f855(x75063,x75062,x75061)))
% 157.55/157.23 [7521]P146(x75211,x75212,x75213)+~P105(f326(x75211,f851(x75213,x75212,x75211)))+P105(f326(f326(f235(a1),x75212),f849(x75213,x75212,x75211)))+~P105(f326(x75211,f2(a1)))
% 157.55/157.23 [7524]P145(x75241,x75242,x75243)+~P105(f326(x75241,x75243))+P105(f326(f326(f234(a1),f2(a1)),f856(x75243,x75242,x75241)))+~P105(f326(x75241,f855(x75243,x75242,x75241)))
% 157.55/157.23 [7541]P146(x75411,x75412,x75413)+P105(f326(f326(f234(a1),f2(a1)),f850(x75413,x75412,x75411)))+~P105(f326(x75411,f853(x75413,x75412,x75411)))+~P105(f326(x75411,f2(a1)))
% 157.55/157.23 [7562]P146(x75622,x75621,x75623)+E(x75621,f2(a1))+~P105(f326(x75622,f851(x75623,x75621,x75622)))+~P105(f326(x75622,f853(x75623,x75621,x75622)))
% 157.55/157.23 [7563]P145(x75632,x75631,x75633)+E(x75631,f2(a1))+~P105(f326(x75632,f856(x75633,x75631,x75632)))+~P105(f326(x75632,f855(x75633,x75631,x75632)))
% 157.55/157.23 [7649]P145(x76491,x76492,x76493)+~P105(f326(x76491,x76493))+~P105(f326(x76491,f856(x76493,x76492,x76491)))+~P105(f326(x76491,f855(x76493,x76492,x76491)))
% 157.55/157.23 [7666]P146(x76661,x76662,x76663)+~P105(f326(x76661,f851(x76663,x76662,x76661)))+~P105(f326(x76661,f853(x76663,x76662,x76661)))+~P105(f326(x76661,f2(a1)))
% 157.55/157.23 [7710]P146(x77102,x77101,x77103)+E(x77101,f2(a1))+P105(f326(f326(f234(a1),f2(a1)),f850(x77103,x77101,x77102)))+P105(f326(f326(f234(a1),f849(x77103,x77101,x77102)),f2(a1)))
% 157.55/157.23 [7711]P145(x77112,x77111,x77113)+E(x77111,f2(a1))+P105(f326(f326(f234(a1),f2(a1)),f856(x77113,x77111,x77112)))+P105(f326(f326(f234(a1),f855(x77113,x77111,x77112)),f2(a1)))
% 157.55/157.23 [7712]~P88(x77121)+~P105(f326(f326(f234(x77121),x77123),f2(x77121)))+~P105(f326(f326(f234(x77121),x77122),f2(x77121)))+P105(f326(f326(f234(x77121),f326(f326(f79(x77121),x77122),x77123)),f2(x77121)))
% 157.55/157.23 [7713]~P140(x77131)+~P105(f326(f326(f328(x77131),x77133),f109(x77131)))+~P105(f326(f326(f328(x77131),x77132),f109(x77131)))+P105(f326(f326(f328(x77131),f326(f326(f3(x77131),x77132),x77133)),f109(x77131)))
% 157.55/157.23 [7714]~P140(x77141)+~P105(f326(f326(f328(x77141),x77143),f109(x77141)))+~P105(f326(f326(f328(x77141),x77142),f109(x77141)))+P105(f326(f326(f328(x77141),f326(f326(f80(x77141),x77142),x77143)),f109(x77141)))
% 157.55/157.23 [7715]~P143(x77151)+~P105(f326(f326(f328(x77151),x77153),f186(x77151)))+~P105(f326(f326(f328(x77151),x77152),f186(x77151)))+P105(f326(f326(f328(x77151),f326(f326(f80(x77151),x77152),x77153)),f186(x77151)))
% 157.55/157.23 [7716]~P140(x77161)+~P105(f326(f326(f328(x77161),x77163),f109(x77161)))+~P105(f326(f326(f328(x77161),x77162),f109(x77161)))+P105(f326(f326(f328(x77161),f326(f326(f79(x77161),x77162),x77163)),f109(x77161)))
% 157.55/157.23 [7717]~P143(x77171)+~P105(f326(f326(f328(x77171),x77173),f186(x77171)))+~P105(f326(f326(f328(x77171),x77172),f186(x77171)))+P105(f326(f326(f328(x77171),f326(f326(f79(x77171),x77172),x77173)),f186(x77171)))
% 157.55/157.23 [7718]~P88(x77181)+~P105(f326(f326(f234(x77181),x77183),f2(x77181)))+~P105(f326(f326(f235(x77181),x77182),f2(x77181)))+P105(f326(f326(f235(x77181),f326(f326(f79(x77181),x77182),x77183)),f2(x77181)))
% 157.55/157.23 [7719]~P88(x77191)+~P105(f326(f326(f234(x77191),x77192),f2(x77191)))+~P105(f326(f326(f235(x77191),x77193),f2(x77191)))+P105(f326(f326(f235(x77191),f326(f326(f79(x77191),x77192),x77193)),f2(x77191)))
% 157.55/157.23 [7720]~P88(x77201)+~P105(f326(f326(f235(x77201),x77203),f2(x77201)))+~P105(f326(f326(f235(x77201),x77202),f2(x77201)))+P105(f326(f326(f235(x77201),f326(f326(f79(x77201),x77202),x77203)),f2(x77201)))
% 157.55/157.23 [7747]P146(x77473,x77471,x77472)+E(x77471,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x77471),f851(x77472,x77471,x77473))),f850(x77472,x77471,x77473)),x77472)+P105(f326(f326(f235(a1),x77471),f2(a1)))
% 157.55/157.23 [7748]P145(x77483,x77481,x77482)+E(x77481,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x77481),f857(x77482,x77481,x77483))),f856(x77482,x77481,x77483)),x77482)+P105(f326(f326(f235(a1),x77481),f2(a1)))
% 157.55/157.23 [7829]P145(x78291,x78292,x78293)+~P105(f326(x78291,x78293))+P105(f326(f326(f234(a1),f2(a1)),f856(x78293,x78292,x78291)))+P105(f326(f326(f234(a1),f855(x78293,x78292,x78291)),f2(a1)))
% 157.55/157.23 [7859]P146(x78591,x78592,x78593)+P105(f326(f326(f234(a1),f2(a1)),f850(x78593,x78592,x78591)))+~P105(f326(x78591,f2(a1)))+P105(f326(f326(f234(a1),f849(x78593,x78592,x78591)),f2(a1)))
% 157.55/157.23 [7868]P145(x78683,x78681,x78682)+~P105(f326(x78683,x78682))+E(f326(f326(f79(a1),f326(f326(f80(a1),x78681),f857(x78682,x78681,x78683))),f856(x78682,x78681,x78683)),x78682)+P105(f326(f326(f235(a1),x78681),f2(a1)))
% 157.55/157.23 [7874]P146(x78742,x78741,x78743)+E(x78741,f2(a1))+~P105(f326(x78742,f851(x78743,x78741,x78742)))+P105(f326(f326(f234(a1),f849(x78743,x78741,x78742)),f2(a1)))
% 157.55/157.23 [7875]P145(x78752,x78751,x78753)+E(x78751,f2(a1))+~P105(f326(x78752,f856(x78753,x78751,x78752)))+P105(f326(f326(f234(a1),f855(x78753,x78751,x78752)),f2(a1)))
% 157.55/157.23 [7880]P146(x78803,x78801,x78802)+E(f326(f326(f79(a1),f326(f326(f80(a1),x78801),f851(x78802,x78801,x78803))),f850(x78802,x78801,x78803)),x78802)+~P105(f326(x78803,f2(a1)))+P105(f326(f326(f235(a1),x78801),f2(a1)))
% 157.55/157.23 [7936]P145(x79361,x79362,x79363)+~P105(f326(x79361,x79363))+~P105(f326(x79361,f856(x79363,x79362,x79361)))+P105(f326(f326(f234(a1),f855(x79363,x79362,x79361)),f2(a1)))
% 157.55/157.23 [7940]P146(x79401,x79402,x79403)+~P105(f326(x79401,f851(x79403,x79402,x79401)))+~P105(f326(x79401,f2(a1)))+P105(f326(f326(f234(a1),f849(x79403,x79402,x79401)),f2(a1)))
% 157.55/157.23 [8005]~P125(x80051)+~P105(f326(f326(f234(x80051),f326(f326(f80(x80051),x80053),x80052)),f2(x80051)))+P105(f326(f326(f234(x80051),x80052),f2(x80051)))+P105(f326(f326(f234(x80051),x80053),f2(x80051)))
% 157.55/157.23 [8006]~P64(x80061)+~P105(f326(f326(f234(x80061),f326(f326(f290(x80061),x80063),x80062)),f2(x80061)))+P105(f326(f326(f234(x80061),x80062),f2(x80061)))+P105(f326(f326(f234(x80061),x80063),f2(x80061)))
% 157.55/157.23 [8007]~P64(x80071)+~P105(f326(f326(f235(x80071),f326(f326(f290(x80071),x80073),x80072)),f2(x80071)))+P105(f326(f326(f235(x80071),x80072),f2(x80071)))+P105(f326(f326(f235(x80071),x80073),f2(x80071)))
% 157.55/157.23 [8119]P146(x81193,x81191,x81192)+E(x81191,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x81191),f851(x81192,x81191,x81193))),f850(x81192,x81191,x81193)),x81192)+P105(f326(f326(f235(a1),x81191),f849(x81192,x81191,x81193)))
% 157.55/157.23 [8120]P145(x81203,x81201,x81202)+E(x81201,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x81201),f857(x81202,x81201,x81203))),f856(x81202,x81201,x81203)),x81202)+P105(f326(f326(f235(a1),x81201),f855(x81202,x81201,x81203)))
% 157.55/157.23 [8132]P146(x81323,x81321,x81322)+E(x81321,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x81321),f853(x81322,x81321,x81323))),f849(x81322,x81321,x81323)),x81322)+P105(f326(f326(f234(a1),f2(a1)),f850(x81322,x81321,x81323)))
% 157.55/157.23 [8133]P145(x81333,x81331,x81332)+E(x81331,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x81331),f858(x81332,x81331,x81333))),f855(x81332,x81331,x81333)),x81332)+P105(f326(f326(f234(a1),f2(a1)),f856(x81332,x81331,x81333)))
% 157.55/157.23 [8175]P145(x81753,x81751,x81752)+~P105(f326(x81753,x81752))+E(f326(f326(f79(a1),f326(f326(f80(a1),x81751),f857(x81752,x81751,x81753))),f856(x81752,x81751,x81753)),x81752)+P105(f326(f326(f235(a1),x81751),f855(x81752,x81751,x81753)))
% 157.55/157.23 [8184]P146(x81843,x81841,x81842)+E(f326(f326(f79(a1),f326(f326(f80(a1),x81841),f851(x81842,x81841,x81843))),f850(x81842,x81841,x81843)),x81842)+P105(f326(f326(f235(a1),x81841),f849(x81842,x81841,x81843)))+~P105(f326(x81843,f2(a1)))
% 157.55/157.23 [8190]P145(x81903,x81901,x81902)+~P105(f326(x81903,x81902))+E(f326(f326(f79(a1),f326(f326(f80(a1),x81901),f858(x81902,x81901,x81903))),f855(x81902,x81901,x81903)),x81902)+P105(f326(f326(f234(a1),f2(a1)),f856(x81902,x81901,x81903)))
% 157.55/157.23 [8196]P146(x81963,x81961,x81962)+E(f326(f326(f79(a1),f326(f326(f80(a1),x81961),f853(x81962,x81961,x81963))),f849(x81962,x81961,x81963)),x81962)+P105(f326(f326(f234(a1),f2(a1)),f850(x81962,x81961,x81963)))+~P105(f326(x81963,f2(a1)))
% 157.55/157.23 [8207]P146(x82073,x82071,x82072)+E(x82071,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x82071),f851(x82072,x82071,x82073))),f850(x82072,x82071,x82073)),x82072)+~P105(f326(x82073,f853(x82072,x82071,x82073)))
% 157.55/157.23 [8208]P145(x82083,x82081,x82082)+E(x82081,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x82081),f857(x82082,x82081,x82083))),f856(x82082,x82081,x82083)),x82082)+~P105(f326(x82083,f855(x82082,x82081,x82083)))
% 157.55/157.23 [8209]P146(x82093,x82091,x82092)+E(x82091,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x82091),f853(x82092,x82091,x82093))),f849(x82092,x82091,x82093)),x82092)+~P105(f326(x82093,f851(x82092,x82091,x82093)))
% 157.55/157.23 [8210]P145(x82103,x82101,x82102)+E(x82101,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x82101),f858(x82102,x82101,x82103))),f855(x82102,x82101,x82103)),x82102)+~P105(f326(x82103,f856(x82102,x82101,x82103)))
% 157.55/157.23 [8269]P145(x82693,x82691,x82692)+~P105(f326(x82693,x82692))+E(f326(f326(f79(a1),f326(f326(f80(a1),x82691),f857(x82692,x82691,x82693))),f856(x82692,x82691,x82693)),x82692)+~P105(f326(x82693,f855(x82692,x82691,x82693)))
% 157.55/157.23 [8270]P145(x82703,x82701,x82702)+~P105(f326(x82703,x82702))+E(f326(f326(f79(a1),f326(f326(f80(a1),x82701),f858(x82702,x82701,x82703))),f855(x82702,x82701,x82703)),x82702)+~P105(f326(x82703,f856(x82702,x82701,x82703)))
% 157.55/157.23 [8280]P146(x82803,x82801,x82802)+E(f326(f326(f79(a1),f326(f326(f80(a1),x82801),f851(x82802,x82801,x82803))),f850(x82802,x82801,x82803)),x82802)+~P105(f326(x82803,f853(x82802,x82801,x82803)))+~P105(f326(x82803,f2(a1)))
% 157.55/157.23 [8281]P146(x82813,x82811,x82812)+E(f326(f326(f79(a1),f326(f326(f80(a1),x82811),f853(x82812,x82811,x82813))),f849(x82812,x82811,x82813)),x82812)+~P105(f326(x82813,f851(x82812,x82811,x82813)))+~P105(f326(x82813,f2(a1)))
% 157.55/157.23 [8377]P146(x83773,x83771,x83772)+E(x83771,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x83771),f851(x83772,x83771,x83773))),f850(x83772,x83771,x83773)),x83772)+P105(f326(f326(f234(a1),f849(x83772,x83771,x83773)),f2(a1)))
% 157.55/157.23 [8378]P145(x83783,x83781,x83782)+E(x83781,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x83781),f857(x83782,x83781,x83783))),f856(x83782,x83781,x83783)),x83782)+P105(f326(f326(f234(a1),f855(x83782,x83781,x83783)),f2(a1)))
% 157.55/157.23 [8417]P145(x84173,x84171,x84172)+~P105(f326(x84173,x84172))+E(f326(f326(f79(a1),f326(f326(f80(a1),x84171),f857(x84172,x84171,x84173))),f856(x84172,x84171,x84173)),x84172)+P105(f326(f326(f234(a1),f855(x84172,x84171,x84173)),f2(a1)))
% 157.55/157.23 [8422]P146(x84223,x84221,x84222)+E(f326(f326(f79(a1),f326(f326(f80(a1),x84221),f851(x84222,x84221,x84223))),f850(x84222,x84221,x84223)),x84222)+~P105(f326(x84223,f2(a1)))+P105(f326(f326(f234(a1),f849(x84222,x84221,x84223)),f2(a1)))
% 157.55/157.23 [8555]P146(x85553,x85551,x85552)+E(x85551,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x85551),f853(x85552,x85551,x85553))),f849(x85552,x85551,x85553)),x85552)+E(f326(f326(f79(a1),f326(f326(f80(a1),x85551),f851(x85552,x85551,x85553))),f850(x85552,x85551,x85553)),x85552)
% 157.55/157.23 [8556]P145(x85563,x85561,x85562)+E(x85561,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x85561),f858(x85562,x85561,x85563))),f855(x85562,x85561,x85563)),x85562)+E(f326(f326(f79(a1),f326(f326(f80(a1),x85561),f857(x85562,x85561,x85563))),f856(x85562,x85561,x85563)),x85562)
% 157.55/157.23 [8576]P145(x85763,x85761,x85762)+~P105(f326(x85763,x85762))+E(f326(f326(f79(a1),f326(f326(f80(a1),x85761),f858(x85762,x85761,x85763))),f855(x85762,x85761,x85763)),x85762)+E(f326(f326(f79(a1),f326(f326(f80(a1),x85761),f857(x85762,x85761,x85763))),f856(x85762,x85761,x85763)),x85762)
% 157.55/157.23 [8587]P146(x85873,x85871,x85872)+E(f326(f326(f79(a1),f326(f326(f80(a1),x85871),f853(x85872,x85871,x85873))),f849(x85872,x85871,x85873)),x85872)+E(f326(f326(f79(a1),f326(f326(f80(a1),x85871),f851(x85872,x85871,x85873))),f850(x85872,x85871,x85873)),x85872)+~P105(f326(x85873,f2(a1)))
% 157.55/157.23 [9247]~P125(x92471)+~E(x92473,f2(x92471))+~E(x92472,f2(x92471))+P105(f326(f326(f234(x92471),f326(f326(f79(x92471),f326(f326(f80(x92471),x92472),x92472)),f326(f326(f80(x92471),x92473),x92473))),f2(x92471)))
% 157.55/157.23 [10307]~P118(x103071)+~E(x103073,f2(x103071))+~E(x103072,f2(x103071))+P105(f326(f326(f234(x103071),f326(f326(f79(x103071),f326(f326(f243(x103071),x103072),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x103071),x103073),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))),f2(x103071)))
% 157.55/157.23 [4954]~E(x49543,x49541)+~P121(x49542)+E(x49541,f2(x49542))+E(f326(f326(f290(x49542),x49543),x49541),f77(x49542))
% 157.55/157.23 [5007]~P78(x50071)+~E(x50073,f188(x50071))+~E(x50072,f188(x50071))+E(f326(f326(f110(x50071),x50072),x50073),f188(x50071))
% 157.55/157.23 [5008]~P99(x50081)+~E(x50083,f241(x50081))+~E(x50082,f241(x50081))+E(f326(f326(f101(x50081),x50082),x50083),f241(x50081))
% 157.55/157.23 [5105]~P121(x51053)+E(x51051,x51052)+E(x51052,f2(x51053))+~E(f326(f326(f290(x51053),x51051),x51052),f77(x51053))
% 157.55/157.23 [5122]~P139(x51222)+E(x51221,f2(x51222))+E(x51223,f2(x51222))+~E(f326(f326(f80(x51222),x51223),x51221),f2(x51222))
% 157.55/157.23 [5124]~P132(x51242)+E(x51241,f2(x51242))+E(x51243,f2(x51242))+~E(f326(f326(f80(x51242),x51243),x51241),f2(x51242))
% 157.55/157.23 [5505]~P120(x55053)+E(x55051,x55052)+E(x55051,f326(f78(x55053),x55052))+~E(f326(f326(f80(x55053),x55051),x55051),f326(f326(f80(x55053),x55052),x55052))
% 157.55/157.23 [5544]~P95(x55441)+E(f326(f78(x55441),x55442),x55443)+~E(f326(f326(f110(x55441),x55442),x55443),f241(x55441))+~E(f326(f326(f101(x55441),x55442),x55443),f188(x55441))
% 157.55/157.23 [5625]~P118(x56253)+E(x56251,x56252)+P105(f326(f326(f235(x56253),x56252),x56251))+P105(f326(f326(f235(x56253),x56251),x56252))
% 157.55/157.23 [5626]~P108(x56263)+E(x56261,x56262)+P105(f326(f326(f235(x56263),x56262),x56261))+P105(f326(f326(f235(x56263),x56261),x56262))
% 157.55/157.23 [5627]~E(x56272,x56273)+~P108(x56271)+P105(f326(f326(f235(x56271),x56272),x56273))+P105(f326(f326(f234(x56271),x56272),x56273))
% 157.55/157.23 [5890]~P109(x58903)+E(x58901,x58902)+~P105(f326(f326(f234(x58903),x58902),x58901))+P105(f326(f326(f235(x58903),x58902),x58901))
% 157.55/157.23 [5892]~P108(x58923)+E(x58921,x58922)+~P105(f326(f326(f234(x58923),x58921),x58922))+P105(f326(f326(f235(x58923),x58921),x58922))
% 157.55/157.23 [5898]~P109(x58983)+E(x58981,x58982)+~P105(f326(f326(f234(x58983),x58981),x58982))+P105(f326(f326(f235(x58983),x58981),x58982))
% 157.55/157.23 [6012]P145(x60121,x60122,x60123)+~P105(f326(x60121,x60123))+P105(f326(f326(f235(a1),x60122),f2(a1)))+P105(f326(f326(f235(a1),f2(a1)),x60122))
% 157.55/157.23 [6062]P146(x60621,x60622,x60623)+~P105(f326(x60621,f2(a1)))+P105(f326(f326(f235(a1),x60622),f2(a1)))+P105(f326(f326(f235(a1),f2(a1)),x60622))
% 157.55/157.23 [6067]~P77(x60671)+E(f326(f326(f110(x60671),x60672),f13(x60671,x60673)),x60672)+~P105(f326(f61(x60671),x60673))+~P105(f326(f326(f328(x60671),x60672),x60673))
% 157.55/157.23 [6068]~P77(x60681)+E(f326(f326(f101(x60681),x60682),f12(x60681,x60683)),x60682)+~P105(f326(f61(x60681),x60683))+~P105(f326(f326(f328(x60681),x60682),x60683))
% 157.55/157.23 [6105]~P77(x61051)+E(f326(f326(f110(x61051),x61052),f12(x61051,x61053)),f12(x61051,x61053))+~P105(f326(f61(x61051),x61053))+~P105(f326(f326(f328(x61051),x61052),x61053))
% 157.55/157.23 [6106]~P77(x61061)+E(f326(f326(f101(x61061),x61062),f13(x61061,x61063)),f13(x61061,x61063))+~P105(f326(f61(x61061),x61063))+~P105(f326(f326(f328(x61061),x61062),x61063))
% 157.55/157.23 [6107]~P108(x61071)+E(f326(f326(f232(x61071),x61072),f16(x61071,x61073)),f16(x61071,x61073))+~P105(f326(f61(x61071),x61073))+~P105(f326(f326(f328(x61071),x61072),x61073))
% 157.55/157.23 [6108]~P108(x61081)+E(f326(f326(f233(x61081),x61082),f17(x61081,x61083)),f17(x61081,x61083))+~P105(f326(f61(x61081),x61083))+~P105(f326(f326(f328(x61081),x61082),x61083))
% 157.55/157.23 [6147]E(x61471,x61472)+~P109(x61473)+~P105(f326(f326(f234(x61473),x61472),x61471))+~P105(f326(f326(f234(x61473),x61471),x61472))
% 157.55/157.23 [6290]~P106(x62901)+P105(f326(f326(f235(x62901),x62903),x62902))+~P105(f326(f326(f234(x62901),x62903),x62902))+P105(f326(f326(f234(x62901),x62902),x62903))
% 157.55/157.23 [6318]~P108(x63181)+~P105(f326(f61(x63181),x63183))+P105(f326(f326(f234(x63181),x63182),f17(x63181,x63183)))+~P105(f326(f326(f328(x63181),x63182),x63183))
% 157.55/157.23 [6364]~P108(x63641)+E(f326(f326(f232(x63641),x63642),f15(x63641,f233(x63641),x63643)),x63642)+~P105(f326(f61(x63641),x63643))+~P105(f326(f326(f328(x63641),x63642),x63643))
% 157.55/157.23 [6365]~P108(x63651)+E(f326(f326(f233(x63651),x63652),f14(x63651,f232(x63651),x63653)),x63652)+~P105(f326(f61(x63651),x63653))+~P105(f326(f326(f328(x63651),x63652),x63653))
% 157.55/157.23 [6507]E(x65071,x65072)+~E(f326(f326(f3(a909),x65071),x65073),f326(f326(f3(a909),x65072),x65073))+~P105(f326(f326(f234(a909),x65073),x65071))+~P105(f326(f326(f234(a909),x65073),x65072))
% 157.55/157.23 [6534]~P108(x65341)+~P105(f326(f61(x65341),x65342))+~P105(f326(f326(f328(x65341),x65343),x65342))+P105(f326(f326(f234(x65341),f16(x65341,x65342)),x65343))
% 157.55/157.23 [6596]P146(x65962,x65961,x65963)+E(x65961,f2(a1))+P105(f326(f326(f235(a1),x65961),f849(x65963,x65961,x65962)))+P105(f326(f326(f235(a1),f2(a1)),x65961))
% 157.55/157.23 [6597]P145(x65972,x65971,x65973)+E(x65971,f2(a1))+P105(f326(f326(f235(a1),x65971),f855(x65973,x65971,x65972)))+P105(f326(f326(f235(a1),f2(a1)),x65971))
% 157.55/157.23 [6598]~P108(x65981)+E(f326(f326(f232(x65981),x65982),f14(x65981,f232(x65981),x65983)),f14(x65981,f232(x65981),x65983))+~P105(f326(f61(x65981),x65983))+~P105(f326(f326(f328(x65981),x65982),x65983))
% 157.55/157.23 [6599]~P108(x65991)+E(f326(f326(f233(x65991),x65992),f15(x65991,f233(x65991),x65993)),f15(x65991,f233(x65991),x65993))+~P105(f326(f61(x65991),x65993))+~P105(f326(f326(f328(x65991),x65992),x65993))
% 157.55/157.23 [6604]~P105(f326(x66041,x66042))+P105(f326(x66041,f379(x66042,x66041,x66043)))+P105(f326(x66041,f2(a909)))+~P105(f326(f326(f235(a909),x66042),x66043))
% 157.55/157.23 [6662]~P105(f326(x66621,x66622))+~P105(f326(f61(x66623),x66622))+P105(f326(x66621,f484(x66621,x66622,x66623)))+P105(f326(x66621,f188(f917(x66623,a905))))
% 157.55/157.23 [6675]~P118(x66751)+~P94(x66751)+P105(f326(f326(f234(x66751),f326(f103(x66751),x66752)),f326(f103(x66751),x66753)))+~P105(f326(f326(f234(a1),x66752),x66753))
% 157.55/157.23 [6676]~P118(x66761)+~P94(x66761)+P105(f326(f326(f235(x66761),f326(f103(x66761),x66762)),f326(f103(x66761),x66763)))+~P105(f326(f326(f235(a1),x66762),x66763))
% 157.55/157.23 [6679]~P105(f326(x66791,x66793))+~P105(f326(f61(x66792),x66793))+P105(f326(f61(x66792),f484(x66791,x66793,x66792)))+P105(f326(x66791,f188(f917(x66792,a905))))
% 157.55/157.23 [6713]P145(x67131,x67132,x67133)+~P105(f326(x67131,x67133))+P105(f326(f326(f235(a1),x67132),f855(x67133,x67132,x67131)))+P105(f326(f326(f235(a1),f2(a1)),x67132))
% 157.55/157.23 [6750]P146(x67501,x67502,x67503)+P105(f326(f326(f235(a1),x67502),f849(x67503,x67502,x67501)))+~P105(f326(x67501,f2(a1)))+P105(f326(f326(f235(a1),f2(a1)),x67502))
% 157.55/157.23 [6780]~P107(x67801)+~P93(x67801)+E(f326(f326(f232(x67801),f326(f103(x67801),x67802)),f326(f103(x67801),x67803)),f326(f103(x67801),x67803))+P105(f326(f326(f234(x67801),f326(f103(x67801),x67802)),f326(f103(x67801),x67803)))
% 157.55/157.23 [6781]~P107(x67811)+~P93(x67811)+E(f326(f326(f233(x67811),f326(f103(x67811),x67812)),f326(f103(x67811),x67813)),f326(f103(x67811),x67812))+P105(f326(f326(f234(x67811),f326(f103(x67811),x67812)),f326(f103(x67811),x67813)))
% 157.55/157.23 [6841]P146(x68412,x68411,x68413)+E(x68411,f2(a1))+~P105(f326(x68412,f853(x68413,x68411,x68412)))+P105(f326(f326(f235(a1),f2(a1)),x68411))
% 157.55/157.23 [6842]P145(x68422,x68421,x68423)+E(x68421,f2(a1))+~P105(f326(x68422,f855(x68423,x68421,x68422)))+P105(f326(f326(f235(a1),f2(a1)),x68421))
% 157.55/157.23 [6846]P105(f326(x68461,x68462))+~P105(f326(f61(x68463),x68462))+P105(f326(x68461,f892(x68461,x68462,x68463)))+~P105(f326(x68461,f188(f917(x68463,a905))))
% 157.55/157.23 [6867]P105(f326(x68671,x68672))+P105(f326(f61(x68673),f892(x68671,x68672,x68673)))+~P105(f326(f61(x68673),x68672))+~P105(f326(x68671,f188(f917(x68673,a905))))
% 157.55/157.23 [6931]P145(x69311,x69312,x69313)+~P105(f326(x69311,x69313))+~P105(f326(x69311,f855(x69313,x69312,x69311)))+P105(f326(f326(f235(a1),f2(a1)),x69312))
% 157.55/157.23 [6961]P146(x69611,x69612,x69613)+~P105(f326(x69611,f853(x69613,x69612,x69611)))+~P105(f326(x69611,f2(a1)))+P105(f326(f326(f235(a1),f2(a1)),x69612))
% 157.55/157.23 [7066]~P94(x70663)+~P118(x70663)+~P105(f326(f326(f234(x70663),f326(f103(x70663),x70661)),f326(f103(x70663),x70662)))+P105(f326(f326(f234(a1),x70661),x70662))
% 157.55/157.23 [7067]~P94(x70673)+~P118(x70673)+~P105(f326(f326(f235(x70673),f326(f103(x70673),x70671)),f326(f103(x70673),x70672)))+P105(f326(f326(f235(a1),x70671),x70672))
% 157.55/157.23 [7094]~P108(x70941)+~P12(x70941,x70943)+P12(x70941,f326(f326(f151(x70941),x70942),x70943))+~P105(f326(f326(f234(x70941),x70942),f705(x70943,x70942,x70941)))
% 157.55/157.23 [7095]~P108(x70951)+~P12(x70951,x70953)+P12(x70951,f326(f326(f151(x70951),x70952),x70953))+~P105(f326(f326(f234(x70951),x70952),f707(x70953,x70952,x70951)))
% 157.55/157.23 [7096]~P108(x70961)+~P12(x70961,x70963)+P12(x70961,f326(f326(f151(x70961),x70962),x70963))+~P105(f326(f326(f234(x70961),x70962),f746(x70962,x70963,x70961)))
% 157.55/157.23 [7183]P146(x71832,x71831,x71833)+E(x71831,f2(a1))+P105(f326(f326(f235(a1),x71831),f2(a1)))+P105(f326(f326(f235(a1),f850(x71833,x71831,x71832)),x71831))
% 157.55/157.23 [7184]P145(x71842,x71841,x71843)+E(x71841,f2(a1))+P105(f326(f326(f235(a1),x71841),f2(a1)))+P105(f326(f326(f235(a1),f856(x71843,x71841,x71842)),x71841))
% 157.55/157.23 [7220]P146(x72202,x72201,x72203)+E(x72201,f2(a1))+P105(f326(f326(f234(a1),f849(x72203,x72201,x72202)),f2(a1)))+P105(f326(f326(f235(a1),f2(a1)),x72201))
% 157.55/157.23 [7221]P145(x72212,x72211,x72213)+E(x72211,f2(a1))+P105(f326(f326(f234(a1),f855(x72213,x72211,x72212)),f2(a1)))+P105(f326(f326(f235(a1),f2(a1)),x72211))
% 157.55/157.23 [7246]~P108(x72461)+~P12(x72461,x72463)+E(f326(f326(f148(x72461,x72461,f7(x72461)),x72462),f170(x72461,x72462,x72463)),x72463)+~P105(f326(f326(f328(x72461),x72462),f326(f172(x72461),x72463)))
% 157.55/157.23 [7293]P145(x72931,x72932,x72933)+~P105(f326(x72931,x72933))+P105(f326(f326(f235(a1),x72932),f2(a1)))+P105(f326(f326(f235(a1),f856(x72933,x72932,x72931)),x72932))
% 157.55/157.23 [7299]~P107(x72991)+~P93(x72991)+E(f326(f326(f232(x72991),f326(f103(x72991),x72992)),f326(f103(x72991),x72993)),f326(f103(x72991),x72992))+~P105(f326(f326(f234(x72991),f326(f103(x72991),x72992)),f326(f103(x72991),x72993)))
% 157.55/157.23 [7300]~P107(x73001)+~P93(x73001)+E(f326(f326(f233(x73001),f326(f103(x73001),x73002)),f326(f103(x73001),x73003)),f326(f103(x73001),x73003))+~P105(f326(f326(f234(x73001),f326(f103(x73001),x73002)),f326(f103(x73001),x73003)))
% 157.55/157.23 [7314]P146(x73141,x73142,x73143)+~P105(f326(x73141,f2(a1)))+P105(f326(f326(f235(a1),x73142),f2(a1)))+P105(f326(f326(f235(a1),f850(x73143,x73142,x73141)),x73142))
% 157.55/157.23 [7322]P145(x73221,x73222,x73223)+~P105(f326(x73221,x73223))+P105(f326(f326(f234(a1),f855(x73223,x73222,x73221)),f2(a1)))+P105(f326(f326(f235(a1),f2(a1)),x73222))
% 157.55/157.23 [7346]P146(x73461,x73462,x73463)+~P105(f326(x73461,f2(a1)))+P105(f326(f326(f234(a1),f849(x73463,x73462,x73461)),f2(a1)))+P105(f326(f326(f235(a1),f2(a1)),x73462))
% 157.55/157.23 [7373]~P105(f326(x73731,x73732))+P105(f326(x73731,f2(a909)))+~P105(f326(f326(f235(a909),x73732),x73733))+P105(f326(f326(f235(a909),f379(x73732,x73731,x73733)),x73733))
% 157.55/157.23 [7390]~P108(x73901)+~P12(x73901,x73903)+P12(x73901,f326(f326(f151(x73901),x73902),x73903))+P105(f326(f326(f328(x73901),f705(x73903,x73902,x73901)),f326(f172(x73901),x73903)))
% 157.55/157.23 [7391]~P108(x73911)+~P12(x73911,x73913)+P12(x73911,f326(f326(f151(x73911),x73912),x73913))+P105(f326(f326(f328(x73911),f707(x73913,x73912,x73911)),f326(f172(x73911),x73913)))
% 157.55/157.23 [7392]~P108(x73921)+~P12(x73921,x73923)+P12(x73921,f326(f326(f151(x73921),x73922),x73923))+P105(f326(f326(f328(x73921),f746(x73922,x73923,x73921)),f326(f172(x73921),x73923)))
% 157.55/157.23 [7510]~P108(x75101)+~P4(x75101)+~P105(f326(f326(f235(x75101),x75103),f37(x75101,x75102)))+P105(f326(f326(f328(x75101),f744(x75102,x75103,x75101)),x75102))
% 157.55/157.23 [7664]~P108(x76641)+~P4(x76641)+~P105(f326(f326(f235(x76641),f38(x76641,x76643)),x76642))+P105(f326(f326(f328(x76641),f385(x76642,x76643,x76641)),x76643))
% 157.55/157.23 [7665]~P108(x76651)+~P4(x76651)+~P105(f326(f326(f235(x76651),f38(x76651,x76653)),x76652))+P105(f326(f326(f235(x76651),f385(x76652,x76653,x76651)),x76652))
% 157.55/157.23 [7677]P146(x76772,x76771,x76773)+E(x76771,f2(a1))+P105(f326(f326(f235(a1),x76771),f849(x76773,x76771,x76772)))+P105(f326(f326(f235(a1),f850(x76773,x76771,x76772)),x76771))
% 157.55/157.23 [7678]P145(x76782,x76781,x76783)+E(x76781,f2(a1))+P105(f326(f326(f235(a1),x76781),f855(x76783,x76781,x76782)))+P105(f326(f326(f235(a1),f856(x76783,x76781,x76782)),x76781))
% 157.55/157.23 [7768]P146(x77683,x77681,x77682)+E(x77681,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x77681),f853(x77682,x77681,x77683))),f849(x77682,x77681,x77683)),x77682)+P105(f326(f326(f235(a1),f2(a1)),x77681))
% 157.55/157.23 [7769]P145(x77693,x77691,x77692)+E(x77691,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x77691),f858(x77692,x77691,x77693))),f855(x77692,x77691,x77693)),x77692)+P105(f326(f326(f235(a1),f2(a1)),x77691))
% 157.55/157.23 [7772]~P133(x77721)+~P105(f326(f326(f234(x77721),x77723),f2(x77721)))+P105(f326(f326(f234(x77721),f326(f326(f80(x77721),x77722),x77723)),f2(x77721)))+~P105(f326(f326(f234(x77721),f2(x77721)),x77722))
% 157.55/157.23 [7774]~P133(x77741)+~P105(f326(f326(f234(x77741),x77742),f2(x77741)))+P105(f326(f326(f234(x77741),f326(f326(f80(x77741),x77742),x77743)),f2(x77741)))+~P105(f326(f326(f234(x77741),f2(x77741)),x77743))
% 157.55/157.23 [7775]~P125(x77751)+~P105(f326(f326(f234(x77751),x77753),f2(x77751)))+P105(f326(f326(f234(x77751),f326(f326(f80(x77751),x77752),x77753)),f2(x77751)))+~P105(f326(f326(f234(x77751),f2(x77751)),x77752))
% 157.55/157.23 [7776]~P125(x77761)+~P105(f326(f326(f234(x77761),x77762),f2(x77761)))+P105(f326(f326(f234(x77761),f326(f326(f80(x77761),x77762),x77763)),f2(x77761)))+~P105(f326(f326(f234(x77761),f2(x77761)),x77763))
% 157.55/157.23 [7777]~P64(x77771)+~P105(f326(f326(f234(x77771),x77773),f2(x77771)))+P105(f326(f326(f234(x77771),f326(f326(f290(x77771),x77772),x77773)),f2(x77771)))+~P105(f326(f326(f234(x77771),f2(x77771)),x77772))
% 157.55/157.23 [7778]~P64(x77781)+~P105(f326(f326(f234(x77781),x77782),f2(x77781)))+P105(f326(f326(f234(x77781),f326(f326(f290(x77781),x77782),x77783)),f2(x77781)))+~P105(f326(f326(f234(x77781),f2(x77781)),x77783))
% 157.55/157.23 [7779]~P65(x77791)+~P105(f326(f326(f234(x77791),x77792),f2(x77791)))+P105(f326(f326(f234(x77791),f326(f326(f290(x77791),x77792),x77793)),f2(x77791)))+~P105(f326(f326(f235(x77791),f2(x77791)),x77793))
% 157.55/157.23 [7780]~P65(x77801)+~P105(f326(f326(f235(x77801),x77803),f2(x77801)))+P105(f326(f326(f234(x77801),f326(f326(f290(x77801),x77802),x77803)),f2(x77801)))+~P105(f326(f326(f234(x77801),f2(x77801)),x77802))
% 157.55/157.23 [7782]~P131(x77821)+~P105(f326(f326(f235(x77821),x77823),f2(x77821)))+P105(f326(f326(f235(x77821),f326(f326(f80(x77821),x77822),x77823)),f2(x77821)))+~P105(f326(f326(f235(x77821),f2(x77821)),x77822))
% 157.55/157.23 [7783]~P131(x77831)+~P105(f326(f326(f235(x77831),x77832),f2(x77831)))+P105(f326(f326(f235(x77831),f326(f326(f80(x77831),x77832),x77833)),f2(x77831)))+~P105(f326(f326(f235(x77831),f2(x77831)),x77833))
% 157.55/157.23 [7784]~P64(x77841)+~P105(f326(f326(f235(x77841),x77843),f2(x77841)))+P105(f326(f326(f235(x77841),f326(f326(f290(x77841),x77842),x77843)),f2(x77841)))+~P105(f326(f326(f235(x77841),f2(x77841)),x77842))
% 157.55/157.23 [7785]~P64(x77851)+~P105(f326(f326(f235(x77851),x77852),f2(x77851)))+P105(f326(f326(f235(x77851),f326(f326(f290(x77851),x77852),x77853)),f2(x77851)))+~P105(f326(f326(f235(x77851),f2(x77851)),x77853))
% 157.55/157.23 [7786]~P65(x77861)+~P105(f326(f326(f235(x77861),x77863),f2(x77861)))+P105(f326(f326(f235(x77861),f326(f326(f290(x77861),x77862),x77863)),f2(x77861)))+~P105(f326(f326(f235(x77861),f2(x77861)),x77862))
% 157.55/157.23 [7787]~P65(x77871)+~P105(f326(f326(f235(x77871),x77872),f2(x77871)))+P105(f326(f326(f235(x77871),f326(f326(f290(x77871),x77872),x77873)),f2(x77871)))+~P105(f326(f326(f235(x77871),f2(x77871)),x77873))
% 157.55/157.23 [7802]P145(x78021,x78022,x78023)+~P105(f326(x78021,x78023))+P105(f326(f326(f235(a1),x78022),f855(x78023,x78022,x78021)))+P105(f326(f326(f235(a1),f856(x78023,x78022,x78021)),x78022))
% 157.55/157.23 [7815]P146(x78151,x78152,x78153)+P105(f326(f326(f235(a1),x78152),f849(x78153,x78152,x78151)))+~P105(f326(x78151,f2(a1)))+P105(f326(f326(f235(a1),f850(x78153,x78152,x78151)),x78152))
% 157.55/157.23 [7866]P146(x78662,x78661,x78663)+E(x78661,f2(a1))+~P105(f326(x78662,f853(x78663,x78661,x78662)))+P105(f326(f326(f235(a1),f850(x78663,x78661,x78662)),x78661))
% 157.55/157.23 [7867]P145(x78672,x78671,x78673)+E(x78671,f2(a1))+~P105(f326(x78672,f855(x78673,x78671,x78672)))+P105(f326(f326(f235(a1),f856(x78673,x78671,x78672)),x78671))
% 157.55/157.23 [7877]P145(x78773,x78771,x78772)+~P105(f326(x78773,x78772))+E(f326(f326(f79(a1),f326(f326(f80(a1),x78771),f858(x78772,x78771,x78773))),f855(x78772,x78771,x78773)),x78772)+P105(f326(f326(f235(a1),f2(a1)),x78771))
% 157.55/157.23 [7892]P146(x78923,x78921,x78922)+E(f326(f326(f79(a1),f326(f326(f80(a1),x78921),f853(x78922,x78921,x78923))),f849(x78922,x78921,x78923)),x78922)+~P105(f326(x78923,f2(a1)))+P105(f326(f326(f235(a1),f2(a1)),x78921))
% 157.55/157.23 [7920]~P105(f326(x79201,x79203))+~P105(f326(f61(x79202),x79203))+P105(f326(f326(f328(x79202),f475(x79201,x79203,x79202)),f484(x79201,x79203,x79202)))+P105(f326(x79201,f188(f917(x79202,a905))))
% 157.55/157.23 [7931]P145(x79311,x79312,x79313)+~P105(f326(x79311,x79313))+~P105(f326(x79311,f855(x79313,x79312,x79311)))+P105(f326(f326(f235(a1),f856(x79313,x79312,x79311)),x79312))
% 157.55/157.23 [7937]P146(x79371,x79372,x79373)+~P105(f326(x79371,f853(x79373,x79372,x79371)))+~P105(f326(x79371,f2(a1)))+P105(f326(f326(f235(a1),f850(x79373,x79372,x79371)),x79372))
% 157.55/157.23 [8036]~P125(x80361)+~P105(f326(f326(f234(x80361),f326(f326(f80(x80361),x80363),x80362)),f2(x80361)))+P105(f326(f326(f234(x80361),x80362),f2(x80361)))+P105(f326(f326(f234(x80361),f2(x80361)),x80362))
% 157.55/157.23 [8037]~P125(x80371)+~P105(f326(f326(f234(x80371),f326(f326(f80(x80371),x80372),x80373)),f2(x80371)))+P105(f326(f326(f234(x80371),x80372),f2(x80371)))+P105(f326(f326(f234(x80371),f2(x80371)),x80372))
% 157.55/157.23 [8038]~P64(x80381)+~P105(f326(f326(f234(x80381),f326(f326(f290(x80381),x80383),x80382)),f2(x80381)))+P105(f326(f326(f234(x80381),x80382),f2(x80381)))+P105(f326(f326(f234(x80381),f2(x80381)),x80382))
% 157.55/157.23 [8039]~P64(x80391)+~P105(f326(f326(f234(x80391),f326(f326(f290(x80391),x80392),x80393)),f2(x80391)))+P105(f326(f326(f234(x80391),x80392),f2(x80391)))+P105(f326(f326(f234(x80391),f2(x80391)),x80392))
% 157.55/157.23 [8040]~P64(x80401)+~P105(f326(f326(f235(x80401),f326(f326(f290(x80401),x80403),x80402)),f2(x80401)))+P105(f326(f326(f235(x80401),x80402),f2(x80401)))+P105(f326(f326(f235(x80401),f2(x80401)),x80402))
% 157.55/157.23 [8041]~P64(x80411)+~P105(f326(f326(f235(x80411),f326(f326(f290(x80411),x80412),x80413)),f2(x80411)))+P105(f326(f326(f235(x80411),x80412),f2(x80411)))+P105(f326(f326(f235(x80411),f2(x80411)),x80412))
% 157.55/157.23 [8064]~P125(x80641)+~P105(f326(f326(f234(x80641),f326(f326(f80(x80641),x80642),x80643)),f2(x80641)))+P105(f326(f326(f234(x80641),f2(x80641)),x80642))+P105(f326(f326(f234(x80641),f2(x80641)),x80643))
% 157.55/157.23 [8065]~P64(x80651)+~P105(f326(f326(f234(x80651),f326(f326(f290(x80651),x80652),x80653)),f2(x80651)))+P105(f326(f326(f234(x80651),f2(x80651)),x80652))+P105(f326(f326(f234(x80651),f2(x80651)),x80653))
% 157.55/157.23 [8066]~P64(x80661)+~P105(f326(f326(f235(x80661),f326(f326(f290(x80661),x80662),x80663)),f2(x80661)))+P105(f326(f326(f235(x80661),f2(x80661)),x80662))+P105(f326(f326(f235(x80661),f2(x80661)),x80663))
% 157.55/157.23 [8088]P146(x80882,x80881,x80883)+E(x80881,f2(a1))+P105(f326(f326(f234(a1),f849(x80883,x80881,x80882)),f2(a1)))+P105(f326(f326(f235(a1),f850(x80883,x80881,x80882)),x80881))
% 157.55/157.23 [8089]P145(x80892,x80891,x80893)+E(x80891,f2(a1))+P105(f326(f326(f234(a1),f855(x80893,x80891,x80892)),f2(a1)))+P105(f326(f326(f235(a1),f856(x80893,x80891,x80892)),x80891))
% 157.55/157.23 [8096]~P124(x80961)+~P105(f326(f326(f235(x80961),x80962),f77(x80961)))+P105(f326(f326(f235(x80961),f326(f326(f243(x80961),x80962),f326(a112,x80963))),f77(x80961)))+~P105(f326(f326(f235(x80961),f2(x80961)),x80962))
% 157.55/157.23 [8149]~P108(x81491)+~E(x81493,f113(x81491))+~P12(x81491,f326(f168(x81491),x81493))+E(f326(f142(x81491,x81491,f326(f9(x81491,x81491,x81491),f233(x81491)),x81492),f326(f168(x81491),x81493)),x81492)
% 157.55/157.23 [8152]P145(x81521,x81522,x81523)+~P105(f326(x81521,x81523))+P105(f326(f326(f234(a1),f855(x81523,x81522,x81521)),f2(a1)))+P105(f326(f326(f235(a1),f856(x81523,x81522,x81521)),x81522))
% 157.55/157.23 [8159]P146(x81591,x81592,x81593)+~P105(f326(x81591,f2(a1)))+P105(f326(f326(f234(a1),f849(x81593,x81592,x81591)),f2(a1)))+P105(f326(f326(f235(a1),f850(x81593,x81592,x81591)),x81592))
% 157.55/157.23 [8372]P146(x83723,x83721,x83722)+E(x83721,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x83721),f853(x83722,x83721,x83723))),f849(x83722,x83721,x83723)),x83722)+P105(f326(f326(f235(a1),f850(x83722,x83721,x83723)),x83721))
% 157.55/157.23 [8373]P145(x83733,x83731,x83732)+E(x83731,f2(a1))+E(f326(f326(f79(a1),f326(f326(f80(a1),x83731),f858(x83732,x83731,x83733))),f855(x83732,x83731,x83733)),x83732)+P105(f326(f326(f235(a1),f856(x83732,x83731,x83733)),x83731))
% 157.55/157.23 [8408]P145(x84083,x84081,x84082)+~P105(f326(x84083,x84082))+E(f326(f326(f79(a1),f326(f326(f80(a1),x84081),f858(x84082,x84081,x84083))),f855(x84082,x84081,x84083)),x84082)+P105(f326(f326(f235(a1),f856(x84082,x84081,x84083)),x84081))
% 157.55/157.23 [8409]~P69(x84091)+~P74(x84091)+~P39(x84093)+E(f326(f326(f8(a909,x84091),f326(f326(f10(a1,x84091,a909),x84092),f100(a1))),f326(f309(a1,a909,a104),x84093)),f326(f326(f8(a1,x84091),x84092),x84093))
% 157.55/157.23 [8410]~P69(x84101)+~P74(x84101)+~P39(x84103)+E(f326(f326(f11(a909,x84101),f326(f326(f10(a1,x84101,a909),x84102),f100(a1))),f326(f309(a1,a909,a104),x84103)),f326(f326(f11(a1,x84101),x84102),x84103))
% 157.55/157.23 [8419]P146(x84193,x84191,x84192)+E(f326(f326(f79(a1),f326(f326(f80(a1),x84191),f853(x84192,x84191,x84193))),f849(x84192,x84191,x84193)),x84192)+~P105(f326(x84193,f2(a1)))+P105(f326(f326(f235(a1),f850(x84192,x84191,x84193)),x84191))
% 157.55/157.23 [8441]~E(x84412,f2(a909))+~E(f326(f250(a909,a909),x84413),f2(a909))+~E(x84411,f326(f326(f79(a909),f326(f326(f80(a909),f326(f250(a909,a909),x84413)),x84412)),f326(f255(a909,a909),x84413)))+P105(f326(f48(x84411,x84412),x84413))
% 157.55/157.23 [8497]P105(f326(x84971,x84972))+~P105(f326(f326(f328(x84973),f896(x84971,x84972,x84973)),f892(x84971,x84972,x84973)))+~P105(f326(f61(x84973),x84972))+~P105(f326(x84971,f188(f917(x84973,a905))))
% 157.55/157.23 [9119]P105(f326(x91191,x91192))+~P105(f326(f61(x91193),x91192))+~P105(f326(x91191,f326(f326(f308(x91193),f896(x91191,x91192,x91193)),f892(x91191,x91192,x91193))))+~P105(f326(x91191,f188(f917(x91193,a905))))
% 157.55/157.23 [9349]P105(f326(f326(f234(a1),x93491),f2(a1)))+~P105(f326(f326(f235(a1),f326(f326(f79(a1),f326(f326(f80(a1),x93493),x93491)),x93492)),f2(a1)))+~P105(f326(f326(f234(a1),f2(a1)),x93492))+~P105(f326(f326(f235(a1),f2(a1)),x93493))
% 157.55/157.23 [5960]~P77(x59602)+E(x59601,f188(f917(x59602,a905)))+~P105(f326(f61(x59602),x59601))+E(f12(x59602,f326(f326(f308(x59602),x59603),x59601)),f326(f326(f110(x59602),x59603),f12(x59602,x59601)))
% 157.55/157.23 [5961]~P77(x59612)+E(x59611,f188(f917(x59612,a905)))+~P105(f326(f61(x59612),x59611))+E(f13(x59612,f326(f326(f308(x59612),x59613),x59611)),f326(f326(f101(x59612),x59613),f13(x59612,x59611)))
% 157.55/157.23 [5962]~P108(x59622)+E(x59621,f188(f917(x59622,a905)))+~P105(f326(f61(x59622),x59621))+E(f16(x59622,f326(f326(f308(x59622),x59623),x59621)),f326(f326(f232(x59622),x59623),f16(x59622,x59621)))
% 157.55/157.23 [5963]~P108(x59632)+E(x59631,f188(f917(x59632,a905)))+~P105(f326(f61(x59632),x59631))+E(f17(x59632,f326(f326(f308(x59632),x59633),x59631)),f326(f326(f233(x59632),x59633),f17(x59632,x59631)))
% 157.55/157.23 [6287]~P125(x62871)+~E(x62873,f2(x62871))+~E(x62872,f2(x62871))+E(f326(f326(f79(x62871),f326(f326(f80(x62871),x62872),x62872)),f326(f326(f80(x62871),x62873),x62873)),f2(x62871))
% 157.55/157.23 [6357]~P96(x63572)+E(x63571,f188(f917(x63572,a905)))+~P105(f326(f61(x63572),x63571))+E(f326(f63(x63572,f80(x63572)),f326(f326(f308(x63572),x63573),x63571)),f326(f326(f80(x63572),x63573),f326(f63(x63572,f80(x63572)),x63571)))
% 157.55/157.23 [6483]~P108(x64832)+E(x64831,f188(f917(x64832,a905)))+~P105(f326(f61(x64832),x64831))+E(f14(x64832,f232(x64832),f326(f326(f308(x64832),x64833),x64831)),f326(f326(f232(x64832),x64833),f14(x64832,f232(x64832),x64831)))
% 157.55/157.23 [6484]~P108(x64842)+E(x64841,f188(f917(x64842,a905)))+~P105(f326(f61(x64842),x64841))+E(f15(x64842,f233(x64842),f326(f326(f308(x64842),x64843),x64841)),f326(f326(f233(x64842),x64843),f15(x64842,f233(x64842),x64841)))
% 157.55/157.23 [6995]~P67(x69951)+~P105(f326(f61(x69951),x69953))+E(f326(f63(x69951,f80(x69951)),f326(f326(f308(x69951),x69952),x69953)),f326(f326(f64(x69951,x69951,f80(x69951)),x69952),x69953))+P105(f326(f326(f328(x69951),x69952),x69953))
% 157.55/157.23 [7073]~E(f326(f326(f79(a1),x70732),f326(f326(f80(a1),x70733),x70731)),x70733)+~P105(f326(f326(f235(a1),f2(a1)),x70733))+P105(f326(f326(f234(a1),f77(a1)),x70731))+~P105(f326(f326(f235(a1),x70732),x70733))
% 157.55/157.23 [7101]~E(f326(f326(f79(a1),x71012),f326(f326(f80(a1),x71013),x71011)),x71013)+P105(f326(f326(f234(a1),x71011),f77(a1)))+~P105(f326(f326(f234(a1),f2(a1)),x71012))+~P105(f326(f326(f235(a1),f2(a1)),x71013))
% 157.55/157.23 [7118]E(x71181,f2(a909))+~P105(f326(f48(x71183,x71181),x71182))+~P105(f326(f326(f235(a909),f2(a909)),x71181))+P105(f326(f326(f235(a909),f326(f255(a909,a909),x71182)),x71181))
% 157.55/157.23 [7150]~P136(x71501)+~P105(f326(f326(f234(x71501),x71502),f2(x71501)))+~P105(f326(f326(f234(x71501),x71503),f2(x71501)))+E(f326(f326(f80(x71501),f326(f75(x71501),x71502)),f326(f75(x71501),x71503)),f326(f75(x71501),f326(f326(f80(x71501),x71502),x71503)))
% 157.55/157.23 [7197]~P136(x71971)+~P105(f326(f326(f234(x71971),x71972),f2(x71971)))+E(f326(f326(f80(x71971),f326(f75(x71971),x71972)),f326(f75(x71971),x71973)),f326(f75(x71971),f326(f326(f80(x71971),x71972),x71973)))+~P105(f326(f326(f234(x71971),f2(x71971)),x71973))
% 157.55/157.23 [7198]~P136(x71981)+~P105(f326(f326(f234(x71981),x71983),f2(x71981)))+E(f326(f326(f80(x71981),f326(f75(x71981),x71982)),f326(f75(x71981),x71983)),f326(f75(x71981),f326(f326(f80(x71981),x71982),x71983)))+~P105(f326(f326(f234(x71981),f2(x71981)),x71982))
% 157.55/157.23 [7254]~P136(x72541)+E(f326(f326(f80(x72541),f326(f75(x72541),x72542)),f326(f75(x72541),x72543)),f326(f75(x72541),f326(f326(f80(x72541),x72542),x72543)))+~P105(f326(f326(f234(x72541),f2(x72541)),x72542))+~P105(f326(f326(f234(x72541),f2(x72541)),x72543))
% 157.55/157.23 [7271]~P111(x72711)+~P105(f326(f326(f234(x72711),x72713),f2(x72711)))+~P105(f326(f326(f234(x72711),x72712),f2(x72711)))+P105(f326(f326(f234(x72711),f2(x72711)),f326(f326(f80(x72711),x72712),x72713)))
% 157.55/157.23 [7272]~P125(x72721)+~P105(f326(f326(f234(x72721),x72723),f2(x72721)))+~P105(f326(f326(f234(x72721),x72722),f2(x72721)))+P105(f326(f326(f234(x72721),f2(x72721)),f326(f326(f80(x72721),x72722),x72723)))
% 157.55/157.23 [7273]~P64(x72731)+~P105(f326(f326(f234(x72731),x72733),f2(x72731)))+~P105(f326(f326(f234(x72731),x72732),f2(x72731)))+P105(f326(f326(f234(x72731),f2(x72731)),f326(f326(f290(x72731),x72732),x72733)))
% 157.55/157.23 [7274]~P65(x72741)+~P105(f326(f326(f235(x72741),x72743),f2(x72741)))+~P105(f326(f326(f234(x72741),x72742),f2(x72741)))+P105(f326(f326(f234(x72741),f2(x72741)),f326(f326(f290(x72741),x72742),x72743)))
% 157.55/157.23 [7275]~P125(x72751)+~P105(f326(f326(f235(x72751),x72753),f2(x72751)))+~P105(f326(f326(f235(x72751),x72752),f2(x72751)))+P105(f326(f326(f235(x72751),f2(x72751)),f326(f326(f80(x72751),x72752),x72753)))
% 157.55/157.23 [7276]~P64(x72761)+~P105(f326(f326(f235(x72761),x72763),f2(x72761)))+~P105(f326(f326(f235(x72761),x72762),f2(x72761)))+P105(f326(f326(f235(x72761),f2(x72761)),f326(f326(f290(x72761),x72762),x72763)))
% 157.55/157.23 [7277]~P65(x72771)+~P105(f326(f326(f235(x72771),x72773),f2(x72771)))+~P105(f326(f326(f235(x72771),x72772),f2(x72771)))+P105(f326(f326(f235(x72771),f2(x72771)),f326(f326(f290(x72771),x72772),x72773)))
% 157.55/157.23 [7278]~P124(x72781)+~P105(f326(f326(f235(a909),f2(a909)),x72783))+~P105(f326(f326(f235(x72781),f77(x72781)),x72782))+P105(f326(f326(f235(x72781),f77(x72781)),f326(f326(f243(x72781),x72782),x72783)))
% 157.55/157.23 [7374]~P111(x73741)+~P105(f326(f326(f234(x73741),f2(x73741)),x73743))+~P105(f326(f326(f234(x73741),f2(x73741)),x73742))+P105(f326(f326(f234(x73741),f2(x73741)),f326(f326(f80(x73741),x73742),x73743)))
% 157.55/157.23 [7375]~P133(x73751)+~P105(f326(f326(f234(x73751),f2(x73751)),x73753))+~P105(f326(f326(f234(x73751),f2(x73751)),x73752))+P105(f326(f326(f234(x73751),f2(x73751)),f326(f326(f80(x73751),x73752),x73753)))
% 157.55/157.23 [7376]~P125(x73761)+~P105(f326(f326(f234(x73761),f2(x73761)),x73763))+~P105(f326(f326(f234(x73761),f2(x73761)),x73762))+P105(f326(f326(f234(x73761),f2(x73761)),f326(f326(f80(x73761),x73762),x73763)))
% 157.55/157.23 [7378]~P64(x73781)+~P105(f326(f326(f234(x73781),f2(x73781)),x73783))+~P105(f326(f326(f234(x73781),f2(x73781)),x73782))+P105(f326(f326(f234(x73781),f2(x73781)),f326(f326(f290(x73781),x73782),x73783)))
% 157.55/157.23 [7379]~P65(x73791)+~P105(f326(f326(f235(x73791),f2(x73791)),x73793))+~P105(f326(f326(f234(x73791),f2(x73791)),x73792))+P105(f326(f326(f234(x73791),f2(x73791)),f326(f326(f290(x73791),x73792),x73793)))
% 157.55/157.23 [7380]~P124(x73801)+~P105(f326(f326(f235(x73801),f77(x73801)),x73803))+~P105(f326(f326(f235(x73801),f77(x73801)),x73802))+P105(f326(f326(f235(x73801),f77(x73801)),f326(f326(f80(x73801),x73802),x73803)))
% 157.55/157.23 [7381]~P131(x73811)+~P105(f326(f326(f235(x73811),f2(x73811)),x73813))+~P105(f326(f326(f235(x73811),f2(x73811)),x73812))+P105(f326(f326(f235(x73811),f2(x73811)),f326(f326(f80(x73811),x73812),x73813)))
% 157.55/157.23 [7384]~P88(x73841)+~P105(f326(f326(f235(x73841),f2(x73841)),x73843))+~P105(f326(f326(f235(x73841),f2(x73841)),x73842))+P105(f326(f326(f235(x73841),f2(x73841)),f326(f326(f79(x73841),x73842),x73843)))
% 157.55/157.23 [7385]~P64(x73851)+~P105(f326(f326(f235(x73851),f2(x73851)),x73853))+~P105(f326(f326(f235(x73851),f2(x73851)),x73852))+P105(f326(f326(f235(x73851),f2(x73851)),f326(f326(f290(x73851),x73852),x73853)))
% 157.55/157.23 [7386]~P65(x73861)+~P105(f326(f326(f235(x73861),f2(x73861)),x73863))+~P105(f326(f326(f235(x73861),f2(x73861)),x73862))+P105(f326(f326(f235(x73861),f2(x73861)),f326(f326(f290(x73861),x73862),x73863)))
% 157.55/157.23 [7467]~P77(x74671)+~P105(f326(f61(x74671),x74673))+E(f12(x74671,f326(f326(f308(x74671),x74672),x74673)),x74672)+~E(f326(f326(f3(f917(x74671,a905)),x74673),f326(f326(f308(x74671),x74672),f188(f917(x74671,a905)))),f188(f917(x74671,a905)))
% 157.55/157.23 [7468]~P77(x74681)+~P105(f326(f61(x74681),x74683))+E(f13(x74681,f326(f326(f308(x74681),x74682),x74683)),x74682)+~E(f326(f326(f3(f917(x74681,a905)),x74683),f326(f326(f308(x74681),x74682),f188(f917(x74681,a905)))),f188(f917(x74681,a905)))
% 157.55/157.23 [7469]~P108(x74691)+~P105(f326(f61(x74691),x74693))+E(f16(x74691,f326(f326(f308(x74691),x74692),x74693)),x74692)+~E(f326(f326(f3(f917(x74691,a905)),x74693),f326(f326(f308(x74691),x74692),f188(f917(x74691,a905)))),f188(f917(x74691,a905)))
% 157.55/157.23 [7470]~P108(x74701)+~P105(f326(f61(x74701),x74703))+E(f17(x74701,f326(f326(f308(x74701),x74702),x74703)),x74702)+~E(f326(f326(f3(f917(x74701,a905)),x74703),f326(f326(f308(x74701),x74702),f188(f917(x74701,a905)))),f188(f917(x74701,a905)))
% 157.55/157.23 [7472]~P125(x74721)+P105(f326(f326(f234(x74721),x74722),f2(x74721)))+P105(f326(f326(f234(x74721),f2(x74721)),x74723))+~P105(f326(f326(f234(x74721),f2(x74721)),f326(f326(f80(x74721),x74723),x74722)))
% 157.55/157.23 [7473]~P125(x74731)+P105(f326(f326(f234(x74731),x74732),f2(x74731)))+P105(f326(f326(f234(x74731),f2(x74731)),x74733))+~P105(f326(f326(f234(x74731),f2(x74731)),f326(f326(f80(x74731),x74732),x74733)))
% 157.55/157.23 [7474]~P64(x74741)+P105(f326(f326(f234(x74741),x74742),f2(x74741)))+P105(f326(f326(f234(x74741),f2(x74741)),x74743))+~P105(f326(f326(f234(x74741),f2(x74741)),f326(f326(f290(x74741),x74743),x74742)))
% 157.55/157.23 [7475]~P64(x74751)+P105(f326(f326(f234(x74751),x74752),f2(x74751)))+P105(f326(f326(f234(x74751),f2(x74751)),x74753))+~P105(f326(f326(f234(x74751),f2(x74751)),f326(f326(f290(x74751),x74752),x74753)))
% 157.55/157.23 [7476]~P125(x74761)+P105(f326(f326(f234(x74761),x74762),f2(x74761)))+P105(f326(f326(f234(x74761),f2(x74761)),x74762))+~P105(f326(f326(f234(x74761),f2(x74761)),f326(f326(f80(x74761),x74763),x74762)))
% 157.55/157.23 [7477]~P125(x74771)+P105(f326(f326(f234(x74771),x74772),f2(x74771)))+P105(f326(f326(f234(x74771),f2(x74771)),x74772))+~P105(f326(f326(f234(x74771),f2(x74771)),f326(f326(f80(x74771),x74772),x74773)))
% 157.55/157.23 [7478]~P64(x74781)+P105(f326(f326(f234(x74781),x74782),f2(x74781)))+P105(f326(f326(f234(x74781),f2(x74781)),x74782))+~P105(f326(f326(f234(x74781),f2(x74781)),f326(f326(f290(x74781),x74783),x74782)))
% 157.55/157.23 [7479]~P64(x74791)+P105(f326(f326(f234(x74791),x74792),f2(x74791)))+P105(f326(f326(f234(x74791),f2(x74791)),x74792))+~P105(f326(f326(f234(x74791),f2(x74791)),f326(f326(f290(x74791),x74792),x74793)))
% 157.55/157.23 [7480]~P64(x74801)+P105(f326(f326(f235(x74801),x74802),f2(x74801)))+P105(f326(f326(f235(x74801),f2(x74801)),x74803))+~P105(f326(f326(f235(x74801),f2(x74801)),f326(f326(f290(x74801),x74803),x74802)))
% 157.55/157.23 [7481]~P64(x74811)+P105(f326(f326(f235(x74811),x74812),f2(x74811)))+P105(f326(f326(f235(x74811),f2(x74811)),x74813))+~P105(f326(f326(f235(x74811),f2(x74811)),f326(f326(f290(x74811),x74812),x74813)))
% 157.55/157.23 [7482]~P64(x74821)+P105(f326(f326(f235(x74821),x74822),f2(x74821)))+P105(f326(f326(f235(x74821),f2(x74821)),x74822))+~P105(f326(f326(f235(x74821),f2(x74821)),f326(f326(f290(x74821),x74823),x74822)))
% 157.55/157.23 [7483]~P64(x74831)+P105(f326(f326(f235(x74831),x74832),f2(x74831)))+P105(f326(f326(f235(x74831),f2(x74831)),x74832))+~P105(f326(f326(f235(x74831),f2(x74831)),f326(f326(f290(x74831),x74832),x74833)))
% 157.55/157.23 [7570]~E(f326(f326(f101(f917(x75701,a905)),f326(f172(x75701),x75702)),f326(f172(x75701),x75703)),f188(f917(x75701,a905)))+~P105(f326(f137(x75701),x75703))+~P105(f326(f137(x75701),x75702))+P105(f326(f137(x75701),f326(f326(f134(x75701),x75702),x75703)))
% 157.55/157.23 [7571]~P108(x75711)+~P105(f326(f61(x75711),x75713))+E(f14(x75711,f232(x75711),f326(f326(f308(x75711),x75712),x75713)),x75712)+~E(f326(f326(f3(f917(x75711,a905)),x75713),f326(f326(f308(x75711),x75712),f188(f917(x75711,a905)))),f188(f917(x75711,a905)))
% 157.55/157.23 [7572]~P108(x75721)+~P105(f326(f61(x75721),x75723))+E(f15(x75721,f233(x75721),f326(f326(f308(x75721),x75722),x75723)),x75722)+~E(f326(f326(f3(f917(x75721,a905)),x75723),f326(f326(f308(x75721),x75722),f188(f917(x75721,a905)))),f188(f917(x75721,a905)))
% 157.55/157.23 [7586]~P86(x75861)+~P105(f326(f326(f234(x75861),x75862),x75863))+~P105(f326(f326(f234(x75861),f326(f78(x75861),x75862)),x75863))+P105(f326(f326(f234(x75861),f326(f75(x75861),x75862)),x75863))
% 157.55/157.23 [7587]~P118(x75871)+~P105(f326(f326(f235(x75871),x75872),x75873))+~P105(f326(f326(f235(x75871),f326(f78(x75871),x75872)),x75873))+P105(f326(f326(f235(x75871),f326(f75(x75871),x75872)),x75873))
% 157.55/157.23 [7654]~P131(x76541)+P105(f326(f326(f235(x76541),f2(x76541)),x76542))+~P105(f326(f326(f235(x76541),f2(x76541)),x76543))+~P105(f326(f326(f235(x76541),f2(x76541)),f326(f326(f80(x76541),x76543),x76542)))
% 157.55/157.23 [7655]~P131(x76551)+P105(f326(f326(f235(x76551),f2(x76551)),x76552))+~P105(f326(f326(f235(x76551),f2(x76551)),x76553))+~P105(f326(f326(f235(x76551),f2(x76551)),f326(f326(f80(x76551),x76552),x76553)))
% 157.55/157.23 [7951]E(x79511,x79512)+~P105(f326(f61(x79513),x79511))+~P105(f326(f326(f234(a909),f326(f35(x79513),x79511)),f326(f35(x79513),x79512)))+~P105(f326(f326(f234(f917(x79513,a905)),x79512),x79511))
% 157.55/157.23 [8093]~P105(f326(f326(f235(a1),x80931),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x80932))+~P105(f326(f326(f234(a1),x80932),x80933))+P105(f326(f326(f234(a1),f326(f326(f36(a1),x80931),x80932)),f326(f326(f36(a1),x80931),x80933)))
% 157.55/157.23 [8103]~P105(f326(f326(f234(a1),f2(a1)),x81031))+~P105(f326(f326(f235(a1),f2(a1)),x81033))+~P105(f326(f326(f234(a1),x81033),x81032))+P105(f326(f326(f234(a1),f326(f326(f36(a1),x81031),x81032)),f326(f326(f36(a1),x81031),x81033)))
% 157.55/157.23 [8237]E(f326(x82371,f352(x82372,x82371,x82373)),x82372)+~P105(f326(f326(f234(a1),x82372),f326(x82371,x82373)))+P105(f326(f326(f235(a909),f353(x82372,x82371,x82373)),x82373))+~P105(f326(f326(f234(a1),f326(x82371,f2(a909))),x82372))
% 157.55/157.23 [8238]E(f326(x82381,f354(x82382,x82381,x82383)),x82382)+~P105(f326(f326(f234(a1),x82382),f326(x82381,x82383)))+P105(f326(f326(f235(a909),f355(x82382,x82381,x82383)),x82383))+~P105(f326(f326(f234(a1),f326(x82381,f2(a909))),x82382))
% 157.55/157.23 [8335]~P105(f326(f61(x83351),x83353))+~P105(f326(f326(f235(a909),f326(f35(x83351),x83352)),f326(f35(x83351),x83353)))+~P105(f326(f326(f234(f917(x83351,a905)),x83352),x83353))+P105(f326(f326(f235(f917(x83351,a905)),x83352),x83353))
% 157.55/157.23 [8362]E(f326(f326(f79(a1),f424(x83623,x83621,x83622)),f425(x83623,x83621,x83622)),x83621)+E(f326(f326(f3(a1),x83621),x83622),x83621)+~P105(f326(f326(f235(a1),f2(a1)),x83622))+~P105(f326(f326(f328(a1),f326(f326(f3(a1),x83621),f77(a1))),x83623))
% 157.55/157.23 [8363]E(f326(f326(f3(a1),f432(x83633,x83631,x83632)),f433(x83633,x83631,x83632)),x83631)+E(f326(f326(f79(a1),x83631),x83632),x83631)+~P105(f326(f326(f235(a1),f2(a1)),x83632))+~P105(f326(f326(f328(a1),f326(f326(f79(a1),x83631),f77(a1))),x83633))
% 157.55/157.23 [8414]~P105(f326(f326(f234(a909),x84143),x84141))+P105(f326(f326(f234(a909),x84141),x84142))+~P105(f326(f326(f234(a909),x84143),x84142))+~P105(f326(f326(f234(a909),f326(f326(f3(a909),x84141),x84143)),f326(f326(f3(a909),x84142),x84143)))
% 157.55/157.23 [8415]~P105(f326(f326(f234(a909),x84153),x84151))+P105(f326(f326(f235(a909),x84151),x84152))+~P105(f326(f326(f234(a909),x84153),x84152))+~P105(f326(f326(f235(a909),f326(f326(f3(a909),x84151),x84153)),f326(f326(f3(a909),x84152),x84153)))
% 157.55/157.23 [8434]~P108(x84342)+E(x84341,f113(x84342))+~P12(x84342,f326(f168(x84342),x84341))+E(f326(f142(x84342,x84342,f326(f9(x84342,x84342,x84342),f233(x84342)),x84343),f326(f168(x84342),x84341)),f326(f326(f233(x84342),f326(f326(f164(x84342),x84341),f2(a909))),x84343))
% 157.55/157.23 [8502]E(f326(f326(f3(a1),x85021),x85022),x85021)+~P105(f326(f326(f235(a1),f2(a1)),x85022))+P105(f326(f326(f328(a1),f424(x85023,x85021,x85022)),x85023))+~P105(f326(f326(f328(a1),f326(f326(f3(a1),x85021),f77(a1))),x85023))
% 157.55/157.23 [8503]E(f326(f326(f79(a1),x85031),x85032),x85031)+~P105(f326(f326(f235(a1),f2(a1)),x85032))+P105(f326(f326(f328(a1),f432(x85033,x85031,x85032)),x85033))+~P105(f326(f326(f328(a1),f326(f326(f79(a1),x85031),f77(a1))),x85033))
% 157.55/157.23 [8574]~P105(f326(f326(f234(a1),x85741),f326(x85742,x85743)))+P105(f326(f326(f235(a909),f353(x85741,x85742,x85743)),x85743))+P105(f326(f326(f234(a909),f352(x85741,x85742,x85743)),x85743))+~P105(f326(f326(f234(a1),f326(x85742,f2(a909))),x85741))
% 157.55/157.23 [8575]~P105(f326(f326(f234(a1),x85751),f326(x85752,x85753)))+P105(f326(f326(f235(a909),f355(x85751,x85752,x85753)),x85753))+P105(f326(f326(f234(a909),f354(x85751,x85752,x85753)),x85753))+~P105(f326(f326(f234(a1),f326(x85752,f2(a909))),x85751))
% 157.55/157.23 [8647]E(f326(f326(f3(a1),x86471),x86472),x86471)+~P105(f326(f326(f235(a1),f2(a1)),x86472))+P105(f326(f326(f328(a1),f425(x86473,x86471,x86472)),f302(a1,f77(a1),x86472)))+~P105(f326(f326(f328(a1),f326(f326(f3(a1),x86471),f77(a1))),x86473))
% 157.55/157.23 [8648]E(f326(f326(f79(a1),x86481),x86482),x86481)+~P105(f326(f326(f235(a1),f2(a1)),x86482))+P105(f326(f326(f328(a1),f433(x86483,x86481,x86482)),f302(a1,f77(a1),x86482)))+~P105(f326(f326(f328(a1),f326(f326(f79(a1),x86481),f77(a1))),x86483))
% 157.55/157.23 [8780]~P124(x87801)+~P105(f326(f326(f235(x87801),x87802),f77(x87801)))+~P105(f326(f326(f235(x87801),f2(x87801)),x87802))+P105(f326(f326(f235(x87801),f326(f326(f80(x87801),x87802),f326(f326(f243(x87801),x87802),x87803))),f326(f326(f243(x87801),x87802),x87803)))
% 157.55/157.23 [8873]~P105(f326(x88731,x88732))+P105(f326(x88731,f2(a909)))+~P105(f326(f326(f235(a909),x88732),x88733))+~P105(f326(x88731,f45(a909,f326(a112,f379(x88732,x88731,x88733)),x88733)))
% 157.55/157.23 [9025]E(f403(x90251,x90252,x90253),f2(a909))+P105(f326(f326(x90251,x90253),x90252))+P105(f326(f326(x90251,f403(x90251,x90252,x90253)),f45(a909,f401(x90251,x90252,x90253),f403(x90251,x90252,x90253))))+~P105(f326(f314(f916(a909,a909),a219),f326(f326(f251(a909,a909),x90253),x90252)))
% 157.55/157.23 [9061]~P24(x90611,x90611,x90612,x90613)+E(f326(f309(x90611,x90611,x90612),x90613),x90613)+~P105(f326(f61(x90611),x90613))+~P105(f326(f326(f234(f917(x90611,a905)),f326(f309(x90611,x90611,x90612),x90613)),x90613))
% 157.55/157.23 [9276]P105(f326(f326(x92761,x92762),x92763))+P105(f326(f326(f235(a1),f766(x92761,x92763,x92762)),f767(x92761,x92763,x92762)))+P105(f326(f326(x92761,f766(x92761,x92763,x92762)),f326(f326(f79(a1),f767(x92761,x92763,x92762)),f77(a1))))+~P105(f326(f314(f916(a1,a1),a133),f326(f326(f251(a1,a1),x92762),x92763)))
% 157.55/157.23 [9293]P105(f326(f326(x92931,x92932),x92933))+~P105(f326(f326(f235(a1),f400(x92931,x92933,x92932)),f2(a1)))+P105(f326(f326(x92931,f326(f78(a1),f397(x92931,x92933,x92932))),f326(f78(a1),f400(x92931,x92933,x92932))))+~P105(f326(f314(f916(a1,a1),a221),f326(f326(f251(a1,a1),x92932),x92933)))
% 157.55/157.23 [9477]P105(f326(f326(x94771,x94772),x94773))+P105(f326(f326(x94771,f326(f326(f79(a1),f671(x94771,x94773,x94772)),f77(a1))),f673(x94771,x94773,x94772)))+~P105(f326(f326(f234(a1),f671(x94771,x94773,x94772)),f673(x94771,x94773,x94772)))+~P105(f326(f314(f916(a1,a1),a182),f326(f326(f251(a1,a1),x94772),x94773)))
% 157.55/157.23 [9909]~P61(x99092)+~P61(x99091)+~P105(f326(f56(f916(x99091,x99092)),x99093))+P105(f326(f56(x99091),f326(f326(f10(f917(x99092,a905),a905,x99091),f56(x99092)),f326(f326(f10(f917(x99092,f916(x99091,x99092)),f917(x99092,a905),x99091),f326(f10(f916(x99091,x99092),a905,x99092),x99093)),f251(x99091,x99092)))))
% 157.55/157.23 [9910]~P61(x99102)+~P61(x99101)+~P105(f326(f57(f916(x99101,x99102)),x99103))+P105(f326(f57(x99101),f326(f326(f10(f917(x99102,a905),a905,x99101),f57(x99102)),f326(f326(f10(f917(x99102,f916(x99101,x99102)),f917(x99102,a905),x99101),f326(f10(f916(x99101,x99102),a905,x99102),x99103)),f251(x99101,x99102)))))
% 157.55/157.23 [10004]~P61(x100042)+~P61(x100041)+P105(f326(f56(f916(x100041,x100042)),x100043))+~P105(f326(f56(x100041),f326(f326(f10(f917(x100042,a905),a905,x100041),f56(x100042)),f326(f326(f10(f917(x100042,f916(x100041,x100042)),f917(x100042,a905),x100041),f326(f10(f916(x100041,x100042),a905,x100042),x100043)),f251(x100041,x100042)))))
% 157.55/157.23 [10005]~P61(x100052)+~P61(x100051)+P105(f326(f57(f916(x100051,x100052)),x100053))+~P105(f326(f57(x100051),f326(f326(f10(f917(x100052,a905),a905,x100051),f57(x100052)),f326(f326(f10(f917(x100052,f916(x100051,x100052)),f917(x100052,a905),x100051),f326(f10(f916(x100051,x100052),a905,x100052),x100053)),f251(x100051,x100052)))))
% 157.55/157.23 [10179]E(f326(x101791,f352(x101792,x101791,x101793)),x101792)+~P105(f326(f326(f234(a1),x101792),f326(x101791,x101793)))+~P105(f326(f326(f234(a1),f326(f75(a1),f326(f326(f3(a1),f326(x101791,f326(f326(f79(a909),f353(x101792,x101791,x101793)),f77(a909)))),f326(x101791,f353(x101792,x101791,x101793))))),f77(a1)))+~P105(f326(f326(f234(a1),f326(x101791,f2(a909))),x101792))
% 157.55/157.23 [10180]E(f326(x101801,f354(x101802,x101801,x101803)),x101802)+~P105(f326(f326(f234(a1),x101802),f326(x101801,x101803)))+~P105(f326(f326(f234(a1),f326(f75(a1),f326(f326(f3(a1),f326(x101801,f326(f326(f79(a909),f355(x101802,x101801,x101803)),f77(a909)))),f326(x101801,f355(x101802,x101801,x101803))))),f77(a1)))+~P105(f326(f326(f234(a1),f326(x101801,f2(a909))),x101802))
% 157.55/157.23 [10183]~P105(f326(f326(f234(a1),x101831),f326(x101832,x101833)))+~P105(f326(f326(f234(a1),f326(f75(a1),f326(f326(f3(a1),f326(x101832,f326(f326(f79(a909),f353(x101831,x101832,x101833)),f77(a909)))),f326(x101832,f353(x101831,x101832,x101833))))),f77(a1)))+P105(f326(f326(f234(a909),f352(x101831,x101832,x101833)),x101833))+~P105(f326(f326(f234(a1),f326(x101832,f2(a909))),x101831))
% 157.55/157.23 [10184]~P105(f326(f326(f234(a1),x101841),f326(x101842,x101843)))+~P105(f326(f326(f234(a1),f326(f75(a1),f326(f326(f3(a1),f326(x101842,f326(f326(f79(a909),f355(x101841,x101842,x101843)),f77(a909)))),f326(x101842,f355(x101841,x101842,x101843))))),f77(a1)))+P105(f326(f326(f234(a909),f354(x101841,x101842,x101843)),x101843))+~P105(f326(f326(f234(a1),f326(x101842,f2(a909))),x101841))
% 157.55/157.23 [10242]E(x102421,x102422)+~E(f326(f142(f910(x102423),f910(x102423),f134(x102423),f113(x102423)),x102421),f326(f142(f910(x102423),f910(x102423),f134(x102423),f113(x102423)),x102422))+~E(f326(f189(f910(f910(x102423))),x102421),f326(f189(f910(f910(x102423))),x102422))+~P105(f326(f326(f256(f910(x102423),f910(x102423),a905),f326(f326(f9(f910(x102423),f917(f910(x102423),a909),f917(f910(x102423),a905)),f326(f326(f10(f917(a909,a905),f917(f917(f910(x102423),a909),f917(f910(x102423),a905)),f910(x102423)),f10(a909,a905,f910(x102423))),f326(f326(f10(a909,f917(a909,a905),f910(x102423)),a323),f189(f910(x102423))))),f189(f910(x102423)))),f697(x102422,x102421,x102423)))
% 157.55/157.23 [10243]E(x102431,x102432)+~E(f326(f142(f910(x102433),f910(x102433),f134(x102433),f113(x102433)),x102431),f326(f142(f910(x102433),f910(x102433),f134(x102433),f113(x102433)),x102432))+~E(f326(f189(f910(f910(x102433))),x102431),f326(f189(f910(f910(x102433))),x102432))+~P105(f326(f326(f256(f910(x102433),f910(x102433),a905),f326(f326(f9(f910(x102433),f917(f910(x102433),a909),f917(f910(x102433),a905)),f326(f326(f10(f917(a909,a905),f917(f917(f910(x102433),a909),f917(f910(x102433),a905)),f910(x102433)),f10(a909,a905,f910(x102433))),f326(f326(f10(a909,f917(a909,a905),f910(x102433)),a323),f189(f910(x102433))))),f189(f910(x102433)))),f698(x102431,x102432,x102433)))
% 157.55/157.23 [6983]~E(f77(a909),f2(a909))+~P105(f326(f61(x69831),x69833))+~P105(f326(f61(x69831),x69832))+E(f326(f326(f79(a909),f326(f35(x69831),x69832)),f326(f35(x69831),x69833)),f326(f35(x69831),f326(f326(f110(f917(x69831,a905)),x69832),x69833)))
% 157.55/157.23 [7393]~P101(x73931)+~P105(f326(f61(x73931),x73932))+~P105(f326(f326(f328(x73931),x73933),x73932))+P105(f326(f326(f234(x73931),f326(f63(x73931,f101(x73931)),x73932)),x73933))
% 157.55/157.23 [7394]~P108(x73941)+~P105(f326(f61(x73941),x73942))+~P105(f326(f326(f328(x73941),x73943),x73942))+P105(f326(f326(f234(x73941),f326(f63(x73941,f232(x73941)),x73942)),x73943))
% 157.55/157.23 [7648]~P105(f326(f61(x76481),x76483))+~P105(f326(f61(x76481),x76482))+~E(f326(f326(f101(f917(x76481,a905)),x76482),x76483),f188(f917(x76481,a905)))+E(f326(f326(f79(a909),f326(f35(x76481),x76482)),f326(f35(x76481),x76483)),f326(f35(x76481),f326(f326(f110(f917(x76481,a905)),x76482),x76483)))
% 157.55/157.23 [8420]~P36(x84201,x84203)+~P36(x84201,x84202)+~E(f326(f326(f101(f917(x84201,a905)),f326(f263(x84201,x84201),x84202)),f326(f283(x84201,x84201),x84203)),f188(f917(x84201,a905)))+P36(x84201,f326(f326(f110(f917(f916(x84201,x84201),a905)),x84202),x84203))
% 157.55/157.23 [8514]E(x85141,f326(f326(f36(a909),x85142),x85143))+~P105(f326(f326(f235(a909),f2(a909)),x85143))+~P105(f326(f326(f235(a909),x85142),f326(f326(f80(a909),x85143),f326(a112,x85141))))+~P105(f326(f326(f234(a909),f326(f326(f80(a909),x85143),x85141)),x85142))
% 157.55/157.23 [8645]~P105(f326(f61(x86451),x86452))+~P105(f326(f61(x86451),x86453))+E(f326(f326(f79(a909),f326(f35(x86451),x86452)),f326(f35(x86451),x86453)),f326(f35(x86451),f326(f326(f110(f917(x86451,a905)),x86452),x86453)))+P105(f326(f326(f328(x86451),f877(x86453,x86452,x86451)),f326(f326(f101(f917(x86451,a905)),x86452),x86453)))
% 157.55/157.23 [9037]~P125(x90372)+~E(x90371,f2(x90372))+~E(x90373,f2(x90372))+~P105(f326(f326(f235(x90372),f2(x90372)),f326(f326(f79(x90372),f326(f326(f80(x90372),x90373),x90373)),f326(f326(f80(x90372),x90371),x90371))))
% 157.55/157.23 [9556]~P36(x95561,x95563)+~P36(x95561,x95562)+P36(x95561,f326(f326(f110(f917(f916(x95561,x95561),a905)),x95562),x95563))+~P105(f326(f326(f234(f917(f916(x95561,x95561),a905)),f326(f326(f288(x95561,x95561,x95561),x95562),x95563)),x95562))
% 157.55/157.23 [9684]~P105(f326(x96841,x96843))+~P105(f326(f61(x96842),x96843))+P105(f326(x96841,f188(f917(x96842,a905))))+~P105(f326(x96841,f326(f326(f3(f917(x96842,a905)),f484(x96841,x96843,x96842)),f326(f326(f308(x96842),f475(x96841,x96843,x96842)),f188(f917(x96842,a905))))))
% 157.55/157.23 [8820]~P105(f326(f326(f235(a1),f2(a1)),x88203))+P105(f326(f326(f234(a1),f2(a1)),x88201))+~P105(f326(f326(f235(a1),x88202),x88203))+~P105(f326(f326(f234(a1),f2(a1)),f326(f326(f79(a1),f326(f326(f80(a1),x88203),x88201)),x88202)))
% 157.55/157.23 [8844]~P77(x88441)+~P105(f326(f61(x88441),x88442))+E(f326(f326(f3(f917(x88441,a905)),x88442),f326(f326(f308(x88441),x88443),f188(f917(x88441,a905)))),f188(f917(x88441,a905)))+E(f326(f326(f110(x88441),x88443),f12(x88441,f326(f326(f3(f917(x88441,a905)),x88442),f326(f326(f308(x88441),x88443),f188(f917(x88441,a905)))))),f12(x88441,f326(f326(f308(x88441),x88443),x88442)))
% 157.55/157.23 [8845]~P77(x88451)+~P105(f326(f61(x88451),x88452))+E(f326(f326(f3(f917(x88451,a905)),x88452),f326(f326(f308(x88451),x88453),f188(f917(x88451,a905)))),f188(f917(x88451,a905)))+E(f326(f326(f101(x88451),x88453),f13(x88451,f326(f326(f3(f917(x88451,a905)),x88452),f326(f326(f308(x88451),x88453),f188(f917(x88451,a905)))))),f13(x88451,f326(f326(f308(x88451),x88453),x88452)))
% 157.55/157.23 [8846]~P108(x88461)+~P105(f326(f61(x88461),x88462))+E(f326(f326(f3(f917(x88461,a905)),x88462),f326(f326(f308(x88461),x88463),f188(f917(x88461,a905)))),f188(f917(x88461,a905)))+E(f326(f326(f232(x88461),x88463),f16(x88461,f326(f326(f3(f917(x88461,a905)),x88462),f326(f326(f308(x88461),x88463),f188(f917(x88461,a905)))))),f16(x88461,f326(f326(f308(x88461),x88463),x88462)))
% 157.55/157.23 [8847]~P108(x88471)+~P105(f326(f61(x88471),x88472))+E(f326(f326(f3(f917(x88471,a905)),x88472),f326(f326(f308(x88471),x88473),f188(f917(x88471,a905)))),f188(f917(x88471,a905)))+E(f326(f326(f233(x88471),x88473),f17(x88471,f326(f326(f3(f917(x88471,a905)),x88472),f326(f326(f308(x88471),x88473),f188(f917(x88471,a905)))))),f17(x88471,f326(f326(f308(x88471),x88473),x88472)))
% 157.55/157.23 [8919]~P108(x89191)+~P105(f326(f61(x89191),x89192))+E(f326(f326(f3(f917(x89191,a905)),x89192),f326(f326(f308(x89191),x89193),f188(f917(x89191,a905)))),f188(f917(x89191,a905)))+E(f326(f326(f232(x89191),x89193),f14(x89191,f232(x89191),f326(f326(f3(f917(x89191,a905)),x89192),f326(f326(f308(x89191),x89193),f188(f917(x89191,a905)))))),f14(x89191,f232(x89191),f326(f326(f308(x89191),x89193),x89192)))
% 157.55/157.23 [8920]~P108(x89201)+~P105(f326(f61(x89201),x89202))+E(f326(f326(f3(f917(x89201,a905)),x89202),f326(f326(f308(x89201),x89203),f188(f917(x89201,a905)))),f188(f917(x89201,a905)))+E(f326(f326(f233(x89201),x89203),f15(x89201,f233(x89201),f326(f326(f3(f917(x89201,a905)),x89202),f326(f326(f308(x89201),x89203),f188(f917(x89201,a905)))))),f15(x89201,f233(x89201),f326(f326(f308(x89201),x89203),x89202)))
% 157.55/157.23 [9496]E(x94961,x94962)+~E(f326(f142(f910(x94963),f910(x94963),f134(x94963),f113(x94963)),x94961),f326(f142(f910(x94963),f910(x94963),f134(x94963),f113(x94963)),x94962))+~E(f326(f189(f910(f910(x94963))),x94961),f326(f189(f910(f910(x94963))),x94962))+P105(f326(f326(f328(f916(f910(x94963),f910(x94963))),f697(x94962,x94961,x94963)),f326(f172(f916(f910(x94963),f910(x94963))),f326(f326(f181(f910(x94963),f910(x94963)),x94961),x94962))))
% 157.55/157.23 [9497]E(x94971,x94972)+~E(f326(f142(f910(x94973),f910(x94973),f134(x94973),f113(x94973)),x94971),f326(f142(f910(x94973),f910(x94973),f134(x94973),f113(x94973)),x94972))+~E(f326(f189(f910(f910(x94973))),x94971),f326(f189(f910(f910(x94973))),x94972))+P105(f326(f326(f328(f916(f910(x94973),f910(x94973))),f698(x94971,x94972,x94973)),f326(f172(f916(f910(x94973),f910(x94973))),f326(f326(f181(f910(x94973),f910(x94973)),x94972),x94971))))
% 157.55/157.23 [10349]~P98(x103492)+E(x103491,f188(f917(x103492,a905)))+~P105(f326(f61(x103492),x103491))+E(f13(x103492,f326(f261(x103492),f326(f326(f10(f917(x103492,a905),a905,x103492),f86(x103492)),f326(f326(f9(x103492,f917(x103492,a905),f917(x103492,a905)),f326(f326(f10(f917(x103492,f917(a905,a905)),f917(f917(x103492,a905),f917(x103492,a905)),x103492),f20(x103492,a905,a905)),f326(f326(f10(f917(x103492,a905),f917(x103492,f917(a905,a905)),x103492),f326(f10(a905,f917(a905,a905),x103492),a324)),f326(f326(f9(x103492,f917(x103492,x103492),f917(x103492,a905)),f326(f326(f10(f917(x103492,a905),f917(f917(x103492,x103492),f917(x103492,a905)),x103492),f10(x103492,a905,x103492)),a323)),f326(f110(x103492),x103493))))),f326(f326(f9(x103492,f917(x103492,a905),a905),f328(x103492)),x103491))))),f326(f326(f110(x103492),x103493),f13(x103492,x103491)))
% 157.55/157.23 [10350]~P98(x103502)+E(x103501,f188(f917(x103502,a905)))+~P105(f326(f61(x103502),x103501))+E(f12(x103502,f326(f261(x103502),f326(f326(f10(f917(x103502,a905),a905,x103502),f86(x103502)),f326(f326(f9(x103502,f917(x103502,a905),f917(x103502,a905)),f326(f326(f10(f917(x103502,f917(a905,a905)),f917(f917(x103502,a905),f917(x103502,a905)),x103502),f20(x103502,a905,a905)),f326(f326(f10(f917(x103502,a905),f917(x103502,f917(a905,a905)),x103502),f326(f10(a905,f917(a905,a905),x103502),a324)),f326(f326(f9(x103502,f917(x103502,x103502),f917(x103502,a905)),f326(f326(f10(f917(x103502,a905),f917(f917(x103502,x103502),f917(x103502,a905)),x103502),f10(x103502,a905,x103502)),a323)),f326(f101(x103502),x103503))))),f326(f326(f9(x103502,f917(x103502,a905),a905),f328(x103502)),x103501))))),f326(f326(f101(x103502),x103503),f12(x103502,x103501)))
% 157.55/157.23 [10351]~P76(x103512)+E(x103511,f188(f917(x103512,a905)))+~P105(f326(f61(x103512),x103511))+E(f16(x103512,f326(f261(x103512),f326(f326(f10(f917(x103512,a905),a905,x103512),f86(x103512)),f326(f326(f9(x103512,f917(x103512,a905),f917(x103512,a905)),f326(f326(f10(f917(x103512,f917(a905,a905)),f917(f917(x103512,a905),f917(x103512,a905)),x103512),f20(x103512,a905,a905)),f326(f326(f10(f917(x103512,a905),f917(x103512,f917(a905,a905)),x103512),f326(f10(a905,f917(a905,a905),x103512),a324)),f326(f326(f9(x103512,f917(x103512,x103512),f917(x103512,a905)),f326(f326(f10(f917(x103512,a905),f917(f917(x103512,x103512),f917(x103512,a905)),x103512),f10(x103512,a905,x103512)),a323)),f326(f79(x103512),x103513))))),f326(f326(f9(x103512,f917(x103512,a905),a905),f328(x103512)),x103511))))),f326(f326(f79(x103512),x103513),f16(x103512,x103511)))
% 157.55/157.23 [10352]~P76(x103522)+E(x103521,f188(f917(x103522,a905)))+~P105(f326(f61(x103522),x103521))+E(f17(x103522,f326(f261(x103522),f326(f326(f10(f917(x103522,a905),a905,x103522),f86(x103522)),f326(f326(f9(x103522,f917(x103522,a905),f917(x103522,a905)),f326(f326(f10(f917(x103522,f917(a905,a905)),f917(f917(x103522,a905),f917(x103522,a905)),x103522),f20(x103522,a905,a905)),f326(f326(f10(f917(x103522,a905),f917(x103522,f917(a905,a905)),x103522),f326(f10(a905,f917(a905,a905),x103522),a324)),f326(f326(f9(x103522,f917(x103522,x103522),f917(x103522,a905)),f326(f326(f10(f917(x103522,a905),f917(f917(x103522,x103522),f917(x103522,a905)),x103522),f10(x103522,a905,x103522)),a323)),f326(f79(x103522),x103523))))),f326(f326(f9(x103522,f917(x103522,a905),a905),f328(x103522)),x103521))))),f326(f326(f79(x103522),x103523),f17(x103522,x103521)))
% 157.55/157.23 [10353]~P108(x103532)+E(x103531,f188(f917(x103532,a905)))+~P105(f326(f61(x103532),x103531))+E(f15(x103532,f233(x103532),f326(f261(x103532),f326(f326(f10(f917(x103532,a905),a905,x103532),f86(x103532)),f326(f326(f9(x103532,f917(x103532,a905),f917(x103532,a905)),f326(f326(f10(f917(x103532,f917(a905,a905)),f917(f917(x103532,a905),f917(x103532,a905)),x103532),f20(x103532,a905,a905)),f326(f326(f10(f917(x103532,a905),f917(x103532,f917(a905,a905)),x103532),f326(f10(a905,f917(a905,a905),x103532),a324)),f326(f326(f9(x103532,f917(x103532,x103532),f917(x103532,a905)),f326(f326(f10(f917(x103532,a905),f917(f917(x103532,x103532),f917(x103532,a905)),x103532),f10(x103532,a905,x103532)),a323)),f326(f232(x103532),x103533))))),f326(f326(f9(x103532,f917(x103532,a905),a905),f328(x103532)),x103531))))),f326(f326(f232(x103532),x103533),f15(x103532,f233(x103532),x103531)))
% 157.55/157.23 [10354]~P108(x103542)+E(x103541,f188(f917(x103542,a905)))+~P105(f326(f61(x103542),x103541))+E(f14(x103542,f232(x103542),f326(f261(x103542),f326(f326(f10(f917(x103542,a905),a905,x103542),f86(x103542)),f326(f326(f9(x103542,f917(x103542,a905),f917(x103542,a905)),f326(f326(f10(f917(x103542,f917(a905,a905)),f917(f917(x103542,a905),f917(x103542,a905)),x103542),f20(x103542,a905,a905)),f326(f326(f10(f917(x103542,a905),f917(x103542,f917(a905,a905)),x103542),f326(f10(a905,f917(a905,a905),x103542),a324)),f326(f326(f9(x103542,f917(x103542,x103542),f917(x103542,a905)),f326(f326(f10(f917(x103542,a905),f917(f917(x103542,x103542),f917(x103542,a905)),x103542),f10(x103542,a905,x103542)),a323)),f326(f233(x103542),x103543))))),f326(f326(f9(x103542,f917(x103542,a905),a905),f328(x103542)),x103541))))),f326(f326(f233(x103542),x103543),f14(x103542,f232(x103542),x103541)))
% 157.55/157.23 [10069]~P118(x100691)+~E(x100693,f2(x100691))+~E(x100692,f2(x100691))+E(f326(f326(f79(x100691),f326(f326(f243(x100691),x100692),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x100691),x100693),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f2(x100691))
% 157.55/157.23 [10223]~P124(x102231)+~P105(f326(f326(f234(x102231),f2(x102231)),x102233))+P105(f326(f326(f234(x102231),x102232),x102233))+~P105(f326(f326(f234(x102231),f326(f326(f243(x102231),x102232),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x102231),x102233),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))))
% 157.55/157.23 [10279]~P118(x102792)+~E(x102791,f2(x102792))+~E(x102793,f2(x102792))+~P105(f326(f326(f235(x102792),f2(x102792)),f326(f326(f79(x102792),f326(f326(f243(x102792),x102793),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97))))),f326(f326(f243(x102792),x102791),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))))
% 157.55/157.23 [6865]~P6(x68653,x68652)+~P105(f326(x68651,x68654))+~P105(f326(f326(f328(x68653),x68654),f269(x68653,x68652)))+P105(f326(x68651,f816(x68651,x68652,x68653)))
% 157.55/157.23 [8755]P25(x87551,x87552,f820(x87553,x87552,x87554,x87551),x87554,x87553)+~E(f326(f35(x87551),x87554),f326(f35(x87552),x87553))+~P105(f326(f61(x87552),x87553))+~P105(f326(f61(x87551),x87554))
% 157.55/157.23 [9459]E(x94591,x94592)+~E(f643(x94591,x94592,x94594,x94593),f646(x94591,x94592,x94594,x94593))+P105(f326(f326(f328(f916(f910(x94593),f910(x94593))),f326(f326(f251(f910(x94593),f910(x94593)),x94592),x94591)),f147(x94593,x94594)))+P105(f326(f326(f328(f916(f910(x94593),f910(x94593))),f326(f326(f251(f910(x94593),f910(x94593)),x94591),x94592)),f147(x94593,x94594)))
% 157.55/157.23 [4992]~P62(x49922)+~E(x49924,f2(x49922))+~E(x49921,f2(x49922))+E(x49921,f326(f326(f290(x49922),x49923),x49924))
% 157.55/157.23 [4993]~P62(x49931)+~E(x49933,f2(x49931))+~E(x49934,f2(x49931))+E(f326(f326(f290(x49931),x49932),x49933),x49934)
% 157.55/157.23 [5113]~P62(x51132)+E(x51131,f2(x51132))+~E(x51133,f2(x51132))+~E(x51131,f326(f326(f290(x51132),x51134),x51133))
% 157.55/157.23 [5114]~P62(x51142)+E(x51141,f2(x51142))+~E(x51143,f2(x51142))+~E(f326(f326(f290(x51142),x51144),x51143),x51141)
% 157.55/157.23 [5297]~P121(x52972)+E(x52971,f2(x52972))+~E(f326(f326(f290(x52972),x52973),x52971),x52974)+E(x52973,f326(f326(f80(x52972),x52974),x52971))
% 157.55/157.23 [5299]~P121(x52992)+E(x52991,f2(x52992))+~E(f326(f326(f80(x52992),x52993),x52991),x52994)+E(x52993,f326(f326(f290(x52992),x52994),x52991))
% 157.55/157.23 [5300]~P62(x53002)+E(x53001,f2(x53002))+~E(f326(f326(f290(x53002),x53003),x53001),x53004)+E(x53003,f326(f326(f80(x53002),x53004),x53001))
% 157.55/157.23 [5301]~P62(x53012)+E(x53011,f2(x53012))+~E(f326(f326(f80(x53012),x53013),x53011),x53014)+E(x53013,f326(f326(f290(x53012),x53014),x53011))
% 157.55/157.23 [5302]~P121(x53022)+E(x53021,f2(x53022))+~E(x53023,f326(f326(f290(x53022),x53024),x53021))+E(f326(f326(f80(x53022),x53023),x53021),x53024)
% 157.55/157.23 [5304]~P121(x53042)+E(x53041,f2(x53042))+~E(x53043,f326(f326(f80(x53042),x53044),x53041))+E(f326(f326(f290(x53042),x53043),x53041),x53044)
% 157.55/157.23 [5305]~P62(x53052)+E(x53051,f2(x53052))+~E(x53053,f326(f326(f290(x53052),x53054),x53051))+E(f326(f326(f80(x53052),x53053),x53051),x53054)
% 157.55/157.23 [5306]~P62(x53062)+E(x53061,f2(x53062))+~E(x53063,f326(f326(f80(x53062),x53064),x53061))+E(f326(f326(f290(x53062),x53063),x53061),x53064)
% 157.55/157.23 [5330]~P62(x53302)+~E(x53301,f2(x53302))+~E(f326(f326(f80(x53302),x53301),x53304),x53303)+E(x53301,f326(f326(f290(x53302),x53303),x53304))
% 157.55/157.23 [5331]~P62(x53311)+~E(x53314,f2(x53311))+~E(x53312,f326(f326(f80(x53311),x53314),x53313))+E(f326(f326(f290(x53311),x53312),x53313),x53314)
% 157.55/157.23 [5406]~E(x54063,x54064)+~E(x54062,x54063)+~P109(x54061)+E(f302(x54061,x54062,x54063),f326(f326(f308(x54061),x54064),f188(f917(x54061,a905))))
% 157.55/157.23 [5615]~E(f114(x56152,x56151),x56153)+~E(f144(x56152,x56151),x56154)+E(x56151,f113(x56152))+E(f326(f326(f134(x56152),x56153),f326(f326(f151(x56152),x56154),f113(x56152))),x56151)
% 157.55/157.23 [6253]~P124(x62533)+E(x62531,x62532)+~E(f326(f326(f243(x62533),x62534),x62531),f326(f326(f243(x62533),x62534),x62532))+~P105(f326(f326(f235(x62533),f77(x62533)),x62534))
% 157.55/157.23 [6254]E(x62541,x62542)+~E(f326(f326(f308(x62543),x62544),x62541),f326(f326(f308(x62543),x62544),x62542))+P105(f326(f326(f328(x62543),x62544),x62542))+P105(f326(f326(f328(x62543),x62544),x62541))
% 157.55/157.23 [6296]E(f326(x62961,x62962),f77(a909))+~E(f326(f326(f11(x62963,a909),x62961),x62964),f77(a909))+~P105(f326(f61(x62963),x62964))+~P105(f326(f326(f328(x62963),x62962),x62964))
% 157.55/157.23 [6297]E(f326(x62971,x62972),f2(a909))+~E(f326(f326(f8(x62973,a909),x62971),x62974),f2(a909))+~P105(f326(f61(x62973),x62974))+~P105(f326(f326(f328(x62973),x62972),x62974))
% 157.55/157.23 [6518]~P109(x65181)+~P105(f326(f326(f234(x65181),x65184),x65183))+P105(f326(f326(f234(x65181),x65182),x65183))+~P105(f326(f326(f234(x65181),x65182),x65184))
% 157.55/157.23 [6519]~P106(x65191)+~P105(f326(f326(f234(x65191),x65192),x65194))+P105(f326(f326(f234(x65191),x65192),x65193))+~P105(f326(f326(f234(x65191),x65194),x65193))
% 157.55/157.23 [6520]~P109(x65201)+~P105(f326(f326(f235(x65201),x65204),x65203))+P105(f326(f326(f235(x65201),x65202),x65203))+~P105(f326(f326(f234(x65201),x65202),x65204))
% 157.55/157.23 [6521]~P109(x65211)+~P105(f326(f326(f235(x65211),x65212),x65214))+P105(f326(f326(f235(x65211),x65212),x65213))+~P105(f326(f326(f234(x65211),x65214),x65213))
% 157.55/157.23 [6522]~P109(x65221)+~P105(f326(f326(f235(x65221),x65224),x65223))+P105(f326(f326(f235(x65221),x65222),x65223))+~P105(f326(f326(f235(x65221),x65222),x65224))
% 157.55/157.23 [6523]~P106(x65231)+~P105(f326(f326(f235(x65231),x65232),x65234))+P105(f326(f326(f235(x65231),x65232),x65233))+~P105(f326(f326(f234(x65231),x65234),x65233))
% 157.55/157.23 [6524]~P106(x65241)+~P105(f326(f326(f235(x65241),x65244),x65243))+P105(f326(f326(f235(x65241),x65242),x65243))+~P105(f326(f326(f234(x65241),x65242),x65244))
% 157.55/157.23 [6525]~P106(x65251)+~P105(f326(f326(f235(x65251),x65252),x65254))+P105(f326(f326(f235(x65251),x65252),x65253))+~P105(f326(f326(f235(x65251),x65254),x65253))
% 157.55/157.23 [6526]~P112(x65261)+~P105(f326(f326(f286(x65261),x65262),x65264))+P105(f326(f326(f286(x65261),x65262),x65263))+~P105(f326(f326(f286(x65261),x65264),x65263))
% 157.55/157.23 [6605]~P34(x66054,x66053,x66052)+E(x66051,f751(x66052,x66053,x66054))+~P105(f326(x66053,x66051))+~P105(f326(f326(f328(x66054),x66051),f326(f172(x66054),x66052)))
% 157.55/157.23 [6606]~P34(x66064,x66063,x66062)+E(x66061,f761(x66062,x66063,x66064))+~P105(f326(x66063,x66061))+~P105(f326(f326(f328(x66064),x66061),f326(f172(x66064),x66062)))
% 157.55/157.23 [6756]~P4(x67561)+~P105(f326(f326(f234(x67561),x67562),f38(x67561,x67564)))+P105(f326(f326(f234(x67561),x67562),x67563))+~P105(f326(f326(f328(x67561),x67563),x67564))
% 157.55/157.23 [6906]~P108(x69061)+~P12(x69061,f326(f326(f151(x69061),x69062),x69064))+~P105(f326(f326(f328(x69061),x69063),f326(f172(x69061),x69064)))+P105(f326(f326(f234(x69061),x69062),x69063))
% 157.55/157.23 [6993]~P4(x69931)+~P105(f326(f326(f234(x69931),f37(x69931,x69934)),x69933))+P105(f326(f326(f234(x69931),x69932),x69933))+~P105(f326(f326(f328(x69931),x69932),x69934))
% 157.55/157.23 [7132]~P59(x71321)+P105(f326(f326(f286(x71321),x71322),f45(x71321,x71323,x71324)))+~P105(f326(f326(f286(x71321),x71322),x71324))+~P105(f326(f326(f286(x71321),x71322),x71323))
% 157.55/157.23 [7396]~P108(x73961)+E(f326(f326(f110(f917(x73961,a905)),f326(f301(x73961,x73962),x73963)),f326(f301(x73961,x73963),x73964)),f326(f301(x73961,x73962),x73964))+~P105(f326(f326(f234(x73961),x73963),x73964))+~P105(f326(f326(f234(x73961),x73962),x73963))
% 157.55/157.23 [7443]P34(x74431,x74432,x74433)+~E(f763(x74433,x74432,x74431,x74434),x74434)+~P105(f326(x74432,x74434))+~P105(f326(f326(f328(x74431),x74434),f326(f172(x74431),x74433)))
% 157.55/157.23 [7444]P34(x74441,x74442,x74443)+~E(f770(x74443,x74442,x74441,x74444),x74444)+~P105(f326(x74442,x74444))+~P105(f326(f326(f328(x74441),x74444),f326(f172(x74441),x74443)))
% 157.55/157.23 [7486]~P59(x74861)+~P105(f326(f326(f286(x74861),x74862),f45(x74861,x74863,x74864)))+P105(f326(f326(f286(x74861),x74862),x74863))+~P105(f326(f326(f286(x74861),x74862),x74864))
% 157.55/157.23 [7520]~P108(x75201)+E(f326(f326(f110(f917(x75201,a905)),f326(f301(x75201,x75202),x75203)),f302(x75201,x75203,x75204)),f302(x75201,x75202,x75204))+~P105(f326(f326(f234(x75201),x75203),x75204))+~P105(f326(f326(f234(x75201),x75202),x75203))
% 157.55/157.23 [7581]~P108(x75811)+E(f326(f326(f110(f917(x75811,a905)),f305(x75811,x75812,x75813)),f326(f301(x75811,x75813),x75814)),f305(x75811,x75812,x75814))+~P105(f326(f326(f234(x75811),x75813),x75814))+~P105(f326(f326(f235(x75811),x75812),x75813))
% 157.55/157.23 [7598]~P108(x75981)+E(f326(f326(f110(f917(x75981,a905)),f302(x75981,x75982,x75983)),f305(x75981,x75983,x75984)),f326(f301(x75981,x75982),x75984))+~P105(f326(f326(f234(x75981),x75982),x75983))+~P105(f326(f326(f235(x75981),x75983),x75984))
% 157.55/157.23 [7629]~P108(x76291)+E(f326(f326(f110(f917(x76291,a905)),f302(x76291,x76292,x76293)),f304(x76291,x76293,x76294)),f302(x76291,x76292,x76294))+~P105(f326(f326(f234(x76291),x76293),x76294))+~P105(f326(f326(f234(x76291),x76292),x76293))
% 157.55/157.23 [7630]~P108(x76301)+E(f326(f326(f110(f917(x76301,a905)),f305(x76301,x76302,x76303)),f302(x76301,x76303,x76304)),f304(x76301,x76302,x76304))+~P105(f326(f326(f234(x76301),x76303),x76304))+~P105(f326(f326(f235(x76301),x76302),x76303))
% 157.55/157.23 [7631]~P108(x76311)+E(f326(f326(f110(f917(x76311,a905)),f304(x76311,x76312,x76313)),f305(x76311,x76313,x76314)),f305(x76311,x76312,x76314))+~P105(f326(f326(f234(x76311),x76312),x76313))+~P105(f326(f326(f235(x76311),x76313),x76314))
% 157.55/157.23 [7632]~P108(x76321)+E(f326(f326(f110(f917(x76321,a905)),f304(x76321,x76322,x76323)),f304(x76321,x76323,x76324)),f304(x76321,x76322,x76324))+~P105(f326(f326(f234(x76321),x76323),x76324))+~P105(f326(f326(f234(x76321),x76322),x76323))
% 157.55/157.23 [8404]P24(x84041,x84042,f520(x84043,x84042,x84044,x84041),x84044)+~P105(f326(f61(x84042),x84043))+~P105(f326(f61(x84041),x84044))+~P105(f326(f326(f234(a909),f326(f35(x84041),x84044)),f326(f35(x84042),x84043)))
% 157.55/157.23 [8425]P34(x84251,x84252,x84253)+~P105(f326(x84252,x84254))+P105(f326(x84252,f763(x84253,x84252,x84251,x84254)))+~P105(f326(f326(f328(x84251),x84254),f326(f172(x84251),x84253)))
% 157.55/157.23 [8426]P34(x84261,x84262,x84263)+~P105(f326(x84262,x84264))+P105(f326(x84262,f770(x84263,x84262,x84261,x84264)))+~P105(f326(f326(f328(x84261),x84264),f326(f172(x84261),x84263)))
% 157.55/157.23 [8480]~P74(x84801)+~E(f326(x84803,f863(x84803,x84804,x84802,x84801)),f77(x84801))+E(f326(f326(f326(f65(x84801,x84802,f80(x84801)),x84803),f77(x84801)),x84804),f77(x84801))+~P105(f326(f61(x84802),x84804))
% 157.55/157.23 [8744]~P124(x87441)+~P105(f326(f326(f234(x87441),f2(x87441)),x87443))+P105(f326(f326(f234(x87441),x87442),x87443))+~P105(f326(f326(f234(x87441),f326(f326(f243(x87441),x87442),f326(a112,x87444))),f326(f326(f243(x87441),x87443),f326(a112,x87444))))
% 157.55/157.23 [9062]P34(x90621,x90622,x90623)+~P105(f326(x90622,x90624))+~P105(f326(f326(f328(x90621),x90624),f326(f172(x90621),x90623)))+P105(f326(f326(f328(x90621),f763(x90623,x90622,x90621,x90624)),f326(f172(x90621),x90623)))
% 157.55/157.23 [9063]P34(x90631,x90632,x90633)+~P105(f326(x90632,x90634))+~P105(f326(f326(f328(x90631),x90634),f326(f172(x90631),x90633)))+P105(f326(f326(f328(x90631),f770(x90633,x90632,x90631,x90634)),f326(f172(x90631),x90633)))
% 157.55/157.23 [9139]~P74(x91391)+E(f326(f326(f326(f65(x91391,x91392,f80(x91391)),x91393),f77(x91391)),x91394),f77(x91391))+~P105(f326(f61(x91392),x91394))+P105(f326(f326(f328(x91392),f863(x91393,x91394,x91392,x91391)),x91394))
% 157.55/157.23 [9627]~P105(f326(f326(f234(a1),x96274),f2(a1)))+P105(f326(f326(f234(a1),f326(f326(f79(a1),f326(f326(f80(a1),x96271),f45(a1,x96272,x96273))),x96274)),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x96273))+~P105(f326(f326(f235(a1),x96271),x96274))
% 157.55/157.23 [10062]~P105(f326(f61(x100621),x100622))+~P105(f326(f326(f328(x100621),x100624),x100622))+~P105(f326(f326(f328(x100621),x100623),x100622))+P105(f326(f326(f235(a909),f326(f35(x100621),f326(f326(f3(f917(x100621,a905)),f326(f326(f3(f917(x100621,a905)),x100622),f326(f326(f308(x100621),x100623),f188(f917(x100621,a905))))),f326(f326(f308(x100621),x100624),f188(f917(x100621,a905)))))),f326(f35(x100621),x100622)))
% 157.55/157.23 [7105]~P101(x71051)+~P105(f326(f326(f234(x71051),x71052),x71054))+~P105(f326(f326(f234(x71051),x71052),x71053))+P105(f326(f326(f234(x71051),x71052),f326(f326(f101(x71051),x71053),x71054)))
% 157.55/157.23 [7108]~P108(x71081)+~P105(f326(f326(f234(x71081),x71082),x71084))+~P105(f326(f326(f234(x71081),x71082),x71083))+P105(f326(f326(f234(x71081),x71082),f326(f326(f232(x71081),x71083),x71084)))
% 157.55/157.23 [7109]~P108(x71091)+~P105(f326(f326(f235(x71091),x71092),x71094))+~P105(f326(f326(f235(x71091),x71092),x71093))+P105(f326(f326(f235(x71091),x71092),f326(f326(f232(x71091),x71093),x71094)))
% 157.55/157.23 [7110]~P112(x71101)+~P105(f326(f326(f286(x71101),x71102),x71104))+~P105(f326(f326(f286(x71101),x71102),x71103))+P105(f326(f326(f286(x71101),x71102),f326(f326(f79(x71101),x71103),x71104)))
% 157.55/157.23 [7130]~P63(x71302)+E(x71301,f2(x71302))+E(f326(f326(f290(x71302),f326(f326(f243(x71302),x71301),x71303)),f326(f326(f243(x71302),x71301),x71304)),f326(f326(f243(x71302),x71301),f326(f326(f3(a909),x71303),x71304)))+~P105(f326(f326(f234(a909),x71304),x71303))
% 157.55/157.23 [7177]~P108(x71771)+~P12(x71771,f326(f326(f151(x71771),x71773),x71774))+P12(x71771,f326(f326(f151(x71771),x71772),f326(f326(f151(x71771),x71773),x71774)))+~P105(f326(f326(f234(x71771),x71772),x71773))
% 157.55/157.23 [7213]~P88(x72131)+~P105(f326(f326(f234(x72131),f2(x72131)),x72134))+~P105(f326(f326(f234(x72131),x72132),x72133))+P105(f326(f326(f234(x72131),x72132),f326(f326(f79(x72131),x72133),x72134)))
% 157.55/157.23 [7214]~P88(x72141)+~P105(f326(f326(f234(x72141),f2(x72141)),x72143))+~P105(f326(f326(f234(x72141),x72142),x72144))+P105(f326(f326(f234(x72141),x72142),f326(f326(f79(x72141),x72143),x72144)))
% 157.55/157.23 [7215]~P124(x72151)+~P105(f326(f326(f235(x72151),f2(x72151)),x72153))+~P105(f326(f326(f235(x72151),x72152),x72154))+P105(f326(f326(f235(x72151),x72152),f326(f326(f79(x72151),x72153),x72154)))
% 157.55/157.23 [7216]~P88(x72161)+~P105(f326(f326(f234(x72161),x72162),x72164))+~P105(f326(f326(f235(x72161),f2(x72161)),x72163))+P105(f326(f326(f235(x72161),x72162),f326(f326(f79(x72161),x72163),x72164)))
% 157.55/157.23 [7217]~P88(x72171)+~P105(f326(f326(f234(x72171),f2(x72171)),x72173))+~P105(f326(f326(f235(x72171),x72172),x72174))+P105(f326(f326(f235(x72171),x72172),f326(f326(f79(x72171),x72173),x72174)))
% 157.55/157.23 [7258]~P108(x72581)+P105(f326(f326(f234(x72581),x72582),x72583))+P105(f326(f326(f234(x72581),x72582),x72584))+~P105(f326(f326(f234(x72581),x72582),f326(f326(f233(x72581),x72584),x72583)))
% 157.55/157.23 [7259]~P108(x72591)+P105(f326(f326(f235(x72591),x72592),x72593))+P105(f326(f326(f235(x72591),x72592),x72594))+~P105(f326(f326(f235(x72591),x72592),f326(f326(f233(x72591),x72594),x72593)))
% 157.55/157.23 [7554]~P109(x75542)+~P61(x75541)+~P105(f326(f326(f235(f917(x75541,x75542)),x75543),x75544))+P105(f326(f326(f234(f917(x75541,x75542)),x75543),x75544))
% 157.55/157.23 [7913]~P65(x79131)+~P105(f326(f326(f235(x79131),x79134),f2(x79131)))+~P105(f326(f326(f234(x79131),x79133),f326(f326(f290(x79131),x79132),x79134)))+P105(f326(f326(f234(x79131),x79132),f326(f326(f80(x79131),x79133),x79134)))
% 157.55/157.23 [7914]~P65(x79141)+~P105(f326(f326(f235(x79141),x79144),f2(x79141)))+~P105(f326(f326(f234(x79141),x79143),f326(f326(f80(x79141),x79142),x79144)))+P105(f326(f326(f234(x79141),x79142),f326(f326(f290(x79141),x79143),x79144)))
% 157.55/157.23 [7915]~P65(x79151)+~P105(f326(f326(f235(x79151),x79154),f2(x79151)))+~P105(f326(f326(f235(x79151),x79153),f326(f326(f290(x79151),x79152),x79154)))+P105(f326(f326(f235(x79151),x79152),f326(f326(f80(x79151),x79153),x79154)))
% 157.55/157.23 [7916]~P65(x79161)+~P105(f326(f326(f235(x79161),x79164),f2(x79161)))+~P105(f326(f326(f235(x79161),x79163),f326(f326(f80(x79161),x79162),x79164)))+P105(f326(f326(f235(x79161),x79162),f326(f326(f290(x79161),x79163),x79164)))
% 157.55/157.23 [8019]~P111(x80191)+~P105(f326(f326(f234(x80191),x80192),f2(x80191)))+~P105(f326(f326(f234(x80191),x80194),x80193))+P105(f326(f326(f234(x80191),f326(f326(f80(x80191),x80192),x80193)),f326(f326(f80(x80191),x80192),x80194)))
% 157.55/157.23 [8020]~P125(x80201)+~P105(f326(f326(f235(x80201),x80202),f2(x80201)))+~P105(f326(f326(f234(x80201),x80204),x80203))+P105(f326(f326(f234(x80201),f326(f326(f80(x80201),x80202),x80203)),f326(f326(f80(x80201),x80202),x80204)))
% 157.55/157.23 [8021]~P111(x80211)+~P105(f326(f326(f234(x80211),x80213),f2(x80211)))+~P105(f326(f326(f234(x80211),x80214),x80212))+P105(f326(f326(f234(x80211),f326(f326(f80(x80211),x80212),x80213)),f326(f326(f80(x80211),x80214),x80213)))
% 157.55/157.23 [8022]~P64(x80221)+~P105(f326(f326(f234(x80221),x80223),f2(x80221)))+~P105(f326(f326(f234(x80221),x80224),x80222))+P105(f326(f326(f234(x80221),f326(f326(f290(x80221),x80222),x80223)),f326(f326(f290(x80221),x80224),x80223)))
% 157.55/157.23 [8026]~P125(x80261)+~P105(f326(f326(f235(x80261),x80263),f2(x80261)))+~P105(f326(f326(f235(x80261),x80264),x80262))+P105(f326(f326(f235(x80261),f326(f326(f80(x80261),x80262),x80263)),f326(f326(f80(x80261),x80264),x80263)))
% 157.55/157.23 [8027]~P125(x80271)+~P105(f326(f326(f235(x80271),x80272),f2(x80271)))+~P105(f326(f326(f235(x80271),x80274),x80273))+P105(f326(f326(f235(x80271),f326(f326(f80(x80271),x80272),x80273)),f326(f326(f80(x80271),x80272),x80274)))
% 157.55/157.23 [8028]~P65(x80281)+~P105(f326(f326(f235(x80281),x80283),f2(x80281)))+~P105(f326(f326(f235(x80281),x80284),x80282))+P105(f326(f326(f235(x80281),f326(f326(f290(x80281),x80282),x80283)),f326(f326(f290(x80281),x80284),x80283)))
% 157.55/157.23 [8029]~P124(x80291)+~P105(f326(f326(f235(x80291),f77(x80291)),x80292))+~P105(f326(f326(f234(a909),x80293),x80294))+P105(f326(f326(f234(x80291),f326(f326(f243(x80291),x80292),x80293)),f326(f326(f243(x80291),x80292),x80294)))
% 157.55/157.23 [8030]~P124(x80301)+~P105(f326(f326(f234(x80301),f77(x80301)),x80302))+~P105(f326(f326(f234(a909),x80303),x80304))+P105(f326(f326(f234(x80301),f326(f326(f243(x80301),x80302),x80303)),f326(f326(f243(x80301),x80302),x80304)))
% 157.55/157.23 [8032]~P124(x80321)+~P105(f326(f326(f235(x80321),f77(x80321)),x80322))+~P105(f326(f326(f235(a909),x80323),x80324))+P105(f326(f326(f235(x80321),f326(f326(f243(x80321),x80322),x80323)),f326(f326(f243(x80321),x80322),x80324)))
% 157.55/157.23 [8059]P105(f326(f326(f235(a909),f2(a909)),f326(x80591,x80592)))+~P105(f326(f61(x80593),x80594))+~P105(f326(f326(f328(x80593),x80592),x80594))+~P105(f326(f326(f235(a909),f2(a909)),f326(f326(f11(x80593,a909),x80591),x80594)))
% 157.55/157.23 [8067]~P135(x80671)+~P105(f326(f326(f234(x80671),x80673),x80674))+~P105(f326(f326(f234(x80671),f2(x80671)),x80672))+P105(f326(f326(f234(x80671),f326(f326(f80(x80671),x80672),x80673)),f326(f326(f80(x80671),x80672),x80674)))
% 157.55/157.23 [8068]~P134(x80681)+~P105(f326(f326(f234(x80681),x80683),x80684))+~P105(f326(f326(f234(x80681),f2(x80681)),x80682))+P105(f326(f326(f234(x80681),f326(f326(f80(x80681),x80682),x80683)),f326(f326(f80(x80681),x80682),x80684)))
% 157.55/157.23 [8069]~P125(x80691)+~P105(f326(f326(f235(x80691),f2(x80691)),x80692))+~P105(f326(f326(f234(x80691),x80693),x80694))+P105(f326(f326(f234(x80691),f326(f326(f80(x80691),x80692),x80693)),f326(f326(f80(x80691),x80692),x80694)))
% 157.55/157.23 [8070]~P135(x80701)+~P105(f326(f326(f234(x80701),x80702),x80704))+~P105(f326(f326(f234(x80701),f2(x80701)),x80703))+P105(f326(f326(f234(x80701),f326(f326(f80(x80701),x80702),x80703)),f326(f326(f80(x80701),x80704),x80703)))
% 157.55/157.23 [8071]~P64(x80711)+~P105(f326(f326(f234(x80711),x80712),x80714))+~P105(f326(f326(f234(x80711),f2(x80711)),x80713))+P105(f326(f326(f234(x80711),f326(f326(f290(x80711),x80712),x80713)),f326(f326(f290(x80711),x80714),x80713)))
% 157.55/157.23 [8072]~P124(x80721)+~P105(f326(f326(f234(x80721),x80722),x80724))+~P105(f326(f326(f234(x80721),f2(x80721)),x80722))+P105(f326(f326(f234(x80721),f326(f326(f243(x80721),x80722),x80723)),f326(f326(f243(x80721),x80724),x80723)))
% 157.55/157.23 [8074]~P131(x80741)+~P105(f326(f326(f235(x80741),x80743),x80744))+~P105(f326(f326(f235(x80741),f2(x80741)),x80742))+P105(f326(f326(f235(x80741),f326(f326(f80(x80741),x80742),x80743)),f326(f326(f80(x80741),x80742),x80744)))
% 157.55/157.23 [8075]~P119(x80751)+~P105(f326(f326(f235(x80751),x80753),x80754))+~P105(f326(f326(f235(x80751),f2(x80751)),x80752))+P105(f326(f326(f235(x80751),f326(f326(f80(x80751),x80752),x80753)),f326(f326(f80(x80751),x80752),x80754)))
% 157.55/157.23 [8076]~P125(x80761)+~P105(f326(f326(f235(x80761),x80762),x80764))+~P105(f326(f326(f235(x80761),f2(x80761)),x80763))+P105(f326(f326(f235(x80761),f326(f326(f80(x80761),x80762),x80763)),f326(f326(f80(x80761),x80764),x80763)))
% 157.55/157.23 [8077]~P131(x80771)+~P105(f326(f326(f235(x80771),x80772),x80774))+~P105(f326(f326(f235(x80771),f2(x80771)),x80773))+P105(f326(f326(f235(x80771),f326(f326(f80(x80771),x80772),x80773)),f326(f326(f80(x80771),x80774),x80773)))
% 157.55/157.23 [8078]~P125(x80781)+~P105(f326(f326(f235(x80781),x80783),x80784))+~P105(f326(f326(f235(x80781),f2(x80781)),x80782))+P105(f326(f326(f235(x80781),f326(f326(f80(x80781),x80782),x80783)),f326(f326(f80(x80781),x80782),x80784)))
% 157.55/157.23 [8079]~P65(x80791)+~P105(f326(f326(f235(x80791),x80792),x80794))+~P105(f326(f326(f235(x80791),f2(x80791)),x80793))+P105(f326(f326(f235(x80791),f326(f326(f290(x80791),x80792),x80793)),f326(f326(f290(x80791),x80794),x80793)))
% 157.55/157.23 [8121]~P107(x81212)+P105(f326(f326(f235(f917(x81211,x81212)),x81214),x81213))+~P105(f326(f326(f234(f917(x81211,x81212)),x81214),x81213))+P105(f326(f326(f234(f917(x81211,x81212)),x81213),x81214))
% 157.55/157.23 [8161]P105(f326(f326(f328(x81611),x81612),x81613))+P105(f326(f326(f328(x81611),x81612),x81614))+~P105(f326(f326(f234(f917(x81611,a905)),x81614),x81613))+P105(f326(f326(f235(f917(x81611,a905)),x81614),f326(f326(f308(x81611),x81612),x81613)))
% 157.55/157.23 [8317]P105(f326(f326(f328(x83171),x83172),x83173))+P105(f326(f326(f328(x83171),x83172),x83174))+~P105(f326(f326(f235(f917(x83171,a905)),x83174),f326(f326(f308(x83171),x83172),x83173)))+P105(f326(f326(f234(f917(x83171,a905)),x83174),x83173))
% 157.55/157.23 [8382]~P125(x83821)+P105(f326(f326(f235(x83821),x83823),x83822))+P105(f326(f326(f235(x83821),x83822),x83823))+~P105(f326(f326(f235(x83821),f326(f326(f80(x83821),x83824),x83822)),f326(f326(f80(x83821),x83824),x83823)))
% 157.55/157.23 [8383]~P125(x83831)+P105(f326(f326(f235(x83831),x83833),x83832))+P105(f326(f326(f235(x83831),x83832),x83833))+~P105(f326(f326(f235(x83831),f326(f326(f80(x83831),x83832),x83834)),f326(f326(f80(x83831),x83833),x83834)))
% 157.55/157.23 [8394]~P125(x83941)+P105(f326(f326(f235(x83941),x83944),f2(x83941)))+P105(f326(f326(f235(x83941),x83942),x83943))+~P105(f326(f326(f235(x83941),f326(f326(f80(x83941),x83942),x83944)),f326(f326(f80(x83941),x83943),x83944)))
% 157.55/157.23 [8395]~P125(x83951)+P105(f326(f326(f235(x83951),x83954),f2(x83951)))+P105(f326(f326(f235(x83951),x83952),x83953))+~P105(f326(f326(f235(x83951),f326(f326(f80(x83951),x83954),x83952)),f326(f326(f80(x83951),x83954),x83953)))
% 157.55/157.23 [8398]~P125(x83981)+P105(f326(f326(f235(x83981),x83982),x83983))+P105(f326(f326(f235(x83981),f2(x83981)),x83984))+~P105(f326(f326(f235(x83981),f326(f326(f80(x83981),x83984),x83983)),f326(f326(f80(x83981),x83984),x83982)))
% 157.55/157.23 [8399]~P125(x83991)+P105(f326(f326(f235(x83991),x83992),x83993))+P105(f326(f326(f235(x83991),f2(x83991)),x83994))+~P105(f326(f326(f235(x83991),f326(f326(f80(x83991),x83993),x83994)),f326(f326(f80(x83991),x83992),x83994)))
% 157.55/157.23 [8412]~P125(x84121)+P105(f326(f326(f235(x84121),x84122),f2(x84121)))+P105(f326(f326(f235(x84121),f2(x84121)),x84122))+~P105(f326(f326(f235(x84121),f326(f326(f80(x84121),x84123),x84122)),f326(f326(f80(x84121),x84124),x84122)))
% 157.55/157.23 [8413]~P125(x84131)+P105(f326(f326(f235(x84131),x84132),f2(x84131)))+P105(f326(f326(f235(x84131),f2(x84131)),x84132))+~P105(f326(f326(f235(x84131),f326(f326(f80(x84131),x84132),x84133)),f326(f326(f80(x84131),x84132),x84134)))
% 157.55/157.23 [8442]~P125(x84421)+~P105(f326(f326(f235(x84421),x84424),f2(x84421)))+P105(f326(f326(f234(x84421),x84422),x84423))+~P105(f326(f326(f234(x84421),f326(f326(f80(x84421),x84424),x84423)),f326(f326(f80(x84421),x84424),x84422)))
% 157.55/157.23 [8443]~P125(x84431)+~P105(f326(f326(f235(x84431),x84434),f2(x84431)))+P105(f326(f326(f235(x84431),x84432),x84433))+~P105(f326(f326(f235(x84431),f326(f326(f80(x84431),x84434),x84433)),f326(f326(f80(x84431),x84434),x84432)))
% 157.55/157.23 [8454]~P124(x84543)+~P105(f326(f326(f235(x84543),f77(x84543)),x84544))+P105(f326(f326(f234(a909),x84541),x84542))+~P105(f326(f326(f234(x84543),f326(f326(f243(x84543),x84544),x84541)),f326(f326(f243(x84543),x84544),x84542)))
% 157.55/157.23 [8456]~P124(x84563)+~P105(f326(f326(f235(x84563),f77(x84563)),x84564))+P105(f326(f326(f235(a909),x84561),x84562))+~P105(f326(f326(f235(x84563),f326(f326(f243(x84563),x84564),x84561)),f326(f326(f243(x84563),x84564),x84562)))
% 157.55/157.23 [8466]~P125(x84661)+P105(f326(f326(f234(x84661),x84662),x84663))+~P105(f326(f326(f235(x84661),f2(x84661)),x84664))+~P105(f326(f326(f234(x84661),f326(f326(f80(x84661),x84664),x84662)),f326(f326(f80(x84661),x84664),x84663)))
% 157.55/157.23 [8467]~P131(x84671)+P105(f326(f326(f234(x84671),x84672),x84673))+~P105(f326(f326(f235(x84671),f2(x84671)),x84674))+~P105(f326(f326(f234(x84671),f326(f326(f80(x84671),x84674),x84672)),f326(f326(f80(x84671),x84674),x84673)))
% 157.55/157.23 [8468]~P131(x84681)+P105(f326(f326(f234(x84681),x84682),x84683))+~P105(f326(f326(f235(x84681),f2(x84681)),x84684))+~P105(f326(f326(f234(x84681),f326(f326(f80(x84681),x84682),x84684)),f326(f326(f80(x84681),x84683),x84684)))
% 157.55/157.23 [8469]~P125(x84691)+P105(f326(f326(f235(x84691),x84692),x84693))+~P105(f326(f326(f235(x84691),f2(x84691)),x84694))+~P105(f326(f326(f235(x84691),f326(f326(f80(x84691),x84694),x84692)),f326(f326(f80(x84691),x84694),x84693)))
% 157.55/157.23 [8470]~P131(x84701)+P105(f326(f326(f235(x84701),x84702),x84703))+~P105(f326(f326(f234(x84701),f2(x84701)),x84704))+~P105(f326(f326(f235(x84701),f326(f326(f80(x84701),x84704),x84702)),f326(f326(f80(x84701),x84704),x84703)))
% 157.55/157.23 [8471]~P128(x84711)+P105(f326(f326(f235(x84711),x84712),x84713))+~P105(f326(f326(f234(x84711),f2(x84711)),x84714))+~P105(f326(f326(f235(x84711),f326(f326(f80(x84711),x84714),x84712)),f326(f326(f80(x84711),x84714),x84713)))
% 157.55/157.23 [8472]~P124(x84721)+~P105(f326(f326(f234(x84721),f2(x84721)),x84723))+P105(f326(f326(f235(x84721),x84722),x84723))+~P105(f326(f326(f235(x84721),f326(f326(f243(x84721),x84722),x84724)),f326(f326(f243(x84721),x84723),x84724)))
% 157.55/157.23 [8473]~P131(x84731)+P105(f326(f326(f235(x84731),x84732),x84733))+~P105(f326(f326(f234(x84731),f2(x84731)),x84734))+~P105(f326(f326(f235(x84731),f326(f326(f80(x84731),x84732),x84734)),f326(f326(f80(x84731),x84733),x84734)))
% 157.55/157.23 [8474]~P128(x84741)+P105(f326(f326(f235(x84741),x84742),x84743))+~P105(f326(f326(f234(x84741),f2(x84741)),x84744))+~P105(f326(f326(f235(x84741),f326(f326(f80(x84741),x84742),x84744)),f326(f326(f80(x84741),x84743),x84744)))
% 157.55/157.23 [8517]P105(f326(f326(f328(x85171),x85172),x85173))+~P105(f326(f326(f234(f917(x85171,a905)),x85173),x85174))+~P105(f326(f326(f235(f917(x85171,a905)),x85173),x85174))+P105(f326(f326(f235(f917(x85171,a905)),x85173),f326(f326(f308(x85171),x85172),x85174)))
% 157.55/157.23 [8894]E(f326(f326(f3(a1),f450(x88941,x88942,x88943,x88944)),f451(x88941,x88942,x88943,x88944)),x88944)+~P105(f326(f326(f235(a1),f2(a1)),x88943))+~P105(f326(f326(f234(a1),x88941),x88944))+P105(f326(f326(f234(a1),x88941),f326(f326(f79(a1),x88944),x88943)))
% 157.55/157.23 [8895]E(f326(f326(f3(a1),f457(x88951,x88952,x88953,x88954)),f458(x88951,x88952,x88953,x88954)),x88954)+~P105(f326(f326(f235(a1),f2(a1)),x88953))+~P105(f326(f326(f235(a1),x88951),x88954))+P105(f326(f326(f235(a1),x88951),f326(f326(f79(a1),x88954),x88953)))
% 157.55/157.23 [9045]~E(f326(f326(f164(x90451),x90453),f672(x90454,x90453,x90451,x90452)),f326(f326(f164(x90451),x90454),f672(x90454,x90453,x90451,x90452)))+E(f326(f326(f175(x90451),x90452),x90453),f326(f326(f175(x90451),x90452),x90454))+~P105(f326(f326(f234(a909),x90452),f326(f189(f910(x90451)),x90453)))+~P105(f326(f326(f234(a909),x90452),f326(f189(f910(x90451)),x90454)))
% 157.55/157.23 [9107]~P105(f326(f326(f235(a1),f2(a1)),x91073))+~P105(f326(f326(f234(a1),x91071),x91074))+P105(f326(f326(f328(a1),f450(x91071,x91072,x91073,x91074)),x91072))+P105(f326(f326(f234(a1),x91071),f326(f326(f79(a1),x91074),x91073)))
% 157.55/157.23 [9108]~P105(f326(f326(f235(a1),f2(a1)),x91083))+~P105(f326(f326(f235(a1),x91081),x91084))+P105(f326(f326(f328(a1),f457(x91081,x91082,x91083,x91084)),x91082))+P105(f326(f326(f235(a1),x91081),f326(f326(f79(a1),x91084),x91083)))
% 157.55/157.23 [9148]~P101(x91481)+~P105(f326(f61(x91481),x91483))+~P105(f326(f326(f328(x91481),x91484),x91483))+P105(f326(f326(f234(x91481),f326(f326(f64(x91481,x91481,f101(x91481)),x91482),x91483)),f326(f326(f101(x91481),x91484),x91482)))
% 157.55/157.23 [9149]~P108(x91491)+~P105(f326(f61(x91491),x91493))+~P105(f326(f326(f328(x91491),x91494),x91493))+P105(f326(f326(f234(x91491),f326(f326(f64(x91491,x91491,f232(x91491)),x91492),x91493)),f326(f326(f232(x91491),x91494),x91492)))
% 157.55/157.23 [9193]E(f326(f326(f175(x91931),x91932),x91933),f326(f326(f175(x91931),x91932),x91934))+P105(f326(f326(f235(a909),f672(x91933,x91934,x91931,x91932)),x91932))+~P105(f326(f326(f234(a909),x91932),f326(f189(f910(x91931)),x91933)))+~P105(f326(f326(f234(a909),x91932),f326(f189(f910(x91931)),x91934)))
% 157.55/157.23 [9198]~P105(f326(f326(f235(a1),f2(a1)),x91983))+~P105(f326(f326(f234(a1),x91981),x91982))+P105(f326(f326(f328(a1),f451(x91981,x91984,x91983,x91982)),f302(a1,f77(a1),x91983)))+P105(f326(f326(f234(a1),x91981),f326(f326(f79(a1),x91982),x91983)))
% 157.55/157.23 [9199]~P105(f326(f326(f235(a1),f2(a1)),x91993))+~P105(f326(f326(f235(a1),x91991),x91992))+P105(f326(f326(f328(a1),f458(x91991,x91994,x91993,x91992)),f302(a1,f77(a1),x91993)))+P105(f326(f326(f235(a1),x91991),f326(f326(f79(a1),x91992),x91993)))
% 157.55/157.23 [9517]~P100(x95171)+~P105(f326(f61(x95171),x95174))+P105(f326(f326(f328(x95171),f895(x95172,x95173,x95174,x95171)),x95174))+P105(f326(f326(f234(x95171),f326(f326(f64(x95171,x95171,f110(x95171)),x95172),x95174)),f326(f326(f110(x95171),x95173),x95172)))
% 157.55/157.23 [9518]~P108(x95181)+~P105(f326(f61(x95181),x95184))+P105(f326(f326(f328(x95181),f601(x95182,x95183,x95184,x95181)),x95184))+P105(f326(f326(f234(x95181),f326(f326(f64(x95181,x95181,f233(x95181)),x95182),x95184)),f326(f326(f233(x95181),x95183),x95182)))
% 157.55/157.23 [9643]~P100(x96431)+~P105(f326(f61(x96431),x96433))+~P105(f326(f326(f234(x96431),f895(x96432,x96434,x96433,x96431)),x96434))+P105(f326(f326(f234(x96431),f326(f326(f64(x96431,x96431,f110(x96431)),x96432),x96433)),f326(f326(f110(x96431),x96434),x96432)))
% 157.55/157.23 [9644]~P108(x96441)+~P105(f326(f61(x96441),x96443))+~P105(f326(f326(f234(x96441),f601(x96442,x96444,x96443,x96441)),x96444))+P105(f326(f326(f234(x96441),f326(f326(f64(x96441,x96441,f233(x96441)),x96442),x96443)),f326(f326(f233(x96441),x96444),x96442)))
% 157.55/157.23 [9646]~P105(f326(f326(f234(a1),f2(a1)),x96464))+~P105(f326(f326(f235(a1),f2(a1)),x96463))+~P105(f326(f326(f235(a1),x96464),x96461))+P105(f326(f326(f235(a1),f326(f326(f79(a1),f326(f326(f80(a1),x96461),f45(a1,x96462,x96463))),x96464)),f326(f326(f80(a1),x96461),x96463)))
% 157.55/157.23 [10033]E(x100331,x100332)+P105(f326(f326(f328(f916(f910(x100333),f910(x100333))),f326(f326(f251(f910(x100333),f910(x100333)),x100332),x100331)),f147(x100333,x100334)))+P105(f326(f326(f328(f916(f910(x100333),f910(x100333))),f326(f326(f251(f910(x100333),f910(x100333)),x100331),x100332)),f147(x100333,x100334)))+~P105(f326(f326(f328(f916(x100333,x100333)),f326(f326(f251(x100333,x100333),f643(x100331,x100332,x100334,x100333)),f646(x100331,x100332,x100334,x100333))),x100334))
% 157.55/157.23 [10034]E(x100341,x100342)+P105(f326(f326(f328(f916(f910(x100343),f910(x100343))),f326(f326(f251(f910(x100343),f910(x100343)),x100342),x100341)),f147(x100343,x100344)))+P105(f326(f326(f328(f916(f910(x100343),f910(x100343))),f326(f326(f251(f910(x100343),f910(x100343)),x100341),x100342)),f147(x100343,x100344)))+~P105(f326(f326(f328(f916(x100343,x100343)),f326(f326(f251(x100343,x100343),f646(x100341,x100342,x100344,x100343)),f643(x100341,x100342,x100344,x100343))),x100344))
% 157.55/157.23 [7620]~P100(x76201)+~P105(f326(f326(f234(x76201),x76203),x76204))+~P105(f326(f326(f234(x76201),x76202),x76204))+P105(f326(f326(f234(x76201),f326(f326(f110(x76201),x76202),x76203)),x76204))
% 157.55/157.23 [7623]~P108(x76231)+~P105(f326(f326(f234(x76231),x76233),x76234))+~P105(f326(f326(f234(x76231),x76232),x76234))+P105(f326(f326(f234(x76231),f326(f326(f233(x76231),x76232),x76233)),x76234))
% 157.55/157.23 [7624]~P108(x76241)+~P105(f326(f326(f235(x76241),x76243),x76244))+~P105(f326(f326(f235(x76241),x76242),x76244))+P105(f326(f326(f235(x76241),f326(f326(f233(x76241),x76242),x76243)),x76244))
% 157.55/157.23 [7856]~P59(x78561)+E(f326(f326(f79(x78561),f326(f326(f36(x78561),x78562),x78563)),f326(f326(f36(x78561),x78564),x78563)),f326(f326(f36(x78561),f326(f326(f79(x78561),x78562),x78564)),x78563))+~P105(f326(f326(f286(x78561),x78563),x78564))+~P105(f326(f326(f286(x78561),x78563),x78562))
% 157.55/157.23 [7938]~E(x79381,x79383)+E(f139(a909,f326(f301(a909,x79381),x79382)),f326(f326(f151(a909),x79383),x79384))+~E(f139(a909,f326(f301(a909,f326(f326(f79(a909),x79381),f77(a909))),x79382)),x79384)+~P105(f326(f326(f235(a909),x79381),x79382))
% 157.55/157.23 [7946]~P108(x79461)+P105(f326(f326(f234(x79461),x79462),x79463))+P105(f326(f326(f234(x79461),x79464),x79463))+~P105(f326(f326(f234(x79461),f326(f326(f232(x79461),x79464),x79462)),x79463))
% 157.55/157.23 [7947]~P108(x79471)+P105(f326(f326(f235(x79471),x79472),x79473))+P105(f326(f326(f235(x79471),x79474),x79473))+~P105(f326(f326(f235(x79471),f326(f326(f232(x79471),x79474),x79472)),x79473))
% 157.55/157.23 [8219]~P64(x82191)+~P105(f326(f326(f235(x82191),f2(x82191)),x82193))+~P105(f326(f326(f234(x82191),x82192),f326(f326(f290(x82191),x82194),x82193)))+P105(f326(f326(f234(x82191),f326(f326(f80(x82191),x82192),x82193)),x82194))
% 157.55/157.23 [8220]~P65(x82201)+~P105(f326(f326(f235(x82201),f2(x82201)),x82203))+~P105(f326(f326(f234(x82201),x82202),f326(f326(f290(x82201),x82204),x82203)))+P105(f326(f326(f234(x82201),f326(f326(f80(x82201),x82202),x82203)),x82204))
% 157.55/157.23 [8221]~P64(x82211)+~P105(f326(f326(f235(x82211),f2(x82211)),x82213))+~P105(f326(f326(f234(x82211),x82212),f326(f326(f80(x82211),x82214),x82213)))+P105(f326(f326(f234(x82211),f326(f326(f290(x82211),x82212),x82213)),x82214))
% 157.55/157.23 [8223]~P65(x82231)+~P105(f326(f326(f235(x82231),f2(x82231)),x82233))+~P105(f326(f326(f234(x82231),x82232),f326(f326(f80(x82231),x82234),x82233)))+P105(f326(f326(f234(x82231),f326(f326(f290(x82231),x82232),x82233)),x82234))
% 157.55/157.23 [8224]~P64(x82241)+~P105(f326(f326(f235(x82241),f2(x82241)),x82243))+~P105(f326(f326(f235(x82241),x82242),f326(f326(f290(x82241),x82244),x82243)))+P105(f326(f326(f235(x82241),f326(f326(f80(x82241),x82242),x82243)),x82244))
% 157.55/157.23 [8225]~P65(x82251)+~P105(f326(f326(f235(x82251),f2(x82251)),x82253))+~P105(f326(f326(f235(x82251),x82252),f326(f326(f290(x82251),x82254),x82253)))+P105(f326(f326(f235(x82251),f326(f326(f80(x82251),x82252),x82253)),x82254))
% 157.55/157.23 [8226]~P64(x82261)+~P105(f326(f326(f235(x82261),f2(x82261)),x82263))+~P105(f326(f326(f235(x82261),x82262),f326(f326(f80(x82261),x82264),x82263)))+P105(f326(f326(f235(x82261),f326(f326(f290(x82261),x82262),x82263)),x82264))
% 157.55/157.23 [8228]~P65(x82281)+~P105(f326(f326(f235(x82281),f2(x82281)),x82283))+~P105(f326(f326(f235(x82281),x82282),f326(f326(f80(x82281),x82284),x82283)))+P105(f326(f326(f235(x82281),f326(f326(f290(x82281),x82282),x82283)),x82284))
% 157.55/157.23 [8352]~P64(x83521)+~P105(f326(f326(f235(x83521),f2(x83521)),x83524))+P105(f326(f326(f234(x83521),x83522),f326(f326(f80(x83521),x83523),x83524)))+~P105(f326(f326(f234(x83521),f326(f326(f290(x83521),x83522),x83524)),x83523))
% 157.55/157.23 [8353]~P64(x83531)+~P105(f326(f326(f235(x83531),f2(x83531)),x83534))+P105(f326(f326(f234(x83531),x83532),f326(f326(f290(x83531),x83533),x83534)))+~P105(f326(f326(f234(x83531),f326(f326(f80(x83531),x83532),x83534)),x83533))
% 157.55/157.23 [8355]~P65(x83551)+~P105(f326(f326(f235(x83551),f2(x83551)),x83554))+P105(f326(f326(f234(x83551),x83552),f326(f326(f80(x83551),x83553),x83554)))+~P105(f326(f326(f234(x83551),f326(f326(f290(x83551),x83552),x83554)),x83553))
% 157.55/157.23 [8356]~P65(x83561)+~P105(f326(f326(f235(x83561),f2(x83561)),x83564))+P105(f326(f326(f234(x83561),x83562),f326(f326(f290(x83561),x83563),x83564)))+~P105(f326(f326(f234(x83561),f326(f326(f80(x83561),x83562),x83564)),x83563))
% 157.55/157.23 [8357]~P64(x83571)+~P105(f326(f326(f235(x83571),f2(x83571)),x83574))+P105(f326(f326(f235(x83571),x83572),f326(f326(f80(x83571),x83573),x83574)))+~P105(f326(f326(f235(x83571),f326(f326(f290(x83571),x83572),x83574)),x83573))
% 157.55/157.23 [8358]~P64(x83581)+~P105(f326(f326(f235(x83581),f2(x83581)),x83584))+P105(f326(f326(f235(x83581),x83582),f326(f326(f290(x83581),x83583),x83584)))+~P105(f326(f326(f235(x83581),f326(f326(f80(x83581),x83582),x83584)),x83583))
% 157.55/157.23 [8360]~P65(x83601)+~P105(f326(f326(f235(x83601),f2(x83601)),x83604))+P105(f326(f326(f235(x83601),x83602),f326(f326(f80(x83601),x83603),x83604)))+~P105(f326(f326(f235(x83601),f326(f326(f290(x83601),x83602),x83604)),x83603))
% 157.55/157.23 [8361]~P65(x83611)+~P105(f326(f326(f235(x83611),f2(x83611)),x83614))+P105(f326(f326(f235(x83611),x83612),f326(f326(f290(x83611),x83613),x83614)))+~P105(f326(f326(f235(x83611),f326(f326(f80(x83611),x83612),x83614)),x83613))
% 157.55/157.23 [8520]~P65(x85201)+~P105(f326(f326(f235(x85201),x85203),f2(x85201)))+~P105(f326(f326(f234(x85201),f326(f326(f290(x85201),x85204),x85203)),x85202))+P105(f326(f326(f234(x85201),f326(f326(f80(x85201),x85202),x85203)),x85204))
% 157.55/157.23 [8521]~P65(x85211)+~P105(f326(f326(f235(x85211),x85213),f2(x85211)))+~P105(f326(f326(f234(x85211),f326(f326(f80(x85211),x85214),x85213)),x85212))+P105(f326(f326(f234(x85211),f326(f326(f290(x85211),x85212),x85213)),x85214))
% 157.55/157.23 [8522]~P65(x85221)+~P105(f326(f326(f235(x85221),x85223),f2(x85221)))+~P105(f326(f326(f235(x85221),f326(f326(f290(x85221),x85224),x85223)),x85222))+P105(f326(f326(f235(x85221),f326(f326(f80(x85221),x85222),x85223)),x85224))
% 157.55/157.23 [8523]~P65(x85231)+~P105(f326(f326(f235(x85231),x85233),f2(x85231)))+~P105(f326(f326(f235(x85231),f326(f326(f80(x85231),x85234),x85233)),x85232))+P105(f326(f326(f235(x85231),f326(f326(f290(x85231),x85232),x85233)),x85234))
% 157.55/157.23 [8535]~P105(f326(x85351,x85354))+~P105(f326(f326(f235(a909),x85352),f326(f326(f80(a909),x85353),f326(a112,x85354))))+P105(f326(x85351,f326(f326(f36(a909),x85352),x85353)))+~P105(f326(f326(f234(a909),f326(f326(f80(a909),x85353),x85354)),x85352))
% 157.55/157.23 [8742]~P100(x87421)+~P105(f326(f61(x87421),x87424))+~P105(f326(f326(f328(x87421),x87422),x87424))+P105(f326(f326(f234(x87421),f326(f326(f110(x87421),x87422),x87423)),f326(f326(f64(x87421,x87421,f110(x87421)),x87423),x87424)))
% 157.55/157.23 [8743]~P108(x87431)+~P105(f326(f61(x87431),x87434))+~P105(f326(f326(f328(x87431),x87432),x87434))+P105(f326(f326(f234(x87431),f326(f326(f233(x87431),x87432),x87433)),f326(f326(f64(x87431,x87431,f233(x87431)),x87433),x87434)))
% 157.55/157.23 [8896]~P105(f326(f61(x88961),x88962))+E(f326(f35(x88961),f326(f326(f3(f917(x88961,a905)),x88962),f326(f326(f308(x88961),x88963),x88964))),f326(f326(f3(a909),f326(f35(x88961),f326(f326(f3(f917(x88961,a905)),x88962),x88964))),f77(a909)))+P105(f326(f326(f328(x88961),x88963),x88964))+~P105(f326(f326(f328(x88961),x88963),x88962))
% 157.55/157.23 [8973]E(f326(f326(f79(a1),f452(x89731,x89732,x89733,x89734)),f453(x89731,x89732,x89733,x89734)),x89734)+~P105(f326(f326(f235(a1),f2(a1)),x89733))+~P105(f326(f326(f234(a1),x89734),x89731))+P105(f326(f326(f234(a1),f326(f326(f3(a1),x89734),x89733)),x89731))
% 157.55/157.23 [8974]E(f326(f326(f79(a1),f459(x89741,x89742,x89743,x89744)),f460(x89741,x89742,x89743,x89744)),x89744)+~P105(f326(f326(f235(a1),f2(a1)),x89743))+~P105(f326(f326(f235(a1),x89744),x89741))+P105(f326(f326(f235(a1),f326(f326(f3(a1),x89744),x89743)),x89741))
% 157.55/157.23 [9178]~P105(f326(f326(f235(a1),f2(a1)),x91783))+~P105(f326(f326(f234(a1),x91784),x91781))+P105(f326(f326(f328(a1),f452(x91781,x91782,x91783,x91784)),x91782))+P105(f326(f326(f234(a1),f326(f326(f3(a1),x91784),x91783)),x91781))
% 157.55/157.23 [9179]~P105(f326(f326(f235(a1),f2(a1)),x91793))+~P105(f326(f326(f235(a1),x91794),x91791))+P105(f326(f326(f328(a1),f459(x91791,x91792,x91793,x91794)),x91792))+P105(f326(f326(f235(a1),f326(f326(f3(a1),x91794),x91793)),x91791))
% 157.55/157.23 [9265]~P105(f326(f326(f235(a1),f2(a1)),x92652))+~P105(f326(f326(f234(a1),x92651),x92653))+P105(f326(f326(f328(a1),f453(x92653,x92654,x92652,x92651)),f302(a1,f77(a1),x92652)))+P105(f326(f326(f234(a1),f326(f326(f3(a1),x92651),x92652)),x92653))
% 157.55/157.23 [9266]~P105(f326(f326(f235(a1),f2(a1)),x92662))+~P105(f326(f326(f235(a1),x92661),x92663))+P105(f326(f326(f328(a1),f460(x92663,x92664,x92662,x92661)),f302(a1,f77(a1),x92662)))+P105(f326(f326(f235(a1),f326(f326(f3(a1),x92661),x92662)),x92663))
% 157.55/157.23 [9284]~P105(f326(f326(f234(a1),f2(a1)),x92844))+~P105(f326(f326(f235(a1),f2(a1)),x92843))+~P105(f326(f326(f235(a1),x92844),x92841))+P105(f326(f326(f234(a1),f2(a1)),f326(f326(f79(a1),f326(f326(f80(a1),x92841),f45(a1,x92842,x92843))),x92844)))
% 157.55/157.23 [9313]E(x93131,x93132)+~P38(x93133,x93134)+~P105(f326(f326(f328(f916(x93133,x93133)),f326(f326(f251(x93133,x93133),x93132),x93131)),x93134))+~P105(f326(f326(f328(f916(x93133,x93133)),f326(f326(f251(x93133,x93133),x93131),x93132)),x93134))
% 157.55/157.23 [9345]~P101(x93451)+~P105(f326(f61(x93451),x93454))+~P105(f326(f326(f234(x93451),x93452),f865(x93453,x93452,x93454,x93451)))+P105(f326(f326(f234(x93451),f326(f326(f101(x93451),x93452),x93453)),f326(f326(f64(x93451,x93451,f101(x93451)),x93453),x93454)))
% 157.55/157.23 [9346]~P108(x93461)+~P105(f326(f61(x93461),x93464))+~P105(f326(f326(f234(x93461),x93462),f356(x93463,x93462,x93464,x93461)))+P105(f326(f326(f234(x93461),f326(f326(f232(x93461),x93462),x93463)),f326(f326(f64(x93461,x93461,f232(x93461)),x93463),x93464)))
% 157.55/157.23 [9360]~P105(f326(f326(f234(a1),x93604),f2(a1)))+~P105(f326(f326(f235(a1),f2(a1)),x93602))+~P105(f326(f326(f235(a1),x93601),x93604))+P105(f326(f326(f235(a1),f326(f326(f80(a1),x93601),x93602)),f326(f326(f79(a1),f326(f326(f80(a1),x93601),f45(a1,x93603,x93602))),x93604)))
% 157.55/157.23 [9385]P105(f326(f61(x93851),x93852))+~P105(f326(f61(x93851),x93853))+~P105(f326(f326(f328(f917(x93851,a905)),x93852),f326(f326(f60(x93851),x93853),x93854)))+~P105(f326(f326(f234(f917(f916(x93851,x93851),a905)),x93854),f326(f326(f253(x93851,x93851),x93853),f326(f18(f917(x93851,a905),x93851),x93853))))
% 157.55/157.23 [9409]~P101(x94091)+~P105(f326(f61(x94091),x94094))+P105(f326(f326(f328(x94091),f865(x94092,x94093,x94094,x94091)),x94094))+P105(f326(f326(f234(x94091),f326(f326(f101(x94091),x94093),x94092)),f326(f326(f64(x94091,x94091,f101(x94091)),x94092),x94094)))
% 157.55/157.23 [9410]~P108(x94101)+~P105(f326(f61(x94101),x94104))+P105(f326(f326(f328(x94101),f356(x94102,x94103,x94104,x94101)),x94104))+P105(f326(f326(f234(x94101),f326(f326(f232(x94101),x94103),x94102)),f326(f326(f64(x94101,x94101,f232(x94101)),x94102),x94104)))
% 157.55/157.23 [9810]~P105(f326(f61(x98102),x98104))+~P105(f326(f61(x98101),x98103))+~P105(f326(f326(f234(a909),f326(f35(x98102),x98104)),f326(f35(x98101),x98103)))+P105(f326(f326(f234(f917(x98101,a905)),f326(f309(x98102,x98101,f520(x98103,x98101,x98104,x98102)),x98104)),x98103))
% 157.55/157.23 [9458]~P105(f326(f326(f328(x94581),x94582),x94584))+P105(f326(f326(f328(x94581),x94582),x94583))+~P105(f326(f326(f235(f917(x94581,a905)),x94584),f326(f326(f308(x94581),x94582),x94583)))+P105(f326(f326(f235(f917(x94581,a905)),f326(f326(f3(f917(x94581,a905)),x94584),f326(f326(f308(x94581),x94582),f188(f917(x94581,a905))))),x94583))
% 157.55/157.23 [9624]~P105(f326(f326(f328(x96241),x96242),x96244))+P105(f326(f326(f328(x96241),x96242),x96243))+P105(f326(f326(f235(f917(x96241,a905)),x96244),f326(f326(f308(x96241),x96242),x96243)))+~P105(f326(f326(f235(f917(x96241,a905)),f326(f326(f3(f917(x96241,a905)),x96244),f326(f326(f308(x96241),x96242),f188(f917(x96241,a905))))),x96243))
% 157.55/157.23 [9649]P105(f326(f326(f328(x96491),x96492),x96493))+~P105(f326(f326(f234(f917(x96491,a905)),x96494),x96493))+P105(f326(f326(f235(f917(x96491,a905)),x96494),f326(f326(f308(x96491),x96492),x96493)))+~P105(f326(f326(f235(f917(x96491,a905)),f326(f326(f3(f917(x96491,a905)),x96494),f326(f326(f308(x96491),x96492),f188(f917(x96491,a905))))),x96493))
% 157.55/157.23 [9654]~P105(f326(f326(f328(x96541),x96543),x96542))+~P105(f326(f326(f235(f917(x96541,a905)),x96542),x96544))+P105(f326(f326(f235(f917(x96541,a905)),x96542),f326(f326(f308(x96541),x96543),x96544)))+~P105(f326(f326(f235(f917(x96541,a905)),f326(f326(f3(f917(x96541,a905)),x96542),f326(f326(f308(x96541),x96543),f188(f917(x96541,a905))))),x96544))
% 157.55/157.23 [9670]~P105(f326(f326(f234(f917(x96701,a905)),x96702),x96704))+~P105(f326(f326(f235(f917(x96701,a905)),x96702),x96704))+P105(f326(f326(f235(f917(x96701,a905)),x96702),f326(f326(f308(x96701),x96703),x96704)))+~P105(f326(f326(f235(f917(x96701,a905)),f326(f326(f3(f917(x96701,a905)),x96702),f326(f326(f308(x96701),x96703),f188(f917(x96701,a905))))),x96704))
% 157.55/157.23 [9715]~P109(x97152)+~P61(x97151)+~P105(f326(f326(f234(f917(x97151,x97152)),x97153),x97154))+P105(f326(f57(x97151),f326(f326(f20(x97151,x97152,a905),f326(f326(f10(x97152,f917(x97152,a905),x97151),f234(x97152)),x97153)),x97154)))
% 157.55/157.23 [9859]~P109(x98592)+~P61(x98591)+P105(f326(f326(f234(f917(x98591,x98592)),x98593),x98594))+~P105(f326(f57(x98591),f326(f326(f20(x98591,x98592,a905),f326(f326(f10(x98592,f917(x98592,a905),x98591),f234(x98592)),x98593)),x98594)))
% 157.55/157.23 [10024]E(f326(f326(f164(x100241),f326(f326(f164(f910(x100241)),f179(x100241,x100242)),x100243)),x100244),f326(f326(f164(x100241),f326(f326(f164(f910(x100241)),x100242),x100244)),x100243))+~P105(f326(f326(f235(a909),x100243),f326(f189(f910(f910(x100241))),f179(x100241,x100242))))+~P12(a909,f326(f168(a909),f326(f326(f154(f910(x100241),a909),f189(f910(x100241))),x100242)))+~P105(f326(f326(f235(a909),x100244),f326(f189(f910(f910(x100241))),f326(f136(f910(x100241),f326(f326(f10(a909,a905,f910(x100241)),f326(f235(a909),x100243)),f189(f910(x100241)))),x100242))))
% 157.55/157.23 [10046]~P105(f326(f326(f328(f916(a909,a909)),x100464),x100461))+~P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),x100464),x100462)),a32))+~P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),x100461),x100463)),a33))+P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),x100461),f326(f326(f308(f916(a909,a909)),x100462),x100463))),a33))
% 157.55/157.23 [10047]~P105(f326(f326(f328(f916(a909,a909)),x100474),x100471))+~P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),x100474),x100472)),a70))+~P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),x100471),x100473)),a71))+P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),x100471),f326(f326(f308(f916(a909,a909)),x100472),x100473))),a71))
% 157.55/157.23 [9936]~P109(x99362)+~P61(x99361)+~P105(f326(f326(f235(f917(x99361,x99362)),x99363),x99364))+P105(f326(f56(x99361),f326(f326(f10(a905,a905,x99361),a321),f326(f326(f20(x99361,x99362,a905),f326(f326(f10(x99362,f917(x99362,a905),x99361),a323),x99363)),x99364))))
% 157.55/157.23 [10058]~P105(f326(f326(f328(f916(a909,a909)),x100584),x100583))+~P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),x100581),x100584)),a70))+~P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),x100582),x100583)),a69))+P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),f326(f326(f308(f916(a909,a909)),x100581),x100582)),x100583)),a69))
% 157.55/157.23 [10059]~P105(f326(f326(f328(f916(a909,a909)),x100594),x100593))+~P105(f326(f326(f328(f916(f916(a909,a909),f916(a909,a909))),f326(f326(f251(f916(a909,a909),f916(a909,a909)),x100591),x100594)),a32))+~P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),x100592),x100593)),a34))+P105(f326(f326(f328(f916(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905))),f326(f326(f251(f917(f916(a909,a909),a905),f917(f916(a909,a909),a905)),f326(f326(f308(f916(a909,a909)),x100591),x100592)),x100593)),a34))
% 157.55/157.23 [6204]~P6(x62044,x62041)+~P105(f326(f326(x62041,x62042),x62045))+P105(f326(f326(x62041,x62042),x62043))+~P105(f326(f326(x62041,x62045),x62043))
% 157.55/157.23 [6205]~P48(x62054,x62051)+~P105(f326(f326(x62051,x62052),x62055))+P105(f326(f326(x62051,x62052),x62053))+~P105(f326(f326(x62051,x62055),x62053))
% 157.55/157.23 [6206]~P14(x62064,x62061)+~P105(f326(f326(x62061,x62062),x62065))+P105(f326(f326(x62061,x62062),x62063))+~P105(f326(f326(x62061,x62065),x62063))
% 157.55/157.23 [8881]~P6(x88814,x88813)+~P105(f326(x88811,x88815))+P105(f326(x88812,f828(x88812,x88811,x88813,x88814)))+P105(f326(x88811,f827(x88812,x88811,x88813,x88814)))
% 157.55/157.23 [9115]~P6(x91154,x91153)+~P105(f326(x91152,x91155))+~P105(f326(x91151,f827(x91151,x91152,x91153,x91154)))+P105(f326(x91151,f828(x91151,x91152,x91153,x91154)))
% 157.55/157.23 [9297]~P6(x92974,x92973)+~P105(f326(x92971,x92975))+P105(f326(f326(f328(x92974),f828(x92972,x92971,x92973,x92974)),f269(x92974,x92973)))+P105(f326(x92971,f827(x92972,x92971,x92973,x92974)))
% 157.55/157.23 [9416]~P6(x94161,x94164)+~P105(f326(x94163,x94165))+~P105(f326(x94162,f827(x94162,x94163,x94164,x94161)))+P105(f326(f326(f328(x94161),f828(x94162,x94163,x94164,x94161)),f269(x94161,x94164)))
% 157.55/157.23 [9704]~P37(x97041,x97044)+P105(f326(f326(f328(f916(f910(x97041),f910(x97041))),f326(f326(f251(f910(x97041),f910(x97041)),x97042),x97043)),f147(x97041,x97044)))+~P105(f326(f326(f328(f916(f910(x97041),f910(x97041))),f326(f326(f251(f910(x97041),f910(x97041)),x97042),x97045)),f147(x97041,x97044)))+~P105(f326(f326(f328(f916(f910(x97041),f910(x97041))),f326(f326(f251(f910(x97041),f910(x97041)),x97045),x97043)),f147(x97041,x97044)))
% 157.55/157.23 [5435]~P66(x54355)+E(x54351,x54352)+~E(x54353,x54354)+~E(f326(f326(f3(x54355),x54353),x54354),f326(f326(f3(x54355),x54351),x54352))
% 157.55/157.23 [6319]~P16(x63195,x63191,x63193)+E(f326(f326(x63191,x63192),f326(x63193,x63194)),f326(x63193,x63194))+~P105(f326(f61(x63195),x63194))+~P105(f326(f326(f328(x63195),x63192),x63194))
% 157.55/157.23 [6509]~P79(x65091)+~E(f326(f326(f3(x65091),x65094),x65095),f326(f326(f3(x65091),x65092),x65093))+~P105(f326(f326(f234(x65091),x65094),x65095))+P105(f326(f326(f234(x65091),x65092),x65093))
% 157.55/157.23 [6511]~P79(x65111)+~E(f326(f326(f3(x65111),x65114),x65115),f326(f326(f3(x65111),x65112),x65113))+~P105(f326(f326(f235(x65111),x65114),x65115))+P105(f326(f326(f235(x65111),x65112),x65113))
% 157.55/157.23 [7487]~E(x74872,f326(f326(f151(x74871),x74874),x74875))+P105(f326(f326(f328(f910(x74871)),x74872),f161(x74871,x74873)))+~P105(f326(f326(f328(f910(x74871)),x74875),f161(x74871,x74873)))+~P105(f326(f326(f328(x74871),x74874),x74873))
% 157.55/157.23 [7887]~E(f326(f189(f910(x78871)),x78873),f326(f189(f910(x78872)),x78874))+~E(f326(f326(f154(f916(x78871,x78872),x78872),f255(x78871,x78872)),x78875),x78874)+~E(f326(f326(f154(f916(x78871,x78872),x78871),f250(x78871,x78872)),x78875),x78873)+E(f326(f326(f181(x78871,x78872),x78873),x78874),x78875)
% 157.55/157.23 [8215]~P109(x82151)+P105(f326(f326(f235(f917(x82151,a905)),f302(x82151,x82152,x82153)),f302(x82151,x82154,x82155)))+~P105(f326(f326(f234(x82151),x82154),x82155))+P105(f326(f326(f234(x82151),x82152),x82153))
% 157.55/157.23 [8310]~P109(x83101)+P105(f326(f326(f234(f917(x83101,a905)),f302(x83101,x83102,x83103)),f302(x83101,x83104,x83105)))+~P105(f326(f326(f234(x83101),x83103),x83105))+~P105(f326(f326(f234(x83101),x83104),x83102))
% 157.55/157.23 [8428]~P108(x84281)+P105(f326(f326(f234(x84281),x84282),x84283))+P105(f326(f326(f234(x84281),x84284),x84283))+~P105(f326(f326(f234(f917(x84281,a905)),f326(f301(x84281,x84283),x84282)),f326(f301(x84281,x84284),x84285)))
% 157.55/157.23 [8429]~P108(x84291)+P105(f326(f326(f234(x84291),x84292),x84293))+P105(f326(f326(f234(x84291),x84292),x84294))+~P105(f326(f326(f234(f917(x84291,a905)),f326(f301(x84291,x84293),x84292)),f326(f301(x84291,x84295),x84294)))
% 157.55/157.23 [8659]~P109(x86591)+~P105(f326(f326(f234(f917(x86591,a905)),f302(x86591,x86594,x86592)),f302(x86591,x86595,x86593)))+P105(f326(f326(f234(x86591),x86592),x86593))+~P105(f326(f326(f234(x86591),x86594),x86592))
% 157.55/157.23 [8660]~P109(x86601)+~P105(f326(f326(f235(f917(x86601,a905)),f302(x86601,x86604,x86602)),f302(x86601,x86605,x86603)))+P105(f326(f326(f234(x86601),x86602),x86603))+~P105(f326(f326(f234(x86601),x86604),x86602))
% 157.55/157.23 [8661]~P109(x86611)+~P105(f326(f326(f234(f917(x86611,a905)),f302(x86611,x86613,x86614)),f302(x86611,x86612,x86615)))+P105(f326(f326(f234(x86611),x86612),x86613))+~P105(f326(f326(f234(x86611),x86613),x86614))
% 157.55/157.23 [8662]~P109(x86621)+~P105(f326(f326(f235(f917(x86621,a905)),f302(x86621,x86623,x86624)),f302(x86621,x86622,x86625)))+P105(f326(f326(f234(x86621),x86622),x86623))+~P105(f326(f326(f234(x86621),x86623),x86624))
% 157.55/157.23 [6203]~P16(x62032,x62035,x62033)+E(x62031,f188(f917(x62032,a905)))+~P105(f326(f61(x62032),x62031))+E(f326(x62033,f326(f326(f308(x62032),x62034),x62031)),f326(f326(x62035,x62034),f326(x62033,x62031)))
% 157.55/157.23 [6981]~E(x69811,x69812)+~E(f326(f326(f101(f917(x69813,a905)),x69814),x69815),f188(f917(x69813,a905)))+~P105(f326(f326(f328(x69813),x69812),x69815))+~P105(f326(f326(f328(x69813),x69811),x69814))
% 157.55/157.23 [7059]~P17(x70592,x70595,x70591)+~P105(f326(f61(x70592),x70594))+E(f326(x70591,f326(f326(f308(x70592),x70593),x70594)),f326(f326(f64(x70592,x70592,x70595),x70593),x70594))+P105(f326(f326(f328(x70592),x70593),x70594))
% 157.55/157.23 [7126]~P69(x71262)+~P105(f326(f61(x71261),x71265))+E(f326(f326(f8(x71261,x71262),x71263),f326(f326(f308(x71261),x71264),x71265)),f326(f326(f79(x71262),f326(x71263,x71264)),f326(f326(f8(x71261,x71262),x71263),x71265)))+P105(f326(f326(f328(x71261),x71264),x71265))
% 157.55/157.23 [7128]~P74(x71282)+~P105(f326(f61(x71281),x71285))+E(f326(f326(f11(x71281,x71282),x71283),f326(f326(f308(x71281),x71284),x71285)),f326(f326(f80(x71282),f326(x71283,x71284)),f326(f326(f11(x71281,x71282),x71283),x71285)))+P105(f326(f326(f328(x71281),x71284),x71285))
% 157.55/157.23 [7534]~P112(x75341)+~P105(f326(f61(x75344),x75345))+~P105(f326(f326(f328(x75344),x75343),x75345))+P105(f326(f326(f286(x75341),f326(x75342,x75343)),f326(f326(f11(x75344,x75341),x75342),x75345)))
% 157.55/157.23 [7633]~P17(x76332,x76335,x76331)+~P105(f326(f61(x76332),x76334))+E(f326(x76331,f326(f326(f308(x76332),x76333),x76334)),x76333)+~E(f326(f326(f3(f917(x76332,a905)),x76334),f326(f326(f308(x76332),x76333),f188(f917(x76332,a905)))),f188(f917(x76332,a905)))
% 157.55/157.23 [7989]~P100(x79891)+~P105(f326(f326(f234(x79891),x79893),x79895))+~P105(f326(f326(f234(x79891),x79892),x79894))+P105(f326(f326(f234(x79891),f326(f326(f110(x79891),x79892),x79893)),f326(f326(f110(x79891),x79894),x79895)))
% 157.55/157.23 [7990]~P101(x79901)+~P105(f326(f326(f234(x79901),x79903),x79905))+~P105(f326(f326(f234(x79901),x79902),x79904))+P105(f326(f326(f234(x79901),f326(f326(f101(x79901),x79902),x79903)),f326(f326(f101(x79901),x79904),x79905)))
% 157.55/157.23 [7991]~P85(x79911)+~P105(f326(f326(f234(x79911),x79913),x79915))+~P105(f326(f326(f234(x79911),x79912),x79914))+P105(f326(f326(f234(x79911),f326(f326(f79(x79911),x79912),x79913)),f326(f326(f79(x79911),x79914),x79915)))
% 157.55/157.23 [7992]~P108(x79921)+~P105(f326(f326(f234(x79921),x79923),x79925))+~P105(f326(f326(f234(x79921),x79922),x79924))+P105(f326(f326(f234(x79921),f326(f326(f232(x79921),x79922),x79923)),f326(f326(f232(x79921),x79924),x79925)))
% 157.55/157.23 [7993]~P108(x79931)+~P105(f326(f326(f234(x79931),x79933),x79935))+~P105(f326(f326(f234(x79931),x79932),x79934))+P105(f326(f326(f234(x79931),f326(f326(f233(x79931),x79932),x79933)),f326(f326(f233(x79931),x79934),x79935)))
% 157.55/157.23 [7994]~P83(x79941)+~P105(f326(f326(f234(x79941),x79943),x79945))+~P105(f326(f326(f235(x79941),x79942),x79944))+P105(f326(f326(f235(x79941),f326(f326(f79(x79941),x79942),x79943)),f326(f326(f79(x79941),x79944),x79945)))
% 157.55/157.23 [7995]~P83(x79951)+~P105(f326(f326(f234(x79951),x79952),x79954))+~P105(f326(f326(f235(x79951),x79953),x79955))+P105(f326(f326(f235(x79951),f326(f326(f79(x79951),x79952),x79953)),f326(f326(f79(x79951),x79954),x79955)))
% 157.55/157.23 [7996]~P83(x79961)+~P105(f326(f326(f235(x79961),x79963),x79965))+~P105(f326(f326(f235(x79961),x79962),x79964))+P105(f326(f326(f235(x79961),f326(f326(f79(x79961),x79962),x79963)),f326(f326(f79(x79961),x79964),x79965)))
% 157.55/157.23 [8131]~P137(x81315)+E(x81311,x81312)+E(x81313,x81314)+~E(f326(f326(f79(x81315),f326(f326(f80(x81315),x81313),x81311)),f326(f326(f80(x81315),x81314),x81312)),f326(f326(f79(x81315),f326(f326(f80(x81315),x81313),x81312)),f326(f326(f80(x81315),x81314),x81311)))
% 157.55/157.23 [8330]~P108(x83304)+~P105(f326(f137(x83301),x83303))+P105(f326(f326(f328(x83301),x83302),f326(f172(x83301),x83303)))+P105(f326(f137(x83301),f326(f326(f148(x83301,x83304,x83305),x83302),x83303)))
% 157.55/157.23 [8475]~P66(x84751)+E(f326(f326(f3(x84751),f326(f326(f8(a909,x84751),x84752),f326(f301(a909,x84753),x84754))),f326(f326(f8(a909,x84751),x84752),f326(f301(a909,x84753),x84755))),f326(f326(f8(a909,x84751),x84752),f326(f301(a909,x84755),x84754)))+~P105(f326(f326(f234(a909),x84755),x84754))+~P105(f326(f326(f234(a909),x84753),x84755))
% 157.55/157.23 [8476]~P69(x84761)+E(f326(f326(f79(x84761),f326(f326(f8(a909,x84761),x84762),f326(f301(a909,x84763),x84764))),f326(f326(f8(a909,x84761),x84762),f326(f301(a909,x84764),x84765))),f326(f326(f8(a909,x84761),x84762),f326(f301(a909,x84763),x84765)))+~P105(f326(f326(f234(a909),x84764),x84765))+~P105(f326(f326(f234(a909),x84763),x84764))
% 157.55/157.23 [8802]~P63(x88022)+E(x88021,f2(x88022))+E(x88023,f2(x88022))+E(f326(f326(f290(x88022),f326(f326(f3(x88022),f326(f326(f80(x88022),x88024),x88021)),f326(f326(f80(x88022),x88025),x88023))),f326(f326(f80(x88022),x88023),x88021)),f326(f326(f3(x88022),f326(f326(f290(x88022),x88024),x88023)),f326(f326(f290(x88022),x88025),x88021)))
% 157.55/157.23 [8803]~P63(x88032)+E(x88031,f2(x88032))+E(x88033,f2(x88032))+E(f326(f326(f290(x88032),f326(f326(f79(x88032),f326(f326(f80(x88032),x88034),x88031)),f326(f326(f80(x88032),x88035),x88033))),f326(f326(f80(x88032),x88033),x88031)),f326(f326(f79(x88032),f326(f326(f290(x88032),x88034),x88033)),f326(f326(f290(x88032),x88035),x88031)))
% 157.55/157.23 [8812]~E(x88122,f326(x88123,x88121))+E(x88121,f515(x88122,x88123,x88124,x88125))+~P24(x88125,x88124,x88123,f241(f917(x88125,a905)))+~P105(f326(f326(f328(x88124),x88122),f326(f309(x88125,x88124,x88123),f241(f917(x88125,a905)))))
% 157.55/157.23 [9029]~P118(x90291)+~P105(f326(f326(f235(x90291),f326(f75(x90291),x90292)),x90294))+P105(f326(f326(f235(x90291),f326(f326(f80(x90291),f326(f75(x90291),x90292)),f326(f75(x90291),x90293))),f326(f326(f80(x90291),x90294),x90295)))+~P105(f326(f326(f235(x90291),f326(f75(x90291),x90293)),x90295))
% 157.55/157.23 [9140]~P24(x91401,x91403,x91405,x91402)+~P105(f326(f61(x91403),x91404))+P105(f326(f326(f234(a909),f326(f35(x91401),x91402)),f326(f35(x91403),x91404)))+~P105(f326(f326(f234(f917(x91403,a905)),f326(f309(x91401,x91403,x91405),x91402)),x91404))
% 157.55/157.23 [9207]~P69(x92072)+~P24(x92071,x92071,x92074,x92075)+~P105(f326(f61(x92071),x92075))+E(f326(f326(f8(x92071,x92072),f326(f72(x92071,x92072,x92071,x92073),x92074)),x92075),f326(f326(f8(x92071,x92072),x92073),f326(f309(x92071,x92071,x92074),x92075)))
% 157.55/157.23 [9208]~P74(x92082)+~P24(x92081,x92081,x92084,x92085)+~P105(f326(f61(x92081),x92085))+E(f326(f326(f11(x92081,x92082),f326(f72(x92081,x92082,x92081,x92083),x92084)),x92085),f326(f326(f11(x92081,x92082),x92083),f326(f309(x92081,x92081,x92084),x92085)))
% 157.55/157.23 [9325]~P36(x93251,x93252)+~P105(f326(f326(f328(x93251),x93253),x93254))+~P105(f326(f326(f328(x93251),x93255),x93254))+~P105(f326(f326(f328(f916(x93251,x93251)),f326(f326(f251(x93251,x93251),x93255),f613(x93252,x93251,x93254))),x93252))
% 157.55/157.23 [9359]~P24(x93592,x93593,x93595,x93591)+E(x93591,f188(f917(x93592,a905)))+E(f326(f309(x93593,x93592,f517(x93594,x93593,x93592,x93591)),x93594),x93591)+~P105(f326(f326(f234(f917(x93593,a905)),f326(f309(x93592,x93593,x93595),x93591)),x93594))
% 157.55/157.23 [9840]~P108(x98405)+~P4(x98405)+P105(f326(f326(f328(x98401),f464(x98402,x98403,x98401,x98404,x98405)),x98403))+~P105(f326(f326(f235(x98405),x98404),f326(f326(f40(x98401,x98405),x98403),x98402)))
% 157.55/157.23 [9845]~P108(x98451)+~P4(x98451)+P105(f326(f326(f235(x98451),x98452),f326(x98453,f464(x98453,x98454,x98455,x98452,x98451))))+~P105(f326(f326(f235(x98451),x98452),f326(f326(f40(x98455,x98451),x98454),x98453)))
% 157.55/157.23 [9923]~P67(x99231)+~P105(f326(f66(x99231,x99231,f80(x99231),x99232,x99233),x99235))+P105(f326(f326(f328(x99231),x99232),x99233))+P105(f326(f66(x99231,x99231,f80(x99231),x99234,f326(f326(f308(x99231),x99232),x99233)),f326(f326(f80(x99231),x99234),x99235)))
% 157.55/157.23 [10137]~P69(x101372)+~P105(f326(f61(x101371),x101375))+E(f326(f326(f8(x101371,x101372),f326(f326(f9(x101371,x101372,x101372),f326(f326(f20(x101371,x101372,f917(x101372,x101372)),f326(f326(f10(a905,f917(x101372,f917(x101372,x101372)),x101371),f96(x101372)),f326(a323,x101373))),x101374)),f2(x101372))),x101375),f2(x101372))+P105(f326(f326(f328(x101371),x101373),x101375))
% 157.55/157.23 [10138]~P74(x101382)+~P105(f326(f61(x101381),x101385))+E(f326(f326(f11(x101381,x101382),f326(f326(f9(x101381,x101382,x101382),f326(f326(f20(x101381,x101382,f917(x101382,x101382)),f326(f326(f10(a905,f917(x101382,f917(x101382,x101382)),x101381),f96(x101382)),f326(a323,x101383))),x101384)),f77(x101382))),x101385),f77(x101382))+P105(f326(f326(f328(x101381),x101383),x101385))
% 157.55/157.23 [10139]~P69(x101392)+~P105(f326(f61(x101391),x101395))+E(f326(f326(f8(x101391,x101392),f326(f326(f9(x101391,x101392,x101392),f326(f326(f20(x101391,x101392,f917(x101392,x101392)),f326(f326(f10(a905,f917(x101392,f917(x101392,x101392)),x101391),f96(x101392)),f326(a323,x101393))),x101394)),f2(x101392))),x101395),f326(x101394,x101393))+~P105(f326(f326(f328(x101391),x101393),x101395))
% 157.55/157.23 [10140]~P74(x101402)+~P105(f326(f61(x101401),x101405))+E(f326(f326(f11(x101401,x101402),f326(f326(f9(x101401,x101402,x101402),f326(f326(f20(x101401,x101402,f917(x101402,x101402)),f326(f326(f10(a905,f917(x101402,f917(x101402,x101402)),x101401),f96(x101402)),f326(a323,x101403))),x101404)),f77(x101402))),x101405),f326(x101404,x101403))+~P105(f326(f326(f328(x101401),x101403),x101405))
% 157.55/157.23 [10197]~P69(x101972)+~P105(f326(f61(x101971),x101975))+E(f326(f326(f8(x101971,x101972),f326(f326(f9(x101971,x101972,x101972),f326(f326(f20(x101971,x101972,f917(x101972,x101972)),f326(f326(f10(a905,f917(x101972,f917(x101972,x101972)),x101971),f96(x101972)),f326(f326(f9(x101971,x101971,a905),a323),x101973))),x101974)),f2(x101972))),x101975),f2(x101972))+P105(f326(f326(f328(x101971),x101973),x101975))
% 157.55/157.23 [10198]~P74(x101982)+~P105(f326(f61(x101981),x101985))+E(f326(f326(f11(x101981,x101982),f326(f326(f9(x101981,x101982,x101982),f326(f326(f20(x101981,x101982,f917(x101982,x101982)),f326(f326(f10(a905,f917(x101982,f917(x101982,x101982)),x101981),f96(x101982)),f326(f326(f9(x101981,x101981,a905),a323),x101983))),x101984)),f77(x101982))),x101985),f77(x101982))+P105(f326(f326(f328(x101981),x101983),x101985))
% 157.55/157.23 [10200]~P69(x102002)+~P105(f326(f61(x102001),x102005))+E(f326(f326(f8(x102001,x102002),f326(f326(f9(x102001,x102002,x102002),f326(f326(f20(x102001,x102002,f917(x102002,x102002)),f326(f326(f10(a905,f917(x102002,f917(x102002,x102002)),x102001),f96(x102002)),f326(f326(f9(x102001,x102001,a905),a323),x102003))),x102004)),f2(x102002))),x102005),f326(x102004,x102003))+~P105(f326(f326(f328(x102001),x102003),x102005))
% 157.55/157.23 [10201]~P74(x102012)+~P105(f326(f61(x102011),x102015))+E(f326(f326(f11(x102011,x102012),f326(f326(f9(x102011,x102012,x102012),f326(f326(f20(x102011,x102012,f917(x102012,x102012)),f326(f326(f10(a905,f917(x102012,f917(x102012,x102012)),x102011),f96(x102012)),f326(f326(f9(x102011,x102011,a905),a323),x102013))),x102014)),f77(x102012))),x102015),f326(x102014,x102013))+~P105(f326(f326(f328(x102011),x102013),x102015))
% 157.55/157.23 [7988]~P66(x79882)+~P105(f326(f61(x79881),x79884))+E(f326(f326(f8(x79881,x79882),x79883),f326(f326(f3(f917(x79881,a905)),x79884),f326(f326(f308(x79881),x79885),f188(f917(x79881,a905))))),f326(f326(f8(x79881,x79882),x79883),x79884))+P105(f326(f326(f328(x79881),x79885),x79884))
% 157.55/157.23 [8483]~P110(x84832)+~P105(f326(f61(x84831),x84834))+E(f326(f326(f8(x84831,x84832),x84833),f326(f326(f3(f917(x84831,a905)),x84834),f326(f326(f308(x84831),x84835),f188(f917(x84831,a905))))),f326(f326(f3(x84832),f326(f326(f8(x84831,x84832),x84833),x84834)),f326(x84833,x84835)))+~P105(f326(f326(f328(x84831),x84835),x84834))
% 157.55/157.23 [8484]~P66(x84842)+~P105(f326(f61(x84841),x84844))+E(f326(f326(f8(x84841,x84842),x84843),f326(f326(f3(f917(x84841,a905)),x84844),f326(f326(f308(x84841),x84845),f188(f917(x84841,a905))))),f326(f326(f3(x84842),f326(f326(f8(x84841,x84842),x84843),x84844)),f326(x84843,x84845)))+~P105(f326(f326(f328(x84841),x84845),x84844))
% 157.55/157.23 [8513]~P66(x85131)+~P105(f326(f61(x85132),x85134))+E(f326(f326(f3(x85131),f326(f326(f8(x85132,x85131),x85133),x85134)),f326(f326(f8(x85132,x85131),x85133),x85135)),f326(f326(f8(x85132,x85131),x85133),f326(f326(f3(f917(x85132,a905)),x85134),x85135)))+~P105(f326(f326(f234(f917(x85132,a905)),x85135),x85134))
% 157.55/157.23 [8532]P105(f326(f61(x85321),f326(x85322,x85323)))+~P105(f326(f61(x85324),x85325))+~P105(f326(f326(f328(x85324),x85323),x85325))+~P105(f326(f61(x85321),f326(f326(f40(x85324,f917(x85321,a905)),x85325),x85322)))
% 157.55/157.23 [8985]~P7(x89851,x89855,x89854)+~E(f326(f284(x89851,x89851,x89854),f326(f326(f308(x89851),x89852),f188(f917(x89851,a905)))),f326(f284(x89851,x89851,x89854),f326(f326(f308(x89851),x89853),f188(f917(x89851,a905)))))+~P105(f326(f326(f328(x89851),x89853),x89855))+P105(f326(f326(f328(f916(x89851,x89851)),f326(f326(f251(x89851,x89851),x89852),x89853)),x89854))
% 157.55/157.23 [9282]~P105(f326(x92821,x92825))+P105(f326(x92821,f903(x92821,x92822,x92823,x92824)))+P105(f326(x92821,f894(x92821,x92822,x92823,x92824)))+~P105(f326(f326(f328(x92824),x92825),f326(f326(f110(f917(x92824,a905)),x92823),x92822)))
% 157.55/157.23 [9463]~P105(f326(x94631,x94635))+P105(f326(x94631,f894(x94631,x94632,x94633,x94634)))+P105(f326(f326(f328(x94634),f903(x94631,x94632,x94633,x94634)),x94632))+~P105(f326(f326(f328(x94634),x94635),f326(f326(f110(f917(x94634,a905)),x94633),x94632)))
% 157.55/157.23 [9464]~P105(f326(x94641,x94645))+P105(f326(x94641,f903(x94641,x94642,x94643,x94644)))+P105(f326(f326(f328(x94644),f894(x94641,x94642,x94643,x94644)),x94643))+~P105(f326(f326(f328(x94644),x94645),f326(f326(f110(f917(x94644,a905)),x94643),x94642)))
% 157.55/157.23 [9468]P105(f326(x94681,x94682))+~P105(f326(x94681,f381(x94681,x94683,x94684,x94685)))+~P105(f326(x94681,f367(x94681,x94683,x94684,x94685)))+~P105(f326(f326(f328(x94685),x94682),f326(f326(f110(f917(x94685,a905)),x94684),x94683)))
% 157.55/157.23 [9473]~P37(x94731,x94734)+~P105(f326(f326(f328(f916(x94731,x94731)),f326(f326(f251(x94731,x94731),x94732),x94735)),x94734))+P105(f326(f326(f328(f916(x94731,x94731)),f326(f326(f251(x94731,x94731),x94732),x94733)),x94734))+~P105(f326(f326(f328(f916(x94731,x94731)),f326(f326(f251(x94731,x94731),x94735),x94733)),x94734))
% 157.55/157.23 [9512]E(x95121,x95122)+~P105(f326(f326(f328(f916(x95123,x95123)),f326(f326(f251(x95123,x95123),x95121),x95122)),f306(x95123,x95125)))+P105(f326(f326(f328(x95123),x95121),x95124))+~P105(f326(f326(f234(f917(f916(x95123,x95123),a905)),x95125),f326(f326(f253(x95123,x95123),x95124),f326(f18(f917(x95123,a905),x95123),x95124))))
% 157.55/157.23 [9530]P105(f326(x95301,x95302))+~P105(f326(x95301,f367(x95301,x95304,x95305,x95303)))+P105(f326(f326(f328(x95303),f381(x95301,x95304,x95305,x95303)),x95304))+~P105(f326(f326(f328(x95303),x95302),f326(f326(f110(f917(x95303,a905)),x95305),x95304)))
% 157.55/157.23 [9531]P105(f326(x95311,x95312))+~P105(f326(x95311,f381(x95311,x95314,x95315,x95313)))+P105(f326(f326(f328(x95313),f367(x95311,x95314,x95315,x95313)),x95315))+~P105(f326(f326(f328(x95313),x95312),f326(f326(f110(f917(x95313,a905)),x95315),x95314)))
% 157.55/157.23 [9596]P105(f326(x95961,x95962))+P105(f326(f326(f328(x95963),f381(x95961,x95964,x95965,x95963)),x95964))+P105(f326(f326(f328(x95963),f367(x95961,x95964,x95965,x95963)),x95965))+~P105(f326(f326(f328(x95963),x95962),f326(f326(f110(f917(x95963,a905)),x95965),x95964)))
% 157.55/157.23 [9598]~P105(f326(x95982,x95985))+P105(f326(f326(f328(x95981),f903(x95982,x95983,x95984,x95981)),x95983))+P105(f326(f326(f328(x95981),f894(x95982,x95983,x95984,x95981)),x95984))+~P105(f326(f326(f328(x95981),x95985),f326(f326(f110(f917(x95981,a905)),x95984),x95983)))
% 157.55/157.23 [9746]~P7(x97461,x97465,x97464)+~P105(f326(f326(f328(x97461),x97463),x97465))+P105(f326(f326(f328(f916(x97461,x97461)),f326(f326(f251(x97461,x97461),x97462),x97463)),x97464))+~P105(f326(f326(f234(f917(x97461,a905)),f326(f284(x97461,x97461,x97464),f326(f326(f308(x97461),x97463),f188(f917(x97461,a905))))),f326(f284(x97461,x97461,x97464),f326(f326(f308(x97461),x97462),f188(f917(x97461,a905))))))
% 157.55/157.23 [9874]~P108(x98745)+~P4(x98745)+P105(f326(f326(f328(x98741),f421(x98742,x98743,x98744,x98741,x98745)),x98744))+~P105(f326(f326(f235(x98745),f326(f326(f39(x98741,x98745),x98744),x98743)),x98742))
% 157.55/157.23 [9906]~P85(x99065)+~P82(x99065)+P105(f326(f326(f328(x99061),f690(x99062,x99063,x99064,x99061,x99065)),f326(f172(x99061),x99064)))+P105(f326(f326(f234(x99065),f326(f165(x99065),f326(f326(f154(x99061,x99065),x99063),x99064))),f326(f165(x99065),f326(f326(f154(x99061,x99065),x99062),x99064))))
% 157.55/157.23 [10014]~P108(x100141)+~P4(x100141)+P105(f326(f326(f235(x100141),f326(x100142,f421(x100143,x100142,x100144,x100145,x100141))),x100143))+~P105(f326(f326(f235(x100141),f326(f326(f39(x100145,x100141),x100144),x100142)),x100143))
% 157.55/157.23 [10155]~P85(x101551)+~P82(x101551)+~P105(f326(f326(f234(x101551),f326(x101553,f690(x101555,x101553,x101554,x101552,x101551))),f326(x101555,f690(x101555,x101553,x101554,x101552,x101551))))+P105(f326(f326(f234(x101551),f326(f165(x101551),f326(f326(f154(x101552,x101551),x101553),x101554))),f326(f165(x101551),f326(f326(f154(x101552,x101551),x101555),x101554))))
% 157.55/157.23 [8825]~P69(x88251)+~P105(f326(f61(x88254),x88255))+~P105(f326(f326(f328(x88254),x88253),x88255))+E(f326(f326(f79(x88251),f326(x88252,x88253)),f326(f326(f8(x88254,x88251),x88252),f326(f326(f3(f917(x88254,a905)),x88255),f326(f326(f308(x88254),x88253),f188(f917(x88254,a905)))))),f326(f326(f8(x88254,x88251),x88252),x88255))
% 157.55/157.23 [8826]~P74(x88261)+~P105(f326(f61(x88264),x88265))+~P105(f326(f326(f328(x88264),x88263),x88265))+E(f326(f326(f80(x88261),f326(x88262,x88263)),f326(f326(f11(x88264,x88261),x88262),f326(f326(f3(f917(x88264,a905)),x88265),f326(f326(f308(x88264),x88263),f188(f917(x88264,a905)))))),f326(f326(f11(x88264,x88261),x88262),x88265))
% 157.55/157.23 [8886]~P17(x88861,x88864,x88865)+~P105(f326(f61(x88861),x88862))+E(f326(f326(f3(f917(x88861,a905)),x88862),f326(f326(f308(x88861),x88863),f188(f917(x88861,a905)))),f188(f917(x88861,a905)))+E(f326(f326(x88864,x88863),f326(x88865,f326(f326(f3(f917(x88861,a905)),x88862),f326(f326(f308(x88861),x88863),f188(f917(x88861,a905)))))),f326(x88865,f326(f326(f308(x88861),x88863),x88862)))
% 157.55/157.23 [9261]~P74(x92611)+~P105(f326(f61(x92612),x92615))+~P105(f326(f61(x92612),x92614))+E(f326(f326(f80(x92611),f326(f326(f11(x92612,x92611),x92613),f326(f326(f110(f917(x92612,a905)),x92614),x92615))),f326(f326(f11(x92612,x92611),x92613),f326(f326(f101(f917(x92612,a905)),x92614),x92615))),f326(f326(f80(x92611),f326(f326(f11(x92612,x92611),x92613),x92614)),f326(f326(f11(x92612,x92611),x92613),x92615)))
% 157.55/157.23 [9262]~P69(x92621)+~P105(f326(f61(x92622),x92625))+~P105(f326(f61(x92622),x92624))+E(f326(f326(f79(x92621),f326(f326(f8(x92622,x92621),x92623),f326(f326(f110(f917(x92622,a905)),x92624),x92625))),f326(f326(f8(x92622,x92621),x92623),f326(f326(f101(f917(x92622,a905)),x92624),x92625))),f326(f326(f79(x92621),f326(f326(f8(x92622,x92621),x92623),x92624)),f326(f326(f8(x92622,x92621),x92623),x92625)))
% 157.55/157.23 [9398]~P66(x93981)+~P105(f326(f61(x93982),x93985))+~P105(f326(f61(x93982),x93984))+E(f326(f326(f3(x93981),f326(f326(f79(x93981),f326(f326(f8(x93982,x93981),x93983),x93984)),f326(f326(f8(x93982,x93981),x93983),x93985))),f326(f326(f8(x93982,x93981),x93983),f326(f326(f101(f917(x93982,a905)),x93984),x93985))),f326(f326(f8(x93982,x93981),x93983),f326(f326(f110(f917(x93982,a905)),x93984),x93985)))
% 157.55/157.23 [9608]~P24(x96081,x96082,x96083,x96085)+~P24(x96081,x96082,x96083,x96084)+P24(x96081,x96082,x96083,f326(f326(f110(f917(x96081,a905)),x96084),x96085))+~E(f326(f326(f101(f917(x96082,a905)),f326(f309(x96081,x96082,x96083),f326(f326(f3(f917(x96081,a905)),x96084),x96085))),f326(f309(x96081,x96082,x96083),f326(f326(f3(f917(x96081,a905)),x96085),x96084))),f188(f917(x96082,a905)))
% 157.55/157.23 [9721]E(x97211,f2(a1))+~P105(f326(f326(f235(a1),f2(a1)),x97213))+~P105(f326(f49(x97212,x97211),f326(f326(f251(a1,a1),x97214),x97215)))+P105(f326(f49(x97212,f326(f326(f80(a1),x97211),x97213)),f326(f326(f251(a1,a1),f326(f326(f36(a1),x97214),x97213)),f326(f326(f79(a1),f326(f326(f80(a1),x97211),f45(a1,x97214,x97213))),x97215))))
% 157.55/157.23 [9729]~P105(f326(f326(f235(a909),f2(a909)),x97293))+~P105(f326(f326(f235(a909),f2(a909)),x97292))+~P105(f326(f48(x97291,x97292),f326(f326(f251(a909,a909),x97294),x97295)))+P105(f326(f48(x97291,f326(f326(f80(a909),x97292),x97293)),f326(f326(f251(a909,a909),f326(f326(f36(a909),x97294),x97293)),f326(f326(f79(a909),f326(f326(f80(a909),x97292),f45(a909,x97294,x97293))),x97295))))
% 157.55/157.23 [9778]~P74(x97781)+~P105(f326(f61(x97782),x97785))+~P105(f326(f61(x97782),x97784))+E(f326(f326(f80(x97781),f326(f326(f326(f65(x97781,x97782,f80(x97781)),x97783),f77(x97781)),f326(f326(f110(f917(x97782,a905)),x97784),x97785))),f326(f326(f326(f65(x97781,x97782,f80(x97781)),x97783),f77(x97781)),f326(f326(f101(f917(x97782,a905)),x97784),x97785))),f326(f326(f80(x97781),f326(f326(f326(f65(x97781,x97782,f80(x97781)),x97783),f77(x97781)),x97784)),f326(f326(f326(f65(x97781,x97782,f80(x97781)),x97783),f77(x97781)),x97785)))
% 157.55/157.23 [9780]~E(f326(f326(f175(x97801),x97805),x97802),f326(f326(f175(x97801),x97805),x97803))+P105(f326(f326(f328(f916(f910(x97801),f910(x97801))),f326(f326(f251(f910(x97801),f910(x97801)),x97802),x97803)),f147(x97801,x97804)))+~P105(f326(f326(f235(a909),x97805),f326(f326(f232(a909),f326(f189(f910(x97801)),x97802)),f326(f189(f910(x97801)),x97803))))+~P105(f326(f326(f328(f916(x97801,x97801)),f326(f326(f251(x97801,x97801),f326(f326(f164(x97801),x97802),x97805)),f326(f326(f164(x97801),x97803),x97805))),x97804))
% 157.55/157.23 [9895]~P85(x98955)+~P143(x98955)+P105(f326(f326(f328(x98951),f349(x98952,x98953,x98954,x98951,x98955)),x98954))+P105(f326(f326(f234(x98955),f326(f326(f8(x98951,x98955),x98953),x98954)),f326(f326(f80(x98955),f326(f100(x98955),f326(f35(x98951),x98954))),x98952)))
% 157.55/157.23 [10072]~P85(x100721)+~P143(x100721)+~P105(f326(f326(f234(x100721),f326(x100723,f349(x100725,x100723,x100724,x100722,x100721))),x100725))+P105(f326(f326(f234(x100721),f326(f326(f8(x100722,x100721),x100723),x100724)),f326(f326(f80(x100721),f326(f100(x100721),f326(f35(x100722),x100724))),x100725)))
% 157.55/157.23 [8854]E(f326(f326(f134(x88541),x88542),x88543),f326(f326(f134(x88541),x88544),x88545))+~E(f326(f326(f175(x88541),f326(f189(f910(x88541)),x88542)),x88544),x88542)+~E(f326(f326(f134(x88541),f326(f326(f138(x88541),f326(f189(f910(x88541)),x88542)),x88544)),x88545),x88543)+P105(f326(f326(f234(a909),f326(f189(f910(x88541)),x88544)),f326(f189(f910(x88541)),x88542)))
% 157.55/157.23 [8984]E(f326(f326(f134(x89841),x89842),x89843),f326(f326(f134(x89841),x89844),x89845))+~E(f326(f326(f175(x89841),f326(f189(f910(x89841)),x89842)),x89844),x89842)+~E(x89843,f326(f326(f134(x89841),f326(f326(f138(x89841),f326(f189(f910(x89841)),x89842)),x89844)),x89845))+~P105(f326(f326(f234(a909),f326(f189(f910(x89841)),x89842)),f326(f189(f910(x89841)),x89844)))
% 157.55/157.23 [10219]~P105(f326(x102195,x102194))+~P105(f326(f61(x102192),f326(f261(x102192),x102195)))+P105(f326(f61(x102191),f326(f261(x102191),f326(f326(f9(x102191,x102192,a905),x102193),x102194))))+~P105(f326(f61(x102191),f326(f261(x102191),f326(f326(f10(f917(x102192,a905),a905,x102191),f86(x102192)),f326(f326(f10(f917(x102192,a905),f917(x102192,a905),x102191),f326(f20(x102192,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102192),a324),x102195))),x102193)))))
% 157.55/157.23 [10290]~P105(f326(f61(x102902),x102905))+~P105(f326(f326(f328(x102902),x102904),x102905))+P105(f326(f61(x102901),f326(f261(x102901),f326(f326(f9(x102901,x102902,a905),x102903),x102904))))+~P105(f326(f61(x102901),f326(f261(x102901),f326(f326(f10(f917(x102902,a905),a905,x102901),f86(x102902)),f326(f326(f10(f917(x102902,a905),f917(x102902,a905),x102901),f326(f20(x102902,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102902),a324),f326(f326(f9(x102902,f917(x102902,a905),a905),f328(x102902)),x102905)))),x102903)))))
% 157.55/157.23 [8641]~P18(x86415,x86411,x86416,x86412)+E(f326(f72(x86411,x86411,x86411,f326(x86412,x86413)),f326(x86412,x86414)),f326(f72(x86411,x86411,x86411,f326(x86412,x86414)),f326(x86412,x86413)))+~P105(f326(f61(x86415),x86414))+~P105(f326(f61(x86415),x86413))
% 157.55/157.23 [8043]~P24(x80431,x80432,x80434,x80433)+~E(f326(x80434,x80436),x80435)+E(f326(f76(x80431,x80432,x80433,x80434),x80435),x80436)+~P105(f326(f326(f328(x80431),x80436),x80433))
% 157.55/157.23 [8044]~P24(x80441,x80442,x80444,x80443)+~E(f326(x80444,x80446),x80445)+E(f326(f90(x80441,x80442,x80443,x80444),x80445),x80446)+~P105(f326(f326(f328(x80441),x80446),x80443))
% 157.55/157.23 [8236]~P19(x82366,x82361,x82364,x82362)+E(f326(f72(x82361,x82361,x82361,f326(x82362,x82363)),f326(x82364,x82365)),f326(x82362,x82363))+~P105(f326(f61(x82366),x82363))+~P105(f326(f326(f328(x82366),x82365),x82363))
% 157.55/157.23 [9351]E(x93511,x93512)+~E(f326(f90(x93513,x93514,x93515,x93516),x93511),f326(f90(x93513,x93514,x93515,x93516),x93512))+~P105(f326(f326(f328(x93514),x93512),f326(f309(x93513,x93514,x93516),x93515)))+~P105(f326(f326(f328(x93514),x93511),f326(f309(x93513,x93514,x93516),x93515)))
% 157.55/157.23 [9447]~P18(x94473,x94471,x94476,x94472)+E(f326(f72(x94471,x94471,x94471,f326(x94472,f326(f326(f3(f917(x94473,a905)),x94474),f326(f326(f308(x94473),x94475),f188(f917(x94473,a905)))))),f326(x94476,x94475)),f326(x94472,x94474))+~P105(f326(f61(x94473),x94474))+~P105(f326(f326(f328(x94473),x94475),x94474))
% 157.55/157.23 [7133]~P60(x71331)+~E(f45(x71331,x71333,x71334),f45(x71331,x71336,x71334))+~E(f45(x71331,x71332,x71334),f45(x71331,x71335,x71334))+E(f45(x71331,f326(f326(f3(x71331),x71332),x71333),x71334),f45(x71331,f326(f326(f3(x71331),x71335),x71336),x71334))
% 157.55/157.23 [7134]~P59(x71341)+~E(f45(x71341,x71343,x71344),f45(x71341,x71346,x71344))+~E(f45(x71341,x71342,x71344),f45(x71341,x71345,x71344))+E(f45(x71341,f326(f326(f80(x71341),x71342),x71343),x71344),f45(x71341,f326(f326(f80(x71341),x71345),x71346),x71344))
% 157.55/157.23 [7135]~P59(x71351)+~E(f45(x71351,x71353,x71354),f45(x71351,x71356,x71354))+~E(f45(x71351,x71352,x71354),f45(x71351,x71355,x71354))+E(f45(x71351,f326(f326(f79(x71351),x71352),x71353),x71354),f45(x71351,f326(f326(f79(x71351),x71355),x71356),x71354))
% 157.55/157.23 [7941]~P15(x79411,x79412,x79413)+~P105(f326(f61(x79411),x79416))+E(f326(f326(f64(x79411,x79412,x79413),x79414),f326(f326(f308(x79411),x79415),x79416)),f326(f326(f64(x79411,x79412,x79413),f326(f326(x79413,x79415),x79414)),x79416))+P105(f326(f326(f328(x79411),x79415),x79416))
% 157.55/157.23 [8002]~P4(x80021)+P105(f326(f326(f234(x80021),x80022),f326(x80023,x80024)))+~P105(f326(f326(f328(x80025),x80024),x80026))+~P105(f326(f326(f234(x80021),x80022),f326(f326(f39(x80025,x80021),x80026),x80023)))
% 157.55/157.23 [8158]~P15(x81581,x81582,x81583)+~P105(f326(f61(x81581),x81586))+E(f326(f326(f64(x81581,x81582,x81583),x81584),f326(f326(f308(x81581),x81585),x81586)),f326(f326(x81583,x81585),f326(f326(f64(x81581,x81582,x81583),x81584),x81586)))+P105(f326(f326(f328(x81581),x81585),x81586))
% 157.55/157.23 [8254]~P108(x82543)+~P105(f326(x82542,x82545))+~P12(x82543,f326(f326(f154(x82541,x82543),x82544),x82546))+E(f326(f136(x82541,x82542),f326(f326(f148(x82541,x82543,x82544),x82545),x82546)),f326(f326(f148(x82541,x82543,x82544),x82545),f326(f136(x82541,x82542),x82546)))
% 157.55/157.23 [8274]E(x82741,x82742)+E(x82743,f2(a1))+~P105(f326(f49(x82744,x82743),f326(f326(f251(a1,a1),x82745),x82742)))+~P105(f326(f49(x82744,x82743),f326(f326(f251(a1,a1),x82746),x82741)))
% 157.55/157.23 [8275]E(x82751,x82752)+E(x82753,f2(a1))+~P105(f326(f49(x82754,x82753),f326(f326(f251(a1,a1),x82752),x82755)))+~P105(f326(f49(x82754,x82753),f326(f326(f251(a1,a1),x82751),x82756)))
% 157.55/157.23 [8296]~P18(x82962,x82965,x82966,x82961)+~P105(f326(f61(x82962),x82964))+E(f326(x82961,f326(f326(f308(x82962),x82963),x82964)),f326(f72(x82965,x82965,x82965,f326(x82961,x82964)),f326(x82966,x82963)))+P105(f326(f326(f328(x82962),x82963),x82964))
% 157.55/157.23 [8516]~P19(x85165,x85161,x85166,x85162)+E(f326(f72(x85161,x85161,x85161,f326(x85162,x85163)),f326(x85162,x85164)),f326(x85162,x85163))+~P105(f326(f61(x85165),x85163))+~P105(f326(f326(f234(f917(x85165,a905)),x85164),x85163))
% 157.55/157.23 [9651]~P24(x96511,x96512,x96514,x96513)+~P105(f326(f326(f328(x96512),x96515),f326(f309(x96511,x96512,x96514),x96513)))+P105(f326(f326(f328(x96511),f326(f76(x96511,x96512,x96513,x96514),x96515)),x96516))+~P105(f326(f326(f234(f917(x96511,a905)),x96513),x96516))
% 157.55/157.23 [10025]~P69(x100252)+~E(f587(x100251,x100253,x100255,x100256,x100254,x100252),f588(x100251,x100253,x100255,x100256,x100254,x100252))+~P105(f326(f61(x100254),x100256))+E(f326(f326(f8(x100251,x100252),x100253),f326(f309(x100254,x100251,x100255),x100256)),f326(f326(f8(x100254,x100252),f326(f72(x100251,x100252,x100254,x100253),x100255)),x100256))
% 157.55/157.23 [10054]~P69(x100546)+E(f326(x100541,f587(x100542,x100543,x100541,x100544,x100545,x100546)),f326(x100541,f588(x100542,x100543,x100541,x100544,x100545,x100546)))+E(f326(f326(f8(x100542,x100546),x100543),f326(f309(x100545,x100542,x100541),x100544)),f326(f326(f8(x100545,x100546),f326(f72(x100542,x100546,x100545,x100543),x100541)),x100544))+~P105(f326(f61(x100545),x100544))
% 157.55/157.23 [10105]~P69(x101052)+~E(f326(x101053,f326(x101055,f588(x101051,x101053,x101055,x101056,x101054,x101052))),f2(x101052))+~P105(f326(f61(x101054),x101056))+E(f326(f326(f8(x101051,x101052),x101053),f326(f309(x101054,x101051,x101055),x101056)),f326(f326(f8(x101054,x101052),f326(f72(x101051,x101052,x101054,x101053),x101055)),x101056))
% 157.55/157.23 [10163]~P69(x101632)+~P105(f326(f61(x101634),x101636))+E(f326(f326(f8(x101631,x101632),x101633),f326(f309(x101634,x101631,x101635),x101636)),f326(f326(f8(x101634,x101632),f326(f72(x101631,x101632,x101634,x101633),x101635)),x101636))+P105(f326(f326(f328(x101634),f588(x101631,x101633,x101635,x101636,x101634,x101632)),x101636))
% 157.55/157.23 [10164]~P69(x101642)+~P105(f326(f61(x101644),x101646))+E(f326(f326(f8(x101641,x101642),x101643),f326(f309(x101644,x101641,x101645),x101646)),f326(f326(f8(x101644,x101642),f326(f72(x101641,x101642,x101644,x101643),x101645)),x101646))+P105(f326(f326(f328(x101644),f587(x101641,x101643,x101645,x101646,x101644,x101642)),x101646))
% 157.55/157.23 [10289]~P74(x102891)+~P105(f326(f61(x102892),x102896))+E(f326(f326(f326(f65(x102891,x102892,f80(x102891)),f326(f326(f20(x102892,f917(x102893,a905),x102891),f326(f326(f9(x102892,x102891,f917(f917(x102893,a905),x102891)),f326(f326(f10(f917(x102893,x102891),f917(x102891,f917(f917(x102893,a905),x102891)),x102892),f65(x102891,x102893,f80(x102891))),x102894)),f77(x102891))),x102895)),f77(x102891)),x102896),f326(f326(f326(f65(x102891,f916(x102892,x102893),f80(x102891)),f326(f256(x102892,x102893,x102891),x102894)),f77(x102891)),f326(f326(f253(x102892,x102893),x102896),x102895)))+P105(f326(f326(f328(x102892),f533(x102894,x102895,x102893,x102896,x102892,x102891)),x102896))
% 157.55/157.23 [10311]~P74(x103111)+~P105(f326(f61(x103112),x103116))+E(f326(f326(f326(f65(x103111,x103112,f80(x103111)),f326(f326(f20(x103112,f917(x103113,a905),x103111),f326(f326(f9(x103112,x103111,f917(f917(x103113,a905),x103111)),f326(f326(f10(f917(x103113,x103111),f917(x103111,f917(f917(x103113,a905),x103111)),x103112),f65(x103111,x103113,f80(x103111))),x103114)),f77(x103111))),x103115)),f77(x103111)),x103116),f326(f326(f326(f65(x103111,f916(x103112,x103113),f80(x103111)),f326(f256(x103112,x103113,x103111),x103114)),f77(x103111)),f326(f326(f253(x103112,x103113),x103116),x103115)))+~P105(f326(f61(x103113),f326(x103115,f533(x103114,x103115,x103113,x103116,x103112,x103111))))
% 157.55/157.23 [8427]~P19(x84272,x84275,x84276,x84271)+~P105(f326(f61(x84272),x84274))+~P105(f326(f61(x84272),x84273))+E(f326(x84271,f326(f326(f110(f917(x84272,a905)),x84273),x84274)),f326(f72(x84275,x84275,x84275,f326(x84271,x84273)),f326(x84271,x84274)))
% 157.55/157.23 [8642]~P4(x86421)+P105(f326(f326(f234(x86421),f326(x86422,x86423)),x86424))+~P105(f326(f326(f328(x86425),x86423),x86426))+~P105(f326(f326(f234(x86421),f326(f326(f40(x86425,x86421),x86426),x86422)),x86424))
% 157.55/157.23 [9070]~P24(x90702,x90701,x90703,x90706)+E(f326(f326(f3(f917(x90701,a905)),f326(f309(x90702,x90701,x90703),x90704)),f326(f309(x90702,x90701,x90703),x90705)),f326(f309(x90702,x90701,x90703),f326(f326(f3(f917(x90702,a905)),x90704),x90705)))+~P105(f326(f326(f234(f917(x90702,a905)),x90705),x90706))+~P105(f326(f326(f234(f917(x90702,a905)),x90704),x90706))
% 157.55/157.23 [9071]~P24(x90712,x90711,x90713,x90716)+E(f326(f326(f101(f917(x90711,a905)),f326(f309(x90712,x90711,x90713),x90714)),f326(f309(x90712,x90711,x90713),x90715)),f326(f309(x90712,x90711,x90713),f326(f326(f101(f917(x90712,a905)),x90714),x90715)))+~P105(f326(f326(f234(f917(x90712,a905)),x90715),x90716))+~P105(f326(f326(f234(f917(x90712,a905)),x90714),x90716))
% 157.55/157.23 [9327]E(x93271,x93272)+~P53(x93273,x93274,x93275)+~P105(f326(f326(f328(f916(x93273,x93274)),f326(f326(f251(x93273,x93274),x93276),x93272)),x93275))+~P105(f326(f326(f328(f916(x93273,x93274)),f326(f326(f251(x93273,x93274),x93276),x93271)),x93275))
% 157.55/157.23 [10101]~P67(x101011)+~E(f326(x101013,f866(x101014,x101016,x101013,x101015,x101012,x101011)),f326(x101016,f866(x101014,x101016,x101013,x101015,x101012,x101011)))+~P105(f326(f61(x101012),x101015))+E(f326(f326(f326(f65(x101011,x101012,f80(x101011)),x101013),x101014),x101015),f326(f326(f326(f65(x101011,x101012,f80(x101011)),x101016),x101014),x101015))
% 157.55/157.23 [10161]~P67(x101611)+~P105(f326(f61(x101612),x101615))+E(f326(f326(f326(f65(x101611,x101612,f80(x101611)),x101613),x101614),x101615),f326(f326(f326(f65(x101611,x101612,f80(x101611)),x101616),x101614),x101615))+P105(f326(f326(f328(x101612),f866(x101614,x101613,x101616,x101615,x101612,x101611)),x101615))
% 157.55/157.23 [8868]~P67(x88681)+~P105(f326(f61(x88682),x88686))+P105(f326(f326(f328(x88682),x88685),x88686))+E(f326(f326(f326(f65(x88681,x88682,f80(x88681)),x88683),x88684),f326(f326(f308(x88682),x88685),x88686)),f326(f326(f80(x88681),f326(x88683,x88685)),f326(f326(f326(f65(x88681,x88682,f80(x88681)),x88683),x88684),x88686)))
% 157.55/157.23 [8921]~P7(x89211,x89216,x89213)+~P10(x89211,f917(x89212,a905),x89213,x89215)+~P105(f326(f326(f328(x89211),x89214),x89216))+E(f326(f326(f40(x89211,f917(x89212,a905)),f326(f284(x89211,x89211,x89213),f326(f326(f308(x89211),x89214),f188(f917(x89211,a905))))),x89215),f326(x89215,x89214))
% 157.55/157.23 [9047]~P15(x90473,x90474,x90471)+~P105(f326(f61(x90473),x90476))+~P105(f326(f326(f328(x90473),x90472),x90476))+E(f326(f326(x90471,x90472),f326(f326(f64(x90473,x90474,x90471),x90475),f326(f326(f3(f917(x90473,a905)),x90476),f326(f326(f308(x90473),x90472),f188(f917(x90473,a905)))))),f326(f326(f64(x90473,x90474,x90471),x90475),x90476))
% 157.55/157.23 [9337]~P18(x93373,x93371,x93376,x93372)+~P105(f326(f61(x93373),x93375))+~P105(f326(f61(x93373),x93374))+E(f326(f72(x93371,x93371,x93371,f326(x93372,f326(f326(f110(f917(x93373,a905)),x93374),x93375))),f326(x93372,f326(f326(f101(f917(x93373,a905)),x93374),x93375))),f326(f72(x93371,x93371,x93371,f326(x93372,x93374)),f326(x93372,x93375)))
% 157.55/157.23 [9674]~E(x96743,f326(f326(f159(x96741,x96742),x96745),x96746))+P105(f326(f326(f328(f916(f910(x96741),f910(x96741))),f326(f326(f251(f910(x96741),f910(x96741)),x96742),x96743)),f157(x96741,x96744)))+~P105(f326(f326(f235(a909),x96745),f326(f189(f910(x96741)),x96742)))+~P105(f326(f326(f328(f916(x96741,x96741)),f326(f326(f251(x96741,x96741),f326(f326(f164(x96741),x96742),x96745)),x96746)),x96744))
% 157.55/157.23 [10177]~P69(x101772)+~P105(f326(f61(x101771),x101776))+P105(f326(f326(f328(x101771),f536(x101774,x101775,x101773,x101776,x101771,x101772)),x101776))+E(f326(f326(f8(x101771,x101772),f326(f326(f20(x101771,f917(x101773,a905),x101772),f326(f326(f10(f917(x101773,x101772),f917(f917(x101773,a905),x101772),x101771),f8(x101773,x101772)),x101774)),x101775)),x101776),f326(f326(f8(f916(x101771,x101773),x101772),f326(f256(x101771,x101773,x101772),x101774)),f326(f326(f253(x101771,x101773),x101776),x101775)))
% 157.55/157.23 [10178]~P74(x101782)+~P105(f326(f61(x101781),x101786))+P105(f326(f326(f328(x101781),f537(x101784,x101785,x101783,x101786,x101781,x101782)),x101786))+E(f326(f326(f11(x101781,x101782),f326(f326(f20(x101781,f917(x101783,a905),x101782),f326(f326(f10(f917(x101783,x101782),f917(f917(x101783,a905),x101782),x101781),f11(x101783,x101782)),x101784)),x101785)),x101786),f326(f326(f11(f916(x101781,x101783),x101782),f326(f256(x101781,x101783,x101782),x101784)),f326(f326(f253(x101781,x101783),x101786),x101785)))
% 157.55/157.23 [10217]~P69(x102172)+~P105(f326(f61(x102171),x102176))+~P105(f326(f61(x102173),f326(x102175,f536(x102174,x102175,x102173,x102176,x102171,x102172))))+E(f326(f326(f8(x102171,x102172),f326(f326(f20(x102171,f917(x102173,a905),x102172),f326(f326(f10(f917(x102173,x102172),f917(f917(x102173,a905),x102172),x102171),f8(x102173,x102172)),x102174)),x102175)),x102176),f326(f326(f8(f916(x102171,x102173),x102172),f326(f256(x102171,x102173,x102172),x102174)),f326(f326(f253(x102171,x102173),x102176),x102175)))
% 157.55/157.23 [10218]~P74(x102182)+~P105(f326(f61(x102181),x102186))+~P105(f326(f61(x102183),f326(x102185,f537(x102184,x102185,x102183,x102186,x102181,x102182))))+E(f326(f326(f11(x102181,x102182),f326(f326(f20(x102181,f917(x102183,a905),x102182),f326(f326(f10(f917(x102183,x102182),f917(f917(x102183,a905),x102182),x102181),f11(x102183,x102182)),x102184)),x102185)),x102186),f326(f326(f11(f916(x102181,x102183),x102182),f326(f256(x102181,x102183,x102182),x102184)),f326(f326(f253(x102181,x102183),x102186),x102185)))
% 157.55/157.23 [10199]~P74(x101992)+~P105(f326(f61(x101991),x101996))+P105(f326(f326(f328(x101991),x101993),x101996))+E(f326(f326(f11(x101991,x101992),f326(f326(f9(x101991,x101992,x101992),f326(f326(f20(x101991,x101992,f917(x101992,x101992)),f326(f326(f10(a905,f917(x101992,f917(x101992,x101992)),x101991),f96(x101992)),f326(f326(f9(x101991,x101991,a905),a323),x101993))),x101994)),x101995)),x101996),f326(f326(f243(x101992),x101995),f326(f35(x101991),x101996)))
% 157.55/157.23 [10202]~P74(x102022)+~P105(f326(f61(x102021),x102026))+~P105(f326(f326(f328(x102021),x102023),x102026))+E(f326(f326(f11(x102021,x102022),f326(f326(f9(x102021,x102022,x102022),f326(f326(f20(x102021,x102022,f917(x102022,x102022)),f326(f326(f10(a905,f917(x102022,f917(x102022,x102022)),x102021),f96(x102022)),f326(f326(f9(x102021,x102021,a905),a323),x102023))),x102024)),x102025)),x102026),f326(f326(f80(x102022),f326(x102024,x102023)),f326(f326(f243(x102022),x102025),f326(f326(f3(a909),f326(f35(x102021),x102026)),f77(a909)))))
% 157.55/157.23 [10280]~P105(f326(f61(x102801),x102805))+~P105(f326(f61(x102802),x102803))+P105(f326(f326(f328(x102802),f552(x102806,x102804,x102803,x102802,x102805,x102801)),x102803))+E(f326(f326(f8(x102801,a909),f326(f326(f10(f917(x102802,a905),a909,x102801),f35(x102802)),f326(f326(f10(f917(x102802,a905),f917(x102802,a905),x102801),f261(x102802)),f326(f326(f10(f917(x102802,a905),f917(x102802,a905),x102801),f326(f20(x102802,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102802),a324),f326(f326(f9(x102802,f917(x102802,a905),a905),f328(x102802)),x102803)))),x102804)))),x102805),f326(f326(f80(a909),x102806),f326(f35(x102802),x102803)))
% 157.55/157.23 [10281]~P105(f326(f61(x102811),x102815))+~P105(f326(f61(x102812),x102813))+P105(f326(f326(f328(x102812),f553(x102816,x102814,x102813,x102812,x102815,x102811)),x102813))+E(f326(f326(f8(x102811,a909),f326(f326(f10(f917(x102812,a905),a909,x102811),f35(x102812)),f326(f326(f10(f917(x102812,a905),f917(x102812,a905),x102811),f261(x102812)),f326(f326(f10(f917(x102812,a905),f917(x102812,a905),x102811),f326(f20(x102812,a905,a905),f326(f326(f10(a905,f917(a905,a905),x102812),a324),f326(f326(f9(x102812,f917(x102812,a905),a905),f328(x102812)),x102813)))),x102814)))),x102815),f326(f326(f8(x102812,a909),x102816),x102813))
% 157.55/157.23 [10325]~P105(f326(f61(x103252),x103253))+~P105(f326(f61(x103251),x103255))+~E(f326(f35(x103251),f326(f261(x103251),f326(f326(f20(x103251,a905,a905),f326(f326(f10(a905,f917(a905,a905),x103251),a324),f326(f326(f9(x103251,f917(x103251,a905),a905),f328(x103251)),x103255))),f326(f326(f9(x103251,x103252,a905),x103254),f552(x103256,x103254,x103253,x103252,x103255,x103251))))),x103256)+E(f326(f326(f8(x103251,a909),f326(f326(f10(f917(x103252,a905),a909,x103251),f35(x103252)),f326(f326(f10(f917(x103252,a905),f917(x103252,a905),x103251),f261(x103252)),f326(f326(f10(f917(x103252,a905),f917(x103252,a905),x103251),f326(f20(x103252,a905,a905),f326(f326(f10(a905,f917(a905,a905),x103252),a324),f326(f326(f9(x103252,f917(x103252,a905),a905),f328(x103252)),x103253)))),x103254)))),x103255),f326(f326(f80(a909),x103256),f326(f35(x103252),x103253)))
% 157.55/157.23 [10327]~P105(f326(f61(x103272),x103273))+~P105(f326(f61(x103271),x103275))+~E(f326(f35(x103271),f326(f261(x103271),f326(f326(f20(x103271,a905,a905),f326(f326(f10(a905,f917(a905,a905),x103271),a324),f326(f326(f9(x103271,f917(x103271,a905),a905),f328(x103271)),x103275))),f326(f326(f9(x103271,x103272,a905),x103274),f553(x103276,x103274,x103273,x103272,x103275,x103271))))),f326(x103276,f553(x103276,x103274,x103273,x103272,x103275,x103271)))+E(f326(f326(f8(x103271,a909),f326(f326(f10(f917(x103272,a905),a909,x103271),f35(x103272)),f326(f326(f10(f917(x103272,a905),f917(x103272,a905),x103271),f261(x103272)),f326(f326(f10(f917(x103272,a905),f917(x103272,a905),x103271),f326(f20(x103272,a905,a905),f326(f326(f10(a905,f917(a905,a905),x103272),a324),f326(f326(f9(x103272,f917(x103272,a905),a905),f328(x103272)),x103273)))),x103274)))),x103275),f326(f326(f8(x103272,a909),x103276),x103273))
% 157.55/157.23 [9951]E(x99511,x99512)+~P15(x99513,x99514,x99515)+~P105(f326(f66(x99513,x99514,x99515,x99516,x99517),x99512))+~P105(f326(f66(x99513,x99514,x99515,x99516,x99517),x99511))
% 157.55/157.23 [9750]P105(f326(x97501,x97502))+~P105(f326(f326(f328(x97507),x97502),f326(x97506,x97504)))+~P105(f326(x97501,f463(x97501,x97506,x97505,x97503,x97507)))+~P105(f326(f326(f328(x97503),x97504),x97505))
% 157.55/157.23 [10191]~P15(x101917,x101916,x101911)+E(f326(f326(x101911,x101912),f625(x101912,x101913,x101914,x101915,x101911,x101916,x101917)),x101913)+~P105(f326(f66(x101917,x101916,x101911,x101915,x101914),x101913))+~P105(f326(f326(f328(x101917),x101912),x101914))
% 157.55/157.23 [10258]~P15(x102581,x102582,x102583)+~P105(f326(f66(x102581,x102582,x102583,x102584,x102585),x102587))+P105(f326(f66(x102581,x102582,x102583,x102584,f326(f326(f3(f917(x102581,a905)),x102585),f326(f326(f308(x102581),x102586),f188(f917(x102581,a905))))),f625(x102586,x102587,x102585,x102584,x102583,x102582,x102581)))+~P105(f326(f326(f328(x102581),x102586),x102585))
% 157.55/157.23 [9405]P25(x94051,x94052,x94053,x94054,x94055)+~P25(x94051,x94052,x94053,x94056,x94057)+~E(f326(f309(x94051,x94052,x94053),x94054),x94055)+~P105(f326(f326(f234(f917(x94051,a905)),x94054),x94056))
% 157.55/157.23 [9642]~P25(x96421,x96422,x96423,x96425,x96427)+~P25(x96421,x96422,x96423,x96424,x96426)+P25(x96421,x96422,x96423,f326(f326(f110(f917(x96421,a905)),x96424),x96425),f326(f326(f110(f917(x96422,a905)),x96426),x96427))+~E(f326(f326(f101(f917(x96422,a905)),x96426),x96427),f188(f917(x96422,a905)))
% 157.55/157.23 [9647]~P67(x96471)+~P24(x96475,x96472,x96476,x96477)+~P105(f326(f61(x96475),x96477))+E(f326(f326(f326(f65(x96471,x96472,f80(x96471)),x96473),x96474),f326(f309(x96475,x96472,x96476),x96477)),f326(f326(f326(f65(x96471,x96475,f80(x96471)),f326(f72(x96472,x96471,x96475,x96473),x96476)),x96474),x96477))
% 157.55/157.23 [9773]~E(f326(f326(f308(x97731),x97735),x97736),f326(f326(f308(x97731),x97732),x97733))+~P105(f326(f66(x97731,x97731,x97734,x97732,x97733),x97737))+P105(f326(f326(f328(x97731),x97732),x97733))+P105(f326(f62(x97731,x97734,f326(f326(f308(x97731),x97735),x97736)),x97737))
% 157.55/157.23 [9858]P105(f326(x98581,x98582))+~P105(f326(f326(f328(x98583),x98582),f326(x98584,x98587)))+~P105(f326(f326(f328(x98586),x98587),x98585))+P105(f326(f326(f328(x98583),f463(x98581,x98584,x98585,x98586,x98583)),f326(f326(f40(x98586,f917(x98583,a905)),x98585),x98584)))
% 157.55/157.23 [9875]~P24(x98752,x98751,x98755,x98754)+~P24(x98751,x98753,x98756,f326(f309(x98752,x98751,x98755),x98754))+E(f326(f326(f72(x98751,x98752,x98753,f76(x98752,x98751,x98754,x98755)),f76(x98751,x98753,f326(f309(x98752,x98751,x98755),x98754),x98756)),x98757),f326(f76(x98752,x98753,x98754,f326(f72(x98751,x98753,x98752,x98756),x98755)),x98757))+~P105(f326(f326(f328(x98753),x98757),f326(f309(x98751,x98753,x98756),f326(f309(x98752,x98751,x98755),x98754))))
% 157.55/157.23 [9876]~P24(x98762,x98761,x98765,x98764)+~P24(x98761,x98763,x98766,f326(f309(x98762,x98761,x98765),x98764))+E(f326(f326(f72(x98761,x98762,x98763,f90(x98762,x98761,x98764,x98765)),f90(x98761,x98763,f326(f309(x98762,x98761,x98765),x98764),x98766)),x98767),f326(f90(x98762,x98763,x98764,f326(f72(x98761,x98763,x98762,x98766),x98765)),x98767))+~P105(f326(f326(f328(x98763),x98767),f326(f309(x98761,x98763,x98766),f326(f309(x98762,x98761,x98765),x98764))))
% 157.55/157.23 [10192]~P15(x101927,x101926,x101921)+E(f326(f326(x101921,x101922),f680(x101923,x101924,x101922,x101925,x101921,x101926,x101927)),x101923)+P105(f326(f326(f328(x101927),x101922),x101924))+~P105(f326(f66(x101927,x101926,x101921,x101925,f326(f326(f308(x101927),x101922),x101924)),x101923))
% 157.55/157.23 [10257]~P15(x102571,x102574,x102575)+P105(f326(f66(x102571,x102574,x102575,x102576,x102573),f680(x102577,x102573,x102572,x102576,x102575,x102574,x102571)))+P105(f326(f326(f328(x102571),x102572),x102573))+~P105(f326(f66(x102571,x102574,x102575,x102576,f326(f326(f308(x102571),x102572),x102573)),x102577))
% 157.55/157.23 [9933]E(x99331,f2(a1))+~P105(f326(f49(x99333,x99331),f326(f326(f251(a1,a1),x99335),x99337)))+~P105(f326(f49(x99332,x99331),f326(f326(f251(a1,a1),x99334),x99336)))+P105(f326(f49(f326(f326(f79(a1),x99332),x99333),x99331),f326(f326(f251(a1,a1),f326(f326(f79(a1),f326(f326(f79(a1),x99334),x99335)),f326(f326(f36(a1),f326(f326(f79(a1),x99336),x99337)),x99331))),f45(a1,f326(f326(f79(a1),x99336),x99337),x99331))))
% 157.55/157.23 [9935]~P105(f326(f326(f235(a909),f2(a909)),x99353))+~P105(f326(f48(x99352,x99353),f326(f326(f251(a909,a909),x99355),x99357)))+~P105(f326(f48(x99351,x99353),f326(f326(f251(a909,a909),x99354),x99356)))+P105(f326(f48(f326(f326(f79(a909),x99351),x99352),x99353),f326(f326(f251(a909,a909),f326(f326(f79(a909),f326(f326(f79(a909),x99354),x99355)),f326(f326(f36(a909),f326(f326(f79(a909),x99356),x99357)),x99353))),f45(a909,f326(f326(f79(a909),x99356),x99357),x99353))))
% 157.55/157.23 [10324]~P69(x103242)+~P105(f326(f61(x103243),x103245))+~P105(f326(f61(x103241),x103247))+E(f326(f326(f8(x103241,x103242),f326(f326(f20(x103241,f917(x103243,a905),x103242),f326(f326(f10(f917(x103243,x103242),f917(f917(x103243,a905),x103242),x103241),f8(x103243,x103242)),x103244)),f326(f326(f10(f917(x103243,a905),f917(x103243,a905),x103241),f261(x103243)),f326(f326(f10(f917(x103243,a905),f917(x103243,a905),x103241),f326(f20(x103243,a905,a905),f326(f326(f10(a905,f917(a905,a905),x103243),a324),f326(f326(f9(x103243,f917(x103243,a905),a905),f328(x103243)),x103245)))),x103246)))),x103247),f326(f326(f8(x103243,x103242),f326(f326(f20(x103243,f917(x103241,a905),x103242),f326(f326(f10(f917(x103241,x103242),f917(f917(x103241,a905),x103242),x103243),f8(x103241,x103242)),f326(f9(x103241,x103243,x103242),x103244))),f326(f326(f10(f917(x103241,a905),f917(x103241,a905),x103243),f261(x103241)),f326(f326(f10(f917(x103241,a905),f917(x103241,a905),x103243),f326(f20(x103241,a905,a905),f326(f326(f10(a905,f917(a905,a905),x103241),a324),f326(f326(f9(x103241,f917(x103241,a905),a905),f328(x103241)),x103247)))),f326(f9(x103241,x103243,a905),x103246))))),x103245))
% 157.55/157.23 [10278]~P20(x102788,x102787,x102786,x102785,x102781)+~E(f326(x102782,f852(x102784,x102782,x102783,x102781,x102785,x102786,x102787)),f326(x102784,f852(x102784,x102782,x102783,x102781,x102785,x102786,x102787)))+E(f326(f326(x102781,x102782),x102783),f326(f326(x102781,x102784),x102783))+~P105(f326(f61(x102787),x102783))
% 157.55/157.23 [9809]~P21(x98097,x98096,x98091,x98098,x98092,x98094)+E(f326(f326(x98091,f326(x98092,x98093)),f326(x98094,x98095)),f326(x98094,x98095))+~P105(f326(f61(x98096),x98095))+~P105(f326(f326(f328(x98096),x98093),x98095))
% 157.55/157.23 [9814]~P11(x98146,x98141,x98142,x98148,x98143,x98144)+~P7(x98146,x98147,x98148)+P10(x98141,x98142,x98143,f326(x98144,x98145))+~P105(f326(f326(f328(x98146),x98145),x98147))
% 157.55/157.23 [10296]~P20(x102968,x102965,x102967,x102966,x102961)+E(f326(f326(x102961,x102962),x102963),f326(f326(x102961,x102964),x102963))+~P105(f326(f61(x102965),x102963))+P105(f326(f326(f328(x102965),f852(x102962,x102964,x102963,x102961,x102966,x102967,x102965)),x102963))
% 157.55/157.23 [10376]~P105(f326(f326(x103761,x103766),x103765))+P105(f326(f326(x103761,f835(x103761,x103764,x103765,x103766,x103763,x103762,x103767,x103768)),f844(x103761,x103764,x103765,x103766,x103763,x103762,x103767,x103768)))+P105(f326(f326(x103761,x103762),x103763))+~P105(f326(f326(f328(f916(f916(x103768,x103767),f916(x103768,x103767))),f326(f326(f251(f916(x103768,x103767),f916(x103768,x103767)),f326(f326(f251(x103768,x103767),x103762),x103763)),f326(f326(f251(x103768,x103767),x103766),x103765))),f306(f916(x103768,x103767),x103764)))
% 157.55/157.23 [10377]~P105(f326(f326(x103771,x103776),x103775))+P105(f326(f326(x103771,f836(x103771,x103774,x103773,x103772,x103775,x103776,x103777,x103778)),f837(x103771,x103774,x103773,x103772,x103775,x103776,x103777,x103778)))+P105(f326(f326(x103771,x103772),x103773))+~P105(f326(f326(f328(f916(f916(x103778,x103777),f916(x103778,x103777))),f326(f326(f251(f916(x103778,x103777),f916(x103778,x103777)),f326(f326(f251(x103778,x103777),x103776),x103775)),f326(f326(f251(x103778,x103777),x103772),x103773))),f306(f916(x103778,x103777),x103774)))
% 157.55/157.23 [10387]~P105(f326(f326(x103871,f838(x103871,x103876,x103875,x103874,x103873,x103872,x103877,x103878)),f843(x103871,x103876,x103875,x103874,x103873,x103872,x103877,x103878)))+P105(f326(f326(x103871,x103872),x103873))+~P105(f326(f326(x103871,x103874),x103875))+~P105(f326(f326(f328(f916(f916(x103878,x103877),f916(x103878,x103877))),f326(f326(f251(f916(x103878,x103877),f916(x103878,x103877)),f326(f326(f251(x103878,x103877),x103872),x103873)),f326(f326(f251(x103878,x103877),x103874),x103875))),f306(f916(x103878,x103877),x103876)))
% 157.55/157.23 [10388]~P105(f326(f326(x103881,f839(x103881,x103886,x103883,x103882,x103885,x103884,x103887,x103888)),f840(x103881,x103886,x103883,x103882,x103885,x103884,x103887,x103888)))+P105(f326(f326(x103881,x103882),x103883))+~P105(f326(f326(x103881,x103884),x103885))+~P105(f326(f326(f328(f916(f916(x103888,x103887),f916(x103888,x103887))),f326(f326(f251(f916(x103888,x103887),f916(x103888,x103887)),f326(f326(f251(x103888,x103887),x103884),x103885)),f326(f326(f251(x103888,x103887),x103882),x103883))),f306(f916(x103888,x103887),x103886)))
% 157.55/157.23 [10401]~P105(f326(f326(x104011,x104016),x104017))+P105(f326(f326(x104011,x104012),x104013))+P105(f326(f326(f328(f916(f916(x104014,x104015),f916(x104014,x104015))),f326(f326(f251(f916(x104014,x104015),f916(x104014,x104015)),f326(f326(f251(x104014,x104015),x104016),x104017)),f326(f326(f251(x104014,x104015),f836(x104011,x104018,x104013,x104012,x104017,x104016,x104015,x104014)),f837(x104011,x104018,x104013,x104012,x104017,x104016,x104015,x104014)))),f306(f916(x104014,x104015),x104018)))+~P105(f326(f326(f328(f916(f916(x104014,x104015),f916(x104014,x104015))),f326(f326(f251(f916(x104014,x104015),f916(x104014,x104015)),f326(f326(f251(x104014,x104015),x104016),x104017)),f326(f326(f251(x104014,x104015),x104012),x104013))),f306(f916(x104014,x104015),x104018)))
% 157.55/157.23 [10403]~P105(f326(f326(x104031,x104038),x104037))+P105(f326(f326(x104031,x104032),x104033))+P105(f326(f326(f328(f916(f916(x104034,x104035),f916(x104034,x104035))),f326(f326(f251(f916(x104034,x104035),f916(x104034,x104035)),f326(f326(f251(x104034,x104035),f835(x104031,x104036,x104037,x104038,x104033,x104032,x104035,x104034)),f844(x104031,x104036,x104037,x104038,x104033,x104032,x104035,x104034))),f326(f326(f251(x104034,x104035),x104038),x104037))),f306(f916(x104034,x104035),x104036)))+~P105(f326(f326(f328(f916(f916(x104034,x104035),f916(x104034,x104035))),f326(f326(f251(f916(x104034,x104035),f916(x104034,x104035)),f326(f326(f251(x104034,x104035),x104032),x104033)),f326(f326(f251(x104034,x104035),x104038),x104037))),f306(f916(x104034,x104035),x104036)))
% 157.55/157.23 [9430]~P18(x94307,x94301,x94308,x94303)+~P105(f326(f61(x94307),x94305))+~P105(f326(f61(x94307),x94304))+E(f326(f72(x94301,x94301,x94302,f326(x94303,x94304)),f326(f72(x94301,x94301,x94302,f326(x94303,x94305)),x94306)),f326(f72(x94301,x94301,x94302,f326(x94303,x94305)),f326(f72(x94301,x94301,x94302,f326(x94303,x94304)),x94306)))
% 157.55/157.23 [9439]~P33(x94391,x94392,x94393,x94394,x94397)+P33(x94391,x94392,x94393,f326(f326(f159(x94391,x94394),x94395),x94396),f326(f326(f159(x94392,x94397),x94395),x94398))+~P105(f326(f326(x94393,x94396),x94398))+~P105(f326(f326(f235(a909),x94395),f326(f189(f910(x94391)),x94394)))
% 157.55/157.23 [9440]~P33(x94401,x94402,x94403,x94404,x94407)+P33(x94401,x94402,x94403,f326(f326(f159(x94401,x94404),x94405),x94406),f326(f326(f159(x94402,x94407),x94405),x94408))+~P105(f326(f326(x94403,x94406),x94408))+~P105(f326(f326(f235(a909),x94405),f326(f189(f910(x94402)),x94407)))
% 157.55/157.23 [9519]~P24(x95192,x95192,x95195,x95196)+~P20(x95193,x95192,x95197,x95198,x95191)+~P105(f326(f61(x95192),x95196))+E(f326(f326(x95191,f326(f72(x95192,x95193,x95192,x95194),x95195)),x95196),f326(f326(x95191,x95194),f326(f309(x95192,x95192,x95195),x95196)))
% 157.55/157.23 [9774]P25(x97741,x97742,x97743,x97744,x97745)+~P25(x97742,x97746,x97747,x97745,x97748)+~P25(x97741,x97746,f326(f72(x97742,x97746,x97741,x97747),x97743),x97744,x97748)+~P105(f326(f326(f234(f917(x97742,a905)),f326(f309(x97741,x97742,x97743),x97744)),x97745))
% 157.55/157.23 [9811]~P22(x98117,x98112,x98115,x98118,x98116,x98111)+~P105(f326(f61(x98112),x98114))+E(f326(x98111,f326(f326(f308(x98112),x98113),x98114)),f326(f326(x98115,f326(x98116,x98113)),f326(x98111,x98114)))+P105(f326(f326(f328(x98112),x98113),x98114))
% 157.55/157.23 [9823]~P21(x98236,x98235,x98231,x98237,x98238,x98232)+E(f326(f326(x98231,f326(x98232,x98233)),f326(x98232,x98234)),f326(x98232,x98234))+~P105(f326(f61(x98235),x98234))+~P105(f326(f326(f234(f917(x98235,a905)),x98233),x98234))
% 157.55/157.23 [10322]P23(x103228,x103227,f326(f326(f308(f908(x103228)),f91(x103228,x103224,x103225,x103223)),f188(f917(f908(x103228),a905))))+~P23(x103228,x103227,f326(f326(f308(f908(x103228)),f91(x103228,x103226,x103225,x103221)),f188(f917(f908(x103228),a905))))+~P105(f326(f326(x103226,x103222),f864(x103223,x103224,x103221,x103225,x103226,x103227,x103228)))+P105(f326(f326(x103221,x103222),f873(x103223,x103224,x103221,x103225,x103226,x103227,x103228)))
% 157.55/157.23 [9417]P105(f326(f326(f328(f916(f910(x94171),f910(x94171))),f326(f326(f251(f910(x94171),f910(x94171)),x94172),x94173)),f157(x94171,x94174)))+~E(x94173,f326(f326(f134(x94171),x94175),f326(f326(f151(x94171),x94176),x94177)))+~E(x94172,f326(f326(f134(x94171),x94175),f326(f326(f151(x94171),x94178),x94177)))+~P105(f326(f326(f328(f916(x94171,x94171)),f326(f326(f251(x94171,x94171),x94178),x94176)),x94174))
% 157.55/157.23 [9817]~P21(x98176,x98172,x98175,x98177,x98178,x98171)+~P105(f326(f61(x98172),x98174))+~P105(f326(f61(x98172),x98173))+E(f326(x98171,f326(f326(f110(f917(x98172,a905)),x98173),x98174)),f326(f326(x98175,f326(x98171,x98173)),f326(x98171,x98174)))
% 157.55/157.23 [10366]~P24(x103664,x103662,x103665,x103668)+E(f326(f326(f39(x103661,f917(x103662,a905)),x103663),f326(f326(f10(f917(x103664,a905),f917(x103662,a905),x103661),f309(x103664,x103662,x103665)),x103666)),f326(f309(x103664,x103662,x103665),f326(f326(f39(x103661,f917(x103664,a905)),x103663),x103666)))+~P105(f326(f326(f328(x103661),x103667),x103663))+P105(f326(f326(f328(x103661),f524(x103667,x103666,x103663,x103661,x103668,x103665,x103662,x103664)),x103663))
% 157.55/157.23 [10392]~P24(x103924,x103922,x103925,x103927)+E(f326(f326(f39(x103921,f917(x103922,a905)),x103923),f326(f326(f10(f917(x103924,a905),f917(x103922,a905),x103921),f309(x103924,x103922,x103925)),x103926)),f326(f309(x103924,x103922,x103925),f326(f326(f39(x103921,f917(x103924,a905)),x103923),x103926)))+~P105(f326(f326(f328(x103921),x103928),x103923))+~P105(f326(f326(f234(f917(x103924,a905)),f326(x103926,f524(x103928,x103926,x103923,x103921,x103927,x103925,x103922,x103924))),x103927))
% 157.55/157.23 [10404]~P105(f326(f326(x104041,x104048),x104047))+P105(f326(f326(x104041,x104042),x104043))+~P105(f326(f326(f328(f916(f916(x104044,x104045),f916(x104044,x104045))),f326(f326(f251(f916(x104044,x104045),f916(x104044,x104045)),f326(f326(f251(x104044,x104045),x104042),x104043)),f326(f326(f251(x104044,x104045),x104048),x104047))),f306(f916(x104044,x104045),x104046)))+P105(f326(f326(f328(f916(f916(x104044,x104045),f916(x104044,x104045))),f326(f326(f251(f916(x104044,x104045),f916(x104044,x104045)),f326(f326(f251(x104044,x104045),f838(x104041,x104046,x104047,x104048,x104043,x104042,x104045,x104044)),f843(x104041,x104046,x104047,x104048,x104043,x104042,x104045,x104044))),f326(f326(f251(x104044,x104045),f835(x104041,x104046,x104047,x104048,x104043,x104042,x104045,x104044)),f844(x104041,x104046,x104047,x104048,x104043,x104042,x104045,x104044)))),x104046))
% 157.55/157.23 [10405]~P105(f326(f326(x104051,x104058),x104057))+P105(f326(f326(x104051,x104052),x104053))+~P105(f326(f326(f328(f916(f916(x104054,x104055),f916(x104054,x104055))),f326(f326(f251(f916(x104054,x104055),f916(x104054,x104055)),f326(f326(f251(x104054,x104055),x104058),x104057)),f326(f326(f251(x104054,x104055),x104052),x104053))),f306(f916(x104054,x104055),x104056)))+P105(f326(f326(f328(f916(f916(x104054,x104055),f916(x104054,x104055))),f326(f326(f251(f916(x104054,x104055),f916(x104054,x104055)),f326(f326(f251(x104054,x104055),f836(x104051,x104056,x104053,x104052,x104057,x104058,x104055,x104054)),f837(x104051,x104056,x104053,x104052,x104057,x104058,x104055,x104054))),f326(f326(f251(x104054,x104055),f839(x104051,x104056,x104053,x104052,x104057,x104058,x104055,x104054)),f840(x104051,x104056,x104053,x104052,x104057,x104058,x104055,x104054)))),x104056))
% 157.55/157.23 [9885]~P22(x98857,x98855,x98851,x98858,x98852,x98854)+~P105(f326(f61(x98855),x98856))+~P105(f326(f326(f328(x98855),x98853),x98856))+E(f326(f326(x98851,f326(x98852,x98853)),f326(x98854,f326(f326(f3(f917(x98855,a905)),x98856),f326(f326(f308(x98855),x98853),f188(f917(x98855,a905)))))),f326(x98854,x98856))
% 157.55/157.23 [9893]~P22(x98936,x98933,x98931,x98937,x98938,x98932)+~P105(f326(f61(x98933),x98935))+~P105(f326(f61(x98933),x98934))+E(f326(f326(x98931,f326(x98932,f326(f326(f110(f917(x98933,a905)),x98934),x98935))),f326(x98932,f326(f326(f101(f917(x98933,a905)),x98934),x98935))),f326(f326(x98931,f326(x98932,x98934)),f326(x98932,x98935)))
% 157.55/157.23 [9975]P41(x99751,x99752,x99753,x99754,x99755,f326(f326(x99753,x99756),x99757))+~P41(x99751,x99752,x99753,x99754,f326(f326(f3(f917(x99751,a905)),x99755),f326(f326(f308(x99751),x99758),f188(f917(x99751,a905)))),x99759)+~E(f326(f326(x99753,x99756),x99757),f326(f326(x99753,x99758),x99759))+~P105(f326(f326(f328(x99751),x99758),x99755))
% 157.55/157.23 [9917]~P11(x99176,x99177,x99178,x99179,x991710,x99171)+E(f326(f326(x99171,x99172),x99173),f326(f326(x99171,x99174),x99175))+~P105(f326(f326(f328(f916(x99177,x99177)),f326(f326(f251(x99177,x99177),x99173),x99175)),x991710))+~P105(f326(f326(f328(f916(x99176,x99176)),f326(f326(f251(x99176,x99176),x99172),x99174)),x99179))
% 157.55/157.23 [9521]~P77(x95212)+E(x95211,f188(f917(x95212,a905)))+~P105(f326(f61(x95212),x95211))+P105(f326(f326(f328(x95212),f12(x95212,x95211)),x95211))+~P105(f326(f326(f328(x95212),f326(f326(f110(x95212),f521(x95211,x95212)),f530(x95211,x95212))),f326(f326(f308(x95212),f521(x95211,x95212)),f326(f326(f308(x95212),f530(x95211,x95212)),f188(f917(x95212,a905))))))
% 157.55/157.23 [9522]~P77(x95222)+E(x95221,f188(f917(x95222,a905)))+~P105(f326(f61(x95222),x95221))+P105(f326(f326(f328(x95222),f13(x95222,x95221)),x95221))+~P105(f326(f326(f328(x95222),f326(f326(f101(x95222),f632(x95221,x95222)),f644(x95221,x95222))),f326(f326(f308(x95222),f632(x95221,x95222)),f326(f326(f308(x95222),f644(x95221,x95222)),f188(f917(x95222,a905))))))
% 157.55/157.23 [9553]~P67(x95532)+E(x95531,f188(f917(x95532,a905)))+~P105(f326(f61(x95532),x95531))+P105(f326(f326(f328(x95532),f326(f63(x95532,f80(x95532)),x95531)),x95531))+~P105(f326(f326(f328(x95532),f326(f326(f80(x95532),f699(x95531,x95532)),f710(x95531,x95532))),f326(f326(f308(x95532),f699(x95531,x95532)),f326(f326(f308(x95532),f710(x95531,x95532)),f188(f917(x95532,a905))))))
% 157.55/157.23 [9558]~P108(x95582)+E(x95581,f188(f917(x95582,a905)))+~P105(f326(f61(x95582),x95581))+P105(f326(f326(f328(x95582),f14(x95582,f232(x95582),x95581)),x95581))+~P105(f326(f326(f328(x95582),f326(f326(f232(x95582),f346(x95581,x95582)),f347(x95581,x95582))),f326(f326(f308(x95582),f346(x95581,x95582)),f326(f326(f308(x95582),f347(x95581,x95582)),f188(f917(x95582,a905))))))
% 157.55/157.23 [9559]~P108(x95592)+E(x95591,f188(f917(x95592,a905)))+~P105(f326(f61(x95592),x95591))+P105(f326(f326(f328(x95592),f15(x95592,f233(x95592),x95591)),x95591))+~P105(f326(f326(f328(x95592),f326(f326(f233(x95592),f406(x95591,x95592)),f410(x95591,x95592))),f326(f326(f308(x95592),f406(x95591,x95592)),f326(f326(f308(x95592),f410(x95591,x95592)),f188(f917(x95592,a905))))))
% 157.55/157.23 [6698]~P88(x66982)+E(x66981,f2(x66982))+~E(f326(f326(f79(x66982),x66983),x66981),f2(x66982))+~P105(f326(f326(f234(x66982),f2(x66982)),x66983))+~P105(f326(f326(f234(x66982),f2(x66982)),x66981))
% 157.55/157.23 [6699]~P88(x66992)+E(x66991,f2(x66992))+~E(f326(f326(f79(x66992),x66991),x66993),f2(x66992))+~P105(f326(f326(f234(x66992),f2(x66992)),x66993))+~P105(f326(f326(f234(x66992),f2(x66992)),x66991))
% 157.55/157.23 [7233]~P108(x72332)+~P12(x72332,x72331)+E(x72331,f113(x72332))+~P105(f326(f326(f328(x72332),x72333),f326(f172(x72332),f702(x72331,x72332))))+P105(f326(f326(f234(x72332),f721(x72331,x72332)),x72333))
% 157.55/157.23 [7401]~P108(x74011)+E(f16(x74011,x74012),x74013)+~P105(f326(f61(x74011),x74012))+~P105(f326(f326(f234(x74011),x74013),f351(x74013,x74012,x74011)))+~P105(f326(f326(f328(x74011),x74013),x74012))
% 157.55/157.23 [7434]~P108(x74341)+~P12(x74341,x74342)+~P12(x74341,x74343)+P12(x74341,f326(f326(f134(x74341),x74342),x74343))+P105(f326(f326(f328(x74341),f708(x74343,x74342,x74341)),f326(f172(x74341),x74342)))
% 157.55/157.23 [7435]~P108(x74351)+~P12(x74351,x74352)+~P12(x74351,x74353)+P12(x74351,f326(f326(f134(x74351),x74352),x74353))+P105(f326(f326(f328(x74351),f709(x74353,x74352,x74351)),f326(f172(x74351),x74353)))
% 157.55/157.23 [7500]~P108(x75001)+E(f16(x75001,x75002),x75003)+~P105(f326(f61(x75001),x75002))+P105(f326(f326(f328(x75001),f351(x75003,x75002,x75001)),x75002))+~P105(f326(f326(f328(x75001),x75003),x75002))
% 157.55/157.23 [7501]~P108(x75011)+E(f17(x75011,x75012),x75013)+~P105(f326(f61(x75011),x75012))+P105(f326(f326(f328(x75011),f600(x75013,x75012,x75011)),x75012))+~P105(f326(f326(f328(x75011),x75013),x75012))
% 157.55/157.23 [8062]~P108(x80621)+E(f17(x80621,x80622),x80623)+~P105(f326(f61(x80621),x80622))+~P105(f326(f326(f328(x80621),x80623),x80622))+~P105(f326(f326(f234(x80621),f600(x80623,x80622,x80621)),x80623))
% 157.55/157.23 [8375]~P108(x83751)+~P12(x83751,x83752)+~P12(x83751,x83753)+P12(x83751,f326(f326(f134(x83751),x83752),x83753))+~P105(f326(f326(f234(x83751),f708(x83753,x83752,x83751)),f709(x83753,x83752,x83751)))
% 157.55/157.23 [9163]~P77(x91632)+E(x91631,f188(f917(x91632,a905)))+~E(f326(f326(f110(x91632),f326(x91633,f487(x91631,x91633,x91632))),f326(x91633,f494(x91631,x91633,x91632))),f326(x91633,f326(f326(f110(x91632),f487(x91631,x91633,x91632)),f494(x91631,x91633,x91632))))+E(f12(x91632,f326(f309(x91632,x91632,x91633),x91631)),f326(x91633,f12(x91632,x91631)))+~P105(f326(f61(x91632),x91631))
% 157.55/157.23 [9164]~P77(x91642)+E(x91641,f188(f917(x91642,a905)))+~E(f326(f326(f101(x91642),f326(x91643,f488(x91641,x91643,x91642))),f326(x91643,f493(x91641,x91643,x91642))),f326(x91643,f326(f326(f101(x91642),f488(x91641,x91643,x91642)),f493(x91641,x91643,x91642))))+E(f13(x91642,f326(f309(x91642,x91642,x91643),x91641)),f326(x91643,f13(x91642,x91641)))+~P105(f326(f61(x91642),x91641))
% 157.55/157.23 [9165]~P108(x91652)+E(x91651,f188(f917(x91652,a905)))+~E(f326(f326(f232(x91652),f326(x91653,f489(x91651,x91653,x91652))),f326(x91653,f492(x91651,x91653,x91652))),f326(x91653,f326(f326(f232(x91652),f489(x91651,x91653,x91652)),f492(x91651,x91653,x91652))))+E(f16(x91652,f326(f309(x91652,x91652,x91653),x91651)),f326(x91653,f16(x91652,x91651)))+~P105(f326(f61(x91652),x91651))
% 157.55/157.23 [9166]~P108(x91662)+E(x91661,f188(f917(x91662,a905)))+~E(f326(f326(f233(x91662),f326(x91663,f490(x91661,x91663,x91662))),f326(x91663,f491(x91661,x91663,x91662))),f326(x91663,f326(f326(f233(x91662),f490(x91661,x91663,x91662)),f491(x91661,x91663,x91662))))+E(f17(x91662,f326(f309(x91662,x91662,x91663),x91661)),f326(x91663,f17(x91662,x91661)))+~P105(f326(f61(x91662),x91661))
% 157.55/157.23 [9234]~P108(x92342)+E(x92341,f188(f917(x92342,a905)))+~E(f326(f326(f232(x92342),f326(x92343,f485(x92341,x92343,x92342))),f326(x92343,f486(x92341,x92343,x92342))),f326(x92343,f326(f326(f232(x92342),f485(x92341,x92343,x92342)),f486(x92341,x92343,x92342))))+E(f14(x92342,f232(x92342),f326(f309(x92342,x92342,x92343),x92341)),f326(x92343,f14(x92342,f232(x92342),x92341)))+~P105(f326(f61(x92342),x92341))
% 157.55/157.23 [9235]~P108(x92352)+E(x92351,f188(f917(x92352,a905)))+~E(f326(f326(f233(x92352),f326(x92353,f481(x92351,x92353,x92352))),f326(x92353,f483(x92351,x92353,x92352))),f326(x92353,f326(f326(f233(x92352),f481(x92351,x92353,x92352)),f483(x92351,x92353,x92352))))+E(f15(x92352,f233(x92352),f326(f309(x92352,x92352,x92353),x92351)),f326(x92353,f15(x92352,f233(x92352),x92351)))+~P105(f326(f61(x92352),x92351))
% 157.55/157.23 [6715]~P67(x67152)+E(x67151,f188(f917(x67152,a905)))+~P105(f326(f61(x67152),x67151))+E(f326(f63(x67152,f80(x67152)),f326(f326(f308(x67152),x67153),x67151)),f326(f326(f80(x67152),x67153),f326(f63(x67152,f80(x67152)),x67151)))+P105(f326(f326(f328(x67152),x67153),x67151))
% 157.55/157.23 [7239]~P77(x72392)+E(f326(f326(f110(x72392),f12(x72392,x72391)),f12(x72392,x72393)),f12(x72392,x72393))+E(x72391,f188(f917(x72392,a905)))+~P105(f326(f61(x72392),x72393))+~P105(f326(f326(f234(f917(x72392,a905)),x72391),x72393))
% 157.55/157.23 [7240]~P77(x72402)+E(f326(f326(f101(x72402),f13(x72402,x72401)),f13(x72402,x72403)),f13(x72402,x72403))+E(x72401,f188(f917(x72402,a905)))+~P105(f326(f61(x72402),x72403))+~P105(f326(f326(f234(f917(x72402,a905)),x72401),x72403))
% 157.55/157.23 [7241]~P108(x72412)+E(f326(f326(f232(x72412),f16(x72412,x72411)),f16(x72412,x72413)),f16(x72412,x72413))+E(x72411,f188(f917(x72412,a905)))+~P105(f326(f61(x72412),x72413))+~P105(f326(f326(f234(f917(x72412,a905)),x72411),x72413))
% 157.55/157.23 [7242]~P108(x72422)+E(f326(f326(f233(x72422),f17(x72422,x72421)),f17(x72422,x72423)),f17(x72422,x72423))+E(x72421,f188(f917(x72422,a905)))+~P105(f326(f61(x72422),x72423))+~P105(f326(f326(f234(f917(x72422,a905)),x72421),x72423))
% 157.55/157.23 [7548]~P108(x75482)+E(x75481,f188(f917(x75482,a905)))+~P105(f326(f61(x75482),x75483))+P105(f326(f326(f234(x75482),f16(x75482,x75483)),f16(x75482,x75481)))+~P105(f326(f326(f234(f917(x75482,a905)),x75481),x75483))
% 157.55/157.23 [7549]~P108(x75492)+E(x75491,f188(f917(x75492,a905)))+~P105(f326(f61(x75492),x75493))+P105(f326(f326(f234(x75492),f17(x75492,x75491)),f17(x75492,x75493)))+~P105(f326(f326(f234(f917(x75492,a905)),x75491),x75493))
% 157.55/157.23 [7602]~P77(x76021)+E(f12(x76021,x76022),x76023)+~P105(f326(f61(x76021),x76022))+~E(f326(f326(f3(f917(x76021,a905)),x76022),f326(f326(f308(x76021),x76023),f188(f917(x76021,a905)))),f188(f917(x76021,a905)))+~P105(f326(f326(f328(x76021),x76023),x76022))
% 157.55/157.23 [7603]~P77(x76031)+E(f13(x76031,x76032),x76033)+~P105(f326(f61(x76031),x76032))+~E(f326(f326(f3(f917(x76031,a905)),x76032),f326(f326(f308(x76031),x76033),f188(f917(x76031,a905)))),f188(f917(x76031,a905)))+~P105(f326(f326(f328(x76031),x76033),x76032))
% 157.55/157.23 [7604]~P108(x76041)+E(f16(x76041,x76042),x76043)+~P105(f326(f61(x76041),x76042))+~E(f326(f326(f3(f917(x76041,a905)),x76042),f326(f326(f308(x76041),x76043),f188(f917(x76041,a905)))),f188(f917(x76041,a905)))+~P105(f326(f326(f328(x76041),x76043),x76042))
% 157.55/157.23 [7605]~P108(x76051)+E(f17(x76051,x76052),x76053)+~P105(f326(f61(x76051),x76052))+~E(f326(f326(f3(f917(x76051,a905)),x76052),f326(f326(f308(x76051),x76053),f188(f917(x76051,a905)))),f188(f917(x76051,a905)))+~P105(f326(f326(f328(x76051),x76053),x76052))
% 157.55/157.23 [7698]~P108(x76981)+E(f14(x76981,f232(x76981),x76982),x76983)+~P105(f326(f61(x76981),x76982))+~E(f326(f326(f3(f917(x76981,a905)),x76982),f326(f326(f308(x76981),x76983),f188(f917(x76981,a905)))),f188(f917(x76981,a905)))+~P105(f326(f326(f328(x76981),x76983),x76982))
% 157.55/157.23 [7699]~P108(x76991)+E(f15(x76991,f233(x76991),x76992),x76993)+~P105(f326(f61(x76991),x76992))+~E(f326(f326(f3(f917(x76991,a905)),x76992),f326(f326(f308(x76991),x76993),f188(f917(x76991,a905)))),f188(f917(x76991,a905)))+~P105(f326(f326(f328(x76991),x76993),x76992))
% 157.55/157.23 [7734]~P101(x77342)+E(x77341,f188(f917(x77342,a905)))+~P105(f326(f61(x77342),x77341))+~P105(f326(f326(f234(x77342),x77343),f688(x77343,x77341,x77342)))+P105(f326(f326(f234(x77342),x77343),f326(f63(x77342,f101(x77342)),x77341)))
% 157.55/157.23 [7735]~P108(x77352)+E(x77351,f188(f917(x77352,a905)))+~P105(f326(f61(x77352),x77351))+~P105(f326(f326(f234(x77352),x77353),f899(x77353,x77351,x77352)))+P105(f326(f326(f234(x77352),x77353),f326(f63(x77352,f232(x77352)),x77351)))
% 157.55/157.23 [7736]~P108(x77362)+E(x77361,f188(f917(x77362,a905)))+~P105(f326(f61(x77362),x77361))+~P105(f326(f326(f235(x77362),x77363),f900(x77363,x77361,x77362)))+P105(f326(f326(f235(x77362),x77363),f326(f63(x77362,f232(x77362)),x77361)))
% 157.55/157.23 [7821]~P101(x78212)+E(x78211,f188(f917(x78212,a905)))+~P105(f326(f61(x78212),x78211))+P105(f326(f326(f328(x78212),f688(x78213,x78211,x78212)),x78211))+P105(f326(f326(f234(x78212),x78213),f326(f63(x78212,f101(x78212)),x78211)))
% 157.55/157.23 [7822]~P108(x78222)+E(x78221,f188(f917(x78222,a905)))+~P105(f326(f61(x78222),x78221))+P105(f326(f326(f328(x78222),f899(x78223,x78221,x78222)),x78221))+P105(f326(f326(f234(x78222),x78223),f326(f63(x78222,f232(x78222)),x78221)))
% 157.55/157.23 [7823]~P108(x78232)+E(x78231,f188(f917(x78232,a905)))+~P105(f326(f61(x78232),x78231))+P105(f326(f326(f328(x78232),f900(x78233,x78231,x78232)),x78231))+P105(f326(f326(f235(x78232),x78233),f326(f63(x78232,f232(x78232)),x78231)))
% 157.55/157.23 [7943]~P108(x79432)+E(x79431,f188(f917(x79432,a905)))+E(f326(f326(f232(x79432),f14(x79432,f232(x79432),x79431)),f14(x79432,f232(x79432),x79433)),f14(x79432,f232(x79432),x79433))+~P105(f326(f61(x79432),x79433))+~P105(f326(f326(f234(f917(x79432,a905)),x79431),x79433))
% 157.55/157.23 [7944]~P108(x79442)+E(x79441,f188(f917(x79442,a905)))+E(f326(f326(f233(x79442),f15(x79442,f233(x79442),x79441)),f15(x79442,f233(x79442),x79443)),f15(x79442,f233(x79442),x79443))+~P105(f326(f61(x79442),x79443))+~P105(f326(f326(f234(f917(x79442,a905)),x79441),x79443))
% 157.55/157.23 [8139]~E(f860(x81391,x81393,x81392),f861(x81391,x81393,x81392))+~E(f326(f35(x81392),f862(x81391,x81393,x81392)),x81391)+E(f326(f326(f80(a909),x81391),f326(f35(f917(x81392,a905)),x81393)),f326(f35(x81392),f37(f917(x81392,a905),x81393)))+~P105(f326(f61(x81392),f37(f917(x81392,a905),x81393)))+~P105(f326(f61(f917(x81392,a905)),x81393))
% 157.55/157.23 [8315]~P108(x83152)+E(x83151,f188(f917(x83152,a905)))+~P105(f326(f61(x83152),x83153))+P105(f326(f326(f234(x83152),f326(f63(x83152,f232(x83152)),x83153)),f326(f63(x83152,f232(x83152)),x83151)))+~P105(f326(f326(f234(f917(x83152,a905)),x83151),x83153))
% 157.55/157.23 [8612]~E(f860(x86121,x86123,x86122),f861(x86121,x86123,x86122))+E(f326(f326(f80(a909),x86121),f326(f35(f917(x86122,a905)),x86123)),f326(f35(x86122),f37(f917(x86122,a905),x86123)))+P105(f326(f326(f328(f917(x86122,a905)),f862(x86121,x86123,x86122)),x86123))+~P105(f326(f61(x86122),f37(f917(x86122,a905),x86123)))+~P105(f326(f61(f917(x86122,a905)),x86123))
% 157.55/157.23 [8638]~E(f326(f35(x86382),f862(x86381,x86383,x86382)),x86381)+E(f326(f326(f80(a909),x86381),f326(f35(f917(x86382,a905)),x86383)),f326(f35(x86382),f37(f917(x86382,a905),x86383)))+P105(f326(f326(f328(f917(x86382,a905)),f861(x86381,x86383,x86382)),x86383))+~P105(f326(f61(x86382),f37(f917(x86382,a905),x86383)))+~P105(f326(f61(f917(x86382,a905)),x86383))
% 157.55/157.23 [8639]~E(f326(f35(x86392),f862(x86391,x86393,x86392)),x86391)+E(f326(f326(f80(a909),x86391),f326(f35(f917(x86392,a905)),x86393)),f326(f35(x86392),f37(f917(x86392,a905),x86393)))+P105(f326(f326(f328(f917(x86392,a905)),f860(x86391,x86393,x86392)),x86393))+~P105(f326(f61(x86392),f37(f917(x86392,a905),x86393)))+~P105(f326(f61(f917(x86392,a905)),x86393))
% 157.55/157.23 [8663]~E(f326(f35(x86632),f862(x86631,x86633,x86632)),x86631)+~E(f326(f326(f101(f917(x86632,a905)),f861(x86631,x86633,x86632)),f860(x86631,x86633,x86632)),f188(f917(x86632,a905)))+E(f326(f326(f80(a909),x86631),f326(f35(f917(x86632,a905)),x86633)),f326(f35(x86632),f37(f917(x86632,a905),x86633)))+~P105(f326(f61(f917(x86632,a905)),x86633))+~P105(f326(f61(x86632),f37(f917(x86632,a905),x86633)))
% 157.55/157.23 [8927]E(f326(f326(f80(a909),x89271),f326(f35(f917(x89272,a905)),x89273)),f326(f35(x89272),f37(f917(x89272,a905),x89273)))+P105(f326(f326(f328(f917(x89272,a905)),f862(x89271,x89273,x89272)),x89273))+P105(f326(f326(f328(f917(x89272,a905)),f861(x89271,x89273,x89272)),x89273))+~P105(f326(f61(f917(x89272,a905)),x89273))+~P105(f326(f61(x89272),f37(f917(x89272,a905),x89273)))
% 157.55/157.23 [8928]E(f326(f326(f80(a909),x89281),f326(f35(f917(x89282,a905)),x89283)),f326(f35(x89282),f37(f917(x89282,a905),x89283)))+P105(f326(f326(f328(f917(x89282,a905)),f862(x89281,x89283,x89282)),x89283))+P105(f326(f326(f328(f917(x89282,a905)),f860(x89281,x89283,x89282)),x89283))+~P105(f326(f61(f917(x89282,a905)),x89283))+~P105(f326(f61(x89282),f37(f917(x89282,a905),x89283)))
% 157.55/157.23 [8954]~E(f326(f326(f101(f917(x89542,a905)),f861(x89541,x89543,x89542)),f860(x89541,x89543,x89542)),f188(f917(x89542,a905)))+E(f326(f326(f80(a909),x89541),f326(f35(f917(x89542,a905)),x89543)),f326(f35(x89542),f37(f917(x89542,a905),x89543)))+~P105(f326(f61(f917(x89542,a905)),x89543))+P105(f326(f326(f328(f917(x89542,a905)),f862(x89541,x89543,x89542)),x89543))+~P105(f326(f61(x89542),f37(f917(x89542,a905),x89543)))
% 157.55/157.23 [9209]~P96(x92092)+E(x92091,f188(f917(x92092,a905)))+~E(f326(f326(f80(x92092),f326(x92093,f496(x92091,x92093,x92092))),f326(x92093,f497(x92091,x92093,x92092))),f326(x92093,f326(f326(f80(x92092),f496(x92091,x92093,x92092)),f497(x92091,x92093,x92092))))+~P105(f326(f61(x92092),x92091))+E(f326(f63(x92092,f80(x92092)),f326(f309(x92092,x92092,x92093),x92091)),f326(x92093,f326(f63(x92092,f80(x92092)),x92091)))
% 157.55/157.23 [10135]P105(f326(f326(x101351,x101352),x101353))+P105(f326(f326(f235(a1),f395(x101351,x101353,x101352)),f396(x101351,x101353,x101352)))+P105(f326(f326(f234(a1),f396(x101351,x101353,x101352)),f2(a1)))+P105(f326(f326(x101351,f395(x101351,x101353,x101352)),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f396(x101351,x101353,x101352))))+~P105(f326(f314(f916(a1,a1),a58),f326(f326(f251(a1,a1),x101352),x101353)))
% 157.55/157.23 [10141]P105(f326(f326(x101411,x101412),x101413))+P105(f326(f326(f234(a1),f394(x101411,x101413,x101412)),f2(a1)))+P105(f326(f326(x101411,f392(x101411,x101413,x101412)),f326(f326(f80(a1),f326(f103(a1),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f394(x101411,x101413,x101412))))+P105(f326(f326(f234(a1),f2(a1)),f326(f326(f79(a1),f392(x101411,x101413,x101412)),f394(x101411,x101413,x101412))))+~P105(f326(f314(f916(a1,a1),a52),f326(f326(f251(a1,a1),x101412),x101413)))
% 157.55/157.23 [8111]~P118(x81111)+~P105(f326(f326(f234(x81111),x81112),f77(x81111)))+~P105(f326(f326(f234(x81111),f2(x81111)),x81112))+~P105(f326(f326(f234(x81111),f2(x81111)),x81113))+P105(f326(f326(f234(x81111),f326(f326(f80(x81111),x81112),x81113)),x81113))
% 157.55/157.23 [8112]~P118(x81121)+~P105(f326(f326(f234(x81121),x81123),f77(x81121)))+~P105(f326(f326(f234(x81121),f2(x81121)),x81123))+~P105(f326(f326(f234(x81121),f2(x81121)),x81122))+P105(f326(f326(f234(x81121),f326(f326(f80(x81121),x81122),x81123)),x81122))
% 157.55/157.23 [8460]~P108(x84602)+E(x84601,f188(f917(x84602,a905)))+~P105(f326(f61(x84602),x84601))+P105(f326(f326(f234(x84602),f901(x84603,x84601,x84602)),x84603))+~P105(f326(f326(f234(x84602),f326(f63(x84602,f232(x84602)),x84601)),x84603))
% 157.55/157.23 [8461]~P108(x84612)+E(x84611,f188(f917(x84612,a905)))+~P105(f326(f61(x84612),x84611))+P105(f326(f326(f328(x84612),f901(x84613,x84611,x84612)),x84611))+~P105(f326(f326(f234(x84612),f326(f63(x84612,f232(x84612)),x84611)),x84613))
% 157.55/157.23 [8462]~P108(x84622)+E(x84621,f188(f917(x84622,a905)))+~P105(f326(f61(x84622),x84621))+P105(f326(f326(f328(x84622),f902(x84623,x84621,x84622)),x84621))+~P105(f326(f326(f235(x84622),f326(f63(x84622,f232(x84622)),x84621)),x84623))
% 157.55/157.23 [8463]~P108(x84632)+E(x84631,f188(f917(x84632,a905)))+~P105(f326(f61(x84632),x84631))+P105(f326(f326(f235(x84632),f902(x84633,x84631,x84632)),x84633))+~P105(f326(f326(f235(x84632),f326(f63(x84632,f232(x84632)),x84631)),x84633))
% 157.55/157.23 [8548]~P105(f326(x85481,x85483))+P105(f326(x85481,f454(x85481,x85482)))+P105(f326(x85481,f449(x85481,x85482)))+~P105(f326(f326(f235(a1),f2(a1)),x85482))+P105(f326(x85481,f326(f326(f3(a1),f449(x85481,x85482)),f326(f326(f80(a1),f455(x85481,x85482)),x85482))))
% 157.55/157.23 [8764]~P105(f326(x87641,x87643))+P105(f326(x87641,f449(x87641,x87642)))+~P105(f326(f326(f235(a1),f2(a1)),x87642))+P105(f326(f326(f328(a1),f454(x87641,x87642)),f302(a1,f77(a1),x87642)))+P105(f326(x87641,f326(f326(f3(a1),f449(x87641,x87642)),f326(f326(f80(a1),f455(x87641,x87642)),x87642))))
% 157.55/157.23 [8976]~P105(f326(x89761,x89763))+~P105(f326(x89761,f449(x89761,x89762)))+P105(f326(x89761,f454(x89761,x89762)))+~P105(f326(f326(f235(a1),f2(a1)),x89762))+~P105(f326(x89761,f326(f326(f3(a1),f449(x89761,x89762)),f326(f326(f80(a1),f455(x89761,x89762)),x89762))))
% 157.55/157.23 [9100]~P105(f326(x91001,x91003))+~P105(f326(x91001,f449(x91001,x91002)))+~P105(f326(f326(f235(a1),f2(a1)),x91002))+P105(f326(f326(f328(a1),f454(x91001,x91002)),f302(a1,f77(a1),x91002)))+~P105(f326(x91001,f326(f326(f3(a1),f449(x91001,x91002)),f326(f326(f80(a1),f455(x91001,x91002)),x91002))))
% 157.55/157.23 [8882]~P77(x88821)+~P105(f326(f61(x88821),x88822))+E(f326(f326(f3(f917(x88821,a905)),x88822),f326(f326(f308(x88821),x88823),f188(f917(x88821,a905)))),f188(f917(x88821,a905)))+~P105(f326(f326(f328(x88821),x88823),x88822))+E(f326(f326(f110(x88821),x88823),f12(x88821,f326(f326(f3(f917(x88821,a905)),x88822),f326(f326(f308(x88821),x88823),f188(f917(x88821,a905)))))),f12(x88821,x88822))
% 157.55/157.23 [8883]~P77(x88831)+~P105(f326(f61(x88831),x88832))+E(f326(f326(f3(f917(x88831,a905)),x88832),f326(f326(f308(x88831),x88833),f188(f917(x88831,a905)))),f188(f917(x88831,a905)))+~P105(f326(f326(f328(x88831),x88833),x88832))+E(f326(f326(f101(x88831),x88833),f13(x88831,f326(f326(f3(f917(x88831,a905)),x88832),f326(f326(f308(x88831),x88833),f188(f917(x88831,a905)))))),f13(x88831,x88832))
% 157.55/157.23 [8884]~P108(x88841)+~P105(f326(f61(x88841),x88842))+E(f326(f326(f3(f917(x88841,a905)),x88842),f326(f326(f308(x88841),x88843),f188(f917(x88841,a905)))),f188(f917(x88841,a905)))+~P105(f326(f326(f328(x88841),x88843),x88842))+E(f326(f326(f232(x88841),x88843),f16(x88841,f326(f326(f3(f917(x88841,a905)),x88842),f326(f326(f308(x88841),x88843),f188(f917(x88841,a905)))))),f16(x88841,x88842))
% 157.55/157.23 [8885]~P108(x88851)+~P105(f326(f61(x88851),x88852))+E(f326(f326(f3(f917(x88851,a905)),x88852),f326(f326(f308(x88851),x88853),f188(f917(x88851,a905)))),f188(f917(x88851,a905)))+~P105(f326(f326(f328(x88851),x88853),x88852))+E(f326(f326(f233(x88851),x88853),f17(x88851,f326(f326(f3(f917(x88851,a905)),x88852),f326(f326(f308(x88851),x88853),f188(f917(x88851,a905)))))),f17(x88851,x88852))
% 157.55/157.23 [8947]~P108(x89471)+~P105(f326(f61(x89471),x89472))+E(f326(f326(f3(f917(x89471,a905)),x89472),f326(f326(f308(x89471),x89473),f188(f917(x89471,a905)))),f188(f917(x89471,a905)))+~P105(f326(f326(f328(x89471),x89473),x89472))+E(f326(f326(f232(x89471),x89473),f14(x89471,f232(x89471),f326(f326(f3(f917(x89471,a905)),x89472),f326(f326(f308(x89471),x89473),f188(f917(x89471,a905)))))),f14(x89471,f232(x89471),x89472))
% 157.55/157.23 [8948]~P108(x89481)+~P105(f326(f61(x89481),x89482))+E(f326(f326(f3(f917(x89481,a905)),x89482),f326(f326(f308(x89481),x89483),f188(f917(x89481,a905)))),f188(f917(x89481,a905)))+~P105(f326(f326(f328(x89481),x89483),x89482))+E(f326(f326(f233(x89481),x89483),f15(x89481,f233(x89481),f326(f326(f3(f917(x89481,a905)),x89482),f326(f326(f308(x89481),x89483),f188(f917(x89481,a905)))))),f15(x89481,f233(x89481),x89482))
% 157.55/157.23 [8963]~P77(x89631)+~P105(f326(f61(x89631),x89633))+~P105(f326(f61(x89631),x89632))+E(f326(f326(f101(f917(x89631,a905)),x89632),x89633),f188(f917(x89631,a905)))+E(f326(f326(f110(x89631),f12(x89631,f326(f326(f110(f917(x89631,a905)),x89632),x89633))),f12(x89631,f326(f326(f101(f917(x89631,a905)),x89632),x89633))),f326(f326(f110(x89631),f12(x89631,x89632)),f12(x89631,x89633)))
% 157.55/157.23 [8964]~P77(x89641)+~P105(f326(f61(x89641),x89643))+~P105(f326(f61(x89641),x89642))+E(f326(f326(f101(f917(x89641,a905)),x89642),x89643),f188(f917(x89641,a905)))+E(f326(f326(f101(x89641),f13(x89641,f326(f326(f110(f917(x89641,a905)),x89642),x89643))),f13(x89641,f326(f326(f101(f917(x89641,a905)),x89642),x89643))),f326(f326(f101(x89641),f13(x89641,x89642)),f13(x89641,x89643)))
% 157.55/157.23 [8965]~P108(x89651)+~P105(f326(f61(x89651),x89653))+~P105(f326(f61(x89651),x89652))+E(f326(f326(f101(f917(x89651,a905)),x89652),x89653),f188(f917(x89651,a905)))+E(f326(f326(f232(x89651),f16(x89651,f326(f326(f110(f917(x89651,a905)),x89652),x89653))),f16(x89651,f326(f326(f101(f917(x89651,a905)),x89652),x89653))),f326(f326(f232(x89651),f16(x89651,x89652)),f16(x89651,x89653)))
% 157.55/157.23 [8966]~P108(x89661)+~P105(f326(f61(x89661),x89663))+~P105(f326(f61(x89661),x89662))+E(f326(f326(f101(f917(x89661,a905)),x89662),x89663),f188(f917(x89661,a905)))+E(f326(f326(f233(x89661),f17(x89661,f326(f326(f110(f917(x89661,a905)),x89662),x89663))),f17(x89661,f326(f326(f101(f917(x89661,a905)),x89662),x89663))),f326(f326(f233(x89661),f17(x89661,x89662)),f17(x89661,x89663)))
% 157.55/157.23 [9181]~P108(x91811)+~P105(f326(f61(x91811),x91813))+~P105(f326(f61(x91811),x91812))+E(f326(f326(f101(f917(x91811,a905)),x91812),x91813),f188(f917(x91811,a905)))+E(f326(f326(f232(x91811),f14(x91811,f232(x91811),f326(f326(f110(f917(x91811,a905)),x91812),x91813))),f14(x91811,f232(x91811),f326(f326(f101(f917(x91811,a905)),x91812),x91813))),f326(f326(f232(x91811),f14(x91811,f232(x91811),x91812)),f14(x91811,f232(x91811),x91813)))
% 157.55/157.23 [9182]~P108(x91821)+~P105(f326(f61(x91821),x91823))+~P105(f326(f61(x91821),x91822))+E(f326(f326(f101(f917(x91821,a905)),x91822),x91823),f188(f917(x91821,a905)))+E(f326(f326(f233(x91821),f15(x91821,f233(x91821),f326(f326(f110(f917(x91821,a905)),x91822),x91823))),f15(x91821,f233(x91821),f326(f326(f101(f917(x91821,a905)),x91822),x91823))),f326(f326(f233(x91821),f15(x91821,f233(x91821),x91822)),f15(x91821,f233(x91821),x91823)))
% 157.55/157.23 [9972]~P124(x99723)+E(x99721,x99722)+~P105(f326(f326(f234(x99723),f2(x99723)),x99722))+~P105(f326(f326(f234(x99723),f2(x99723)),x99721))+~E(f326(f326(f243(x99723),x99721),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))),f326(f326(f243(x99723),x99722),f326(f103(a909),f326(f326(f79(a1),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)),f326(f326(f3(a1),f326(f326(f79(a1),a82),a82)),a97)))))
% 157.55/157.23 [6513]E(f867(x65131,x65132,x65133),x65134)+E(f326(x65131,x65134),f2(a909))+~E(f326(f326(f8(x65133,a909),x65131),x65132),f77(a909))+~P105(f326(f61(x65133),x65132))+~P105(f326(f326(f328(x65133),x65134),x65132))
% 157.55/157.23 [6575]E(f869(x65751,x65752,x65753),x65754)+E(f326(x65751,x65754),f2(a909))+~E(f326(f326(f8(x65753,a909),x65751),x65752),f326(a112,f2(a909)))+~P105(f326(f61(x65753),x65752))+~P105(f326(f326(f328(x65753),x65754),x65752))
% 157.55/157.23 [6684]~P108(x66841)+~P4(x66841)+P105(f326(f326(f235(x66841),x66842),f37(x66841,x66843)))+~P105(f326(f326(f235(x66841),x66842),x66844))+~P105(f326(f326(f328(x66841),x66844),x66843))
% 157.55/157.23 [6860]~P108(x68601)+~P4(x68601)+~P105(f326(f326(f235(x68601),x68604),x68603))+P105(f326(f326(f235(x68601),f38(x68601,x68602)),x68603))+~P105(f326(f326(f328(x68601),x68604),x68602))
% 157.55/157.23 [7117]~P124(x71173)+E(x71171,x71172)+~E(f326(f326(f243(x71173),x71171),f326(a112,x71174)),f326(f326(f243(x71173),x71172),f326(a112,x71174)))+~P105(f326(f326(f234(x71173),f2(x71173)),x71172))+~P105(f326(f326(f234(x71173),f2(x71173)),x71171))
% 157.55/157.23 [7328]~E(f875(x73282,x73283,x73281,x73284),x73284)+~E(f326(x73282,x73284),f77(a909))+E(f326(f326(f8(x73281,a909),x73282),x73283),f77(a909))+~P105(f326(f61(x73281),x73283))+~P105(f326(f326(f328(x73281),x73284),x73283))
% 157.55/157.23 [7335]~P112(x73354)+~P132(x73354)+E(f326(x73351,f859(x73351,x73352,x73353,x73354)),f2(x73354))+~E(f326(f326(f11(x73353,x73354),x73351),x73352),f2(x73354))+~P105(f326(f61(x73353),x73352))
% 157.55/157.23 [7424]~E(f872(x74242,x74243,x74241,x74244),x74244)+~E(f326(x74242,x74244),f326(a112,f2(a909)))+E(f326(f326(f8(x74241,a909),x74242),x74243),f326(a112,f2(a909)))+~P105(f326(f61(x74241),x74243))+~P105(f326(f326(f328(x74241),x74244),x74243))
% 157.55/157.23 [8151]~E(f326(x81512,x81514),f77(a909))+~E(f326(x81512,f875(x81512,x81513,x81511,x81514)),f2(a909))+E(f326(f326(f8(x81511,a909),x81512),x81513),f77(a909))+~P105(f326(f61(x81511),x81513))+~P105(f326(f326(f328(x81511),x81514),x81513))
% 157.55/157.23 [8189]~E(f326(x81892,x81894),f326(a112,f2(a909)))+~E(f326(x81892,f872(x81892,x81893,x81891,x81894)),f2(a909))+E(f326(f326(f8(x81891,a909),x81892),x81893),f326(a112,f2(a909)))+~P105(f326(f61(x81891),x81893))+~P105(f326(f326(f328(x81891),x81894),x81893))
% 157.55/157.23 [8731]~P108(x87311)+~P12(x87311,x87314)+P12(x87311,x87312)+~E(x87312,f326(f326(f151(x87311),x87313),x87314))+~P105(f326(f326(f234(x87311),x87313),f723(x87312,x87311,x87314,x87313)))
% 157.55/157.23 [8768]E(x87681,x87682)+E(f326(f326(f3(a1),f434(x87683,x87682,x87684,x87681)),f435(x87683,x87682,x87684,x87681)),x87681)+~E(f326(f326(f79(a1),x87681),x87684),x87682)+~P105(f326(f326(f235(a1),f2(a1)),x87684))+~P105(f326(f326(f328(a1),x87682),x87683))
% 157.55/157.23 [8769]E(x87691,x87692)+E(f326(f326(f79(a1),f437(x87693,x87692,x87694,x87691)),f438(x87693,x87692,x87694,x87691)),x87691)+~E(f326(f326(f3(a1),x87691),x87694),x87692)+~P105(f326(f326(f235(a1),f2(a1)),x87694))+~P105(f326(f326(f328(a1),x87692),x87693))
% 157.55/157.23 [8961]E(f326(x89611,f358(x89612,x89611,x89613,x89614)),x89612)+P105(f326(f326(f234(a909),x89614),f359(x89612,x89611,x89613,x89614)))+~P105(f326(f326(f234(a1),x89612),f326(x89611,x89613)))+~P105(f326(f326(f235(a909),x89614),x89613))+~P105(f326(f326(f234(a1),f326(x89611,x89614)),x89612))
% 157.55/157.23 [8962]~P108(x89621)+~P12(x89621,x89623)+P12(x89621,x89622)+~E(x89622,f326(f326(f151(x89621),x89624),x89623))+P105(f326(f326(f328(x89621),f723(x89622,x89621,x89623,x89624)),f326(f172(x89621),x89623)))
% 157.55/157.23 [8980]~P112(x89804)+~P132(x89804)+~E(f326(f326(f11(x89801,x89804),x89802),x89803),f2(x89804))+~P105(f326(f61(x89801),x89803))+P105(f326(f326(f328(x89801),f859(x89802,x89803,x89801,x89804)),x89803))
% 157.55/157.23 [9018]~E(f326(x90182,x90184),f77(a909))+E(f326(f326(f8(x90181,a909),x90182),x90183),f77(a909))+~P105(f326(f61(x90181),x90183))+~P105(f326(f326(f328(x90181),x90184),x90183))+P105(f326(f326(f328(x90181),f875(x90182,x90183,x90181,x90184)),x90183))
% 157.55/157.23 [9030]E(x90301,x90302)+~E(f326(f326(f79(a1),x90302),x90304),x90301)+~P105(f326(f326(f235(a1),f2(a1)),x90304))+~P105(f326(f326(f328(a1),x90301),x90303))+P105(f326(f326(f328(a1),f434(x90303,x90301,x90304,x90302)),x90303))
% 157.55/157.23 [9031]E(x90311,x90312)+~E(f326(f326(f3(a1),x90312),x90314),x90311)+~P105(f326(f326(f235(a1),f2(a1)),x90314))+~P105(f326(f326(f328(a1),x90311),x90313))+P105(f326(f326(f328(a1),f437(x90313,x90311,x90314,x90312)),x90313))
% 157.55/157.23 [9033]~E(f326(x90332,x90334),f326(a112,f2(a909)))+E(f326(f326(f8(x90331,a909),x90332),x90333),f326(a112,f2(a909)))+~P105(f326(f61(x90331),x90333))+~P105(f326(f326(f328(x90331),x90334),x90333))+P105(f326(f326(f328(x90331),f872(x90332,x90333,x90331,x90334)),x90333))
% 157.55/157.23 [9038]P57(x90382,x90383,x90384,x90381)+E(x90381,f188(f917(x90382,a905)))+~P105(f326(f61(x90382),x90384))+~P105(f326(f61(x90382),x90381))+P105(f326(f326(f328(x90382),f789(x90383,x90381,x90384,x90382)),x90384))
% 157.55/157.23 [9039]P57(x90392,x90393,x90394,x90391)+E(x90391,f188(f917(x90392,a905)))+~P105(f326(f61(x90392),x90394))+~P105(f326(f61(x90392),x90391))+P105(f326(f326(f328(x90392),f522(x90391,x90394,x90393,x90392)),x90394))
% 157.55/157.23 [9040]P57(x90402,x90403,x90404,x90401)+E(x90401,f188(f917(x90402,a905)))+~P105(f326(f61(x90402),x90404))+~P105(f326(f61(x90402),x90401))+P105(f326(f326(f328(x90402),f790(x90401,x90404,x90403,x90402)),x90404))
% 157.55/157.23 [9113]E(x91131,x91132)+~E(f326(f326(f79(a1),x91132),x91134),x91131)+~P105(f326(f326(f235(a1),f2(a1)),x91134))+~P105(f326(f326(f328(a1),x91131),x91133))+P105(f326(f326(f328(a1),f435(x91133,x91131,x91134,x91132)),f302(a1,f77(a1),x91134)))
% 157.55/157.23 [9114]E(x91141,x91142)+~E(f326(f326(f3(a1),x91142),x91144),x91141)+~P105(f326(f326(f235(a1),f2(a1)),x91144))+~P105(f326(f326(f328(a1),x91141),x91143))+P105(f326(f326(f328(a1),f438(x91143,x91141,x91144,x91142)),f302(a1,f77(a1),x91144)))
% 157.55/157.23 [9187]P105(f326(f326(f234(a909),x91871),f358(x91872,x91873,x91874,x91871)))+~P105(f326(f326(f234(a1),x91872),f326(x91873,x91874)))+P105(f326(f326(f234(a909),x91871),f359(x91872,x91873,x91874,x91871)))+~P105(f326(f326(f235(a909),x91871),x91874))+~P105(f326(f326(f234(a1),f326(x91873,x91871)),x91872))
% 157.55/157.23 [9301]E(f326(x93011,f358(x93012,x93011,x93013,x93014)),x93012)+~P105(f326(f326(f234(a1),x93012),f326(x93011,x93013)))+P105(f326(f326(f235(a909),f359(x93012,x93011,x93013,x93014)),x93013))+~P105(f326(f326(f235(a909),x93014),x93013))+~P105(f326(f326(f234(a1),f326(x93011,x93014)),x93012))
% 157.55/157.23 [9427]~P105(f326(f326(f234(a1),x94272),f326(x94273,x94274)))+P105(f326(f326(f234(a909),x94271),f359(x94272,x94273,x94274,x94271)))+P105(f326(f326(f234(a909),f358(x94272,x94273,x94274,x94271)),x94274))+~P105(f326(f326(f235(a909),x94271),x94274))+~P105(f326(f326(f234(a1),f326(x94273,x94271)),x94272))
% 157.55/157.23 [9428]~P105(f326(f326(f234(a1),x94282),f326(x94283,x94284)))+P105(f326(f326(f234(a909),x94281),f358(x94282,x94283,x94284,x94281)))+P105(f326(f326(f235(a909),f359(x94282,x94283,x94284,x94281)),x94284))+~P105(f326(f326(f235(a909),x94281),x94284))+~P105(f326(f326(f234(a1),f326(x94283,x94281)),x94282))
% 157.55/157.23 [9536]~P105(f326(f326(f234(a1),x95361),f326(x95362,x95363)))+P105(f326(f326(f235(a909),f359(x95361,x95362,x95363,x95364)),x95363))+~P105(f326(f326(f235(a909),x95364),x95363))+~P105(f326(f326(f234(a1),f326(x95362,x95364)),x95361))+P105(f326(f326(f234(a909),f358(x95361,x95362,x95363,x95364)),x95363))
% 157.55/157.23 [9620]E(x96201,f188(f917(x96202,a905)))+~P105(f326(f61(x96202),x96204))+~P105(f326(f61(x96202),x96201))+P105(f326(f326(f328(f916(f917(x96202,a905),f917(x96202,a905))),f326(f326(f251(f917(x96202,a905),f917(x96202,a905)),x96204),x96201)),f318(x96202,x96203)))+P105(f326(f326(f328(x96202),f525(x96203,x96201,x96204,x96202)),x96204))
% 157.55/157.23 [9621]E(x96211,f188(f917(x96212,a905)))+~P105(f326(f61(x96212),x96214))+~P105(f326(f61(x96212),x96211))+P105(f326(f326(f328(f916(f917(x96212,a905),f917(x96212,a905))),f326(f326(f251(f917(x96212,a905),f917(x96212,a905)),x96214),x96211)),f318(x96212,x96213)))+P105(f326(f326(f328(x96212),f598(x96213,x96211,x96214,x96212)),x96214))
% 157.55/157.23 [10291]E(f326(x102911,f358(x102912,x102911,x102913,x102914)),x102912)+~P105(f326(f326(f234(a1),x102912),f326(x102911,x102913)))+~P105(f326(f326(f234(a1),f326(f75(a1),f326(f326(f3(a1),f326(x102911,f326(f326(f79(a909),f359(x102912,x102911,x102913,x102914)),f77(a909)))),f326(x102911,f359(x102912,x102911,x102913,x102914))))),f77(a1)))+~P105(f326(f326(f235(a909),x102914),x102913))+~P105(f326(f326(f234(a1),f326(x102911,x102914)),x102912))
% 157.55/157.23 [10292]~P105(f326(f326(f234(a1),x102922),f326(x102923,x102924)))+P105(f326(f326(f234(a909),x102921),f358(x102922,x102923,x102924,x102921)))+~P105(f326(f326(f234(a1),f326(f75(a1),f326(f326(f3(a1),f326(x102923,f326(f326(f79(a909),f359(x102922,x102923,x102924,x102921)),f77(a909)))),f326(x102923,f359(x102922,x102923,x102924,x102921))))),f77(a1)))+~P105(f326(f326(f235(a909),x102921),x102924))+~P105(f326(f326(f234(a1),f326(x102923,x102921)),x102922))
% 157.55/157.23 [10293]~P105(f326(f326(f234(a1),x102931),f326(x102932,x102933)))+~P105(f326(f326(f234(a1),f326(f75(a1),f326(f326(f3(a1),f326(x102932,f326(f326(f79(a909),f359(x102931,x102932,x102933,x102934)),f77(a909)))),f326(x102932,f359(x102931,x102932,x102933,x102934))))),f77(a1)))+~P105(f326(f326(f235(a909),x102934),x102933))+~P105(f326(f326(f234(a1),f326(x102932,x102934)),x102931))+P105(f326(f326(f234(a909),f358(x102931,x102932,x102933,x102934)),x102933))
% 157.55/157.23 [7387]~P64(x73871)+P105(f326(f326(f235(x73871),x73872),f2(x73871)))+~P105(f326(f326(f234(x73871),x73873),f2(x73871)))+P105(f326(f326(f235(x73871),f2(x73871)),x73872))+P105(f326(f326(f234(x73871),x73873),f326(f326(f290(x73871),x73874),x73872)))
% 157.55/157.23 [7388]~P64(x73881)+P105(f326(f326(f235(x73881),x73882),f2(x73881)))+~P105(f326(f326(f235(x73881),x73883),f2(x73881)))+P105(f326(f326(f235(x73881),f2(x73881)),x73882))+P105(f326(f326(f235(x73881),x73883),f326(f326(f290(x73881),x73884),x73882)))
% 157.55/157.23 [7639]~P64(x76391)+P105(f326(f326(f234(x76391),x76392),f2(x76391)))+P105(f326(f326(f235(x76391),x76393),f2(x76391)))+P105(f326(f326(f235(x76391),f2(x76391)),x76393))+~P105(f326(f326(f234(x76391),x76392),f326(f326(f290(x76391),x76394),x76393)))
% 157.55/157.23 [7640]~P64(x76401)+P105(f326(f326(f235(x76401),x76402),f2(x76401)))+P105(f326(f326(f235(x76401),x76403),f2(x76401)))+P105(f326(f326(f235(x76401),f2(x76401)),x76403))+~P105(f326(f326(f235(x76401),x76402),f326(f326(f290(x76401),x76404),x76403)))
% 157.55/157.23 [7755]E(x77551,x77552)+~E(f326(f326(f164(x77553),x77554),x77551),f326(f326(f164(x77553),x77554),x77552))+~P105(f326(f137(x77553),x77554))+~P105(f326(f326(f235(a909),x77552),f326(f189(f910(x77553)),x77554)))+~P105(f326(f326(f235(a909),x77551),f326(f189(f910(x77553)),x77554)))
% 157.55/157.23 [8113]~P64(x81131)+~P105(f326(f326(f234(x81131),x81133),f2(x81131)))+P105(f326(f326(f235(x81131),f2(x81131)),x81132))+~P105(f326(f326(f234(x81131),x81134),f326(f326(f80(x81131),x81133),x81132)))+P105(f326(f326(f234(x81131),x81133),f326(f326(f290(x81131),x81134),x81132)))
% 157.55/157.23 [8114]~P64(x81141)+~P105(f326(f326(f235(x81141),x81143),f2(x81141)))+P105(f326(f326(f235(x81141),f2(x81141)),x81142))+~P105(f326(f326(f235(x81141),x81144),f326(f326(f80(x81141),x81143),x81142)))+P105(f326(f326(f235(x81141),x81143),f326(f326(f290(x81141),x81144),x81142)))
% 157.55/157.23 [8115]~P64(x81151)+~P105(f326(f326(f235(x81151),x81152),f2(x81151)))+P105(f326(f326(f235(x81151),f2(x81151)),x81152))+~P105(f326(f326(f234(x81151),x81154),f326(f326(f80(x81151),x81153),x81152)))+P105(f326(f326(f234(x81151),x81153),f326(f326(f290(x81151),x81154),x81152)))
% 157.55/157.23 [8116]~P64(x81161)+~P105(f326(f326(f235(x81161),x81162),f2(x81161)))+P105(f326(f326(f235(x81161),f2(x81161)),x81162))+~P105(f326(f326(f234(x81161),x81164),f326(f326(f290(x81161),x81163),x81162)))+P105(f326(f326(f234(x81161),x81163),f326(f326(f80(x81161),x81164),x81162)))
% 157.55/157.23 [8117]~P64(x81171)+~P105(f326(f326(f235(x81171),x81172),f2(x81171)))+P105(f326(f326(f235(x81171),f2(x81171)),x81172))+~P105(f326(f326(f235(x81171),x81174),f326(f326(f80(x81171),x81173),x81172)))+P105(f326(f326(f235(x81171),x81173),f326(f326(f290(x81171),x81174),x81172)))
% 157.55/157.23 [8118]~P64(x81181)+~P105(f326(f326(f235(x81181),x81182),f2(x81181)))+P105(f326(f326(f235(x81181),f2(x81181)),x81182))+~P105(f326(f326(f235(x81181),x81184),f326(f326(f290(x81181),x81183),x81182)))+P105(f326(f326(f235(x81181),x81183),f326(f326(f80(x81181),x81184),x81182)))
% 157.55/157.23 [8243]~P59(x82431)+~P105(f326(f326(f286(x82431),x82433),x82434))+~P105(f326(f326(f286(x82431),x82433),x82432))+~P105(f326(f326(f286(x82431),x82432),x82434))+P105(f326(f326(f286(x82431),f326(f326(f36(x82431),x82432),x82433)),f326(f326(f36(x82431),x82434),x82433)))
% 157.55/157.23 [8258]~P108(x82581)+~P12(x82581,x82582)+~P105(f326(f326(f234(a909),x82583),x82584))+P105(f326(f326(f234(x82581),f326(f326(f164(x82581),x82582),x82583)),f326(f326(f164(x82581),x82582),x82584)))+~P105(f326(f326(f235(a909),x82584),f326(f189(f910(x82581)),x82582)))
% 157.55/157.23 [8306]~P124(x83061)+~P105(f326(f326(f234(x83061),x83062),f77(x83061)))+~P105(f326(f326(f234(x83061),f2(x83061)),x83062))+~P105(f326(f326(f234(a909),x83064),x83063))+P105(f326(f326(f234(x83061),f326(f326(f243(x83061),x83062),x83063)),f326(f326(f243(x83061),x83062),x83064)))
% 157.55/157.23 [8307]~P124(x83071)+~P105(f326(f326(f235(x83071),x83072),f77(x83071)))+~P105(f326(f326(f235(x83071),f2(x83071)),x83072))+~P105(f326(f326(f235(a909),x83074),x83073))+P105(f326(f326(f235(x83071),f326(f326(f243(x83071),x83072),x83073)),f326(f326(f243(x83071),x83072),x83074)))
% 157.55/157.23 [8308]~P124(x83081)+~P105(f326(f326(f234(x83081),f2(x83081)),x83082))+~P105(f326(f326(f235(a909),f2(a909)),x83083))+~P105(f326(f326(f235(x83081),x83082),x83084))+P105(f326(f326(f235(x83081),f326(f326(f243(x83081),x83082),x83083)),f326(f326(f243(x83081),x83084),x83083)))
% 157.55/157.23 [8326]~P108(x83261)+~P12(x83261,f326(f168(x83261),x83262))+~P105(f326(f326(f234(a909),x83264),x83263))+P105(f326(f326(f234(x83261),f326(f326(f164(x83261),x83262),x83263)),f326(f326(f164(x83261),x83262),x83264)))+~P105(f326(f326(f235(a909),x83263),f326(f189(f910(x83261)),x83262)))
% 157.55/157.23 [8554]~P59(x85541)+P105(f326(f326(f286(x85541),x85542),x85543))+~P105(f326(f326(f286(x85541),x85544),x85543))+~P105(f326(f326(f286(x85541),x85544),x85542))+~P105(f326(f326(f286(x85541),f326(f326(f36(x85541),x85542),x85544)),f326(f326(f36(x85541),x85543),x85544)))
% 157.55/157.23 [8569]~P64(x85691)+~P105(f326(f326(f234(x85691),x85692),f2(x85691)))+~P105(f326(f326(f234(x85691),x85693),x85694))+~P105(f326(f326(f235(x85691),f2(x85691)),f326(f326(f80(x85691),x85693),x85694)))+P105(f326(f326(f234(x85691),f326(f326(f290(x85691),x85692),x85693)),f326(f326(f290(x85691),x85692),x85694)))
% 157.55/157.23 [8570]~P65(x85701)+~P105(f326(f326(f235(x85701),x85702),f2(x85701)))+~P105(f326(f326(f235(x85701),x85703),x85704))+~P105(f326(f326(f235(x85701),f2(x85701)),f326(f326(f80(x85701),x85703),x85704)))+P105(f326(f326(f235(x85701),f326(f326(f290(x85701),x85702),x85703)),f326(f326(f290(x85701),x85702),x85704)))
% 157.55/157.23 [8579]~P65(x85791)+~P105(f326(f326(f234(x85791),x85794),x85793))+~P105(f326(f326(f234(x85791),f2(x85791)),x85792))+~P105(f326(f326(f235(x85791),f2(x85791)),f326(f326(f80(x85791),x85793),x85794)))+P105(f326(f326(f234(x85791),f326(f326(f290(x85791),x85792),x85793)),f326(f326(f290(x85791),x85792),x85794)))
% 157.55/157.23 [8580]~P65(x85801)+~P105(f326(f326(f235(x85801),x85804),x85803))+~P105(f326(f326(f235(x85801),f2(x85801)),x85802))+~P105(f326(f326(f235(x85801),f2(x85801)),f326(f326(f80(x85801),x85803),x85804)))+P105(f326(f326(f235(x85801),f326(f326(f290(x85801),x85802),x85803)),f326(f326(f290(x85801),x85802),x85804)))
% 157.55/157.23 [8679]P105(f326(x86791,x86792))+~P105(f326(f61(x86794),x86792))+P105(f326(x86791,f507(x86791,x86793,x86792,x86794)))+~P105(f326(x86791,f188(f917(x86794,a905))))+~P105(f326(f326(f234(f917(x86794,a905)),x86792),x86793))
% 157.55/157.23 [8688]P105(f326(x86881,x86882))+P105(f326(f61(x86883),f507(x86881,x86884,x86882,x86883)))+~P105(f326(f61(x86883),x86882))+~P105(f326(x86881,f188(f917(x86883,a905))))+~P105(f326(f326(f234(f917(x86883,a905)),x86882),x86884))
% 157.55/157.23 [8956]E(f326(f326(f79(a1),f439(x89561,x89562,x89563,x89564)),f440(x89561,x89562,x89563,x89564)),x89564)+~P105(f326(f326(f235(a1),f2(a1)),x89563))+~P105(f326(f326(f235(a1),x89562),x89564))+~P105(f326(f326(f328(a1),x89562),x89561))+P105(f326(f326(f235(a1),x89562),f326(f326(f3(a1),x89564),x89563)))
% 157.55/157.23 [9169]~P105(f326(f326(f235(a1),f2(a1)),x91693))+~P105(f326(f326(f235(a1),x91692),x91694))+~P105(f326(f326(f328(a1),x91692),x91691))+P105(f326(f326(f328(a1),f439(x91691,x91692,x91693,x91694)),x91691))+P105(f326(f326(f235(a1),x91692),f326(f326(f3(a1),x91694),x91693)))
% 157.55/157.23 [9180]P105(f326(x91801,x91802))+~P105(f326(f61(x91803),x91802))+P105(f326(f326(f328(x91803),f495(x91801,x91804,x91802,x91803)),x91804))+~P105(f326(x91801,f188(f917(x91803,a905))))+~P105(f326(f326(f234(f917(x91803,a905)),x91802),x91804))
% 157.55/157.23 [9197]E(f326(f326(f79(a1),f426(x91971,x91972,x91973,x91974)),f427(x91971,x91972,x91973,x91974)),x91974)+~P105(f326(f326(f235(a1),f2(a1)),x91973))+~P105(f326(f326(f234(a1),x91972),x91974))+P105(f326(f326(f234(a1),x91972),f326(f326(f3(a1),x91974),x91973)))+~P105(f326(f326(f328(a1),f326(f326(f3(a1),x91972),f77(a1))),x91971))
% 157.55/157.23 [9251]~P105(f326(f326(f235(a1),f2(a1)),x92513))+~P105(f326(f326(f235(a1),x92511),x92512))+~P105(f326(f326(f328(a1),x92511),x92514))+P105(f326(f326(f328(a1),f440(x92514,x92511,x92513,x92512)),f302(a1,f77(a1),x92513)))+P105(f326(f326(f235(a1),x92511),f326(f326(f3(a1),x92512),x92513)))
% 157.55/157.23 [9277]~P69(x92772)+~E(f771(x92773,x92774,x92771,x92772),f772(x92773,x92774,x92771,x92772))+~P105(f326(f61(x92771),f773(x92773,x92774,x92771,x92772)))+E(f326(f326(f8(f917(x92771,a905),x92772),f326(f8(x92771,x92772),x92773)),x92774),f326(f326(f8(x92771,x92772),x92773),f37(f917(x92771,a905),x92774)))+~P105(f326(f61(f917(x92771,a905)),x92774))
% 157.55/157.23 [9281]~P69(x92812)+~E(f326(x92813,f774(x92813,x92814,x92811,x92812)),f2(x92812))+~P105(f326(f61(x92811),f773(x92813,x92814,x92811,x92812)))+E(f326(f326(f8(f917(x92811,a905),x92812),f326(f8(x92811,x92812),x92813)),x92814),f326(f326(f8(x92811,x92812),x92813),f37(f917(x92811,a905),x92814)))+~P105(f326(f61(f917(x92811,a905)),x92814))
% 157.55/157.23 [9344]~P105(f326(f326(f235(a1),f2(a1)),x93443))+~P105(f326(f326(f234(a1),x93442),x93444))+P105(f326(f326(f328(a1),f426(x93441,x93442,x93443,x93444)),x93441))+P105(f326(f326(f234(a1),x93442),f326(f326(f3(a1),x93444),x93443)))+~P105(f326(f326(f328(a1),f326(f326(f3(a1),x93442),f77(a1))),x93441))
% 157.55/157.23 [9386]~P105(f326(f326(f235(a1),f2(a1)),x93863))+~P105(f326(f326(f234(a1),x93861),x93862))+P105(f326(f326(f328(a1),f427(x93864,x93861,x93863,x93862)),f302(a1,f77(a1),x93863)))+P105(f326(f326(f234(a1),x93861),f326(f326(f3(a1),x93862),x93863)))+~P105(f326(f326(f328(a1),f326(f326(f3(a1),x93861),f77(a1))),x93864))
% 157.55/157.23 [9407]~P69(x94072)+~E(f771(x94073,x94074,x94071,x94072),f772(x94073,x94074,x94071,x94072))+E(f326(f326(f8(f917(x94071,a905),x94072),f326(f8(x94071,x94072),x94073)),x94074),f326(f326(f8(x94071,x94072),x94073),f37(f917(x94071,a905),x94074)))+P105(f326(f326(f328(f917(x94071,a905)),f773(x94073,x94074,x94071,x94072)),x94074))+~P105(f326(f61(f917(x94071,a905)),x94074))
% 157.55/157.23 [9412]~P69(x94122)+~E(f326(x94123,f774(x94123,x94124,x94121,x94122)),f2(x94122))+E(f326(f326(f8(f917(x94121,a905),x94122),f326(f8(x94121,x94122),x94123)),x94124),f326(f326(f8(x94121,x94122),x94123),f37(f917(x94121,a905),x94124)))+P105(f326(f326(f328(f917(x94121,a905)),f773(x94123,x94124,x94121,x94122)),x94124))+~P105(f326(f61(f917(x94121,a905)),x94124))
% 157.55/157.23 [9513]~P69(x95132)+~P105(f326(f61(x95131),f773(x95133,x95134,x95131,x95132)))+E(f326(f326(f8(f917(x95131,a905),x95132),f326(f8(x95131,x95132),x95133)),x95134),f326(f326(f8(x95131,x95132),x95133),f37(f917(x95131,a905),x95134)))+P105(f326(f326(f328(f917(x95131,a905)),f772(x95133,x95134,x95131,x95132)),x95134))+~P105(f326(f61(f917(x95131,a905)),x95134))
% 157.55/157.23 [9514]~P69(x95142)+~P105(f326(f61(x95141),f773(x95143,x95144,x95141,x95142)))+E(f326(f326(f8(f917(x95141,a905),x95142),f326(f8(x95141,x95142),x95143)),x95144),f326(f326(f8(x95141,x95142),x95143),f37(f917(x95141,a905),x95144)))+P105(f326(f326(f328(f917(x95141,a905)),f771(x95143,x95144,x95141,x95142)),x95144))+~P105(f326(f61(f917(x95141,a905)),x95144))
% 157.55/157.23 [9591]~P69(x95912)+E(f326(f326(f8(f917(x95911,a905),x95912),f326(f8(x95911,x95912),x95913)),x95914),f326(f326(f8(x95911,x95912),x95913),f37(f917(x95911,a905),x95914)))+P105(f326(f326(f328(f917(x95911,a905)),f773(x95913,x95914,x95911,x95912)),x95914))+P105(f326(f326(f328(f917(x95911,a905)),f772(x95913,x95914,x95911,x95912)),x95914))+~P105(f326(f61(f917(x95911,a905)),x95914))
% 157.55/157.23 [9592]~P69(x95922)+E(f326(f326(f8(f917(x95921,a905),x95922),f326(f8(x95921,x95922),x95923)),x95924),f326(f326(f8(x95921,x95922),x95923),f37(f917(x95921,a905),x95924)))+P105(f326(f326(f328(f917(x95921,a905)),f773(x95923,x95924,x95921,x95922)),x95924))+P105(f326(f326(f328(f917(x95921,a905)),f771(x95923,x95924,x95921,x95922)),x95924))+~P105(f326(f61(f917(x95921,a905)),x95924))
% 157.55/157.23 [9609]~P69(x96092)+P105(f326(f326(f328(x96091),f774(x96093,x96094,x96091,x96092)),f772(x96093,x96094,x96091,x96092)))+~P105(f326(f61(x96091),f773(x96093,x96094,x96091,x96092)))+E(f326(f326(f8(f917(x96091,a905),x96092),f326(f8(x96091,x96092),x96093)),x96094),f326(f326(f8(x96091,x96092),x96093),f37(f917(x96091,a905),x96094)))+~P105(f326(f61(f917(x96091,a905)),x96094))
% 157.55/157.23 [9610]~P69(x96102)+P105(f326(f326(f328(x96101),f774(x96103,x96104,x96101,x96102)),f771(x96103,x96104,x96101,x96102)))+~P105(f326(f61(x96101),f773(x96103,x96104,x96101,x96102)))+E(f326(f326(f8(f917(x96101,a905),x96102),f326(f8(x96101,x96102),x96103)),x96104),f326(f326(f8(x96101,x96102),x96103),f37(f917(x96101,a905),x96104)))+~P105(f326(f61(f917(x96101,a905)),x96104))
% 157.55/157.23 [9623]P105(f326(x96231,x96232))+~P105(f326(f326(f328(x96233),f495(x96231,x96234,x96232,x96233)),f507(x96231,x96234,x96232,x96233)))+~P105(f326(f61(x96233),x96232))+~P105(f326(x96231,f188(f917(x96233,a905))))+~P105(f326(f326(f234(f917(x96233,a905)),x96232),x96234))
% 157.55/157.23 [9660]~P69(x96602)+P105(f326(f326(f328(x96601),f774(x96603,x96604,x96601,x96602)),f772(x96603,x96604,x96601,x96602)))+E(f326(f326(f8(f917(x96601,a905),x96602),f326(f8(x96601,x96602),x96603)),x96604),f326(f326(f8(x96601,x96602),x96603),f37(f917(x96601,a905),x96604)))+P105(f326(f326(f328(f917(x96601,a905)),f773(x96603,x96604,x96601,x96602)),x96604))+~P105(f326(f61(f917(x96601,a905)),x96604))
% 157.55/157.23 [9661]~P69(x96612)+P105(f326(f326(f328(x96611),f774(x96613,x96614,x96611,x96612)),f771(x96613,x96614,x96611,x96612)))+E(f326(f326(f8(f917(x96611,a905),x96612),f326(f8(x96611,x96612),x96613)),x96614),f326(f326(f8(x96611,x96612),x96613),f37(f917(x96611,a905),x96614)))+P105(f326(f326(f328(f917(x96611,a905)),f773(x96613,x96614,x96611,x96612)),x96614))+~P105(f326(f61(f917(x96611,a905)),x96614))
% 157.55/157.23 [9837]P105(f326(x98371,x98372))+~P105(f326(f61(x98373),x98372))+~P105(f326(x98371,f326(f326(f308(x98373),f495(x98371,x98374,x98372,x98373)),f507(x98371,x98374,x98372,x98373))))+~P105(f326(x98371,f188(f917(x98373,a905))))+~P105(f326(f326(f234(f917(x98373,a905)),x98372),x98374))
% 157.55/157.23 [7888]~P64(x78881)+P105(f326(f326(f235(x78881),x78882),f2(x78881)))+~P105(f326(f326(f234(x78881),f2(x78881)),x78884))+P105(f326(f326(f235(x78881),f2(x78881)),x78882))+P105(f326(f326(f234(x78881),f326(f326(f290(x78881),x78883),x78882)),x78884))
% 157.55/157.23 [7889]~P64(x78891)+P105(f326(f326(f235(x78891),x78892),f2(x78891)))+P105(f326(f326(f235(x78891),f2(x78891)),x78892))+~P105(f326(f326(f235(x78891),f2(x78891)),x78894))+P105(f326(f326(f235(x78891),f326(f326(f290(x78891),x78893),x78892)),x78894))
% 157.55/157.23 [8164]~P105(f326(f326(f234(a1),x81644),f2(a1)))+~E(x81642,f326(f326(f79(a1),f326(f326(f80(a1),x81641),x81643)),x81644))+P105(f326(f326(f235(a1),f2(a1)),x81641))+~P105(f326(f326(f235(a1),x81641),x81644))+P105(f326(f49(x81642,x81641),f326(f326(f251(a1,a1),x81643),x81644)))
% 157.55/157.23 [8198]~P105(f326(x81981,x81984))+P105(f326(x81981,f343(x81982,x81981,x81983)))+~P105(f326(f326(f234(a1),f2(a1)),x81982))+~P105(f326(f326(f235(a1),f2(a1)),x81983))+P105(f326(x81981,f326(f326(f3(a1),x81984),f326(f326(f80(a1),x81982),x81983))))
% 157.55/157.23 [8199]~P105(f326(x81991,x81994))+P105(f326(x81991,f350(x81992,x81991,x81993)))+~P105(f326(f326(f234(a1),f2(a1)),x81992))+~P105(f326(f326(f235(a1),f2(a1)),x81993))+P105(f326(x81991,f326(f326(f79(a1),x81994),f326(f326(f80(a1),x81992),x81993))))
% 157.55/157.23 [8200]~P64(x82001)+P105(f326(f326(f235(x82001),x82002),f2(x82001)))+P105(f326(f326(f235(x82001),f2(x82001)),x82002))+P105(f326(f326(f234(x82001),f2(x82001)),x82003))+~P105(f326(f326(f234(x82001),f326(f326(f290(x82001),x82004),x82002)),x82003))
% 157.55/157.23 [8201]~P64(x82011)+P105(f326(f326(f235(x82011),x82012),f2(x82011)))+P105(f326(f326(f235(x82011),f2(x82011)),x82012))+P105(f326(f326(f235(x82011),f2(x82011)),x82013))+~P105(f326(f326(f235(x82011),f326(f326(f290(x82011),x82014),x82012)),x82013))
% 157.55/157.23 [8253]~E(x82531,f326(f326(f79(a1),f326(f326(f80(a1),x82532),x82533)),x82534))+~P105(f326(f326(f234(a1),f2(a1)),x82534))+~P105(f326(f326(f235(a1),f2(a1)),x82532))+~P105(f326(f326(f235(a1),x82534),x82532))+P105(f326(f49(x82531,x82532),f326(f326(f251(a1,a1),x82533),x82534)))
% 157.55/157.23 [8365]~P64(x83651)+P105(f326(f326(f235(x83651),x83652),f2(x83651)))+~P105(f326(f326(f234(x83651),f2(x83651)),x83654))+~P105(f326(f326(f234(x83651),x83653),f326(f326(f80(x83651),x83654),x83652)))+P105(f326(f326(f234(x83651),f326(f326(f290(x83651),x83653),x83652)),x83654))
% 157.55/157.23 [8366]~P64(x83661)+P105(f326(f326(f235(x83661),x83662),f2(x83661)))+~P105(f326(f326(f235(x83661),f2(x83661)),x83664))+~P105(f326(f326(f235(x83661),x83663),f326(f326(f80(x83661),x83664),x83662)))+P105(f326(f326(f235(x83661),f326(f326(f290(x83661),x83663),x83662)),x83664))
% 157.55/157.23 [8450]~P64(x84501)+P105(f326(f326(f235(x84501),x84502),f2(x84501)))+~P105(f326(f326(f234(x84501),x84503),f2(x84501)))+P105(f326(f326(f234(x84501),x84503),f326(f326(f290(x84501),x84504),x84502)))+~P105(f326(f326(f234(x84501),f326(f326(f80(x84501),x84503),x84502)),x84504))
% 157.55/157.23 [8451]~P64(x84511)+P105(f326(f326(f235(x84511),x84512),f2(x84511)))+~P105(f326(f326(f235(x84511),x84513),f2(x84511)))+P105(f326(f326(f235(x84511),x84513),f326(f326(f290(x84511),x84514),x84512)))+~P105(f326(f326(f235(x84511),f326(f326(f80(x84511),x84513),x84512)),x84514))
% 157.55/157.23 [8601]~P64(x86011)+~P105(f326(f326(f235(x86011),x86012),f2(x86011)))+P105(f326(f326(f235(x86011),f2(x86011)),x86012))+~P105(f326(f326(f234(x86011),f326(f326(f290(x86011),x86014),x86012)),x86013))+P105(f326(f326(f234(x86011),f326(f326(f80(x86011),x86013),x86012)),x86014))
% 157.55/157.23 [8602]~P64(x86021)+~P105(f326(f326(f235(x86021),x86022),f2(x86021)))+P105(f326(f326(f235(x86021),f2(x86021)),x86022))+~P105(f326(f326(f234(x86021),f326(f326(f80(x86021),x86024),x86022)),x86023))+P105(f326(f326(f234(x86021),f326(f326(f290(x86021),x86023),x86022)),x86024))
% 157.55/157.23 [8603]~P64(x86031)+~P105(f326(f326(f235(x86031),x86032),f2(x86031)))+P105(f326(f326(f235(x86031),f2(x86031)),x86032))+~P105(f326(f326(f235(x86031),f326(f326(f290(x86031),x86034),x86032)),x86033))+P105(f326(f326(f235(x86031),f326(f326(f80(x86031),x86033),x86032)),x86034))
% 157.55/157.23 [8604]~P64(x86041)+~P105(f326(f326(f235(x86041),x86042),f2(x86041)))+P105(f326(f326(f235(x86041),f2(x86041)),x86042))+~P105(f326(f326(f235(x86041),f326(f326(f80(x86041),x86044),x86042)),x86043))+P105(f326(f326(f235(x86041),f326(f326(f290(x86041),x86043),x86042)),x86044))
% 157.55/157.23 [8620]~P64(x86201)+~P105(f326(f326(f234(x86201),f2(x86201)),x86204))+P105(f326(f326(f235(x86201),f2(x86201)),x86202))+~P105(f326(f326(f234(x86201),f326(f326(f80(x86201),x86204),x86202)),x86203))+P105(f326(f326(f234(x86201),f326(f326(f290(x86201),x86203),x86202)),x86204))
% 157.55/157.23 [8621]~P64(x86211)+~P105(f326(f326(f235(x86211),f2(x86211)),x86214))+P105(f326(f326(f235(x86211),f2(x86211)),x86212))+~P105(f326(f326(f235(x86211),f326(f326(f80(x86211),x86214),x86212)),x86213))+P105(f326(f326(f235(x86211),f326(f326(f290(x86211),x86213),x86212)),x86214))
% 157.55/157.23 [8696]~P64(x86961)+~P105(f326(f326(f235(x86961),x86964),f2(x86961)))+~P105(f326(f326(f234(x86961),x86963),f326(f326(f80(x86961),x86962),x86964)))+P105(f326(f326(f234(x86961),x86962),f326(f326(f290(x86961),x86963),x86964)))+~P105(f326(f326(f234(x86961),f326(f326(f80(x86961),x86962),x86964)),x86963))
% 157.55/157.23 [8697]~P64(x86971)+~P105(f326(f326(f234(x86971),x86972),f2(x86971)))+~P105(f326(f326(f234(x86971),x86973),f326(f326(f80(x86971),x86972),x86974)))+P105(f326(f326(f234(x86971),x86972),f326(f326(f290(x86971),x86973),x86974)))+~P105(f326(f326(f234(x86971),f326(f326(f80(x86971),x86972),x86974)),x86973))
% 157.55/157.23 [8698]~P64(x86981)+~P105(f326(f326(f235(x86981),x86984),f2(x86981)))+~P105(f326(f326(f235(x86981),x86983),f326(f326(f80(x86981),x86982),x86984)))+P105(f326(f326(f235(x86981),x86982),f326(f326(f290(x86981),x86983),x86984)))+~P105(f326(f326(f235(x86981),f326(f326(f80(x86981),x86982),x86984)),x86983))
% 157.55/157.23 [8699]~P64(x86991)+~P105(f326(f326(f235(x86991),x86992),f2(x86991)))+~P105(f326(f326(f235(x86991),x86993),f326(f326(f80(x86991),x86992),x86994)))+P105(f326(f326(f235(x86991),x86992),f326(f326(f290(x86991),x86993),x86994)))+~P105(f326(f326(f235(x86991),f326(f326(f80(x86991),x86992),x86994)),x86993))
% 157.55/157.23 [8821]~P64(x88211)+~P105(f326(f326(f235(x88211),x88213),f2(x88211)))+~P105(f326(f326(f234(x88211),x88212),f326(f326(f80(x88211),x88214),x88213)))+~P105(f326(f326(f234(x88211),f326(f326(f80(x88211),x88214),x88213)),x88212))+P105(f326(f326(f234(x88211),f326(f326(f290(x88211),x88212),x88213)),x88214))
% 157.55/157.23 [8822]~P64(x88221)+~P105(f326(f326(f235(x88221),x88223),f2(x88221)))+~P105(f326(f326(f235(x88221),x88222),f326(f326(f80(x88221),x88224),x88223)))+~P105(f326(f326(f235(x88221),f326(f326(f80(x88221),x88224),x88223)),x88222))+P105(f326(f326(f235(x88221),f326(f326(f290(x88221),x88222),x88223)),x88224))
% 157.55/157.23 [8839]~P64(x88391)+~P105(f326(f326(f234(x88391),f2(x88391)),x88394))+~P105(f326(f326(f234(x88391),x88392),f326(f326(f80(x88391),x88394),x88393)))+~P105(f326(f326(f234(x88391),f326(f326(f80(x88391),x88394),x88393)),x88392))+P105(f326(f326(f234(x88391),f326(f326(f290(x88391),x88392),x88393)),x88394))
% 157.55/157.23 [8840]~P64(x88401)+~P105(f326(f326(f235(x88401),f2(x88401)),x88404))+~P105(f326(f326(f235(x88401),x88402),f326(f326(f80(x88401),x88404),x88403)))+~P105(f326(f326(f235(x88401),f326(f326(f80(x88401),x88404),x88403)),x88402))+P105(f326(f326(f235(x88401),f326(f326(f290(x88401),x88402),x88403)),x88404))
% 157.55/157.23 [9023]E(f326(f326(f3(a1),f441(x90231,x90232,x90233,x90234)),f442(x90231,x90232,x90233,x90234)),x90234)+~P105(f326(f326(f235(a1),f2(a1)),x90233))+~P105(f326(f326(f328(a1),x90232),x90231))+~P105(f326(f326(f235(a1),x90234),x90232))+P105(f326(f326(f235(a1),f326(f326(f79(a1),x90234),x90233)),x90232))
% 157.55/157.23 [9094]~P105(f326(x90941,x90942))+~P105(f326(f326(f234(a1),f2(a1)),x90943))+~P105(f326(f326(f235(a1),f2(a1)),x90944))+~P105(f326(x90941,f326(f326(f3(a1),f343(x90943,x90941,x90944)),x90944)))+P105(f326(x90941,f326(f326(f3(a1),x90942),f326(f326(f80(a1),x90943),x90944))))
% 157.55/157.23 [9095]~P105(f326(x90951,x90952))+~P105(f326(f326(f234(a1),f2(a1)),x90953))+~P105(f326(f326(f235(a1),f2(a1)),x90954))+~P105(f326(x90951,f326(f326(f79(a1),f350(x90953,x90951,x90954)),x90954)))+P105(f326(x90951,f326(f326(f79(a1),x90952),f326(f326(f80(a1),x90953),x90954))))
% 157.55/157.23 [9245]~P105(f326(f326(f235(a1),f2(a1)),x92453))+~P105(f326(f326(f328(a1),x92452),x92451))+~P105(f326(f326(f235(a1),x92454),x92452))+P105(f326(f326(f328(a1),f441(x92451,x92452,x92453,x92454)),x92451))+P105(f326(f326(f235(a1),f326(f326(f79(a1),x92454),x92453)),x92452))
% 157.55/157.23 [9264]E(f326(f326(f3(a1),f430(x92641,x92642,x92643,x92644)),f431(x92641,x92642,x92643,x92644)),x92644)+~P105(f326(f326(f235(a1),f2(a1)),x92643))+~P105(f326(f326(f234(a1),x92644),x92642))+~P105(f326(f326(f328(a1),f326(f326(f79(a1),x92642),f77(a1))),x92641))+P105(f326(f326(f234(a1),f326(f326(f79(a1),x92644),x92643)),x92642))
% 157.55/157.23 [9292]~P105(f326(f326(f235(a1),f2(a1)),x92922))+~P105(f326(f326(f328(a1),x92923),x92924))+~P105(f326(f326(f235(a1),x92921),x92923))+P105(f326(f326(f328(a1),f442(x92924,x92923,x92922,x92921)),f302(a1,f77(a1),x92922)))+P105(f326(f326(f235(a1),f326(f326(f79(a1),x92921),x92922)),x92923))
% 157.55/157.23 [9378]~P105(f326(f326(f235(a1),f2(a1)),x93783))+~P105(f326(f326(f234(a1),x93784),x93782))+P105(f326(f326(f328(a1),f430(x93781,x93782,x93783,x93784)),x93781))+~P105(f326(f326(f328(a1),f326(f326(f79(a1),x93782),f77(a1))),x93781))+P105(f326(f326(f234(a1),f326(f326(f79(a1),x93784),x93783)),x93782))
% 157.55/157.23 [9423]~P105(f326(f326(f235(a1),f2(a1)),x94232))+~P105(f326(f326(f234(a1),x94231),x94233))+P105(f326(f326(f328(a1),f431(x94234,x94233,x94232,x94231)),f302(a1,f77(a1),x94232)))+~P105(f326(f326(f328(a1),f326(f326(f79(a1),x94233),f77(a1))),x94234))+P105(f326(f326(f234(a1),f326(f326(f79(a1),x94231),x94232)),x94233))
% 157.55/157.23 [9714]~P36(x97141,x97143)+~P26(x97141,x97144)+P36(x97141,f326(f326(f110(f917(f916(x97141,x97141),a905)),x97142),x97143))+~P105(f326(f326(f234(f917(f916(x97141,x97141),a905)),x97142),f326(f250(f917(f916(x97141,x97141),a905),f917(f916(x97141,x97141),a905)),x97144)))+~P105(f326(f326(f234(f917(f916(x97141,x97141),a905)),x97143),f326(f255(f917(f916(x97141,x97141),a905),f917(f916(x97141,x97141),a905)),x97144)))
% 157.55/157.23 [10104]~P17(x101042,x101044,x101043)+E(x101041,f188(f917(x101042,a905)))+~P105(f326(f61(x101042),x101041))+P105(f326(f326(f328(x101042),f326(x101043,x101041)),x101041))+~P105(f326(f326(f328(x101042),f326(f326(x101044,f461(x101041,x101043,x101044,x101042)),f470(x101041,x101043,x101044,x101042))),f326(f326(f308(x101042),f461(x101041,x101043,x101044,x101042)),f326(f326(f308(x101042),f470(x101041,x101043,x101044,x101042)),f188(f917(x101042,a905))))))
% 157.55/157.23 [10027]~P109(x100272)+~P61(x100271)+~P105(f326(f326(f234(f917(x100271,x100272)),x100273),x100274))+P105(f326(f326(f235(f917(x100271,x100272)),x100273),x100274))+~P105(f326(f56(x100271),f326(f326(f10(a905,a905,x100271),a321),f326(f326(f20(x100271,x100272,a905),f326(f326(f10(x100272,f917(x100272,a905),x100271),a323),x100273)),x100274))))
% 157.55/157.23 [9629]~P53(x96291,x96291,x96294)+P105(f326(f326(f328(f916(x96291,x96291)),f326(f326(f251(x96291,x96291),x96292),x96293)),f306(x96291,x96294)))+P105(f326(f326(f328(f916(x96291,x96291)),f326(f326(f251(x96291,x96291),x96293),x96292)),f306(x96291,x96294)))+~P105(f326(f326(f328(f916(x96291,x96291)),f326(f326(f251(x96291,x96291),x96295),x96292)),f306(x96291,x96294)))+~P105(f326(f326(f328(f916(x96291,x96291)),f326(f326(f251(x96291,x96291),x96295),x96293)),f306(x96291,x96294)))
% 157.55/157.23 [5780]E(x57801,f2(a909))+~E(f326(f35(x57802),x57805),x57801)+E(f326(f35(x57802),x57803),f326(a112,x57801))+~E(x57803,f326(f326(f308(x57802),x57804),x57805))+P105(f326(f326(f328(x57802),x57804),x57805))
% 157.55/157.23 [5902]~P63(x59022)+E(x59021,f2(x59022))+E(x59023,f2(x59022))+~E(f326(f326(f290(x59022),x59024),x59023),f326(f326(f290(x59022),x59025),x59021))+E(f326(f326(f80(x59022),x59024),x59021),f326(f326(f80(x59022),x59025),x59023))
% 157.55/157.23 [5903]~P63(x59032)+E(x59031,f2(x59032))+E(x59033,f2(x59032))+~E(f326(f326(f80(x59032),x59034),x59033),f326(f326(f80(x59032),x59035),x59031))+E(f326(f326(f290(x59032),x59034),x59031),f326(f326(f290(x59032),x59035),x59033))
% 157.55/157.23 [5981]~E(f326(f35(x59811),x59815),x59813)+~E(x59815,f188(f917(x59811,a905)))+E(f326(f35(x59811),x59812),f326(a112,x59813))+~E(x59812,f326(f326(f308(x59811),x59814),x59815))+P105(f326(f326(f328(x59811),x59814),x59815))
% 157.55/157.23 [6215]~P112(x62152)+~E(f326(x62153,x62155),f2(x62152))+E(f326(f326(f11(x62151,x62152),x62153),x62154),f2(x62152))+~P105(f326(f61(x62151),x62154))+~P105(f326(f326(f328(x62151),x62155),x62154))
% 157.55/157.23 [6588]~P108(x65883)+E(x65881,x65882)+~E(f326(f301(x65883,x65884),x65881),f326(f301(x65883,x65885),x65882))+~P105(f326(f326(f235(x65883),x65885),x65882))+~P105(f326(f326(f235(x65883),x65884),x65881))
% 157.55/157.23 [6589]~P108(x65893)+E(x65891,x65892)+~E(f326(f301(x65893,x65891),x65894),f326(f301(x65893,x65892),x65895))+~P105(f326(f326(f235(x65893),x65892),x65895))+~P105(f326(f326(f235(x65893),x65891),x65894))
% 157.55/157.23 [7656]~P108(x76561)+~P12(x76561,f326(f326(f134(x76561),x76564),x76565))+~P105(f326(f326(f328(x76561),x76563),f326(f172(x76561),x76565)))+~P105(f326(f326(f328(x76561),x76562),f326(f172(x76561),x76564)))+P105(f326(f326(f234(x76561),x76562),x76563))
% 157.55/157.23 [8733]~P109(x87331)+~P105(f326(f326(f235(f917(x87331,a905)),f302(x87331,x87335,x87332)),f302(x87331,x87334,x87333)))+~P105(f326(f326(f234(x87331),x87335),x87332))+P105(f326(f326(f235(x87331),x87332),x87333))+P105(f326(f326(f235(x87331),x87334),x87335))
% 157.55/157.23 [10147]~P16(x101472,x101475,x101473)+E(x101471,f188(f917(x101472,a905)))+~E(f326(f326(x101475,f326(x101474,f527(x101471,x101474,x101473,x101475,x101472))),f326(x101474,f528(x101471,x101474,x101473,x101475,x101472))),f326(x101474,f326(f326(x101475,f527(x101471,x101474,x101473,x101475,x101472)),f528(x101471,x101474,x101473,x101475,x101472))))+E(f326(x101473,f326(f309(x101472,x101472,x101474),x101471)),f326(x101474,f326(x101473,x101471)))+~P105(f326(f61(x101472),x101471))
% 157.55/157.23 [6585]~P17(x65852,x65855,x65853)+E(x65851,f188(f917(x65852,a905)))+~P105(f326(f61(x65852),x65851))+E(f326(x65853,f326(f326(f308(x65852),x65854),x65851)),f326(f326(x65855,x65854),f326(x65853,x65851)))+P105(f326(f326(f328(x65852),x65854),x65851))
% 157.55/157.23 [7415]~P16(x74152,x74153,x74154)+E(f326(f326(x74153,f326(x74154,x74151)),f326(x74154,x74155)),f326(x74154,x74155))+E(x74151,f188(f917(x74152,a905)))+~P105(f326(f61(x74152),x74155))+~P105(f326(f326(f234(f917(x74152,a905)),x74151),x74155))
% 157.55/157.23 [7788]~P17(x77884,x77885,x77881)+E(f326(x77881,x77882),x77883)+~P105(f326(f61(x77884),x77882))+~E(f326(f326(f3(f917(x77884,a905)),x77882),f326(f326(f308(x77884),x77883),f188(f917(x77884,a905)))),f188(f917(x77884,a905)))+~P105(f326(f326(f328(x77884),x77883),x77882))
% 157.55/157.23 [8703]E(x87031,x87032)+~P7(x87033,x87034,x87035)+E(f326(f326(f101(f917(x87033,a905)),x87031),x87032),f188(f917(x87033,a905)))+~P105(f326(f326(f328(f917(x87033,a905)),x87032),f326(f326(f60(x87033),x87034),x87035)))+~P105(f326(f326(f328(f917(x87033,a905)),x87031),f326(f326(f60(x87033),x87034),x87035)))
% 157.55/157.23 [9506]~P69(x95062)+~E(f326(x95063,f886(x95063,x95064,x95065,x95061,x95062)),f2(x95062))+E(f326(f326(f8(x95061,x95062),x95063),x95064),f326(f326(f8(x95061,x95062),x95063),x95065))+~P105(f326(f61(x95061),x95065))+~P105(f326(f326(f234(f917(x95061,a905)),x95064),x95065))
% 157.55/157.23 [9507]~P69(x95072)+~E(f326(x95073,f887(x95073,x95074,x95075,x95071,x95072)),f2(x95072))+E(f326(f326(f8(x95071,x95072),x95073),x95074),f326(f326(f8(x95071,x95072),x95073),x95075))+~P105(f326(f61(x95071),x95075))+~P105(f326(f326(f234(f917(x95071,a905)),x95074),x95075))
% 157.55/157.23 [9508]~P74(x95082)+~E(f326(x95083,f829(x95083,x95084,x95085,x95081,x95082)),f77(x95082))+E(f326(f326(f11(x95081,x95082),x95083),x95084),f326(f326(f11(x95081,x95082),x95083),x95085))+~P105(f326(f61(x95081),x95085))+~P105(f326(f326(f234(f917(x95081,a905)),x95084),x95085))
% 157.55/157.23 [9509]~P74(x95092)+~E(f326(x95093,f834(x95093,x95094,x95095,x95091,x95092)),f77(x95092))+E(f326(f326(f11(x95091,x95092),x95093),x95094),f326(f326(f11(x95091,x95092),x95093),x95095))+~P105(f326(f61(x95091),x95095))+~P105(f326(f326(f234(f917(x95091,a905)),x95094),x95095))
% 157.55/157.23 [9980]~P88(x99801)+~P105(f326(f61(x99802),x99805))+~P105(f326(f326(f234(x99801),f2(x99801)),f326(x99803,f878(x99803,x99804,x99805,x99802,x99801))))+P105(f326(f326(f234(x99801),f326(f326(f8(x99802,x99801),x99803),x99804)),f326(f326(f8(x99802,x99801),x99803),x99805)))+~P105(f326(f326(f234(f917(x99802,a905)),x99804),x99805))
% 157.55/157.23 [7653]E(x76531,f2(a909))+P105(f326(x76532,x76533))+~E(x76534,f326(f326(f79(a909),f326(f326(f80(a909),x76531),x76533)),x76535))+~P105(f326(f326(f235(a909),x76535),x76531))+~P105(f326(x76532,f326(f326(f36(a909),x76534),x76531)))
% 157.55/157.23 [7728]E(x77281,f2(a909))+P105(f326(x77282,x77283))+~P105(f326(x77282,f45(a909,x77284,x77281)))+~E(x77284,f326(f326(f79(a909),f326(f326(f80(a909),x77281),x77285)),x77283))+~P105(f326(f326(f235(a909),x77283),x77281))
% 157.55/157.23 [8015]~P63(x80153)+E(f326(x80151,x80152),f2(x80153))+~P105(f326(f61(x80154),x80155))+E(f326(f326(f11(x80154,x80153),x80151),f326(f326(f3(f917(x80154,a905)),x80155),f326(f326(f308(x80154),x80152),f188(f917(x80154,a905))))),f326(f326(f11(x80154,x80153),x80151),x80155))+P105(f326(f326(f328(x80154),x80152),x80155))
% 157.55/157.23 [8405]~P69(x84051)+~P105(f326(f61(x84052),x84055))+~P105(f326(f61(x84052),x84054))+~E(f326(f326(f101(f917(x84052,a905)),x84054),x84055),f188(f917(x84052,a905)))+E(f326(f326(f79(x84051),f326(f326(f8(x84052,x84051),x84053),x84054)),f326(f326(f8(x84052,x84051),x84053),x84055)),f326(f326(f8(x84052,x84051),x84053),f326(f326(f110(f917(x84052,a905)),x84054),x84055)))
% 157.55/157.23 [8407]~P74(x84071)+~P105(f326(f61(x84072),x84075))+~P105(f326(f61(x84072),x84074))+~E(f326(f326(f101(f917(x84072,a905)),x84074),x84075),f188(f917(x84072,a905)))+E(f326(f326(f80(x84071),f326(f326(f11(x84072,x84071),x84073),x84074)),f326(f326(f11(x84072,x84071),x84073),x84075)),f326(f326(f11(x84072,x84071),x84073),f326(f326(f110(f917(x84072,a905)),x84074),x84075)))
% 157.55/157.23 [8505]~P63(x85053)+E(f326(x85051,x85052),f2(x85053))+~P105(f326(f61(x85054),x85055))+E(f326(f326(f11(x85054,x85053),x85051),f326(f326(f3(f917(x85054,a905)),x85055),f326(f326(f308(x85054),x85052),f188(f917(x85054,a905))))),f326(f326(f290(x85053),f326(f326(f11(x85054,x85053),x85051),x85055)),f326(x85051,x85052)))+~P105(f326(f326(f328(x85054),x85052),x85055))
% 157.55/157.23 [9222]~P7(x92221,x92225,x92224)+~E(f326(f326(f60(x92221),f326(f326(f308(x92221),x92222),f188(f917(x92221,a905)))),x92224),f326(f326(f60(x92221),f326(f326(f308(x92221),x92223),f188(f917(x92221,a905)))),x92224))+~P105(f326(f326(f328(x92221),x92223),x92225))+~P105(f326(f326(f328(x92221),x92222),x92225))+P105(f326(f326(f328(f916(x92221,x92221)),f326(f326(f251(x92221,x92221),x92222),x92223)),x92224))
% 157.55/157.23 [9244]~P7(x92441,x92445,x92443)+E(f326(f326(f60(x92441),f326(f326(f308(x92441),x92442),f188(f917(x92441,a905)))),x92443),f326(f326(f60(x92441),f326(f326(f308(x92441),x92444),f188(f917(x92441,a905)))),x92443))+~P105(f326(f326(f328(x92441),x92444),x92445))+~P105(f326(f326(f328(x92441),x92442),x92445))+~P105(f326(f326(f328(f916(x92441,x92441)),f326(f326(f251(x92441,x92441),x92442),x92444)),x92443))
% 157.55/157.23 [9535]~P74(x95351)+~P105(f326(f61(x95352),x95355))+~P105(f326(f61(x95352),x95354))+~E(f326(f326(f101(f917(x95352,a905)),x95354),x95355),f188(f917(x95352,a905)))+E(f326(f326(f80(x95351),f326(f326(f326(f65(x95351,x95352,f80(x95351)),x95353),f77(x95351)),x95354)),f326(f326(f326(f65(x95351,x95352,f80(x95351)),x95353),f77(x95351)),x95355)),f326(f326(f326(f65(x95351,x95352,f80(x95351)),x95353),f77(x95351)),f326(f326(f110(f917(x95352,a905)),x95354),x95355)))
% 157.55/157.23 [9544]~P69(x95441)+~E(f326(x95443,f879(x95443,x95445,x95444,x95442,x95441)),f2(x95441))+~P105(f326(f61(x95442),x95444))+~P105(f326(f61(x95442),x95445))+E(f326(f326(f79(x95441),f326(f326(f8(x95442,x95441),x95443),x95444)),f326(f326(f8(x95442,x95441),x95443),x95445)),f326(f326(f8(x95442,x95441),x95443),f326(f326(f110(f917(x95442,a905)),x95444),x95445)))
% 157.55/157.23 [9545]~P69(x95451)+~E(f326(x95453,f880(x95453,x95455,x95454,x95452,x95451)),f2(x95451))+~P105(f326(f61(x95452),x95454))+~P105(f326(f61(x95452),x95455))+E(f326(f326(f79(x95451),f326(f326(f8(x95452,x95451),x95453),x95454)),f326(f326(f8(x95452,x95451),x95453),x95455)),f326(f326(f8(x95452,x95451),x95453),f326(f326(f110(f917(x95452,a905)),x95454),x95455)))
% 157.55/157.23 [9546]~P74(x95461)+~E(f326(x95463,f806(x95463,x95465,x95464,x95462,x95461)),f77(x95461))+~P105(f326(f61(x95462),x95464))+~P105(f326(f61(x95462),x95465))+E(f326(f326(f80(x95461),f326(f326(f11(x95462,x95461),x95463),x95464)),f326(f326(f11(x95462,x95461),x95463),x95465)),f326(f326(f11(x95462,x95461),x95463),f326(f326(f110(f917(x95462,a905)),x95464),x95465)))
% 157.55/157.23 [9547]~P74(x95471)+~E(f326(x95473,f822(x95473,x95475,x95474,x95472,x95471)),f77(x95471))+~P105(f326(f61(x95472),x95474))+~P105(f326(f61(x95472),x95475))+E(f326(f326(f80(x95471),f326(f326(f11(x95472,x95471),x95473),x95474)),f326(f326(f11(x95472,x95471),x95473),x95475)),f326(f326(f11(x95472,x95471),x95473),f326(f326(f110(f917(x95472,a905)),x95474),x95475)))
% 157.55/157.23 [9757]~P74(x97571)+~E(f326(x97573,f854(x97573,x97575,x97574,x97572,x97571)),f77(x97571))+~P105(f326(f61(x97572),x97574))+~P105(f326(f61(x97572),x97575))+E(f326(f326(f80(x97571),f326(f326(f326(f65(x97571,x97572,f80(x97571)),x97573),f77(x97571)),x97574)),f326(f326(f326(f65(x97571,x97572,f80(x97571)),x97573),f77(x97571)),x97575)),f326(f326(f326(f65(x97571,x97572,f80(x97571)),x97573),f77(x97571)),f326(f326(f110(f917(x97572,a905)),x97574),x97575)))
% 157.55/157.23 [9868]~P69(x98682)+E(f326(f326(f8(x98681,x98682),x98683),x98684),f326(f326(f8(x98681,x98682),x98683),x98685))+~P105(f326(f61(x98681),x98685))+~P105(f326(f326(f234(f917(x98681,a905)),x98684),x98685))+P105(f326(f326(f328(x98681),f886(x98683,x98684,x98685,x98681,x98682)),f326(f326(f3(f917(x98681,a905)),x98685),x98684)))
% 157.55/157.23 [9869]~P69(x98692)+E(f326(f326(f8(x98691,x98692),x98693),x98694),f326(f326(f8(x98691,x98692),x98693),x98695))+~P105(f326(f61(x98691),x98695))+~P105(f326(f326(f234(f917(x98691,a905)),x98694),x98695))+P105(f326(f326(f328(x98691),f887(x98693,x98694,x98695,x98691,x98692)),f326(f326(f3(f917(x98691,a905)),x98695),x98694)))
% 157.55/157.23 [9870]~P74(x98702)+E(f326(f326(f11(x98701,x98702),x98703),x98704),f326(f326(f11(x98701,x98702),x98703),x98705))+~P105(f326(f61(x98701),x98705))+~P105(f326(f326(f234(f917(x98701,a905)),x98704),x98705))+P105(f326(f326(f328(x98701),f829(x98703,x98704,x98705,x98701,x98702)),f326(f326(f3(f917(x98701,a905)),x98705),x98704)))
% 157.55/157.23 [9871]~P74(x98712)+E(f326(f326(f11(x98711,x98712),x98713),x98714),f326(f326(f11(x98711,x98712),x98713),x98715))+~P105(f326(f61(x98711),x98715))+~P105(f326(f326(f234(f917(x98711,a905)),x98714),x98715))+P105(f326(f326(f328(x98711),f834(x98713,x98714,x98715,x98711,x98712)),f326(f326(f3(f917(x98711,a905)),x98715),x98714)))
% 157.55/157.23 [9889]~P69(x98891)+~P105(f326(f61(x98892),x98894))+~P105(f326(f61(x98892),x98895))+E(f326(f326(f79(x98891),f326(f326(f8(x98892,x98891),x98893),x98894)),f326(f326(f8(x98892,x98891),x98893),x98895)),f326(f326(f8(x98892,x98891),x98893),f326(f326(f110(f917(x98892,a905)),x98894),x98895)))+P105(f326(f326(f328(x98892),f879(x98893,x98895,x98894,x98892,x98891)),f326(f326(f101(f917(x98892,a905)),x98894),x98895)))
% 157.55/157.23 [9890]~P69(x98901)+~P105(f326(f61(x98902),x98904))+~P105(f326(f61(x98902),x98905))+E(f326(f326(f79(x98901),f326(f326(f8(x98902,x98901),x98903),x98904)),f326(f326(f8(x98902,x98901),x98903),x98905)),f326(f326(f8(x98902,x98901),x98903),f326(f326(f110(f917(x98902,a905)),x98904),x98905)))+P105(f326(f326(f328(x98902),f880(x98903,x98905,x98904,x98902,x98901)),f326(f326(f101(f917(x98902,a905)),x98904),x98905)))
% 157.55/157.23 [9891]~P74(x98911)+~P105(f326(f61(x98912),x98914))+~P105(f326(f61(x98912),x98915))+E(f326(f326(f80(x98911),f326(f326(f11(x98912,x98911),x98913),x98914)),f326(f326(f11(x98912,x98911),x98913),x98915)),f326(f326(f11(x98912,x98911),x98913),f326(f326(f110(f917(x98912,a905)),x98914),x98915)))+P105(f326(f326(f328(x98912),f806(x98913,x98915,x98914,x98912,x98911)),f326(f326(f101(f917(x98912,a905)),x98914),x98915)))
% 157.55/157.23 [9892]~P74(x98921)+~P105(f326(f61(x98922),x98924))+~P105(f326(f61(x98922),x98925))+E(f326(f326(f80(x98921),f326(f326(f11(x98922,x98921),x98923),x98924)),f326(f326(f11(x98922,x98921),x98923),x98925)),f326(f326(f11(x98922,x98921),x98923),f326(f326(f110(f917(x98922,a905)),x98924),x98925)))+P105(f326(f326(f328(x98922),f822(x98923,x98925,x98924,x98922,x98921)),f326(f326(f101(f917(x98922,a905)),x98924),x98925)))
% 157.55/157.23 [9898]~P88(x98985)+~P105(f326(f61(x98981),x98984))+P105(f326(f326(f234(x98985),f326(f326(f8(x98981,x98985),x98982),x98983)),f326(f326(f8(x98981,x98985),x98982),x98984)))+~P105(f326(f326(f234(f917(x98981,a905)),x98983),x98984))+P105(f326(f326(f328(x98981),f878(x98982,x98983,x98984,x98981,x98985)),f326(f326(f3(f917(x98981,a905)),x98984),x98983)))
% 157.55/157.23 [9942]~P74(x99421)+~P105(f326(f61(x99422),x99424))+~P105(f326(f61(x99422),x99425))+E(f326(f326(f80(x99421),f326(f326(f326(f65(x99421,x99422,f80(x99421)),x99423),f77(x99421)),x99424)),f326(f326(f326(f65(x99421,x99422,f80(x99421)),x99423),f77(x99421)),x99425)),f326(f326(f326(f65(x99421,x99422,f80(x99421)),x99423),f77(x99421)),f326(f326(f110(f917(x99422,a905)),x99424),x99425)))+P105(f326(f326(f328(x99422),f854(x99423,x99425,x99424,x99422,x99421)),f326(f326(f101(f917(x99422,a905)),x99424),x99425)))
% 157.55/157.23 [8912]~P17(x89121,x89124,x89125)+~P105(f326(f61(x89121),x89122))+E(f326(f326(f3(f917(x89121,a905)),x89122),f326(f326(f308(x89121),x89123),f188(f917(x89121,a905)))),f188(f917(x89121,a905)))+~P105(f326(f326(f328(x89121),x89123),x89122))+E(f326(f326(x89124,x89123),f326(x89125,f326(f326(f3(f917(x89121,a905)),x89122),f326(f326(f308(x89121),x89123),f188(f917(x89121,a905)))))),f326(x89125,x89122))
% 157.55/157.23 [8990]~P17(x89901,x89904,x89905)+~P105(f326(f61(x89901),x89903))+~P105(f326(f61(x89901),x89902))+E(f326(f326(f101(f917(x89901,a905)),x89902),x89903),f188(f917(x89901,a905)))+E(f326(f326(x89904,f326(x89905,f326(f326(f110(f917(x89901,a905)),x89902),x89903))),f326(x89905,f326(f326(f101(f917(x89901,a905)),x89902),x89903))),f326(f326(x89904,f326(x89905,x89902)),f326(x89905,x89903)))
% 157.55/157.23 [9549]~P105(f326(f326(f234(a1),x95494),f2(a1)))+~P105(f326(f326(f235(a1),x95493),x95495))+P105(f326(f326(f234(a1),x95491),x95492))+~P105(f326(f326(f235(a1),x95493),x95494))+~P105(f326(f326(f234(a1),f326(f326(f79(a1),f326(f326(f80(a1),x95493),x95492)),x95495)),f326(f326(f79(a1),f326(f326(f80(a1),x95493),x95491)),x95494)))
% 157.55/157.23 [9551]~P105(f326(f326(f234(a1),f2(a1)),x95515))+P105(f326(f326(f234(a1),x95511),x95512))+~P105(f326(f326(f235(a1),x95513),x95514))+~P105(f326(f326(f235(a1),x95515),x95514))+~P105(f326(f326(f234(a1),f326(f326(f79(a1),f326(f326(f80(a1),x95514),x95511)),x95515)),f326(f326(f79(a1),f326(f326(f80(a1),x95514),x95512)),x95513)))
% 157.55/157.23 [9666]~P63(x96665)+E(f326(x96661,f888(x96661,x96662,x96663,x96664,x96665)),f2(x96665))+~P105(f326(f61(x96664),x96663))+~P105(f326(f61(x96664),x96662))+E(f326(f326(f290(x96665),f326(f326(f80(x96665),f326(f326(f11(x96664,x96665),x96661),x96663)),f326(f326(f11(x96664,x96665),x96661),x96662))),f326(f326(f11(x96664,x96665),x96661),f326(f326(f101(f917(x96664,a905)),x96663),x96662))),f326(f326(f11(x96664,x96665),x96661),f326(f326(f110(f917(x96664,a905)),x96663),x96662)))
% 157.55/157.23 [9934]~P63(x99341)+~P105(f326(f61(x99342),x99344))+~P105(f326(f61(x99342),x99345))+E(f326(f326(f290(x99341),f326(f326(f80(x99341),f326(f326(f11(x99342,x99341),x99343),x99344)),f326(f326(f11(x99342,x99341),x99343),x99345))),f326(f326(f11(x99342,x99341),x99343),f326(f326(f101(f917(x99342,a905)),x99344),x99345))),f326(f326(f11(x99342,x99341),x99343),f326(f326(f110(f917(x99342,a905)),x99344),x99345)))+P105(f326(f326(f328(x99342),f888(x99343,x99345,x99344,x99342,x99341)),f326(f326(f101(f917(x99342,a905)),x99344),x99345)))
% 157.55/157.23 [9263]E(f326(f326(f134(x92631),x92632),x92633),f326(f326(f134(x92631),x92634),x92635))+~E(f326(f326(f175(x92631),f326(f189(f910(x92631)),x92634)),x92632),x92634)+~E(f326(f326(f175(x92631),f326(f189(f910(x92631)),x92632)),x92634),x92632)+~E(x92635,f326(f326(f134(x92631),f326(f326(f138(x92631),f326(f189(f910(x92631)),x92634)),x92632)),x92633))+~E(f326(f326(f134(x92631),f326(f326(f138(x92631),f326(f189(f910(x92631)),x92632)),x92634)),x92635),x92633)
% 157.55/157.23 [9664]~P108(x96642)+E(f326(f326(f148(x96641,x96642,x96643),x96644),f170(x96641,x96644,x96645)),x96645)+~P12(x96642,f326(f326(f154(x96641,x96642),x96643),x96645))+~P105(f326(f326(f328(x96641),x96644),f326(f172(x96641),x96645)))+~E(f326(f141(x96641),f326(f136(x96641,f326(f326(f10(x96642,a905,x96641),f326(a323,f326(x96643,x96644))),x96643)),x96645)),x96644)
% 157.55/157.23 [9998]~P67(x99981)+~P105(f326(f66(x99981,x99981,f80(x99981),x99982,x99983),x99985))+~P105(f326(f326(f328(x99981),x99984),x99983))+P105(f326(f326(f328(x99981),x99982),x99983))+P105(f326(f66(x99981,x99981,f80(x99981),x99984,f326(f326(f308(x99981),x99982),f326(f326(f3(f917(x99981,a905)),x99983),f326(f326(f308(x99981),x99984),f188(f917(x99981,a905)))))),x99985))
% 157.55/157.23 [7423]E(x74231,x74232)+~P24(x74234,x74235,x74233,x74236)+~E(f326(x74233,x74231),f326(x74233,x74232))+~P105(f326(f326(f328(x74234),x74232),x74236))+~P105(f326(f326(f328(x74234),x74231),x74236))
% 157.55/157.23 [6678]~P137(x66784)+E(x66781,x66782)+~E(x66785,x66786)+E(x66783,f2(x66784))+~E(f326(f326(f79(x66784),x66785),f326(f326(f80(x66784),x66783),x66781)),f326(f326(f79(x66784),x66786),f326(f326(f80(x66784),x66783),x66782)))
% 157.55/157.23 [7708]~P108(x77081)+~P4(x77081)+~P105(f326(f326(f235(x77081),x77082),f326(x77085,x77086)))+~P105(f326(f326(f328(x77083),x77086),x77084))+P105(f326(f326(f235(x77081),x77082),f326(f326(f40(x77083,x77081),x77084),x77085)))
% 157.55/157.23 [9994]~P24(x99942,x99941,x99943,x99944)+~P24(x99941,x99942,x99946,x99945)+P25(x99941,x99942,f821(x99943,x99944,x99945,x99946,x99942,x99941),x99945,x99944)+~P105(f326(f326(f234(f917(x99942,a905)),f326(f309(x99941,x99942,x99946),x99945)),x99944))+~P105(f326(f326(f234(f917(x99941,a905)),f326(f309(x99942,x99941,x99943),x99944)),x99945))
% 157.55/157.23 [8376]~P108(x83761)+~P4(x83761)+~P105(f326(f326(f235(x83761),f326(x83764,x83766)),x83765))+~P105(f326(f326(f328(x83762),x83766),x83763))+P105(f326(f326(f235(x83761),f326(f326(f39(x83762,x83761),x83763),x83764)),x83765))
% 157.55/157.23 [8627]~P18(x86272,x86275,x86276,x86271)+~P105(f326(f61(x86272),x86274))+~P105(f326(f61(x86272),x86273))+~E(f326(f326(f101(f917(x86272,a905)),x86273),x86274),f188(f917(x86272,a905)))+E(f326(x86271,f326(f326(f110(f917(x86272,a905)),x86273),x86274)),f326(f72(x86275,x86275,x86275,f326(x86271,x86273)),f326(x86271,x86274)))
% 157.55/157.23 [10207]~P74(x102071)+~E(f809(x102074,x102075,x102073,x102076,x102072,x102071),f810(x102074,x102075,x102073,x102076,x102072,x102071))+~P105(f326(f61(x102072),x102076))+E(f326(f326(f326(f65(x102071,x102072,f80(x102071)),f326(f326(f10(f917(x102073,a905),x102071,x102072),f326(f326(f65(x102071,x102073,f80(x102071)),x102074),f77(x102071))),x102075)),f77(x102071)),x102076),f326(f326(f326(f65(x102071,x102073,f80(x102071)),x102074),f77(x102071)),f326(f326(f40(x102072,f917(x102073,a905)),x102076),x102075)))+P105(f326(f326(f328(x102072),f808(x102074,x102075,x102073,x102076,x102072,x102071)),x102076))
% 157.55/157.23 [10237]~P74(x102371)+~E(f809(x102374,x102375,x102373,x102376,x102372,x102371),f810(x102374,x102375,x102373,x102376,x102372,x102371))+~P105(f326(f61(x102372),x102376))+E(f326(f326(f326(f65(x102371,x102372,f80(x102371)),f326(f326(f10(f917(x102373,a905),x102371,x102372),f326(f326(f65(x102371,x102373,f80(x102371)),x102374),f77(x102371))),x102375)),f77(x102371)),x102376),f326(f326(f326(f65(x102371,x102373,f80(x102371)),x102374),f77(x102371)),f326(f326(f40(x102372,f917(x102373,a905)),x102376),x102375)))+~P105(f326(f61(x102373),f326(x102375,f808(x102374,x102375,x102373,x102376,x102372,x102371))))
% 157.55/157.23 [10240]~P74(x102401)+~P105(f326(f61(x102402),x102406))+E(f326(f326(f326(f65(x102401,x102402,f80(x102401)),f326(f326(f10(f917(x102403,a905),x102401,x102402),f326(f326(f65(x102401,x102403,f80(x102401)),x102404),f77(x102401))),x102405)),f77(x102401)),x102406),f326(f326(f326(f65(x102401,x102403,f80(x102401)),x102404),f77(x102401)),f326(f326(f40(x102402,f917(x102403,a905)),x102406),x102405)))+P105(f326(f326(f328(x102402),f808(x102404,x102405,x102403,x102406,x102402,x102401)),x102406))+P105(f326(f326(f328(x102402),f810(x102404,x102405,x102403,x102406,x102402,x102401)),x102406))
% 157.55/157.23 [10241]~P74(x102411)+~P105(f326(f61(x102412),x102416))+E(f326(f326(f326(f65(x102411,x102412,f80(x102411)),f326(f326(f10(f917(x102413,a905),x102411,x102412),f326(f326(f65(x102411,x102413,f80(x102411)),x102414),f77(x102411))),x102415)),f77(x102411)),x102416),f326(f326(f326(f65(x102411,x102413,f80(x102411)),x102414),f77(x102411)),f326(f326(f40(x102412,f917(x102413,a905)),x102416),x102415)))+P105(f326(f326(f328(x102412),f808(x102414,x102415,x102413,x102416,x102412,x102411)),x102416))+P105(f326(f326(f328(x102412),f809(x102414,x102415,x102413,x102416,x102412,x102411)),x102416))
% 157.55/157.23 [10259]~P74(x102591)+~P105(f326(f61(x102592),x102596))+E(f326(f326(f326(f65(x102591,x102592,f80(x102591)),f326(f326(f10(f917(x102593,a905),x102591,x102592),f326(f326(f65(x102591,x102593,f80(x102591)),x102594),f77(x102591))),x102595)),f77(x102591)),x102596),f326(f326(f326(f65(x102591,x102593,f80(x102591)),x102594),f77(x102591)),f326(f326(f40(x102592,f917(x102593,a905)),x102596),x102595)))+P105(f326(f326(f328(x102592),f810(x102594,x102595,x102593,x102596,x102592,x102591)),x102596))+~P105(f326(f61(x102593),f326(x102595,f808(x102594,x102595,x102593,x102596,x102592,x102591))))
% 157.55/157.23 [10260]~P74(x102601)+~P105(f326(f61(x102602),x102606))+E(f326(f326(f326(f65(x102601,x102602,f80(x102601)),f326(f326(f10(f917(x102603,a905),x102601,x102602),f326(f326(f65(x102601,x102603,f80(x102601)),x102604),f77(x102601))),x102605)),f77(x102601)),x102606),f326(f326(f326(f65(x102601,x102603,f80(x102601)),x102604),f77(x102601)),f326(f326(f40(x102602,f917(x102603,a905)),x102606),x102605)))+P105(f326(f326(f328(x102602),f809(x102604,x102605,x102603,x102606,x102602,x102601)),x102606))+~P105(f326(f61(x102603),f326(x102605,f808(x102604,x102605,x102603,x102606,x102602,x102601))))
% 157.55/157.23 [10271]~P74(x102711)+~E(f326(f326(f101(f917(x102713,a905)),f326(x102715,f810(x102714,x102715,x102713,x102716,x102712,x102711))),f326(x102715,f809(x102714,x102715,x102713,x102716,x102712,x102711))),f188(f917(x102713,a905)))+~P105(f326(f61(x102712),x102716))+E(f326(f326(f326(f65(x102711,x102712,f80(x102711)),f326(f326(f10(f917(x102713,a905),x102711,x102712),f326(f326(f65(x102711,x102713,f80(x102711)),x102714),f77(x102711))),x102715)),f77(x102711)),x102716),f326(f326(f326(f65(x102711,x102713,f80(x102711)),x102714),f77(x102711)),f326(f326(f40(x102712,f917(x102713,a905)),x102716),x102715)))+P105(f326(f326(f328(x102712),f808(x102714,x102715,x102713,x102716,x102712,x102711)),x102716))
% 157.55/157.23 [10282]~P74(x102821)+~E(f326(f326(f101(f917(x102823,a905)),f326(x102825,f810(x102824,x102825,x102823,x102826,x102822,x102821))),f326(x102825,f809(x102824,x102825,x102823,x102826,x102822,x102821))),f188(f917(x102823,a905)))+~P105(f326(f61(x102822),x102826))+E(f326(f326(f326(f65(x102821,x102822,f80(x102821)),f326(f326(f10(f917(x102823,a905),x102821,x102822),f326(f326(f65(x102821,x102823,f80(x102821)),x102824),f77(x102821))),x102825)),f77(x102821)),x102826),f326(f326(f326(f65(x102821,x102823,f80(x102821)),x102824),f77(x102821)),f326(f326(f40(x102822,f917(x102823,a905)),x102826),x102825)))+~P105(f326(f61(x102823),f326(x102825,f808(x102824,x102825,x102823,x102826,x102822,x102821))))
% 157.55/157.23 [8960]E(x89601,x89602)+~P55(x89604,x89605,x89606,x89603,x89607)+~E(f326(x89603,x89601),f326(x89603,x89602))+~P105(f326(f326(f328(x89605),x89602),x89607))+~P105(f326(f326(f328(x89605),x89601),x89607))
% 157.55/157.23 [10249]~P105(f326(x102492,x102494))+~E(x102495,f326(f136(x102491,x102492),x102497))+E(f326(f136(x102491,x102492),x102493),f326(f326(f151(x102491),x102494),x102495))+~E(x102493,f326(f326(f134(x102491),x102496),f326(f326(f151(x102491),x102494),x102497)))+P105(f326(x102492,f742(x102495,x102494,x102493,x102492,x102491,x102496,x102497)))
% 157.55/157.23 [10250]~P105(f326(x102504,x102502))+~E(x102503,f326(f136(x102501,x102504),x102507))+E(f326(f326(f151(x102501),x102502),x102503),f326(f136(x102501,x102504),x102505))+~E(x102505,f326(f326(f134(x102501),x102506),f326(f326(f151(x102501),x102502),x102507)))+P105(f326(x102504,f741(x102505,x102504,x102503,x102502,x102501,x102506,x102507)))
% 157.55/157.23 [10294]~P105(f326(x102942,x102944))+~E(x102945,f326(f136(x102941,x102942),x102947))+E(f326(f136(x102941,x102942),x102943),f326(f326(f151(x102941),x102944),x102945))+~E(x102943,f326(f326(f134(x102941),x102946),f326(f326(f151(x102941),x102944),x102947)))+P105(f326(f326(f328(x102941),f742(x102945,x102944,x102943,x102942,x102941,x102946,x102947)),f326(f172(x102941),x102946)))
% 157.55/157.23 [10295]~P105(f326(x102954,x102952))+~E(x102953,f326(f136(x102951,x102954),x102957))+E(f326(f326(f151(x102951),x102952),x102953),f326(f136(x102951,x102954),x102955))+~E(x102955,f326(f326(f134(x102951),x102956),f326(f326(f151(x102951),x102952),x102957)))+P105(f326(f326(f328(x102951),f741(x102955,x102954,x102953,x102952,x102951,x102956,x102957)),f326(f172(x102951),x102956)))
% 157.55/157.23 [10299]~P7(x102991,x102997,x102996)+~P10(x102991,f917(x102995,a905),x102996,x102994)+P105(f326(f326(f328(x102991),f511(x102992,x102993,x102994,x102995,x102996,x102997,x102991)),x102997))+~P105(f326(f326(f328(f917(x102991,a905)),x102993),f326(f326(f60(x102991),x102997),x102996)))+P105(f326(f326(f328(f917(x102995,a905)),f326(f326(f40(x102991,f917(x102995,a905)),x102993),x102994)),x102992))
% 157.55/157.23 [10357]~P7(x103572,x103576,x103577)+~P10(x103572,f917(x103571,a905),x103577,x103574)+~P105(f326(f326(f328(f917(x103572,a905)),x103573),f326(f326(f60(x103572),x103576),x103577)))+~P105(f326(f326(f328(f917(x103571,a905)),f326(x103574,f511(x103575,x103573,x103574,x103571,x103577,x103576,x103572))),x103575))+P105(f326(f326(f328(f917(x103571,a905)),f326(f326(f40(x103572,f917(x103571,a905)),x103573),x103574)),x103575))
% 157.55/157.23 [8547]~P74(x85472)+~P24(x85471,x85475,x85478,x85474)+~E(x85473,f326(f72(x85475,x85472,x85471,x85476),x85478))+~E(x85477,f326(f309(x85471,x85475,x85478),x85474))+E(f326(f326(f11(x85471,x85472),x85473),x85474),f326(f326(f11(x85475,x85472),x85476),x85477))
% 157.55/157.23 [10361]~P74(x103612)+~P24(x103615,x103611,x103618,x103617)+~E(f326(x103616,f589(x103613,x103616,x103614,x103617,x103618,x103611,x103615,x103612)),f326(f326(f72(x103611,x103612,x103615,x103613),x103618),f589(x103613,x103616,x103614,x103617,x103618,x103611,x103615,x103612)))+~E(x103614,f326(f309(x103615,x103611,x103618),x103617))+E(f326(f326(f11(x103611,x103612),x103613),x103614),f326(f326(f11(x103615,x103612),x103616),x103617))
% 157.55/157.23 [10364]~P69(x103642)+~P24(x103641,x103645,x103648,x103644)+~E(x103647,f326(f309(x103641,x103645,x103648),x103644))+E(f326(f326(f8(x103641,x103642),x103643),x103644),f326(f326(f8(x103645,x103642),x103646),x103647))+P105(f326(f326(f328(x103641),f605(x103646,x103643,x103647,x103644,x103648,x103645,x103641,x103642)),x103644))
% 157.55/157.23 [10365]~P74(x103652)+~P24(x103651,x103655,x103658,x103654)+~E(x103657,f326(f309(x103651,x103655,x103658),x103654))+E(f326(f326(f11(x103651,x103652),x103653),x103654),f326(f326(f11(x103655,x103652),x103656),x103657))+P105(f326(f326(f328(x103651),f589(x103656,x103653,x103657,x103654,x103658,x103655,x103651,x103652)),x103654))
% 157.55/157.23 [10370]~P69(x103702)+~P24(x103705,x103701,x103708,x103707)+~E(x103704,f326(f309(x103705,x103701,x103708),x103707))+~E(f326(x103706,f605(x103703,x103706,x103704,x103707,x103708,x103701,x103705,x103702)),f326(x103703,f326(x103708,f605(x103703,x103706,x103704,x103707,x103708,x103701,x103705,x103702))))+E(f326(f326(f8(x103701,x103702),x103703),x103704),f326(f326(f8(x103705,x103702),x103706),x103707))
% 157.55/157.23 [9831]~P22(x98316,x98312,x98315,x98317,x98318,x98311)+~P105(f326(f61(x98312),x98314))+~P105(f326(f61(x98312),x98313))+~E(f326(f326(f101(f917(x98312,a905)),x98313),x98314),f188(f917(x98312,a905)))+E(f326(x98311,f326(f326(f110(f917(x98312,a905)),x98313),x98314)),f326(f326(x98315,f326(x98311,x98313)),f326(x98311,x98314)))
% 157.55/157.23 [10234]~P22(x102348,x102342,x102345,x102347,x102346,x102341)+~E(f326(x102346,f665(x102344,x102343,x102341,x102346,x102347,x102345,x102342)),x102347)+~P105(f326(f61(x102342),x102343))+~P105(f326(f61(x102342),x102344))+E(f326(x102341,f326(f326(f110(f917(x102342,a905)),x102343),x102344)),f326(f326(x102345,f326(x102341,x102343)),f326(x102341,x102344)))
% 157.55/157.23 [10306]~P22(x103068,x103062,x103065,x103067,x103066,x103061)+~P105(f326(f61(x103062),x103063))+~P105(f326(f61(x103062),x103064))+E(f326(x103061,f326(f326(f110(f917(x103062,a905)),x103063),x103064)),f326(f326(x103065,f326(x103061,x103063)),f326(x103061,x103064)))+P105(f326(f326(f328(x103062),f665(x103064,x103063,x103061,x103066,x103067,x103065,x103062)),f326(f326(f101(f917(x103062,a905)),x103063),x103064)))
% 157.55/157.23 [9985]~P7(x99854,x99858,x99855)+~P7(x99851,x99859,x99853)+~P11(x99851,x99854,f917(x99852,a905),x99853,x99855,x99857)+P10(x99851,f917(x99852,a905),x99853,f326(f326(f10(f917(x99854,f917(x99852,a905)),f917(x99852,a905),x99851),f326(f40(x99854,f917(x99852,a905)),f326(f284(x99854,x99854,x99855),f326(f326(f308(x99854),x99856),f188(f917(x99854,a905)))))),x99857))+~P105(f326(f326(f328(x99854),x99856),x99858))
% 157.55/157.23 [5575]~P108(x55753)+~P12(x55753,x55751)+E(x55751,f719(x55752,x55753))+~E(f326(f172(x55753),x55751),x55752)+~P105(f326(f61(x55753),x55752))+~P105(f326(f137(x55753),x55751))
% 157.55/157.23 [7414]P14(x74141,x74142)+~E(f326(x74142,f800(x74142)),f326(x74142,f801(x74142)))+~P105(f326(f326(x74142,f800(x74142)),f800(x74142)))+~P105(f326(f326(x74142,f800(x74142)),f801(x74142)))+~P105(f326(f326(x74142,f801(x74142)),f801(x74142)))+~P105(f326(f326(x74142,x74143),x74143))
% 157.55/157.23 [5195]~P130(x51952)+~P132(x51952)+~P142(x51952)+~P115(x51952)+E(x51951,f2(x51952))+~E(f326(f326(f243(x51952),x51951),x51953),f2(x51952))
% 157.55/157.23 [5196]~P130(x51962)+~P132(x51962)+~P142(x51962)+~P115(x51962)+~E(x51961,f2(a909))+~E(f326(f326(f243(x51962),x51963),x51961),f2(x51962))
% 157.55/157.23 [6660]~P88(x66601)+~E(x66603,f2(x66601))+~E(x66602,f2(x66601))+E(f326(f326(f79(x66601),x66602),x66603),f2(x66601))+~P105(f326(f326(f234(x66601),f2(x66601)),x66603))+~P105(f326(f326(f234(x66601),f2(x66601)),x66602))
% 157.55/157.23 [9028]~E(f326(f250(a909,a909),x90283),f2(a909))+~E(x90281,f326(f326(f79(a909),f326(f326(f80(a909),f326(f250(a909,a909),x90283)),x90282)),f326(f255(a909,a909),x90283)))+P105(f326(f48(x90281,x90282),x90283))+~P105(f326(f326(f234(a909),f326(f255(a909,a909),x90283)),f2(a909)))+P105(f326(f326(f235(a909),f2(a909)),x90282))+~P105(f326(f326(f235(a909),x90282),f326(f255(a909,a909),x90283)))
% 157.55/157.23 [9036]E(x90361,f2(a909))+~E(x90362,f326(f326(f79(a909),f326(f326(f80(a909),f326(f250(a909,a909),x90363)),x90361)),f326(f255(a909,a909),x90363)))+P105(f326(f48(x90362,x90361),x90363))+~P105(f326(f326(f235(a909),f2(a909)),x90361))+~P105(f326(f326(f234(a909),f2(a909)),f326(f255(a909,a909),x90363)))+~P105(f326(f326(f235(a909),f326(f255(a909,a909),x90363)),x90361))
% 157.55/157.23 [9054]~E(f326(f250(a909,a909),x90543),f2(a909))+~E(x90541,f326(f326(f79(a909),f326(f326(f80(a909),f326(f250(a909,a909),x90543)),x90542)),f326(f255(a909,a909),x90543)))+P105(f326(f48(x90541,x90542),x90543))+~P105(f326(f326(f235(a909),f2(a909)),x90542))+~P105(f326(f326(f234(a909),f2(a909)),f326(f255(a909,a909),x90543)))+~P105(f326(f326(f235(a909),f326(f255(a909,a909),x90543)),x90542))
% 157.55/157.23 [7043]~P77(x70432)+E(x70431,f188(f917(x70432,a905)))+E(x70433,f188(f917(x70432,a905)))+~P105(f326(f61(x70432),x70431))+~P105(f326(f61(x70432),x70433))+E(f12(x70432,f326(f326(f110(f917(x70432,a905)),x70433),x70431)),f326(f326(f110(x70432),f12(x70432,x70433)),f12(x70432,x70431)))
% 157.55/157.23 [7044]~P77(x70442)+E(x70441,f188(f917(x70442,a905)))+E(x70443,f188(f917(x70442,a905)))+~P105(f326(f61(x70442),x70441))+~P105(f326(f61(x70442),x70443))+E(f13(x70442,f326(f326(f110(f917(x70442,a905)),x70443),x70441)),f326(f326(f101(x70442),f13(x70442,x70443)),f13(x70442,x70441)))
% 157.55/157.23 [7045]~P108(x70452)+E(x70451,f188(f917(x70452,a905)))+E(x70453,f188(f917(x70452,a905)))+~P105(f326(f61(x70452),x70451))+~P105(f326(f61(x70452),x70453))+E(f16(x70452,f326(f326(f110(f917(x70452,a905)),x70453),x70451)),f326(f326(f232(x70452),f16(x70452,x70453)),f16(x70452,x70451)))
% 157.55/157.23 [7046]~P108(x70462)+E(x70461,f188(f917(x70462,a905)))+E(x70463,f188(f917(x70462,a905)))+~P105(f326(f61(x70462),x70461))+~P105(f326(f61(x70462),x70463))+E(f17(x70462,f326(f326(f110(f917(x70462,a905)),x70463),x70461)),f326(f326(f233(x70462),f17(x70462,x70463)),f17(x70462,x70461)))
% 157.55/157.23 [7684]~P96(x76842)+E(x76841,f188(f917(x76842,a905)))+E(x76843,f188(f917(x76842,a905)))+~P105(f326(f61(x76842),x76841))+~P105(f326(f61(x76842),x76843))+E(f326(f326(f80(x76842),f326(f63(x76842,f80(x76842)),x76843)),f326(f63(x76842,f80(x76842)),x76841)),f326(f63(x76842,f80(x76842)),f326(f326(f110(f917(x76842,a905)),x76843),x76841)))
% 157.55/157.23 [7841]~P108(x78412)+E(x78411,f188(f917(x78412,a905)))+E(x78413,f188(f917(x78412,a905)))+~P105(f326(f61(x78412),x78411))+~P105(f326(f61(x78412),x78413))+E(f326(f326(f232(x78412),f14(x78412,f232(x78412),x78413)),f14(x78412,f232(x78412),x78411)),f14(x78412,f232(x78412),f326(f326(f110(f917(x78412,a905)),x78413),x78411)))
% 157.55/157.23 [7842]~P108(x78422)+E(x78421,f188(f917(x78422,a905)))+E(x78423,f188(f917(x78422,a905)))+~P105(f326(f61(x78422),x78421))+~P105(f326(f61(x78422),x78423))+E(f326(f326(f233(x78422),f15(x78422,f233(x78422),x78423)),f15(x78422,f233(x78422),x78421)),f15(x78422,f233(x78422),f326(f326(f110(f917(x78422,a905)),x78423),x78421)))
% 157.55/157.23 [8861]~P105(f326(x88611,x88613))+P105(f326(x88611,f456(x88611,x88612)))+P105(f326(x88611,f449(x88611,x88612)))+~P105(f326(f326(f235(a1),f2(a1)),x88612))+~P105(f326(f326(f328(a1),x88613),f302(a1,f77(a1),x88612)))+P105(f326(x88611,f326(f326(f3(a1),f449(x88611,x88612)),f326(f326(f80(a1),f455(x88611,x88612)),x88612))))
% 157.55/157.23 [9162]~P105(f326(x91621,x91623))+~P105(f326(x91621,f449(x91621,x91622)))+P105(f326(x91621,f456(x91621,x91622)))+~P105(f326(f326(f235(a1),f2(a1)),x91622))+~P105(f326(f326(f328(a1),x91623),f302(a1,f77(a1),x91622)))+~P105(f326(x91621,f326(f326(f3(a1),f449(x91621,x91622)),f326(f326(f80(a1),f455(x91621,x91622)),x91622))))
% 157.55/157.23 [10397]~P98(x103972)+E(x103971,f188(f917(x103972,a905)))+E(x103973,f188(f917(x103972,a905)))+~P105(f326(f61(x103972),x103971))+~P105(f326(f61(x103972),x103973))+E(f13(x103972,f326(f261(x103972),f326(f326(f10(f917(x103972,a905),a905,x103972),f86(x103972)),f326(f326(f10(f917(x103972,f917(x103972,a905)),f917(x103972,a905),x103972),f326(f10(f917(x103972,a905),a905,x103972),f86(x103972))),f326(f326(f9(x103972,f917(x103972,f917(x103972,a905)),f917(x103972,f917(x103972,a905))),f326(f326(f10(f917(x103972,f917(f917(x103972,a905),f917(x103972,a905))),f917(f917(x103972,f917(x103972,a905)),f917(x103972,f917(x103972,a905))),x103972),f20(x103972,f917(x103972,a905),f917(x103972,a905))),f326(f326(f10(f917(x103972,f917(x103972,f917(a905,a905))),f917(x103972,f917(f917(x103972,a905),f917(x103972,a905))),x103972),f326(f10(f917(x103972,f917(a905,a905)),f917(f917(x103972,a905),f917(x103972,a905)),x103972),f20(x103972,a905,a905))),f326(f326(f10(f917(x103972,f917(x103972,a905)),f917(x103972,f917(x103972,f917(a905,a905))),x103972),f326(f10(f917(x103972,a905),f917(x103972,f917(a905,a905)),x103972),f326(f10(a905,f917(a905,a905),x103972),a324))),f326(f326(f9(x103972,f917(x103972,f917(x103972,x103972)),f917(x103972,f917(x103972,a905))),f326(f326(f10(f917(f917(x103972,x103972),f917(x103972,a905)),f917(f917(x103972,f917(x103972,x103972)),f917(x103972,f917(x103972,a905))),x103972),f10(f917(x103972,x103972),f917(x103972,a905),x103972)),f326(f326(f10(f917(x103972,a905),f917(f917(x103972,x103972),f917(x103972,a905)),x103972),f10(x103972,a905,x103972)),a323))),f110(x103972)))))),f326(f326(f9(x103972,f917(x103972,a905),f917(x103972,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x103972,a905),f917(x103972,a905)),x103972),f10(a905,a905,x103972)),f326(f326(f10(a905,f917(a905,a905),x103972),a324),f326(f326(f9(x103972,f917(x103972,a905),a905),f328(x103972)),x103973)))),f326(f326(f9(x103972,f917(x103972,a905),a905),f328(x103972)),x103971))))))),f326(f326(f110(x103972),f13(x103972,x103973)),f13(x103972,x103971)))
% 157.55/157.23 [10398]~P98(x103982)+E(x103981,f188(f917(x103982,a905)))+E(x103983,f188(f917(x103982,a905)))+~P105(f326(f61(x103982),x103981))+~P105(f326(f61(x103982),x103983))+E(f12(x103982,f326(f261(x103982),f326(f326(f10(f917(x103982,a905),a905,x103982),f86(x103982)),f326(f326(f10(f917(x103982,f917(x103982,a905)),f917(x103982,a905),x103982),f326(f10(f917(x103982,a905),a905,x103982),f86(x103982))),f326(f326(f9(x103982,f917(x103982,f917(x103982,a905)),f917(x103982,f917(x103982,a905))),f326(f326(f10(f917(x103982,f917(f917(x103982,a905),f917(x103982,a905))),f917(f917(x103982,f917(x103982,a905)),f917(x103982,f917(x103982,a905))),x103982),f20(x103982,f917(x103982,a905),f917(x103982,a905))),f326(f326(f10(f917(x103982,f917(x103982,f917(a905,a905))),f917(x103982,f917(f917(x103982,a905),f917(x103982,a905))),x103982),f326(f10(f917(x103982,f917(a905,a905)),f917(f917(x103982,a905),f917(x103982,a905)),x103982),f20(x103982,a905,a905))),f326(f326(f10(f917(x103982,f917(x103982,a905)),f917(x103982,f917(x103982,f917(a905,a905))),x103982),f326(f10(f917(x103982,a905),f917(x103982,f917(a905,a905)),x103982),f326(f10(a905,f917(a905,a905),x103982),a324))),f326(f326(f9(x103982,f917(x103982,f917(x103982,x103982)),f917(x103982,f917(x103982,a905))),f326(f326(f10(f917(f917(x103982,x103982),f917(x103982,a905)),f917(f917(x103982,f917(x103982,x103982)),f917(x103982,f917(x103982,a905))),x103982),f10(f917(x103982,x103982),f917(x103982,a905),x103982)),f326(f326(f10(f917(x103982,a905),f917(f917(x103982,x103982),f917(x103982,a905)),x103982),f10(x103982,a905,x103982)),a323))),f101(x103982)))))),f326(f326(f9(x103982,f917(x103982,a905),f917(x103982,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x103982,a905),f917(x103982,a905)),x103982),f10(a905,a905,x103982)),f326(f326(f10(a905,f917(a905,a905),x103982),a324),f326(f326(f9(x103982,f917(x103982,a905),a905),f328(x103982)),x103983)))),f326(f326(f9(x103982,f917(x103982,a905),a905),f328(x103982)),x103981))))))),f326(f326(f101(x103982),f12(x103982,x103983)),f12(x103982,x103981)))
% 157.55/157.23 [10399]~P108(x103992)+E(x103991,f188(f917(x103992,a905)))+E(x103993,f188(f917(x103992,a905)))+~P105(f326(f61(x103992),x103991))+~P105(f326(f61(x103992),x103993))+E(f15(x103992,f233(x103992),f326(f261(x103992),f326(f326(f10(f917(x103992,a905),a905,x103992),f86(x103992)),f326(f326(f10(f917(x103992,f917(x103992,a905)),f917(x103992,a905),x103992),f326(f10(f917(x103992,a905),a905,x103992),f86(x103992))),f326(f326(f9(x103992,f917(x103992,f917(x103992,a905)),f917(x103992,f917(x103992,a905))),f326(f326(f10(f917(x103992,f917(f917(x103992,a905),f917(x103992,a905))),f917(f917(x103992,f917(x103992,a905)),f917(x103992,f917(x103992,a905))),x103992),f20(x103992,f917(x103992,a905),f917(x103992,a905))),f326(f326(f10(f917(x103992,f917(x103992,f917(a905,a905))),f917(x103992,f917(f917(x103992,a905),f917(x103992,a905))),x103992),f326(f10(f917(x103992,f917(a905,a905)),f917(f917(x103992,a905),f917(x103992,a905)),x103992),f20(x103992,a905,a905))),f326(f326(f10(f917(x103992,f917(x103992,a905)),f917(x103992,f917(x103992,f917(a905,a905))),x103992),f326(f10(f917(x103992,a905),f917(x103992,f917(a905,a905)),x103992),f326(f10(a905,f917(a905,a905),x103992),a324))),f326(f326(f9(x103992,f917(x103992,f917(x103992,x103992)),f917(x103992,f917(x103992,a905))),f326(f326(f10(f917(f917(x103992,x103992),f917(x103992,a905)),f917(f917(x103992,f917(x103992,x103992)),f917(x103992,f917(x103992,a905))),x103992),f10(f917(x103992,x103992),f917(x103992,a905),x103992)),f326(f326(f10(f917(x103992,a905),f917(f917(x103992,x103992),f917(x103992,a905)),x103992),f10(x103992,a905,x103992)),a323))),f232(x103992)))))),f326(f326(f9(x103992,f917(x103992,a905),f917(x103992,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x103992,a905),f917(x103992,a905)),x103992),f10(a905,a905,x103992)),f326(f326(f10(a905,f917(a905,a905),x103992),a324),f326(f326(f9(x103992,f917(x103992,a905),a905),f328(x103992)),x103993)))),f326(f326(f9(x103992,f917(x103992,a905),a905),f328(x103992)),x103991))))))),f326(f326(f232(x103992),f15(x103992,f233(x103992),x103993)),f15(x103992,f233(x103992),x103991)))
% 157.55/157.23 [10400]~P108(x104002)+E(x104001,f188(f917(x104002,a905)))+E(x104003,f188(f917(x104002,a905)))+~P105(f326(f61(x104002),x104001))+~P105(f326(f61(x104002),x104003))+E(f14(x104002,f232(x104002),f326(f261(x104002),f326(f326(f10(f917(x104002,a905),a905,x104002),f86(x104002)),f326(f326(f10(f917(x104002,f917(x104002,a905)),f917(x104002,a905),x104002),f326(f10(f917(x104002,a905),a905,x104002),f86(x104002))),f326(f326(f9(x104002,f917(x104002,f917(x104002,a905)),f917(x104002,f917(x104002,a905))),f326(f326(f10(f917(x104002,f917(f917(x104002,a905),f917(x104002,a905))),f917(f917(x104002,f917(x104002,a905)),f917(x104002,f917(x104002,a905))),x104002),f20(x104002,f917(x104002,a905),f917(x104002,a905))),f326(f326(f10(f917(x104002,f917(x104002,f917(a905,a905))),f917(x104002,f917(f917(x104002,a905),f917(x104002,a905))),x104002),f326(f10(f917(x104002,f917(a905,a905)),f917(f917(x104002,a905),f917(x104002,a905)),x104002),f20(x104002,a905,a905))),f326(f326(f10(f917(x104002,f917(x104002,a905)),f917(x104002,f917(x104002,f917(a905,a905))),x104002),f326(f10(f917(x104002,a905),f917(x104002,f917(a905,a905)),x104002),f326(f10(a905,f917(a905,a905),x104002),a324))),f326(f326(f9(x104002,f917(x104002,f917(x104002,x104002)),f917(x104002,f917(x104002,a905))),f326(f326(f10(f917(f917(x104002,x104002),f917(x104002,a905)),f917(f917(x104002,f917(x104002,x104002)),f917(x104002,f917(x104002,a905))),x104002),f10(f917(x104002,x104002),f917(x104002,a905),x104002)),f326(f326(f10(f917(x104002,a905),f917(f917(x104002,x104002),f917(x104002,a905)),x104002),f10(x104002,a905,x104002)),a323))),f233(x104002)))))),f326(f326(f9(x104002,f917(x104002,a905),f917(x104002,a905)),f326(f326(f10(f917(a905,a905),f917(f917(x104002,a905),f917(x104002,a905)),x104002),f10(a905,a905,x104002)),f326(f326(f10(a905,f917(a905,a905),x104002),a324),f326(f326(f9(x104002,f917(x104002,a905),a905),f328(x104002)),x104003)))),f326(f326(f9(x104002,f917(x104002,a905),a905),f328(x104002)),x104001))))))),f326(f326(f233(x104002),f14(x104002,f232(x104002),x104003)),f14(x104002,f232(x104002),x104001)))
% 157.55/157.23 [7370]~P124(x73703)+E(x73701,x73702)+~E(f326(f326(f243(x73703),x73701),x73704),f326(f326(f243(x73703),x73702),x73704))+~P105(f326(f326(f234(x73703),f2(x73703)),x73702))+~P105(f326(f326(f234(x73703),f2(x73703)),x73701))+~P105(f326(f326(f235(a909),f2(a909)),x73704))
% 157.55/157.23 [7645]~P108(x76452)+E(x76451,f188(f917(x76452,a905)))+~P105(f326(f61(x76452),x76451))+~P105(f326(f326(f328(x76452),x76454),x76451))+P105(f326(f326(f234(x76452),x76453),x76454))+~P105(f326(f326(f234(x76452),x76453),f326(f63(x76452,f232(x76452)),x76451)))
% 157.55/157.23 [7646]~P101(x76462)+E(x76461,f188(f917(x76462,a905)))+~P105(f326(f61(x76462),x76461))+~P105(f326(f326(f328(x76462),x76464),x76461))+P105(f326(f326(f234(x76462),x76463),x76464))+~P105(f326(f326(f234(x76462),x76463),f326(f63(x76462,f101(x76462)),x76461)))
% 157.55/157.23 [7647]~P108(x76472)+E(x76471,f188(f917(x76472,a905)))+~P105(f326(f61(x76472),x76471))+~P105(f326(f326(f328(x76472),x76474),x76471))+P105(f326(f326(f235(x76472),x76473),x76474))+~P105(f326(f326(f235(x76472),x76473),f326(f63(x76472,f232(x76472)),x76471)))
% 157.55/157.23 [7552]E(x75521,f2(a1))+E(f326(f326(f36(a1),x75522),x75521),x75523)+~P105(f326(f326(f234(a1),x75524),f2(a1)))+~E(x75522,f326(f326(f79(a1),f326(f326(f80(a1),x75521),x75523)),x75524))+P105(f326(f326(f235(a1),f2(a1)),x75521))+~P105(f326(f326(f235(a1),x75521),x75524))
% 157.55/157.23 [7567]E(f45(a1,x75672,x75671),x75673)+E(x75671,f2(a1))+~P105(f326(f326(f234(a1),x75673),f2(a1)))+~E(x75672,f326(f326(f79(a1),f326(f326(f80(a1),x75671),x75674)),x75673))+P105(f326(f326(f235(a1),f2(a1)),x75671))+~P105(f326(f326(f235(a1),x75671),x75673))
% 157.55/157.23 [7683]E(x76831,f2(a1))+E(f326(f326(f36(a1),x76832),x76831),x76833)+~E(x76832,f326(f326(f79(a1),f326(f326(f80(a1),x76831),x76833)),x76834))+~P105(f326(f326(f234(a1),f2(a1)),x76834))+~P105(f326(f326(f235(a1),f2(a1)),x76831))+~P105(f326(f326(f235(a1),x76834),x76831))
% 157.55/157.23 [7704]E(f45(a1,x77042,x77041),x77043)+E(x77041,f2(a1))+~E(x77042,f326(f326(f79(a1),f326(f326(f80(a1),x77041),x77044)),x77043))+~P105(f326(f326(f234(a1),f2(a1)),x77043))+~P105(f326(f326(f235(a1),f2(a1)),x77041))+~P105(f326(f326(f235(a1),x77043),x77041))
% 157.55/157.23 [7845]~P108(x78452)+E(x78451,f188(f917(x78452,a905)))+~P105(f326(f61(x78452),x78451))+~P105(f326(f326(f328(x78452),x78454),x78451))+~P105(f326(f326(f234(x78452),x78454),x78453))+P105(f326(f326(f234(x78452),f326(f63(x78452,f232(x78452)),x78451)),x78453))
% 157.55/157.23 [7846]~P108(x78462)+E(x78461,f188(f917(x78462,a905)))+~P105(f326(f61(x78462),x78461))+~P105(f326(f326(f235(x78462),x78464),x78463))+~P105(f326(f326(f328(x78462),x78464),x78461))+P105(f326(f326(f235(x78462),f326(f63(x78462,f232(x78462)),x78461)),x78463))
% 157.55/157.23 [8400]~P105(f326(f326(f234(a1),x84004),f2(a1)))+~E(x84001,f326(f326(f79(a1),f326(f326(f80(a1),x84002),x84003)),x84004))+~P105(f326(f326(f234(a1),f2(a1)),x84004))+~P105(f326(f326(f235(a1),x84004),x84002))+~P105(f326(f326(f235(a1),x84002),x84004))+P105(f326(f49(x84001,x84002),f326(f326(f251(a1,a1),x84003),x84004)))
% 157.55/157.23 [8566]~P109(x85661)+P105(f326(f326(f235(f917(x85661,a905)),f302(x85661,x85662,x85663)),f302(x85661,x85664,x85665)))+~P105(f326(f326(f234(x85661),x85664),x85662))+~P105(f326(f326(f234(x85661),x85664),x85665))+~P105(f326(f326(f234(x85661),x85663),x85665))+~P105(f326(f326(f235(x85661),x85663),x85665))
% 157.55/157.23 [8567]~P109(x85671)+P105(f326(f326(f235(f917(x85671,a905)),f302(x85671,x85672,x85673)),f302(x85671,x85674,x85675)))+~P105(f326(f326(f234(x85671),x85673),x85675))+~P105(f326(f326(f234(x85671),x85674),x85675))+~P105(f326(f326(f234(x85671),x85674),x85672))+~P105(f326(f326(f235(x85671),x85674),x85672))
% 157.55/157.23 [9419]P57(x94192,x94193,x94194,x94191)+E(x94191,f188(f917(x94192,a905)))+~P105(f326(f61(x94192),x94194))+~P105(f326(f61(x94192),x94191))+~P105(f326(f326(x94193,f522(x94191,x94194,x94193,x94192)),x94195))+~P105(f326(f326(f328(x94192),x94195),x94191))
% 157.55/157.23 [9420]P57(x94202,x94203,x94204,x94201)+E(x94201,f188(f917(x94202,a905)))+~P105(f326(f61(x94202),x94204))+~P105(f326(f61(x94202),x94201))+~P105(f326(f326(x94203,f789(x94203,x94201,x94204,x94202)),x94205))+~P105(f326(f326(f328(x94202),x94205),x94201))
% 157.55/157.23 [9421]P57(x94212,x94213,x94214,x94211)+E(x94211,f188(f917(x94212,a905)))+~P105(f326(f61(x94212),x94214))+~P105(f326(f61(x94212),x94211))+~P105(f326(f326(x94213,f790(x94211,x94214,x94213,x94212)),x94215))+~P105(f326(f326(f328(x94212),x94215),x94211))
% 157.55/157.23 [9567]~E(x95673,x95675)+~P69(x95671)+~P74(x95671)+~P39(x95673)+E(f326(f326(f8(a1,x95671),x95672),x95673),f326(f326(f8(a1,x95671),x95674),x95675))+P105(f326(f326(f234(a1),f2(a1)),f510(x95672,x95674,x95673,x95675,x95671)))
% 157.55/157.23 [9568]~E(x95683,x95685)+~P69(x95681)+~P74(x95681)+~P39(x95683)+E(f326(f326(f11(a1,x95681),x95682),x95683),f326(f326(f11(a1,x95681),x95684),x95685))+P105(f326(f326(f234(a1),f2(a1)),f498(x95682,x95684,x95683,x95685,x95681)))
% 157.55/157.23 [9740]~E(x97405,x97403)+~P69(x97401)+~P74(x97401)+~P39(x97405)+~E(f326(x97402,f510(x97404,x97402,x97405,x97403,x97401)),f326(x97404,f510(x97404,x97402,x97405,x97403,x97401)))+E(f326(f326(f8(a1,x97401),x97402),x97403),f326(f326(f8(a1,x97401),x97404),x97405))
% 157.55/157.23 [9741]~E(x97415,x97413)+~P69(x97411)+~P74(x97411)+~P39(x97415)+~E(f326(x97412,f498(x97414,x97412,x97415,x97413,x97411)),f326(x97414,f498(x97414,x97412,x97415,x97413,x97411)))+E(f326(f326(f11(a1,x97411),x97412),x97413),f326(f326(f11(a1,x97411),x97414),x97415))
% 157.55/157.23 [9829]~P79(x98293)+E(f326(x98291,x98292),f2(x98293))+~E(f326(f326(f8(x98294,x98293),x98291),x98295),f2(x98293))+~P105(f326(f61(x98294),x98295))+P105(f326(f326(f328(x98294),f408(x98292,x98291,x98295,x98294,x98293)),x98295))+~P105(f326(f326(f328(x98294),x98292),x98295))
% 157.55/157.23 [9956]~P79(x99563)+E(f326(x99561,x99562),f2(x99563))+~E(f326(f326(f8(x99564,x99563),x99561),x99565),f2(x99563))+~P105(f326(f61(x99564),x99565))+~P105(f326(f326(f328(x99564),x99562),x99565))+~P105(f326(f326(f234(x99563),f2(x99563)),f326(x99561,f408(x99562,x99561,x99565,x99564,x99563))))
% 157.55/157.23 [8485]~P135(x84851)+~P105(f326(f326(f234(x84851),x84853),x84855))+~P105(f326(f326(f234(x84851),x84852),x84854))+~P105(f326(f326(f234(x84851),f2(x84851)),x84853))+~P105(f326(f326(f234(x84851),f2(x84851)),x84854))+P105(f326(f326(f234(x84851),f326(f326(f80(x84851),x84852),x84853)),f326(f326(f80(x84851),x84854),x84855)))
% 157.55/157.23 [8486]~P135(x84861)+~P105(f326(f326(f234(x84861),x84863),x84865))+~P105(f326(f326(f234(x84861),x84862),x84864))+~P105(f326(f326(f234(x84861),f2(x84861)),x84863))+~P105(f326(f326(f234(x84861),f2(x84861)),x84862))+P105(f326(f326(f234(x84861),f326(f326(f80(x84861),x84862),x84863)),f326(f326(f80(x84861),x84864),x84865)))
% 157.55/157.23 [8487]~P65(x84871)+~P105(f326(f326(f235(x84871),f2(x84871)),x84875))+~P105(f326(f326(f234(x84871),x84875),x84873))+~P105(f326(f326(f234(x84871),x84872),x84874))+~P105(f326(f326(f234(x84871),f2(x84871)),x84872))+P105(f326(f326(f234(x84871),f326(f326(f290(x84871),x84872),x84873)),f326(f326(f290(x84871),x84874),x84875)))
% 157.55/157.23 [8488]~P131(x84881)+~P105(f326(f326(f234(x84881),x84883),x84885))+~P105(f326(f326(f234(x84881),f2(x84881)),x84882))+~P105(f326(f326(f235(x84881),x84882),x84884))+~P105(f326(f326(f235(x84881),f2(x84881)),x84883))+P105(f326(f326(f235(x84881),f326(f326(f80(x84881),x84882),x84883)),f326(f326(f80(x84881),x84884),x84885)))
% 157.55/157.23 [8489]~P131(x84891)+~P105(f326(f326(f234(x84891),x84892),x84894))+~P105(f326(f326(f234(x84891),f2(x84891)),x84893))+~P105(f326(f326(f235(x84891),x84893),x84895))+~P105(f326(f326(f235(x84891),f2(x84891)),x84892))+P105(f326(f326(f235(x84891),f326(f326(f80(x84891),x84892),x84893)),f326(f326(f80(x84891),x84894),x84895)))
% 157.55/157.23 [8490]~P131(x84901)+~P105(f326(f326(f234(x84901),f2(x84901)),x84903))+~P105(f326(f326(f234(x84901),f2(x84901)),x84902))+~P105(f326(f326(f235(x84901),x84903),x84905))+~P105(f326(f326(f235(x84901),x84902),x84904))+P105(f326(f326(f235(x84901),f326(f326(f80(x84901),x84902),x84903)),f326(f326(f80(x84901),x84904),x84905)))
% 157.55/157.23 [8491]~P131(x84911)+~P105(f326(f326(f234(x84911),f2(x84911)),x84913))+~P105(f326(f326(f235(x84911),x84913),x84915))+~P105(f326(f326(f235(x84911),x84912),x84914))+~P105(f326(f326(f235(x84911),f2(x84911)),x84914))+P105(f326(f326(f235(x84911),f326(f326(f80(x84911),x84912),x84913)),f326(f326(f80(x84911),x84914),x84915)))
% 157.55/157.23 [8492]~P65(x84921)+~P105(f326(f326(f234(x84921),x84925),x84923))+~P105(f326(f326(f234(x84921),f2(x84921)),x84922))+~P105(f326(f326(f235(x84921),x84922),x84924))+~P105(f326(f326(f235(x84921),f2(x84921)),x84925))+P105(f326(f326(f235(x84921),f326(f326(f290(x84921),x84922),x84923)),f326(f326(f290(x84921),x84924),x84925)))
% 157.55/157.23 [8493]~P65(x84931)+~P105(f326(f326(f234(x84931),x84932),x84934))+~P105(f326(f326(f235(x84931),x84935),x84933))+~P105(f326(f326(f235(x84931),f2(x84931)),x84935))+~P105(f326(f326(f235(x84931),f2(x84931)),x84932))+P105(f326(f326(f235(x84931),f326(f326(f290(x84931),x84932),x84933)),f326(f326(f290(x84931),x84934),x84935)))
% 157.55/157.23 [9872]~P69(x98725)+~P83(x98725)+E(x98721,f188(f917(x98722,a905)))+~P105(f326(f61(x98722),x98721))+P105(f326(f326(f328(x98722),f610(x98723,x98724,x98721,x98722,x98725)),x98721))+P105(f326(f326(f235(x98725),f326(f326(f8(x98722,x98725),x98724),x98721)),f326(f326(f8(x98722,x98725),x98723),x98721)))
% 157.55/157.23 [9981]~P69(x99811)+~P85(x99811)+~P105(f326(f61(x99812),x99815))+~P105(f326(f326(f234(x99811),f2(x99811)),f326(x99813,f881(x99813,x99814,x99815,x99812,x99811))))+P105(f326(f326(f234(x99811),f326(f326(f8(x99812,x99811),x99813),x99814)),f326(f326(f8(x99812,x99811),x99813),x99815)))+~P105(f326(f326(f234(f917(x99812,a905)),x99814),x99815))
% 157.55/157.23 [10152]~P69(x101523)+~P83(x101523)+E(x101521,f188(f917(x101522,a905)))+~P105(f326(f61(x101522),x101521))+~P105(f326(f326(f235(x101523),f326(x101524,f610(x101525,x101524,x101521,x101522,x101523))),f326(x101525,f610(x101525,x101524,x101521,x101522,x101523))))+P105(f326(f326(f235(x101523),f326(f326(f8(x101522,x101523),x101524),x101521)),f326(f326(f8(x101522,x101523),x101525),x101521)))
% 157.55/157.23 [7227]~P16(x72272,x72275,x72274)+E(x72271,f188(f917(x72272,a905)))+E(x72273,f188(f917(x72272,a905)))+~P105(f326(f61(x72272),x72271))+~P105(f326(f61(x72272),x72273))+E(f326(x72274,f326(f326(f110(f917(x72272,a905)),x72273),x72271)),f326(f326(x72275,f326(x72274,x72273)),f326(x72274,x72271)))
% 157.55/157.23 [7812]~P146(x78121,x78124,x78123)+P105(f326(x78121,x78122))+~P105(f326(f326(f235(a1),x78124),f2(a1)))+~P105(f326(f326(f234(a1),x78125),f2(a1)))+~E(x78123,f326(f326(f79(a1),f326(f326(f80(a1),x78124),x78122)),x78125))+~P105(f326(f326(f235(a1),x78124),x78125))
% 157.55/157.23 [7813]~P145(x78131,x78134,x78133)+P105(f326(x78131,x78132))+~P105(f326(f326(f235(a1),x78134),f2(a1)))+~P105(f326(f326(f234(a1),x78132),f2(a1)))+~E(x78133,f326(f326(f79(a1),f326(f326(f80(a1),x78134),x78135)),x78132))+~P105(f326(f326(f235(a1),x78134),x78132))
% 157.55/157.23 [7854]~P146(x78541,x78544,x78543)+P105(f326(x78541,x78542))+~E(x78543,f326(f326(f79(a1),f326(f326(f80(a1),x78544),x78542)),x78545))+~P105(f326(f326(f234(a1),f2(a1)),x78545))+~P105(f326(f326(f235(a1),f2(a1)),x78544))+~P105(f326(f326(f235(a1),x78545),x78544))
% 157.55/157.23 [7855]~P145(x78551,x78554,x78553)+P105(f326(x78551,x78552))+~E(x78553,f326(f326(f79(a1),f326(f326(f80(a1),x78554),x78555)),x78552))+~P105(f326(f326(f234(a1),f2(a1)),x78552))+~P105(f326(f326(f235(a1),f2(a1)),x78554))+~P105(f326(f326(f235(a1),x78552),x78554))
% 157.55/157.23 [8774]P105(f326(f326(x87741,x87742),x87743))+~P105(f326(f326(x87741,f326(f326(f36(a1),x87744),x87745)),f45(a1,x87744,x87745)))+~P105(f326(f326(f235(a1),x87745),f2(a1)))+~P105(f326(f326(f234(a1),x87743),f2(a1)))+~E(x87744,f326(f326(f79(a1),f326(f326(f80(a1),x87745),x87742)),x87743))+~P105(f326(f326(f235(a1),x87745),x87743))
% 157.55/157.23 [8783]P105(f326(f326(x87831,x87832),x87833))+~P105(f326(f326(x87831,f326(f326(f36(a1),x87834),x87835)),f45(a1,x87834,x87835)))+~E(x87834,f326(f326(f79(a1),f326(f326(f80(a1),x87835),x87832)),x87833))+~P105(f326(f326(f234(a1),f2(a1)),x87833))+~P105(f326(f326(f235(a1),f2(a1)),x87835))+~P105(f326(f326(f235(a1),x87833),x87835))
% 157.55/157.23 [9044]E(x90441,x90442)+~P54(x90443,x90445,x90444)+~P105(f326(f326(f328(x90443),x90442),x90445))+~P105(f326(f326(f328(x90443),x90441),x90445))+P105(f326(f326(f328(f916(x90443,x90443)),f326(f326(f251(x90443,x90443),x90441),x90442)),x90444))+P105(f326(f326(f328(f916(x90443,x90443)),f326(f326(f251(x90443,x90443),x90442),x90441)),x90444))
% 157.55/157.23 [9899]~P69(x98995)+~P85(x98995)+~P105(f326(f61(x98991),x98994))+P105(f326(f326(f234(x98995),f326(f326(f8(x98991,x98995),x98992),x98993)),f326(f326(f8(x98991,x98995),x98992),x98994)))+~P105(f326(f326(f234(f917(x98991,a905)),x98993),x98994))+P105(f326(f326(f328(x98991),f881(x98992,x98993,x98994,x98991,x98995)),f326(f326(f3(f917(x98991,a905)),x98994),x98993)))
% 157.55/157.23 [9989]E(x99891,f188(f917(x99892,a905)))+~P105(f326(f61(x99892),x99893))+~P105(f326(f61(x99892),x99891))+P105(f326(f326(f328(f916(f917(x99892,a905),f917(x99892,a905))),f326(f326(f251(f917(x99892,a905),f917(x99892,a905)),x99893),x99891)),f318(x99892,x99894)))+~P105(f326(f326(f328(x99892),x99895),x99891))+~P105(f326(f326(f328(f916(x99892,x99892)),f326(f326(f251(x99892,x99892),f525(x99894,x99891,x99893,x99892)),x99895)),x99894))
% 157.55/157.23 [9990]E(x99901,f188(f917(x99902,a905)))+~P105(f326(f61(x99902),x99903))+~P105(f326(f61(x99902),x99901))+P105(f326(f326(f328(f916(f917(x99902,a905),f917(x99902,a905))),f326(f326(f251(f917(x99902,a905),f917(x99902,a905)),x99903),x99901)),f318(x99902,x99904)))+~P105(f326(f326(f328(x99902),x99905),x99901))+~P105(f326(f326(f328(f916(x99902,x99902)),f326(f326(f251(x99902,x99902),f598(x99904,x99901,x99903,x99902)),x99905)),x99904))
% 157.55/157.23 [10156]~P79(x101561)+~E(f326(f326(f8(x101565,x101561),x101562),x101566),x101564)+~P105(f326(f61(x101565),x101566))+P105(f326(f326(f328(x101565),f409(x101563,x101564,x101562,x101566,x101565,x101561)),x101566))+P105(f326(f326(f234(x101561),f326(x101562,x101563)),x101564))+~P105(f326(f326(f328(x101565),x101563),x101566))
% 157.55/157.23 [10203]~P79(x102031)+~E(f326(f326(f8(x102035,x102031),x102032),x102036),x102034)+~P105(f326(f61(x102035),x102036))+~P105(f326(f326(f328(x102035),x102033),x102036))+~P105(f326(f326(f234(x102031),f2(x102031)),f326(x102032,f409(x102033,x102034,x102032,x102036,x102035,x102031))))+P105(f326(f326(f234(x102031),f326(x102032,x102033)),x102034))
% 157.55/157.23 [10344]~E(x103445,x103448)+~E(x103444,x103447)+~P107(x103441)+~P69(x103442)+E(f326(f326(f8(x103441,x103442),x103443),f326(f301(x103441,x103444),x103445)),f326(f326(f8(x103441,x103442),x103446),f326(f301(x103441,x103447),x103448)))+P105(f326(f326(f234(x103441),x103444),f604(x103443,x103446,x103445,x103448,x103444,x103447,x103441,x103442)))
% 157.55/157.23 [10360]~E(x103607,x103604)+~E(x103608,x103605)+~P107(x103601)+~P69(x103602)+~E(f326(x103603,f604(x103606,x103603,x103608,x103605,x103607,x103604,x103601,x103602)),f326(x103606,f604(x103606,x103603,x103608,x103605,x103607,x103604,x103601,x103602)))+E(f326(f326(f8(x103601,x103602),x103603),f326(f301(x103601,x103604),x103605)),f326(f326(f8(x103601,x103602),x103606),f326(f301(x103601,x103607),x103608)))
% 157.55/157.23 [10363]~E(x103634,x103637)+~E(x103635,x103638)+~P107(x103631)+~P69(x103632)+E(f326(f326(f8(x103631,x103632),x103633),f326(f301(x103631,x103634),x103635)),f326(f326(f8(x103631,x103632),x103636),f326(f301(x103631,x103637),x103638)))+P105(f326(f326(f235(x103631),f604(x103633,x103636,x103635,x103638,x103634,x103637,x103631,x103632)),x103635))
% 157.55/157.23 [9996]~P7(x99965,x99969,x99966)+~P7(x99961,x999610,x99963)+~P11(x99961,x99965,f917(x99962,a905),x99963,x99966,x99968)+~P105(f326(f326(f328(x99965),x99967),x99969))+~P105(f326(f326(f328(x99961),x99964),x999610))+E(f326(f326(f40(x99961,f917(x99962,a905)),f326(f284(x99961,x99961,x99963),f326(f326(f308(x99961),x99964),f188(f917(x99961,a905))))),f326(f326(f10(f917(x99965,f917(x99962,a905)),f917(x99962,a905),x99961),f326(f40(x99965,f917(x99962,a905)),f326(f284(x99965,x99965,x99966),f326(f326(f308(x99965),x99967),f188(f917(x99965,a905)))))),x99968)),f326(f326(x99968,x99964),x99967))
% 157.55/157.23 [5750]~P108(x57503)+~P12(x57503,x57502)+~P12(x57503,x57501)+E(x57501,x57502)+~E(f326(f172(x57503),x57501),f326(f172(x57503),x57502))+~P105(f326(f137(x57503),x57502))+~P105(f326(f137(x57503),x57501))
% 157.55/157.23 [5069]~P130(x50692)+~P132(x50692)+~P142(x50692)+~P115(x50692)+~E(x50693,f2(x50692))+E(x50691,f2(a909))+E(f326(f326(f243(x50692),x50693),x50691),f2(x50692))
% 157.55/157.23 [9299]E(x92991,f2(a909))+~E(x92992,f326(f326(f79(a909),f326(f326(f80(a909),f326(f250(a909,a909),x92993)),x92991)),f326(f255(a909,a909),x92993)))+P105(f326(f48(x92992,x92991),x92993))+~P105(f326(f326(f234(a909),f326(f255(a909,a909),x92993)),f2(a909)))+~P105(f326(f326(f234(a909),f2(a909)),f326(f255(a909,a909),x92993)))+~P105(f326(f326(f235(a909),x92991),f326(f255(a909,a909),x92993)))+~P105(f326(f326(f235(a909),f326(f255(a909,a909),x92993)),x92991))
% 157.55/157.23 [9307]~E(f326(f250(a909,a909),x93073),f2(a909))+~E(x93071,f326(f326(f79(a909),f326(f326(f80(a909),f326(f250(a909,a909),x93073)),x93072)),f326(f255(a909,a909),x93073)))+P105(f326(f48(x93071,x93072),x93073))+~P105(f326(f326(f234(a909),f326(f255(a909,a909),x93073)),f2(a909)))+~P105(f326(f326(f234(a909),f2(a909)),f326(f255(a909,a909),x93073)))+~P105(f326(f326(f235(a909),x93072),f326(f255(a909,a909),x93073)))+~P105(f326(f326(f235(a909),f326(f255(a909,a909),x93073)),x93072))
% 157.55/157.23 [8160]~P67(x81602)+E(x81601,f188(f917(x81602,a905)))+E(x81603,f188(f917(x81602,a905)))+~P105(f326(f61(x81602),x81601))+~P105(f326(f61(x81602),x81603))+~E(f326(f326(f101(f917(x81602,a905)),x81603),x81601),f188(f917(x81602,a905)))+E(f326(f326(f80(x81602),f326(f63(x81602,f80(x81602)),x81603)),f326(f63(x81602,f80(x81602)),x81601)),f326(f63(x81602,f80(x81602)),f326(f326(f110(f917(x81602,a905)),x81603),x81601)))
% 157.55/157.23 [7949]E(x79491,f2(a1))+E(f326(f326(f36(a1),x79492),x79491),x79493)+~P105(f326(f326(f234(a1),x79494),f2(a1)))+~E(x79492,f326(f326(f79(a1),f326(f326(f80(a1),x79491),x79493)),x79494))+~P105(f326(f326(f234(a1),f2(a1)),x79494))+~P105(f326(f326(f235(a1),x79494),x79491))+~P105(f326(f326(f235(a1),x79491),x79494))
% 157.55/157.23 [7957]E(f45(a1,x79572,x79571),x79573)+E(x79571,f2(a1))+~P105(f326(f326(f234(a1),x79573),f2(a1)))+~E(x79572,f326(f326(f79(a1),f326(f326(f80(a1),x79571),x79574)),x79573))+~P105(f326(f326(f234(a1),f2(a1)),x79573))+~P105(f326(f326(f235(a1),x79573),x79571))+~P105(f326(f326(f235(a1),x79571),x79573))
% 157.55/157.23 [7864]~P17(x78642,x78645,x78644)+E(x78641,f188(f917(x78642,a905)))+E(x78643,f188(f917(x78642,a905)))+~P105(f326(f61(x78642),x78641))+~P105(f326(f61(x78642),x78643))+~E(f326(f326(f101(f917(x78642,a905)),x78643),x78641),f188(f917(x78642,a905)))+E(f326(x78644,f326(f326(f110(f917(x78642,a905)),x78643),x78641)),f326(f326(x78645,f326(x78644,x78643)),f326(x78644,x78641)))
% 157.55/157.23 [9540]~P24(x95403,x95401,x95405,x95404)+~P24(x95401,x95403,x95406,x95402)+E(f326(f35(x95401),x95402),f326(f35(x95403),x95404))+~P105(f326(f61(x95403),x95404))+~P105(f326(f61(x95401),x95402))+~P105(f326(f326(f234(f917(x95403,a905)),f326(f309(x95401,x95403,x95406),x95402)),x95404))+~P105(f326(f326(f234(f917(x95401,a905)),f326(f309(x95403,x95401,x95405),x95404)),x95402))
% 157.55/157.23 [9484]~P105(f326(f326(f235(a1),f326(f326(f79(a1),f326(f326(f80(a1),x94845),x94841)),x94846)),f2(a1)))+~E(f326(f326(f79(a1),f326(f326(f80(a1),x94843),x94842)),x94844),f326(f326(f79(a1),f326(f326(f80(a1),x94845),x94841)),x94846))+~P105(f326(f326(f234(a1),f2(a1)),x94846))+~P105(f326(f326(f235(a1),f2(a1)),x94845))+~P105(f326(f326(f234(a1),x94845),x94843))+~P105(f326(f326(f235(a1),x94844),x94843))+P105(f326(f326(f234(a1),x94841),x94842))
% 157.55/157.23 [9250]~E(f326(f326(f79(a1),f326(f326(f80(a1),x92503),x92501)),x92504),f326(f326(f79(a1),f326(f326(f80(a1),x92505),x92502)),x92506))+~P105(f326(f326(f234(a1),f2(a1)),x92504))+~P105(f326(f326(f235(a1),f2(a1)),x92505))+~P105(f326(f326(f234(a1),x92505),x92503))+~P105(f326(f326(f235(a1),x92506),x92505))+P105(f326(f326(f234(a1),x92501),x92502))+~P105(f326(f326(f234(a1),f2(a1)),f326(f326(f79(a1),f326(f326(f80(a1),x92505),x92502)),x92506)))
% 157.55/157.23 [9424]~P129(x94241)+~E(f326(f326(f79(x94241),x94242),x94244),f77(x94241))+~P105(f326(f326(f234(x94241),x94245),x94246))+~P105(f326(f326(f234(x94241),x94243),x94246))+~P105(f326(f326(f234(x94241),f2(x94241)),x94244))+~P105(f326(f326(f234(x94241),f2(x94241)),x94242))+P105(f326(f326(f234(x94241),f326(f326(f79(x94241),f326(f326(f80(x94241),x94242),x94243)),f326(f326(f80(x94241),x94244),x94245))),x94246))
% 157.55/157.23 [9425]~P127(x94251)+~E(f326(f326(f79(x94251),x94252),x94254),f77(x94251))+~P105(f326(f326(f234(x94251),f2(x94251)),x94254))+~P105(f326(f326(f234(x94251),f2(x94251)),x94252))+~P105(f326(f326(f235(x94251),x94255),x94256))+~P105(f326(f326(f235(x94251),x94253),x94256))+P105(f326(f326(f235(x94251),f326(f326(f79(x94251),f326(f326(f80(x94251),x94252),x94253)),f326(f326(f80(x94251),x94254),x94255))),x94256))
% 157.55/157.23 [10252]~P7(x102527,x102526,x102525)+E(x102521,x102522)+~P10(x102527,f917(x102524,a905),x102525,x102523)+E(f326(x102523,f508(x102521,x102522,x102523,x102524,x102525,x102526,x102527)),f326(x102523,f509(x102521,x102522,x102523,x102524,x102525,x102526,x102527)))+~E(f326(f326(f40(x102527,f917(x102524,a905)),x102521),x102523),f326(f326(f40(x102527,f917(x102524,a905)),x102522),x102523))+~P105(f326(f326(f328(f917(x102527,a905)),x102522),f326(f326(f60(x102527),x102526),x102525)))+~P105(f326(f326(f328(f917(x102527,a905)),x102521),f326(f326(f60(x102527),x102526),x102525)))
% 157.55/157.23 [10297]~P7(x102973,x102977,x102976)+E(x102971,x102972)+~P10(x102973,f917(x102975,a905),x102976,x102974)+~E(f326(f326(f40(x102973,f917(x102975,a905)),x102971),x102974),f326(f326(f40(x102973,f917(x102975,a905)),x102972),x102974))+P105(f326(f326(f328(x102973),f509(x102971,x102972,x102974,x102975,x102976,x102977,x102973)),x102977))+~P105(f326(f326(f328(f917(x102973,a905)),x102972),f326(f326(f60(x102973),x102977),x102976)))+~P105(f326(f326(f328(f917(x102973,a905)),x102971),f326(f326(f60(x102973),x102977),x102976)))
% 157.55/157.23 [10298]~P7(x102983,x102987,x102986)+E(x102981,x102982)+~P10(x102983,f917(x102985,a905),x102986,x102984)+~E(f326(f326(f40(x102983,f917(x102985,a905)),x102981),x102984),f326(f326(f40(x102983,f917(x102985,a905)),x102982),x102984))+P105(f326(f326(f328(x102983),f508(x102981,x102982,x102984,x102985,x102986,x102987,x102983)),x102987))+~P105(f326(f326(f328(f917(x102983,a905)),x102982),f326(f326(f60(x102983),x102987),x102986)))+~P105(f326(f326(f328(f917(x102983,a905)),x102981),f326(f326(f60(x102983),x102987),x102986)))
% 157.55/157.23 [10379]E(x103791,x103792)+~P7(x103793,x103796,x103797)+~P10(x103793,f917(x103794,a905),x103797,x103795)+~E(f326(f326(f40(x103793,f917(x103794,a905)),x103791),x103795),f326(f326(f40(x103793,f917(x103794,a905)),x103792),x103795))+~P105(f326(f326(f328(f916(x103793,x103793)),f326(f326(f251(x103793,x103793),f509(x103791,x103792,x103795,x103794,x103797,x103796,x103793)),f508(x103791,x103792,x103795,x103794,x103797,x103796,x103793))),x103797))+~P105(f326(f326(f328(f917(x103793,a905)),x103792),f326(f326(f60(x103793),x103796),x103797)))+~P105(f326(f326(f328(f917(x103793,a905)),x103791),f326(f326(f60(x103793),x103796),x103797)))
% 157.55/157.23 [9249]~P7(x92491,x92497,x92494)+~E(x92495,x92496)+~P105(f326(f326(f328(x92491),x92493),x92496))+~P105(f326(f326(f328(x92491),x92492),x92495))+~P105(f326(f326(f328(f917(x92491,a905)),x92496),f326(f326(f60(x92491),x92497),x92494)))+~P105(f326(f326(f328(f917(x92491,a905)),x92495),f326(f326(f60(x92491),x92497),x92494)))+P105(f326(f326(f328(f916(x92491,x92491)),f326(f326(f251(x92491,x92491),x92492),x92493)),x92494))
% 157.55/157.23 [9383]E(x93831,x93832)+~P7(x93833,x93834,x93835)+~P105(f326(f326(f328(x93833),x93836),x93832))+~P105(f326(f326(f328(x93833),x93837),x93831))+~P105(f326(f326(f328(f917(x93833,a905)),x93832),f326(f326(f60(x93833),x93834),x93835)))+~P105(f326(f326(f328(f917(x93833,a905)),x93831),f326(f326(f60(x93833),x93834),x93835)))+~P105(f326(f326(f328(f916(x93833,x93833)),f326(f326(f251(x93833,x93833),x93837),x93836)),x93835))
% 157.55/157.23 [10406]~P7(x104069,x104068,x104067)+~P7(x104061,x1040611,x1040610)+~P11(x104061,x104069,f917(x104066,a905),x1040610,x104067,x104065)+P105(f326(f326(f328(x104061),f512(x104062,x104063,x104064,x104065,x104066,x104067,x104068,x104069,x1040610,x1040611,x104061)),x1040611))+~P105(f326(f326(f328(f917(x104069,a905)),x104063),f326(f326(f60(x104069),x104068),x104067)))+~P105(f326(f326(f328(f917(x104061,a905)),x104064),f326(f326(f60(x104061),x1040611),x1040610)))+P105(f326(f326(f328(f917(x104066,a905)),f326(f326(f40(x104061,f917(x104066,a905)),x104064),f326(f326(f10(f917(x104069,f917(x104066,a905)),f917(x104066,a905),x104061),f326(f40(x104069,f917(x104066,a905)),x104063)),x104065))),x104062))
% 157.55/157.23 [10407]~P7(x1040711,x1040710,x104079)+~P7(x104071,x104078,x104077)+~P11(x1040711,x104071,f917(x104076,a905),x104079,x104077,x104075)+P105(f326(f326(f328(x104071),f513(x104072,x104073,x104074,x104075,x104076,x104077,x104078,x104071,x104079,x1040710,x1040711)),x104078))+~P105(f326(f326(f328(f917(x1040711,a905)),x104074),f326(f326(f60(x1040711),x1040710),x104079)))+~P105(f326(f326(f328(f917(x104071,a905)),x104073),f326(f326(f60(x104071),x104078),x104077)))+P105(f326(f326(f328(f917(x104076,a905)),f326(f326(f40(x1040711,f917(x104076,a905)),x104074),f326(f326(f10(f917(x104071,f917(x104076,a905)),f917(x104076,a905),x1040711),f326(f40(x104071,f917(x104076,a905)),x104073)),x104075))),x104072))
% 157.55/157.23 [10408]~P7(x104082,x104088,x104089)+~P7(x104084,x1040810,x1040811)+~P11(x104082,x104084,f917(x104081,a905),x104089,x1040811,x104086)+~P105(f326(f326(f328(f917(x104082,a905)),x104083),f326(f326(f60(x104082),x104088),x104089)))+~P105(f326(f326(f328(f917(x104084,a905)),x104085),f326(f326(f60(x104084),x1040810),x1040811)))+~P105(f326(f326(f328(f917(x104081,a905)),f326(f326(x104086,f512(x104087,x104085,x104083,x104086,x104081,x1040811,x1040810,x104084,x104089,x104088,x104082)),f513(x104087,x104085,x104083,x104086,x104081,x1040811,x1040810,x104084,x104089,x104088,x104082))),x104087))+P105(f326(f326(f328(f917(x104081,a905)),f326(f326(f40(x104082,f917(x104081,a905)),x104083),f326(f326(f10(f917(x104084,f917(x104081,a905)),f917(x104081,a905),x104082),f326(f40(x104084,f917(x104081,a905)),x104085)),x104086))),x104087))
% 157.55/157.23 [9285]E(x92851,x92852)+~P108(x92854)+~P24(x92853,x92854,x92855,f326(f326(f110(f917(x92853,a905)),f326(f172(x92853),x92851)),f326(f172(x92853),x92852)))+~E(f326(f172(x92853),x92851),f326(f172(x92853),x92852))+~P12(x92854,f326(f326(f154(x92853,x92854),x92855),x92852))+~P12(x92854,f326(f326(f154(x92853,x92854),x92855),x92851))+~P105(f326(f137(x92854),f326(f326(f154(x92853,x92854),x92855),x92852)))+~P105(f326(f137(x92854),f326(f326(f154(x92853,x92854),x92855),x92851)))
% 157.55/157.23 %EqnAxiom
% 157.55/157.23 [1]E(x11,x11)
% 157.55/157.23 [2]E(x22,x21)+~E(x21,x22)
% 157.55/157.23 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 157.55/157.23 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 157.55/157.23 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 157.55/157.23 [6]~E(x61,x62)+E(f100(x61),f100(x62))
% 157.55/157.23 [7]~E(x71,x72)+E(f188(x71),f188(x72))
% 157.55/157.23 [8]~E(x81,x82)+E(f326(x81,x83),f326(x82,x83))
% 157.55/157.23 [9]~E(x91,x92)+E(f326(x93,x91),f326(x93,x92))
% 157.55/157.23 [10]~E(x101,x102)+E(f28(x101),f28(x102))
% 157.55/157.23 [11]~E(x111,x112)+E(f79(x111),f79(x112))
% 157.55/157.23 [12]~E(x121,x122)+E(f101(x121),f101(x122))
% 157.55/157.23 [13]~E(x131,x132)+E(f232(x131),f232(x132))
% 157.55/157.23 [14]~E(x141,x142)+E(f110(x141),f110(x142))
% 157.55/157.23 [15]~E(x151,x152)+E(f233(x151),f233(x152))
% 157.55/157.23 [16]~E(x161,x162)+E(f102(x161),f102(x162))
% 157.55/157.23 [17]~E(x171,x172)+E(f31(x171),f31(x172))
% 157.55/157.23 [18]~E(x181,x182)+E(f83(x181),f83(x182))
% 157.55/157.23 [19]~E(x191,x192)+E(f917(x191,x193),f917(x192,x193))
% 157.55/157.23 [20]~E(x201,x202)+E(f917(x203,x201),f917(x203,x202))
% 157.55/157.23 [21]~E(x211,x212)+E(f36(x211),f36(x212))
% 157.55/157.23 [22]~E(x221,x222)+E(f513(x221,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f513(x222,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212))
% 157.55/157.23 [23]~E(x231,x232)+E(f513(x233,x231,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312),f513(x233,x232,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312))
% 157.55/157.23 [24]~E(x241,x242)+E(f513(x243,x244,x241,x245,x246,x247,x248,x249,x2410,x2411,x2412),f513(x243,x244,x242,x245,x246,x247,x248,x249,x2410,x2411,x2412))
% 157.55/157.23 [25]~E(x251,x252)+E(f513(x253,x254,x255,x251,x256,x257,x258,x259,x2510,x2511,x2512),f513(x253,x254,x255,x252,x256,x257,x258,x259,x2510,x2511,x2512))
% 157.55/157.23 [26]~E(x261,x262)+E(f513(x263,x264,x265,x266,x261,x267,x268,x269,x2610,x2611,x2612),f513(x263,x264,x265,x266,x262,x267,x268,x269,x2610,x2611,x2612))
% 157.55/157.23 [27]~E(x271,x272)+E(f513(x273,x274,x275,x276,x277,x271,x278,x279,x2710,x2711,x2712),f513(x273,x274,x275,x276,x277,x272,x278,x279,x2710,x2711,x2712))
% 157.55/157.23 [28]~E(x281,x282)+E(f513(x283,x284,x285,x286,x287,x288,x281,x289,x2810,x2811,x2812),f513(x283,x284,x285,x286,x287,x288,x282,x289,x2810,x2811,x2812))
% 157.55/157.23 [29]~E(x291,x292)+E(f513(x293,x294,x295,x296,x297,x298,x299,x291,x2910,x2911,x2912),f513(x293,x294,x295,x296,x297,x298,x299,x292,x2910,x2911,x2912))
% 157.55/157.23 [30]~E(x301,x302)+E(f513(x303,x304,x305,x306,x307,x308,x309,x3010,x301,x3011,x3012),f513(x303,x304,x305,x306,x307,x308,x309,x3010,x302,x3011,x3012))
% 157.55/157.23 [31]~E(x311,x312)+E(f513(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x311,x3112),f513(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x312,x3112))
% 157.55/157.23 [32]~E(x321,x322)+E(f513(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x321),f513(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x322))
% 157.55/157.23 [33]~E(x331,x332)+E(f77(x331),f77(x332))
% 157.55/157.23 [34]~E(x341,x342)+E(f908(x341),f908(x342))
% 157.55/157.23 [35]~E(x351,x352)+E(f512(x351,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f512(x352,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512))
% 157.55/157.23 [36]~E(x361,x362)+E(f512(x363,x361,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f512(x363,x362,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612))
% 157.55/157.23 [37]~E(x371,x372)+E(f512(x373,x374,x371,x375,x376,x377,x378,x379,x3710,x3711,x3712),f512(x373,x374,x372,x375,x376,x377,x378,x379,x3710,x3711,x3712))
% 157.55/157.23 [38]~E(x381,x382)+E(f512(x383,x384,x385,x381,x386,x387,x388,x389,x3810,x3811,x3812),f512(x383,x384,x385,x382,x386,x387,x388,x389,x3810,x3811,x3812))
% 157.55/157.23 [39]~E(x391,x392)+E(f512(x393,x394,x395,x396,x391,x397,x398,x399,x3910,x3911,x3912),f512(x393,x394,x395,x396,x392,x397,x398,x399,x3910,x3911,x3912))
% 157.55/157.23 [40]~E(x401,x402)+E(f512(x403,x404,x405,x406,x407,x401,x408,x409,x4010,x4011,x4012),f512(x403,x404,x405,x406,x407,x402,x408,x409,x4010,x4011,x4012))
% 157.55/157.23 [41]~E(x411,x412)+E(f512(x413,x414,x415,x416,x417,x418,x411,x419,x4110,x4111,x4112),f512(x413,x414,x415,x416,x417,x418,x412,x419,x4110,x4111,x4112))
% 157.55/157.23 [42]~E(x421,x422)+E(f512(x423,x424,x425,x426,x427,x428,x429,x421,x4210,x4211,x4212),f512(x423,x424,x425,x426,x427,x428,x429,x422,x4210,x4211,x4212))
% 157.55/157.23 [43]~E(x431,x432)+E(f512(x433,x434,x435,x436,x437,x438,x439,x4310,x431,x4311,x4312),f512(x433,x434,x435,x436,x437,x438,x439,x4310,x432,x4311,x4312))
% 157.55/157.23 [44]~E(x441,x442)+E(f512(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x441,x4412),f512(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x442,x4412))
% 157.55/157.23 [45]~E(x451,x452)+E(f512(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x451),f512(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x452))
% 157.55/157.23 [46]~E(x461,x462)+E(f6(x461),f6(x462))
% 157.55/157.23 [47]~E(x471,x472)+E(f328(x471),f328(x472))
% 157.55/157.23 [48]~E(x481,x482)+E(f235(x481),f235(x482))
% 157.55/157.23 [49]~E(x491,x492)+E(f111(x491),f111(x492))
% 157.55/157.23 [50]~E(x501,x502)+E(f78(x501),f78(x502))
% 157.55/157.23 [51]~E(x511,x512)+E(f103(x511),f103(x512))
% 157.55/157.23 [52]~E(x521,x522)+E(f913(x521),f913(x522))
% 157.55/157.23 [53]~E(x531,x532)+E(f910(x531),f910(x532))
% 157.55/157.23 [54]~E(x541,x542)+E(f911(x541),f911(x542))
% 157.55/157.23 [55]~E(x551,x552)+E(f80(x551),f80(x552))
% 157.55/157.23 [56]~E(x561,x562)+E(f39(x561,x563),f39(x562,x563))
% 157.55/157.23 [57]~E(x571,x572)+E(f39(x573,x571),f39(x573,x572))
% 157.55/157.23 [58]~E(x581,x582)+E(f189(x581),f189(x582))
% 157.55/157.23 [59]~E(x591,x592)+E(f10(x591,x593,x594),f10(x592,x593,x594))
% 157.55/157.23 [60]~E(x601,x602)+E(f10(x603,x601,x604),f10(x603,x602,x604))
% 157.55/157.23 [61]~E(x611,x612)+E(f10(x613,x614,x611),f10(x613,x614,x612))
% 157.55/157.23 [62]~E(x621,x622)+E(f234(x621),f234(x622))
% 157.55/157.23 [63]~E(x631,x632)+E(f243(x631),f243(x632))
% 157.55/157.23 [64]~E(x641,x642)+E(f8(x641,x643),f8(x642,x643))
% 157.55/157.23 [65]~E(x651,x652)+E(f8(x653,x651),f8(x653,x652))
% 157.55/157.23 [66]~E(x661,x662)+E(f569(x661,x663,x664),f569(x662,x663,x664))
% 157.55/157.23 [67]~E(x671,x672)+E(f569(x673,x671,x674),f569(x673,x672,x674))
% 157.55/157.23 [68]~E(x681,x682)+E(f569(x683,x684,x681),f569(x683,x684,x682))
% 157.55/157.23 [69]~E(x691,x692)+E(f315(x691,x693),f315(x692,x693))
% 157.55/157.23 [70]~E(x701,x702)+E(f315(x703,x701),f315(x703,x702))
% 157.55/157.23 [71]~E(x711,x712)+E(f280(x711),f280(x712))
% 157.55/157.23 [72]~E(x721,x722)+E(f61(x721),f61(x722))
% 157.55/157.23 [73]~E(x731,x732)+E(f289(x731,x733,x734,x735),f289(x732,x733,x734,x735))
% 157.55/157.23 [74]~E(x741,x742)+E(f289(x743,x741,x744,x745),f289(x743,x742,x744,x745))
% 157.55/157.23 [75]~E(x751,x752)+E(f289(x753,x754,x751,x755),f289(x753,x754,x752,x755))
% 157.55/157.23 [76]~E(x761,x762)+E(f289(x763,x764,x765,x761),f289(x763,x764,x765,x762))
% 157.55/157.23 [77]~E(x771,x772)+E(f286(x771),f286(x772))
% 157.55/157.23 [78]~E(x781,x782)+E(f165(x781),f165(x782))
% 157.55/157.23 [79]~E(x791,x792)+E(f75(x791),f75(x792))
% 157.55/157.23 [80]~E(x801,x802)+E(f281(x801),f281(x802))
% 157.55/157.23 [81]~E(x811,x812)+E(f576(x811,x813),f576(x812,x813))
% 157.55/157.23 [82]~E(x821,x822)+E(f576(x823,x821),f576(x823,x822))
% 157.55/157.23 [83]~E(x831,x832)+E(f60(x831),f60(x832))
% 157.55/157.23 [84]~E(x841,x842)+E(f510(x841,x843,x844,x845,x846),f510(x842,x843,x844,x845,x846))
% 157.55/157.23 [85]~E(x851,x852)+E(f510(x853,x851,x854,x855,x856),f510(x853,x852,x854,x855,x856))
% 157.55/157.23 [86]~E(x861,x862)+E(f510(x863,x864,x861,x865,x866),f510(x863,x864,x862,x865,x866))
% 157.55/157.23 [87]~E(x871,x872)+E(f510(x873,x874,x875,x871,x876),f510(x873,x874,x875,x872,x876))
% 157.55/157.23 [88]~E(x881,x882)+E(f510(x883,x884,x885,x886,x881),f510(x883,x884,x885,x886,x882))
% 157.55/157.23 [89]~E(x891,x892)+E(f308(x891),f308(x892))
% 157.55/157.23 [90]~E(x901,x902)+E(f137(x901),f137(x902))
% 157.55/157.23 [91]~E(x911,x912)+E(f241(x911),f241(x912))
% 157.55/157.23 [92]~E(x921,x922)+E(f302(x921,x923,x924),f302(x922,x923,x924))
% 157.55/157.23 [93]~E(x931,x932)+E(f302(x933,x931,x934),f302(x933,x932,x934))
% 157.55/157.23 [94]~E(x941,x942)+E(f302(x943,x944,x941),f302(x943,x944,x942))
% 157.55/157.23 [95]~E(x951,x952)+E(f154(x951,x953),f154(x952,x953))
% 157.55/157.23 [96]~E(x961,x962)+E(f154(x963,x961),f154(x963,x962))
% 157.55/157.23 [97]~E(x971,x972)+E(f304(x971,x973,x974),f304(x972,x973,x974))
% 157.55/157.23 [98]~E(x981,x982)+E(f304(x983,x981,x984),f304(x983,x982,x984))
% 157.55/157.23 [99]~E(x991,x992)+E(f304(x993,x994,x991),f304(x993,x994,x992))
% 157.55/157.23 [100]~E(x1001,x1002)+E(f9(x1001,x1003,x1004),f9(x1002,x1003,x1004))
% 157.55/157.23 [101]~E(x1011,x1012)+E(f9(x1013,x1011,x1014),f9(x1013,x1012,x1014))
% 157.55/157.23 [102]~E(x1021,x1022)+E(f9(x1023,x1024,x1021),f9(x1023,x1024,x1022))
% 157.55/157.23 [103]~E(x1031,x1032)+E(f37(x1031,x1033),f37(x1032,x1033))
% 157.55/157.23 [104]~E(x1041,x1042)+E(f37(x1043,x1041),f37(x1043,x1042))
% 157.55/157.23 [105]~E(x1051,x1052)+E(f164(x1051),f164(x1052))
% 157.55/157.23 [106]~E(x1061,x1062)+E(f172(x1061),f172(x1062))
% 157.55/157.23 [107]~E(x1071,x1072)+E(f282(x1071),f282(x1072))
% 157.55/157.23 [108]~E(x1081,x1082)+E(f802(x1081),f802(x1082))
% 157.55/157.23 [109]~E(x1091,x1092)+E(f309(x1091,x1093,x1094),f309(x1092,x1093,x1094))
% 157.55/157.23 [110]~E(x1101,x1102)+E(f309(x1103,x1101,x1104),f309(x1103,x1102,x1104))
% 157.55/157.23 [111]~E(x1111,x1112)+E(f309(x1113,x1114,x1111),f309(x1113,x1114,x1112))
% 157.55/157.23 [112]~E(x1121,x1122)+E(f113(x1121),f113(x1122))
% 157.55/157.23 [113]~E(x1131,x1132)+E(f251(x1131,x1133),f251(x1132,x1133))
% 157.55/157.23 [114]~E(x1141,x1142)+E(f251(x1143,x1141),f251(x1143,x1142))
% 157.55/157.23 [115]~E(x1151,x1152)+E(f114(x1151,x1153),f114(x1152,x1153))
% 157.55/157.23 [116]~E(x1161,x1162)+E(f114(x1163,x1161),f114(x1163,x1162))
% 157.55/157.23 [117]~E(x1171,x1172)+E(f801(x1171),f801(x1172))
% 157.55/157.23 [118]~E(x1181,x1182)+E(f136(x1181,x1183),f136(x1182,x1183))
% 157.55/157.23 [119]~E(x1191,x1192)+E(f136(x1193,x1191),f136(x1193,x1192))
% 157.55/157.23 [120]~E(x1201,x1202)+E(f288(x1201,x1203,x1204),f288(x1202,x1203,x1204))
% 157.55/157.23 [121]~E(x1211,x1212)+E(f288(x1213,x1211,x1214),f288(x1213,x1212,x1214))
% 157.55/157.23 [122]~E(x1221,x1222)+E(f288(x1223,x1224,x1221),f288(x1223,x1224,x1222))
% 157.55/157.23 [123]~E(x1231,x1232)+E(f215(x1231,x1233),f215(x1232,x1233))
% 157.55/157.23 [124]~E(x1241,x1242)+E(f215(x1243,x1241),f215(x1243,x1242))
% 157.55/157.23 [125]~E(x1251,x1252)+E(f170(x1251,x1253,x1254),f170(x1252,x1253,x1254))
% 157.55/157.23 [126]~E(x1261,x1262)+E(f170(x1263,x1261,x1264),f170(x1263,x1262,x1264))
% 157.55/157.23 [127]~E(x1271,x1272)+E(f170(x1273,x1274,x1271),f170(x1273,x1274,x1272))
% 157.55/157.23 [128]~E(x1281,x1282)+E(f916(x1281,x1283),f916(x1282,x1283))
% 157.55/157.23 [129]~E(x1291,x1292)+E(f916(x1293,x1291),f916(x1293,x1292))
% 157.55/157.23 [130]~E(x1301,x1302)+E(f290(x1301),f290(x1302))
% 157.55/157.23 [131]~E(x1311,x1312)+E(f851(x1311,x1313,x1314),f851(x1312,x1313,x1314))
% 157.55/157.23 [132]~E(x1321,x1322)+E(f851(x1323,x1321,x1324),f851(x1323,x1322,x1324))
% 157.55/157.23 [133]~E(x1331,x1332)+E(f851(x1333,x1334,x1331),f851(x1333,x1334,x1332))
% 157.55/157.23 [134]~E(x1341,x1342)+E(f672(x1341,x1343,x1344,x1345),f672(x1342,x1343,x1344,x1345))
% 157.55/157.23 [135]~E(x1351,x1352)+E(f672(x1353,x1351,x1354,x1355),f672(x1353,x1352,x1354,x1355))
% 157.55/157.23 [136]~E(x1361,x1362)+E(f672(x1363,x1364,x1361,x1365),f672(x1363,x1364,x1362,x1365))
% 157.55/157.23 [137]~E(x1371,x1372)+E(f672(x1373,x1374,x1375,x1371),f672(x1373,x1374,x1375,x1372))
% 157.55/157.23 [138]~E(x1381,x1382)+E(f310(x1381,x1383,x1384),f310(x1382,x1383,x1384))
% 157.55/157.23 [139]~E(x1391,x1392)+E(f310(x1393,x1391,x1394),f310(x1393,x1392,x1394))
% 157.55/157.23 [140]~E(x1401,x1402)+E(f310(x1403,x1404,x1401),f310(x1403,x1404,x1402))
% 157.55/157.23 [141]~E(x1411,x1412)+E(f105(x1411),f105(x1412))
% 157.55/157.23 [142]~E(x1421,x1422)+E(f106(x1421),f106(x1422))
% 157.55/157.23 [143]~E(x1431,x1432)+E(f327(x1431),f327(x1432))
% 157.55/157.23 [144]~E(x1441,x1442)+E(f255(x1441,x1443),f255(x1442,x1443))
% 157.55/157.23 [145]~E(x1451,x1452)+E(f255(x1453,x1451),f255(x1453,x1452))
% 157.55/157.23 [146]~E(x1461,x1462)+E(f574(x1461),f574(x1462))
% 157.55/157.23 [147]~E(x1471,x1472)+E(f11(x1471,x1473),f11(x1472,x1473))
% 157.55/157.23 [148]~E(x1481,x1482)+E(f11(x1483,x1481),f11(x1483,x1482))
% 157.55/157.23 [149]~E(x1491,x1492)+E(f134(x1491),f134(x1492))
% 157.55/157.23 [150]~E(x1501,x1502)+E(f240(x1501,x1503),f240(x1502,x1503))
% 157.55/157.23 [151]~E(x1511,x1512)+E(f240(x1513,x1511),f240(x1513,x1512))
% 157.55/157.23 [152]~E(x1521,x1522)+E(f250(x1521,x1523),f250(x1522,x1523))
% 157.55/157.23 [153]~E(x1531,x1532)+E(f250(x1533,x1531),f250(x1533,x1532))
% 157.55/157.23 [154]~E(x1541,x1542)+E(f152(x1541,x1543),f152(x1542,x1543))
% 157.55/157.23 [155]~E(x1551,x1552)+E(f152(x1553,x1551),f152(x1553,x1552))
% 157.55/157.23 [156]~E(x1561,x1562)+E(f701(x1561,x1563),f701(x1562,x1563))
% 157.55/157.23 [157]~E(x1571,x1572)+E(f701(x1573,x1571),f701(x1573,x1572))
% 157.55/157.23 [158]~E(x1581,x1582)+E(f394(x1581,x1583,x1584),f394(x1582,x1583,x1584))
% 157.55/157.23 [159]~E(x1591,x1592)+E(f394(x1593,x1591,x1594),f394(x1593,x1592,x1594))
% 157.55/157.23 [160]~E(x1601,x1602)+E(f394(x1603,x1604,x1601),f394(x1603,x1604,x1602))
% 157.55/157.23 [161]~E(x1611,x1612)+E(f7(x1611),f7(x1612))
% 157.55/157.23 [162]~E(x1621,x1622)+E(f20(x1621,x1623,x1624),f20(x1622,x1623,x1624))
% 157.55/157.23 [163]~E(x1631,x1632)+E(f20(x1633,x1631,x1634),f20(x1633,x1632,x1634))
% 157.55/157.23 [164]~E(x1641,x1642)+E(f20(x1643,x1644,x1641),f20(x1643,x1644,x1642))
% 157.55/157.23 [165]~E(x1651,x1652)+E(f261(x1651),f261(x1652))
% 157.55/157.23 [166]~E(x1661,x1662)+E(f72(x1661,x1663,x1664,x1665),f72(x1662,x1663,x1664,x1665))
% 157.55/157.23 [167]~E(x1671,x1672)+E(f72(x1673,x1671,x1674,x1675),f72(x1673,x1672,x1674,x1675))
% 157.55/157.23 [168]~E(x1681,x1682)+E(f72(x1683,x1684,x1681,x1685),f72(x1683,x1684,x1682,x1685))
% 157.55/157.23 [169]~E(x1691,x1692)+E(f72(x1693,x1694,x1695,x1691),f72(x1693,x1694,x1695,x1692))
% 157.55/157.23 [170]~E(x1701,x1702)+E(f64(x1701,x1703,x1704),f64(x1702,x1703,x1704))
% 157.55/157.23 [171]~E(x1711,x1712)+E(f64(x1713,x1711,x1714),f64(x1713,x1712,x1714))
% 157.55/157.23 [172]~E(x1721,x1722)+E(f64(x1723,x1724,x1721),f64(x1723,x1724,x1722))
% 157.55/157.23 [173]~E(x1731,x1732)+E(f45(x1731,x1733,x1734),f45(x1732,x1733,x1734))
% 157.55/157.23 [174]~E(x1741,x1742)+E(f45(x1743,x1741,x1744),f45(x1743,x1742,x1744))
% 157.55/157.23 [175]~E(x1751,x1752)+E(f45(x1753,x1754,x1751),f45(x1753,x1754,x1752))
% 157.55/157.23 [176]~E(x1761,x1762)+E(f38(x1761,x1763),f38(x1762,x1763))
% 157.55/157.23 [177]~E(x1771,x1772)+E(f38(x1773,x1771),f38(x1773,x1772))
% 157.55/157.23 [178]~E(x1781,x1782)+E(f285(x1781,x1783),f285(x1782,x1783))
% 157.55/157.23 [179]~E(x1791,x1792)+E(f285(x1793,x1791),f285(x1793,x1792))
% 157.55/157.23 [180]~E(x1801,x1802)+E(f40(x1801,x1803),f40(x1802,x1803))
% 157.55/157.23 [181]~E(x1811,x1812)+E(f40(x1813,x1811),f40(x1813,x1812))
% 157.55/157.23 [182]~E(x1821,x1822)+E(f212(x1821),f212(x1822))
% 157.55/157.23 [183]~E(x1831,x1832)+E(f753(x1831,x1833),f753(x1832,x1833))
% 157.55/157.23 [184]~E(x1841,x1842)+E(f753(x1843,x1841),f753(x1843,x1842))
% 157.55/157.23 [185]~E(x1851,x1852)+E(f300(x1851),f300(x1852))
% 157.55/157.23 [186]~E(x1861,x1862)+E(f849(x1861,x1863,x1864),f849(x1862,x1863,x1864))
% 157.55/157.23 [187]~E(x1871,x1872)+E(f849(x1873,x1871,x1874),f849(x1873,x1872,x1874))
% 157.55/157.23 [188]~E(x1881,x1882)+E(f849(x1883,x1884,x1881),f849(x1883,x1884,x1882))
% 157.55/157.23 [189]~E(x1891,x1892)+E(f662(x1891,x1893,x1894,x1895),f662(x1892,x1893,x1894,x1895))
% 157.55/157.23 [190]~E(x1901,x1902)+E(f662(x1903,x1901,x1904,x1905),f662(x1903,x1902,x1904,x1905))
% 157.55/157.23 [191]~E(x1911,x1912)+E(f662(x1913,x1914,x1911,x1915),f662(x1913,x1914,x1912,x1915))
% 157.55/157.23 [192]~E(x1921,x1922)+E(f662(x1923,x1924,x1925,x1921),f662(x1923,x1924,x1925,x1922))
% 157.55/157.23 [193]~E(x1931,x1932)+E(f86(x1931),f86(x1932))
% 157.55/157.23 [194]~E(x1941,x1942)+E(f151(x1941),f151(x1942))
% 157.55/157.23 [195]~E(x1951,x1952)+E(f853(x1951,x1953,x1954),f853(x1952,x1953,x1954))
% 157.55/157.23 [196]~E(x1961,x1962)+E(f853(x1963,x1961,x1964),f853(x1963,x1962,x1964))
% 157.55/157.23 [197]~E(x1971,x1972)+E(f853(x1973,x1974,x1971),f853(x1973,x1974,x1972))
% 157.55/157.23 [198]~E(x1981,x1982)+E(f12(x1981,x1983),f12(x1982,x1983))
% 157.55/157.23 [199]~E(x1991,x1992)+E(f12(x1993,x1991),f12(x1993,x1992))
% 157.55/157.23 [200]~E(x2001,x2002)+E(f306(x2001,x2003),f306(x2002,x2003))
% 157.55/157.23 [201]~E(x2011,x2012)+E(f306(x2013,x2011),f306(x2013,x2012))
% 157.55/157.23 [202]~E(x2021,x2022)+E(f253(x2021,x2023),f253(x2022,x2023))
% 157.55/157.23 [203]~E(x2031,x2032)+E(f253(x2033,x2031),f253(x2033,x2032))
% 157.55/157.23 [204]~E(x2041,x2042)+E(f301(x2041,x2043),f301(x2042,x2043))
% 157.55/157.23 [205]~E(x2051,x2052)+E(f301(x2053,x2051),f301(x2053,x2052))
% 157.55/157.23 [206]~E(x2061,x2062)+E(f138(x2061),f138(x2062))
% 157.55/157.23 [207]~E(x2071,x2072)+E(f655(x2071,x2073,x2074,x2075),f655(x2072,x2073,x2074,x2075))
% 157.55/157.23 [208]~E(x2081,x2082)+E(f655(x2083,x2081,x2084,x2085),f655(x2083,x2082,x2084,x2085))
% 157.55/157.23 [209]~E(x2091,x2092)+E(f655(x2093,x2094,x2091,x2095),f655(x2093,x2094,x2092,x2095))
% 157.55/157.23 [210]~E(x2101,x2102)+E(f655(x2103,x2104,x2105,x2101),f655(x2103,x2104,x2105,x2102))
% 157.55/157.23 [211]~E(x2111,x2112)+E(f307(x2111),f307(x2112))
% 157.55/157.23 [212]~E(x2121,x2122)+E(f159(x2121,x2123),f159(x2122,x2123))
% 157.55/157.23 [213]~E(x2131,x2132)+E(f159(x2133,x2131),f159(x2133,x2132))
% 157.55/157.23 [214]~E(x2141,x2142)+E(f840(x2141,x2143,x2144,x2145,x2146,x2147,x2148,x2149),f840(x2142,x2143,x2144,x2145,x2146,x2147,x2148,x2149))
% 157.55/157.23 [215]~E(x2151,x2152)+E(f840(x2153,x2151,x2154,x2155,x2156,x2157,x2158,x2159),f840(x2153,x2152,x2154,x2155,x2156,x2157,x2158,x2159))
% 157.55/157.23 [216]~E(x2161,x2162)+E(f840(x2163,x2164,x2161,x2165,x2166,x2167,x2168,x2169),f840(x2163,x2164,x2162,x2165,x2166,x2167,x2168,x2169))
% 157.55/157.23 [217]~E(x2171,x2172)+E(f840(x2173,x2174,x2175,x2171,x2176,x2177,x2178,x2179),f840(x2173,x2174,x2175,x2172,x2176,x2177,x2178,x2179))
% 157.55/157.23 [218]~E(x2181,x2182)+E(f840(x2183,x2184,x2185,x2186,x2181,x2187,x2188,x2189),f840(x2183,x2184,x2185,x2186,x2182,x2187,x2188,x2189))
% 157.55/157.23 [219]~E(x2191,x2192)+E(f840(x2193,x2194,x2195,x2196,x2197,x2191,x2198,x2199),f840(x2193,x2194,x2195,x2196,x2197,x2192,x2198,x2199))
% 157.55/157.23 [220]~E(x2201,x2202)+E(f840(x2203,x2204,x2205,x2206,x2207,x2208,x2201,x2209),f840(x2203,x2204,x2205,x2206,x2207,x2208,x2202,x2209))
% 157.55/157.23 [221]~E(x2211,x2212)+E(f840(x2213,x2214,x2215,x2216,x2217,x2218,x2219,x2211),f840(x2213,x2214,x2215,x2216,x2217,x2218,x2219,x2212))
% 157.55/157.23 [222]~E(x2221,x2222)+E(f766(x2221,x2223,x2224),f766(x2222,x2223,x2224))
% 157.55/157.23 [223]~E(x2231,x2232)+E(f766(x2233,x2231,x2234),f766(x2233,x2232,x2234))
% 157.55/157.23 [224]~E(x2241,x2242)+E(f766(x2243,x2244,x2241),f766(x2243,x2244,x2242))
% 157.55/157.23 [225]~E(x2251,x2252)+E(f168(x2251),f168(x2252))
% 157.55/157.23 [226]~E(x2261,x2262)+E(f161(x2261,x2263),f161(x2262,x2263))
% 157.55/157.23 [227]~E(x2271,x2272)+E(f161(x2273,x2271),f161(x2273,x2272))
% 157.55/157.23 [228]~E(x2281,x2282)+E(f696(x2281,x2283,x2284,x2285,x2286),f696(x2282,x2283,x2284,x2285,x2286))
% 157.55/157.23 [229]~E(x2291,x2292)+E(f696(x2293,x2291,x2294,x2295,x2296),f696(x2293,x2292,x2294,x2295,x2296))
% 157.55/157.23 [230]~E(x2301,x2302)+E(f696(x2303,x2304,x2301,x2305,x2306),f696(x2303,x2304,x2302,x2305,x2306))
% 157.55/157.23 [231]~E(x2311,x2312)+E(f696(x2313,x2314,x2315,x2311,x2316),f696(x2313,x2314,x2315,x2312,x2316))
% 157.55/157.23 [232]~E(x2321,x2322)+E(f696(x2323,x2324,x2325,x2326,x2321),f696(x2323,x2324,x2325,x2326,x2322))
% 157.55/157.23 [233]~E(x2331,x2332)+E(f738(x2331,x2333,x2334,x2335,x2336),f738(x2332,x2333,x2334,x2335,x2336))
% 157.55/157.23 [234]~E(x2341,x2342)+E(f738(x2343,x2341,x2344,x2345,x2346),f738(x2343,x2342,x2344,x2345,x2346))
% 157.55/157.23 [235]~E(x2351,x2352)+E(f738(x2353,x2354,x2351,x2355,x2356),f738(x2353,x2354,x2352,x2355,x2356))
% 157.55/157.23 [236]~E(x2361,x2362)+E(f738(x2363,x2364,x2365,x2361,x2366),f738(x2363,x2364,x2365,x2362,x2366))
% 157.55/157.23 [237]~E(x2371,x2372)+E(f738(x2373,x2374,x2375,x2376,x2371),f738(x2373,x2374,x2375,x2376,x2372))
% 157.55/157.23 [238]~E(x2381,x2382)+E(f177(x2381,x2383,x2384),f177(x2382,x2383,x2384))
% 157.55/157.23 [239]~E(x2391,x2392)+E(f177(x2393,x2391,x2394),f177(x2393,x2392,x2394))
% 157.55/157.23 [240]~E(x2401,x2402)+E(f177(x2403,x2404,x2401),f177(x2403,x2404,x2402))
% 157.55/157.23 [241]~E(x2411,x2412)+E(f35(x2411),f35(x2412))
% 157.55/157.23 [242]~E(x2421,x2422)+E(f196(x2421,x2423,x2424,x2425),f196(x2422,x2423,x2424,x2425))
% 157.55/157.23 [243]~E(x2431,x2432)+E(f196(x2433,x2431,x2434,x2435),f196(x2433,x2432,x2434,x2435))
% 157.55/157.23 [244]~E(x2441,x2442)+E(f196(x2443,x2444,x2441,x2445),f196(x2443,x2444,x2442,x2445))
% 157.55/157.23 [245]~E(x2451,x2452)+E(f196(x2453,x2454,x2455,x2451),f196(x2453,x2454,x2455,x2452))
% 157.55/157.23 [246]~E(x2461,x2462)+E(f303(x2461),f303(x2462))
% 157.55/157.23 [247]~E(x2471,x2472)+E(f855(x2471,x2473,x2474),f855(x2472,x2473,x2474))
% 157.55/157.23 [248]~E(x2481,x2482)+E(f855(x2483,x2481,x2484),f855(x2483,x2482,x2484))
% 157.55/157.23 [249]~E(x2491,x2492)+E(f855(x2493,x2494,x2491),f855(x2493,x2494,x2492))
% 157.55/157.23 [250]~E(x2501,x2502)+E(f227(x2501,x2503),f227(x2502,x2503))
% 157.55/157.23 [251]~E(x2511,x2512)+E(f227(x2513,x2511),f227(x2513,x2512))
% 157.55/157.23 [252]~E(x2521,x2522)+E(f149(x2521,x2523,x2524,x2525,x2526),f149(x2522,x2523,x2524,x2525,x2526))
% 157.55/157.23 [253]~E(x2531,x2532)+E(f149(x2533,x2531,x2534,x2535,x2536),f149(x2533,x2532,x2534,x2535,x2536))
% 157.55/157.23 [254]~E(x2541,x2542)+E(f149(x2543,x2544,x2541,x2545,x2546),f149(x2543,x2544,x2542,x2545,x2546))
% 157.55/157.23 [255]~E(x2551,x2552)+E(f149(x2553,x2554,x2555,x2551,x2556),f149(x2553,x2554,x2555,x2552,x2556))
% 157.55/157.23 [256]~E(x2561,x2562)+E(f149(x2563,x2564,x2565,x2566,x2561),f149(x2563,x2564,x2565,x2566,x2562))
% 157.55/157.23 [257]~E(x2571,x2572)+E(f230(x2571,x2573,x2574),f230(x2572,x2573,x2574))
% 157.55/157.23 [258]~E(x2581,x2582)+E(f230(x2583,x2581,x2584),f230(x2583,x2582,x2584))
% 157.55/157.23 [259]~E(x2591,x2592)+E(f230(x2593,x2594,x2591),f230(x2593,x2594,x2592))
% 157.55/157.23 [260]~E(x2601,x2602)+E(f18(x2601,x2603),f18(x2602,x2603))
% 157.55/157.23 [261]~E(x2611,x2612)+E(f18(x2613,x2611),f18(x2613,x2612))
% 157.55/157.23 [262]~E(x2621,x2622)+E(f254(x2621,x2623,x2624,x2625),f254(x2622,x2623,x2624,x2625))
% 157.55/157.23 [263]~E(x2631,x2632)+E(f254(x2633,x2631,x2634,x2635),f254(x2633,x2632,x2634,x2635))
% 157.55/157.23 [264]~E(x2641,x2642)+E(f254(x2643,x2644,x2641,x2645),f254(x2643,x2644,x2642,x2645))
% 157.55/157.23 [265]~E(x2651,x2652)+E(f254(x2653,x2654,x2655,x2651),f254(x2653,x2654,x2655,x2652))
% 157.55/157.23 [266]~E(x2661,x2662)+E(f143(x2661,x2663),f143(x2662,x2663))
% 157.55/157.23 [267]~E(x2671,x2672)+E(f143(x2673,x2671),f143(x2673,x2672))
% 157.55/157.23 [268]~E(x2681,x2682)+E(f191(x2681),f191(x2682))
% 157.55/157.23 [269]~E(x2691,x2692)+E(f147(x2691,x2693),f147(x2692,x2693))
% 157.55/157.23 [270]~E(x2701,x2702)+E(f147(x2703,x2701),f147(x2703,x2702))
% 157.55/157.23 [271]~E(x2711,x2712)+E(f115(x2711),f115(x2712))
% 157.55/157.23 [272]~E(x2721,x2722)+E(f915(x2721,x2723),f915(x2722,x2723))
% 157.55/157.23 [273]~E(x2731,x2732)+E(f915(x2733,x2731),f915(x2733,x2732))
% 157.55/157.23 [274]~E(x2741,x2742)+E(f914(x2741,x2743),f914(x2742,x2743))
% 157.55/157.23 [275]~E(x2751,x2752)+E(f914(x2753,x2751),f914(x2753,x2752))
% 157.55/157.23 [276]~E(x2761,x2762)+E(f41(x2761),f41(x2762))
% 157.55/157.23 [277]~E(x2771,x2772)+E(f167(x2771),f167(x2772))
% 157.55/157.23 [278]~E(x2781,x2782)+E(f85(x2781,x2783),f85(x2782,x2783))
% 157.55/157.23 [279]~E(x2791,x2792)+E(f85(x2793,x2791),f85(x2793,x2792))
% 157.55/157.23 [280]~E(x2801,x2802)+E(f87(x2801),f87(x2802))
% 157.55/157.23 [281]~E(x2811,x2812)+E(f843(x2811,x2813,x2814,x2815,x2816,x2817,x2818,x2819),f843(x2812,x2813,x2814,x2815,x2816,x2817,x2818,x2819))
% 157.55/157.23 [282]~E(x2821,x2822)+E(f843(x2823,x2821,x2824,x2825,x2826,x2827,x2828,x2829),f843(x2823,x2822,x2824,x2825,x2826,x2827,x2828,x2829))
% 157.55/157.23 [283]~E(x2831,x2832)+E(f843(x2833,x2834,x2831,x2835,x2836,x2837,x2838,x2839),f843(x2833,x2834,x2832,x2835,x2836,x2837,x2838,x2839))
% 157.55/157.23 [284]~E(x2841,x2842)+E(f843(x2843,x2844,x2845,x2841,x2846,x2847,x2848,x2849),f843(x2843,x2844,x2845,x2842,x2846,x2847,x2848,x2849))
% 157.55/157.23 [285]~E(x2851,x2852)+E(f843(x2853,x2854,x2855,x2856,x2851,x2857,x2858,x2859),f843(x2853,x2854,x2855,x2856,x2852,x2857,x2858,x2859))
% 157.55/157.23 [286]~E(x2861,x2862)+E(f843(x2863,x2864,x2865,x2866,x2867,x2861,x2868,x2869),f843(x2863,x2864,x2865,x2866,x2867,x2862,x2868,x2869))
% 157.55/157.23 [287]~E(x2871,x2872)+E(f843(x2873,x2874,x2875,x2876,x2877,x2878,x2871,x2879),f843(x2873,x2874,x2875,x2876,x2877,x2878,x2872,x2879))
% 157.55/157.23 [288]~E(x2881,x2882)+E(f843(x2883,x2884,x2885,x2886,x2887,x2888,x2889,x2881),f843(x2883,x2884,x2885,x2886,x2887,x2888,x2889,x2882))
% 157.55/157.23 [289]~E(x2891,x2892)+E(f171(x2891),f171(x2892))
% 157.55/157.23 [290]~E(x2901,x2902)+E(f57(x2901),f57(x2902))
% 157.55/157.23 [291]~E(x2911,x2912)+E(f13(x2911,x2913),f13(x2912,x2913))
% 157.55/157.23 [292]~E(x2921,x2922)+E(f13(x2923,x2921),f13(x2923,x2922))
% 157.55/157.23 [293]~E(x2931,x2932)+E(f144(x2931,x2933),f144(x2932,x2933))
% 157.55/157.23 [294]~E(x2941,x2942)+E(f144(x2943,x2941),f144(x2943,x2942))
% 157.55/157.23 [295]~E(x2951,x2952)+E(f47(x2951,x2953),f47(x2952,x2953))
% 157.55/157.23 [296]~E(x2961,x2962)+E(f47(x2963,x2961),f47(x2963,x2962))
% 157.55/157.23 [297]~E(x2971,x2972)+E(f156(x2971,x2973,x2974,x2975),f156(x2972,x2973,x2974,x2975))
% 157.55/157.23 [298]~E(x2981,x2982)+E(f156(x2983,x2981,x2984,x2985),f156(x2983,x2982,x2984,x2985))
% 157.55/157.23 [299]~E(x2991,x2992)+E(f156(x2993,x2994,x2991,x2995),f156(x2993,x2994,x2992,x2995))
% 157.55/157.23 [300]~E(x3001,x3002)+E(f156(x3003,x3004,x3005,x3001),f156(x3003,x3004,x3005,x3002))
% 157.55/157.23 [301]~E(x3011,x3012)+E(f169(x3011,x3013,x3014),f169(x3012,x3013,x3014))
% 157.55/157.23 [302]~E(x3021,x3022)+E(f169(x3023,x3021,x3024),f169(x3023,x3022,x3024))
% 157.55/157.23 [303]~E(x3031,x3032)+E(f169(x3033,x3034,x3031),f169(x3033,x3034,x3032))
% 157.55/157.23 [304]~E(x3041,x3042)+E(f850(x3041,x3043,x3044),f850(x3042,x3043,x3044))
% 157.55/157.23 [305]~E(x3051,x3052)+E(f850(x3053,x3051,x3054),f850(x3053,x3052,x3054))
% 157.55/157.23 [306]~E(x3061,x3062)+E(f850(x3063,x3064,x3061),f850(x3063,x3064,x3062))
% 157.55/157.23 [307]~E(x3071,x3072)+E(f63(x3071,x3073),f63(x3072,x3073))
% 157.55/157.23 [308]~E(x3081,x3082)+E(f63(x3083,x3081),f63(x3083,x3082))
% 157.55/157.23 [309]~E(x3091,x3092)+E(f65(x3091,x3093,x3094),f65(x3092,x3093,x3094))
% 157.55/157.23 [310]~E(x3101,x3102)+E(f65(x3103,x3101,x3104),f65(x3103,x3102,x3104))
% 157.55/157.23 [311]~E(x3111,x3112)+E(f65(x3113,x3114,x3111),f65(x3113,x3114,x3112))
% 157.55/157.23 [312]~E(x3121,x3122)+E(f17(x3121,x3123),f17(x3122,x3123))
% 157.55/157.23 [313]~E(x3131,x3132)+E(f17(x3133,x3131),f17(x3133,x3132))
% 157.55/157.23 [314]~E(x3141,x3142)+E(f452(x3141,x3143,x3144,x3145),f452(x3142,x3143,x3144,x3145))
% 157.55/157.23 [315]~E(x3151,x3152)+E(f452(x3153,x3151,x3154,x3155),f452(x3153,x3152,x3154,x3155))
% 157.55/157.23 [316]~E(x3161,x3162)+E(f452(x3163,x3164,x3161,x3165),f452(x3163,x3164,x3162,x3165))
% 157.55/157.23 [317]~E(x3171,x3172)+E(f452(x3173,x3174,x3175,x3171),f452(x3173,x3174,x3175,x3172))
% 157.55/157.23 [318]~E(x3181,x3182)+E(f48(x3181,x3183),f48(x3182,x3183))
% 157.55/157.23 [319]~E(x3191,x3192)+E(f48(x3193,x3191),f48(x3193,x3192))
% 157.55/157.23 [320]~E(x3201,x3202)+E(f317(x3201,x3203),f317(x3202,x3203))
% 157.55/157.23 [321]~E(x3211,x3212)+E(f317(x3213,x3211),f317(x3213,x3212))
% 157.55/157.23 [322]~E(x3221,x3222)+E(f222(x3221,x3223,x3224),f222(x3222,x3223,x3224))
% 157.55/157.23 [323]~E(x3231,x3232)+E(f222(x3233,x3231,x3234),f222(x3233,x3232,x3234))
% 157.55/157.23 [324]~E(x3241,x3242)+E(f222(x3243,x3244,x3241),f222(x3243,x3244,x3242))
% 157.55/157.23 [325]~E(x3251,x3252)+E(f318(x3251,x3253),f318(x3252,x3253))
% 157.55/157.23 [326]~E(x3261,x3262)+E(f318(x3263,x3261),f318(x3263,x3262))
% 157.55/157.23 [327]~E(x3271,x3272)+E(f141(x3271),f141(x3272))
% 157.55/157.23 [328]~E(x3281,x3282)+E(f139(x3281,x3283),f139(x3282,x3283))
% 157.55/157.23 [329]~E(x3291,x3292)+E(f139(x3293,x3291),f139(x3293,x3292))
% 157.55/157.23 [330]~E(x3301,x3302)+E(f247(x3301,x3303),f247(x3302,x3303))
% 157.55/157.23 [331]~E(x3311,x3312)+E(f247(x3313,x3311),f247(x3313,x3312))
% 157.55/157.23 [332]~E(x3321,x3322)+E(f299(x3321,x3323,x3324,x3325,x3326),f299(x3322,x3323,x3324,x3325,x3326))
% 157.55/157.23 [333]~E(x3331,x3332)+E(f299(x3333,x3331,x3334,x3335,x3336),f299(x3333,x3332,x3334,x3335,x3336))
% 157.55/157.23 [334]~E(x3341,x3342)+E(f299(x3343,x3344,x3341,x3345,x3346),f299(x3343,x3344,x3342,x3345,x3346))
% 157.55/157.23 [335]~E(x3351,x3352)+E(f299(x3353,x3354,x3355,x3351,x3356),f299(x3353,x3354,x3355,x3352,x3356))
% 157.55/157.23 [336]~E(x3361,x3362)+E(f299(x3363,x3364,x3365,x3366,x3361),f299(x3363,x3364,x3365,x3366,x3362))
% 157.55/157.23 [337]~E(x3371,x3372)+E(f773(x3371,x3373,x3374,x3375),f773(x3372,x3373,x3374,x3375))
% 157.55/157.23 [338]~E(x3381,x3382)+E(f773(x3383,x3381,x3384,x3385),f773(x3383,x3382,x3384,x3385))
% 157.55/157.23 [339]~E(x3391,x3392)+E(f773(x3393,x3394,x3391,x3395),f773(x3393,x3394,x3392,x3395))
% 157.55/157.23 [340]~E(x3401,x3402)+E(f773(x3403,x3404,x3405,x3401),f773(x3403,x3404,x3405,x3402))
% 157.55/157.23 [341]~E(x3411,x3412)+E(f809(x3411,x3413,x3414,x3415,x3416,x3417),f809(x3412,x3413,x3414,x3415,x3416,x3417))
% 157.55/157.23 [342]~E(x3421,x3422)+E(f809(x3423,x3421,x3424,x3425,x3426,x3427),f809(x3423,x3422,x3424,x3425,x3426,x3427))
% 157.55/157.23 [343]~E(x3431,x3432)+E(f809(x3433,x3434,x3431,x3435,x3436,x3437),f809(x3433,x3434,x3432,x3435,x3436,x3437))
% 157.55/157.23 [344]~E(x3441,x3442)+E(f809(x3443,x3444,x3445,x3441,x3446,x3447),f809(x3443,x3444,x3445,x3442,x3446,x3447))
% 157.55/157.23 [345]~E(x3451,x3452)+E(f809(x3453,x3454,x3455,x3456,x3451,x3457),f809(x3453,x3454,x3455,x3456,x3452,x3457))
% 157.55/157.23 [346]~E(x3461,x3462)+E(f809(x3463,x3464,x3465,x3466,x3467,x3461),f809(x3463,x3464,x3465,x3466,x3467,x3462))
% 157.55/157.23 [347]~E(x3471,x3472)+E(f142(x3471,x3473,x3474,x3475),f142(x3472,x3473,x3474,x3475))
% 157.55/157.23 [348]~E(x3481,x3482)+E(f142(x3483,x3481,x3484,x3485),f142(x3483,x3482,x3484,x3485))
% 157.55/157.23 [349]~E(x3491,x3492)+E(f142(x3493,x3494,x3491,x3495),f142(x3493,x3494,x3492,x3495))
% 157.55/157.23 [350]~E(x3501,x3502)+E(f142(x3503,x3504,x3505,x3501),f142(x3503,x3504,x3505,x3502))
% 157.55/157.23 [351]~E(x3511,x3512)+E(f890(x3511,x3513,x3514,x3515),f890(x3512,x3513,x3514,x3515))
% 157.55/157.23 [352]~E(x3521,x3522)+E(f890(x3523,x3521,x3524,x3525),f890(x3523,x3522,x3524,x3525))
% 157.55/157.23 [353]~E(x3531,x3532)+E(f890(x3533,x3534,x3531,x3535),f890(x3533,x3534,x3532,x3535))
% 157.55/157.23 [354]~E(x3541,x3542)+E(f890(x3543,x3544,x3545,x3541),f890(x3543,x3544,x3545,x3542))
% 157.55/157.23 [355]~E(x3551,x3552)+E(f14(x3551,x3553,x3554),f14(x3552,x3553,x3554))
% 157.55/157.23 [356]~E(x3561,x3562)+E(f14(x3563,x3561,x3564),f14(x3563,x3562,x3564))
% 157.55/157.23 [357]~E(x3571,x3572)+E(f14(x3573,x3574,x3571),f14(x3573,x3574,x3572))
% 157.55/157.23 [358]~E(x3581,x3582)+E(f284(x3581,x3583,x3584),f284(x3582,x3583,x3584))
% 157.55/157.23 [359]~E(x3591,x3592)+E(f284(x3593,x3591,x3594),f284(x3593,x3592,x3594))
% 157.55/157.23 [360]~E(x3601,x3602)+E(f284(x3603,x3604,x3601),f284(x3603,x3604,x3602))
% 157.55/157.23 [361]~E(x3611,x3612)+E(f870(x3611,x3613,x3614),f870(x3612,x3613,x3614))
% 157.55/157.23 [362]~E(x3621,x3622)+E(f870(x3623,x3621,x3624),f870(x3623,x3622,x3624))
% 157.55/157.23 [363]~E(x3631,x3632)+E(f870(x3633,x3634,x3631),f870(x3633,x3634,x3632))
% 157.55/157.23 [364]~E(x3641,x3642)+E(f256(x3641,x3643,x3644),f256(x3642,x3643,x3644))
% 157.55/157.23 [365]~E(x3651,x3652)+E(f256(x3653,x3651,x3654),f256(x3653,x3652,x3654))
% 157.55/157.23 [366]~E(x3661,x3662)+E(f256(x3663,x3664,x3661),f256(x3663,x3664,x3662))
% 157.55/157.23 [367]~E(x3671,x3672)+E(f380(x3671,x3673,x3674),f380(x3672,x3673,x3674))
% 157.55/157.23 [368]~E(x3681,x3682)+E(f380(x3683,x3681,x3684),f380(x3683,x3682,x3684))
% 157.55/157.23 [369]~E(x3691,x3692)+E(f380(x3693,x3694,x3691),f380(x3693,x3694,x3692))
% 157.55/157.23 [370]~E(x3701,x3702)+E(f90(x3701,x3703,x3704,x3705),f90(x3702,x3703,x3704,x3705))
% 157.55/157.23 [371]~E(x3711,x3712)+E(f90(x3713,x3711,x3714,x3715),f90(x3713,x3712,x3714,x3715))
% 157.55/157.23 [372]~E(x3721,x3722)+E(f90(x3723,x3724,x3721,x3725),f90(x3723,x3724,x3722,x3725))
% 157.55/157.23 [373]~E(x3731,x3732)+E(f90(x3733,x3734,x3735,x3731),f90(x3733,x3734,x3735,x3732))
% 157.55/157.23 [374]~E(x3741,x3742)+E(f119(x3741),f119(x3742))
% 157.55/157.23 [375]~E(x3751,x3752)+E(f120(x3751,x3753),f120(x3752,x3753))
% 157.55/157.23 [376]~E(x3761,x3762)+E(f120(x3763,x3761),f120(x3763,x3762))
% 157.55/157.23 [377]~E(x3771,x3772)+E(f283(x3771,x3773),f283(x3772,x3773))
% 157.55/157.23 [378]~E(x3781,x3782)+E(f283(x3783,x3781),f283(x3783,x3782))
% 157.55/157.23 [379]~E(x3791,x3792)+E(f439(x3791,x3793,x3794,x3795),f439(x3792,x3793,x3794,x3795))
% 157.55/157.23 [380]~E(x3801,x3802)+E(f439(x3803,x3801,x3804,x3805),f439(x3803,x3802,x3804,x3805))
% 157.55/157.23 [381]~E(x3811,x3812)+E(f439(x3813,x3814,x3811,x3815),f439(x3813,x3814,x3812,x3815))
% 157.55/157.23 [382]~E(x3821,x3822)+E(f439(x3823,x3824,x3825,x3821),f439(x3823,x3824,x3825,x3822))
% 157.55/157.23 [383]~E(x3831,x3832)+E(f312(x3831,x3833,x3834,x3835),f312(x3832,x3833,x3834,x3835))
% 157.55/157.23 [384]~E(x3841,x3842)+E(f312(x3843,x3841,x3844,x3845),f312(x3843,x3842,x3844,x3845))
% 157.55/157.23 [385]~E(x3851,x3852)+E(f312(x3853,x3854,x3851,x3855),f312(x3853,x3854,x3852,x3855))
% 157.55/157.23 [386]~E(x3861,x3862)+E(f312(x3863,x3864,x3865,x3861),f312(x3863,x3864,x3865,x3862))
% 157.55/157.23 [387]~E(x3871,x3872)+E(f514(x3871,x3873,x3874,x3875),f514(x3872,x3873,x3874,x3875))
% 157.55/157.23 [388]~E(x3881,x3882)+E(f514(x3883,x3881,x3884,x3885),f514(x3883,x3882,x3884,x3885))
% 157.55/157.23 [389]~E(x3891,x3892)+E(f514(x3893,x3894,x3891,x3895),f514(x3893,x3894,x3892,x3895))
% 157.55/157.23 [390]~E(x3901,x3902)+E(f514(x3903,x3904,x3905,x3901),f514(x3903,x3904,x3905,x3902))
% 157.55/157.23 [391]~E(x3911,x3912)+E(f84(x3911,x3913),f84(x3912,x3913))
% 157.55/157.23 [392]~E(x3921,x3922)+E(f84(x3923,x3921),f84(x3923,x3922))
% 157.55/157.23 [393]~E(x3931,x3932)+E(f803(x3931,x3933),f803(x3932,x3933))
% 157.55/157.23 [394]~E(x3941,x3942)+E(f803(x3943,x3941),f803(x3943,x3942))
% 157.55/157.23 [395]~E(x3951,x3952)+E(f89(x3951,x3953),f89(x3952,x3953))
% 157.55/157.23 [396]~E(x3961,x3962)+E(f89(x3963,x3961),f89(x3963,x3962))
% 157.55/157.23 [397]~E(x3971,x3972)+E(f178(x3971,x3973),f178(x3972,x3973))
% 157.55/157.23 [398]~E(x3981,x3982)+E(f178(x3983,x3981),f178(x3983,x3982))
% 157.55/157.23 [399]~E(x3991,x3992)+E(f153(x3991,x3993),f153(x3992,x3993))
% 157.55/157.23 [400]~E(x4001,x4002)+E(f153(x4003,x4001),f153(x4003,x4002))
% 157.55/157.23 [401]~E(x4011,x4012)+E(f262(x4011,x4013),f262(x4012,x4013))
% 157.55/157.23 [402]~E(x4021,x4022)+E(f262(x4023,x4021),f262(x4023,x4022))
% 157.55/157.23 [403]~E(x4031,x4032)+E(f96(x4031),f96(x4032))
% 157.55/157.23 [404]~E(x4041,x4042)+E(f718(x4041,x4043,x4044,x4045),f718(x4042,x4043,x4044,x4045))
% 157.55/157.23 [405]~E(x4051,x4052)+E(f718(x4053,x4051,x4054,x4055),f718(x4053,x4052,x4054,x4055))
% 157.55/157.23 [406]~E(x4061,x4062)+E(f718(x4063,x4064,x4061,x4065),f718(x4063,x4064,x4062,x4065))
% 157.55/157.23 [407]~E(x4071,x4072)+E(f718(x4073,x4074,x4075,x4071),f718(x4073,x4074,x4075,x4072))
% 157.55/157.23 [408]~E(x4081,x4082)+E(f74(x4081,x4083,x4084,x4085,x4086),f74(x4082,x4083,x4084,x4085,x4086))
% 157.55/157.23 [409]~E(x4091,x4092)+E(f74(x4093,x4091,x4094,x4095,x4096),f74(x4093,x4092,x4094,x4095,x4096))
% 157.55/157.23 [410]~E(x4101,x4102)+E(f74(x4103,x4104,x4101,x4105,x4106),f74(x4103,x4104,x4102,x4105,x4106))
% 157.55/157.23 [411]~E(x4111,x4112)+E(f74(x4113,x4114,x4115,x4111,x4116),f74(x4113,x4114,x4115,x4112,x4116))
% 157.55/157.23 [412]~E(x4121,x4122)+E(f74(x4123,x4124,x4125,x4126,x4121),f74(x4123,x4124,x4125,x4126,x4122))
% 157.55/157.23 [413]~E(x4131,x4132)+E(f772(x4131,x4133,x4134,x4135),f772(x4132,x4133,x4134,x4135))
% 157.55/157.23 [414]~E(x4141,x4142)+E(f772(x4143,x4141,x4144,x4145),f772(x4143,x4142,x4144,x4145))
% 157.55/157.23 [415]~E(x4151,x4152)+E(f772(x4153,x4154,x4151,x4155),f772(x4153,x4154,x4152,x4155))
% 157.55/157.23 [416]~E(x4161,x4162)+E(f772(x4163,x4164,x4165,x4161),f772(x4163,x4164,x4165,x4162))
% 157.55/157.23 [417]~E(x4171,x4172)+E(f66(x4171,x4173,x4174,x4175,x4176),f66(x4172,x4173,x4174,x4175,x4176))
% 157.55/157.23 [418]~E(x4181,x4182)+E(f66(x4183,x4181,x4184,x4185,x4186),f66(x4183,x4182,x4184,x4185,x4186))
% 157.55/157.23 [419]~E(x4191,x4192)+E(f66(x4193,x4194,x4191,x4195,x4196),f66(x4193,x4194,x4192,x4195,x4196))
% 157.55/157.23 [420]~E(x4201,x4202)+E(f66(x4203,x4204,x4205,x4201,x4206),f66(x4203,x4204,x4205,x4202,x4206))
% 157.55/157.23 [421]~E(x4211,x4212)+E(f66(x4213,x4214,x4215,x4216,x4211),f66(x4213,x4214,x4215,x4216,x4212))
% 157.55/157.23 [422]~E(x4221,x4222)+E(f181(x4221,x4223),f181(x4222,x4223))
% 157.55/157.23 [423]~E(x4231,x4232)+E(f181(x4233,x4231),f181(x4233,x4232))
% 157.55/157.23 [424]~E(x4241,x4242)+E(f15(x4241,x4243,x4244),f15(x4242,x4243,x4244))
% 157.55/157.23 [425]~E(x4251,x4252)+E(f15(x4253,x4251,x4254),f15(x4253,x4252,x4254))
% 157.55/157.23 [426]~E(x4261,x4262)+E(f15(x4263,x4264,x4261),f15(x4263,x4264,x4262))
% 157.55/157.23 [427]~E(x4271,x4272)+E(f183(x4271,x4273),f183(x4272,x4273))
% 157.55/157.23 [428]~E(x4281,x4282)+E(f183(x4283,x4281),f183(x4283,x4282))
% 157.55/157.23 [429]~E(x4291,x4292)+E(f50(x4291,x4293),f50(x4292,x4293))
% 157.55/157.23 [430]~E(x4301,x4302)+E(f50(x4303,x4301),f50(x4303,x4302))
% 157.55/157.23 [431]~E(x4311,x4312)+E(f815(x4311,x4313,x4314),f815(x4312,x4313,x4314))
% 157.55/157.23 [432]~E(x4321,x4322)+E(f815(x4323,x4321,x4324),f815(x4323,x4322,x4324))
% 157.55/157.23 [433]~E(x4331,x4332)+E(f815(x4333,x4334,x4331),f815(x4333,x4334,x4332))
% 157.55/157.23 [434]~E(x4341,x4342)+E(f258(x4341,x4343,x4344,x4345),f258(x4342,x4343,x4344,x4345))
% 157.55/157.23 [435]~E(x4351,x4352)+E(f258(x4353,x4351,x4354,x4355),f258(x4353,x4352,x4354,x4355))
% 157.55/157.23 [436]~E(x4361,x4362)+E(f258(x4363,x4364,x4361,x4365),f258(x4363,x4364,x4362,x4365))
% 157.55/157.23 [437]~E(x4371,x4372)+E(f258(x4373,x4374,x4375,x4371),f258(x4373,x4374,x4375,x4372))
% 157.55/157.23 [438]~E(x4381,x4382)+E(f686(x4381,x4383,x4384),f686(x4382,x4383,x4384))
% 157.55/157.23 [439]~E(x4391,x4392)+E(f686(x4393,x4391,x4394),f686(x4393,x4392,x4394))
% 157.55/157.23 [440]~E(x4401,x4402)+E(f686(x4403,x4404,x4401),f686(x4403,x4404,x4402))
% 157.55/157.23 [441]~E(x4411,x4412)+E(f67(x4411,x4413,x4414),f67(x4412,x4413,x4414))
% 157.55/157.23 [442]~E(x4421,x4422)+E(f67(x4423,x4421,x4424),f67(x4423,x4422,x4424))
% 157.55/157.23 [443]~E(x4431,x4432)+E(f67(x4433,x4434,x4431),f67(x4433,x4434,x4432))
% 157.55/157.23 [444]~E(x4441,x4442)+E(f674(x4441,x4443,x4444,x4445,x4446),f674(x4442,x4443,x4444,x4445,x4446))
% 157.55/157.23 [445]~E(x4451,x4452)+E(f674(x4453,x4451,x4454,x4455,x4456),f674(x4453,x4452,x4454,x4455,x4456))
% 157.55/157.23 [446]~E(x4461,x4462)+E(f674(x4463,x4464,x4461,x4465,x4466),f674(x4463,x4464,x4462,x4465,x4466))
% 157.55/157.23 [447]~E(x4471,x4472)+E(f674(x4473,x4474,x4475,x4471,x4476),f674(x4473,x4474,x4475,x4472,x4476))
% 157.55/157.23 [448]~E(x4481,x4482)+E(f674(x4483,x4484,x4485,x4486,x4481),f674(x4483,x4484,x4485,x4486,x4482))
% 157.55/157.23 [449]~E(x4491,x4492)+E(f800(x4491),f800(x4492))
% 157.55/157.23 [450]~E(x4501,x4502)+E(f257(x4501,x4503,x4504,x4505,x4506,x4507),f257(x4502,x4503,x4504,x4505,x4506,x4507))
% 157.55/157.23 [451]~E(x4511,x4512)+E(f257(x4513,x4511,x4514,x4515,x4516,x4517),f257(x4513,x4512,x4514,x4515,x4516,x4517))
% 157.55/157.23 [452]~E(x4521,x4522)+E(f257(x4523,x4524,x4521,x4525,x4526,x4527),f257(x4523,x4524,x4522,x4525,x4526,x4527))
% 157.55/157.23 [453]~E(x4531,x4532)+E(f257(x4533,x4534,x4535,x4531,x4536,x4537),f257(x4533,x4534,x4535,x4532,x4536,x4537))
% 157.55/157.23 [454]~E(x4541,x4542)+E(f257(x4543,x4544,x4545,x4546,x4541,x4547),f257(x4543,x4544,x4545,x4546,x4542,x4547))
% 157.55/157.23 [455]~E(x4551,x4552)+E(f257(x4553,x4554,x4555,x4556,x4557,x4551),f257(x4553,x4554,x4555,x4556,x4557,x4552))
% 157.55/157.23 [456]~E(x4561,x4562)+E(f296(x4561,x4563,x4564,x4565,x4566),f296(x4562,x4563,x4564,x4565,x4566))
% 157.55/157.23 [457]~E(x4571,x4572)+E(f296(x4573,x4571,x4574,x4575,x4576),f296(x4573,x4572,x4574,x4575,x4576))
% 157.55/157.23 [458]~E(x4581,x4582)+E(f296(x4583,x4584,x4581,x4585,x4586),f296(x4583,x4584,x4582,x4585,x4586))
% 157.55/157.23 [459]~E(x4591,x4592)+E(f296(x4593,x4594,x4595,x4591,x4596),f296(x4593,x4594,x4595,x4592,x4596))
% 157.55/157.23 [460]~E(x4601,x4602)+E(f296(x4603,x4604,x4605,x4606,x4601),f296(x4603,x4604,x4605,x4606,x4602))
% 157.55/157.23 [461]~E(x4611,x4612)+E(f23(x4611,x4613),f23(x4612,x4613))
% 157.55/157.23 [462]~E(x4621,x4622)+E(f23(x4623,x4621),f23(x4623,x4622))
% 157.55/157.23 [463]~E(x4631,x4632)+E(f436(x4631,x4633,x4634,x4635,x4636,x4637,x4638),f436(x4632,x4633,x4634,x4635,x4636,x4637,x4638))
% 157.55/157.23 [464]~E(x4641,x4642)+E(f436(x4643,x4641,x4644,x4645,x4646,x4647,x4648),f436(x4643,x4642,x4644,x4645,x4646,x4647,x4648))
% 157.55/157.23 [465]~E(x4651,x4652)+E(f436(x4653,x4654,x4651,x4655,x4656,x4657,x4658),f436(x4653,x4654,x4652,x4655,x4656,x4657,x4658))
% 157.55/157.23 [466]~E(x4661,x4662)+E(f436(x4663,x4664,x4665,x4661,x4666,x4667,x4668),f436(x4663,x4664,x4665,x4662,x4666,x4667,x4668))
% 157.55/157.23 [467]~E(x4671,x4672)+E(f436(x4673,x4674,x4675,x4676,x4671,x4677,x4678),f436(x4673,x4674,x4675,x4676,x4672,x4677,x4678))
% 157.55/157.23 [468]~E(x4681,x4682)+E(f436(x4683,x4684,x4685,x4686,x4687,x4681,x4688),f436(x4683,x4684,x4685,x4686,x4687,x4682,x4688))
% 157.55/157.23 [469]~E(x4691,x4692)+E(f436(x4693,x4694,x4695,x4696,x4697,x4698,x4691),f436(x4693,x4694,x4695,x4696,x4697,x4698,x4692))
% 157.55/157.23 [470]~E(x4701,x4702)+E(f632(x4701,x4703),f632(x4702,x4703))
% 157.55/157.23 [471]~E(x4711,x4712)+E(f632(x4713,x4711),f632(x4713,x4712))
% 157.55/157.23 [472]~E(x4721,x4722)+E(f810(x4721,x4723,x4724,x4725,x4726,x4727),f810(x4722,x4723,x4724,x4725,x4726,x4727))
% 157.55/157.23 [473]~E(x4731,x4732)+E(f810(x4733,x4731,x4734,x4735,x4736,x4737),f810(x4733,x4732,x4734,x4735,x4736,x4737))
% 157.55/157.23 [474]~E(x4741,x4742)+E(f810(x4743,x4744,x4741,x4745,x4746,x4747),f810(x4743,x4744,x4742,x4745,x4746,x4747))
% 157.55/157.23 [475]~E(x4751,x4752)+E(f810(x4753,x4754,x4755,x4751,x4756,x4757),f810(x4753,x4754,x4755,x4752,x4756,x4757))
% 157.55/157.23 [476]~E(x4761,x4762)+E(f810(x4763,x4764,x4765,x4766,x4761,x4767),f810(x4763,x4764,x4765,x4766,x4762,x4767))
% 157.55/157.23 [477]~E(x4771,x4772)+E(f810(x4773,x4774,x4775,x4776,x4777,x4771),f810(x4773,x4774,x4775,x4776,x4777,x4772))
% 157.55/157.23 [478]~E(x4781,x4782)+E(f157(x4781,x4783),f157(x4782,x4783))
% 157.55/157.23 [479]~E(x4791,x4792)+E(f157(x4793,x4791),f157(x4793,x4792))
% 157.55/157.23 [480]~E(x4801,x4802)+E(f365(x4801),f365(x4802))
% 157.55/157.23 [481]~E(x4811,x4812)+E(f175(x4811),f175(x4812))
% 157.55/157.23 [482]~E(x4821,x4822)+E(f179(x4821,x4823),f179(x4822,x4823))
% 157.55/157.23 [483]~E(x4831,x4832)+E(f179(x4833,x4831),f179(x4833,x4832))
% 157.55/157.23 [484]~E(x4841,x4842)+E(f216(x4841,x4843),f216(x4842,x4843))
% 157.55/157.23 [485]~E(x4851,x4852)+E(f216(x4853,x4851),f216(x4853,x4852))
% 157.55/157.23 [486]~E(x4861,x4862)+E(f872(x4861,x4863,x4864,x4865),f872(x4862,x4863,x4864,x4865))
% 157.55/157.23 [487]~E(x4871,x4872)+E(f872(x4873,x4871,x4874,x4875),f872(x4873,x4872,x4874,x4875))
% 157.55/157.23 [488]~E(x4881,x4882)+E(f872(x4883,x4884,x4881,x4885),f872(x4883,x4884,x4882,x4885))
% 157.55/157.23 [489]~E(x4891,x4892)+E(f872(x4893,x4894,x4895,x4891),f872(x4893,x4894,x4895,x4892))
% 157.55/157.23 [490]~E(x4901,x4902)+E(f242(x4901,x4903,x4904),f242(x4902,x4903,x4904))
% 157.55/157.23 [491]~E(x4911,x4912)+E(f242(x4913,x4911,x4914),f242(x4913,x4912,x4914))
% 157.55/157.23 [492]~E(x4921,x4922)+E(f242(x4923,x4924,x4921),f242(x4923,x4924,x4922))
% 157.55/157.23 [493]~E(x4931,x4932)+E(f313(x4931),f313(x4932))
% 157.55/157.23 [494]~E(x4941,x4942)+E(f148(x4941,x4943,x4944),f148(x4942,x4943,x4944))
% 157.55/157.23 [495]~E(x4951,x4952)+E(f148(x4953,x4951,x4954),f148(x4953,x4952,x4954))
% 157.55/157.23 [496]~E(x4961,x4962)+E(f148(x4963,x4964,x4961),f148(x4963,x4964,x4962))
% 157.55/157.23 [497]~E(x4971,x4972)+E(f81(x4971,x4973),f81(x4972,x4973))
% 157.55/157.23 [498]~E(x4981,x4982)+E(f81(x4983,x4981),f81(x4983,x4982))
% 157.55/157.23 [499]~E(x4991,x4992)+E(f667(x4991,x4993,x4994),f667(x4992,x4993,x4994))
% 157.55/157.23 [500]~E(x5001,x5002)+E(f667(x5003,x5001,x5004),f667(x5003,x5002,x5004))
% 157.55/157.23 [501]~E(x5011,x5012)+E(f667(x5013,x5014,x5011),f667(x5013,x5014,x5012))
% 157.55/157.23 [502]~E(x5021,x5022)+E(f236(x5021,x5023),f236(x5022,x5023))
% 157.55/157.23 [503]~E(x5031,x5032)+E(f236(x5033,x5031),f236(x5033,x5032))
% 157.55/157.23 [504]~E(x5041,x5042)+E(f498(x5041,x5043,x5044,x5045,x5046),f498(x5042,x5043,x5044,x5045,x5046))
% 157.55/157.23 [505]~E(x5051,x5052)+E(f498(x5053,x5051,x5054,x5055,x5056),f498(x5053,x5052,x5054,x5055,x5056))
% 157.55/157.23 [506]~E(x5061,x5062)+E(f498(x5063,x5064,x5061,x5065,x5066),f498(x5063,x5064,x5062,x5065,x5066))
% 157.55/157.23 [507]~E(x5071,x5072)+E(f498(x5073,x5074,x5075,x5071,x5076),f498(x5073,x5074,x5075,x5072,x5076))
% 157.55/157.23 [508]~E(x5081,x5082)+E(f498(x5083,x5084,x5085,x5086,x5081),f498(x5083,x5084,x5085,x5086,x5082))
% 157.55/157.23 [509]~E(x5091,x5092)+E(f836(x5091,x5093,x5094,x5095,x5096,x5097,x5098,x5099),f836(x5092,x5093,x5094,x5095,x5096,x5097,x5098,x5099))
% 157.55/157.23 [510]~E(x5101,x5102)+E(f836(x5103,x5101,x5104,x5105,x5106,x5107,x5108,x5109),f836(x5103,x5102,x5104,x5105,x5106,x5107,x5108,x5109))
% 157.55/157.23 [511]~E(x5111,x5112)+E(f836(x5113,x5114,x5111,x5115,x5116,x5117,x5118,x5119),f836(x5113,x5114,x5112,x5115,x5116,x5117,x5118,x5119))
% 157.55/157.23 [512]~E(x5121,x5122)+E(f836(x5123,x5124,x5125,x5121,x5126,x5127,x5128,x5129),f836(x5123,x5124,x5125,x5122,x5126,x5127,x5128,x5129))
% 157.55/157.23 [513]~E(x5131,x5132)+E(f836(x5133,x5134,x5135,x5136,x5131,x5137,x5138,x5139),f836(x5133,x5134,x5135,x5136,x5132,x5137,x5138,x5139))
% 157.55/157.23 [514]~E(x5141,x5142)+E(f836(x5143,x5144,x5145,x5146,x5147,x5141,x5148,x5149),f836(x5143,x5144,x5145,x5146,x5147,x5142,x5148,x5149))
% 157.55/157.23 [515]~E(x5151,x5152)+E(f836(x5153,x5154,x5155,x5156,x5157,x5158,x5151,x5159),f836(x5153,x5154,x5155,x5156,x5157,x5158,x5152,x5159))
% 157.55/157.23 [516]~E(x5161,x5162)+E(f836(x5163,x5164,x5165,x5166,x5167,x5168,x5169,x5161),f836(x5163,x5164,x5165,x5166,x5167,x5168,x5169,x5162))
% 157.55/157.23 [517]~E(x5171,x5172)+E(f865(x5171,x5173,x5174,x5175),f865(x5172,x5173,x5174,x5175))
% 157.55/157.23 [518]~E(x5181,x5182)+E(f865(x5183,x5181,x5184,x5185),f865(x5183,x5182,x5184,x5185))
% 157.55/157.23 [519]~E(x5191,x5192)+E(f865(x5193,x5194,x5191,x5195),f865(x5193,x5194,x5192,x5195))
% 157.55/157.23 [520]~E(x5201,x5202)+E(f865(x5203,x5204,x5205,x5201),f865(x5203,x5204,x5205,x5202))
% 157.55/157.23 [521]~E(x5211,x5212)+E(f76(x5211,x5213,x5214,x5215),f76(x5212,x5213,x5214,x5215))
% 157.55/157.23 [522]~E(x5221,x5222)+E(f76(x5223,x5221,x5224,x5225),f76(x5223,x5222,x5224,x5225))
% 157.55/157.23 [523]~E(x5231,x5232)+E(f76(x5233,x5234,x5231,x5235),f76(x5233,x5234,x5232,x5235))
% 157.55/157.23 [524]~E(x5241,x5242)+E(f76(x5243,x5244,x5245,x5241),f76(x5243,x5244,x5245,x5242))
% 157.55/157.23 [525]~E(x5251,x5252)+E(f726(x5251,x5253),f726(x5252,x5253))
% 157.55/157.23 [526]~E(x5261,x5262)+E(f726(x5263,x5261),f726(x5263,x5262))
% 157.55/157.23 [527]~E(x5271,x5272)+E(f697(x5271,x5273,x5274),f697(x5272,x5273,x5274))
% 157.55/157.23 [528]~E(x5281,x5282)+E(f697(x5283,x5281,x5284),f697(x5283,x5282,x5284))
% 157.55/157.23 [529]~E(x5291,x5292)+E(f697(x5293,x5294,x5291),f697(x5293,x5294,x5292))
% 157.55/157.23 [530]~E(x5301,x5302)+E(f727(x5301,x5303,x5304,x5305,x5306,x5307,x5308,x5309),f727(x5302,x5303,x5304,x5305,x5306,x5307,x5308,x5309))
% 157.55/157.23 [531]~E(x5311,x5312)+E(f727(x5313,x5311,x5314,x5315,x5316,x5317,x5318,x5319),f727(x5313,x5312,x5314,x5315,x5316,x5317,x5318,x5319))
% 157.55/157.23 [532]~E(x5321,x5322)+E(f727(x5323,x5324,x5321,x5325,x5326,x5327,x5328,x5329),f727(x5323,x5324,x5322,x5325,x5326,x5327,x5328,x5329))
% 157.55/157.23 [533]~E(x5331,x5332)+E(f727(x5333,x5334,x5335,x5331,x5336,x5337,x5338,x5339),f727(x5333,x5334,x5335,x5332,x5336,x5337,x5338,x5339))
% 157.55/157.23 [534]~E(x5341,x5342)+E(f727(x5343,x5344,x5345,x5346,x5341,x5347,x5348,x5349),f727(x5343,x5344,x5345,x5346,x5342,x5347,x5348,x5349))
% 157.55/157.23 [535]~E(x5351,x5352)+E(f727(x5353,x5354,x5355,x5356,x5357,x5351,x5358,x5359),f727(x5353,x5354,x5355,x5356,x5357,x5352,x5358,x5359))
% 157.55/157.23 [536]~E(x5361,x5362)+E(f727(x5363,x5364,x5365,x5366,x5367,x5368,x5361,x5369),f727(x5363,x5364,x5365,x5366,x5367,x5368,x5362,x5369))
% 157.55/157.23 [537]~E(x5371,x5372)+E(f727(x5373,x5374,x5375,x5376,x5377,x5378,x5379,x5371),f727(x5373,x5374,x5375,x5376,x5377,x5378,x5379,x5372))
% 157.55/157.23 [538]~E(x5381,x5382)+E(f46(x5381,x5383),f46(x5382,x5383))
% 157.55/157.23 [539]~E(x5391,x5392)+E(f46(x5393,x5391),f46(x5393,x5392))
% 157.55/157.23 [540]~E(x5401,x5402)+E(f550(x5401,x5403),f550(x5402,x5403))
% 157.55/157.23 [541]~E(x5411,x5412)+E(f550(x5413,x5411),f550(x5413,x5412))
% 157.55/157.23 [542]~E(x5421,x5422)+E(f565(x5421,x5423,x5424,x5425),f565(x5422,x5423,x5424,x5425))
% 157.55/157.23 [543]~E(x5431,x5432)+E(f565(x5433,x5431,x5434,x5435),f565(x5433,x5432,x5434,x5435))
% 157.55/157.23 [544]~E(x5441,x5442)+E(f565(x5443,x5444,x5441,x5445),f565(x5443,x5444,x5442,x5445))
% 157.55/157.23 [545]~E(x5451,x5452)+E(f565(x5453,x5454,x5455,x5451),f565(x5453,x5454,x5455,x5452))
% 157.55/157.23 [546]~E(x5461,x5462)+E(f346(x5461,x5463),f346(x5462,x5463))
% 157.55/157.23 [547]~E(x5471,x5472)+E(f346(x5473,x5471),f346(x5473,x5472))
% 157.55/157.23 [548]~E(x5481,x5482)+E(f197(x5481,x5483,x5484,x5485),f197(x5482,x5483,x5484,x5485))
% 157.55/157.23 [549]~E(x5491,x5492)+E(f197(x5493,x5491,x5494,x5495),f197(x5493,x5492,x5494,x5495))
% 157.55/157.23 [550]~E(x5501,x5502)+E(f197(x5503,x5504,x5501,x5505),f197(x5503,x5504,x5502,x5505))
% 157.55/157.23 [551]~E(x5511,x5512)+E(f197(x5513,x5514,x5515,x5511),f197(x5513,x5514,x5515,x5512))
% 157.55/157.23 [552]~E(x5521,x5522)+E(f642(x5521,x5523,x5524,x5525),f642(x5522,x5523,x5524,x5525))
% 157.55/157.23 [553]~E(x5531,x5532)+E(f642(x5533,x5531,x5534,x5535),f642(x5533,x5532,x5534,x5535))
% 157.55/157.23 [554]~E(x5541,x5542)+E(f642(x5543,x5544,x5541,x5545),f642(x5543,x5544,x5542,x5545))
% 157.55/157.23 [555]~E(x5551,x5552)+E(f642(x5553,x5554,x5555,x5551),f642(x5553,x5554,x5555,x5552))
% 157.55/157.23 [556]~E(x5561,x5562)+E(f420(x5561,x5563,x5564,x5565,x5566),f420(x5562,x5563,x5564,x5565,x5566))
% 157.55/157.23 [557]~E(x5571,x5572)+E(f420(x5573,x5571,x5574,x5575,x5576),f420(x5573,x5572,x5574,x5575,x5576))
% 157.55/157.23 [558]~E(x5581,x5582)+E(f420(x5583,x5584,x5581,x5585,x5586),f420(x5583,x5584,x5582,x5585,x5586))
% 157.55/157.23 [559]~E(x5591,x5592)+E(f420(x5593,x5594,x5595,x5591,x5596),f420(x5593,x5594,x5595,x5592,x5596))
% 157.55/157.23 [560]~E(x5601,x5602)+E(f420(x5603,x5604,x5605,x5606,x5601),f420(x5603,x5604,x5605,x5606,x5602))
% 157.55/157.23 [561]~E(x5611,x5612)+E(f363(x5611,x5613,x5614),f363(x5612,x5613,x5614))
% 157.55/157.23 [562]~E(x5621,x5622)+E(f363(x5623,x5621,x5624),f363(x5623,x5622,x5624))
% 157.55/157.23 [563]~E(x5631,x5632)+E(f363(x5633,x5634,x5631),f363(x5633,x5634,x5632))
% 157.55/157.23 [564]~E(x5641,x5642)+E(f665(x5641,x5643,x5644,x5645,x5646,x5647,x5648),f665(x5642,x5643,x5644,x5645,x5646,x5647,x5648))
% 157.55/157.23 [565]~E(x5651,x5652)+E(f665(x5653,x5651,x5654,x5655,x5656,x5657,x5658),f665(x5653,x5652,x5654,x5655,x5656,x5657,x5658))
% 157.55/157.23 [566]~E(x5661,x5662)+E(f665(x5663,x5664,x5661,x5665,x5666,x5667,x5668),f665(x5663,x5664,x5662,x5665,x5666,x5667,x5668))
% 157.55/157.23 [567]~E(x5671,x5672)+E(f665(x5673,x5674,x5675,x5671,x5676,x5677,x5678),f665(x5673,x5674,x5675,x5672,x5676,x5677,x5678))
% 157.55/157.23 [568]~E(x5681,x5682)+E(f665(x5683,x5684,x5685,x5686,x5681,x5687,x5688),f665(x5683,x5684,x5685,x5686,x5682,x5687,x5688))
% 157.55/157.23 [569]~E(x5691,x5692)+E(f665(x5693,x5694,x5695,x5696,x5697,x5691,x5698),f665(x5693,x5694,x5695,x5696,x5697,x5692,x5698))
% 157.55/157.23 [570]~E(x5701,x5702)+E(f665(x5703,x5704,x5705,x5706,x5707,x5708,x5701),f665(x5703,x5704,x5705,x5706,x5707,x5708,x5702))
% 157.55/157.23 [571]~E(x5711,x5712)+E(f862(x5711,x5713,x5714),f862(x5712,x5713,x5714))
% 157.55/157.23 [572]~E(x5721,x5722)+E(f862(x5723,x5721,x5724),f862(x5723,x5722,x5724))
% 157.55/157.23 [573]~E(x5731,x5732)+E(f862(x5733,x5734,x5731),f862(x5733,x5734,x5732))
% 157.55/157.23 [574]~E(x5741,x5742)+E(f579(x5741,x5743,x5744,x5745),f579(x5742,x5743,x5744,x5745))
% 157.55/157.23 [575]~E(x5751,x5752)+E(f579(x5753,x5751,x5754,x5755),f579(x5753,x5752,x5754,x5755))
% 157.55/157.23 [576]~E(x5761,x5762)+E(f579(x5763,x5764,x5761,x5765),f579(x5763,x5764,x5762,x5765))
% 157.55/157.23 [577]~E(x5771,x5772)+E(f579(x5773,x5774,x5775,x5771),f579(x5773,x5774,x5775,x5772))
% 157.55/157.23 [578]~E(x5781,x5782)+E(f710(x5781,x5783),f710(x5782,x5783))
% 157.55/157.23 [579]~E(x5791,x5792)+E(f710(x5793,x5791),f710(x5793,x5792))
% 157.55/157.23 [580]~E(x5801,x5802)+E(f858(x5801,x5803,x5804),f858(x5802,x5803,x5804))
% 157.55/157.23 [581]~E(x5811,x5812)+E(f858(x5813,x5811,x5814),f858(x5813,x5812,x5814))
% 157.55/157.23 [582]~E(x5821,x5822)+E(f858(x5823,x5824,x5821),f858(x5823,x5824,x5822))
% 157.55/157.23 [583]~E(x5831,x5832)+E(f770(x5831,x5833,x5834,x5835),f770(x5832,x5833,x5834,x5835))
% 157.55/157.23 [584]~E(x5841,x5842)+E(f770(x5843,x5841,x5844,x5845),f770(x5843,x5842,x5844,x5845))
% 157.55/157.23 [585]~E(x5851,x5852)+E(f770(x5853,x5854,x5851,x5855),f770(x5853,x5854,x5852,x5855))
% 157.55/157.23 [586]~E(x5861,x5862)+E(f770(x5863,x5864,x5865,x5861),f770(x5863,x5864,x5865,x5862))
% 157.55/157.23 [587]~E(x5871,x5872)+E(f479(x5871,x5873,x5874,x5875),f479(x5872,x5873,x5874,x5875))
% 157.55/157.23 [588]~E(x5881,x5882)+E(f479(x5883,x5881,x5884,x5885),f479(x5883,x5882,x5884,x5885))
% 157.55/157.23 [589]~E(x5891,x5892)+E(f479(x5893,x5894,x5891,x5895),f479(x5893,x5894,x5892,x5895))
% 157.55/157.23 [590]~E(x5901,x5902)+E(f479(x5903,x5904,x5905,x5901),f479(x5903,x5904,x5905,x5902))
% 157.55/157.23 [591]~E(x5911,x5912)+E(f269(x5911,x5913),f269(x5912,x5913))
% 157.55/157.23 [592]~E(x5921,x5922)+E(f269(x5923,x5921),f269(x5923,x5922))
% 157.55/157.23 [593]~E(x5931,x5932)+E(f125(x5931,x5933),f125(x5932,x5933))
% 157.55/157.23 [594]~E(x5941,x5942)+E(f125(x5943,x5941),f125(x5943,x5942))
% 157.55/157.23 [595]~E(x5951,x5952)+E(f272(x5951,x5953,x5954,x5955),f272(x5952,x5953,x5954,x5955))
% 157.55/157.23 [596]~E(x5961,x5962)+E(f272(x5963,x5961,x5964,x5965),f272(x5963,x5962,x5964,x5965))
% 157.55/157.23 [597]~E(x5971,x5972)+E(f272(x5973,x5974,x5971,x5975),f272(x5973,x5974,x5972,x5975))
% 157.55/157.23 [598]~E(x5981,x5982)+E(f272(x5983,x5984,x5985,x5981),f272(x5983,x5984,x5985,x5982))
% 157.55/157.23 [599]~E(x5991,x5992)+E(f118(x5991,x5993,x5994),f118(x5992,x5993,x5994))
% 157.55/157.23 [600]~E(x6001,x6002)+E(f118(x6003,x6001,x6004),f118(x6003,x6002,x6004))
% 157.55/157.23 [601]~E(x6011,x6012)+E(f118(x6013,x6014,x6011),f118(x6013,x6014,x6012))
% 157.55/157.23 [602]~E(x6021,x6022)+E(f451(x6021,x6023,x6024,x6025),f451(x6022,x6023,x6024,x6025))
% 157.55/157.23 [603]~E(x6031,x6032)+E(f451(x6033,x6031,x6034,x6035),f451(x6033,x6032,x6034,x6035))
% 157.55/157.23 [604]~E(x6041,x6042)+E(f451(x6043,x6044,x6041,x6045),f451(x6043,x6044,x6042,x6045))
% 157.55/157.23 [605]~E(x6051,x6052)+E(f451(x6053,x6054,x6055,x6051),f451(x6053,x6054,x6055,x6052))
% 157.55/157.23 [606]~E(x6061,x6062)+E(f339(x6061),f339(x6062))
% 157.55/157.23 [607]~E(x6071,x6072)+E(f252(x6071,x6073,x6074,x6075,x6076),f252(x6072,x6073,x6074,x6075,x6076))
% 157.55/157.23 [608]~E(x6081,x6082)+E(f252(x6083,x6081,x6084,x6085,x6086),f252(x6083,x6082,x6084,x6085,x6086))
% 157.55/157.23 [609]~E(x6091,x6092)+E(f252(x6093,x6094,x6091,x6095,x6096),f252(x6093,x6094,x6092,x6095,x6096))
% 157.55/157.23 [610]~E(x6101,x6102)+E(f252(x6103,x6104,x6105,x6101,x6106),f252(x6103,x6104,x6105,x6102,x6106))
% 157.55/157.23 [611]~E(x6111,x6112)+E(f252(x6113,x6114,x6115,x6116,x6111),f252(x6113,x6114,x6115,x6116,x6112))
% 157.55/157.23 [612]~E(x6121,x6122)+E(f466(x6121,x6123,x6124,x6125,x6126),f466(x6122,x6123,x6124,x6125,x6126))
% 157.55/157.23 [613]~E(x6131,x6132)+E(f466(x6133,x6131,x6134,x6135,x6136),f466(x6133,x6132,x6134,x6135,x6136))
% 157.55/157.23 [614]~E(x6141,x6142)+E(f466(x6143,x6144,x6141,x6145,x6146),f466(x6143,x6144,x6142,x6145,x6146))
% 157.55/157.23 [615]~E(x6151,x6152)+E(f466(x6153,x6154,x6155,x6151,x6156),f466(x6153,x6154,x6155,x6152,x6156))
% 157.55/157.23 [616]~E(x6161,x6162)+E(f466(x6163,x6164,x6165,x6166,x6161),f466(x6163,x6164,x6165,x6166,x6162))
% 157.55/157.23 [617]~E(x6171,x6172)+E(f450(x6171,x6173,x6174,x6175),f450(x6172,x6173,x6174,x6175))
% 157.55/157.23 [618]~E(x6181,x6182)+E(f450(x6183,x6181,x6184,x6185),f450(x6183,x6182,x6184,x6185))
% 157.55/157.23 [619]~E(x6191,x6192)+E(f450(x6193,x6194,x6191,x6195),f450(x6193,x6194,x6192,x6195))
% 157.55/157.23 [620]~E(x6201,x6202)+E(f450(x6203,x6204,x6205,x6201),f450(x6203,x6204,x6205,x6202))
% 157.55/157.23 [621]~E(x6211,x6212)+E(f472(x6211,x6213,x6214,x6215,x6216,x6217,x6218),f472(x6212,x6213,x6214,x6215,x6216,x6217,x6218))
% 157.55/157.23 [622]~E(x6221,x6222)+E(f472(x6223,x6221,x6224,x6225,x6226,x6227,x6228),f472(x6223,x6222,x6224,x6225,x6226,x6227,x6228))
% 157.55/157.23 [623]~E(x6231,x6232)+E(f472(x6233,x6234,x6231,x6235,x6236,x6237,x6238),f472(x6233,x6234,x6232,x6235,x6236,x6237,x6238))
% 157.55/157.23 [624]~E(x6241,x6242)+E(f472(x6243,x6244,x6245,x6241,x6246,x6247,x6248),f472(x6243,x6244,x6245,x6242,x6246,x6247,x6248))
% 157.55/157.23 [625]~E(x6251,x6252)+E(f472(x6253,x6254,x6255,x6256,x6251,x6257,x6258),f472(x6253,x6254,x6255,x6256,x6252,x6257,x6258))
% 157.55/157.23 [626]~E(x6261,x6262)+E(f472(x6263,x6264,x6265,x6266,x6267,x6261,x6268),f472(x6263,x6264,x6265,x6266,x6267,x6262,x6268))
% 157.55/157.23 [627]~E(x6271,x6272)+E(f472(x6273,x6274,x6275,x6276,x6277,x6278,x6271),f472(x6273,x6274,x6275,x6276,x6277,x6278,x6272))
% 157.55/157.23 [628]~E(x6281,x6282)+E(f781(x6281,x6283,x6284,x6285,x6286,x6287,x6288),f781(x6282,x6283,x6284,x6285,x6286,x6287,x6288))
% 157.55/157.23 [629]~E(x6291,x6292)+E(f781(x6293,x6291,x6294,x6295,x6296,x6297,x6298),f781(x6293,x6292,x6294,x6295,x6296,x6297,x6298))
% 157.55/157.23 [630]~E(x6301,x6302)+E(f781(x6303,x6304,x6301,x6305,x6306,x6307,x6308),f781(x6303,x6304,x6302,x6305,x6306,x6307,x6308))
% 157.55/157.23 [631]~E(x6311,x6312)+E(f781(x6313,x6314,x6315,x6311,x6316,x6317,x6318),f781(x6313,x6314,x6315,x6312,x6316,x6317,x6318))
% 157.55/157.23 [632]~E(x6321,x6322)+E(f781(x6323,x6324,x6325,x6326,x6321,x6327,x6328),f781(x6323,x6324,x6325,x6326,x6322,x6327,x6328))
% 157.55/157.23 [633]~E(x6331,x6332)+E(f781(x6333,x6334,x6335,x6336,x6337,x6331,x6338),f781(x6333,x6334,x6335,x6336,x6337,x6332,x6338))
% 157.55/157.23 [634]~E(x6341,x6342)+E(f781(x6343,x6344,x6345,x6346,x6347,x6348,x6341),f781(x6343,x6344,x6345,x6346,x6347,x6348,x6342))
% 157.55/157.23 [635]~E(x6351,x6352)+E(f314(x6351,x6353),f314(x6352,x6353))
% 157.55/157.23 [636]~E(x6361,x6362)+E(f314(x6363,x6361),f314(x6363,x6362))
% 157.55/157.23 [637]~E(x6371,x6372)+E(f714(x6371,x6373,x6374,x6375,x6376),f714(x6372,x6373,x6374,x6375,x6376))
% 157.55/157.23 [638]~E(x6381,x6382)+E(f714(x6383,x6381,x6384,x6385,x6386),f714(x6383,x6382,x6384,x6385,x6386))
% 157.55/157.23 [639]~E(x6391,x6392)+E(f714(x6393,x6394,x6391,x6395,x6396),f714(x6393,x6394,x6392,x6395,x6396))
% 157.55/157.23 [640]~E(x6401,x6402)+E(f714(x6403,x6404,x6405,x6401,x6406),f714(x6403,x6404,x6405,x6402,x6406))
% 157.55/157.23 [641]~E(x6411,x6412)+E(f714(x6413,x6414,x6415,x6416,x6411),f714(x6413,x6414,x6415,x6416,x6412))
% 157.55/157.23 [642]~E(x6421,x6422)+E(f723(x6421,x6423,x6424,x6425),f723(x6422,x6423,x6424,x6425))
% 157.55/157.23 [643]~E(x6431,x6432)+E(f723(x6433,x6431,x6434,x6435),f723(x6433,x6432,x6434,x6435))
% 157.55/157.23 [644]~E(x6441,x6442)+E(f723(x6443,x6444,x6441,x6445),f723(x6443,x6444,x6442,x6445))
% 157.55/157.23 [645]~E(x6451,x6452)+E(f723(x6453,x6454,x6455,x6451),f723(x6453,x6454,x6455,x6452))
% 157.55/157.23 [646]~E(x6461,x6462)+E(f619(x6461,x6463,x6464,x6465,x6466),f619(x6462,x6463,x6464,x6465,x6466))
% 157.55/157.23 [647]~E(x6471,x6472)+E(f619(x6473,x6471,x6474,x6475,x6476),f619(x6473,x6472,x6474,x6475,x6476))
% 157.55/157.23 [648]~E(x6481,x6482)+E(f619(x6483,x6484,x6481,x6485,x6486),f619(x6483,x6484,x6482,x6485,x6486))
% 157.55/157.23 [649]~E(x6491,x6492)+E(f619(x6493,x6494,x6495,x6491,x6496),f619(x6493,x6494,x6495,x6492,x6496))
% 157.55/157.23 [650]~E(x6501,x6502)+E(f619(x6503,x6504,x6505,x6506,x6501),f619(x6503,x6504,x6505,x6506,x6502))
% 157.55/157.23 [651]~E(x6511,x6512)+E(f207(x6511,x6513,x6514,x6515,x6516,x6517,x6518),f207(x6512,x6513,x6514,x6515,x6516,x6517,x6518))
% 157.55/157.23 [652]~E(x6521,x6522)+E(f207(x6523,x6521,x6524,x6525,x6526,x6527,x6528),f207(x6523,x6522,x6524,x6525,x6526,x6527,x6528))
% 157.55/157.23 [653]~E(x6531,x6532)+E(f207(x6533,x6534,x6531,x6535,x6536,x6537,x6538),f207(x6533,x6534,x6532,x6535,x6536,x6537,x6538))
% 157.55/157.23 [654]~E(x6541,x6542)+E(f207(x6543,x6544,x6545,x6541,x6546,x6547,x6548),f207(x6543,x6544,x6545,x6542,x6546,x6547,x6548))
% 157.55/157.23 [655]~E(x6551,x6552)+E(f207(x6553,x6554,x6555,x6556,x6551,x6557,x6558),f207(x6553,x6554,x6555,x6556,x6552,x6557,x6558))
% 157.55/157.23 [656]~E(x6561,x6562)+E(f207(x6563,x6564,x6565,x6566,x6567,x6561,x6568),f207(x6563,x6564,x6565,x6566,x6567,x6562,x6568))
% 157.55/157.23 [657]~E(x6571,x6572)+E(f207(x6573,x6574,x6575,x6576,x6577,x6578,x6571),f207(x6573,x6574,x6575,x6576,x6577,x6578,x6572))
% 157.55/157.23 [658]~E(x6581,x6582)+E(f899(x6581,x6583,x6584),f899(x6582,x6583,x6584))
% 157.55/157.23 [659]~E(x6591,x6592)+E(f899(x6593,x6591,x6594),f899(x6593,x6592,x6594))
% 157.55/157.23 [660]~E(x6601,x6602)+E(f899(x6603,x6604,x6601),f899(x6603,x6604,x6602))
% 157.55/157.23 [661]~E(x6611,x6612)+E(f856(x6611,x6613,x6614),f856(x6612,x6613,x6614))
% 157.55/157.23 [662]~E(x6621,x6622)+E(f856(x6623,x6621,x6624),f856(x6623,x6622,x6624))
% 157.55/157.23 [663]~E(x6631,x6632)+E(f856(x6633,x6634,x6631),f856(x6633,x6634,x6632))
% 157.55/157.23 [664]~E(x6641,x6642)+E(f776(x6641,x6643,x6644),f776(x6642,x6643,x6644))
% 157.55/157.23 [665]~E(x6651,x6652)+E(f776(x6653,x6651,x6654),f776(x6653,x6652,x6654))
% 157.55/157.23 [666]~E(x6661,x6662)+E(f776(x6663,x6664,x6661),f776(x6663,x6664,x6662))
% 157.55/157.23 [667]~E(x6671,x6672)+E(f91(x6671,x6673,x6674,x6675),f91(x6672,x6673,x6674,x6675))
% 157.55/157.23 [668]~E(x6681,x6682)+E(f91(x6683,x6681,x6684,x6685),f91(x6683,x6682,x6684,x6685))
% 157.55/157.23 [669]~E(x6691,x6692)+E(f91(x6693,x6694,x6691,x6695),f91(x6693,x6694,x6692,x6695))
% 157.55/157.23 [670]~E(x6701,x6702)+E(f91(x6703,x6704,x6705,x6701),f91(x6703,x6704,x6705,x6702))
% 157.55/157.23 [671]~E(x6711,x6712)+E(f129(x6711),f129(x6712))
% 157.55/157.23 [672]~E(x6721,x6722)+E(f176(x6721,x6723,x6724),f176(x6722,x6723,x6724))
% 157.55/157.23 [673]~E(x6731,x6732)+E(f176(x6733,x6731,x6734),f176(x6733,x6732,x6734))
% 157.55/157.23 [674]~E(x6741,x6742)+E(f176(x6743,x6744,x6741),f176(x6743,x6744,x6742))
% 157.55/157.23 [675]~E(x6751,x6752)+E(f861(x6751,x6753,x6754),f861(x6752,x6753,x6754))
% 157.55/157.23 [676]~E(x6761,x6762)+E(f861(x6763,x6761,x6764),f861(x6763,x6762,x6764))
% 157.55/157.23 [677]~E(x6771,x6772)+E(f861(x6773,x6774,x6771),f861(x6773,x6774,x6772))
% 157.55/157.23 [678]~E(x6781,x6782)+E(f860(x6781,x6783,x6784),f860(x6782,x6783,x6784))
% 157.55/157.23 [679]~E(x6791,x6792)+E(f860(x6793,x6791,x6794),f860(x6793,x6792,x6794))
% 157.55/157.23 [680]~E(x6801,x6802)+E(f860(x6803,x6804,x6801),f860(x6803,x6804,x6802))
% 157.55/157.23 [681]~E(x6811,x6812)+E(f62(x6811,x6813,x6814),f62(x6812,x6813,x6814))
% 157.55/157.23 [682]~E(x6821,x6822)+E(f62(x6823,x6821,x6824),f62(x6823,x6822,x6824))
% 157.55/157.23 [683]~E(x6831,x6832)+E(f62(x6833,x6834,x6831),f62(x6833,x6834,x6832))
% 157.55/157.23 [684]~E(x6841,x6842)+E(f16(x6841,x6843),f16(x6842,x6843))
% 157.55/157.23 [685]~E(x6851,x6852)+E(f16(x6853,x6851),f16(x6853,x6852))
% 157.55/157.23 [686]~E(x6861,x6862)+E(f155(x6861,x6863,x6864),f155(x6862,x6863,x6864))
% 157.55/157.23 [687]~E(x6871,x6872)+E(f155(x6873,x6871,x6874),f155(x6873,x6872,x6874))
% 157.55/157.23 [688]~E(x6881,x6882)+E(f155(x6883,x6884,x6881),f155(x6883,x6884,x6882))
% 157.55/157.23 [689]~E(x6891,x6892)+E(f806(x6891,x6893,x6894,x6895,x6896),f806(x6892,x6893,x6894,x6895,x6896))
% 157.55/157.23 [690]~E(x6901,x6902)+E(f806(x6903,x6901,x6904,x6905,x6906),f806(x6903,x6902,x6904,x6905,x6906))
% 157.55/157.23 [691]~E(x6911,x6912)+E(f806(x6913,x6914,x6911,x6915,x6916),f806(x6913,x6914,x6912,x6915,x6916))
% 157.55/157.23 [692]~E(x6921,x6922)+E(f806(x6923,x6924,x6925,x6921,x6926),f806(x6923,x6924,x6925,x6922,x6926))
% 157.55/157.23 [693]~E(x6931,x6932)+E(f806(x6933,x6934,x6935,x6936,x6931),f806(x6933,x6934,x6935,x6936,x6932))
% 157.55/157.23 [694]~E(x6941,x6942)+E(f294(x6941,x6943,x6944),f294(x6942,x6943,x6944))
% 157.55/157.23 [695]~E(x6951,x6952)+E(f294(x6953,x6951,x6954),f294(x6953,x6952,x6954))
% 157.55/157.23 [696]~E(x6961,x6962)+E(f294(x6963,x6964,x6961),f294(x6963,x6964,x6962))
% 157.55/157.23 [697]~E(x6971,x6972)+E(f158(x6971,x6973),f158(x6972,x6973))
% 157.55/157.23 [698]~E(x6981,x6982)+E(f158(x6983,x6981),f158(x6983,x6982))
% 157.55/157.23 [699]~E(x6991,x6992)+E(f378(x6991,x6993,x6994),f378(x6992,x6993,x6994))
% 157.55/157.23 [700]~E(x7001,x7002)+E(f378(x7003,x7001,x7004),f378(x7003,x7002,x7004))
% 157.55/157.23 [701]~E(x7011,x7012)+E(f378(x7013,x7014,x7011),f378(x7013,x7014,x7012))
% 157.55/157.23 [702]~E(x7021,x7022)+E(f362(x7021,x7023,x7024),f362(x7022,x7023,x7024))
% 157.55/157.23 [703]~E(x7031,x7032)+E(f362(x7033,x7031,x7034),f362(x7033,x7032,x7034))
% 157.55/157.23 [704]~E(x7041,x7042)+E(f362(x7043,x7044,x7041),f362(x7043,x7044,x7042))
% 157.55/157.23 [705]~E(x7051,x7052)+E(f376(x7051,x7053,x7054),f376(x7052,x7053,x7054))
% 157.55/157.23 [706]~E(x7061,x7062)+E(f376(x7063,x7061,x7064),f376(x7063,x7062,x7064))
% 157.55/157.23 [707]~E(x7071,x7072)+E(f376(x7073,x7074,x7071),f376(x7073,x7074,x7072))
% 157.55/157.23 [708]~E(x7081,x7082)+E(f779(x7081,x7083,x7084,x7085,x7086,x7087,x7088),f779(x7082,x7083,x7084,x7085,x7086,x7087,x7088))
% 157.55/157.23 [709]~E(x7091,x7092)+E(f779(x7093,x7091,x7094,x7095,x7096,x7097,x7098),f779(x7093,x7092,x7094,x7095,x7096,x7097,x7098))
% 157.55/157.23 [710]~E(x7101,x7102)+E(f779(x7103,x7104,x7101,x7105,x7106,x7107,x7108),f779(x7103,x7104,x7102,x7105,x7106,x7107,x7108))
% 157.55/157.23 [711]~E(x7111,x7112)+E(f779(x7113,x7114,x7115,x7111,x7116,x7117,x7118),f779(x7113,x7114,x7115,x7112,x7116,x7117,x7118))
% 157.55/157.23 [712]~E(x7121,x7122)+E(f779(x7123,x7124,x7125,x7126,x7121,x7127,x7128),f779(x7123,x7124,x7125,x7126,x7122,x7127,x7128))
% 157.55/157.23 [713]~E(x7131,x7132)+E(f779(x7133,x7134,x7135,x7136,x7137,x7131,x7138),f779(x7133,x7134,x7135,x7136,x7137,x7132,x7138))
% 157.55/157.23 [714]~E(x7141,x7142)+E(f779(x7143,x7144,x7145,x7146,x7147,x7148,x7141),f779(x7143,x7144,x7145,x7146,x7147,x7148,x7142))
% 157.55/157.23 [715]~E(x7151,x7152)+E(f875(x7151,x7153,x7154,x7155),f875(x7152,x7153,x7154,x7155))
% 157.55/157.23 [716]~E(x7161,x7162)+E(f875(x7163,x7161,x7164,x7165),f875(x7163,x7162,x7164,x7165))
% 157.55/157.23 [717]~E(x7171,x7172)+E(f875(x7173,x7174,x7171,x7175),f875(x7173,x7174,x7172,x7175))
% 157.55/157.23 [718]~E(x7181,x7182)+E(f875(x7183,x7184,x7185,x7181),f875(x7183,x7184,x7185,x7182))
% 157.55/157.23 [719]~E(x7191,x7192)+E(f589(x7191,x7193,x7194,x7195,x7196,x7197,x7198,x7199),f589(x7192,x7193,x7194,x7195,x7196,x7197,x7198,x7199))
% 157.55/157.23 [720]~E(x7201,x7202)+E(f589(x7203,x7201,x7204,x7205,x7206,x7207,x7208,x7209),f589(x7203,x7202,x7204,x7205,x7206,x7207,x7208,x7209))
% 157.55/157.23 [721]~E(x7211,x7212)+E(f589(x7213,x7214,x7211,x7215,x7216,x7217,x7218,x7219),f589(x7213,x7214,x7212,x7215,x7216,x7217,x7218,x7219))
% 157.55/157.23 [722]~E(x7221,x7222)+E(f589(x7223,x7224,x7225,x7221,x7226,x7227,x7228,x7229),f589(x7223,x7224,x7225,x7222,x7226,x7227,x7228,x7229))
% 157.55/157.23 [723]~E(x7231,x7232)+E(f589(x7233,x7234,x7235,x7236,x7231,x7237,x7238,x7239),f589(x7233,x7234,x7235,x7236,x7232,x7237,x7238,x7239))
% 157.55/157.23 [724]~E(x7241,x7242)+E(f589(x7243,x7244,x7245,x7246,x7247,x7241,x7248,x7249),f589(x7243,x7244,x7245,x7246,x7247,x7242,x7248,x7249))
% 157.55/157.23 [725]~E(x7251,x7252)+E(f589(x7253,x7254,x7255,x7256,x7257,x7258,x7251,x7259),f589(x7253,x7254,x7255,x7256,x7257,x7258,x7252,x7259))
% 157.55/157.23 [726]~E(x7261,x7262)+E(f589(x7263,x7264,x7265,x7266,x7267,x7268,x7269,x7261),f589(x7263,x7264,x7265,x7266,x7267,x7268,x7269,x7262))
% 157.55/157.23 [727]~E(x7271,x7272)+E(f891(x7271,x7273,x7274),f891(x7272,x7273,x7274))
% 157.55/157.23 [728]~E(x7281,x7282)+E(f891(x7283,x7281,x7284),f891(x7283,x7282,x7284))
% 157.55/157.23 [729]~E(x7291,x7292)+E(f891(x7293,x7294,x7291),f891(x7293,x7294,x7292))
% 157.55/157.23 [730]~E(x7301,x7302)+E(f126(x7301,x7303,x7304),f126(x7302,x7303,x7304))
% 157.55/157.23 [731]~E(x7311,x7312)+E(f126(x7313,x7311,x7314),f126(x7313,x7312,x7314))
% 157.55/157.23 [732]~E(x7321,x7322)+E(f126(x7323,x7324,x7321),f126(x7323,x7324,x7322))
% 157.55/157.23 [733]~E(x7331,x7332)+E(f547(x7331,x7333),f547(x7332,x7333))
% 157.55/157.23 [734]~E(x7341,x7342)+E(f547(x7343,x7341),f547(x7343,x7342))
% 157.55/157.23 [735]~E(x7351,x7352)+E(f383(x7351,x7353,x7354),f383(x7352,x7353,x7354))
% 157.55/157.23 [736]~E(x7361,x7362)+E(f383(x7363,x7361,x7364),f383(x7363,x7362,x7364))
% 157.55/157.23 [737]~E(x7371,x7372)+E(f383(x7373,x7374,x7371),f383(x7373,x7374,x7372))
% 157.55/157.23 [738]~E(x7381,x7382)+E(f43(x7381),f43(x7382))
% 157.55/157.23 [739]~E(x7391,x7392)+E(f166(x7391,x7393,x7394),f166(x7392,x7393,x7394))
% 157.55/157.23 [740]~E(x7401,x7402)+E(f166(x7403,x7401,x7404),f166(x7403,x7402,x7404))
% 157.55/157.23 [741]~E(x7411,x7412)+E(f166(x7413,x7414,x7411),f166(x7413,x7414,x7412))
% 157.55/157.23 [742]~E(x7421,x7422)+E(f429(x7421,x7423,x7424,x7425,x7426,x7427,x7428),f429(x7422,x7423,x7424,x7425,x7426,x7427,x7428))
% 157.55/157.23 [743]~E(x7431,x7432)+E(f429(x7433,x7431,x7434,x7435,x7436,x7437,x7438),f429(x7433,x7432,x7434,x7435,x7436,x7437,x7438))
% 157.55/157.23 [744]~E(x7441,x7442)+E(f429(x7443,x7444,x7441,x7445,x7446,x7447,x7448),f429(x7443,x7444,x7442,x7445,x7446,x7447,x7448))
% 157.55/157.23 [745]~E(x7451,x7452)+E(f429(x7453,x7454,x7455,x7451,x7456,x7457,x7458),f429(x7453,x7454,x7455,x7452,x7456,x7457,x7458))
% 157.55/157.23 [746]~E(x7461,x7462)+E(f429(x7463,x7464,x7465,x7466,x7461,x7467,x7468),f429(x7463,x7464,x7465,x7466,x7462,x7467,x7468))
% 157.55/157.23 [747]~E(x7471,x7472)+E(f429(x7473,x7474,x7475,x7476,x7477,x7471,x7478),f429(x7473,x7474,x7475,x7476,x7477,x7472,x7478))
% 157.55/157.23 [748]~E(x7481,x7482)+E(f429(x7483,x7484,x7485,x7486,x7487,x7488,x7481),f429(x7483,x7484,x7485,x7486,x7487,x7488,x7482))
% 157.55/157.23 [749]~E(x7491,x7492)+E(f893(x7491,x7493,x7494),f893(x7492,x7493,x7494))
% 157.55/157.23 [750]~E(x7501,x7502)+E(f893(x7503,x7501,x7504),f893(x7503,x7502,x7504))
% 157.55/157.23 [751]~E(x7511,x7512)+E(f893(x7513,x7514,x7511),f893(x7513,x7514,x7512))
% 157.55/157.23 [752]~E(x7521,x7522)+E(f527(x7521,x7523,x7524,x7525,x7526),f527(x7522,x7523,x7524,x7525,x7526))
% 157.55/157.23 [753]~E(x7531,x7532)+E(f527(x7533,x7531,x7534,x7535,x7536),f527(x7533,x7532,x7534,x7535,x7536))
% 157.55/157.23 [754]~E(x7541,x7542)+E(f527(x7543,x7544,x7541,x7545,x7546),f527(x7543,x7544,x7542,x7545,x7546))
% 157.55/157.23 [755]~E(x7551,x7552)+E(f527(x7553,x7554,x7555,x7551,x7556),f527(x7553,x7554,x7555,x7552,x7556))
% 157.55/157.23 [756]~E(x7561,x7562)+E(f527(x7563,x7564,x7565,x7566,x7561),f527(x7563,x7564,x7565,x7566,x7562))
% 157.55/157.23 [757]~E(x7571,x7572)+E(f578(x7571,x7573),f578(x7572,x7573))
% 157.55/157.23 [758]~E(x7581,x7582)+E(f578(x7583,x7581),f578(x7583,x7582))
% 157.55/157.23 [759]~E(x7591,x7592)+E(f287(x7591,x7593),f287(x7592,x7593))
% 157.55/157.23 [760]~E(x7601,x7602)+E(f287(x7603,x7601),f287(x7603,x7602))
% 157.55/157.23 [761]~E(x7611,x7612)+E(f897(x7611,x7613,x7614,x7615),f897(x7612,x7613,x7614,x7615))
% 157.55/157.23 [762]~E(x7621,x7622)+E(f897(x7623,x7621,x7624,x7625),f897(x7623,x7622,x7624,x7625))
% 157.55/157.23 [763]~E(x7631,x7632)+E(f897(x7633,x7634,x7631,x7635),f897(x7633,x7634,x7632,x7635))
% 157.55/157.23 [764]~E(x7641,x7642)+E(f897(x7643,x7644,x7645,x7641),f897(x7643,x7644,x7645,x7642))
% 157.55/157.23 [765]~E(x7651,x7652)+E(f30(x7651,x7653),f30(x7652,x7653))
% 157.55/157.23 [766]~E(x7661,x7662)+E(f30(x7663,x7661),f30(x7663,x7662))
% 157.55/157.23 [767]~E(x7671,x7672)+E(f885(x7671,x7673,x7674),f885(x7672,x7673,x7674))
% 157.55/157.23 [768]~E(x7681,x7682)+E(f885(x7683,x7681,x7684),f885(x7683,x7682,x7684))
% 157.55/157.23 [769]~E(x7691,x7692)+E(f885(x7693,x7694,x7691),f885(x7693,x7694,x7692))
% 157.55/157.23 [770]~E(x7701,x7702)+E(f357(x7701,x7703,x7704,x7705),f357(x7702,x7703,x7704,x7705))
% 157.55/157.23 [771]~E(x7711,x7712)+E(f357(x7713,x7711,x7714,x7715),f357(x7713,x7712,x7714,x7715))
% 157.55/157.23 [772]~E(x7721,x7722)+E(f357(x7723,x7724,x7721,x7725),f357(x7723,x7724,x7722,x7725))
% 157.55/157.23 [773]~E(x7731,x7732)+E(f357(x7733,x7734,x7735,x7731),f357(x7733,x7734,x7735,x7732))
% 157.55/157.23 [774]~E(x7741,x7742)+E(f381(x7741,x7743,x7744,x7745),f381(x7742,x7743,x7744,x7745))
% 157.55/157.23 [775]~E(x7751,x7752)+E(f381(x7753,x7751,x7754,x7755),f381(x7753,x7752,x7754,x7755))
% 157.55/157.23 [776]~E(x7761,x7762)+E(f381(x7763,x7764,x7761,x7765),f381(x7763,x7764,x7762,x7765))
% 157.55/157.23 [777]~E(x7771,x7772)+E(f381(x7773,x7774,x7775,x7771),f381(x7773,x7774,x7775,x7772))
% 157.55/157.23 [778]~E(x7781,x7782)+E(f499(x7781,x7783,x7784,x7785,x7786),f499(x7782,x7783,x7784,x7785,x7786))
% 157.55/157.23 [779]~E(x7791,x7792)+E(f499(x7793,x7791,x7794,x7795,x7796),f499(x7793,x7792,x7794,x7795,x7796))
% 157.55/157.23 [780]~E(x7801,x7802)+E(f499(x7803,x7804,x7801,x7805,x7806),f499(x7803,x7804,x7802,x7805,x7806))
% 157.55/157.23 [781]~E(x7811,x7812)+E(f499(x7813,x7814,x7815,x7811,x7816),f499(x7813,x7814,x7815,x7812,x7816))
% 157.55/157.23 [782]~E(x7821,x7822)+E(f499(x7823,x7824,x7825,x7826,x7821),f499(x7823,x7824,x7825,x7826,x7822))
% 157.55/157.23 [783]~E(x7831,x7832)+E(f246(x7831,x7833,x7834),f246(x7832,x7833,x7834))
% 157.55/157.23 [784]~E(x7841,x7842)+E(f246(x7843,x7841,x7844),f246(x7843,x7842,x7844))
% 157.55/157.23 [785]~E(x7851,x7852)+E(f246(x7853,x7854,x7851),f246(x7853,x7854,x7852))
% 157.55/157.23 [786]~E(x7861,x7862)+E(f263(x7861,x7863),f263(x7862,x7863))
% 157.55/157.23 [787]~E(x7871,x7872)+E(f263(x7873,x7871),f263(x7873,x7872))
% 157.55/157.23 [788]~E(x7881,x7882)+E(f892(x7881,x7883,x7884),f892(x7882,x7883,x7884))
% 157.55/157.23 [789]~E(x7891,x7892)+E(f892(x7893,x7891,x7894),f892(x7893,x7892,x7894))
% 157.55/157.23 [790]~E(x7901,x7902)+E(f892(x7903,x7904,x7901),f892(x7903,x7904,x7902))
% 157.55/157.23 [791]~E(x7911,x7912)+E(f737(x7911,x7913,x7914,x7915,x7916),f737(x7912,x7913,x7914,x7915,x7916))
% 157.55/157.23 [792]~E(x7921,x7922)+E(f737(x7923,x7921,x7924,x7925,x7926),f737(x7923,x7922,x7924,x7925,x7926))
% 157.55/157.23 [793]~E(x7931,x7932)+E(f737(x7933,x7934,x7931,x7935,x7936),f737(x7933,x7934,x7932,x7935,x7936))
% 157.55/157.23 [794]~E(x7941,x7942)+E(f737(x7943,x7944,x7945,x7941,x7946),f737(x7943,x7944,x7945,x7942,x7946))
% 157.55/157.23 [795]~E(x7951,x7952)+E(f737(x7953,x7954,x7955,x7956,x7951),f737(x7953,x7954,x7955,x7956,x7952))
% 157.55/157.23 [796]~E(x7961,x7962)+E(f353(x7961,x7963,x7964),f353(x7962,x7963,x7964))
% 157.55/157.23 [797]~E(x7971,x7972)+E(f353(x7973,x7971,x7974),f353(x7973,x7972,x7974))
% 157.55/157.23 [798]~E(x7981,x7982)+E(f353(x7983,x7984,x7981),f353(x7983,x7984,x7982))
% 157.55/157.23 [799]~E(x7991,x7992)+E(f511(x7991,x7993,x7994,x7995,x7996,x7997,x7998),f511(x7992,x7993,x7994,x7995,x7996,x7997,x7998))
% 157.55/157.23 [800]~E(x8001,x8002)+E(f511(x8003,x8001,x8004,x8005,x8006,x8007,x8008),f511(x8003,x8002,x8004,x8005,x8006,x8007,x8008))
% 157.55/157.23 [801]~E(x8011,x8012)+E(f511(x8013,x8014,x8011,x8015,x8016,x8017,x8018),f511(x8013,x8014,x8012,x8015,x8016,x8017,x8018))
% 157.55/157.23 [802]~E(x8021,x8022)+E(f511(x8023,x8024,x8025,x8021,x8026,x8027,x8028),f511(x8023,x8024,x8025,x8022,x8026,x8027,x8028))
% 157.55/157.23 [803]~E(x8031,x8032)+E(f511(x8033,x8034,x8035,x8036,x8031,x8037,x8038),f511(x8033,x8034,x8035,x8036,x8032,x8037,x8038))
% 157.55/157.23 [804]~E(x8041,x8042)+E(f511(x8043,x8044,x8045,x8046,x8047,x8041,x8048),f511(x8043,x8044,x8045,x8046,x8047,x8042,x8048))
% 157.55/157.23 [805]~E(x8051,x8052)+E(f511(x8053,x8054,x8055,x8056,x8057,x8058,x8051),f511(x8053,x8054,x8055,x8056,x8057,x8058,x8052))
% 157.55/157.23 [806]~E(x8061,x8062)+E(f55(x8061,x8063,x8064),f55(x8062,x8063,x8064))
% 157.55/157.23 [807]~E(x8071,x8072)+E(f55(x8073,x8071,x8074),f55(x8073,x8072,x8074))
% 157.55/157.23 [808]~E(x8081,x8082)+E(f55(x8083,x8084,x8081),f55(x8083,x8084,x8082))
% 157.55/157.23 [809]~E(x8091,x8092)+E(f771(x8091,x8093,x8094,x8095),f771(x8092,x8093,x8094,x8095))
% 157.55/157.23 [810]~E(x8101,x8102)+E(f771(x8103,x8101,x8104,x8105),f771(x8103,x8102,x8104,x8105))
% 157.55/157.23 [811]~E(x8111,x8112)+E(f771(x8113,x8114,x8111,x8115),f771(x8113,x8114,x8112,x8115))
% 157.55/157.23 [812]~E(x8121,x8122)+E(f771(x8123,x8124,x8125,x8121),f771(x8123,x8124,x8125,x8122))
% 157.55/157.23 [813]~E(x8131,x8132)+E(f163(x8131,x8133,x8134,x8135),f163(x8132,x8133,x8134,x8135))
% 157.55/157.23 [814]~E(x8141,x8142)+E(f163(x8143,x8141,x8144,x8145),f163(x8143,x8142,x8144,x8145))
% 157.55/157.23 [815]~E(x8151,x8152)+E(f163(x8153,x8154,x8151,x8155),f163(x8153,x8154,x8152,x8155))
% 157.55/157.23 [816]~E(x8161,x8162)+E(f163(x8163,x8164,x8165,x8161),f163(x8163,x8164,x8165,x8162))
% 157.55/157.23 [817]~E(x8171,x8172)+E(f610(x8171,x8173,x8174,x8175,x8176),f610(x8172,x8173,x8174,x8175,x8176))
% 157.55/157.23 [818]~E(x8181,x8182)+E(f610(x8183,x8181,x8184,x8185,x8186),f610(x8183,x8182,x8184,x8185,x8186))
% 157.55/157.23 [819]~E(x8191,x8192)+E(f610(x8193,x8194,x8191,x8195,x8196),f610(x8193,x8194,x8192,x8195,x8196))
% 157.55/157.23 [820]~E(x8201,x8202)+E(f610(x8203,x8204,x8205,x8201,x8206),f610(x8203,x8204,x8205,x8202,x8206))
% 157.55/157.23 [821]~E(x8211,x8212)+E(f610(x8213,x8214,x8215,x8216,x8211),f610(x8213,x8214,x8215,x8216,x8212))
% 157.55/157.23 [822]~E(x8221,x8222)+E(f490(x8221,x8223,x8224),f490(x8222,x8223,x8224))
% 157.55/157.23 [823]~E(x8231,x8232)+E(f490(x8233,x8231,x8234),f490(x8233,x8232,x8234))
% 157.55/157.23 [824]~E(x8241,x8242)+E(f490(x8243,x8244,x8241),f490(x8243,x8244,x8242))
% 157.55/157.23 [825]~E(x8251,x8252)+E(f673(x8251,x8253,x8254),f673(x8252,x8253,x8254))
% 157.55/157.23 [826]~E(x8261,x8262)+E(f673(x8263,x8261,x8264),f673(x8263,x8262,x8264))
% 157.55/157.23 [827]~E(x8271,x8272)+E(f673(x8273,x8274,x8271),f673(x8273,x8274,x8272))
% 157.55/157.23 [828]~E(x8281,x8282)+E(f432(x8281,x8283,x8284),f432(x8282,x8283,x8284))
% 157.55/157.23 [829]~E(x8291,x8292)+E(f432(x8293,x8291,x8294),f432(x8293,x8292,x8294))
% 157.55/157.23 [830]~E(x8301,x8302)+E(f432(x8303,x8304,x8301),f432(x8303,x8304,x8302))
% 157.55/157.23 [831]~E(x8311,x8312)+E(f209(x8311,x8313,x8314,x8315),f209(x8312,x8313,x8314,x8315))
% 157.55/157.23 [832]~E(x8321,x8322)+E(f209(x8323,x8321,x8324,x8325),f209(x8323,x8322,x8324,x8325))
% 157.55/157.23 [833]~E(x8331,x8332)+E(f209(x8333,x8334,x8331,x8335),f209(x8333,x8334,x8332,x8335))
% 157.55/157.23 [834]~E(x8341,x8342)+E(f209(x8343,x8344,x8345,x8341),f209(x8343,x8344,x8345,x8342))
% 157.55/157.23 [835]~E(x8351,x8352)+E(f305(x8351,x8353,x8354),f305(x8352,x8353,x8354))
% 157.55/157.23 [836]~E(x8361,x8362)+E(f305(x8363,x8361,x8364),f305(x8363,x8362,x8364))
% 157.55/157.23 [837]~E(x8371,x8372)+E(f305(x8373,x8374,x8371),f305(x8373,x8374,x8372))
% 157.55/157.23 [838]~E(x8381,x8382)+E(f392(x8381,x8383,x8384),f392(x8382,x8383,x8384))
% 157.55/157.23 [839]~E(x8391,x8392)+E(f392(x8393,x8391,x8394),f392(x8393,x8392,x8394))
% 157.55/157.23 [840]~E(x8401,x8402)+E(f392(x8403,x8404,x8401),f392(x8403,x8404,x8402))
% 157.55/157.23 [841]~E(x8411,x8412)+E(f631(x8411,x8413,x8414,x8415),f631(x8412,x8413,x8414,x8415))
% 157.55/157.23 [842]~E(x8421,x8422)+E(f631(x8423,x8421,x8424,x8425),f631(x8423,x8422,x8424,x8425))
% 157.55/157.23 [843]~E(x8431,x8432)+E(f631(x8433,x8434,x8431,x8435),f631(x8433,x8434,x8432,x8435))
% 157.55/157.23 [844]~E(x8441,x8442)+E(f631(x8443,x8444,x8445,x8441),f631(x8443,x8444,x8445,x8442))
% 157.55/157.23 [845]~E(x8451,x8452)+E(f867(x8451,x8453,x8454),f867(x8452,x8453,x8454))
% 157.55/157.23 [846]~E(x8461,x8462)+E(f867(x8463,x8461,x8464),f867(x8463,x8462,x8464))
% 157.55/157.23 [847]~E(x8471,x8472)+E(f867(x8473,x8474,x8471),f867(x8473,x8474,x8472))
% 157.55/157.23 [848]~E(x8481,x8482)+E(f500(x8481),f500(x8482))
% 157.55/157.23 [849]~E(x8491,x8492)+E(f808(x8491,x8493,x8494,x8495,x8496,x8497),f808(x8492,x8493,x8494,x8495,x8496,x8497))
% 157.55/157.23 [850]~E(x8501,x8502)+E(f808(x8503,x8501,x8504,x8505,x8506,x8507),f808(x8503,x8502,x8504,x8505,x8506,x8507))
% 157.55/157.23 [851]~E(x8511,x8512)+E(f808(x8513,x8514,x8511,x8515,x8516,x8517),f808(x8513,x8514,x8512,x8515,x8516,x8517))
% 157.55/157.23 [852]~E(x8521,x8522)+E(f808(x8523,x8524,x8525,x8521,x8526,x8527),f808(x8523,x8524,x8525,x8522,x8526,x8527))
% 157.55/157.23 [853]~E(x8531,x8532)+E(f808(x8533,x8534,x8535,x8536,x8531,x8537),f808(x8533,x8534,x8535,x8536,x8532,x8537))
% 157.55/157.23 [854]~E(x8541,x8542)+E(f808(x8543,x8544,x8545,x8546,x8547,x8541),f808(x8543,x8544,x8545,x8546,x8547,x8542))
% 157.55/157.23 [855]~E(x8551,x8552)+E(f747(x8551,x8553,x8554,x8555),f747(x8552,x8553,x8554,x8555))
% 157.55/157.23 [856]~E(x8561,x8562)+E(f747(x8563,x8561,x8564,x8565),f747(x8563,x8562,x8564,x8565))
% 157.55/157.23 [857]~E(x8571,x8572)+E(f747(x8573,x8574,x8571,x8575),f747(x8573,x8574,x8572,x8575))
% 157.55/157.23 [858]~E(x8581,x8582)+E(f747(x8583,x8584,x8585,x8581),f747(x8583,x8584,x8585,x8582))
% 157.55/157.23 [859]~E(x8591,x8592)+E(f140(x8591,x8593,x8594),f140(x8592,x8593,x8594))
% 157.55/157.23 [860]~E(x8601,x8602)+E(f140(x8603,x8601,x8604),f140(x8603,x8602,x8604))
% 157.55/157.23 [861]~E(x8611,x8612)+E(f140(x8613,x8614,x8611),f140(x8613,x8614,x8612))
% 157.55/157.23 [862]~E(x8621,x8622)+E(f109(x8621),f109(x8622))
% 157.55/157.23 [863]~E(x8631,x8632)+E(f558(x8631,x8633,x8634,x8635),f558(x8632,x8633,x8634,x8635))
% 157.55/157.23 [864]~E(x8641,x8642)+E(f558(x8643,x8641,x8644,x8645),f558(x8643,x8642,x8644,x8645))
% 157.55/157.23 [865]~E(x8651,x8652)+E(f558(x8653,x8654,x8651,x8655),f558(x8653,x8654,x8652,x8655))
% 157.55/157.23 [866]~E(x8661,x8662)+E(f558(x8663,x8664,x8665,x8661),f558(x8663,x8664,x8665,x8662))
% 157.55/157.23 [867]~E(x8671,x8672)+E(f484(x8671,x8673,x8674),f484(x8672,x8673,x8674))
% 157.55/157.23 [868]~E(x8681,x8682)+E(f484(x8683,x8681,x8684),f484(x8683,x8682,x8684))
% 157.55/157.23 [869]~E(x8691,x8692)+E(f484(x8693,x8694,x8691),f484(x8693,x8694,x8692))
% 157.55/157.23 [870]~E(x8701,x8702)+E(f879(x8701,x8703,x8704,x8705,x8706),f879(x8702,x8703,x8704,x8705,x8706))
% 157.55/157.23 [871]~E(x8711,x8712)+E(f879(x8713,x8711,x8714,x8715,x8716),f879(x8713,x8712,x8714,x8715,x8716))
% 157.55/157.23 [872]~E(x8721,x8722)+E(f879(x8723,x8724,x8721,x8725,x8726),f879(x8723,x8724,x8722,x8725,x8726))
% 157.55/157.23 [873]~E(x8731,x8732)+E(f879(x8733,x8734,x8735,x8731,x8736),f879(x8733,x8734,x8735,x8732,x8736))
% 157.55/157.23 [874]~E(x8741,x8742)+E(f879(x8743,x8744,x8745,x8746,x8741),f879(x8743,x8744,x8745,x8746,x8742))
% 157.55/157.23 [875]~E(x8751,x8752)+E(f767(x8751,x8753,x8754),f767(x8752,x8753,x8754))
% 157.55/157.23 [876]~E(x8761,x8762)+E(f767(x8763,x8761,x8764),f767(x8763,x8762,x8764))
% 157.55/157.23 [877]~E(x8771,x8772)+E(f767(x8773,x8774,x8771),f767(x8773,x8774,x8772))
% 157.55/157.23 [878]~E(x8781,x8782)+E(f274(x8781,x8783),f274(x8782,x8783))
% 157.55/157.23 [879]~E(x8791,x8792)+E(f274(x8793,x8791),f274(x8793,x8792))
% 157.55/157.23 [880]~E(x8801,x8802)+E(f377(x8801,x8803,x8804),f377(x8802,x8803,x8804))
% 157.55/157.23 [881]~E(x8811,x8812)+E(f377(x8813,x8811,x8814),f377(x8813,x8812,x8814))
% 157.55/157.23 [882]~E(x8821,x8822)+E(f377(x8823,x8824,x8821),f377(x8823,x8824,x8822))
% 157.55/157.23 [883]~E(x8831,x8832)+E(f775(x8831,x8833,x8834),f775(x8832,x8833,x8834))
% 157.55/157.23 [884]~E(x8841,x8842)+E(f775(x8843,x8841,x8844),f775(x8843,x8842,x8844))
% 157.55/157.23 [885]~E(x8851,x8852)+E(f775(x8853,x8854,x8851),f775(x8853,x8854,x8852))
% 157.55/157.23 [886]~E(x8861,x8862)+E(f508(x8861,x8863,x8864,x8865,x8866,x8867,x8868),f508(x8862,x8863,x8864,x8865,x8866,x8867,x8868))
% 157.55/157.23 [887]~E(x8871,x8872)+E(f508(x8873,x8871,x8874,x8875,x8876,x8877,x8878),f508(x8873,x8872,x8874,x8875,x8876,x8877,x8878))
% 157.55/157.23 [888]~E(x8881,x8882)+E(f508(x8883,x8884,x8881,x8885,x8886,x8887,x8888),f508(x8883,x8884,x8882,x8885,x8886,x8887,x8888))
% 157.55/157.23 [889]~E(x8891,x8892)+E(f508(x8893,x8894,x8895,x8891,x8896,x8897,x8898),f508(x8893,x8894,x8895,x8892,x8896,x8897,x8898))
% 157.55/157.23 [890]~E(x8901,x8902)+E(f508(x8903,x8904,x8905,x8906,x8901,x8907,x8908),f508(x8903,x8904,x8905,x8906,x8902,x8907,x8908))
% 157.55/157.23 [891]~E(x8911,x8912)+E(f508(x8913,x8914,x8915,x8916,x8917,x8911,x8918),f508(x8913,x8914,x8915,x8916,x8917,x8912,x8918))
% 157.55/157.23 [892]~E(x8921,x8922)+E(f508(x8923,x8924,x8925,x8926,x8927,x8928,x8921),f508(x8923,x8924,x8925,x8926,x8927,x8928,x8922))
% 157.55/157.23 [893]~E(x8931,x8932)+E(f495(x8931,x8933,x8934,x8935),f495(x8932,x8933,x8934,x8935))
% 157.55/157.23 [894]~E(x8941,x8942)+E(f495(x8943,x8941,x8944,x8945),f495(x8943,x8942,x8944,x8945))
% 157.55/157.23 [895]~E(x8951,x8952)+E(f495(x8953,x8954,x8951,x8955),f495(x8953,x8954,x8952,x8955))
% 157.55/157.23 [896]~E(x8961,x8962)+E(f495(x8963,x8964,x8965,x8961),f495(x8963,x8964,x8965,x8962))
% 157.55/157.23 [897]~E(x8971,x8972)+E(f27(x8971,x8973,x8974),f27(x8972,x8973,x8974))
% 157.55/157.23 [898]~E(x8981,x8982)+E(f27(x8983,x8981,x8984),f27(x8983,x8982,x8984))
% 157.55/157.23 [899]~E(x8991,x8992)+E(f27(x8993,x8994,x8991),f27(x8993,x8994,x8992))
% 157.55/157.23 [900]~E(x9001,x9002)+E(f441(x9001,x9003,x9004,x9005),f441(x9002,x9003,x9004,x9005))
% 157.55/157.23 [901]~E(x9011,x9012)+E(f441(x9013,x9011,x9014,x9015),f441(x9013,x9012,x9014,x9015))
% 157.55/157.23 [902]~E(x9021,x9022)+E(f441(x9023,x9024,x9021,x9025),f441(x9023,x9024,x9022,x9025))
% 157.55/157.23 [903]~E(x9031,x9032)+E(f441(x9033,x9034,x9035,x9031),f441(x9033,x9034,x9035,x9032))
% 157.55/157.23 [904]~E(x9041,x9042)+E(f145(x9041,x9043),f145(x9042,x9043))
% 157.55/157.23 [905]~E(x9051,x9052)+E(f145(x9053,x9051),f145(x9053,x9052))
% 157.55/157.23 [906]~E(x9061,x9062)+E(f425(x9061,x9063,x9064),f425(x9062,x9063,x9064))
% 157.55/157.23 [907]~E(x9071,x9072)+E(f425(x9073,x9071,x9074),f425(x9073,x9072,x9074))
% 157.55/157.23 [908]~E(x9081,x9082)+E(f425(x9083,x9084,x9081),f425(x9083,x9084,x9082))
% 157.55/157.23 [909]~E(x9091,x9092)+E(f160(x9091,x9093),f160(x9092,x9093))
% 157.55/157.23 [910]~E(x9101,x9102)+E(f160(x9103,x9101),f160(x9103,x9102))
% 157.55/157.23 [911]~E(x9111,x9112)+E(f403(x9111,x9113,x9114),f403(x9112,x9113,x9114))
% 157.55/157.23 [912]~E(x9121,x9122)+E(f403(x9123,x9121,x9124),f403(x9123,x9122,x9124))
% 157.55/157.23 [913]~E(x9131,x9132)+E(f403(x9133,x9134,x9131),f403(x9133,x9134,x9132))
% 157.55/157.23 [914]~E(x9141,x9142)+E(f345(x9141,x9143),f345(x9142,x9143))
% 157.55/157.23 [915]~E(x9151,x9152)+E(f345(x9153,x9151),f345(x9153,x9152))
% 157.55/157.23 [916]~E(x9161,x9162)+E(f29(x9161,x9163),f29(x9162,x9163))
% 157.55/157.23 [917]~E(x9171,x9172)+E(f29(x9173,x9171),f29(x9173,x9172))
% 157.55/157.23 [918]~E(x9181,x9182)+E(f564(x9181,x9183,x9184,x9185,x9186),f564(x9182,x9183,x9184,x9185,x9186))
% 157.55/157.23 [919]~E(x9191,x9192)+E(f564(x9193,x9191,x9194,x9195,x9196),f564(x9193,x9192,x9194,x9195,x9196))
% 157.55/157.23 [920]~E(x9201,x9202)+E(f564(x9203,x9204,x9201,x9205,x9206),f564(x9203,x9204,x9202,x9205,x9206))
% 157.55/157.23 [921]~E(x9211,x9212)+E(f564(x9213,x9214,x9215,x9211,x9216),f564(x9213,x9214,x9215,x9212,x9216))
% 157.55/157.23 [922]~E(x9221,x9222)+E(f564(x9223,x9224,x9225,x9226,x9221),f564(x9223,x9224,x9225,x9226,x9222))
% 157.55/157.23 [923]~E(x9231,x9232)+E(f92(x9231,x9233,x9234),f92(x9232,x9233,x9234))
% 157.55/157.23 [924]~E(x9241,x9242)+E(f92(x9243,x9241,x9244),f92(x9243,x9242,x9244))
% 157.55/157.23 [925]~E(x9251,x9252)+E(f92(x9253,x9254,x9251),f92(x9253,x9254,x9252))
% 157.55/157.23 [926]~E(x9261,x9262)+E(f706(x9261,x9263,x9264),f706(x9262,x9263,x9264))
% 157.55/157.23 [927]~E(x9271,x9272)+E(f706(x9273,x9271,x9274),f706(x9273,x9272,x9274))
% 157.55/157.23 [928]~E(x9281,x9282)+E(f706(x9283,x9284,x9281),f706(x9283,x9284,x9282))
% 157.55/157.23 [929]~E(x9291,x9292)+E(f863(x9291,x9293,x9294,x9295),f863(x9292,x9293,x9294,x9295))
% 157.55/157.23 [930]~E(x9301,x9302)+E(f863(x9303,x9301,x9304,x9305),f863(x9303,x9302,x9304,x9305))
% 157.55/157.23 [931]~E(x9311,x9312)+E(f863(x9313,x9314,x9311,x9315),f863(x9313,x9314,x9312,x9315))
% 157.55/157.23 [932]~E(x9321,x9322)+E(f863(x9323,x9324,x9325,x9321),f863(x9323,x9324,x9325,x9322))
% 157.55/157.23 [933]~E(x9331,x9332)+E(f174(x9331,x9333,x9334),f174(x9332,x9333,x9334))
% 157.55/157.23 [934]~E(x9341,x9342)+E(f174(x9343,x9341,x9344),f174(x9343,x9342,x9344))
% 157.55/157.23 [935]~E(x9351,x9352)+E(f174(x9353,x9354,x9351),f174(x9353,x9354,x9352))
% 157.55/157.24 [936]~E(x9361,x9362)+E(f566(x9361,x9363,x9364,x9365),f566(x9362,x9363,x9364,x9365))
% 157.55/157.24 [937]~E(x9371,x9372)+E(f566(x9373,x9371,x9374,x9375),f566(x9373,x9372,x9374,x9375))
% 157.55/157.24 [938]~E(x9381,x9382)+E(f566(x9383,x9384,x9381,x9385),f566(x9383,x9384,x9382,x9385))
% 157.55/157.24 [939]~E(x9391,x9392)+E(f566(x9393,x9394,x9395,x9391),f566(x9393,x9394,x9395,x9392))
% 157.55/157.24 [940]~E(x9401,x9402)+E(f192(x9401,x9403),f192(x9402,x9403))
% 157.55/157.24 [941]~E(x9411,x9412)+E(f192(x9413,x9411),f192(x9413,x9412))
% 157.55/157.24 [942]~E(x9421,x9422)+E(f516(x9421,x9423,x9424,x9425,x9426),f516(x9422,x9423,x9424,x9425,x9426))
% 157.55/157.24 [943]~E(x9431,x9432)+E(f516(x9433,x9431,x9434,x9435,x9436),f516(x9433,x9432,x9434,x9435,x9436))
% 157.55/157.24 [944]~E(x9441,x9442)+E(f516(x9443,x9444,x9441,x9445,x9446),f516(x9443,x9444,x9442,x9445,x9446))
% 157.55/157.24 [945]~E(x9451,x9452)+E(f516(x9453,x9454,x9455,x9451,x9456),f516(x9453,x9454,x9455,x9452,x9456))
% 157.55/157.24 [946]~E(x9461,x9462)+E(f516(x9463,x9464,x9465,x9466,x9461),f516(x9463,x9464,x9465,x9466,x9462))
% 157.55/157.24 [947]~E(x9471,x9472)+E(f121(x9471,x9473),f121(x9472,x9473))
% 157.55/157.24 [948]~E(x9481,x9482)+E(f121(x9483,x9481),f121(x9483,x9482))
% 157.55/157.24 [949]~E(x9491,x9492)+E(f373(x9491,x9493),f373(x9492,x9493))
% 157.55/157.24 [950]~E(x9501,x9502)+E(f373(x9503,x9501),f373(x9503,x9502))
% 157.55/157.24 [951]~E(x9511,x9512)+E(f620(x9511,x9513,x9514,x9515,x9516),f620(x9512,x9513,x9514,x9515,x9516))
% 157.55/157.24 [952]~E(x9521,x9522)+E(f620(x9523,x9521,x9524,x9525,x9526),f620(x9523,x9522,x9524,x9525,x9526))
% 157.55/157.24 [953]~E(x9531,x9532)+E(f620(x9533,x9534,x9531,x9535,x9536),f620(x9533,x9534,x9532,x9535,x9536))
% 157.55/157.24 [954]~E(x9541,x9542)+E(f620(x9543,x9544,x9545,x9541,x9546),f620(x9543,x9544,x9545,x9542,x9546))
% 157.55/157.24 [955]~E(x9551,x9552)+E(f620(x9553,x9554,x9555,x9556,x9551),f620(x9553,x9554,x9555,x9556,x9552))
% 157.55/157.24 [956]~E(x9561,x9562)+E(f745(x9561,x9563,x9564),f745(x9562,x9563,x9564))
% 157.55/157.24 [957]~E(x9571,x9572)+E(f745(x9573,x9571,x9574),f745(x9573,x9572,x9574))
% 157.55/157.24 [958]~E(x9581,x9582)+E(f745(x9583,x9584,x9581),f745(x9583,x9584,x9582))
% 157.55/157.24 [959]~E(x9591,x9592)+E(f792(x9591,x9593),f792(x9592,x9593))
% 157.55/157.24 [960]~E(x9601,x9602)+E(f792(x9603,x9601),f792(x9603,x9602))
% 157.55/157.24 [961]~E(x9611,x9612)+E(f26(x9611,x9613,x9614),f26(x9612,x9613,x9614))
% 157.55/157.24 [962]~E(x9621,x9622)+E(f26(x9623,x9621,x9624),f26(x9623,x9622,x9624))
% 157.55/157.24 [963]~E(x9631,x9632)+E(f26(x9633,x9634,x9631),f26(x9633,x9634,x9632))
% 157.55/157.24 [964]~E(x9641,x9642)+E(f56(x9641),f56(x9642))
% 157.55/157.24 [965]~E(x9651,x9652)+E(f421(x9651,x9653,x9654,x9655,x9656),f421(x9652,x9653,x9654,x9655,x9656))
% 157.55/157.24 [966]~E(x9661,x9662)+E(f421(x9663,x9661,x9664,x9665,x9666),f421(x9663,x9662,x9664,x9665,x9666))
% 157.55/157.24 [967]~E(x9671,x9672)+E(f421(x9673,x9674,x9671,x9675,x9676),f421(x9673,x9674,x9672,x9675,x9676))
% 157.55/157.24 [968]~E(x9681,x9682)+E(f421(x9683,x9684,x9685,x9681,x9686),f421(x9683,x9684,x9685,x9682,x9686))
% 157.55/157.24 [969]~E(x9691,x9692)+E(f421(x9693,x9694,x9695,x9696,x9691),f421(x9693,x9694,x9695,x9696,x9692))
% 157.55/157.24 [970]~E(x9701,x9702)+E(f453(x9701,x9703,x9704,x9705),f453(x9702,x9703,x9704,x9705))
% 157.55/157.24 [971]~E(x9711,x9712)+E(f453(x9713,x9711,x9714,x9715),f453(x9713,x9712,x9714,x9715))
% 157.55/157.24 [972]~E(x9721,x9722)+E(f453(x9723,x9724,x9721,x9725),f453(x9723,x9724,x9722,x9725))
% 157.55/157.24 [973]~E(x9731,x9732)+E(f453(x9733,x9734,x9735,x9731),f453(x9733,x9734,x9735,x9732))
% 157.55/157.24 [974]~E(x9741,x9742)+E(f410(x9741,x9743),f410(x9742,x9743))
% 157.55/157.24 [975]~E(x9751,x9752)+E(f410(x9753,x9751),f410(x9753,x9752))
% 157.55/157.24 [976]~E(x9761,x9762)+E(f636(x9761,x9763,x9764,x9765),f636(x9762,x9763,x9764,x9765))
% 157.55/157.24 [977]~E(x9771,x9772)+E(f636(x9773,x9771,x9774,x9775),f636(x9773,x9772,x9774,x9775))
% 157.55/157.24 [978]~E(x9781,x9782)+E(f636(x9783,x9784,x9781,x9785),f636(x9783,x9784,x9782,x9785))
% 157.55/157.24 [979]~E(x9791,x9792)+E(f636(x9793,x9794,x9795,x9791),f636(x9793,x9794,x9795,x9792))
% 157.55/157.24 [980]~E(x9801,x9802)+E(f374(x9801,x9803),f374(x9802,x9803))
% 157.55/157.24 [981]~E(x9811,x9812)+E(f374(x9813,x9811),f374(x9813,x9812))
% 157.55/157.24 [982]~E(x9821,x9822)+E(f509(x9821,x9823,x9824,x9825,x9826,x9827,x9828),f509(x9822,x9823,x9824,x9825,x9826,x9827,x9828))
% 157.55/157.24 [983]~E(x9831,x9832)+E(f509(x9833,x9831,x9834,x9835,x9836,x9837,x9838),f509(x9833,x9832,x9834,x9835,x9836,x9837,x9838))
% 157.55/157.24 [984]~E(x9841,x9842)+E(f509(x9843,x9844,x9841,x9845,x9846,x9847,x9848),f509(x9843,x9844,x9842,x9845,x9846,x9847,x9848))
% 157.55/157.24 [985]~E(x9851,x9852)+E(f509(x9853,x9854,x9855,x9851,x9856,x9857,x9858),f509(x9853,x9854,x9855,x9852,x9856,x9857,x9858))
% 157.55/157.24 [986]~E(x9861,x9862)+E(f509(x9863,x9864,x9865,x9866,x9861,x9867,x9868),f509(x9863,x9864,x9865,x9866,x9862,x9867,x9868))
% 157.55/157.24 [987]~E(x9871,x9872)+E(f509(x9873,x9874,x9875,x9876,x9877,x9871,x9878),f509(x9873,x9874,x9875,x9876,x9877,x9872,x9878))
% 157.55/157.24 [988]~E(x9881,x9882)+E(f509(x9883,x9884,x9885,x9886,x9887,x9888,x9881),f509(x9883,x9884,x9885,x9886,x9887,x9888,x9882))
% 157.55/157.24 [989]~E(x9891,x9892)+E(f277(x9891),f277(x9892))
% 157.55/157.24 [990]~E(x9901,x9902)+E(f291(x9901,x9903),f291(x9902,x9903))
% 157.55/157.24 [991]~E(x9911,x9912)+E(f291(x9913,x9911),f291(x9913,x9912))
% 157.55/157.24 [992]~E(x9921,x9922)+E(f438(x9921,x9923,x9924,x9925),f438(x9922,x9923,x9924,x9925))
% 157.55/157.24 [993]~E(x9931,x9932)+E(f438(x9933,x9931,x9934,x9935),f438(x9933,x9932,x9934,x9935))
% 157.55/157.24 [994]~E(x9941,x9942)+E(f438(x9943,x9944,x9941,x9945),f438(x9943,x9944,x9942,x9945))
% 157.55/157.24 [995]~E(x9951,x9952)+E(f438(x9953,x9954,x9955,x9951),f438(x9953,x9954,x9955,x9952))
% 157.55/157.24 [996]~E(x9961,x9962)+E(f852(x9961,x9963,x9964,x9965,x9966,x9967,x9968),f852(x9962,x9963,x9964,x9965,x9966,x9967,x9968))
% 157.55/157.24 [997]~E(x9971,x9972)+E(f852(x9973,x9971,x9974,x9975,x9976,x9977,x9978),f852(x9973,x9972,x9974,x9975,x9976,x9977,x9978))
% 157.55/157.24 [998]~E(x9981,x9982)+E(f852(x9983,x9984,x9981,x9985,x9986,x9987,x9988),f852(x9983,x9984,x9982,x9985,x9986,x9987,x9988))
% 157.55/157.24 [999]~E(x9991,x9992)+E(f852(x9993,x9994,x9995,x9991,x9996,x9997,x9998),f852(x9993,x9994,x9995,x9992,x9996,x9997,x9998))
% 157.55/157.24 [1000]~E(x10001,x10002)+E(f852(x10003,x10004,x10005,x10006,x10001,x10007,x10008),f852(x10003,x10004,x10005,x10006,x10002,x10007,x10008))
% 157.55/157.24 [1001]~E(x10011,x10012)+E(f852(x10013,x10014,x10015,x10016,x10017,x10011,x10018),f852(x10013,x10014,x10015,x10016,x10017,x10012,x10018))
% 157.55/157.24 [1002]~E(x10021,x10022)+E(f852(x10023,x10024,x10025,x10026,x10027,x10028,x10021),f852(x10023,x10024,x10025,x10026,x10027,x10028,x10022))
% 157.55/157.24 [1003]~E(x10031,x10032)+E(f267(x10031,x10033),f267(x10032,x10033))
% 157.55/157.24 [1004]~E(x10041,x10042)+E(f267(x10043,x10041),f267(x10043,x10042))
% 157.55/157.24 [1005]~E(x10051,x10052)+E(f461(x10051,x10053,x10054,x10055),f461(x10052,x10053,x10054,x10055))
% 157.55/157.24 [1006]~E(x10061,x10062)+E(f461(x10063,x10061,x10064,x10065),f461(x10063,x10062,x10064,x10065))
% 157.55/157.24 [1007]~E(x10071,x10072)+E(f461(x10073,x10074,x10071,x10075),f461(x10073,x10074,x10072,x10075))
% 157.55/157.24 [1008]~E(x10081,x10082)+E(f461(x10083,x10084,x10085,x10081),f461(x10083,x10084,x10085,x10082))
% 157.55/157.24 [1009]~E(x10091,x10092)+E(f49(x10091,x10093),f49(x10092,x10093))
% 157.55/157.24 [1010]~E(x10101,x10102)+E(f49(x10103,x10101),f49(x10103,x10102))
% 157.55/157.24 [1011]~E(x10111,x10112)+E(f538(x10111,x10113,x10114,x10115,x10116),f538(x10112,x10113,x10114,x10115,x10116))
% 157.55/157.24 [1012]~E(x10121,x10122)+E(f538(x10123,x10121,x10124,x10125,x10126),f538(x10123,x10122,x10124,x10125,x10126))
% 157.55/157.24 [1013]~E(x10131,x10132)+E(f538(x10133,x10134,x10131,x10135,x10136),f538(x10133,x10134,x10132,x10135,x10136))
% 157.55/157.24 [1014]~E(x10141,x10142)+E(f538(x10143,x10144,x10145,x10141,x10146),f538(x10143,x10144,x10145,x10142,x10146))
% 157.55/157.24 [1015]~E(x10151,x10152)+E(f538(x10153,x10154,x10155,x10156,x10151),f538(x10153,x10154,x10155,x10156,x10152))
% 157.55/157.24 [1016]~E(x10161,x10162)+E(f795(x10161,x10163),f795(x10162,x10163))
% 157.55/157.24 [1017]~E(x10171,x10172)+E(f795(x10173,x10171),f795(x10173,x10172))
% 157.55/157.24 [1018]~E(x10181,x10182)+E(f446(x10181,x10183),f446(x10182,x10183))
% 157.55/157.24 [1019]~E(x10191,x10192)+E(f446(x10193,x10191),f446(x10193,x10192))
% 157.55/157.24 [1020]~E(x10201,x10202)+E(f722(x10201,x10203,x10204),f722(x10202,x10203,x10204))
% 157.55/157.24 [1021]~E(x10211,x10212)+E(f722(x10213,x10211,x10214),f722(x10213,x10212,x10214))
% 157.55/157.24 [1022]~E(x10221,x10222)+E(f722(x10223,x10224,x10221),f722(x10223,x10224,x10222))
% 157.55/157.24 [1023]~E(x10231,x10232)+E(f633(x10231,x10233,x10234),f633(x10232,x10233,x10234))
% 157.55/157.24 [1024]~E(x10241,x10242)+E(f633(x10243,x10241,x10244),f633(x10243,x10242,x10244))
% 157.55/157.24 [1025]~E(x10251,x10252)+E(f633(x10253,x10254,x10251),f633(x10253,x10254,x10252))
% 157.55/157.24 [1026]~E(x10261,x10262)+E(f271(x10261,x10263),f271(x10262,x10263))
% 157.55/157.24 [1027]~E(x10271,x10272)+E(f271(x10273,x10271),f271(x10273,x10272))
% 157.55/157.24 [1028]~E(x10281,x10282)+E(f551(x10281,x10283,x10284,x10285),f551(x10282,x10283,x10284,x10285))
% 157.55/157.24 [1029]~E(x10291,x10292)+E(f551(x10293,x10291,x10294,x10295),f551(x10293,x10292,x10294,x10295))
% 157.55/157.24 [1030]~E(x10301,x10302)+E(f551(x10303,x10304,x10301,x10305),f551(x10303,x10304,x10302,x10305))
% 157.55/157.24 [1031]~E(x10311,x10312)+E(f551(x10313,x10314,x10315,x10311),f551(x10313,x10314,x10315,x10312))
% 157.55/157.24 [1032]~E(x10321,x10322)+E(f797(x10321,x10323),f797(x10322,x10323))
% 157.55/157.24 [1033]~E(x10331,x10332)+E(f797(x10333,x10331),f797(x10333,x10332))
% 157.55/157.24 [1034]~E(x10341,x10342)+E(f393(x10341,x10343,x10344),f393(x10342,x10343,x10344))
% 157.55/157.24 [1035]~E(x10351,x10352)+E(f393(x10353,x10351,x10354),f393(x10353,x10352,x10354))
% 157.55/157.24 [1036]~E(x10361,x10362)+E(f393(x10363,x10364,x10361),f393(x10363,x10364,x10362))
% 157.55/157.24 [1037]~E(x10371,x10372)+E(f532(x10371,x10373,x10374,x10375),f532(x10372,x10373,x10374,x10375))
% 157.55/157.24 [1038]~E(x10381,x10382)+E(f532(x10383,x10381,x10384,x10385),f532(x10383,x10382,x10384,x10385))
% 157.55/157.24 [1039]~E(x10391,x10392)+E(f532(x10393,x10394,x10391,x10395),f532(x10393,x10394,x10392,x10395))
% 157.55/157.24 [1040]~E(x10401,x10402)+E(f532(x10403,x10404,x10405,x10401),f532(x10403,x10404,x10405,x10402))
% 157.55/157.24 [1041]~E(x10411,x10412)+E(f356(x10411,x10413,x10414,x10415),f356(x10412,x10413,x10414,x10415))
% 157.55/157.24 [1042]~E(x10421,x10422)+E(f356(x10423,x10421,x10424,x10425),f356(x10423,x10422,x10424,x10425))
% 157.55/157.24 [1043]~E(x10431,x10432)+E(f356(x10433,x10434,x10431,x10435),f356(x10433,x10434,x10432,x10435))
% 157.55/157.24 [1044]~E(x10441,x10442)+E(f356(x10443,x10444,x10445,x10441),f356(x10443,x10444,x10445,x10442))
% 157.55/157.24 [1045]~E(x10451,x10452)+E(f454(x10451,x10453),f454(x10452,x10453))
% 157.55/157.24 [1046]~E(x10461,x10462)+E(f454(x10463,x10461),f454(x10463,x10462))
% 157.55/157.24 [1047]~E(x10471,x10472)+E(f629(x10471,x10473,x10474,x10475,x10476),f629(x10472,x10473,x10474,x10475,x10476))
% 157.55/157.24 [1048]~E(x10481,x10482)+E(f629(x10483,x10481,x10484,x10485,x10486),f629(x10483,x10482,x10484,x10485,x10486))
% 157.55/157.24 [1049]~E(x10491,x10492)+E(f629(x10493,x10494,x10491,x10495,x10496),f629(x10493,x10494,x10492,x10495,x10496))
% 157.55/157.24 [1050]~E(x10501,x10502)+E(f629(x10503,x10504,x10505,x10501,x10506),f629(x10503,x10504,x10505,x10502,x10506))
% 157.55/157.24 [1051]~E(x10511,x10512)+E(f629(x10513,x10514,x10515,x10516,x10511),f629(x10513,x10514,x10515,x10516,x10512))
% 157.55/157.24 [1052]~E(x10521,x10522)+E(f477(x10521,x10523,x10524,x10525),f477(x10522,x10523,x10524,x10525))
% 157.55/157.24 [1053]~E(x10531,x10532)+E(f477(x10533,x10531,x10534,x10535),f477(x10533,x10532,x10534,x10535))
% 157.55/157.24 [1054]~E(x10541,x10542)+E(f477(x10543,x10544,x10541,x10545),f477(x10543,x10544,x10542,x10545))
% 157.55/157.24 [1055]~E(x10551,x10552)+E(f477(x10553,x10554,x10555,x10551),f477(x10553,x10554,x10555,x10552))
% 157.55/157.24 [1056]~E(x10561,x10562)+E(f684(x10561,x10563,x10564),f684(x10562,x10563,x10564))
% 157.55/157.24 [1057]~E(x10571,x10572)+E(f684(x10573,x10571,x10574),f684(x10573,x10572,x10574))
% 157.55/157.24 [1058]~E(x10581,x10582)+E(f684(x10583,x10584,x10581),f684(x10583,x10584,x10582))
% 157.55/157.24 [1059]~E(x10591,x10592)+E(f198(x10591,x10593,x10594,x10595),f198(x10592,x10593,x10594,x10595))
% 157.55/157.24 [1060]~E(x10601,x10602)+E(f198(x10603,x10601,x10604,x10605),f198(x10603,x10602,x10604,x10605))
% 157.55/157.24 [1061]~E(x10611,x10612)+E(f198(x10613,x10614,x10611,x10615),f198(x10613,x10614,x10612,x10615))
% 157.55/157.24 [1062]~E(x10621,x10622)+E(f198(x10623,x10624,x10625,x10621),f198(x10623,x10624,x10625,x10622))
% 157.55/157.24 [1063]~E(x10631,x10632)+E(f228(x10631,x10633,x10634),f228(x10632,x10633,x10634))
% 157.55/157.24 [1064]~E(x10641,x10642)+E(f228(x10643,x10641,x10644),f228(x10643,x10642,x10644))
% 157.55/157.24 [1065]~E(x10651,x10652)+E(f228(x10653,x10654,x10651),f228(x10653,x10654,x10652))
% 157.55/157.24 [1066]~E(x10661,x10662)+E(f842(x10661,x10663,x10664,x10665,x10666,x10667,x10668),f842(x10662,x10663,x10664,x10665,x10666,x10667,x10668))
% 157.55/157.24 [1067]~E(x10671,x10672)+E(f842(x10673,x10671,x10674,x10675,x10676,x10677,x10678),f842(x10673,x10672,x10674,x10675,x10676,x10677,x10678))
% 157.55/157.24 [1068]~E(x10681,x10682)+E(f842(x10683,x10684,x10681,x10685,x10686,x10687,x10688),f842(x10683,x10684,x10682,x10685,x10686,x10687,x10688))
% 157.55/157.24 [1069]~E(x10691,x10692)+E(f842(x10693,x10694,x10695,x10691,x10696,x10697,x10698),f842(x10693,x10694,x10695,x10692,x10696,x10697,x10698))
% 157.55/157.24 [1070]~E(x10701,x10702)+E(f842(x10703,x10704,x10705,x10706,x10701,x10707,x10708),f842(x10703,x10704,x10705,x10706,x10702,x10707,x10708))
% 157.55/157.24 [1071]~E(x10711,x10712)+E(f842(x10713,x10714,x10715,x10716,x10717,x10711,x10718),f842(x10713,x10714,x10715,x10716,x10717,x10712,x10718))
% 157.55/157.24 [1072]~E(x10721,x10722)+E(f842(x10723,x10724,x10725,x10726,x10727,x10728,x10721),f842(x10723,x10724,x10725,x10726,x10727,x10728,x10722))
% 157.55/157.24 [1073]~E(x10731,x10732)+E(f724(x10731,x10733),f724(x10732,x10733))
% 157.55/157.24 [1074]~E(x10741,x10742)+E(f724(x10743,x10741),f724(x10743,x10742))
% 157.55/157.24 [1075]~E(x10751,x10752)+E(f741(x10751,x10753,x10754,x10755,x10756,x10757,x10758),f741(x10752,x10753,x10754,x10755,x10756,x10757,x10758))
% 157.55/157.24 [1076]~E(x10761,x10762)+E(f741(x10763,x10761,x10764,x10765,x10766,x10767,x10768),f741(x10763,x10762,x10764,x10765,x10766,x10767,x10768))
% 157.55/157.24 [1077]~E(x10771,x10772)+E(f741(x10773,x10774,x10771,x10775,x10776,x10777,x10778),f741(x10773,x10774,x10772,x10775,x10776,x10777,x10778))
% 157.55/157.24 [1078]~E(x10781,x10782)+E(f741(x10783,x10784,x10785,x10781,x10786,x10787,x10788),f741(x10783,x10784,x10785,x10782,x10786,x10787,x10788))
% 157.55/157.24 [1079]~E(x10791,x10792)+E(f741(x10793,x10794,x10795,x10796,x10791,x10797,x10798),f741(x10793,x10794,x10795,x10796,x10792,x10797,x10798))
% 157.55/157.24 [1080]~E(x10801,x10802)+E(f741(x10803,x10804,x10805,x10806,x10807,x10801,x10808),f741(x10803,x10804,x10805,x10806,x10807,x10802,x10808))
% 157.55/157.24 [1081]~E(x10811,x10812)+E(f741(x10813,x10814,x10815,x10816,x10817,x10818,x10811),f741(x10813,x10814,x10815,x10816,x10817,x10818,x10812))
% 157.55/157.24 [1082]~E(x10821,x10822)+E(f150(x10821,x10823,x10824,x10825),f150(x10822,x10823,x10824,x10825))
% 157.55/157.24 [1083]~E(x10831,x10832)+E(f150(x10833,x10831,x10834,x10835),f150(x10833,x10832,x10834,x10835))
% 157.55/157.24 [1084]~E(x10841,x10842)+E(f150(x10843,x10844,x10841,x10845),f150(x10843,x10844,x10842,x10845))
% 157.55/157.24 [1085]~E(x10851,x10852)+E(f150(x10853,x10854,x10855,x10851),f150(x10853,x10854,x10855,x10852))
% 157.55/157.24 [1086]~E(x10861,x10862)+E(f223(x10861,x10863,x10864,x10865,x10866),f223(x10862,x10863,x10864,x10865,x10866))
% 157.55/157.24 [1087]~E(x10871,x10872)+E(f223(x10873,x10871,x10874,x10875,x10876),f223(x10873,x10872,x10874,x10875,x10876))
% 157.55/157.24 [1088]~E(x10881,x10882)+E(f223(x10883,x10884,x10881,x10885,x10886),f223(x10883,x10884,x10882,x10885,x10886))
% 157.55/157.24 [1089]~E(x10891,x10892)+E(f223(x10893,x10894,x10895,x10891,x10896),f223(x10893,x10894,x10895,x10892,x10896))
% 157.55/157.24 [1090]~E(x10901,x10902)+E(f223(x10903,x10904,x10905,x10906,x10901),f223(x10903,x10904,x10905,x10906,x10902))
% 157.55/157.24 [1091]~E(x10911,x10912)+E(f194(x10911,x10913),f194(x10912,x10913))
% 157.55/157.24 [1092]~E(x10921,x10922)+E(f194(x10923,x10921),f194(x10923,x10922))
% 157.55/157.24 [1093]~E(x10931,x10932)+E(f204(x10931),f204(x10932))
% 157.55/157.24 [1094]~E(x10941,x10942)+E(f765(x10941,x10943,x10944,x10945),f765(x10942,x10943,x10944,x10945))
% 157.55/157.24 [1095]~E(x10951,x10952)+E(f765(x10953,x10951,x10954,x10955),f765(x10953,x10952,x10954,x10955))
% 157.55/157.24 [1096]~E(x10961,x10962)+E(f765(x10963,x10964,x10961,x10965),f765(x10963,x10964,x10962,x10965))
% 157.55/157.24 [1097]~E(x10971,x10972)+E(f765(x10973,x10974,x10975,x10971),f765(x10973,x10974,x10975,x10972))
% 157.55/157.24 [1098]~E(x10981,x10982)+E(f220(x10981,x10983,x10984,x10985),f220(x10982,x10983,x10984,x10985))
% 157.55/157.24 [1099]~E(x10991,x10992)+E(f220(x10993,x10991,x10994,x10995),f220(x10993,x10992,x10994,x10995))
% 157.55/157.24 [1100]~E(x11001,x11002)+E(f220(x11003,x11004,x11001,x11005),f220(x11003,x11004,x11002,x11005))
% 157.55/157.24 [1101]~E(x11011,x11012)+E(f220(x11013,x11014,x11015,x11011),f220(x11013,x11014,x11015,x11012))
% 157.55/157.24 [1102]~E(x11021,x11022)+E(f185(x11021,x11023,x11024,x11025),f185(x11022,x11023,x11024,x11025))
% 157.55/157.24 [1103]~E(x11031,x11032)+E(f185(x11033,x11031,x11034,x11035),f185(x11033,x11032,x11034,x11035))
% 157.55/157.24 [1104]~E(x11041,x11042)+E(f185(x11043,x11044,x11041,x11045),f185(x11043,x11044,x11042,x11045))
% 157.55/157.24 [1105]~E(x11051,x11052)+E(f185(x11053,x11054,x11055,x11051),f185(x11053,x11054,x11055,x11052))
% 157.55/157.24 [1106]~E(x11061,x11062)+E(f903(x11061,x11063,x11064,x11065),f903(x11062,x11063,x11064,x11065))
% 157.55/157.24 [1107]~E(x11071,x11072)+E(f903(x11073,x11071,x11074,x11075),f903(x11073,x11072,x11074,x11075))
% 157.55/157.24 [1108]~E(x11081,x11082)+E(f903(x11083,x11084,x11081,x11085),f903(x11083,x11084,x11082,x11085))
% 157.55/157.24 [1109]~E(x11091,x11092)+E(f903(x11093,x11094,x11095,x11091),f903(x11093,x11094,x11095,x11092))
% 157.55/157.24 [1110]~E(x11101,x11102)+E(f248(x11101,x11103,x11104),f248(x11102,x11103,x11104))
% 157.55/157.24 [1111]~E(x11111,x11112)+E(f248(x11113,x11111,x11114),f248(x11113,x11112,x11114))
% 157.55/157.24 [1112]~E(x11121,x11122)+E(f248(x11123,x11124,x11121),f248(x11123,x11124,x11122))
% 157.55/157.24 [1113]~E(x11131,x11132)+E(f406(x11131,x11133),f406(x11132,x11133))
% 157.55/157.24 [1114]~E(x11141,x11142)+E(f406(x11143,x11141),f406(x11143,x11142))
% 157.55/157.24 [1115]~E(x11151,x11152)+E(f628(x11151,x11153,x11154,x11155,x11156),f628(x11152,x11153,x11154,x11155,x11156))
% 157.55/157.24 [1116]~E(x11161,x11162)+E(f628(x11163,x11161,x11164,x11165,x11166),f628(x11163,x11162,x11164,x11165,x11166))
% 157.55/157.24 [1117]~E(x11171,x11172)+E(f628(x11173,x11174,x11171,x11175,x11176),f628(x11173,x11174,x11172,x11175,x11176))
% 157.55/157.24 [1118]~E(x11181,x11182)+E(f628(x11183,x11184,x11185,x11181,x11186),f628(x11183,x11184,x11185,x11182,x11186))
% 157.55/157.24 [1119]~E(x11191,x11192)+E(f628(x11193,x11194,x11195,x11196,x11191),f628(x11193,x11194,x11195,x11196,x11192))
% 157.55/157.24 [1120]~E(x11201,x11202)+E(f347(x11201,x11203),f347(x11202,x11203))
% 157.55/157.24 [1121]~E(x11211,x11212)+E(f347(x11213,x11211),f347(x11213,x11212))
% 157.55/157.24 [1122]~E(x11221,x11222)+E(f742(x11221,x11223,x11224,x11225,x11226,x11227,x11228),f742(x11222,x11223,x11224,x11225,x11226,x11227,x11228))
% 157.55/157.24 [1123]~E(x11231,x11232)+E(f742(x11233,x11231,x11234,x11235,x11236,x11237,x11238),f742(x11233,x11232,x11234,x11235,x11236,x11237,x11238))
% 157.55/157.24 [1124]~E(x11241,x11242)+E(f742(x11243,x11244,x11241,x11245,x11246,x11247,x11248),f742(x11243,x11244,x11242,x11245,x11246,x11247,x11248))
% 157.55/157.24 [1125]~E(x11251,x11252)+E(f742(x11253,x11254,x11255,x11251,x11256,x11257,x11258),f742(x11253,x11254,x11255,x11252,x11256,x11257,x11258))
% 157.55/157.24 [1126]~E(x11261,x11262)+E(f742(x11263,x11264,x11265,x11266,x11261,x11267,x11268),f742(x11263,x11264,x11265,x11266,x11262,x11267,x11268))
% 157.55/157.24 [1127]~E(x11271,x11272)+E(f742(x11273,x11274,x11275,x11276,x11277,x11271,x11278),f742(x11273,x11274,x11275,x11276,x11277,x11272,x11278))
% 157.55/157.24 [1128]~E(x11281,x11282)+E(f742(x11283,x11284,x11285,x11286,x11287,x11288,x11281),f742(x11283,x11284,x11285,x11286,x11287,x11288,x11282))
% 157.55/157.24 [1129]~E(x11291,x11292)+E(f536(x11291,x11293,x11294,x11295,x11296,x11297),f536(x11292,x11293,x11294,x11295,x11296,x11297))
% 157.55/157.24 [1130]~E(x11301,x11302)+E(f536(x11303,x11301,x11304,x11305,x11306,x11307),f536(x11303,x11302,x11304,x11305,x11306,x11307))
% 157.55/157.24 [1131]~E(x11311,x11312)+E(f536(x11313,x11314,x11311,x11315,x11316,x11317),f536(x11313,x11314,x11312,x11315,x11316,x11317))
% 157.55/157.24 [1132]~E(x11321,x11322)+E(f536(x11323,x11324,x11325,x11321,x11326,x11327),f536(x11323,x11324,x11325,x11322,x11326,x11327))
% 157.55/157.24 [1133]~E(x11331,x11332)+E(f536(x11333,x11334,x11335,x11336,x11331,x11337),f536(x11333,x11334,x11335,x11336,x11332,x11337))
% 157.55/157.24 [1134]~E(x11341,x11342)+E(f536(x11343,x11344,x11345,x11346,x11347,x11341),f536(x11343,x11344,x11345,x11346,x11347,x11342))
% 157.55/157.24 [1135]~E(x11351,x11352)+E(f621(x11351,x11353,x11354,x11355,x11356),f621(x11352,x11353,x11354,x11355,x11356))
% 157.55/157.24 [1136]~E(x11361,x11362)+E(f621(x11363,x11361,x11364,x11365,x11366),f621(x11363,x11362,x11364,x11365,x11366))
% 157.55/157.24 [1137]~E(x11371,x11372)+E(f621(x11373,x11374,x11371,x11375,x11376),f621(x11373,x11374,x11372,x11375,x11376))
% 157.55/157.24 [1138]~E(x11381,x11382)+E(f621(x11383,x11384,x11385,x11381,x11386),f621(x11383,x11384,x11385,x11382,x11386))
% 157.55/157.24 [1139]~E(x11391,x11392)+E(f621(x11393,x11394,x11395,x11396,x11391),f621(x11393,x11394,x11395,x11396,x11392))
% 157.55/157.24 [1140]~E(x11401,x11402)+E(f648(x11401,x11403,x11404,x11405,x11406),f648(x11402,x11403,x11404,x11405,x11406))
% 157.55/157.24 [1141]~E(x11411,x11412)+E(f648(x11413,x11411,x11414,x11415,x11416),f648(x11413,x11412,x11414,x11415,x11416))
% 157.55/157.24 [1142]~E(x11421,x11422)+E(f648(x11423,x11424,x11421,x11425,x11426),f648(x11423,x11424,x11422,x11425,x11426))
% 157.55/157.24 [1143]~E(x11431,x11432)+E(f648(x11433,x11434,x11435,x11431,x11436),f648(x11433,x11434,x11435,x11432,x11436))
% 157.55/157.24 [1144]~E(x11441,x11442)+E(f648(x11443,x11444,x11445,x11446,x11441),f648(x11443,x11444,x11445,x11446,x11442))
% 157.55/157.24 [1145]~E(x11451,x11452)+E(f841(x11451,x11453,x11454,x11455,x11456,x11457,x11458),f841(x11452,x11453,x11454,x11455,x11456,x11457,x11458))
% 157.55/157.24 [1146]~E(x11461,x11462)+E(f841(x11463,x11461,x11464,x11465,x11466,x11467,x11468),f841(x11463,x11462,x11464,x11465,x11466,x11467,x11468))
% 157.55/157.24 [1147]~E(x11471,x11472)+E(f841(x11473,x11474,x11471,x11475,x11476,x11477,x11478),f841(x11473,x11474,x11472,x11475,x11476,x11477,x11478))
% 157.55/157.24 [1148]~E(x11481,x11482)+E(f841(x11483,x11484,x11485,x11481,x11486,x11487,x11488),f841(x11483,x11484,x11485,x11482,x11486,x11487,x11488))
% 157.55/157.24 [1149]~E(x11491,x11492)+E(f841(x11493,x11494,x11495,x11496,x11491,x11497,x11498),f841(x11493,x11494,x11495,x11496,x11492,x11497,x11498))
% 157.55/157.24 [1150]~E(x11501,x11502)+E(f841(x11503,x11504,x11505,x11506,x11507,x11501,x11508),f841(x11503,x11504,x11505,x11506,x11507,x11502,x11508))
% 157.55/157.24 [1151]~E(x11511,x11512)+E(f841(x11513,x11514,x11515,x11516,x11517,x11518,x11511),f841(x11513,x11514,x11515,x11516,x11517,x11518,x11512))
% 157.55/157.24 [1152]~E(x11521,x11522)+E(f504(x11521),f504(x11522))
% 157.55/157.24 [1153]~E(x11531,x11532)+E(f760(x11531,x11533,x11534),f760(x11532,x11533,x11534))
% 157.55/157.24 [1154]~E(x11541,x11542)+E(f760(x11543,x11541,x11544),f760(x11543,x11542,x11544))
% 157.55/157.24 [1155]~E(x11551,x11552)+E(f760(x11553,x11554,x11551),f760(x11553,x11554,x11552))
% 157.55/157.24 [1156]~E(x11561,x11562)+E(f680(x11561,x11563,x11564,x11565,x11566,x11567,x11568),f680(x11562,x11563,x11564,x11565,x11566,x11567,x11568))
% 157.55/157.24 [1157]~E(x11571,x11572)+E(f680(x11573,x11571,x11574,x11575,x11576,x11577,x11578),f680(x11573,x11572,x11574,x11575,x11576,x11577,x11578))
% 157.55/157.24 [1158]~E(x11581,x11582)+E(f680(x11583,x11584,x11581,x11585,x11586,x11587,x11588),f680(x11583,x11584,x11582,x11585,x11586,x11587,x11588))
% 157.55/157.24 [1159]~E(x11591,x11592)+E(f680(x11593,x11594,x11595,x11591,x11596,x11597,x11598),f680(x11593,x11594,x11595,x11592,x11596,x11597,x11598))
% 157.55/157.24 [1160]~E(x11601,x11602)+E(f680(x11603,x11604,x11605,x11606,x11601,x11607,x11608),f680(x11603,x11604,x11605,x11606,x11602,x11607,x11608))
% 157.55/157.24 [1161]~E(x11611,x11612)+E(f680(x11613,x11614,x11615,x11616,x11617,x11611,x11618),f680(x11613,x11614,x11615,x11616,x11617,x11612,x11618))
% 157.55/157.24 [1162]~E(x11621,x11622)+E(f680(x11623,x11624,x11625,x11626,x11627,x11628,x11621),f680(x11623,x11624,x11625,x11626,x11627,x11628,x11622))
% 157.55/157.24 [1163]~E(x11631,x11632)+E(f643(x11631,x11633,x11634,x11635),f643(x11632,x11633,x11634,x11635))
% 157.55/157.24 [1164]~E(x11641,x11642)+E(f643(x11643,x11641,x11644,x11645),f643(x11643,x11642,x11644,x11645))
% 157.55/157.24 [1165]~E(x11651,x11652)+E(f643(x11653,x11654,x11651,x11655),f643(x11653,x11654,x11652,x11655))
% 157.55/157.24 [1166]~E(x11661,x11662)+E(f643(x11663,x11664,x11665,x11661),f643(x11663,x11664,x11665,x11662))
% 157.55/157.24 [1167]~E(x11671,x11672)+E(f762(x11671,x11673,x11674),f762(x11672,x11673,x11674))
% 157.55/157.24 [1168]~E(x11681,x11682)+E(f762(x11683,x11681,x11684),f762(x11683,x11682,x11684))
% 157.55/157.24 [1169]~E(x11691,x11692)+E(f762(x11693,x11694,x11691),f762(x11693,x11694,x11692))
% 157.55/157.24 [1170]~E(x11701,x11702)+E(f838(x11701,x11703,x11704,x11705,x11706,x11707,x11708,x11709),f838(x11702,x11703,x11704,x11705,x11706,x11707,x11708,x11709))
% 157.55/157.24 [1171]~E(x11711,x11712)+E(f838(x11713,x11711,x11714,x11715,x11716,x11717,x11718,x11719),f838(x11713,x11712,x11714,x11715,x11716,x11717,x11718,x11719))
% 157.55/157.24 [1172]~E(x11721,x11722)+E(f838(x11723,x11724,x11721,x11725,x11726,x11727,x11728,x11729),f838(x11723,x11724,x11722,x11725,x11726,x11727,x11728,x11729))
% 157.55/157.24 [1173]~E(x11731,x11732)+E(f838(x11733,x11734,x11735,x11731,x11736,x11737,x11738,x11739),f838(x11733,x11734,x11735,x11732,x11736,x11737,x11738,x11739))
% 157.55/157.24 [1174]~E(x11741,x11742)+E(f838(x11743,x11744,x11745,x11746,x11741,x11747,x11748,x11749),f838(x11743,x11744,x11745,x11746,x11742,x11747,x11748,x11749))
% 157.55/157.24 [1175]~E(x11751,x11752)+E(f838(x11753,x11754,x11755,x11756,x11757,x11751,x11758,x11759),f838(x11753,x11754,x11755,x11756,x11757,x11752,x11758,x11759))
% 157.55/157.24 [1176]~E(x11761,x11762)+E(f838(x11763,x11764,x11765,x11766,x11767,x11768,x11761,x11769),f838(x11763,x11764,x11765,x11766,x11767,x11768,x11762,x11769))
% 157.55/157.24 [1177]~E(x11771,x11772)+E(f838(x11773,x11774,x11775,x11776,x11777,x11778,x11779,x11771),f838(x11773,x11774,x11775,x11776,x11777,x11778,x11779,x11772))
% 157.55/157.24 [1178]~E(x11781,x11782)+E(f493(x11781,x11783,x11784),f493(x11782,x11783,x11784))
% 157.55/157.24 [1179]~E(x11791,x11792)+E(f493(x11793,x11791,x11794),f493(x11793,x11792,x11794))
% 157.55/157.24 [1180]~E(x11801,x11802)+E(f493(x11803,x11804,x11801),f493(x11803,x11804,x11802))
% 157.55/157.24 [1181]~E(x11811,x11812)+E(f128(x11811,x11813),f128(x11812,x11813))
% 157.55/157.24 [1182]~E(x11821,x11822)+E(f128(x11823,x11821),f128(x11823,x11822))
% 157.55/157.24 [1183]~E(x11831,x11832)+E(f132(x11831,x11833),f132(x11832,x11833))
% 157.55/157.24 [1184]~E(x11841,x11842)+E(f132(x11843,x11841),f132(x11843,x11842))
% 157.55/157.24 [1185]~E(x11851,x11852)+E(f587(x11851,x11853,x11854,x11855,x11856,x11857),f587(x11852,x11853,x11854,x11855,x11856,x11857))
% 157.55/157.24 [1186]~E(x11861,x11862)+E(f587(x11863,x11861,x11864,x11865,x11866,x11867),f587(x11863,x11862,x11864,x11865,x11866,x11867))
% 157.55/157.24 [1187]~E(x11871,x11872)+E(f587(x11873,x11874,x11871,x11875,x11876,x11877),f587(x11873,x11874,x11872,x11875,x11876,x11877))
% 157.55/157.24 [1188]~E(x11881,x11882)+E(f587(x11883,x11884,x11885,x11881,x11886,x11887),f587(x11883,x11884,x11885,x11882,x11886,x11887))
% 157.55/157.24 [1189]~E(x11891,x11892)+E(f587(x11893,x11894,x11895,x11896,x11891,x11897),f587(x11893,x11894,x11895,x11896,x11892,x11897))
% 157.55/157.24 [1190]~E(x11901,x11902)+E(f587(x11903,x11904,x11905,x11906,x11907,x11901),f587(x11903,x11904,x11905,x11906,x11907,x11902))
% 157.55/157.24 [1191]~E(x11911,x11912)+E(f552(x11911,x11913,x11914,x11915,x11916,x11917),f552(x11912,x11913,x11914,x11915,x11916,x11917))
% 157.55/157.24 [1192]~E(x11921,x11922)+E(f552(x11923,x11921,x11924,x11925,x11926,x11927),f552(x11923,x11922,x11924,x11925,x11926,x11927))
% 157.55/157.24 [1193]~E(x11931,x11932)+E(f552(x11933,x11934,x11931,x11935,x11936,x11937),f552(x11933,x11934,x11932,x11935,x11936,x11937))
% 157.55/157.24 [1194]~E(x11941,x11942)+E(f552(x11943,x11944,x11945,x11941,x11946,x11947),f552(x11943,x11944,x11945,x11942,x11946,x11947))
% 157.55/157.24 [1195]~E(x11951,x11952)+E(f552(x11953,x11954,x11955,x11956,x11951,x11957),f552(x11953,x11954,x11955,x11956,x11952,x11957))
% 157.55/157.24 [1196]~E(x11961,x11962)+E(f552(x11963,x11964,x11965,x11966,x11967,x11961),f552(x11963,x11964,x11965,x11966,x11967,x11962))
% 157.55/157.24 [1197]~E(x11971,x11972)+E(f359(x11971,x11973,x11974,x11975),f359(x11972,x11973,x11974,x11975))
% 157.55/157.24 [1198]~E(x11981,x11982)+E(f359(x11983,x11981,x11984,x11985),f359(x11983,x11982,x11984,x11985))
% 157.55/157.24 [1199]~E(x11991,x11992)+E(f359(x11993,x11994,x11991,x11995),f359(x11993,x11994,x11992,x11995))
% 157.55/157.24 [1200]~E(x12001,x12002)+E(f359(x12003,x12004,x12005,x12001),f359(x12003,x12004,x12005,x12002))
% 157.55/157.24 [1201]~E(x12011,x12012)+E(f455(x12011,x12013),f455(x12012,x12013))
% 157.55/157.24 [1202]~E(x12021,x12022)+E(f455(x12023,x12021),f455(x12023,x12022))
% 157.55/157.24 [1203]~E(x12031,x12032)+E(f370(x12031,x12033),f370(x12032,x12033))
% 157.55/157.24 [1204]~E(x12041,x12042)+E(f370(x12043,x12041),f370(x12043,x12042))
% 157.55/157.24 [1205]~E(x12051,x12052)+E(f507(x12051,x12053,x12054,x12055),f507(x12052,x12053,x12054,x12055))
% 157.55/157.24 [1206]~E(x12061,x12062)+E(f507(x12063,x12061,x12064,x12065),f507(x12063,x12062,x12064,x12065))
% 157.55/157.24 [1207]~E(x12071,x12072)+E(f507(x12073,x12074,x12071,x12075),f507(x12073,x12074,x12072,x12075))
% 157.55/157.24 [1208]~E(x12081,x12082)+E(f507(x12083,x12084,x12085,x12081),f507(x12083,x12084,x12085,x12082))
% 157.55/157.24 [1209]~E(x12091,x12092)+E(f623(x12091,x12093,x12094,x12095,x12096),f623(x12092,x12093,x12094,x12095,x12096))
% 157.55/157.24 [1210]~E(x12101,x12102)+E(f623(x12103,x12101,x12104,x12105,x12106),f623(x12103,x12102,x12104,x12105,x12106))
% 157.55/157.24 [1211]~E(x12111,x12112)+E(f623(x12113,x12114,x12111,x12115,x12116),f623(x12113,x12114,x12112,x12115,x12116))
% 157.55/157.24 [1212]~E(x12121,x12122)+E(f623(x12123,x12124,x12125,x12121,x12126),f623(x12123,x12124,x12125,x12122,x12126))
% 157.55/157.24 [1213]~E(x12131,x12132)+E(f623(x12133,x12134,x12135,x12136,x12131),f623(x12133,x12134,x12135,x12136,x12132))
% 157.55/157.24 [1214]~E(x12141,x12142)+E(f364(x12141),f364(x12142))
% 157.55/157.24 [1215]~E(x12151,x12152)+E(f418(x12151,x12153,x12154,x12155,x12156),f418(x12152,x12153,x12154,x12155,x12156))
% 157.55/157.24 [1216]~E(x12161,x12162)+E(f418(x12163,x12161,x12164,x12165,x12166),f418(x12163,x12162,x12164,x12165,x12166))
% 157.55/157.24 [1217]~E(x12171,x12172)+E(f418(x12173,x12174,x12171,x12175,x12176),f418(x12173,x12174,x12172,x12175,x12176))
% 157.55/157.24 [1218]~E(x12181,x12182)+E(f418(x12183,x12184,x12185,x12181,x12186),f418(x12183,x12184,x12185,x12182,x12186))
% 157.55/157.24 [1219]~E(x12191,x12192)+E(f418(x12193,x12194,x12195,x12196,x12191),f418(x12193,x12194,x12195,x12196,x12192))
% 157.55/157.24 [1220]~E(x12201,x12202)+E(f876(x12201,x12203,x12204),f876(x12202,x12203,x12204))
% 157.55/157.24 [1221]~E(x12211,x12212)+E(f876(x12213,x12211,x12214),f876(x12213,x12212,x12214))
% 157.55/157.24 [1222]~E(x12221,x12222)+E(f876(x12223,x12224,x12221),f876(x12223,x12224,x12222))
% 157.55/157.24 [1223]~E(x12231,x12232)+E(f634(x12231,x12233,x12234),f634(x12232,x12233,x12234))
% 157.55/157.24 [1224]~E(x12241,x12242)+E(f634(x12243,x12241,x12244),f634(x12243,x12242,x12244))
% 157.55/157.24 [1225]~E(x12251,x12252)+E(f634(x12253,x12254,x12251),f634(x12253,x12254,x12252))
% 157.55/157.24 [1226]~E(x12261,x12262)+E(f575(x12261),f575(x12262))
% 157.55/157.24 [1227]~E(x12271,x12272)+E(f199(x12271,x12273),f199(x12272,x12273))
% 157.55/157.24 [1228]~E(x12281,x12282)+E(f199(x12283,x12281),f199(x12283,x12282))
% 157.55/157.24 [1229]~E(x12291,x12292)+E(f837(x12291,x12293,x12294,x12295,x12296,x12297,x12298,x12299),f837(x12292,x12293,x12294,x12295,x12296,x12297,x12298,x12299))
% 157.55/157.24 [1230]~E(x12301,x12302)+E(f837(x12303,x12301,x12304,x12305,x12306,x12307,x12308,x12309),f837(x12303,x12302,x12304,x12305,x12306,x12307,x12308,x12309))
% 157.55/157.24 [1231]~E(x12311,x12312)+E(f837(x12313,x12314,x12311,x12315,x12316,x12317,x12318,x12319),f837(x12313,x12314,x12312,x12315,x12316,x12317,x12318,x12319))
% 157.55/157.24 [1232]~E(x12321,x12322)+E(f837(x12323,x12324,x12325,x12321,x12326,x12327,x12328,x12329),f837(x12323,x12324,x12325,x12322,x12326,x12327,x12328,x12329))
% 157.55/157.24 [1233]~E(x12331,x12332)+E(f837(x12333,x12334,x12335,x12336,x12331,x12337,x12338,x12339),f837(x12333,x12334,x12335,x12336,x12332,x12337,x12338,x12339))
% 157.55/157.24 [1234]~E(x12341,x12342)+E(f837(x12343,x12344,x12345,x12346,x12347,x12341,x12348,x12349),f837(x12343,x12344,x12345,x12346,x12347,x12342,x12348,x12349))
% 157.55/157.24 [1235]~E(x12351,x12352)+E(f837(x12353,x12354,x12355,x12356,x12357,x12358,x12351,x12359),f837(x12353,x12354,x12355,x12356,x12357,x12358,x12352,x12359))
% 157.55/157.24 [1236]~E(x12361,x12362)+E(f837(x12363,x12364,x12365,x12366,x12367,x12368,x12369,x12361),f837(x12363,x12364,x12365,x12366,x12367,x12368,x12369,x12362))
% 157.55/157.24 [1237]~E(x12371,x12372)+E(f200(x12371),f200(x12372))
% 157.55/157.24 [1238]~E(x12381,x12382)+E(f671(x12381,x12383,x12384),f671(x12382,x12383,x12384))
% 157.55/157.24 [1239]~E(x12391,x12392)+E(f671(x12393,x12391,x12394),f671(x12393,x12392,x12394))
% 157.55/157.24 [1240]~E(x12401,x12402)+E(f671(x12403,x12404,x12401),f671(x12403,x12404,x12402))
% 157.55/157.24 [1241]~E(x12411,x12412)+E(f659(x12411,x12413),f659(x12412,x12413))
% 157.55/157.24 [1242]~E(x12421,x12422)+E(f659(x12423,x12421),f659(x12423,x12422))
% 157.55/157.24 [1243]~E(x12431,x12432)+E(f699(x12431,x12433),f699(x12432,x12433))
% 157.55/157.24 [1244]~E(x12441,x12442)+E(f699(x12443,x12441),f699(x12443,x12442))
% 157.55/157.24 [1245]~E(x12451,x12452)+E(f419(x12451,x12453,x12454,x12455,x12456),f419(x12452,x12453,x12454,x12455,x12456))
% 157.55/157.24 [1246]~E(x12461,x12462)+E(f419(x12463,x12461,x12464,x12465,x12466),f419(x12463,x12462,x12464,x12465,x12466))
% 157.55/157.24 [1247]~E(x12471,x12472)+E(f419(x12473,x12474,x12471,x12475,x12476),f419(x12473,x12474,x12472,x12475,x12476))
% 157.55/157.24 [1248]~E(x12481,x12482)+E(f419(x12483,x12484,x12485,x12481,x12486),f419(x12483,x12484,x12485,x12482,x12486))
% 157.55/157.24 [1249]~E(x12491,x12492)+E(f419(x12493,x12494,x12495,x12496,x12491),f419(x12493,x12494,x12495,x12496,x12492))
% 157.55/157.24 [1250]~E(x12501,x12502)+E(f478(x12501,x12503,x12504),f478(x12502,x12503,x12504))
% 157.55/157.24 [1251]~E(x12511,x12512)+E(f478(x12513,x12511,x12514),f478(x12513,x12512,x12514))
% 157.55/157.24 [1252]~E(x12521,x12522)+E(f478(x12523,x12524,x12521),f478(x12523,x12524,x12522))
% 157.55/157.24 [1253]~E(x12531,x12532)+E(f358(x12531,x12533,x12534,x12535),f358(x12532,x12533,x12534,x12535))
% 157.55/157.24 [1254]~E(x12541,x12542)+E(f358(x12543,x12541,x12544,x12545),f358(x12543,x12542,x12544,x12545))
% 157.55/157.24 [1255]~E(x12551,x12552)+E(f358(x12553,x12554,x12551,x12555),f358(x12553,x12554,x12552,x12555))
% 157.55/157.24 [1256]~E(x12561,x12562)+E(f358(x12563,x12564,x12565,x12561),f358(x12563,x12564,x12565,x12562))
% 157.55/157.24 [1257]~E(x12571,x12572)+E(f229(x12571,x12573,x12574,x12575),f229(x12572,x12573,x12574,x12575))
% 157.55/157.24 [1258]~E(x12581,x12582)+E(f229(x12583,x12581,x12584,x12585),f229(x12583,x12582,x12584,x12585))
% 157.55/157.24 [1259]~E(x12591,x12592)+E(f229(x12593,x12594,x12591,x12595),f229(x12593,x12594,x12592,x12595))
% 157.55/157.24 [1260]~E(x12601,x12602)+E(f229(x12603,x12604,x12605,x12601),f229(x12603,x12604,x12605,x12602))
% 157.55/157.24 [1261]~E(x12611,x12612)+E(f822(x12611,x12613,x12614,x12615,x12616),f822(x12612,x12613,x12614,x12615,x12616))
% 157.55/157.24 [1262]~E(x12621,x12622)+E(f822(x12623,x12621,x12624,x12625,x12626),f822(x12623,x12622,x12624,x12625,x12626))
% 157.55/157.24 [1263]~E(x12631,x12632)+E(f822(x12633,x12634,x12631,x12635,x12636),f822(x12633,x12634,x12632,x12635,x12636))
% 157.55/157.24 [1264]~E(x12641,x12642)+E(f822(x12643,x12644,x12645,x12641,x12646),f822(x12643,x12644,x12645,x12642,x12646))
% 157.55/157.24 [1265]~E(x12651,x12652)+E(f822(x12653,x12654,x12655,x12656,x12651),f822(x12653,x12654,x12655,x12656,x12652))
% 157.55/157.24 [1266]~E(x12661,x12662)+E(f162(x12661,x12663),f162(x12662,x12663))
% 157.55/157.24 [1267]~E(x12671,x12672)+E(f162(x12673,x12671),f162(x12673,x12672))
% 157.55/157.24 [1268]~E(x12681,x12682)+E(f515(x12681,x12683,x12684,x12685),f515(x12682,x12683,x12684,x12685))
% 157.55/157.24 [1269]~E(x12691,x12692)+E(f515(x12693,x12691,x12694,x12695),f515(x12693,x12692,x12694,x12695))
% 157.55/157.24 [1270]~E(x12701,x12702)+E(f515(x12703,x12704,x12701,x12705),f515(x12703,x12704,x12702,x12705))
% 157.55/157.24 [1271]~E(x12711,x12712)+E(f515(x12713,x12714,x12715,x12711),f515(x12713,x12714,x12715,x12712))
% 157.55/157.24 [1272]~E(x12721,x12722)+E(f351(x12721,x12723,x12724),f351(x12722,x12723,x12724))
% 157.55/157.24 [1273]~E(x12731,x12732)+E(f351(x12733,x12731,x12734),f351(x12733,x12732,x12734))
% 157.55/157.24 [1274]~E(x12741,x12742)+E(f351(x12743,x12744,x12741),f351(x12743,x12744,x12742))
% 157.55/157.24 [1275]~E(x12751,x12752)+E(f491(x12751,x12753,x12754),f491(x12752,x12753,x12754))
% 157.55/157.24 [1276]~E(x12761,x12762)+E(f491(x12763,x12761,x12764),f491(x12763,x12762,x12764))
% 157.55/157.24 [1277]~E(x12771,x12772)+E(f491(x12773,x12774,x12771),f491(x12773,x12774,x12772))
% 157.55/157.24 [1278]~E(x12781,x12782)+E(f902(x12781,x12783,x12784),f902(x12782,x12783,x12784))
% 157.55/157.24 [1279]~E(x12791,x12792)+E(f902(x12793,x12791,x12794),f902(x12793,x12792,x12794))
% 157.55/157.24 [1280]~E(x12801,x12802)+E(f902(x12803,x12804,x12801),f902(x12803,x12804,x12802))
% 157.55/157.24 [1281]~E(x12811,x12812)+E(f173(x12811,x12813,x12814),f173(x12812,x12813,x12814))
% 157.55/157.24 [1282]~E(x12821,x12822)+E(f173(x12823,x12821,x12824),f173(x12823,x12822,x12824))
% 157.55/157.24 [1283]~E(x12831,x12832)+E(f173(x12833,x12834,x12831),f173(x12833,x12834,x12832))
% 157.55/157.24 [1284]~E(x12841,x12842)+E(f496(x12841,x12843,x12844),f496(x12842,x12843,x12844))
% 157.55/157.24 [1285]~E(x12851,x12852)+E(f496(x12853,x12851,x12854),f496(x12853,x12852,x12854))
% 157.55/157.24 [1286]~E(x12861,x12862)+E(f496(x12863,x12864,x12861),f496(x12863,x12864,x12862))
% 157.55/157.24 [1287]~E(x12871,x12872)+E(f895(x12871,x12873,x12874,x12875),f895(x12872,x12873,x12874,x12875))
% 157.55/157.24 [1288]~E(x12881,x12882)+E(f895(x12883,x12881,x12884,x12885),f895(x12883,x12882,x12884,x12885))
% 157.55/157.24 [1289]~E(x12891,x12892)+E(f895(x12893,x12894,x12891,x12895),f895(x12893,x12894,x12892,x12895))
% 157.55/157.24 [1290]~E(x12901,x12902)+E(f895(x12903,x12904,x12905,x12901),f895(x12903,x12904,x12905,x12902))
% 157.55/157.24 [1291]~E(x12911,x12912)+E(f707(x12911,x12913,x12914),f707(x12912,x12913,x12914))
% 157.55/157.24 [1292]~E(x12921,x12922)+E(f707(x12923,x12921,x12924),f707(x12923,x12922,x12924))
% 157.55/157.24 [1293]~E(x12931,x12932)+E(f707(x12933,x12934,x12931),f707(x12933,x12934,x12932))
% 157.55/157.24 [1294]~E(x12941,x12942)+E(f116(x12941,x12943,x12944),f116(x12942,x12943,x12944))
% 157.55/157.24 [1295]~E(x12951,x12952)+E(f116(x12953,x12951,x12954),f116(x12953,x12952,x12954))
% 157.55/157.24 [1296]~E(x12961,x12962)+E(f116(x12963,x12964,x12961),f116(x12963,x12964,x12962))
% 157.55/157.24 [1297]~E(x12971,x12972)+E(f637(x12971,x12973),f637(x12972,x12973))
% 157.55/157.24 [1298]~E(x12981,x12982)+E(f637(x12983,x12981),f637(x12983,x12982))
% 157.55/157.24 [1299]~E(x12991,x12992)+E(f237(x12991,x12993),f237(x12992,x12993))
% 157.55/157.24 [1300]~E(x13001,x13002)+E(f237(x13003,x13001),f237(x13003,x13002))
% 157.55/157.24 [1301]~E(x13011,x13012)+E(f839(x13011,x13013,x13014,x13015,x13016,x13017,x13018,x13019),f839(x13012,x13013,x13014,x13015,x13016,x13017,x13018,x13019))
% 157.55/157.24 [1302]~E(x13021,x13022)+E(f839(x13023,x13021,x13024,x13025,x13026,x13027,x13028,x13029),f839(x13023,x13022,x13024,x13025,x13026,x13027,x13028,x13029))
% 157.55/157.24 [1303]~E(x13031,x13032)+E(f839(x13033,x13034,x13031,x13035,x13036,x13037,x13038,x13039),f839(x13033,x13034,x13032,x13035,x13036,x13037,x13038,x13039))
% 157.55/157.24 [1304]~E(x13041,x13042)+E(f839(x13043,x13044,x13045,x13041,x13046,x13047,x13048,x13049),f839(x13043,x13044,x13045,x13042,x13046,x13047,x13048,x13049))
% 157.55/157.24 [1305]~E(x13051,x13052)+E(f839(x13053,x13054,x13055,x13056,x13051,x13057,x13058,x13059),f839(x13053,x13054,x13055,x13056,x13052,x13057,x13058,x13059))
% 157.55/157.24 [1306]~E(x13061,x13062)+E(f839(x13063,x13064,x13065,x13066,x13067,x13061,x13068,x13069),f839(x13063,x13064,x13065,x13066,x13067,x13062,x13068,x13069))
% 157.55/157.24 [1307]~E(x13071,x13072)+E(f839(x13073,x13074,x13075,x13076,x13077,x13078,x13071,x13079),f839(x13073,x13074,x13075,x13076,x13077,x13078,x13072,x13079))
% 157.55/157.24 [1308]~E(x13081,x13082)+E(f839(x13083,x13084,x13085,x13086,x13087,x13088,x13089,x13081),f839(x13083,x13084,x13085,x13086,x13087,x13088,x13089,x13082))
% 157.55/157.24 [1309]~E(x13091,x13092)+E(f650(x13091,x13093,x13094,x13095,x13096),f650(x13092,x13093,x13094,x13095,x13096))
% 157.55/157.24 [1310]~E(x13101,x13102)+E(f650(x13103,x13101,x13104,x13105,x13106),f650(x13103,x13102,x13104,x13105,x13106))
% 157.55/157.24 [1311]~E(x13111,x13112)+E(f650(x13113,x13114,x13111,x13115,x13116),f650(x13113,x13114,x13112,x13115,x13116))
% 157.55/157.24 [1312]~E(x13121,x13122)+E(f650(x13123,x13124,x13125,x13121,x13126),f650(x13123,x13124,x13125,x13122,x13126))
% 157.55/157.24 [1313]~E(x13131,x13132)+E(f650(x13133,x13134,x13135,x13136,x13131),f650(x13133,x13134,x13135,x13136,x13132))
% 157.55/157.24 [1314]~E(x13141,x13142)+E(f526(x13141,x13143,x13144,x13145),f526(x13142,x13143,x13144,x13145))
% 157.55/157.24 [1315]~E(x13151,x13152)+E(f526(x13153,x13151,x13154,x13155),f526(x13153,x13152,x13154,x13155))
% 157.55/157.24 [1316]~E(x13161,x13162)+E(f526(x13163,x13164,x13161,x13165),f526(x13163,x13164,x13162,x13165))
% 157.55/157.24 [1317]~E(x13171,x13172)+E(f526(x13173,x13174,x13175,x13171),f526(x13173,x13174,x13175,x13172))
% 157.55/157.24 [1318]~E(x13181,x13182)+E(f804(x13181,x13183,x13184),f804(x13182,x13183,x13184))
% 157.55/157.24 [1319]~E(x13191,x13192)+E(f804(x13193,x13191,x13194),f804(x13193,x13192,x13194))
% 157.55/157.24 [1320]~E(x13201,x13202)+E(f804(x13203,x13204,x13201),f804(x13203,x13204,x13202))
% 157.55/157.24 [1321]~E(x13211,x13212)+E(f639(x13211,x13213,x13214,x13215,x13216,x13217),f639(x13212,x13213,x13214,x13215,x13216,x13217))
% 157.55/157.24 [1322]~E(x13221,x13222)+E(f639(x13223,x13221,x13224,x13225,x13226,x13227),f639(x13223,x13222,x13224,x13225,x13226,x13227))
% 157.55/157.24 [1323]~E(x13231,x13232)+E(f639(x13233,x13234,x13231,x13235,x13236,x13237),f639(x13233,x13234,x13232,x13235,x13236,x13237))
% 157.55/157.24 [1324]~E(x13241,x13242)+E(f639(x13243,x13244,x13245,x13241,x13246,x13247),f639(x13243,x13244,x13245,x13242,x13246,x13247))
% 157.55/157.24 [1325]~E(x13251,x13252)+E(f639(x13253,x13254,x13255,x13256,x13251,x13257),f639(x13253,x13254,x13255,x13256,x13252,x13257))
% 157.55/157.24 [1326]~E(x13261,x13262)+E(f639(x13263,x13264,x13265,x13266,x13267,x13261),f639(x13263,x13264,x13265,x13266,x13267,x13262))
% 157.55/157.24 [1327]~E(x13271,x13272)+E(f543(x13271,x13273,x13274),f543(x13272,x13273,x13274))
% 157.55/157.24 [1328]~E(x13281,x13282)+E(f543(x13283,x13281,x13284),f543(x13283,x13282,x13284))
% 157.55/157.24 [1329]~E(x13291,x13292)+E(f543(x13293,x13294,x13291),f543(x13293,x13294,x13292))
% 157.55/157.24 [1330]~E(x13301,x13302)+E(f354(x13301,x13303,x13304),f354(x13302,x13303,x13304))
% 157.55/157.24 [1331]~E(x13311,x13312)+E(f354(x13313,x13311,x13314),f354(x13313,x13312,x13314))
% 157.55/157.24 [1332]~E(x13321,x13322)+E(f354(x13323,x13324,x13321),f354(x13323,x13324,x13322))
% 157.55/157.24 [1333]~E(x13331,x13332)+E(f534(x13331,x13333,x13334),f534(x13332,x13333,x13334))
% 157.55/157.24 [1334]~E(x13341,x13342)+E(f534(x13343,x13341,x13344),f534(x13343,x13342,x13344))
% 157.55/157.24 [1335]~E(x13351,x13352)+E(f534(x13353,x13354,x13351),f534(x13353,x13354,x13352))
% 157.55/157.24 [1336]~E(x13361,x13362)+E(f311(x13361,x13363),f311(x13362,x13363))
% 157.55/157.24 [1337]~E(x13371,x13372)+E(f311(x13373,x13371),f311(x13373,x13372))
% 157.55/157.24 [1338]~E(x13381,x13382)+E(f372(x13381,x13383,x13384),f372(x13382,x13383,x13384))
% 157.55/157.24 [1339]~E(x13391,x13392)+E(f372(x13393,x13391,x13394),f372(x13393,x13392,x13394))
% 157.55/157.24 [1340]~E(x13401,x13402)+E(f372(x13403,x13404,x13401),f372(x13403,x13404,x13402))
% 157.55/157.24 [1341]~E(x13411,x13412)+E(f827(x13411,x13413,x13414,x13415),f827(x13412,x13413,x13414,x13415))
% 157.55/157.24 [1342]~E(x13421,x13422)+E(f827(x13423,x13421,x13424,x13425),f827(x13423,x13422,x13424,x13425))
% 157.55/157.24 [1343]~E(x13431,x13432)+E(f827(x13433,x13434,x13431,x13435),f827(x13433,x13434,x13432,x13435))
% 157.55/157.24 [1344]~E(x13441,x13442)+E(f827(x13443,x13444,x13445,x13441),f827(x13443,x13444,x13445,x13442))
% 157.55/157.24 [1345]~E(x13451,x13452)+E(f715(x13451,x13453),f715(x13452,x13453))
% 157.55/157.24 [1346]~E(x13461,x13462)+E(f715(x13463,x13461),f715(x13463,x13462))
% 157.55/157.24 [1347]~E(x13471,x13472)+E(f857(x13471,x13473,x13474),f857(x13472,x13473,x13474))
% 157.55/157.24 [1348]~E(x13481,x13482)+E(f857(x13483,x13481,x13484),f857(x13483,x13482,x13484))
% 157.55/157.24 [1349]~E(x13491,x13492)+E(f857(x13493,x13494,x13491),f857(x13493,x13494,x13492))
% 157.55/157.24 [1350]~E(x13501,x13502)+E(f73(x13501,x13503),f73(x13502,x13503))
% 157.55/157.24 [1351]~E(x13511,x13512)+E(f73(x13513,x13511),f73(x13513,x13512))
% 157.55/157.24 [1352]~E(x13521,x13522)+E(f444(x13521,x13523),f444(x13522,x13523))
% 157.55/157.24 [1353]~E(x13531,x13532)+E(f444(x13533,x13531),f444(x13533,x13532))
% 157.55/157.24 [1354]~E(x13541,x13542)+E(f467(x13541,x13543,x13544,x13545,x13546),f467(x13542,x13543,x13544,x13545,x13546))
% 157.55/157.24 [1355]~E(x13551,x13552)+E(f467(x13553,x13551,x13554,x13555,x13556),f467(x13553,x13552,x13554,x13555,x13556))
% 157.55/157.24 [1356]~E(x13561,x13562)+E(f467(x13563,x13564,x13561,x13565,x13566),f467(x13563,x13564,x13562,x13565,x13566))
% 157.55/157.24 [1357]~E(x13571,x13572)+E(f467(x13573,x13574,x13575,x13571,x13576),f467(x13573,x13574,x13575,x13572,x13576))
% 157.55/157.24 [1358]~E(x13581,x13582)+E(f467(x13583,x13584,x13585,x13586,x13581),f467(x13583,x13584,x13585,x13586,x13582))
% 157.55/157.24 [1359]~E(x13591,x13592)+E(f768(x13591,x13593,x13594,x13595,x13596),f768(x13592,x13593,x13594,x13595,x13596))
% 157.55/157.24 [1360]~E(x13601,x13602)+E(f768(x13603,x13601,x13604,x13605,x13606),f768(x13603,x13602,x13604,x13605,x13606))
% 157.55/157.24 [1361]~E(x13611,x13612)+E(f768(x13613,x13614,x13611,x13615,x13616),f768(x13613,x13614,x13612,x13615,x13616))
% 157.55/157.24 [1362]~E(x13621,x13622)+E(f768(x13623,x13624,x13625,x13621,x13626),f768(x13623,x13624,x13625,x13622,x13626))
% 157.55/157.24 [1363]~E(x13631,x13632)+E(f768(x13633,x13634,x13635,x13636,x13631),f768(x13633,x13634,x13635,x13636,x13632))
% 157.55/157.24 [1364]~E(x13641,x13642)+E(f790(x13641,x13643,x13644,x13645),f790(x13642,x13643,x13644,x13645))
% 157.55/157.24 [1365]~E(x13651,x13652)+E(f790(x13653,x13651,x13654,x13655),f790(x13653,x13652,x13654,x13655))
% 157.55/157.24 [1366]~E(x13661,x13662)+E(f790(x13663,x13664,x13661,x13665),f790(x13663,x13664,x13662,x13665))
% 157.55/157.24 [1367]~E(x13671,x13672)+E(f790(x13673,x13674,x13675,x13671),f790(x13673,x13674,x13675,x13672))
% 157.55/157.24 [1368]~E(x13681,x13682)+E(f791(x13681,x13683,x13684,x13685,x13686),f791(x13682,x13683,x13684,x13685,x13686))
% 157.55/157.24 [1369]~E(x13691,x13692)+E(f791(x13693,x13691,x13694,x13695,x13696),f791(x13693,x13692,x13694,x13695,x13696))
% 157.55/157.24 [1370]~E(x13701,x13702)+E(f791(x13703,x13704,x13701,x13705,x13706),f791(x13703,x13704,x13702,x13705,x13706))
% 157.55/157.24 [1371]~E(x13711,x13712)+E(f791(x13713,x13714,x13715,x13711,x13716),f791(x13713,x13714,x13715,x13712,x13716))
% 157.55/157.24 [1372]~E(x13721,x13722)+E(f791(x13723,x13724,x13725,x13726,x13721),f791(x13723,x13724,x13725,x13726,x13722))
% 157.55/157.24 [1373]~E(x13731,x13732)+E(f501(x13731),f501(x13732))
% 157.55/157.24 [1374]~E(x13741,x13742)+E(f757(x13741,x13743,x13744),f757(x13742,x13743,x13744))
% 157.55/157.24 [1375]~E(x13751,x13752)+E(f757(x13753,x13751,x13754),f757(x13753,x13752,x13754))
% 157.55/157.24 [1376]~E(x13761,x13762)+E(f757(x13763,x13764,x13761),f757(x13763,x13764,x13762))
% 157.55/157.24 [1377]~E(x13771,x13772)+E(f130(x13771,x13773,x13774,x13775),f130(x13772,x13773,x13774,x13775))
% 157.55/157.24 [1378]~E(x13781,x13782)+E(f130(x13783,x13781,x13784,x13785),f130(x13783,x13782,x13784,x13785))
% 157.55/157.24 [1379]~E(x13791,x13792)+E(f130(x13793,x13794,x13791,x13795),f130(x13793,x13794,x13792,x13795))
% 157.55/157.24 [1380]~E(x13801,x13802)+E(f130(x13803,x13804,x13805,x13801),f130(x13803,x13804,x13805,x13802))
% 157.55/157.24 [1381]~E(x13811,x13812)+E(f678(x13811,x13813,x13814,x13815),f678(x13812,x13813,x13814,x13815))
% 157.55/157.24 [1382]~E(x13821,x13822)+E(f678(x13823,x13821,x13824,x13825),f678(x13823,x13822,x13824,x13825))
% 157.55/157.24 [1383]~E(x13831,x13832)+E(f678(x13833,x13834,x13831,x13835),f678(x13833,x13834,x13832,x13835))
% 157.55/157.24 [1384]~E(x13841,x13842)+E(f678(x13843,x13844,x13845,x13841),f678(x13843,x13844,x13845,x13842))
% 157.55/157.24 [1385]~E(x13851,x13852)+E(f746(x13851,x13853,x13854),f746(x13852,x13853,x13854))
% 157.55/157.24 [1386]~E(x13861,x13862)+E(f746(x13863,x13861,x13864),f746(x13863,x13862,x13864))
% 157.55/157.24 [1387]~E(x13871,x13872)+E(f746(x13873,x13874,x13871),f746(x13873,x13874,x13872))
% 157.55/157.24 [1388]~E(x13881,x13882)+E(f676(x13881,x13883,x13884,x13885,x13886),f676(x13882,x13883,x13884,x13885,x13886))
% 157.55/157.24 [1389]~E(x13891,x13892)+E(f676(x13893,x13891,x13894,x13895,x13896),f676(x13893,x13892,x13894,x13895,x13896))
% 157.55/157.24 [1390]~E(x13901,x13902)+E(f676(x13903,x13904,x13901,x13905,x13906),f676(x13903,x13904,x13902,x13905,x13906))
% 157.55/157.24 [1391]~E(x13911,x13912)+E(f676(x13913,x13914,x13915,x13911,x13916),f676(x13913,x13914,x13915,x13912,x13916))
% 157.55/157.24 [1392]~E(x13921,x13922)+E(f676(x13923,x13924,x13925,x13926,x13921),f676(x13923,x13924,x13925,x13926,x13922))
% 157.55/157.24 [1393]~E(x13931,x13932)+E(f901(x13931,x13933,x13934),f901(x13932,x13933,x13934))
% 157.55/157.24 [1394]~E(x13941,x13942)+E(f901(x13943,x13941,x13944),f901(x13943,x13942,x13944))
% 157.55/157.24 [1395]~E(x13951,x13952)+E(f901(x13953,x13954,x13951),f901(x13953,x13954,x13952))
% 157.55/157.24 [1396]~E(x13961,x13962)+E(f647(x13961,x13963,x13964,x13965,x13966),f647(x13962,x13963,x13964,x13965,x13966))
% 157.55/157.24 [1397]~E(x13971,x13972)+E(f647(x13973,x13971,x13974,x13975,x13976),f647(x13973,x13972,x13974,x13975,x13976))
% 157.55/157.24 [1398]~E(x13981,x13982)+E(f647(x13983,x13984,x13981,x13985,x13986),f647(x13983,x13984,x13982,x13985,x13986))
% 157.55/157.24 [1399]~E(x13991,x13992)+E(f647(x13993,x13994,x13995,x13991,x13996),f647(x13993,x13994,x13995,x13992,x13996))
% 157.55/157.24 [1400]~E(x14001,x14002)+E(f647(x14003,x14004,x14005,x14006,x14001),f647(x14003,x14004,x14005,x14006,x14002))
% 157.55/157.24 [1401]~E(x14011,x14012)+E(f122(x14011,x14013,x14014,x14015),f122(x14012,x14013,x14014,x14015))
% 157.55/157.24 [1402]~E(x14021,x14022)+E(f122(x14023,x14021,x14024,x14025),f122(x14023,x14022,x14024,x14025))
% 157.55/157.24 [1403]~E(x14031,x14032)+E(f122(x14033,x14034,x14031,x14035),f122(x14033,x14034,x14032,x14035))
% 157.55/157.24 [1404]~E(x14041,x14042)+E(f122(x14043,x14044,x14045,x14041),f122(x14043,x14044,x14045,x14042))
% 157.55/157.24 [1405]~E(x14051,x14052)+E(f624(x14051,x14053,x14054,x14055,x14056),f624(x14052,x14053,x14054,x14055,x14056))
% 157.55/157.24 [1406]~E(x14061,x14062)+E(f624(x14063,x14061,x14064,x14065,x14066),f624(x14063,x14062,x14064,x14065,x14066))
% 157.55/157.24 [1407]~E(x14071,x14072)+E(f624(x14073,x14074,x14071,x14075,x14076),f624(x14073,x14074,x14072,x14075,x14076))
% 157.55/157.24 [1408]~E(x14081,x14082)+E(f624(x14083,x14084,x14085,x14081,x14086),f624(x14083,x14084,x14085,x14082,x14086))
% 157.55/157.24 [1409]~E(x14091,x14092)+E(f624(x14093,x14094,x14095,x14096,x14091),f624(x14093,x14094,x14095,x14096,x14092))
% 157.55/157.24 [1410]~E(x14101,x14102)+E(f878(x14101,x14103,x14104,x14105,x14106),f878(x14102,x14103,x14104,x14105,x14106))
% 157.55/157.24 [1411]~E(x14111,x14112)+E(f878(x14113,x14111,x14114,x14115,x14116),f878(x14113,x14112,x14114,x14115,x14116))
% 157.55/157.24 [1412]~E(x14121,x14122)+E(f878(x14123,x14124,x14121,x14125,x14126),f878(x14123,x14124,x14122,x14125,x14126))
% 157.55/157.24 [1413]~E(x14131,x14132)+E(f878(x14133,x14134,x14135,x14131,x14136),f878(x14133,x14134,x14135,x14132,x14136))
% 157.55/157.24 [1414]~E(x14141,x14142)+E(f878(x14143,x14144,x14145,x14146,x14141),f878(x14143,x14144,x14145,x14146,x14142))
% 157.55/157.24 [1415]~E(x14151,x14152)+E(f518(x14151),f518(x14152))
% 157.55/157.24 [1416]~E(x14161,x14162)+E(f784(x14161,x14163,x14164),f784(x14162,x14163,x14164))
% 157.55/157.24 [1417]~E(x14171,x14172)+E(f784(x14173,x14171,x14174),f784(x14173,x14172,x14174))
% 157.55/157.24 [1418]~E(x14181,x14182)+E(f784(x14183,x14184,x14181),f784(x14183,x14184,x14182))
% 157.55/157.24 [1419]~E(x14191,x14192)+E(f445(x14191,x14193),f445(x14192,x14193))
% 157.55/157.24 [1420]~E(x14201,x14202)+E(f445(x14203,x14201),f445(x14203,x14202))
% 157.55/157.24 [1421]~E(x14211,x14212)+E(f19(x14211,x14213,x14214,x14215),f19(x14212,x14213,x14214,x14215))
% 157.55/157.24 [1422]~E(x14221,x14222)+E(f19(x14223,x14221,x14224,x14225),f19(x14223,x14222,x14224,x14225))
% 157.55/157.24 [1423]~E(x14231,x14232)+E(f19(x14233,x14234,x14231,x14235),f19(x14233,x14234,x14232,x14235))
% 157.55/157.24 [1424]~E(x14241,x14242)+E(f19(x14243,x14244,x14245,x14241),f19(x14243,x14244,x14245,x14242))
% 157.55/157.24 [1425]~E(x14251,x14252)+E(f442(x14251,x14253,x14254,x14255),f442(x14252,x14253,x14254,x14255))
% 157.55/157.24 [1426]~E(x14261,x14262)+E(f442(x14263,x14261,x14264,x14265),f442(x14263,x14262,x14264,x14265))
% 157.55/157.24 [1427]~E(x14271,x14272)+E(f442(x14273,x14274,x14271,x14275),f442(x14273,x14274,x14272,x14275))
% 157.55/157.24 [1428]~E(x14281,x14282)+E(f442(x14283,x14284,x14285,x14281),f442(x14283,x14284,x14285,x14282))
% 157.55/157.24 [1429]~E(x14291,x14292)+E(f774(x14291,x14293,x14294,x14295),f774(x14292,x14293,x14294,x14295))
% 157.55/157.24 [1430]~E(x14301,x14302)+E(f774(x14303,x14301,x14304,x14305),f774(x14303,x14302,x14304,x14305))
% 157.55/157.24 [1431]~E(x14311,x14312)+E(f774(x14313,x14314,x14311,x14315),f774(x14313,x14314,x14312,x14315))
% 157.55/157.24 [1432]~E(x14321,x14322)+E(f774(x14323,x14324,x14325,x14321),f774(x14323,x14324,x14325,x14322))
% 157.55/157.24 [1433]~E(x14331,x14332)+E(f249(x14331,x14333,x14334),f249(x14332,x14333,x14334))
% 157.55/157.24 [1434]~E(x14341,x14342)+E(f249(x14343,x14341,x14344),f249(x14343,x14342,x14344))
% 157.55/157.24 [1435]~E(x14351,x14352)+E(f249(x14353,x14354,x14351),f249(x14353,x14354,x14352))
% 157.55/157.24 [1436]~E(x14361,x14362)+E(f440(x14361,x14363,x14364,x14365),f440(x14362,x14363,x14364,x14365))
% 157.55/157.24 [1437]~E(x14371,x14372)+E(f440(x14373,x14371,x14374,x14375),f440(x14373,x14372,x14374,x14375))
% 157.55/157.24 [1438]~E(x14381,x14382)+E(f440(x14383,x14384,x14381,x14385),f440(x14383,x14384,x14382,x14385))
% 157.55/157.24 [1439]~E(x14391,x14392)+E(f440(x14393,x14394,x14395,x14391),f440(x14393,x14394,x14395,x14392))
% 157.55/157.24 [1440]~E(x14401,x14402)+E(f481(x14401,x14403,x14404),f481(x14402,x14403,x14404))
% 157.55/157.24 [1441]~E(x14411,x14412)+E(f481(x14413,x14411,x14414),f481(x14413,x14412,x14414))
% 157.55/157.24 [1442]~E(x14421,x14422)+E(f481(x14423,x14424,x14421),f481(x14423,x14424,x14422))
% 157.55/157.24 [1443]~E(x14431,x14432)+E(f344(x14431,x14433,x14434,x14435),f344(x14432,x14433,x14434,x14435))
% 157.55/157.24 [1444]~E(x14441,x14442)+E(f344(x14443,x14441,x14444,x14445),f344(x14443,x14442,x14444,x14445))
% 157.55/157.24 [1445]~E(x14451,x14452)+E(f344(x14453,x14454,x14451,x14455),f344(x14453,x14454,x14452,x14455))
% 157.55/157.24 [1446]~E(x14461,x14462)+E(f344(x14463,x14464,x14465,x14461),f344(x14463,x14464,x14465,x14462))
% 157.55/157.24 [1447]~E(x14471,x14472)+E(f740(x14471,x14473,x14474,x14475,x14476),f740(x14472,x14473,x14474,x14475,x14476))
% 157.55/157.24 [1448]~E(x14481,x14482)+E(f740(x14483,x14481,x14484,x14485,x14486),f740(x14483,x14482,x14484,x14485,x14486))
% 157.55/157.24 [1449]~E(x14491,x14492)+E(f740(x14493,x14494,x14491,x14495,x14496),f740(x14493,x14494,x14492,x14495,x14496))
% 157.55/157.24 [1450]~E(x14501,x14502)+E(f740(x14503,x14504,x14505,x14501,x14506),f740(x14503,x14504,x14505,x14502,x14506))
% 157.55/157.24 [1451]~E(x14511,x14512)+E(f740(x14513,x14514,x14515,x14516,x14511),f740(x14513,x14514,x14515,x14516,x14512))
% 157.55/157.24 [1452]~E(x14521,x14522)+E(f830(x14521,x14523,x14524,x14525,x14526),f830(x14522,x14523,x14524,x14525,x14526))
% 157.55/157.24 [1453]~E(x14531,x14532)+E(f830(x14533,x14531,x14534,x14535,x14536),f830(x14533,x14532,x14534,x14535,x14536))
% 157.55/157.24 [1454]~E(x14541,x14542)+E(f830(x14543,x14544,x14541,x14545,x14546),f830(x14543,x14544,x14542,x14545,x14546))
% 157.55/157.24 [1455]~E(x14551,x14552)+E(f830(x14553,x14554,x14555,x14551,x14556),f830(x14553,x14554,x14555,x14552,x14556))
% 157.55/157.24 [1456]~E(x14561,x14562)+E(f830(x14563,x14564,x14565,x14566,x14561),f830(x14563,x14564,x14565,x14566,x14562))
% 157.55/157.24 [1457]~E(x14571,x14572)+E(f664(x14571,x14573,x14574,x14575,x14576,x14577),f664(x14572,x14573,x14574,x14575,x14576,x14577))
% 157.55/157.24 [1458]~E(x14581,x14582)+E(f664(x14583,x14581,x14584,x14585,x14586,x14587),f664(x14583,x14582,x14584,x14585,x14586,x14587))
% 157.55/157.24 [1459]~E(x14591,x14592)+E(f664(x14593,x14594,x14591,x14595,x14596,x14597),f664(x14593,x14594,x14592,x14595,x14596,x14597))
% 157.55/157.24 [1460]~E(x14601,x14602)+E(f664(x14603,x14604,x14605,x14601,x14606,x14607),f664(x14603,x14604,x14605,x14602,x14606,x14607))
% 157.55/157.24 [1461]~E(x14611,x14612)+E(f664(x14613,x14614,x14615,x14616,x14611,x14617),f664(x14613,x14614,x14615,x14616,x14612,x14617))
% 157.55/157.24 [1462]~E(x14621,x14622)+E(f664(x14623,x14624,x14625,x14626,x14627,x14621),f664(x14623,x14624,x14625,x14626,x14627,x14622))
% 157.55/157.24 [1463]~E(x14631,x14632)+E(f449(x14631,x14633),f449(x14632,x14633))
% 157.55/157.24 [1464]~E(x14641,x14642)+E(f449(x14643,x14641),f449(x14643,x14642))
% 157.55/157.24 [1465]~E(x14651,x14652)+E(f544(x14651,x14653,x14654,x14655,x14656,x14657),f544(x14652,x14653,x14654,x14655,x14656,x14657))
% 157.55/157.24 [1466]~E(x14661,x14662)+E(f544(x14663,x14661,x14664,x14665,x14666,x14667),f544(x14663,x14662,x14664,x14665,x14666,x14667))
% 157.55/157.24 [1467]~E(x14671,x14672)+E(f544(x14673,x14674,x14671,x14675,x14676,x14677),f544(x14673,x14674,x14672,x14675,x14676,x14677))
% 157.55/157.24 [1468]~E(x14681,x14682)+E(f544(x14683,x14684,x14685,x14681,x14686,x14687),f544(x14683,x14684,x14685,x14682,x14686,x14687))
% 157.55/157.24 [1469]~E(x14691,x14692)+E(f544(x14693,x14694,x14695,x14696,x14691,x14697),f544(x14693,x14694,x14695,x14696,x14692,x14697))
% 157.55/157.24 [1470]~E(x14701,x14702)+E(f544(x14703,x14704,x14705,x14706,x14707,x14701),f544(x14703,x14704,x14705,x14706,x14707,x14702))
% 157.55/157.24 [1471]~E(x14711,x14712)+E(f275(x14711,x14713,x14714,x14715),f275(x14712,x14713,x14714,x14715))
% 157.55/157.24 [1472]~E(x14721,x14722)+E(f275(x14723,x14721,x14724,x14725),f275(x14723,x14722,x14724,x14725))
% 157.55/157.24 [1473]~E(x14731,x14732)+E(f275(x14733,x14734,x14731,x14735),f275(x14733,x14734,x14732,x14735))
% 157.55/157.24 [1474]~E(x14741,x14742)+E(f275(x14743,x14744,x14745,x14741),f275(x14743,x14744,x14745,x14742))
% 157.55/157.24 [1475]~E(x14751,x14752)+E(f278(x14751,x14753,x14754,x14755),f278(x14752,x14753,x14754,x14755))
% 157.55/157.24 [1476]~E(x14761,x14762)+E(f278(x14763,x14761,x14764,x14765),f278(x14763,x14762,x14764,x14765))
% 157.55/157.24 [1477]~E(x14771,x14772)+E(f278(x14773,x14774,x14771,x14775),f278(x14773,x14774,x14772,x14775))
% 157.55/157.24 [1478]~E(x14781,x14782)+E(f278(x14783,x14784,x14785,x14781),f278(x14783,x14784,x14785,x14782))
% 157.55/157.24 [1479]~E(x14791,x14792)+E(f675(x14791,x14793,x14794,x14795,x14796),f675(x14792,x14793,x14794,x14795,x14796))
% 157.55/157.24 [1480]~E(x14801,x14802)+E(f675(x14803,x14801,x14804,x14805,x14806),f675(x14803,x14802,x14804,x14805,x14806))
% 157.55/157.24 [1481]~E(x14811,x14812)+E(f675(x14813,x14814,x14811,x14815,x14816),f675(x14813,x14814,x14812,x14815,x14816))
% 157.55/157.24 [1482]~E(x14821,x14822)+E(f675(x14823,x14824,x14825,x14821,x14826),f675(x14823,x14824,x14825,x14822,x14826))
% 157.55/157.24 [1483]~E(x14831,x14832)+E(f675(x14833,x14834,x14835,x14836,x14831),f675(x14833,x14834,x14835,x14836,x14832))
% 157.55/157.24 [1484]~E(x14841,x14842)+E(f591(x14841,x14843),f591(x14842,x14843))
% 157.55/157.24 [1485]~E(x14851,x14852)+E(f591(x14853,x14851),f591(x14853,x14852))
% 157.55/157.24 [1486]~E(x14861,x14862)+E(f717(x14861,x14863,x14864,x14865),f717(x14862,x14863,x14864,x14865))
% 157.55/157.24 [1487]~E(x14871,x14872)+E(f717(x14873,x14871,x14874,x14875),f717(x14873,x14872,x14874,x14875))
% 157.55/157.24 [1488]~E(x14881,x14882)+E(f717(x14883,x14884,x14881,x14885),f717(x14883,x14884,x14882,x14885))
% 157.55/157.24 [1489]~E(x14891,x14892)+E(f717(x14893,x14894,x14895,x14891),f717(x14893,x14894,x14895,x14892))
% 157.55/157.24 [1490]~E(x14901,x14902)+E(f646(x14901,x14903,x14904,x14905),f646(x14902,x14903,x14904,x14905))
% 157.55/157.24 [1491]~E(x14911,x14912)+E(f646(x14913,x14911,x14914,x14915),f646(x14913,x14912,x14914,x14915))
% 157.55/157.24 [1492]~E(x14921,x14922)+E(f646(x14923,x14924,x14921,x14925),f646(x14923,x14924,x14922,x14925))
% 157.55/157.24 [1493]~E(x14931,x14932)+E(f646(x14933,x14934,x14935,x14931),f646(x14933,x14934,x14935,x14932))
% 157.55/157.24 [1494]~E(x14941,x14942)+E(f190(x14941,x14943,x14944,x14945),f190(x14942,x14943,x14944,x14945))
% 157.55/157.24 [1495]~E(x14951,x14952)+E(f190(x14953,x14951,x14954,x14955),f190(x14953,x14952,x14954,x14955))
% 157.55/157.24 [1496]~E(x14961,x14962)+E(f190(x14963,x14964,x14961,x14965),f190(x14963,x14964,x14962,x14965))
% 157.55/157.24 [1497]~E(x14971,x14972)+E(f190(x14973,x14974,x14975,x14971),f190(x14973,x14974,x14975,x14972))
% 157.55/157.24 [1498]~E(x14981,x14982)+E(f787(x14981,x14983,x14984,x14985),f787(x14982,x14983,x14984,x14985))
% 157.55/157.24 [1499]~E(x14991,x14992)+E(f787(x14993,x14991,x14994,x14995),f787(x14993,x14992,x14994,x14995))
% 157.55/157.24 [1500]~E(x15001,x15002)+E(f787(x15003,x15004,x15001,x15005),f787(x15003,x15004,x15002,x15005))
% 157.55/157.24 [1501]~E(x15011,x15012)+E(f787(x15013,x15014,x15015,x15011),f787(x15013,x15014,x15015,x15012))
% 157.55/157.24 [1502]~E(x15021,x15022)+E(f400(x15021,x15023,x15024),f400(x15022,x15023,x15024))
% 157.55/157.24 [1503]~E(x15031,x15032)+E(f400(x15033,x15031,x15034),f400(x15033,x15032,x15034))
% 157.55/157.24 [1504]~E(x15041,x15042)+E(f400(x15043,x15044,x15041),f400(x15043,x15044,x15042))
% 157.55/157.24 [1505]~E(x15051,x15052)+E(f554(x15051,x15053,x15054,x15055,x15056),f554(x15052,x15053,x15054,x15055,x15056))
% 157.55/157.24 [1506]~E(x15061,x15062)+E(f554(x15063,x15061,x15064,x15065,x15066),f554(x15063,x15062,x15064,x15065,x15066))
% 157.55/157.24 [1507]~E(x15071,x15072)+E(f554(x15073,x15074,x15071,x15075,x15076),f554(x15073,x15074,x15072,x15075,x15076))
% 157.55/157.24 [1508]~E(x15081,x15082)+E(f554(x15083,x15084,x15085,x15081,x15086),f554(x15083,x15084,x15085,x15082,x15086))
% 157.55/157.24 [1509]~E(x15091,x15092)+E(f554(x15093,x15094,x15095,x15096,x15091),f554(x15093,x15094,x15095,x15096,x15092))
% 157.55/157.24 [1510]~E(x15101,x15102)+E(f423(x15101,x15103),f423(x15102,x15103))
% 157.55/157.24 [1511]~E(x15111,x15112)+E(f423(x15113,x15111),f423(x15113,x15112))
% 157.55/157.24 [1512]~E(x15121,x15122)+E(f535(x15121,x15123,x15124,x15125),f535(x15122,x15123,x15124,x15125))
% 157.55/157.24 [1513]~E(x15131,x15132)+E(f535(x15133,x15131,x15134,x15135),f535(x15133,x15132,x15134,x15135))
% 157.55/157.24 [1514]~E(x15141,x15142)+E(f535(x15143,x15144,x15141,x15145),f535(x15143,x15144,x15142,x15145))
% 157.55/157.24 [1515]~E(x15151,x15152)+E(f535(x15153,x15154,x15155,x15151),f535(x15153,x15154,x15155,x15152))
% 157.55/157.24 [1516]~E(x15161,x15162)+E(f599(x15161,x15163,x15164,x15165,x15166),f599(x15162,x15163,x15164,x15165,x15166))
% 157.55/157.24 [1517]~E(x15171,x15172)+E(f599(x15173,x15171,x15174,x15175,x15176),f599(x15173,x15172,x15174,x15175,x15176))
% 157.55/157.24 [1518]~E(x15181,x15182)+E(f599(x15183,x15184,x15181,x15185,x15186),f599(x15183,x15184,x15182,x15185,x15186))
% 157.55/157.24 [1519]~E(x15191,x15192)+E(f599(x15193,x15194,x15195,x15191,x15196),f599(x15193,x15194,x15195,x15192,x15196))
% 157.55/157.24 [1520]~E(x15201,x15202)+E(f599(x15203,x15204,x15205,x15206,x15201),f599(x15203,x15204,x15205,x15206,x15202))
% 157.55/157.24 [1521]~E(x15211,x15212)+E(f505(x15211,x15213,x15214,x15215),f505(x15212,x15213,x15214,x15215))
% 157.55/157.24 [1522]~E(x15221,x15222)+E(f505(x15223,x15221,x15224,x15225),f505(x15223,x15222,x15224,x15225))
% 157.55/157.24 [1523]~E(x15231,x15232)+E(f505(x15233,x15234,x15231,x15235),f505(x15233,x15234,x15232,x15235))
% 157.55/157.24 [1524]~E(x15241,x15242)+E(f505(x15243,x15244,x15245,x15241),f505(x15243,x15244,x15245,x15242))
% 157.55/157.24 [1525]~E(x15251,x15252)+E(f330(x15251,x15253,x15254,x15255),f330(x15252,x15253,x15254,x15255))
% 157.55/157.24 [1526]~E(x15261,x15262)+E(f330(x15263,x15261,x15264,x15265),f330(x15263,x15262,x15264,x15265))
% 157.55/157.24 [1527]~E(x15271,x15272)+E(f330(x15273,x15274,x15271,x15275),f330(x15273,x15274,x15272,x15275))
% 157.55/157.24 [1528]~E(x15281,x15282)+E(f330(x15283,x15284,x15285,x15281),f330(x15283,x15284,x15285,x15282))
% 157.55/157.24 [1529]~E(x15291,x15292)+E(f894(x15291,x15293,x15294,x15295),f894(x15292,x15293,x15294,x15295))
% 157.55/157.24 [1530]~E(x15301,x15302)+E(f894(x15303,x15301,x15304,x15305),f894(x15303,x15302,x15304,x15305))
% 157.55/157.24 [1531]~E(x15311,x15312)+E(f894(x15313,x15314,x15311,x15315),f894(x15313,x15314,x15312,x15315))
% 157.55/157.24 [1532]~E(x15321,x15322)+E(f894(x15323,x15324,x15325,x15321),f894(x15323,x15324,x15325,x15322))
% 157.55/157.24 [1533]~E(x15331,x15332)+E(f528(x15331,x15333,x15334,x15335,x15336),f528(x15332,x15333,x15334,x15335,x15336))
% 157.55/157.24 [1534]~E(x15341,x15342)+E(f528(x15343,x15341,x15344,x15345,x15346),f528(x15343,x15342,x15344,x15345,x15346))
% 157.55/157.24 [1535]~E(x15351,x15352)+E(f528(x15353,x15354,x15351,x15355,x15356),f528(x15353,x15354,x15352,x15355,x15356))
% 157.55/157.24 [1536]~E(x15361,x15362)+E(f528(x15363,x15364,x15365,x15361,x15366),f528(x15363,x15364,x15365,x15362,x15366))
% 157.55/157.24 [1537]~E(x15371,x15372)+E(f528(x15373,x15374,x15375,x15376,x15371),f528(x15373,x15374,x15375,x15376,x15372))
% 157.55/157.24 [1538]~E(x15381,x15382)+E(f687(x15381,x15383,x15384),f687(x15382,x15383,x15384))
% 157.55/157.24 [1539]~E(x15391,x15392)+E(f687(x15393,x15391,x15394),f687(x15393,x15392,x15394))
% 157.55/157.24 [1540]~E(x15401,x15402)+E(f687(x15403,x15404,x15401),f687(x15403,x15404,x15402))
% 157.55/157.24 [1541]~E(x15411,x15412)+E(f688(x15411,x15413,x15414),f688(x15412,x15413,x15414))
% 157.55/157.24 [1542]~E(x15421,x15422)+E(f688(x15423,x15421,x15424),f688(x15423,x15422,x15424))
% 157.55/157.24 [1543]~E(x15431,x15432)+E(f688(x15433,x15434,x15431),f688(x15433,x15434,x15432))
% 157.55/157.24 [1544]~E(x15441,x15442)+E(f607(x15441,x15443,x15444,x15445,x15446),f607(x15442,x15443,x15444,x15445,x15446))
% 157.55/157.24 [1545]~E(x15451,x15452)+E(f607(x15453,x15451,x15454,x15455,x15456),f607(x15453,x15452,x15454,x15455,x15456))
% 157.55/157.24 [1546]~E(x15461,x15462)+E(f607(x15463,x15464,x15461,x15465,x15466),f607(x15463,x15464,x15462,x15465,x15466))
% 157.55/157.24 [1547]~E(x15471,x15472)+E(f607(x15473,x15474,x15475,x15471,x15476),f607(x15473,x15474,x15475,x15472,x15476))
% 157.55/157.24 [1548]~E(x15481,x15482)+E(f607(x15483,x15484,x15485,x15486,x15481),f607(x15483,x15484,x15485,x15486,x15482))
% 157.55/157.24 [1549]~E(x15491,x15492)+E(f604(x15491,x15493,x15494,x15495,x15496,x15497,x15498,x15499),f604(x15492,x15493,x15494,x15495,x15496,x15497,x15498,x15499))
% 157.55/157.24 [1550]~E(x15501,x15502)+E(f604(x15503,x15501,x15504,x15505,x15506,x15507,x15508,x15509),f604(x15503,x15502,x15504,x15505,x15506,x15507,x15508,x15509))
% 157.55/157.24 [1551]~E(x15511,x15512)+E(f604(x15513,x15514,x15511,x15515,x15516,x15517,x15518,x15519),f604(x15513,x15514,x15512,x15515,x15516,x15517,x15518,x15519))
% 157.55/157.24 [1552]~E(x15521,x15522)+E(f604(x15523,x15524,x15525,x15521,x15526,x15527,x15528,x15529),f604(x15523,x15524,x15525,x15522,x15526,x15527,x15528,x15529))
% 157.55/157.24 [1553]~E(x15531,x15532)+E(f604(x15533,x15534,x15535,x15536,x15531,x15537,x15538,x15539),f604(x15533,x15534,x15535,x15536,x15532,x15537,x15538,x15539))
% 157.55/157.24 [1554]~E(x15541,x15542)+E(f604(x15543,x15544,x15545,x15546,x15547,x15541,x15548,x15549),f604(x15543,x15544,x15545,x15546,x15547,x15542,x15548,x15549))
% 157.55/157.24 [1555]~E(x15551,x15552)+E(f604(x15553,x15554,x15555,x15556,x15557,x15558,x15551,x15559),f604(x15553,x15554,x15555,x15556,x15557,x15558,x15552,x15559))
% 157.55/157.24 [1556]~E(x15561,x15562)+E(f604(x15563,x15564,x15565,x15566,x15567,x15568,x15569,x15561),f604(x15563,x15564,x15565,x15566,x15567,x15568,x15569,x15562))
% 157.55/157.24 [1557]~E(x15571,x15572)+E(f184(x15571,x15573,x15574),f184(x15572,x15573,x15574))
% 157.55/157.24 [1558]~E(x15581,x15582)+E(f184(x15583,x15581,x15584),f184(x15583,x15582,x15584))
% 157.55/157.24 [1559]~E(x15591,x15592)+E(f184(x15593,x15594,x15591),f184(x15593,x15594,x15592))
% 157.55/157.24 [1560]~E(x15601,x15602)+E(f600(x15601,x15603,x15604),f600(x15602,x15603,x15604))
% 157.55/157.24 [1561]~E(x15611,x15612)+E(f600(x15613,x15611,x15614),f600(x15613,x15612,x15614))
% 157.55/157.24 [1562]~E(x15621,x15622)+E(f600(x15623,x15624,x15621),f600(x15623,x15624,x15622))
% 157.55/157.24 [1563]~E(x15631,x15632)+E(f59(x15631,x15633,x15634,x15635),f59(x15632,x15633,x15634,x15635))
% 157.55/157.24 [1564]~E(x15641,x15642)+E(f59(x15643,x15641,x15644,x15645),f59(x15643,x15642,x15644,x15645))
% 157.55/157.24 [1565]~E(x15651,x15652)+E(f59(x15653,x15654,x15651,x15655),f59(x15653,x15654,x15652,x15655))
% 157.55/157.24 [1566]~E(x15661,x15662)+E(f59(x15663,x15664,x15665,x15661),f59(x15663,x15664,x15665,x15662))
% 157.55/157.24 [1567]~E(x15671,x15672)+E(f764(x15671,x15673,x15674,x15675),f764(x15672,x15673,x15674,x15675))
% 157.55/157.24 [1568]~E(x15681,x15682)+E(f764(x15683,x15681,x15684,x15685),f764(x15683,x15682,x15684,x15685))
% 157.55/157.24 [1569]~E(x15691,x15692)+E(f764(x15693,x15694,x15691,x15695),f764(x15693,x15694,x15692,x15695))
% 157.55/157.24 [1570]~E(x15701,x15702)+E(f764(x15703,x15704,x15705,x15701),f764(x15703,x15704,x15705,x15702))
% 157.55/157.24 [1571]~E(x15711,x15712)+E(f273(x15711,x15713,x15714),f273(x15712,x15713,x15714))
% 157.55/157.24 [1572]~E(x15721,x15722)+E(f273(x15723,x15721,x15724),f273(x15723,x15722,x15724))
% 157.55/157.24 [1573]~E(x15731,x15732)+E(f273(x15733,x15734,x15731),f273(x15733,x15734,x15732))
% 157.55/157.24 [1574]~E(x15741,x15742)+E(f828(x15741,x15743,x15744,x15745),f828(x15742,x15743,x15744,x15745))
% 157.55/157.24 [1575]~E(x15751,x15752)+E(f828(x15753,x15751,x15754,x15755),f828(x15753,x15752,x15754,x15755))
% 157.55/157.24 [1576]~E(x15761,x15762)+E(f828(x15763,x15764,x15761,x15765),f828(x15763,x15764,x15762,x15765))
% 157.55/157.24 [1577]~E(x15771,x15772)+E(f828(x15773,x15774,x15775,x15771),f828(x15773,x15774,x15775,x15772))
% 157.55/157.24 [1578]~E(x15781,x15782)+E(f214(x15781,x15783),f214(x15782,x15783))
% 157.55/157.24 [1579]~E(x15791,x15792)+E(f214(x15793,x15791),f214(x15793,x15792))
% 157.55/157.24 [1580]~E(x15801,x15802)+E(f433(x15801,x15803,x15804),f433(x15802,x15803,x15804))
% 157.55/157.24 [1581]~E(x15811,x15812)+E(f433(x15813,x15811,x15814),f433(x15813,x15812,x15814))
% 157.55/157.24 [1582]~E(x15821,x15822)+E(f433(x15823,x15824,x15821),f433(x15823,x15824,x15822))
% 157.55/157.24 [1583]~E(x15831,x15832)+E(f635(x15831,x15833,x15834,x15835),f635(x15832,x15833,x15834,x15835))
% 157.55/157.24 [1584]~E(x15841,x15842)+E(f635(x15843,x15841,x15844,x15845),f635(x15843,x15842,x15844,x15845))
% 157.55/157.24 [1585]~E(x15851,x15852)+E(f635(x15853,x15854,x15851,x15855),f635(x15853,x15854,x15852,x15855))
% 157.55/157.24 [1586]~E(x15861,x15862)+E(f635(x15863,x15864,x15865,x15861),f635(x15863,x15864,x15865,x15862))
% 157.55/157.24 [1587]~E(x15871,x15872)+E(f645(x15871,x15873),f645(x15872,x15873))
% 157.55/157.24 [1588]~E(x15881,x15882)+E(f645(x15883,x15881),f645(x15883,x15882))
% 157.55/157.24 [1589]~E(x15891,x15892)+E(f265(x15891,x15893),f265(x15892,x15893))
% 157.55/157.24 [1590]~E(x15901,x15902)+E(f265(x15903,x15901),f265(x15903,x15902))
% 157.55/157.24 [1591]~E(x15911,x15912)+E(f422(x15911,x15913),f422(x15912,x15913))
% 157.55/157.24 [1592]~E(x15921,x15922)+E(f422(x15923,x15921),f422(x15923,x15922))
% 157.55/157.24 [1593]~E(x15931,x15932)+E(f814(x15931,x15933),f814(x15932,x15933))
% 157.55/157.24 [1594]~E(x15941,x15942)+E(f814(x15943,x15941),f814(x15943,x15942))
% 157.55/157.24 [1595]~E(x15951,x15952)+E(f405(x15951),f405(x15952))
% 157.55/157.24 [1596]~E(x15961,x15962)+E(f54(x15961,x15963),f54(x15962,x15963))
% 157.55/157.24 [1597]~E(x15971,x15972)+E(f54(x15973,x15971),f54(x15973,x15972))
% 157.55/157.24 [1598]~E(x15981,x15982)+E(f758(x15981,x15983,x15984),f758(x15982,x15983,x15984))
% 157.55/157.24 [1599]~E(x15991,x15992)+E(f758(x15993,x15991,x15994),f758(x15993,x15992,x15994))
% 157.55/157.24 [1600]~E(x16001,x16002)+E(f758(x16003,x16004,x16001),f758(x16003,x16004,x16002))
% 157.55/157.24 [1601]~E(x16011,x16012)+E(f677(x16011,x16013,x16014,x16015,x16016),f677(x16012,x16013,x16014,x16015,x16016))
% 157.55/157.24 [1602]~E(x16021,x16022)+E(f677(x16023,x16021,x16024,x16025,x16026),f677(x16023,x16022,x16024,x16025,x16026))
% 157.55/157.24 [1603]~E(x16031,x16032)+E(f677(x16033,x16034,x16031,x16035,x16036),f677(x16033,x16034,x16032,x16035,x16036))
% 157.55/157.24 [1604]~E(x16041,x16042)+E(f677(x16043,x16044,x16045,x16041,x16046),f677(x16043,x16044,x16045,x16042,x16046))
% 157.55/157.24 [1605]~E(x16051,x16052)+E(f677(x16053,x16054,x16055,x16056,x16051),f677(x16053,x16054,x16055,x16056,x16052))
% 157.55/157.24 [1606]~E(x16061,x16062)+E(f537(x16061,x16063,x16064,x16065,x16066,x16067),f537(x16062,x16063,x16064,x16065,x16066,x16067))
% 157.55/157.24 [1607]~E(x16071,x16072)+E(f537(x16073,x16071,x16074,x16075,x16076,x16077),f537(x16073,x16072,x16074,x16075,x16076,x16077))
% 157.55/157.24 [1608]~E(x16081,x16082)+E(f537(x16083,x16084,x16081,x16085,x16086,x16087),f537(x16083,x16084,x16082,x16085,x16086,x16087))
% 157.55/157.24 [1609]~E(x16091,x16092)+E(f537(x16093,x16094,x16095,x16091,x16096,x16097),f537(x16093,x16094,x16095,x16092,x16096,x16097))
% 157.55/157.24 [1610]~E(x16101,x16102)+E(f537(x16103,x16104,x16105,x16106,x16101,x16107),f537(x16103,x16104,x16105,x16106,x16102,x16107))
% 157.55/157.24 [1611]~E(x16111,x16112)+E(f537(x16113,x16114,x16115,x16116,x16117,x16111),f537(x16113,x16114,x16115,x16116,x16117,x16112))
% 157.55/157.24 [1612]~E(x16121,x16122)+E(f407(x16121,x16123,x16124),f407(x16122,x16123,x16124))
% 157.55/157.24 [1613]~E(x16131,x16132)+E(f407(x16133,x16131,x16134),f407(x16133,x16132,x16134))
% 157.55/157.24 [1614]~E(x16141,x16142)+E(f407(x16143,x16144,x16141),f407(x16143,x16144,x16142))
% 157.55/157.24 [1615]~E(x16151,x16152)+E(f320(x16151,x16153,x16154),f320(x16152,x16153,x16154))
% 157.55/157.24 [1616]~E(x16161,x16162)+E(f320(x16163,x16161,x16164),f320(x16163,x16162,x16164))
% 157.55/157.24 [1617]~E(x16171,x16172)+E(f320(x16173,x16174,x16171),f320(x16173,x16174,x16172))
% 157.55/157.24 [1618]~E(x16181,x16182)+E(f695(x16181,x16183,x16184,x16185,x16186),f695(x16182,x16183,x16184,x16185,x16186))
% 157.55/157.24 [1619]~E(x16191,x16192)+E(f695(x16193,x16191,x16194,x16195,x16196),f695(x16193,x16192,x16194,x16195,x16196))
% 157.55/157.24 [1620]~E(x16201,x16202)+E(f695(x16203,x16204,x16201,x16205,x16206),f695(x16203,x16204,x16202,x16205,x16206))
% 157.55/157.24 [1621]~E(x16211,x16212)+E(f695(x16213,x16214,x16215,x16211,x16216),f695(x16213,x16214,x16215,x16212,x16216))
% 157.55/157.24 [1622]~E(x16221,x16222)+E(f695(x16223,x16224,x16225,x16226,x16221),f695(x16223,x16224,x16225,x16226,x16222))
% 157.55/157.24 [1623]~E(x16231,x16232)+E(f489(x16231,x16233,x16234),f489(x16232,x16233,x16234))
% 157.55/157.24 [1624]~E(x16241,x16242)+E(f489(x16243,x16241,x16244),f489(x16243,x16242,x16244))
% 157.55/157.24 [1625]~E(x16251,x16252)+E(f489(x16253,x16254,x16251),f489(x16253,x16254,x16252))
% 157.55/157.24 [1626]~E(x16261,x16262)+E(f459(x16261,x16263,x16264,x16265),f459(x16262,x16263,x16264,x16265))
% 157.55/157.24 [1627]~E(x16271,x16272)+E(f459(x16273,x16271,x16274,x16275),f459(x16273,x16272,x16274,x16275))
% 157.55/157.24 [1628]~E(x16281,x16282)+E(f459(x16283,x16284,x16281,x16285),f459(x16283,x16284,x16282,x16285))
% 157.55/157.24 [1629]~E(x16291,x16292)+E(f459(x16293,x16294,x16295,x16291),f459(x16293,x16294,x16295,x16292))
% 157.55/157.24 [1630]~E(x16301,x16302)+E(f782(x16301,x16303,x16304,x16305,x16306,x16307,x16308),f782(x16302,x16303,x16304,x16305,x16306,x16307,x16308))
% 157.55/157.24 [1631]~E(x16311,x16312)+E(f782(x16313,x16311,x16314,x16315,x16316,x16317,x16318),f782(x16313,x16312,x16314,x16315,x16316,x16317,x16318))
% 157.55/157.24 [1632]~E(x16321,x16322)+E(f782(x16323,x16324,x16321,x16325,x16326,x16327,x16328),f782(x16323,x16324,x16322,x16325,x16326,x16327,x16328))
% 157.55/157.24 [1633]~E(x16331,x16332)+E(f782(x16333,x16334,x16335,x16331,x16336,x16337,x16338),f782(x16333,x16334,x16335,x16332,x16336,x16337,x16338))
% 157.55/157.24 [1634]~E(x16341,x16342)+E(f782(x16343,x16344,x16345,x16346,x16341,x16347,x16348),f782(x16343,x16344,x16345,x16346,x16342,x16347,x16348))
% 157.55/157.24 [1635]~E(x16351,x16352)+E(f782(x16353,x16354,x16355,x16356,x16357,x16351,x16358),f782(x16353,x16354,x16355,x16356,x16357,x16352,x16358))
% 157.55/157.24 [1636]~E(x16361,x16362)+E(f782(x16363,x16364,x16365,x16366,x16367,x16368,x16361),f782(x16363,x16364,x16365,x16366,x16367,x16368,x16362))
% 157.55/157.24 [1637]~E(x16371,x16372)+E(f700(x16371,x16373),f700(x16372,x16373))
% 157.55/157.24 [1638]~E(x16381,x16382)+E(f700(x16383,x16381),f700(x16383,x16382))
% 157.55/157.24 [1639]~E(x16391,x16392)+E(f379(x16391,x16393,x16394),f379(x16392,x16393,x16394))
% 157.55/157.24 [1640]~E(x16401,x16402)+E(f379(x16403,x16401,x16404),f379(x16403,x16402,x16404))
% 157.55/157.24 [1641]~E(x16411,x16412)+E(f379(x16413,x16414,x16411),f379(x16413,x16414,x16412))
% 157.55/157.24 [1642]~E(x16421,x16422)+E(f690(x16421,x16423,x16424,x16425,x16426),f690(x16422,x16423,x16424,x16425,x16426))
% 157.55/157.24 [1643]~E(x16431,x16432)+E(f690(x16433,x16431,x16434,x16435,x16436),f690(x16433,x16432,x16434,x16435,x16436))
% 157.55/157.24 [1644]~E(x16441,x16442)+E(f690(x16443,x16444,x16441,x16445,x16446),f690(x16443,x16444,x16442,x16445,x16446))
% 157.55/157.24 [1645]~E(x16451,x16452)+E(f690(x16453,x16454,x16455,x16451,x16456),f690(x16453,x16454,x16455,x16452,x16456))
% 157.55/157.24 [1646]~E(x16461,x16462)+E(f690(x16463,x16464,x16465,x16466,x16461),f690(x16463,x16464,x16465,x16466,x16462))
% 157.55/157.24 [1647]~E(x16471,x16472)+E(f541(x16471,x16473,x16474,x16475,x16476,x16477,x16478,x16479),f541(x16472,x16473,x16474,x16475,x16476,x16477,x16478,x16479))
% 157.55/157.24 [1648]~E(x16481,x16482)+E(f541(x16483,x16481,x16484,x16485,x16486,x16487,x16488,x16489),f541(x16483,x16482,x16484,x16485,x16486,x16487,x16488,x16489))
% 157.55/157.24 [1649]~E(x16491,x16492)+E(f541(x16493,x16494,x16491,x16495,x16496,x16497,x16498,x16499),f541(x16493,x16494,x16492,x16495,x16496,x16497,x16498,x16499))
% 157.55/157.24 [1650]~E(x16501,x16502)+E(f541(x16503,x16504,x16505,x16501,x16506,x16507,x16508,x16509),f541(x16503,x16504,x16505,x16502,x16506,x16507,x16508,x16509))
% 157.55/157.24 [1651]~E(x16511,x16512)+E(f541(x16513,x16514,x16515,x16516,x16511,x16517,x16518,x16519),f541(x16513,x16514,x16515,x16516,x16512,x16517,x16518,x16519))
% 157.55/157.24 [1652]~E(x16521,x16522)+E(f541(x16523,x16524,x16525,x16526,x16527,x16521,x16528,x16529),f541(x16523,x16524,x16525,x16526,x16527,x16522,x16528,x16529))
% 157.55/157.24 [1653]~E(x16531,x16532)+E(f541(x16533,x16534,x16535,x16536,x16537,x16538,x16531,x16539),f541(x16533,x16534,x16535,x16536,x16537,x16538,x16532,x16539))
% 157.55/157.24 [1654]~E(x16541,x16542)+E(f541(x16543,x16544,x16545,x16546,x16547,x16548,x16549,x16541),f541(x16543,x16544,x16545,x16546,x16547,x16548,x16549,x16542))
% 157.55/157.24 [1655]~E(x16551,x16552)+E(f533(x16551,x16553,x16554,x16555,x16556,x16557),f533(x16552,x16553,x16554,x16555,x16556,x16557))
% 157.55/157.24 [1656]~E(x16561,x16562)+E(f533(x16563,x16561,x16564,x16565,x16566,x16567),f533(x16563,x16562,x16564,x16565,x16566,x16567))
% 157.55/157.24 [1657]~E(x16571,x16572)+E(f533(x16573,x16574,x16571,x16575,x16576,x16577),f533(x16573,x16574,x16572,x16575,x16576,x16577))
% 157.55/157.24 [1658]~E(x16581,x16582)+E(f533(x16583,x16584,x16585,x16581,x16586,x16587),f533(x16583,x16584,x16585,x16582,x16586,x16587))
% 157.55/157.24 [1659]~E(x16591,x16592)+E(f533(x16593,x16594,x16595,x16596,x16591,x16597),f533(x16593,x16594,x16595,x16596,x16592,x16597))
% 157.55/157.24 [1660]~E(x16601,x16602)+E(f533(x16603,x16604,x16605,x16606,x16607,x16601),f533(x16603,x16604,x16605,x16606,x16607,x16602))
% 157.55/157.24 [1661]~E(x16611,x16612)+E(f297(x16611,x16613,x16614),f297(x16612,x16613,x16614))
% 157.55/157.24 [1662]~E(x16621,x16622)+E(f297(x16623,x16621,x16624),f297(x16623,x16622,x16624))
% 157.55/157.24 [1663]~E(x16631,x16632)+E(f297(x16633,x16634,x16631),f297(x16633,x16634,x16632))
% 157.55/157.24 [1664]~E(x16641,x16642)+E(f649(x16641,x16643,x16644,x16645,x16646),f649(x16642,x16643,x16644,x16645,x16646))
% 157.55/157.24 [1665]~E(x16651,x16652)+E(f649(x16653,x16651,x16654,x16655,x16656),f649(x16653,x16652,x16654,x16655,x16656))
% 157.55/157.24 [1666]~E(x16661,x16662)+E(f649(x16663,x16664,x16661,x16665,x16666),f649(x16663,x16664,x16662,x16665,x16666))
% 157.55/157.24 [1667]~E(x16671,x16672)+E(f649(x16673,x16674,x16675,x16671,x16676),f649(x16673,x16674,x16675,x16672,x16676))
% 157.55/157.24 [1668]~E(x16681,x16682)+E(f649(x16683,x16684,x16685,x16686,x16681),f649(x16683,x16684,x16685,x16686,x16682))
% 157.55/157.24 [1669]~E(x16691,x16692)+E(f352(x16691,x16693,x16694),f352(x16692,x16693,x16694))
% 157.55/157.24 [1670]~E(x16701,x16702)+E(f352(x16703,x16701,x16704),f352(x16703,x16702,x16704))
% 157.55/157.24 [1671]~E(x16711,x16712)+E(f352(x16713,x16714,x16711),f352(x16713,x16714,x16712))
% 157.55/157.24 [1672]~E(x16721,x16722)+E(f437(x16721,x16723,x16724,x16725),f437(x16722,x16723,x16724,x16725))
% 157.55/157.24 [1673]~E(x16731,x16732)+E(f437(x16733,x16731,x16734,x16735),f437(x16733,x16732,x16734,x16735))
% 157.55/157.24 [1674]~E(x16741,x16742)+E(f437(x16743,x16744,x16741,x16745),f437(x16743,x16744,x16742,x16745))
% 157.55/157.24 [1675]~E(x16751,x16752)+E(f437(x16753,x16754,x16755,x16751),f437(x16753,x16754,x16755,x16752))
% 157.55/157.24 [1676]~E(x16761,x16762)+E(f525(x16761,x16763,x16764,x16765),f525(x16762,x16763,x16764,x16765))
% 157.55/157.24 [1677]~E(x16771,x16772)+E(f525(x16773,x16771,x16774,x16775),f525(x16773,x16772,x16774,x16775))
% 157.55/157.24 [1678]~E(x16781,x16782)+E(f525(x16783,x16784,x16781,x16785),f525(x16783,x16784,x16782,x16785))
% 157.55/157.24 [1679]~E(x16791,x16792)+E(f525(x16793,x16794,x16795,x16791),f525(x16793,x16794,x16795,x16792))
% 157.55/157.24 [1680]~E(x16801,x16802)+E(f435(x16801,x16803,x16804,x16805),f435(x16802,x16803,x16804,x16805))
% 157.55/157.24 [1681]~E(x16811,x16812)+E(f435(x16813,x16811,x16814,x16815),f435(x16813,x16812,x16814,x16815))
% 157.55/157.24 [1682]~E(x16821,x16822)+E(f435(x16823,x16824,x16821,x16825),f435(x16823,x16824,x16822,x16825))
% 157.55/157.24 [1683]~E(x16831,x16832)+E(f435(x16833,x16834,x16835,x16831),f435(x16833,x16834,x16835,x16832))
% 157.55/157.24 [1684]~E(x16841,x16842)+E(f847(x16841,x16843,x16844,x16845,x16846,x16847),f847(x16842,x16843,x16844,x16845,x16846,x16847))
% 157.55/157.24 [1685]~E(x16851,x16852)+E(f847(x16853,x16851,x16854,x16855,x16856,x16857),f847(x16853,x16852,x16854,x16855,x16856,x16857))
% 157.55/157.24 [1686]~E(x16861,x16862)+E(f847(x16863,x16864,x16861,x16865,x16866,x16867),f847(x16863,x16864,x16862,x16865,x16866,x16867))
% 157.55/157.24 [1687]~E(x16871,x16872)+E(f847(x16873,x16874,x16875,x16871,x16876,x16877),f847(x16873,x16874,x16875,x16872,x16876,x16877))
% 157.55/157.24 [1688]~E(x16881,x16882)+E(f847(x16883,x16884,x16885,x16886,x16881,x16887),f847(x16883,x16884,x16885,x16886,x16882,x16887))
% 157.55/157.24 [1689]~E(x16891,x16892)+E(f847(x16893,x16894,x16895,x16896,x16897,x16891),f847(x16893,x16894,x16895,x16896,x16897,x16892))
% 157.55/157.24 [1690]~E(x16901,x16902)+E(f594(x16901,x16903,x16904),f594(x16902,x16903,x16904))
% 157.55/157.24 [1691]~E(x16911,x16912)+E(f594(x16913,x16911,x16914),f594(x16913,x16912,x16914))
% 157.55/157.24 [1692]~E(x16921,x16922)+E(f594(x16923,x16924,x16921),f594(x16923,x16924,x16922))
% 157.55/157.24 [1693]~E(x16931,x16932)+E(f709(x16931,x16933,x16934),f709(x16932,x16933,x16934))
% 157.55/157.24 [1694]~E(x16941,x16942)+E(f709(x16943,x16941,x16944),f709(x16943,x16942,x16944))
% 157.55/157.24 [1695]~E(x16951,x16952)+E(f709(x16953,x16954,x16951),f709(x16953,x16954,x16952))
% 157.55/157.24 [1696]~E(x16961,x16962)+E(f413(x16961,x16963),f413(x16962,x16963))
% 157.55/157.24 [1697]~E(x16971,x16972)+E(f413(x16973,x16971),f413(x16973,x16972))
% 157.55/157.24 [1698]~E(x16981,x16982)+E(f592(x16981,x16983,x16984),f592(x16982,x16983,x16984))
% 157.55/157.24 [1699]~E(x16991,x16992)+E(f592(x16993,x16991,x16994),f592(x16993,x16992,x16994))
% 157.55/157.24 [1700]~E(x17001,x17002)+E(f592(x17003,x17004,x17001),f592(x17003,x17004,x17002))
% 157.55/157.24 [1701]~E(x17011,x17012)+E(f824(x17011,x17013,x17014),f824(x17012,x17013,x17014))
% 157.55/157.24 [1702]~E(x17021,x17022)+E(f824(x17023,x17021,x17024),f824(x17023,x17022,x17024))
% 157.55/157.24 [1703]~E(x17031,x17032)+E(f824(x17033,x17034,x17031),f824(x17033,x17034,x17032))
% 157.55/157.24 [1704]~E(x17041,x17042)+E(f387(x17041,x17043),f387(x17042,x17043))
% 157.55/157.24 [1705]~E(x17051,x17052)+E(f387(x17053,x17051),f387(x17053,x17052))
% 157.55/157.24 [1706]~E(x17061,x17062)+E(f736(x17061,x17063,x17064,x17065,x17066),f736(x17062,x17063,x17064,x17065,x17066))
% 157.55/157.24 [1707]~E(x17071,x17072)+E(f736(x17073,x17071,x17074,x17075,x17076),f736(x17073,x17072,x17074,x17075,x17076))
% 157.55/157.24 [1708]~E(x17081,x17082)+E(f736(x17083,x17084,x17081,x17085,x17086),f736(x17083,x17084,x17082,x17085,x17086))
% 157.55/157.24 [1709]~E(x17091,x17092)+E(f736(x17093,x17094,x17095,x17091,x17096),f736(x17093,x17094,x17095,x17092,x17096))
% 157.55/157.24 [1710]~E(x17101,x17102)+E(f736(x17103,x17104,x17105,x17106,x17101),f736(x17103,x17104,x17105,x17106,x17102))
% 157.55/157.24 [1711]~E(x17111,x17112)+E(f559(x17111,x17113),f559(x17112,x17113))
% 157.55/157.24 [1712]~E(x17121,x17122)+E(f559(x17123,x17121),f559(x17123,x17122))
% 157.55/157.24 [1713]~E(x17131,x17132)+E(f332(x17131),f332(x17132))
% 157.55/157.24 [1714]~E(x17141,x17142)+E(f388(x17141,x17143,x17144),f388(x17142,x17143,x17144))
% 157.55/157.24 [1715]~E(x17151,x17152)+E(f388(x17153,x17151,x17154),f388(x17153,x17152,x17154))
% 157.55/157.24 [1716]~E(x17161,x17162)+E(f388(x17163,x17164,x17161),f388(x17163,x17164,x17162))
% 157.55/157.24 [1717]~E(x17171,x17172)+E(f611(x17171,x17173),f611(x17172,x17173))
% 157.55/157.24 [1718]~E(x17181,x17182)+E(f611(x17183,x17181),f611(x17183,x17182))
% 157.55/157.24 [1719]~E(x17191,x17192)+E(f545(x17191),f545(x17192))
% 157.55/157.24 [1720]~E(x17201,x17202)+E(f224(x17201,x17203,x17204,x17205,x17206),f224(x17202,x17203,x17204,x17205,x17206))
% 157.55/157.24 [1721]~E(x17211,x17212)+E(f224(x17213,x17211,x17214,x17215,x17216),f224(x17213,x17212,x17214,x17215,x17216))
% 157.55/157.24 [1722]~E(x17221,x17222)+E(f224(x17223,x17224,x17221,x17225,x17226),f224(x17223,x17224,x17222,x17225,x17226))
% 157.55/157.24 [1723]~E(x17231,x17232)+E(f224(x17233,x17234,x17235,x17231,x17236),f224(x17233,x17234,x17235,x17232,x17236))
% 157.55/157.24 [1724]~E(x17241,x17242)+E(f224(x17243,x17244,x17245,x17246,x17241),f224(x17243,x17244,x17245,x17246,x17242))
% 157.55/157.24 [1725]~E(x17251,x17252)+E(f371(x17251,x17253,x17254),f371(x17252,x17253,x17254))
% 157.55/157.24 [1726]~E(x17261,x17262)+E(f371(x17263,x17261,x17264),f371(x17263,x17262,x17264))
% 157.55/157.24 [1727]~E(x17271,x17272)+E(f371(x17273,x17274,x17271),f371(x17273,x17274,x17272))
% 157.55/157.24 [1728]~E(x17281,x17282)+E(f725(x17281,x17283),f725(x17282,x17283))
% 157.55/157.24 [1729]~E(x17291,x17292)+E(f725(x17293,x17291),f725(x17293,x17292))
% 157.55/157.24 [1730]~E(x17301,x17302)+E(f334(x17301),f334(x17302))
% 157.55/157.24 [1731]~E(x17311,x17312)+E(f398(x17311,x17313,x17314),f398(x17312,x17313,x17314))
% 157.55/157.24 [1732]~E(x17321,x17322)+E(f398(x17323,x17321,x17324),f398(x17323,x17322,x17324))
% 157.55/157.24 [1733]~E(x17331,x17332)+E(f398(x17333,x17334,x17331),f398(x17333,x17334,x17332))
% 157.55/157.24 [1734]~E(x17341,x17342)+E(f739(x17341,x17343,x17344,x17345,x17346),f739(x17342,x17343,x17344,x17345,x17346))
% 157.55/157.24 [1735]~E(x17351,x17352)+E(f739(x17353,x17351,x17354,x17355,x17356),f739(x17353,x17352,x17354,x17355,x17356))
% 157.55/157.24 [1736]~E(x17361,x17362)+E(f739(x17363,x17364,x17361,x17365,x17366),f739(x17363,x17364,x17362,x17365,x17366))
% 157.55/157.24 [1737]~E(x17371,x17372)+E(f739(x17373,x17374,x17375,x17371,x17376),f739(x17373,x17374,x17375,x17372,x17376))
% 157.55/157.24 [1738]~E(x17381,x17382)+E(f739(x17383,x17384,x17385,x17386,x17381),f739(x17383,x17384,x17385,x17386,x17382))
% 157.55/157.24 [1739]~E(x17391,x17392)+E(f205(x17391,x17393,x17394,x17395),f205(x17392,x17393,x17394,x17395))
% 157.55/157.24 [1740]~E(x17401,x17402)+E(f205(x17403,x17401,x17404,x17405),f205(x17403,x17402,x17404,x17405))
% 157.55/157.24 [1741]~E(x17411,x17412)+E(f205(x17413,x17414,x17411,x17415),f205(x17413,x17414,x17412,x17415))
% 157.55/157.24 [1742]~E(x17421,x17422)+E(f205(x17423,x17424,x17425,x17421),f205(x17423,x17424,x17425,x17422))
% 157.55/157.24 [1743]~E(x17431,x17432)+E(f630(x17431,x17433,x17434,x17435,x17436),f630(x17432,x17433,x17434,x17435,x17436))
% 157.55/157.24 [1744]~E(x17441,x17442)+E(f630(x17443,x17441,x17444,x17445,x17446),f630(x17443,x17442,x17444,x17445,x17446))
% 157.55/157.24 [1745]~E(x17451,x17452)+E(f630(x17453,x17454,x17451,x17455,x17456),f630(x17453,x17454,x17452,x17455,x17456))
% 157.55/157.24 [1746]~E(x17461,x17462)+E(f630(x17463,x17464,x17465,x17461,x17466),f630(x17463,x17464,x17465,x17462,x17466))
% 157.55/157.24 [1747]~E(x17471,x17472)+E(f630(x17473,x17474,x17475,x17476,x17471),f630(x17473,x17474,x17475,x17476,x17472))
% 157.55/157.24 [1748]~E(x17481,x17482)+E(f730(x17481,x17483,x17484,x17485),f730(x17482,x17483,x17484,x17485))
% 157.55/157.24 [1749]~E(x17491,x17492)+E(f730(x17493,x17491,x17494,x17495),f730(x17493,x17492,x17494,x17495))
% 157.55/157.24 [1750]~E(x17501,x17502)+E(f730(x17503,x17504,x17501,x17505),f730(x17503,x17504,x17502,x17505))
% 157.55/157.24 [1751]~E(x17511,x17512)+E(f730(x17513,x17514,x17515,x17511),f730(x17513,x17514,x17515,x17512))
% 157.55/157.24 [1752]~E(x17521,x17522)+E(f785(x17521,x17523,x17524),f785(x17522,x17523,x17524))
% 157.55/157.24 [1753]~E(x17531,x17532)+E(f785(x17533,x17531,x17534),f785(x17533,x17532,x17534))
% 157.55/157.24 [1754]~E(x17541,x17542)+E(f785(x17543,x17544,x17541),f785(x17543,x17544,x17542))
% 157.55/157.24 [1755]~E(x17551,x17552)+E(f854(x17551,x17553,x17554,x17555,x17556),f854(x17552,x17553,x17554,x17555,x17556))
% 157.55/157.24 [1756]~E(x17561,x17562)+E(f854(x17563,x17561,x17564,x17565,x17566),f854(x17563,x17562,x17564,x17565,x17566))
% 157.55/157.24 [1757]~E(x17571,x17572)+E(f854(x17573,x17574,x17571,x17575,x17576),f854(x17573,x17574,x17572,x17575,x17576))
% 157.55/157.24 [1758]~E(x17581,x17582)+E(f854(x17583,x17584,x17585,x17581,x17586),f854(x17583,x17584,x17585,x17582,x17586))
% 157.55/157.24 [1759]~E(x17591,x17592)+E(f854(x17593,x17594,x17595,x17596,x17591),f854(x17593,x17594,x17595,x17596,x17592))
% 157.55/157.24 [1760]~E(x17601,x17602)+E(f266(x17601),f266(x17602))
% 157.55/157.24 [1761]~E(x17611,x17612)+E(f396(x17611,x17613,x17614),f396(x17612,x17613,x17614))
% 157.55/157.24 [1762]~E(x17621,x17622)+E(f396(x17623,x17621,x17624),f396(x17623,x17622,x17624))
% 157.55/157.24 [1763]~E(x17631,x17632)+E(f396(x17633,x17634,x17631),f396(x17633,x17634,x17632))
% 157.55/157.24 [1764]~E(x17641,x17642)+E(f399(x17641,x17643,x17644),f399(x17642,x17643,x17644))
% 157.55/157.24 [1765]~E(x17651,x17652)+E(f399(x17653,x17651,x17654),f399(x17653,x17652,x17654))
% 157.55/157.24 [1766]~E(x17661,x17662)+E(f399(x17663,x17664,x17661),f399(x17663,x17664,x17662))
% 157.55/157.24 [1767]~E(x17671,x17672)+E(f42(x17671),f42(x17672))
% 157.55/157.24 [1768]~E(x17681,x17682)+E(f732(x17681,x17683),f732(x17682,x17683))
% 157.55/157.24 [1769]~E(x17691,x17692)+E(f732(x17693,x17691),f732(x17693,x17692))
% 157.55/157.24 [1770]~E(x17701,x17702)+E(f530(x17701,x17703),f530(x17702,x17703))
% 157.55/157.24 [1771]~E(x17711,x17712)+E(f530(x17713,x17711),f530(x17713,x17712))
% 157.55/157.24 [1772]~E(x17721,x17722)+E(f653(x17721,x17723,x17724),f653(x17722,x17723,x17724))
% 157.55/157.24 [1773]~E(x17731,x17732)+E(f653(x17733,x17731,x17734),f653(x17733,x17732,x17734))
% 157.55/157.24 [1774]~E(x17741,x17742)+E(f653(x17743,x17744,x17741),f653(x17743,x17744,x17742))
% 157.55/157.24 [1775]~E(x17751,x17752)+E(f244(x17751,x17753,x17754),f244(x17752,x17753,x17754))
% 157.55/157.24 [1776]~E(x17761,x17762)+E(f244(x17763,x17761,x17764),f244(x17763,x17762,x17764))
% 157.55/157.24 [1777]~E(x17771,x17772)+E(f244(x17773,x17774,x17771),f244(x17773,x17774,x17772))
% 157.55/157.24 [1778]~E(x17781,x17782)+E(f658(x17781,x17783,x17784,x17785),f658(x17782,x17783,x17784,x17785))
% 157.55/157.24 [1779]~E(x17791,x17792)+E(f658(x17793,x17791,x17794,x17795),f658(x17793,x17792,x17794,x17795))
% 157.55/157.24 [1780]~E(x17801,x17802)+E(f658(x17803,x17804,x17801,x17805),f658(x17803,x17804,x17802,x17805))
% 157.55/157.24 [1781]~E(x17811,x17812)+E(f658(x17813,x17814,x17815,x17811),f658(x17813,x17814,x17815,x17812))
% 157.55/157.24 [1782]~E(x17821,x17822)+E(f279(x17821,x17823,x17824,x17825),f279(x17822,x17823,x17824,x17825))
% 157.55/157.24 [1783]~E(x17831,x17832)+E(f279(x17833,x17831,x17834,x17835),f279(x17833,x17832,x17834,x17835))
% 157.55/157.24 [1784]~E(x17841,x17842)+E(f279(x17843,x17844,x17841,x17845),f279(x17843,x17844,x17842,x17845))
% 157.55/157.24 [1785]~E(x17851,x17852)+E(f279(x17853,x17854,x17855,x17851),f279(x17853,x17854,x17855,x17852))
% 157.55/157.24 [1786]~E(x17861,x17862)+E(f411(x17861,x17863),f411(x17862,x17863))
% 157.55/157.24 [1787]~E(x17871,x17872)+E(f411(x17873,x17871),f411(x17873,x17872))
% 157.55/157.24 [1788]~E(x17881,x17882)+E(f777(x17881,x17883,x17884),f777(x17882,x17883,x17884))
% 157.55/157.24 [1789]~E(x17891,x17892)+E(f777(x17893,x17891,x17894),f777(x17893,x17892,x17894))
% 157.55/157.24 [1790]~E(x17901,x17902)+E(f777(x17903,x17904,x17901),f777(x17903,x17904,x17902))
% 157.55/157.24 [1791]~E(x17911,x17912)+E(f597(x17911,x17913,x17914),f597(x17912,x17913,x17914))
% 157.55/157.24 [1792]~E(x17921,x17922)+E(f597(x17923,x17921,x17924),f597(x17923,x17922,x17924))
% 157.55/157.24 [1793]~E(x17931,x17932)+E(f597(x17933,x17934,x17931),f597(x17933,x17934,x17932))
% 157.55/157.24 [1794]~E(x17941,x17942)+E(f751(x17941,x17943,x17944),f751(x17942,x17943,x17944))
% 157.55/157.24 [1795]~E(x17951,x17952)+E(f751(x17953,x17951,x17954),f751(x17953,x17952,x17954))
% 157.55/157.24 [1796]~E(x17961,x17962)+E(f751(x17963,x17964,x17961),f751(x17963,x17964,x17962))
% 157.55/157.24 [1797]~E(x17971,x17972)+E(f553(x17971,x17973,x17974,x17975,x17976,x17977),f553(x17972,x17973,x17974,x17975,x17976,x17977))
% 157.55/157.24 [1798]~E(x17981,x17982)+E(f553(x17983,x17981,x17984,x17985,x17986,x17987),f553(x17983,x17982,x17984,x17985,x17986,x17987))
% 157.55/157.24 [1799]~E(x17991,x17992)+E(f553(x17993,x17994,x17991,x17995,x17996,x17997),f553(x17993,x17994,x17992,x17995,x17996,x17997))
% 157.55/157.24 [1800]~E(x18001,x18002)+E(f553(x18003,x18004,x18005,x18001,x18006,x18007),f553(x18003,x18004,x18005,x18002,x18006,x18007))
% 157.55/157.24 [1801]~E(x18011,x18012)+E(f553(x18013,x18014,x18015,x18016,x18011,x18017),f553(x18013,x18014,x18015,x18016,x18012,x18017))
% 157.55/157.24 [1802]~E(x18021,x18022)+E(f553(x18023,x18024,x18025,x18026,x18027,x18021),f553(x18023,x18024,x18025,x18026,x18027,x18022))
% 157.55/157.24 [1803]~E(x18031,x18032)+E(f681(x18031,x18033,x18034,x18035),f681(x18032,x18033,x18034,x18035))
% 157.55/157.24 [1804]~E(x18041,x18042)+E(f681(x18043,x18041,x18044,x18045),f681(x18043,x18042,x18044,x18045))
% 157.55/157.24 [1805]~E(x18051,x18052)+E(f681(x18053,x18054,x18051,x18055),f681(x18053,x18054,x18052,x18055))
% 157.55/157.24 [1806]~E(x18061,x18062)+E(f681(x18063,x18064,x18065,x18061),f681(x18063,x18064,x18065,x18062))
% 157.55/157.24 [1807]~E(x18071,x18072)+E(f458(x18071,x18073,x18074,x18075),f458(x18072,x18073,x18074,x18075))
% 157.55/157.24 [1808]~E(x18081,x18082)+E(f458(x18083,x18081,x18084,x18085),f458(x18083,x18082,x18084,x18085))
% 157.55/157.24 [1809]~E(x18091,x18092)+E(f458(x18093,x18094,x18091,x18095),f458(x18093,x18094,x18092,x18095))
% 157.55/157.24 [1810]~E(x18101,x18102)+E(f458(x18103,x18104,x18105,x18101),f458(x18103,x18104,x18105,x18102))
% 157.55/157.24 [1811]~E(x18111,x18112)+E(f618(x18111,x18113,x18114,x18115,x18116),f618(x18112,x18113,x18114,x18115,x18116))
% 157.55/157.24 [1812]~E(x18121,x18122)+E(f618(x18123,x18121,x18124,x18125,x18126),f618(x18123,x18122,x18124,x18125,x18126))
% 157.55/157.24 [1813]~E(x18131,x18132)+E(f618(x18133,x18134,x18131,x18135,x18136),f618(x18133,x18134,x18132,x18135,x18136))
% 157.55/157.24 [1814]~E(x18141,x18142)+E(f618(x18143,x18144,x18145,x18141,x18146),f618(x18143,x18144,x18145,x18142,x18146))
% 157.55/157.24 [1815]~E(x18151,x18152)+E(f618(x18153,x18154,x18155,x18156,x18151),f618(x18153,x18154,x18155,x18156,x18152))
% 157.55/157.24 [1816]~E(x18161,x18162)+E(f582(x18161,x18163,x18164),f582(x18162,x18163,x18164))
% 157.55/157.24 [1817]~E(x18171,x18172)+E(f582(x18173,x18171,x18174),f582(x18173,x18172,x18174))
% 157.55/157.24 [1818]~E(x18181,x18182)+E(f582(x18183,x18184,x18181),f582(x18183,x18184,x18182))
% 157.55/157.24 [1819]~E(x18191,x18192)+E(f473(x18191,x18193),f473(x18192,x18193))
% 157.55/157.24 [1820]~E(x18201,x18202)+E(f473(x18203,x18201),f473(x18203,x18202))
% 157.55/157.24 [1821]~E(x18211,x18212)+E(f716(x18211,x18213,x18214),f716(x18212,x18213,x18214))
% 157.55/157.24 [1822]~E(x18221,x18222)+E(f716(x18223,x18221,x18224),f716(x18223,x18222,x18224))
% 157.55/157.24 [1823]~E(x18231,x18232)+E(f716(x18233,x18234,x18231),f716(x18233,x18234,x18232))
% 157.55/157.24 [1824]~E(x18241,x18242)+E(f833(x18241,x18243,x18244,x18245,x18246,x18247),f833(x18242,x18243,x18244,x18245,x18246,x18247))
% 157.55/157.24 [1825]~E(x18251,x18252)+E(f833(x18253,x18251,x18254,x18255,x18256,x18257),f833(x18253,x18252,x18254,x18255,x18256,x18257))
% 157.55/157.24 [1826]~E(x18261,x18262)+E(f833(x18263,x18264,x18261,x18265,x18266,x18267),f833(x18263,x18264,x18262,x18265,x18266,x18267))
% 157.55/157.24 [1827]~E(x18271,x18272)+E(f833(x18273,x18274,x18275,x18271,x18276,x18277),f833(x18273,x18274,x18275,x18272,x18276,x18277))
% 157.55/157.24 [1828]~E(x18281,x18282)+E(f833(x18283,x18284,x18285,x18286,x18281,x18287),f833(x18283,x18284,x18285,x18286,x18282,x18287))
% 157.55/157.24 [1829]~E(x18291,x18292)+E(f833(x18293,x18294,x18295,x18296,x18297,x18291),f833(x18293,x18294,x18295,x18296,x18297,x18292))
% 157.55/157.24 [1830]~E(x18301,x18302)+E(f729(x18301,x18303,x18304),f729(x18302,x18303,x18304))
% 157.55/157.24 [1831]~E(x18311,x18312)+E(f729(x18313,x18311,x18314),f729(x18313,x18312,x18314))
% 157.55/157.24 [1832]~E(x18321,x18322)+E(f729(x18323,x18324,x18321),f729(x18323,x18324,x18322))
% 157.55/157.24 [1833]~E(x18331,x18332)+E(f577(x18331,x18333,x18334),f577(x18332,x18333,x18334))
% 157.55/157.24 [1834]~E(x18341,x18342)+E(f577(x18343,x18341,x18344),f577(x18343,x18342,x18344))
% 157.55/157.24 [1835]~E(x18351,x18352)+E(f577(x18353,x18354,x18351),f577(x18353,x18354,x18352))
% 157.55/157.24 [1836]~E(x18361,x18362)+E(f180(x18361),f180(x18362))
% 157.55/157.24 [1837]~E(x18371,x18372)+E(f494(x18371,x18373,x18374),f494(x18372,x18373,x18374))
% 157.55/157.24 [1838]~E(x18381,x18382)+E(f494(x18383,x18381,x18384),f494(x18383,x18382,x18384))
% 157.55/157.24 [1839]~E(x18391,x18392)+E(f494(x18393,x18394,x18391),f494(x18393,x18394,x18392))
% 157.55/157.24 [1840]~E(x18401,x18402)+E(f382(x18401,x18403,x18404),f382(x18402,x18403,x18404))
% 157.55/157.24 [1841]~E(x18411,x18412)+E(f382(x18413,x18411,x18414),f382(x18413,x18412,x18414))
% 157.55/157.24 [1842]~E(x18421,x18422)+E(f382(x18423,x18424,x18421),f382(x18423,x18424,x18422))
% 157.55/157.24 [1843]~E(x18431,x18432)+E(f602(x18431,x18433),f602(x18432,x18433))
% 157.55/157.24 [1844]~E(x18441,x18442)+E(f602(x18443,x18441),f602(x18443,x18442))
% 157.55/157.24 [1845]~E(x18451,x18452)+E(f794(x18451),f794(x18452))
% 157.55/157.24 [1846]~E(x18461,x18462)+E(f529(x18461,x18463),f529(x18462,x18463))
% 157.55/157.24 [1847]~E(x18471,x18472)+E(f529(x18473,x18471),f529(x18473,x18472))
% 157.55/157.24 [1848]~E(x18481,x18482)+E(f457(x18481,x18483,x18484,x18485),f457(x18482,x18483,x18484,x18485))
% 157.55/157.24 [1849]~E(x18491,x18492)+E(f457(x18493,x18491,x18494,x18495),f457(x18493,x18492,x18494,x18495))
% 157.55/157.24 [1850]~E(x18501,x18502)+E(f457(x18503,x18504,x18501,x18505),f457(x18503,x18504,x18502,x18505))
% 157.55/157.24 [1851]~E(x18511,x18512)+E(f457(x18513,x18514,x18515,x18511),f457(x18513,x18514,x18515,x18512))
% 157.55/157.24 [1852]~E(x18521,x18522)+E(f654(x18521,x18523,x18524),f654(x18522,x18523,x18524))
% 157.55/157.24 [1853]~E(x18531,x18532)+E(f654(x18533,x18531,x18534),f654(x18533,x18532,x18534))
% 157.55/157.24 [1854]~E(x18541,x18542)+E(f654(x18543,x18544,x18541),f654(x18543,x18544,x18542))
% 157.55/157.24 [1855]~E(x18551,x18552)+E(f778(x18551,x18553),f778(x18552,x18553))
% 157.55/157.24 [1856]~E(x18561,x18562)+E(f778(x18563,x18561),f778(x18563,x18562))
% 157.55/157.24 [1857]~E(x18571,x18572)+E(f844(x18571,x18573,x18574,x18575,x18576,x18577,x18578,x18579),f844(x18572,x18573,x18574,x18575,x18576,x18577,x18578,x18579))
% 157.55/157.24 [1858]~E(x18581,x18582)+E(f844(x18583,x18581,x18584,x18585,x18586,x18587,x18588,x18589),f844(x18583,x18582,x18584,x18585,x18586,x18587,x18588,x18589))
% 157.55/157.24 [1859]~E(x18591,x18592)+E(f844(x18593,x18594,x18591,x18595,x18596,x18597,x18598,x18599),f844(x18593,x18594,x18592,x18595,x18596,x18597,x18598,x18599))
% 157.55/157.24 [1860]~E(x18601,x18602)+E(f844(x18603,x18604,x18605,x18601,x18606,x18607,x18608,x18609),f844(x18603,x18604,x18605,x18602,x18606,x18607,x18608,x18609))
% 157.55/157.24 [1861]~E(x18611,x18612)+E(f844(x18613,x18614,x18615,x18616,x18611,x18617,x18618,x18619),f844(x18613,x18614,x18615,x18616,x18612,x18617,x18618,x18619))
% 157.55/157.24 [1862]~E(x18621,x18622)+E(f844(x18623,x18624,x18625,x18626,x18627,x18621,x18628,x18629),f844(x18623,x18624,x18625,x18626,x18627,x18622,x18628,x18629))
% 157.55/157.24 [1863]~E(x18631,x18632)+E(f844(x18633,x18634,x18635,x18636,x18637,x18638,x18631,x18639),f844(x18633,x18634,x18635,x18636,x18637,x18638,x18632,x18639))
% 157.55/157.24 [1864]~E(x18641,x18642)+E(f844(x18643,x18644,x18645,x18646,x18647,x18648,x18649,x18641),f844(x18643,x18644,x18645,x18646,x18647,x18648,x18649,x18642))
% 157.55/157.24 [1865]~E(x18651,x18652)+E(f480(x18651,x18653,x18654,x18655),f480(x18652,x18653,x18654,x18655))
% 157.55/157.24 [1866]~E(x18661,x18662)+E(f480(x18663,x18661,x18664,x18665),f480(x18663,x18662,x18664,x18665))
% 157.55/157.24 [1867]~E(x18671,x18672)+E(f480(x18673,x18674,x18671,x18675),f480(x18673,x18674,x18672,x18675))
% 157.55/157.24 [1868]~E(x18681,x18682)+E(f480(x18683,x18684,x18685,x18681),f480(x18683,x18684,x18685,x18682))
% 157.55/157.24 [1869]~E(x18691,x18692)+E(f401(x18691,x18693,x18694),f401(x18692,x18693,x18694))
% 157.55/157.24 [1870]~E(x18701,x18702)+E(f401(x18703,x18701,x18704),f401(x18703,x18702,x18704))
% 157.55/157.24 [1871]~E(x18711,x18712)+E(f401(x18713,x18714,x18711),f401(x18713,x18714,x18712))
% 157.55/157.24 [1872]~E(x18721,x18722)+E(f640(x18721,x18723,x18724,x18725,x18726,x18727),f640(x18722,x18723,x18724,x18725,x18726,x18727))
% 157.55/157.24 [1873]~E(x18731,x18732)+E(f640(x18733,x18731,x18734,x18735,x18736,x18737),f640(x18733,x18732,x18734,x18735,x18736,x18737))
% 157.55/157.24 [1874]~E(x18741,x18742)+E(f640(x18743,x18744,x18741,x18745,x18746,x18747),f640(x18743,x18744,x18742,x18745,x18746,x18747))
% 157.55/157.24 [1875]~E(x18751,x18752)+E(f640(x18753,x18754,x18755,x18751,x18756,x18757),f640(x18753,x18754,x18755,x18752,x18756,x18757))
% 157.55/157.24 [1876]~E(x18761,x18762)+E(f640(x18763,x18764,x18765,x18766,x18761,x18767),f640(x18763,x18764,x18765,x18766,x18762,x18767))
% 157.55/157.24 [1877]~E(x18771,x18772)+E(f640(x18773,x18774,x18775,x18776,x18777,x18771),f640(x18773,x18774,x18775,x18776,x18777,x18772))
% 157.55/157.24 [1878]~E(x18781,x18782)+E(f555(x18781,x18783,x18784,x18785,x18786,x18787),f555(x18782,x18783,x18784,x18785,x18786,x18787))
% 157.55/157.24 [1879]~E(x18791,x18792)+E(f555(x18793,x18791,x18794,x18795,x18796,x18797),f555(x18793,x18792,x18794,x18795,x18796,x18797))
% 157.55/157.24 [1880]~E(x18801,x18802)+E(f555(x18803,x18804,x18801,x18805,x18806,x18807),f555(x18803,x18804,x18802,x18805,x18806,x18807))
% 157.55/157.24 [1881]~E(x18811,x18812)+E(f555(x18813,x18814,x18815,x18811,x18816,x18817),f555(x18813,x18814,x18815,x18812,x18816,x18817))
% 157.55/157.24 [1882]~E(x18821,x18822)+E(f555(x18823,x18824,x18825,x18826,x18821,x18827),f555(x18823,x18824,x18825,x18826,x18822,x18827))
% 157.55/157.24 [1883]~E(x18831,x18832)+E(f555(x18833,x18834,x18835,x18836,x18837,x18831),f555(x18833,x18834,x18835,x18836,x18837,x18832))
% 157.55/157.24 [1884]~E(x18841,x18842)+E(f434(x18841,x18843,x18844,x18845),f434(x18842,x18843,x18844,x18845))
% 157.55/157.24 [1885]~E(x18851,x18852)+E(f434(x18853,x18851,x18854,x18855),f434(x18853,x18852,x18854,x18855))
% 157.55/157.24 [1886]~E(x18861,x18862)+E(f434(x18863,x18864,x18861,x18865),f434(x18863,x18864,x18862,x18865))
% 157.55/157.24 [1887]~E(x18871,x18872)+E(f434(x18873,x18874,x18875,x18871),f434(x18873,x18874,x18875,x18872))
% 157.55/157.24 [1888]~E(x18881,x18882)+E(f595(x18881,x18883,x18884),f595(x18882,x18883,x18884))
% 157.55/157.24 [1889]~E(x18891,x18892)+E(f595(x18893,x18891,x18894),f595(x18893,x18892,x18894))
% 157.55/157.24 [1890]~E(x18901,x18902)+E(f595(x18903,x18904,x18901),f595(x18903,x18904,x18902))
% 157.55/157.24 [1891]~E(x18911,x18912)+E(f570(x18911,x18913,x18914),f570(x18912,x18913,x18914))
% 157.55/157.24 [1892]~E(x18921,x18922)+E(f570(x18923,x18921,x18924),f570(x18923,x18922,x18924))
% 157.55/157.24 [1893]~E(x18931,x18932)+E(f570(x18933,x18934,x18931),f570(x18933,x18934,x18932))
% 157.55/157.24 [1894]~E(x18941,x18942)+E(f186(x18941),f186(x18942))
% 157.55/157.24 [1895]~E(x18951,x18952)+E(f127(x18951,x18953,x18954,x18955,x18956),f127(x18952,x18953,x18954,x18955,x18956))
% 157.55/157.24 [1896]~E(x18961,x18962)+E(f127(x18963,x18961,x18964,x18965,x18966),f127(x18963,x18962,x18964,x18965,x18966))
% 157.55/157.24 [1897]~E(x18971,x18972)+E(f127(x18973,x18974,x18971,x18975,x18976),f127(x18973,x18974,x18972,x18975,x18976))
% 157.55/157.24 [1898]~E(x18981,x18982)+E(f127(x18983,x18984,x18985,x18981,x18986),f127(x18983,x18984,x18985,x18982,x18986))
% 157.55/157.24 [1899]~E(x18991,x18992)+E(f127(x18993,x18994,x18995,x18996,x18991),f127(x18993,x18994,x18995,x18996,x18992))
% 157.55/157.24 [1900]~E(x19001,x19002)+E(f53(x19001,x19003),f53(x19002,x19003))
% 157.55/157.24 [1901]~E(x19011,x19012)+E(f53(x19013,x19011),f53(x19013,x19012))
% 157.55/157.24 [1902]~E(x19021,x19022)+E(f613(x19021,x19023,x19024),f613(x19022,x19023,x19024))
% 157.55/157.24 [1903]~E(x19031,x19032)+E(f613(x19033,x19031,x19034),f613(x19033,x19032,x19034))
% 157.55/157.24 [1904]~E(x19041,x19042)+E(f613(x19043,x19044,x19041),f613(x19043,x19044,x19042))
% 157.55/157.24 [1905]~E(x19051,x19052)+E(f627(x19051,x19053,x19054,x19055,x19056),f627(x19052,x19053,x19054,x19055,x19056))
% 157.55/157.24 [1906]~E(x19061,x19062)+E(f627(x19063,x19061,x19064,x19065,x19066),f627(x19063,x19062,x19064,x19065,x19066))
% 157.55/157.24 [1907]~E(x19071,x19072)+E(f627(x19073,x19074,x19071,x19075,x19076),f627(x19073,x19074,x19072,x19075,x19076))
% 157.55/157.24 [1908]~E(x19081,x19082)+E(f627(x19083,x19084,x19085,x19081,x19086),f627(x19083,x19084,x19085,x19082,x19086))
% 157.55/157.24 [1909]~E(x19091,x19092)+E(f627(x19093,x19094,x19095,x19096,x19091),f627(x19093,x19094,x19095,x19096,x19092))
% 157.55/157.24 [1910]~E(x19101,x19102)+E(f873(x19101,x19103,x19104,x19105,x19106,x19107,x19108),f873(x19102,x19103,x19104,x19105,x19106,x19107,x19108))
% 157.55/157.24 [1911]~E(x19111,x19112)+E(f873(x19113,x19111,x19114,x19115,x19116,x19117,x19118),f873(x19113,x19112,x19114,x19115,x19116,x19117,x19118))
% 157.55/157.24 [1912]~E(x19121,x19122)+E(f873(x19123,x19124,x19121,x19125,x19126,x19127,x19128),f873(x19123,x19124,x19122,x19125,x19126,x19127,x19128))
% 157.55/157.24 [1913]~E(x19131,x19132)+E(f873(x19133,x19134,x19135,x19131,x19136,x19137,x19138),f873(x19133,x19134,x19135,x19132,x19136,x19137,x19138))
% 157.55/157.24 [1914]~E(x19141,x19142)+E(f873(x19143,x19144,x19145,x19146,x19141,x19147,x19148),f873(x19143,x19144,x19145,x19146,x19142,x19147,x19148))
% 157.55/157.24 [1915]~E(x19151,x19152)+E(f873(x19153,x19154,x19155,x19156,x19157,x19151,x19158),f873(x19153,x19154,x19155,x19156,x19157,x19152,x19158))
% 157.55/157.24 [1916]~E(x19161,x19162)+E(f873(x19163,x19164,x19165,x19166,x19167,x19168,x19161),f873(x19163,x19164,x19165,x19166,x19167,x19168,x19162))
% 157.55/157.24 [1917]~E(x19171,x19172)+E(f596(x19171,x19173,x19174,x19175,x19176,x19177),f596(x19172,x19173,x19174,x19175,x19176,x19177))
% 157.55/157.24 [1918]~E(x19181,x19182)+E(f596(x19183,x19181,x19184,x19185,x19186,x19187),f596(x19183,x19182,x19184,x19185,x19186,x19187))
% 157.55/157.24 [1919]~E(x19191,x19192)+E(f596(x19193,x19194,x19191,x19195,x19196,x19197),f596(x19193,x19194,x19192,x19195,x19196,x19197))
% 157.55/157.24 [1920]~E(x19201,x19202)+E(f596(x19203,x19204,x19205,x19201,x19206,x19207),f596(x19203,x19204,x19205,x19202,x19206,x19207))
% 157.55/157.24 [1921]~E(x19211,x19212)+E(f596(x19213,x19214,x19215,x19216,x19211,x19217),f596(x19213,x19214,x19215,x19216,x19212,x19217))
% 157.55/157.24 [1922]~E(x19221,x19222)+E(f596(x19223,x19224,x19225,x19226,x19227,x19221),f596(x19223,x19224,x19225,x19226,x19227,x19222))
% 157.55/157.24 [1923]~E(x19231,x19232)+E(f402(x19231),f402(x19232))
% 157.55/157.24 [1924]~E(x19241,x19242)+E(f465(x19241,x19243,x19244,x19245,x19246),f465(x19242,x19243,x19244,x19245,x19246))
% 157.55/157.24 [1925]~E(x19251,x19252)+E(f465(x19253,x19251,x19254,x19255,x19256),f465(x19253,x19252,x19254,x19255,x19256))
% 157.55/157.24 [1926]~E(x19261,x19262)+E(f465(x19263,x19264,x19261,x19265,x19266),f465(x19263,x19264,x19262,x19265,x19266))
% 157.55/157.24 [1927]~E(x19271,x19272)+E(f465(x19273,x19274,x19275,x19271,x19276),f465(x19273,x19274,x19275,x19272,x19276))
% 157.55/157.24 [1928]~E(x19281,x19282)+E(f465(x19283,x19284,x19285,x19286,x19281),f465(x19283,x19284,x19285,x19286,x19282))
% 157.55/157.24 [1929]~E(x19291,x19292)+E(f608(x19291,x19293,x19294),f608(x19292,x19293,x19294))
% 157.55/157.24 [1930]~E(x19301,x19302)+E(f608(x19303,x19301,x19304),f608(x19303,x19302,x19304))
% 157.55/157.24 [1931]~E(x19311,x19312)+E(f608(x19313,x19314,x19311),f608(x19313,x19314,x19312))
% 157.55/157.24 [1932]~E(x19321,x19322)+E(f462(x19321,x19323,x19324,x19325),f462(x19322,x19323,x19324,x19325))
% 157.55/157.24 [1933]~E(x19331,x19332)+E(f462(x19333,x19331,x19334,x19335),f462(x19333,x19332,x19334,x19335))
% 157.55/157.24 [1934]~E(x19341,x19342)+E(f462(x19343,x19344,x19341,x19345),f462(x19343,x19344,x19342,x19345))
% 157.55/157.24 [1935]~E(x19351,x19352)+E(f462(x19353,x19354,x19355,x19351),f462(x19353,x19354,x19355,x19352))
% 157.55/157.24 [1936]~E(x19361,x19362)+E(f712(x19361,x19363,x19364),f712(x19362,x19363,x19364))
% 157.55/157.24 [1937]~E(x19371,x19372)+E(f712(x19373,x19371,x19374),f712(x19373,x19372,x19374))
% 157.55/157.24 [1938]~E(x19381,x19382)+E(f712(x19383,x19384,x19381),f712(x19383,x19384,x19382))
% 157.55/157.24 [1939]~E(x19391,x19392)+E(f603(x19391,x19393,x19394),f603(x19392,x19393,x19394))
% 157.55/157.24 [1940]~E(x19401,x19402)+E(f603(x19403,x19401,x19404),f603(x19403,x19402,x19404))
% 157.55/157.24 [1941]~E(x19411,x19412)+E(f603(x19413,x19414,x19411),f603(x19413,x19414,x19412))
% 157.55/157.24 [1942]~E(x19421,x19422)+E(f616(x19421,x19423),f616(x19422,x19423))
% 157.55/157.24 [1943]~E(x19431,x19432)+E(f616(x19433,x19431),f616(x19433,x19432))
% 157.55/157.24 [1944]~E(x19441,x19442)+E(f201(x19441),f201(x19442))
% 157.55/157.24 [1945]~E(x19451,x19452)+E(f468(x19451,x19453,x19454,x19455,x19456),f468(x19452,x19453,x19454,x19455,x19456))
% 157.55/157.24 [1946]~E(x19461,x19462)+E(f468(x19463,x19461,x19464,x19465,x19466),f468(x19463,x19462,x19464,x19465,x19466))
% 157.55/157.24 [1947]~E(x19471,x19472)+E(f468(x19473,x19474,x19471,x19475,x19476),f468(x19473,x19474,x19472,x19475,x19476))
% 157.55/157.24 [1948]~E(x19481,x19482)+E(f468(x19483,x19484,x19485,x19481,x19486),f468(x19483,x19484,x19485,x19482,x19486))
% 157.55/157.24 [1949]~E(x19491,x19492)+E(f468(x19493,x19494,x19495,x19496,x19491),f468(x19493,x19494,x19495,x19496,x19492))
% 157.55/157.24 [1950]~E(x19501,x19502)+E(f561(x19501,x19503,x19504),f561(x19502,x19503,x19504))
% 157.55/157.24 [1951]~E(x19511,x19512)+E(f561(x19513,x19511,x19514),f561(x19513,x19512,x19514))
% 157.55/157.24 [1952]~E(x19521,x19522)+E(f561(x19523,x19524,x19521),f561(x19523,x19524,x19522))
% 157.55/157.24 [1953]~E(x19531,x19532)+E(f759(x19531,x19533,x19534),f759(x19532,x19533,x19534))
% 157.55/157.24 [1954]~E(x19541,x19542)+E(f759(x19543,x19541,x19544),f759(x19543,x19542,x19544))
% 157.55/157.24 [1955]~E(x19551,x19552)+E(f759(x19553,x19554,x19551),f759(x19553,x19554,x19552))
% 157.55/157.24 [1956]~E(x19561,x19562)+E(f202(x19561,x19563),f202(x19562,x19563))
% 157.55/157.24 [1957]~E(x19571,x19572)+E(f202(x19573,x19571),f202(x19573,x19572))
% 157.55/157.24 [1958]~E(x19581,x19582)+E(f270(x19581,x19583,x19584,x19585),f270(x19582,x19583,x19584,x19585))
% 157.55/157.24 [1959]~E(x19591,x19592)+E(f270(x19593,x19591,x19594,x19595),f270(x19593,x19592,x19594,x19595))
% 157.55/157.24 [1960]~E(x19601,x19602)+E(f270(x19603,x19604,x19601,x19605),f270(x19603,x19604,x19602,x19605))
% 157.55/157.24 [1961]~E(x19611,x19612)+E(f270(x19613,x19614,x19615,x19611),f270(x19613,x19614,x19615,x19612))
% 157.55/157.24 [1962]~E(x19621,x19622)+E(f588(x19621,x19623,x19624,x19625,x19626,x19627),f588(x19622,x19623,x19624,x19625,x19626,x19627))
% 157.55/157.24 [1963]~E(x19631,x19632)+E(f588(x19633,x19631,x19634,x19635,x19636,x19637),f588(x19633,x19632,x19634,x19635,x19636,x19637))
% 157.55/157.24 [1964]~E(x19641,x19642)+E(f588(x19643,x19644,x19641,x19645,x19646,x19647),f588(x19643,x19644,x19642,x19645,x19646,x19647))
% 157.55/157.24 [1965]~E(x19651,x19652)+E(f588(x19653,x19654,x19655,x19651,x19656,x19657),f588(x19653,x19654,x19655,x19652,x19656,x19657))
% 157.55/157.24 [1966]~E(x19661,x19662)+E(f588(x19663,x19664,x19665,x19666,x19661,x19667),f588(x19663,x19664,x19665,x19666,x19662,x19667))
% 157.55/157.24 [1967]~E(x19671,x19672)+E(f588(x19673,x19674,x19675,x19676,x19677,x19671),f588(x19673,x19674,x19675,x19676,x19677,x19672))
% 157.55/157.24 [1968]~E(x19681,x19682)+E(f702(x19681,x19683),f702(x19682,x19683))
% 157.55/157.24 [1969]~E(x19691,x19692)+E(f702(x19693,x19691),f702(x19693,x19692))
% 157.55/157.24 [1970]~E(x19701,x19702)+E(f68(x19701,x19703,x19704),f68(x19702,x19703,x19704))
% 157.55/157.24 [1971]~E(x19711,x19712)+E(f68(x19713,x19711,x19714),f68(x19713,x19712,x19714))
% 157.55/157.24 [1972]~E(x19721,x19722)+E(f68(x19723,x19724,x19721),f68(x19723,x19724,x19722))
% 157.55/157.24 [1973]~E(x19731,x19732)+E(f761(x19731,x19733,x19734),f761(x19732,x19733,x19734))
% 157.55/157.24 [1974]~E(x19741,x19742)+E(f761(x19743,x19741,x19744),f761(x19743,x19742,x19744))
% 157.55/157.24 [1975]~E(x19751,x19752)+E(f761(x19753,x19754,x19751),f761(x19753,x19754,x19752))
% 157.55/157.24 [1976]~E(x19761,x19762)+E(f517(x19761,x19763,x19764,x19765),f517(x19762,x19763,x19764,x19765))
% 157.55/157.24 [1977]~E(x19771,x19772)+E(f517(x19773,x19771,x19774,x19775),f517(x19773,x19772,x19774,x19775))
% 157.55/157.24 [1978]~E(x19781,x19782)+E(f517(x19783,x19784,x19781,x19785),f517(x19783,x19784,x19782,x19785))
% 157.55/157.24 [1979]~E(x19791,x19792)+E(f517(x19793,x19794,x19795,x19791),f517(x19793,x19794,x19795,x19792))
% 157.55/157.24 [1980]~E(x19801,x19802)+E(f342(x19801,x19803),f342(x19802,x19803))
% 157.55/157.24 [1981]~E(x19811,x19812)+E(f342(x19813,x19811),f342(x19813,x19812))
% 157.55/157.24 [1982]~E(x19821,x19822)+E(f586(x19821,x19823,x19824,x19825,x19826,x19827),f586(x19822,x19823,x19824,x19825,x19826,x19827))
% 157.55/157.24 [1983]~E(x19831,x19832)+E(f586(x19833,x19831,x19834,x19835,x19836,x19837),f586(x19833,x19832,x19834,x19835,x19836,x19837))
% 157.55/157.24 [1984]~E(x19841,x19842)+E(f586(x19843,x19844,x19841,x19845,x19846,x19847),f586(x19843,x19844,x19842,x19845,x19846,x19847))
% 157.55/157.24 [1985]~E(x19851,x19852)+E(f586(x19853,x19854,x19855,x19851,x19856,x19857),f586(x19853,x19854,x19855,x19852,x19856,x19857))
% 157.55/157.24 [1986]~E(x19861,x19862)+E(f586(x19863,x19864,x19865,x19866,x19861,x19867),f586(x19863,x19864,x19865,x19866,x19862,x19867))
% 157.55/157.24 [1987]~E(x19871,x19872)+E(f586(x19873,x19874,x19875,x19876,x19877,x19871),f586(x19873,x19874,x19875,x19876,x19877,x19872))
% 157.55/157.24 [1988]~E(x19881,x19882)+E(f583(x19881,x19883,x19884,x19885,x19886,x19887),f583(x19882,x19883,x19884,x19885,x19886,x19887))
% 157.55/157.24 [1989]~E(x19891,x19892)+E(f583(x19893,x19891,x19894,x19895,x19896,x19897),f583(x19893,x19892,x19894,x19895,x19896,x19897))
% 157.55/157.24 [1990]~E(x19901,x19902)+E(f583(x19903,x19904,x19901,x19905,x19906,x19907),f583(x19903,x19904,x19902,x19905,x19906,x19907))
% 157.55/157.24 [1991]~E(x19911,x19912)+E(f583(x19913,x19914,x19915,x19911,x19916,x19917),f583(x19913,x19914,x19915,x19912,x19916,x19917))
% 157.55/157.24 [1992]~E(x19921,x19922)+E(f583(x19923,x19924,x19925,x19926,x19921,x19927),f583(x19923,x19924,x19925,x19926,x19922,x19927))
% 157.55/157.24 [1993]~E(x19931,x19932)+E(f583(x19933,x19934,x19935,x19936,x19937,x19931),f583(x19933,x19934,x19935,x19936,x19937,x19932))
% 157.55/157.24 [1994]~E(x19941,x19942)+E(f131(x19941,x19943,x19944,x19945),f131(x19942,x19943,x19944,x19945))
% 157.55/157.24 [1995]~E(x19951,x19952)+E(f131(x19953,x19951,x19954,x19955),f131(x19953,x19952,x19954,x19955))
% 157.55/157.24 [1996]~E(x19961,x19962)+E(f131(x19963,x19964,x19961,x19965),f131(x19963,x19964,x19962,x19965))
% 157.55/157.24 [1997]~E(x19971,x19972)+E(f131(x19973,x19974,x19975,x19971),f131(x19973,x19974,x19975,x19972))
% 157.55/157.24 [1998]~E(x19981,x19982)+E(f340(x19981,x19983),f340(x19982,x19983))
% 157.55/157.24 [1999]~E(x19991,x19992)+E(f340(x19993,x19991),f340(x19993,x19992))
% 157.55/157.24 [2000]~E(x20001,x20002)+E(f386(x20001,x20003,x20004),f386(x20002,x20003,x20004))
% 157.55/157.24 [2001]~E(x20011,x20012)+E(f386(x20013,x20011,x20014),f386(x20013,x20012,x20014))
% 157.55/157.24 [2002]~E(x20021,x20022)+E(f386(x20023,x20024,x20021),f386(x20023,x20024,x20022))
% 157.55/157.24 [2003]~E(x20031,x20032)+E(f520(x20031,x20033,x20034,x20035),f520(x20032,x20033,x20034,x20035))
% 157.55/157.24 [2004]~E(x20041,x20042)+E(f520(x20043,x20041,x20044,x20045),f520(x20043,x20042,x20044,x20045))
% 157.55/157.24 [2005]~E(x20051,x20052)+E(f520(x20053,x20054,x20051,x20055),f520(x20053,x20054,x20052,x20055))
% 157.55/157.24 [2006]~E(x20061,x20062)+E(f520(x20063,x20064,x20065,x20061),f520(x20063,x20064,x20065,x20062))
% 157.55/157.24 [2007]~E(x20071,x20072)+E(f598(x20071,x20073,x20074,x20075),f598(x20072,x20073,x20074,x20075))
% 157.55/157.24 [2008]~E(x20081,x20082)+E(f598(x20083,x20081,x20084,x20085),f598(x20083,x20082,x20084,x20085))
% 157.55/157.24 [2009]~E(x20091,x20092)+E(f598(x20093,x20094,x20091,x20095),f598(x20093,x20094,x20092,x20095))
% 157.55/157.24 [2010]~E(x20101,x20102)+E(f598(x20103,x20104,x20105,x20101),f598(x20103,x20104,x20105,x20102))
% 157.55/157.24 [2011]~E(x20111,x20112)+E(f539(x20111,x20113,x20114,x20115,x20116),f539(x20112,x20113,x20114,x20115,x20116))
% 157.55/157.24 [2012]~E(x20121,x20122)+E(f539(x20123,x20121,x20124,x20125,x20126),f539(x20123,x20122,x20124,x20125,x20126))
% 157.55/157.24 [2013]~E(x20131,x20132)+E(f539(x20133,x20134,x20131,x20135,x20136),f539(x20133,x20134,x20132,x20135,x20136))
% 157.55/157.24 [2014]~E(x20141,x20142)+E(f539(x20143,x20144,x20145,x20141,x20146),f539(x20143,x20144,x20145,x20142,x20146))
% 157.55/157.24 [2015]~E(x20151,x20152)+E(f539(x20153,x20154,x20155,x20156,x20151),f539(x20153,x20154,x20155,x20156,x20152))
% 157.55/157.24 [2016]~E(x20161,x20162)+E(f417(x20161,x20163),f417(x20162,x20163))
% 157.55/157.24 [2017]~E(x20171,x20172)+E(f417(x20173,x20171),f417(x20173,x20172))
% 157.55/157.24 [2018]~E(x20181,x20182)+E(f497(x20181,x20183,x20184),f497(x20182,x20183,x20184))
% 157.55/157.24 [2019]~E(x20191,x20192)+E(f497(x20193,x20191,x20194),f497(x20193,x20192,x20194))
% 157.55/157.24 [2020]~E(x20201,x20202)+E(f497(x20203,x20204,x20201),f497(x20203,x20204,x20202))
% 157.55/157.24 [2021]~E(x20211,x20212)+E(f866(x20211,x20213,x20214,x20215,x20216,x20217),f866(x20212,x20213,x20214,x20215,x20216,x20217))
% 157.55/157.24 [2022]~E(x20221,x20222)+E(f866(x20223,x20221,x20224,x20225,x20226,x20227),f866(x20223,x20222,x20224,x20225,x20226,x20227))
% 157.55/157.24 [2023]~E(x20231,x20232)+E(f866(x20233,x20234,x20231,x20235,x20236,x20237),f866(x20233,x20234,x20232,x20235,x20236,x20237))
% 157.55/157.24 [2024]~E(x20241,x20242)+E(f866(x20243,x20244,x20245,x20241,x20246,x20247),f866(x20243,x20244,x20245,x20242,x20246,x20247))
% 157.55/157.24 [2025]~E(x20251,x20252)+E(f866(x20253,x20254,x20255,x20256,x20251,x20257),f866(x20253,x20254,x20255,x20256,x20252,x20257))
% 157.55/157.24 [2026]~E(x20261,x20262)+E(f866(x20263,x20264,x20265,x20266,x20267,x20261),f866(x20263,x20264,x20265,x20266,x20267,x20262))
% 157.55/157.24 [2027]~E(x20271,x20272)+E(f848(x20271,x20273,x20274,x20275,x20276,x20277),f848(x20272,x20273,x20274,x20275,x20276,x20277))
% 157.55/157.24 [2028]~E(x20281,x20282)+E(f848(x20283,x20281,x20284,x20285,x20286,x20287),f848(x20283,x20282,x20284,x20285,x20286,x20287))
% 157.55/157.24 [2029]~E(x20291,x20292)+E(f848(x20293,x20294,x20291,x20295,x20296,x20297),f848(x20293,x20294,x20292,x20295,x20296,x20297))
% 157.55/157.24 [2030]~E(x20301,x20302)+E(f848(x20303,x20304,x20305,x20301,x20306,x20307),f848(x20303,x20304,x20305,x20302,x20306,x20307))
% 157.55/157.24 [2031]~E(x20311,x20312)+E(f848(x20313,x20314,x20315,x20316,x20311,x20317),f848(x20313,x20314,x20315,x20316,x20312,x20317))
% 157.55/157.24 [2032]~E(x20321,x20322)+E(f848(x20323,x20324,x20325,x20326,x20327,x20321),f848(x20323,x20324,x20325,x20326,x20327,x20322))
% 157.55/157.24 [2033]~E(x20331,x20332)+E(f689(x20331,x20333,x20334,x20335,x20336),f689(x20332,x20333,x20334,x20335,x20336))
% 157.55/157.24 [2034]~E(x20341,x20342)+E(f689(x20343,x20341,x20344,x20345,x20346),f689(x20343,x20342,x20344,x20345,x20346))
% 157.55/157.24 [2035]~E(x20351,x20352)+E(f689(x20353,x20354,x20351,x20355,x20356),f689(x20353,x20354,x20352,x20355,x20356))
% 157.55/157.24 [2036]~E(x20361,x20362)+E(f689(x20363,x20364,x20365,x20361,x20366),f689(x20363,x20364,x20365,x20362,x20366))
% 157.55/157.24 [2037]~E(x20371,x20372)+E(f689(x20373,x20374,x20375,x20376,x20371),f689(x20373,x20374,x20375,x20376,x20372))
% 157.55/157.24 [2038]~E(x20381,x20382)+E(f669(x20381,x20383,x20384),f669(x20382,x20383,x20384))
% 157.55/157.24 [2039]~E(x20391,x20392)+E(f669(x20393,x20391,x20394),f669(x20393,x20392,x20394))
% 157.55/157.24 [2040]~E(x20401,x20402)+E(f669(x20403,x20404,x20401),f669(x20403,x20404,x20402))
% 157.55/157.24 [2041]~E(x20411,x20412)+E(f349(x20411,x20413,x20414,x20415,x20416),f349(x20412,x20413,x20414,x20415,x20416))
% 157.55/157.24 [2042]~E(x20421,x20422)+E(f349(x20423,x20421,x20424,x20425,x20426),f349(x20423,x20422,x20424,x20425,x20426))
% 157.55/157.24 [2043]~E(x20431,x20432)+E(f349(x20433,x20434,x20431,x20435,x20436),f349(x20433,x20434,x20432,x20435,x20436))
% 157.55/157.24 [2044]~E(x20441,x20442)+E(f349(x20443,x20444,x20445,x20441,x20446),f349(x20443,x20444,x20445,x20442,x20446))
% 157.55/157.24 [2045]~E(x20451,x20452)+E(f349(x20453,x20454,x20455,x20456,x20451),f349(x20453,x20454,x20455,x20456,x20452))
% 157.55/157.24 [2046]~E(x20461,x20462)+E(f789(x20461,x20463,x20464,x20465),f789(x20462,x20463,x20464,x20465))
% 157.55/157.24 [2047]~E(x20471,x20472)+E(f789(x20473,x20471,x20474,x20475),f789(x20473,x20472,x20474,x20475))
% 157.55/157.24 [2048]~E(x20481,x20482)+E(f789(x20483,x20484,x20481,x20485),f789(x20483,x20484,x20482,x20485))
% 157.55/157.24 [2049]~E(x20491,x20492)+E(f789(x20493,x20494,x20495,x20491),f789(x20493,x20494,x20495,x20492))
% 157.55/157.24 [2050]~E(x20501,x20502)+E(f338(x20501),f338(x20502))
% 157.55/157.24 [2051]~E(x20511,x20512)+E(f799(x20511,x20513),f799(x20512,x20513))
% 157.55/157.24 [2052]~E(x20521,x20522)+E(f799(x20523,x20521),f799(x20523,x20522))
% 157.55/157.24 [2053]~E(x20531,x20532)+E(f367(x20531,x20533,x20534,x20535),f367(x20532,x20533,x20534,x20535))
% 157.55/157.24 [2054]~E(x20541,x20542)+E(f367(x20543,x20541,x20544,x20545),f367(x20543,x20542,x20544,x20545))
% 157.55/157.24 [2055]~E(x20551,x20552)+E(f367(x20553,x20554,x20551,x20555),f367(x20553,x20554,x20552,x20555))
% 157.55/157.24 [2056]~E(x20561,x20562)+E(f367(x20563,x20564,x20565,x20561),f367(x20563,x20564,x20565,x20562))
% 157.55/157.24 [2057]~E(x20571,x20572)+E(f409(x20571,x20573,x20574,x20575,x20576,x20577),f409(x20572,x20573,x20574,x20575,x20576,x20577))
% 157.55/157.24 [2058]~E(x20581,x20582)+E(f409(x20583,x20581,x20584,x20585,x20586,x20587),f409(x20583,x20582,x20584,x20585,x20586,x20587))
% 157.55/157.24 [2059]~E(x20591,x20592)+E(f409(x20593,x20594,x20591,x20595,x20596,x20597),f409(x20593,x20594,x20592,x20595,x20596,x20597))
% 157.55/157.24 [2060]~E(x20601,x20602)+E(f409(x20603,x20604,x20605,x20601,x20606,x20607),f409(x20603,x20604,x20605,x20602,x20606,x20607))
% 157.55/157.24 [2061]~E(x20611,x20612)+E(f409(x20613,x20614,x20615,x20616,x20611,x20617),f409(x20613,x20614,x20615,x20616,x20612,x20617))
% 157.55/157.24 [2062]~E(x20621,x20622)+E(f409(x20623,x20624,x20625,x20626,x20627,x20621),f409(x20623,x20624,x20625,x20626,x20627,x20622))
% 157.55/157.24 [2063]~E(x20631,x20632)+E(f443(x20631,x20633,x20634,x20635,x20636,x20637,x20638),f443(x20632,x20633,x20634,x20635,x20636,x20637,x20638))
% 157.55/157.24 [2064]~E(x20641,x20642)+E(f443(x20643,x20641,x20644,x20645,x20646,x20647,x20648),f443(x20643,x20642,x20644,x20645,x20646,x20647,x20648))
% 157.55/157.24 [2065]~E(x20651,x20652)+E(f443(x20653,x20654,x20651,x20655,x20656,x20657,x20658),f443(x20653,x20654,x20652,x20655,x20656,x20657,x20658))
% 157.55/157.24 [2066]~E(x20661,x20662)+E(f443(x20663,x20664,x20665,x20661,x20666,x20667,x20668),f443(x20663,x20664,x20665,x20662,x20666,x20667,x20668))
% 157.55/157.24 [2067]~E(x20671,x20672)+E(f443(x20673,x20674,x20675,x20676,x20671,x20677,x20678),f443(x20673,x20674,x20675,x20676,x20672,x20677,x20678))
% 157.55/157.24 [2068]~E(x20681,x20682)+E(f443(x20683,x20684,x20685,x20686,x20687,x20681,x20688),f443(x20683,x20684,x20685,x20686,x20687,x20682,x20688))
% 157.55/157.24 [2069]~E(x20691,x20692)+E(f443(x20693,x20694,x20695,x20696,x20697,x20698,x20691),f443(x20693,x20694,x20695,x20696,x20697,x20698,x20692))
% 157.55/157.24 [2070]~E(x20701,x20702)+E(f752(x20701,x20703,x20704),f752(x20702,x20703,x20704))
% 157.55/157.24 [2071]~E(x20711,x20712)+E(f752(x20713,x20711,x20714),f752(x20713,x20712,x20714))
% 157.55/157.24 [2072]~E(x20721,x20722)+E(f752(x20723,x20724,x20721),f752(x20723,x20724,x20722))
% 157.55/157.24 [2073]~E(x20731,x20732)+E(f859(x20731,x20733,x20734,x20735),f859(x20732,x20733,x20734,x20735))
% 157.55/157.24 [2074]~E(x20741,x20742)+E(f859(x20743,x20741,x20744,x20745),f859(x20743,x20742,x20744,x20745))
% 157.55/157.24 [2075]~E(x20751,x20752)+E(f859(x20753,x20754,x20751,x20755),f859(x20753,x20754,x20752,x20755))
% 157.55/157.24 [2076]~E(x20761,x20762)+E(f859(x20763,x20764,x20765,x20761),f859(x20763,x20764,x20765,x20762))
% 157.55/157.24 [2077]~E(x20771,x20772)+E(f835(x20771,x20773,x20774,x20775,x20776,x20777,x20778,x20779),f835(x20772,x20773,x20774,x20775,x20776,x20777,x20778,x20779))
% 157.55/157.24 [2078]~E(x20781,x20782)+E(f835(x20783,x20781,x20784,x20785,x20786,x20787,x20788,x20789),f835(x20783,x20782,x20784,x20785,x20786,x20787,x20788,x20789))
% 157.55/157.24 [2079]~E(x20791,x20792)+E(f835(x20793,x20794,x20791,x20795,x20796,x20797,x20798,x20799),f835(x20793,x20794,x20792,x20795,x20796,x20797,x20798,x20799))
% 157.55/157.24 [2080]~E(x20801,x20802)+E(f835(x20803,x20804,x20805,x20801,x20806,x20807,x20808,x20809),f835(x20803,x20804,x20805,x20802,x20806,x20807,x20808,x20809))
% 157.55/157.24 [2081]~E(x20811,x20812)+E(f835(x20813,x20814,x20815,x20816,x20811,x20817,x20818,x20819),f835(x20813,x20814,x20815,x20816,x20812,x20817,x20818,x20819))
% 157.55/157.24 [2082]~E(x20821,x20822)+E(f835(x20823,x20824,x20825,x20826,x20827,x20821,x20828,x20829),f835(x20823,x20824,x20825,x20826,x20827,x20822,x20828,x20829))
% 157.55/157.24 [2083]~E(x20831,x20832)+E(f835(x20833,x20834,x20835,x20836,x20837,x20838,x20831,x20839),f835(x20833,x20834,x20835,x20836,x20837,x20838,x20832,x20839))
% 157.55/157.24 [2084]~E(x20841,x20842)+E(f835(x20843,x20844,x20845,x20846,x20847,x20848,x20849,x20841),f835(x20843,x20844,x20845,x20846,x20847,x20848,x20849,x20842))
% 157.55/157.24 [2085]~E(x20851,x20852)+E(f506(x20851,x20853,x20854,x20855),f506(x20852,x20853,x20854,x20855))
% 157.55/157.24 [2086]~E(x20861,x20862)+E(f506(x20863,x20861,x20864,x20865),f506(x20863,x20862,x20864,x20865))
% 157.55/157.24 [2087]~E(x20871,x20872)+E(f506(x20873,x20874,x20871,x20875),f506(x20873,x20874,x20872,x20875))
% 157.55/157.24 [2088]~E(x20881,x20882)+E(f506(x20883,x20884,x20885,x20881),f506(x20883,x20884,x20885,x20882))
% 157.55/157.24 [2089]~E(x20891,x20892)+E(f888(x20891,x20893,x20894,x20895,x20896),f888(x20892,x20893,x20894,x20895,x20896))
% 157.55/157.24 [2090]~E(x20901,x20902)+E(f888(x20903,x20901,x20904,x20905,x20906),f888(x20903,x20902,x20904,x20905,x20906))
% 157.55/157.24 [2091]~E(x20911,x20912)+E(f888(x20913,x20914,x20911,x20915,x20916),f888(x20913,x20914,x20912,x20915,x20916))
% 157.55/157.24 [2092]~E(x20921,x20922)+E(f888(x20923,x20924,x20925,x20921,x20926),f888(x20923,x20924,x20925,x20922,x20926))
% 157.55/157.24 [2093]~E(x20931,x20932)+E(f888(x20933,x20934,x20935,x20936,x20931),f888(x20933,x20934,x20935,x20936,x20932))
% 157.55/157.24 [2094]~E(x20941,x20942)+E(f355(x20941,x20943,x20944),f355(x20942,x20943,x20944))
% 157.55/157.24 [2095]~E(x20951,x20952)+E(f355(x20953,x20951,x20954),f355(x20953,x20952,x20954))
% 157.55/157.24 [2096]~E(x20961,x20962)+E(f355(x20963,x20964,x20961),f355(x20963,x20964,x20962))
% 157.55/157.24 [2097]~E(x20971,x20972)+E(f656(x20971,x20973,x20974),f656(x20972,x20973,x20974))
% 157.55/157.24 [2098]~E(x20981,x20982)+E(f656(x20983,x20981,x20984),f656(x20983,x20982,x20984))
% 157.55/157.24 [2099]~E(x20991,x20992)+E(f656(x20993,x20994,x20991),f656(x20993,x20994,x20992))
% 157.55/157.24 [2100]~E(x21001,x21002)+E(f783(x21001,x21003,x21004,x21005,x21006,x21007,x21008),f783(x21002,x21003,x21004,x21005,x21006,x21007,x21008))
% 157.55/157.24 [2101]~E(x21011,x21012)+E(f783(x21013,x21011,x21014,x21015,x21016,x21017,x21018),f783(x21013,x21012,x21014,x21015,x21016,x21017,x21018))
% 157.55/157.24 [2102]~E(x21021,x21022)+E(f783(x21023,x21024,x21021,x21025,x21026,x21027,x21028),f783(x21023,x21024,x21022,x21025,x21026,x21027,x21028))
% 157.55/157.24 [2103]~E(x21031,x21032)+E(f783(x21033,x21034,x21035,x21031,x21036,x21037,x21038),f783(x21033,x21034,x21035,x21032,x21036,x21037,x21038))
% 157.55/157.24 [2104]~E(x21041,x21042)+E(f783(x21043,x21044,x21045,x21046,x21041,x21047,x21048),f783(x21043,x21044,x21045,x21046,x21042,x21047,x21048))
% 157.55/157.24 [2105]~E(x21051,x21052)+E(f783(x21053,x21054,x21055,x21056,x21057,x21051,x21058),f783(x21053,x21054,x21055,x21056,x21057,x21052,x21058))
% 157.55/157.24 [2106]~E(x21061,x21062)+E(f783(x21063,x21064,x21065,x21066,x21067,x21068,x21061),f783(x21063,x21064,x21065,x21066,x21067,x21068,x21062))
% 157.55/157.24 [2107]~E(x21071,x21072)+E(f829(x21071,x21073,x21074,x21075,x21076),f829(x21072,x21073,x21074,x21075,x21076))
% 157.55/157.24 [2108]~E(x21081,x21082)+E(f829(x21083,x21081,x21084,x21085,x21086),f829(x21083,x21082,x21084,x21085,x21086))
% 157.55/157.24 [2109]~E(x21091,x21092)+E(f829(x21093,x21094,x21091,x21095,x21096),f829(x21093,x21094,x21092,x21095,x21096))
% 157.55/157.24 [2110]~E(x21101,x21102)+E(f829(x21103,x21104,x21105,x21101,x21106),f829(x21103,x21104,x21105,x21102,x21106))
% 157.55/157.24 [2111]~E(x21111,x21112)+E(f829(x21113,x21114,x21115,x21116,x21111),f829(x21113,x21114,x21115,x21116,x21112))
% 157.55/157.24 [2112]~E(x21121,x21122)+E(f769(x21121,x21123,x21124,x21125),f769(x21122,x21123,x21124,x21125))
% 157.55/157.24 [2113]~E(x21131,x21132)+E(f769(x21133,x21131,x21134,x21135),f769(x21133,x21132,x21134,x21135))
% 157.55/157.24 [2114]~E(x21141,x21142)+E(f769(x21143,x21144,x21141,x21145),f769(x21143,x21144,x21142,x21145))
% 157.55/157.24 [2115]~E(x21151,x21152)+E(f769(x21153,x21154,x21155,x21151),f769(x21153,x21154,x21155,x21152))
% 157.55/157.24 [2116]~E(x21161,x21162)+E(f211(x21161,x21163,x21164,x21165,x21166,x21167,x21168),f211(x21162,x21163,x21164,x21165,x21166,x21167,x21168))
% 157.55/157.24 [2117]~E(x21171,x21172)+E(f211(x21173,x21171,x21174,x21175,x21176,x21177,x21178),f211(x21173,x21172,x21174,x21175,x21176,x21177,x21178))
% 157.55/157.24 [2118]~E(x21181,x21182)+E(f211(x21183,x21184,x21181,x21185,x21186,x21187,x21188),f211(x21183,x21184,x21182,x21185,x21186,x21187,x21188))
% 157.55/157.24 [2119]~E(x21191,x21192)+E(f211(x21193,x21194,x21195,x21191,x21196,x21197,x21198),f211(x21193,x21194,x21195,x21192,x21196,x21197,x21198))
% 157.55/157.24 [2120]~E(x21201,x21202)+E(f211(x21203,x21204,x21205,x21206,x21201,x21207,x21208),f211(x21203,x21204,x21205,x21206,x21202,x21207,x21208))
% 157.55/157.24 [2121]~E(x21211,x21212)+E(f211(x21213,x21214,x21215,x21216,x21217,x21211,x21218),f211(x21213,x21214,x21215,x21216,x21217,x21212,x21218))
% 157.55/157.24 [2122]~E(x21221,x21222)+E(f211(x21223,x21224,x21225,x21226,x21227,x21228,x21221),f211(x21223,x21224,x21225,x21226,x21227,x21228,x21222))
% 157.55/157.24 [2123]~E(x21231,x21232)+E(f615(x21231,x21233,x21234),f615(x21232,x21233,x21234))
% 157.55/157.24 [2124]~E(x21241,x21242)+E(f615(x21243,x21241,x21244),f615(x21243,x21242,x21244))
% 157.55/157.24 [2125]~E(x21251,x21252)+E(f615(x21253,x21254,x21251),f615(x21253,x21254,x21252))
% 157.55/157.24 [2126]~E(x21261,x21262)+E(f580(x21261,x21263,x21264),f580(x21262,x21263,x21264))
% 157.55/157.24 [2127]~E(x21271,x21272)+E(f580(x21273,x21271,x21274),f580(x21273,x21272,x21274))
% 157.55/157.24 [2128]~E(x21281,x21282)+E(f580(x21283,x21284,x21281),f580(x21283,x21284,x21282))
% 157.55/157.24 [2129]~E(x21291,x21292)+E(f135(x21291),f135(x21292))
% 157.55/157.24 [2130]~E(x21301,x21302)+E(f733(x21301,x21303,x21304),f733(x21302,x21303,x21304))
% 157.55/157.24 [2131]~E(x21311,x21312)+E(f733(x21313,x21311,x21314),f733(x21313,x21312,x21314))
% 157.55/157.24 [2132]~E(x21321,x21322)+E(f733(x21323,x21324,x21321),f733(x21323,x21324,x21322))
% 157.55/157.24 [2133]~E(x21331,x21332)+E(f572(x21331,x21333,x21334,x21335),f572(x21332,x21333,x21334,x21335))
% 157.55/157.24 [2134]~E(x21341,x21342)+E(f572(x21343,x21341,x21344,x21345),f572(x21343,x21342,x21344,x21345))
% 157.55/157.24 [2135]~E(x21351,x21352)+E(f572(x21353,x21354,x21351,x21355),f572(x21353,x21354,x21352,x21355))
% 157.55/157.24 [2136]~E(x21361,x21362)+E(f572(x21363,x21364,x21365,x21361),f572(x21363,x21364,x21365,x21362))
% 157.55/157.24 [2137]~E(x21371,x21372)+E(f117(x21371,x21373,x21374),f117(x21372,x21373,x21374))
% 157.55/157.24 [2138]~E(x21381,x21382)+E(f117(x21383,x21381,x21384),f117(x21383,x21382,x21384))
% 157.55/157.24 [2139]~E(x21391,x21392)+E(f117(x21393,x21394,x21391),f117(x21393,x21394,x21392))
% 157.55/157.24 [2140]~E(x21401,x21402)+E(f698(x21401,x21403,x21404),f698(x21402,x21403,x21404))
% 157.55/157.24 [2141]~E(x21411,x21412)+E(f698(x21413,x21411,x21414),f698(x21413,x21412,x21414))
% 157.55/157.24 [2142]~E(x21421,x21422)+E(f698(x21423,x21424,x21421),f698(x21423,x21424,x21422))
% 157.55/157.24 [2143]~E(x21431,x21432)+E(f470(x21431,x21433,x21434,x21435),f470(x21432,x21433,x21434,x21435))
% 157.55/157.24 [2144]~E(x21441,x21442)+E(f470(x21443,x21441,x21444,x21445),f470(x21443,x21442,x21444,x21445))
% 157.55/157.24 [2145]~E(x21451,x21452)+E(f470(x21453,x21454,x21451,x21455),f470(x21453,x21454,x21452,x21455))
% 157.55/157.24 [2146]~E(x21461,x21462)+E(f470(x21463,x21464,x21465,x21461),f470(x21463,x21464,x21465,x21462))
% 157.55/157.24 [2147]~E(x21471,x21472)+E(f609(x21471,x21473,x21474),f609(x21472,x21473,x21474))
% 157.55/157.24 [2148]~E(x21481,x21482)+E(f609(x21483,x21481,x21484),f609(x21483,x21482,x21484))
% 157.55/157.24 [2149]~E(x21491,x21492)+E(f609(x21493,x21494,x21491),f609(x21493,x21494,x21492))
% 157.55/157.24 [2150]~E(x21501,x21502)+E(f195(x21501,x21503,x21504,x21505),f195(x21502,x21503,x21504,x21505))
% 157.55/157.24 [2151]~E(x21511,x21512)+E(f195(x21513,x21511,x21514,x21515),f195(x21513,x21512,x21514,x21515))
% 157.55/157.24 [2152]~E(x21521,x21522)+E(f195(x21523,x21524,x21521,x21525),f195(x21523,x21524,x21522,x21525))
% 157.55/157.24 [2153]~E(x21531,x21532)+E(f195(x21533,x21534,x21535,x21531),f195(x21533,x21534,x21535,x21532))
% 157.55/157.24 [2154]~E(x21541,x21542)+E(f390(x21541,x21543,x21544),f390(x21542,x21543,x21544))
% 157.55/157.24 [2155]~E(x21551,x21552)+E(f390(x21553,x21551,x21554),f390(x21553,x21552,x21554))
% 157.55/157.24 [2156]~E(x21561,x21562)+E(f390(x21563,x21564,x21561),f390(x21563,x21564,x21562))
% 157.55/157.24 [2157]~E(x21571,x21572)+E(f360(x21571,x21573,x21574),f360(x21572,x21573,x21574))
% 157.55/157.24 [2158]~E(x21581,x21582)+E(f360(x21583,x21581,x21584),f360(x21583,x21582,x21584))
% 157.55/157.24 [2159]~E(x21591,x21592)+E(f360(x21593,x21594,x21591),f360(x21593,x21594,x21592))
% 157.55/157.24 [2160]~E(x21601,x21602)+E(f397(x21601,x21603,x21604),f397(x21602,x21603,x21604))
% 157.55/157.24 [2161]~E(x21611,x21612)+E(f397(x21613,x21611,x21614),f397(x21613,x21612,x21614))
% 157.55/157.24 [2162]~E(x21621,x21622)+E(f397(x21623,x21624,x21621),f397(x21623,x21624,x21622))
% 157.55/157.24 [2163]~E(x21631,x21632)+E(f562(x21631,x21633,x21634,x21635),f562(x21632,x21633,x21634,x21635))
% 157.55/157.24 [2164]~E(x21641,x21642)+E(f562(x21643,x21641,x21644,x21645),f562(x21643,x21642,x21644,x21645))
% 157.55/157.24 [2165]~E(x21651,x21652)+E(f562(x21653,x21654,x21651,x21655),f562(x21653,x21654,x21652,x21655))
% 157.55/157.24 [2166]~E(x21661,x21662)+E(f562(x21663,x21664,x21665,x21661),f562(x21663,x21664,x21665,x21662))
% 157.55/157.24 [2167]~E(x21671,x21672)+E(f668(x21671,x21673,x21674),f668(x21672,x21673,x21674))
% 157.55/157.24 [2168]~E(x21681,x21682)+E(f668(x21683,x21681,x21684),f668(x21683,x21682,x21684))
% 157.55/157.24 [2169]~E(x21691,x21692)+E(f668(x21693,x21694,x21691),f668(x21693,x21694,x21692))
% 157.55/157.24 [2170]~E(x21701,x21702)+E(f571(x21701,x21703,x21704,x21705),f571(x21702,x21703,x21704,x21705))
% 157.55/157.24 [2171]~E(x21711,x21712)+E(f571(x21713,x21711,x21714,x21715),f571(x21713,x21712,x21714,x21715))
% 157.55/157.24 [2172]~E(x21721,x21722)+E(f571(x21723,x21724,x21721,x21725),f571(x21723,x21724,x21722,x21725))
% 157.55/157.24 [2173]~E(x21731,x21732)+E(f571(x21733,x21734,x21735,x21731),f571(x21733,x21734,x21735,x21732))
% 157.55/157.24 [2174]~E(x21741,x21742)+E(f812(x21741,x21743,x21744),f812(x21742,x21743,x21744))
% 157.55/157.24 [2175]~E(x21751,x21752)+E(f812(x21753,x21751,x21754),f812(x21753,x21752,x21754))
% 157.55/157.24 [2176]~E(x21761,x21762)+E(f812(x21763,x21764,x21761),f812(x21763,x21764,x21762))
% 157.55/157.24 [2177]~E(x21771,x21772)+E(f146(x21771,x21773),f146(x21772,x21773))
% 157.55/157.24 [2178]~E(x21781,x21782)+E(f146(x21783,x21781),f146(x21783,x21782))
% 157.55/157.24 [2179]~E(x21791,x21792)+E(f612(x21791,x21793),f612(x21792,x21793))
% 157.55/157.24 [2180]~E(x21801,x21802)+E(f612(x21803,x21801),f612(x21803,x21802))
% 157.55/157.24 [2181]~E(x21811,x21812)+E(f522(x21811,x21813,x21814,x21815),f522(x21812,x21813,x21814,x21815))
% 157.55/157.24 [2182]~E(x21821,x21822)+E(f522(x21823,x21821,x21824,x21825),f522(x21823,x21822,x21824,x21825))
% 157.55/157.24 [2183]~E(x21831,x21832)+E(f522(x21833,x21834,x21831,x21835),f522(x21833,x21834,x21832,x21835))
% 157.55/157.24 [2184]~E(x21841,x21842)+E(f522(x21843,x21844,x21845,x21841),f522(x21843,x21844,x21845,x21842))
% 157.55/157.24 [2185]~E(x21851,x21852)+E(f483(x21851,x21853,x21854),f483(x21852,x21853,x21854))
% 157.55/157.24 [2186]~E(x21861,x21862)+E(f483(x21863,x21861,x21864),f483(x21863,x21862,x21864))
% 157.55/157.24 [2187]~E(x21871,x21872)+E(f483(x21873,x21874,x21871),f483(x21873,x21874,x21872))
% 157.55/157.24 [2188]~E(x21881,x21882)+E(f464(x21881,x21883,x21884,x21885,x21886),f464(x21882,x21883,x21884,x21885,x21886))
% 157.55/157.24 [2189]~E(x21891,x21892)+E(f464(x21893,x21891,x21894,x21895,x21896),f464(x21893,x21892,x21894,x21895,x21896))
% 157.55/157.24 [2190]~E(x21901,x21902)+E(f464(x21903,x21904,x21901,x21905,x21906),f464(x21903,x21904,x21902,x21905,x21906))
% 157.55/157.24 [2191]~E(x21911,x21912)+E(f464(x21913,x21914,x21915,x21911,x21916),f464(x21913,x21914,x21915,x21912,x21916))
% 157.55/157.24 [2192]~E(x21921,x21922)+E(f464(x21923,x21924,x21925,x21926,x21921),f464(x21923,x21924,x21925,x21926,x21922))
% 157.55/157.24 [2193]~E(x21931,x21932)+E(f705(x21931,x21933,x21934),f705(x21932,x21933,x21934))
% 157.55/157.24 [2194]~E(x21941,x21942)+E(f705(x21943,x21941,x21944),f705(x21943,x21942,x21944))
% 157.55/157.24 [2195]~E(x21951,x21952)+E(f705(x21953,x21954,x21951),f705(x21953,x21954,x21952))
% 157.55/157.24 [2196]~E(x21961,x21962)+E(f763(x21961,x21963,x21964,x21965),f763(x21962,x21963,x21964,x21965))
% 157.55/157.24 [2197]~E(x21971,x21972)+E(f763(x21973,x21971,x21974,x21975),f763(x21973,x21972,x21974,x21975))
% 157.55/157.24 [2198]~E(x21981,x21982)+E(f763(x21983,x21984,x21981,x21985),f763(x21983,x21984,x21982,x21985))
% 157.55/157.24 [2199]~E(x21991,x21992)+E(f763(x21993,x21994,x21995,x21991),f763(x21993,x21994,x21995,x21992))
% 157.55/157.24 [2200]~E(x22001,x22002)+E(f295(x22001,x22003,x22004),f295(x22002,x22003,x22004))
% 157.55/157.24 [2201]~E(x22011,x22012)+E(f295(x22013,x22011,x22014),f295(x22013,x22012,x22014))
% 157.55/157.24 [2202]~E(x22021,x22022)+E(f295(x22023,x22024,x22021),f295(x22023,x22024,x22022))
% 157.55/157.24 [2203]~E(x22031,x22032)+E(f206(x22031,x22033,x22034,x22035),f206(x22032,x22033,x22034,x22035))
% 157.55/157.24 [2204]~E(x22041,x22042)+E(f206(x22043,x22041,x22044,x22045),f206(x22043,x22042,x22044,x22045))
% 157.55/157.24 [2205]~E(x22051,x22052)+E(f206(x22053,x22054,x22051,x22055),f206(x22053,x22054,x22052,x22055))
% 157.55/157.24 [2206]~E(x22061,x22062)+E(f206(x22063,x22064,x22065,x22061),f206(x22063,x22064,x22065,x22062))
% 157.55/157.24 [2207]~E(x22071,x22072)+E(f661(x22071,x22073,x22074,x22075),f661(x22072,x22073,x22074,x22075))
% 157.55/157.24 [2208]~E(x22081,x22082)+E(f661(x22083,x22081,x22084,x22085),f661(x22083,x22082,x22084,x22085))
% 157.55/157.24 [2209]~E(x22091,x22092)+E(f661(x22093,x22094,x22091,x22095),f661(x22093,x22094,x22092,x22095))
% 157.55/157.24 [2210]~E(x22101,x22102)+E(f661(x22103,x22104,x22105,x22101),f661(x22103,x22104,x22105,x22102))
% 157.55/157.24 [2211]~E(x22111,x22112)+E(f825(x22111,x22113,x22114,x22115),f825(x22112,x22113,x22114,x22115))
% 157.55/157.24 [2212]~E(x22121,x22122)+E(f825(x22123,x22121,x22124,x22125),f825(x22123,x22122,x22124,x22125))
% 157.55/157.24 [2213]~E(x22131,x22132)+E(f825(x22133,x22134,x22131,x22135),f825(x22133,x22134,x22132,x22135))
% 157.55/157.24 [2214]~E(x22141,x22142)+E(f825(x22143,x22144,x22145,x22141),f825(x22143,x22144,x22145,x22142))
% 157.55/157.24 [2215]~E(x22151,x22152)+E(f874(x22151,x22153,x22154),f874(x22152,x22153,x22154))
% 157.55/157.24 [2216]~E(x22161,x22162)+E(f874(x22163,x22161,x22164),f874(x22163,x22162,x22164))
% 157.55/157.24 [2217]~E(x22171,x22172)+E(f874(x22173,x22174,x22171),f874(x22173,x22174,x22172))
% 157.55/157.24 [2218]~E(x22181,x22182)+E(f210(x22181,x22183,x22184,x22185),f210(x22182,x22183,x22184,x22185))
% 157.55/157.24 [2219]~E(x22191,x22192)+E(f210(x22193,x22191,x22194,x22195),f210(x22193,x22192,x22194,x22195))
% 157.55/157.24 [2220]~E(x22201,x22202)+E(f210(x22203,x22204,x22201,x22205),f210(x22203,x22204,x22202,x22205))
% 157.55/157.24 [2221]~E(x22211,x22212)+E(f210(x22213,x22214,x22215,x22211),f210(x22213,x22214,x22215,x22212))
% 157.55/157.24 [2222]~E(x22221,x22222)+E(f694(x22221,x22223,x22224,x22225,x22226),f694(x22222,x22223,x22224,x22225,x22226))
% 157.55/157.24 [2223]~E(x22231,x22232)+E(f694(x22233,x22231,x22234,x22235,x22236),f694(x22233,x22232,x22234,x22235,x22236))
% 157.55/157.24 [2224]~E(x22241,x22242)+E(f694(x22243,x22244,x22241,x22245,x22246),f694(x22243,x22244,x22242,x22245,x22246))
% 157.55/157.24 [2225]~E(x22251,x22252)+E(f694(x22253,x22254,x22255,x22251,x22256),f694(x22253,x22254,x22255,x22252,x22256))
% 157.55/157.24 [2226]~E(x22261,x22262)+E(f694(x22263,x22264,x22265,x22266,x22261),f694(x22263,x22264,x22265,x22266,x22262))
% 157.55/157.24 [2227]~E(x22271,x22272)+E(f319(x22271,x22273,x22274,x22275),f319(x22272,x22273,x22274,x22275))
% 157.55/157.24 [2228]~E(x22281,x22282)+E(f319(x22283,x22281,x22284,x22285),f319(x22283,x22282,x22284,x22285))
% 157.55/157.24 [2229]~E(x22291,x22292)+E(f319(x22293,x22294,x22291,x22295),f319(x22293,x22294,x22292,x22295))
% 157.55/157.24 [2230]~E(x22301,x22302)+E(f319(x22303,x22304,x22305,x22301),f319(x22303,x22304,x22305,x22302))
% 157.55/157.24 [2231]~E(x22311,x22312)+E(f298(x22311,x22313,x22314,x22315),f298(x22312,x22313,x22314,x22315))
% 157.55/157.24 [2232]~E(x22321,x22322)+E(f298(x22323,x22321,x22324,x22325),f298(x22323,x22322,x22324,x22325))
% 157.55/157.24 [2233]~E(x22331,x22332)+E(f298(x22333,x22334,x22331,x22335),f298(x22333,x22334,x22332,x22335))
% 157.55/157.24 [2234]~E(x22341,x22342)+E(f298(x22343,x22344,x22345,x22341),f298(x22343,x22344,x22345,x22342))
% 157.55/157.24 [2235]~E(x22351,x22352)+E(f448(x22351,x22353,x22354,x22355),f448(x22352,x22353,x22354,x22355))
% 157.55/157.24 [2236]~E(x22361,x22362)+E(f448(x22363,x22361,x22364,x22365),f448(x22363,x22362,x22364,x22365))
% 157.55/157.24 [2237]~E(x22371,x22372)+E(f448(x22373,x22374,x22371,x22375),f448(x22373,x22374,x22372,x22375))
% 157.55/157.24 [2238]~E(x22381,x22382)+E(f448(x22383,x22384,x22385,x22381),f448(x22383,x22384,x22385,x22382))
% 157.55/157.24 [2239]~E(x22391,x22392)+E(f666(x22391,x22393),f666(x22392,x22393))
% 157.55/157.24 [2240]~E(x22401,x22402)+E(f666(x22403,x22401),f666(x22403,x22402))
% 157.55/157.24 [2241]~E(x22411,x22412)+E(f428(x22411,x22413,x22414,x22415,x22416),f428(x22412,x22413,x22414,x22415,x22416))
% 157.55/157.24 [2242]~E(x22421,x22422)+E(f428(x22423,x22421,x22424,x22425,x22426),f428(x22423,x22422,x22424,x22425,x22426))
% 157.55/157.24 [2243]~E(x22431,x22432)+E(f428(x22433,x22434,x22431,x22435,x22436),f428(x22433,x22434,x22432,x22435,x22436))
% 157.55/157.24 [2244]~E(x22441,x22442)+E(f428(x22443,x22444,x22445,x22441,x22446),f428(x22443,x22444,x22445,x22442,x22446))
% 157.55/157.24 [2245]~E(x22451,x22452)+E(f428(x22453,x22454,x22455,x22456,x22451),f428(x22453,x22454,x22455,x22456,x22452))
% 157.55/157.24 [2246]~E(x22461,x22462)+E(f469(x22461,x22463,x22464,x22465,x22466),f469(x22462,x22463,x22464,x22465,x22466))
% 157.55/157.24 [2247]~E(x22471,x22472)+E(f469(x22473,x22471,x22474,x22475,x22476),f469(x22473,x22472,x22474,x22475,x22476))
% 157.55/157.24 [2248]~E(x22481,x22482)+E(f469(x22483,x22484,x22481,x22485,x22486),f469(x22483,x22484,x22482,x22485,x22486))
% 157.55/157.24 [2249]~E(x22491,x22492)+E(f469(x22493,x22494,x22495,x22491,x22496),f469(x22493,x22494,x22495,x22492,x22496))
% 157.55/157.24 [2250]~E(x22501,x22502)+E(f469(x22503,x22504,x22505,x22506,x22501),f469(x22503,x22504,x22505,x22506,x22502))
% 157.55/157.24 [2251]~E(x22511,x22512)+E(f460(x22511,x22513,x22514,x22515),f460(x22512,x22513,x22514,x22515))
% 157.55/157.24 [2252]~E(x22521,x22522)+E(f460(x22523,x22521,x22524,x22525),f460(x22523,x22522,x22524,x22525))
% 157.55/157.24 [2253]~E(x22531,x22532)+E(f460(x22533,x22534,x22531,x22535),f460(x22533,x22534,x22532,x22535))
% 157.55/157.24 [2254]~E(x22541,x22542)+E(f460(x22543,x22544,x22545,x22541),f460(x22543,x22544,x22545,x22542))
% 157.55/157.24 [2255]~E(x22551,x22552)+E(f404(x22551,x22553),f404(x22552,x22553))
% 157.55/157.24 [2256]~E(x22561,x22562)+E(f404(x22563,x22561),f404(x22563,x22562))
% 157.55/157.24 [2257]~E(x22571,x22572)+E(f845(x22571,x22573,x22574,x22575,x22576,x22577),f845(x22572,x22573,x22574,x22575,x22576,x22577))
% 157.55/157.24 [2258]~E(x22581,x22582)+E(f845(x22583,x22581,x22584,x22585,x22586,x22587),f845(x22583,x22582,x22584,x22585,x22586,x22587))
% 157.55/157.24 [2259]~E(x22591,x22592)+E(f845(x22593,x22594,x22591,x22595,x22596,x22597),f845(x22593,x22594,x22592,x22595,x22596,x22597))
% 157.55/157.24 [2260]~E(x22601,x22602)+E(f845(x22603,x22604,x22605,x22601,x22606,x22607),f845(x22603,x22604,x22605,x22602,x22606,x22607))
% 157.55/157.24 [2261]~E(x22611,x22612)+E(f845(x22613,x22614,x22615,x22616,x22611,x22617),f845(x22613,x22614,x22615,x22616,x22612,x22617))
% 157.55/157.24 [2262]~E(x22621,x22622)+E(f845(x22623,x22624,x22625,x22626,x22627,x22621),f845(x22623,x22624,x22625,x22626,x22627,x22622))
% 157.55/157.24 [2263]~E(x22631,x22632)+E(f780(x22631,x22633,x22634,x22635,x22636,x22637,x22638),f780(x22632,x22633,x22634,x22635,x22636,x22637,x22638))
% 157.55/157.24 [2264]~E(x22641,x22642)+E(f780(x22643,x22641,x22644,x22645,x22646,x22647,x22648),f780(x22643,x22642,x22644,x22645,x22646,x22647,x22648))
% 157.55/157.24 [2265]~E(x22651,x22652)+E(f780(x22653,x22654,x22651,x22655,x22656,x22657,x22658),f780(x22653,x22654,x22652,x22655,x22656,x22657,x22658))
% 157.55/157.24 [2266]~E(x22661,x22662)+E(f780(x22663,x22664,x22665,x22661,x22666,x22667,x22668),f780(x22663,x22664,x22665,x22662,x22666,x22667,x22668))
% 157.55/157.24 [2267]~E(x22671,x22672)+E(f780(x22673,x22674,x22675,x22676,x22671,x22677,x22678),f780(x22673,x22674,x22675,x22676,x22672,x22677,x22678))
% 157.55/157.24 [2268]~E(x22681,x22682)+E(f780(x22683,x22684,x22685,x22686,x22687,x22681,x22688),f780(x22683,x22684,x22685,x22686,x22687,x22682,x22688))
% 157.55/157.24 [2269]~E(x22691,x22692)+E(f780(x22693,x22694,x22695,x22696,x22697,x22698,x22691),f780(x22693,x22694,x22695,x22696,x22697,x22698,x22692))
% 157.55/157.24 [2270]~E(x22701,x22702)+E(f832(x22701,x22703,x22704),f832(x22702,x22703,x22704))
% 157.55/157.24 [2271]~E(x22711,x22712)+E(f832(x22713,x22711,x22714),f832(x22713,x22712,x22714))
% 157.55/157.24 [2272]~E(x22721,x22722)+E(f832(x22723,x22724,x22721),f832(x22723,x22724,x22722))
% 157.55/157.24 [2273]~E(x22731,x22732)+E(f245(x22731,x22733,x22734,x22735,x22736,x22737),f245(x22732,x22733,x22734,x22735,x22736,x22737))
% 157.55/157.24 [2274]~E(x22741,x22742)+E(f245(x22743,x22741,x22744,x22745,x22746,x22747),f245(x22743,x22742,x22744,x22745,x22746,x22747))
% 157.55/157.24 [2275]~E(x22751,x22752)+E(f245(x22753,x22754,x22751,x22755,x22756,x22757),f245(x22753,x22754,x22752,x22755,x22756,x22757))
% 157.55/157.24 [2276]~E(x22761,x22762)+E(f245(x22763,x22764,x22765,x22761,x22766,x22767),f245(x22763,x22764,x22765,x22762,x22766,x22767))
% 157.55/157.24 [2277]~E(x22771,x22772)+E(f245(x22773,x22774,x22775,x22776,x22771,x22777),f245(x22773,x22774,x22775,x22776,x22772,x22777))
% 157.55/157.24 [2278]~E(x22781,x22782)+E(f245(x22783,x22784,x22785,x22786,x22787,x22781),f245(x22783,x22784,x22785,x22786,x22787,x22782))
% 157.55/157.24 [2279]~E(x22791,x22792)+E(f471(x22791,x22793,x22794,x22795,x22796),f471(x22792,x22793,x22794,x22795,x22796))
% 157.55/157.24 [2280]~E(x22801,x22802)+E(f471(x22803,x22801,x22804,x22805,x22806),f471(x22803,x22802,x22804,x22805,x22806))
% 157.55/157.24 [2281]~E(x22811,x22812)+E(f471(x22813,x22814,x22811,x22815,x22816),f471(x22813,x22814,x22812,x22815,x22816))
% 157.55/157.24 [2282]~E(x22821,x22822)+E(f471(x22823,x22824,x22825,x22821,x22826),f471(x22823,x22824,x22825,x22822,x22826))
% 157.55/157.24 [2283]~E(x22831,x22832)+E(f471(x22833,x22834,x22835,x22836,x22831),f471(x22833,x22834,x22835,x22836,x22832))
% 157.55/157.24 [2284]~E(x22841,x22842)+E(f682(x22841,x22843,x22844,x22845),f682(x22842,x22843,x22844,x22845))
% 157.55/157.24 [2285]~E(x22851,x22852)+E(f682(x22853,x22851,x22854,x22855),f682(x22853,x22852,x22854,x22855))
% 157.55/157.24 [2286]~E(x22861,x22862)+E(f682(x22863,x22864,x22861,x22865),f682(x22863,x22864,x22862,x22865))
% 157.55/157.24 [2287]~E(x22871,x22872)+E(f682(x22873,x22874,x22875,x22871),f682(x22873,x22874,x22875,x22872))
% 157.55/157.24 [2288]~E(x22881,x22882)+E(f384(x22881,x22883,x22884),f384(x22882,x22883,x22884))
% 157.55/157.24 [2289]~E(x22891,x22892)+E(f384(x22893,x22891,x22894),f384(x22893,x22892,x22894))
% 157.55/157.24 [2290]~E(x22901,x22902)+E(f384(x22903,x22904,x22901),f384(x22903,x22904,x22902))
% 157.55/157.24 [2291]~E(x22911,x22912)+E(f614(x22911,x22913),f614(x22912,x22913))
% 157.55/157.24 [2292]~E(x22921,x22922)+E(f614(x22923,x22921),f614(x22923,x22922))
% 157.55/157.24 [2293]~E(x22931,x22932)+E(f617(x22931,x22933,x22934),f617(x22932,x22933,x22934))
% 157.55/157.24 [2294]~E(x22941,x22942)+E(f617(x22943,x22941,x22944),f617(x22943,x22942,x22944))
% 157.55/157.24 [2295]~E(x22951,x22952)+E(f617(x22953,x22954,x22951),f617(x22953,x22954,x22952))
% 157.55/157.24 [2296]~E(x22961,x22962)+E(f886(x22961,x22963,x22964,x22965,x22966),f886(x22962,x22963,x22964,x22965,x22966))
% 157.55/157.24 [2297]~E(x22971,x22972)+E(f886(x22973,x22971,x22974,x22975,x22976),f886(x22973,x22972,x22974,x22975,x22976))
% 157.55/157.24 [2298]~E(x22981,x22982)+E(f886(x22983,x22984,x22981,x22985,x22986),f886(x22983,x22984,x22982,x22985,x22986))
% 157.55/157.24 [2299]~E(x22991,x22992)+E(f886(x22993,x22994,x22995,x22991,x22996),f886(x22993,x22994,x22995,x22992,x22996))
% 157.55/157.24 [2300]~E(x23001,x23002)+E(f886(x23003,x23004,x23005,x23006,x23001),f886(x23003,x23004,x23005,x23006,x23002))
% 157.55/157.24 [2301]~E(x23011,x23012)+E(f415(x23011,x23013,x23014,x23015),f415(x23012,x23013,x23014,x23015))
% 157.55/157.24 [2302]~E(x23021,x23022)+E(f415(x23023,x23021,x23024,x23025),f415(x23023,x23022,x23024,x23025))
% 157.55/157.24 [2303]~E(x23031,x23032)+E(f415(x23033,x23034,x23031,x23035),f415(x23033,x23034,x23032,x23035))
% 157.55/157.24 [2304]~E(x23041,x23042)+E(f415(x23043,x23044,x23045,x23041),f415(x23043,x23044,x23045,x23042))
% 157.55/157.24 [2305]~E(x23051,x23052)+E(f412(x23051,x23053),f412(x23052,x23053))
% 157.55/157.24 [2306]~E(x23061,x23062)+E(f412(x23063,x23061),f412(x23063,x23062))
% 157.55/157.24 [2307]~E(x23071,x23072)+E(f44(x23071),f44(x23072))
% 157.55/157.24 [2308]~E(x23081,x23082)+E(f416(x23081,x23083),f416(x23082,x23083))
% 157.55/157.24 [2309]~E(x23091,x23092)+E(f416(x23093,x23091),f416(x23093,x23092))
% 157.55/157.24 [2310]~E(x23101,x23102)+E(f584(x23101,x23103,x23104,x23105,x23106,x23107),f584(x23102,x23103,x23104,x23105,x23106,x23107))
% 157.55/157.24 [2311]~E(x23111,x23112)+E(f584(x23113,x23111,x23114,x23115,x23116,x23117),f584(x23113,x23112,x23114,x23115,x23116,x23117))
% 157.55/157.24 [2312]~E(x23121,x23122)+E(f584(x23123,x23124,x23121,x23125,x23126,x23127),f584(x23123,x23124,x23122,x23125,x23126,x23127))
% 157.55/157.24 [2313]~E(x23131,x23132)+E(f584(x23133,x23134,x23135,x23131,x23136,x23137),f584(x23133,x23134,x23135,x23132,x23136,x23137))
% 157.55/157.24 [2314]~E(x23141,x23142)+E(f584(x23143,x23144,x23145,x23146,x23141,x23147),f584(x23143,x23144,x23145,x23146,x23142,x23147))
% 157.55/157.24 [2315]~E(x23151,x23152)+E(f584(x23153,x23154,x23155,x23156,x23157,x23151),f584(x23153,x23154,x23155,x23156,x23157,x23152))
% 157.55/157.24 [2316]~E(x23161,x23162)+E(f395(x23161,x23163,x23164),f395(x23162,x23163,x23164))
% 157.55/157.24 [2317]~E(x23171,x23172)+E(f395(x23173,x23171,x23174),f395(x23173,x23172,x23174))
% 157.55/157.24 [2318]~E(x23181,x23182)+E(f395(x23183,x23184,x23181),f395(x23183,x23184,x23182))
% 157.55/157.24 [2319]~E(x23191,x23192)+E(f463(x23191,x23193,x23194,x23195,x23196),f463(x23192,x23193,x23194,x23195,x23196))
% 157.55/157.24 [2320]~E(x23201,x23202)+E(f463(x23203,x23201,x23204,x23205,x23206),f463(x23203,x23202,x23204,x23205,x23206))
% 157.55/157.24 [2321]~E(x23211,x23212)+E(f463(x23213,x23214,x23211,x23215,x23216),f463(x23213,x23214,x23212,x23215,x23216))
% 157.55/157.24 [2322]~E(x23221,x23222)+E(f463(x23223,x23224,x23225,x23221,x23226),f463(x23223,x23224,x23225,x23222,x23226))
% 157.55/157.24 [2323]~E(x23231,x23232)+E(f463(x23233,x23234,x23235,x23236,x23231),f463(x23233,x23234,x23235,x23236,x23232))
% 157.55/157.24 [2324]~E(x23241,x23242)+E(f798(x23241,x23243),f798(x23242,x23243))
% 157.55/157.24 [2325]~E(x23251,x23252)+E(f798(x23253,x23251),f798(x23253,x23252))
% 157.55/157.24 [2326]~E(x23261,x23262)+E(f487(x23261,x23263,x23264),f487(x23262,x23263,x23264))
% 157.55/157.24 [2327]~E(x23271,x23272)+E(f487(x23273,x23271,x23274),f487(x23273,x23272,x23274))
% 157.55/157.24 [2328]~E(x23281,x23282)+E(f487(x23283,x23284,x23281),f487(x23283,x23284,x23282))
% 157.55/157.24 [2329]~E(x23291,x23292)+E(f728(x23291,x23293),f728(x23292,x23293))
% 157.55/157.24 [2330]~E(x23301,x23302)+E(f728(x23303,x23301),f728(x23303,x23302))
% 157.55/157.24 [2331]~E(x23311,x23312)+E(f482(x23311,x23313,x23314,x23315,x23316),f482(x23312,x23313,x23314,x23315,x23316))
% 157.55/157.24 [2332]~E(x23321,x23322)+E(f482(x23323,x23321,x23324,x23325,x23326),f482(x23323,x23322,x23324,x23325,x23326))
% 157.55/157.24 [2333]~E(x23331,x23332)+E(f482(x23333,x23334,x23331,x23335,x23336),f482(x23333,x23334,x23332,x23335,x23336))
% 157.55/157.24 [2334]~E(x23341,x23342)+E(f482(x23343,x23344,x23345,x23341,x23346),f482(x23343,x23344,x23345,x23342,x23346))
% 157.55/157.24 [2335]~E(x23351,x23352)+E(f482(x23353,x23354,x23355,x23356,x23351),f482(x23353,x23354,x23355,x23356,x23352))
% 157.55/157.24 [2336]~E(x23361,x23362)+E(f567(x23361,x23363),f567(x23362,x23363))
% 157.55/157.24 [2337]~E(x23371,x23372)+E(f567(x23373,x23371),f567(x23373,x23372))
% 157.55/157.24 [2338]~E(x23381,x23382)+E(f663(x23381,x23383,x23384,x23385),f663(x23382,x23383,x23384,x23385))
% 157.55/157.24 [2339]~E(x23391,x23392)+E(f663(x23393,x23391,x23394,x23395),f663(x23393,x23392,x23394,x23395))
% 157.55/157.24 [2340]~E(x23401,x23402)+E(f663(x23403,x23404,x23401,x23405),f663(x23403,x23404,x23402,x23405))
% 157.55/157.24 [2341]~E(x23411,x23412)+E(f663(x23413,x23414,x23415,x23411),f663(x23413,x23414,x23415,x23412))
% 157.55/157.24 [2342]~E(x23421,x23422)+E(f719(x23421,x23423),f719(x23422,x23423))
% 157.55/157.24 [2343]~E(x23431,x23432)+E(f719(x23433,x23431),f719(x23433,x23432))
% 157.55/157.24 [2344]~E(x23441,x23442)+E(f331(x23441),f331(x23442))
% 157.55/157.24 [2345]~E(x23451,x23452)+E(f711(x23451,x23453),f711(x23452,x23453))
% 157.55/157.24 [2346]~E(x23461,x23462)+E(f711(x23463,x23461),f711(x23463,x23462))
% 157.55/157.24 [2347]~E(x23471,x23472)+E(f337(x23471),f337(x23472))
% 157.55/157.24 [2348]~E(x23481,x23482)+E(f391(x23481,x23483),f391(x23482,x23483))
% 157.55/157.24 [2349]~E(x23491,x23492)+E(f391(x23493,x23491),f391(x23493,x23492))
% 157.55/157.24 [2350]~E(x23501,x23502)+E(f492(x23501,x23503,x23504),f492(x23502,x23503,x23504))
% 157.55/157.24 [2351]~E(x23511,x23512)+E(f492(x23513,x23511,x23514),f492(x23513,x23512,x23514))
% 157.55/157.24 [2352]~E(x23521,x23522)+E(f492(x23523,x23524,x23521),f492(x23523,x23524,x23522))
% 157.55/157.24 [2353]~E(x23531,x23532)+E(f573(x23531,x23533,x23534,x23535,x23536),f573(x23532,x23533,x23534,x23535,x23536))
% 157.55/157.24 [2354]~E(x23541,x23542)+E(f573(x23543,x23541,x23544,x23545,x23546),f573(x23543,x23542,x23544,x23545,x23546))
% 157.55/157.24 [2355]~E(x23551,x23552)+E(f573(x23553,x23554,x23551,x23555,x23556),f573(x23553,x23554,x23552,x23555,x23556))
% 157.55/157.24 [2356]~E(x23561,x23562)+E(f573(x23563,x23564,x23565,x23561,x23566),f573(x23563,x23564,x23565,x23562,x23566))
% 157.55/157.24 [2357]~E(x23571,x23572)+E(f573(x23573,x23574,x23575,x23576,x23571),f573(x23573,x23574,x23575,x23576,x23572))
% 157.55/157.24 [2358]~E(x23581,x23582)+E(f651(x23581,x23583,x23584),f651(x23582,x23583,x23584))
% 157.55/157.24 [2359]~E(x23591,x23592)+E(f651(x23593,x23591,x23594),f651(x23593,x23592,x23594))
% 157.55/157.24 [2360]~E(x23601,x23602)+E(f651(x23603,x23604,x23601),f651(x23603,x23604,x23602))
% 157.55/157.24 [2361]~E(x23611,x23612)+E(f343(x23611,x23613,x23614),f343(x23612,x23613,x23614))
% 157.55/157.24 [2362]~E(x23621,x23622)+E(f343(x23623,x23621,x23624),f343(x23623,x23622,x23624))
% 157.55/157.24 [2363]~E(x23631,x23632)+E(f343(x23633,x23634,x23631),f343(x23633,x23634,x23632))
% 157.55/157.24 [2364]~E(x23641,x23642)+E(f524(x23641,x23643,x23644,x23645,x23646,x23647,x23648,x23649),f524(x23642,x23643,x23644,x23645,x23646,x23647,x23648,x23649))
% 157.55/157.24 [2365]~E(x23651,x23652)+E(f524(x23653,x23651,x23654,x23655,x23656,x23657,x23658,x23659),f524(x23653,x23652,x23654,x23655,x23656,x23657,x23658,x23659))
% 157.55/157.24 [2366]~E(x23661,x23662)+E(f524(x23663,x23664,x23661,x23665,x23666,x23667,x23668,x23669),f524(x23663,x23664,x23662,x23665,x23666,x23667,x23668,x23669))
% 157.55/157.24 [2367]~E(x23671,x23672)+E(f524(x23673,x23674,x23675,x23671,x23676,x23677,x23678,x23679),f524(x23673,x23674,x23675,x23672,x23676,x23677,x23678,x23679))
% 157.55/157.24 [2368]~E(x23681,x23682)+E(f524(x23683,x23684,x23685,x23686,x23681,x23687,x23688,x23689),f524(x23683,x23684,x23685,x23686,x23682,x23687,x23688,x23689))
% 157.55/157.24 [2369]~E(x23691,x23692)+E(f524(x23693,x23694,x23695,x23696,x23697,x23691,x23698,x23699),f524(x23693,x23694,x23695,x23696,x23697,x23692,x23698,x23699))
% 157.55/157.24 [2370]~E(x23701,x23702)+E(f524(x23703,x23704,x23705,x23706,x23707,x23708,x23701,x23709),f524(x23703,x23704,x23705,x23706,x23707,x23708,x23702,x23709))
% 157.55/157.24 [2371]~E(x23711,x23712)+E(f524(x23713,x23714,x23715,x23716,x23717,x23718,x23719,x23711),f524(x23713,x23714,x23715,x23716,x23717,x23718,x23719,x23712))
% 157.55/157.24 [2372]~E(x23721,x23722)+E(f456(x23721,x23723),f456(x23722,x23723))
% 157.55/157.24 [2373]~E(x23731,x23732)+E(f456(x23733,x23731),f456(x23733,x23732))
% 157.55/157.24 [2374]~E(x23741,x23742)+E(f426(x23741,x23743,x23744,x23745),f426(x23742,x23743,x23744,x23745))
% 157.55/157.24 [2375]~E(x23751,x23752)+E(f426(x23753,x23751,x23754,x23755),f426(x23753,x23752,x23754,x23755))
% 157.55/157.24 [2376]~E(x23761,x23762)+E(f426(x23763,x23764,x23761,x23765),f426(x23763,x23764,x23762,x23765))
% 157.55/157.24 [2377]~E(x23771,x23772)+E(f426(x23773,x23774,x23775,x23771),f426(x23773,x23774,x23775,x23772))
% 157.55/157.24 [2378]~E(x23781,x23782)+E(f823(x23781,x23783,x23784,x23785,x23786),f823(x23782,x23783,x23784,x23785,x23786))
% 157.55/157.24 [2379]~E(x23791,x23792)+E(f823(x23793,x23791,x23794,x23795,x23796),f823(x23793,x23792,x23794,x23795,x23796))
% 157.55/157.24 [2380]~E(x23801,x23802)+E(f823(x23803,x23804,x23801,x23805,x23806),f823(x23803,x23804,x23802,x23805,x23806))
% 157.55/157.24 [2381]~E(x23811,x23812)+E(f823(x23813,x23814,x23815,x23811,x23816),f823(x23813,x23814,x23815,x23812,x23816))
% 157.55/157.24 [2382]~E(x23821,x23822)+E(f823(x23823,x23824,x23825,x23826,x23821),f823(x23823,x23824,x23825,x23826,x23822))
% 157.55/157.24 [2383]~E(x23831,x23832)+E(f660(x23831,x23833),f660(x23832,x23833))
% 157.55/157.24 [2384]~E(x23841,x23842)+E(f660(x23843,x23841),f660(x23843,x23842))
% 157.55/157.24 [2385]~E(x23851,x23852)+E(f568(x23851,x23853,x23854),f568(x23852,x23853,x23854))
% 157.55/157.24 [2386]~E(x23861,x23862)+E(f568(x23863,x23861,x23864),f568(x23863,x23862,x23864))
% 157.55/157.24 [2387]~E(x23871,x23872)+E(f568(x23873,x23874,x23871),f568(x23873,x23874,x23872))
% 157.55/157.24 [2388]~E(x23881,x23882)+E(f431(x23881,x23883,x23884,x23885),f431(x23882,x23883,x23884,x23885))
% 157.55/157.24 [2389]~E(x23891,x23892)+E(f431(x23893,x23891,x23894,x23895),f431(x23893,x23892,x23894,x23895))
% 157.55/157.24 [2390]~E(x23901,x23902)+E(f431(x23903,x23904,x23901,x23905),f431(x23903,x23904,x23902,x23905))
% 157.55/157.24 [2391]~E(x23911,x23912)+E(f431(x23913,x23914,x23915,x23911),f431(x23913,x23914,x23915,x23912))
% 157.55/157.24 [2392]~E(x23921,x23922)+E(f735(x23921,x23923,x23924,x23925),f735(x23922,x23923,x23924,x23925))
% 157.55/157.24 [2393]~E(x23931,x23932)+E(f735(x23933,x23931,x23934,x23935),f735(x23933,x23932,x23934,x23935))
% 157.55/157.24 [2394]~E(x23941,x23942)+E(f735(x23943,x23944,x23941,x23945),f735(x23943,x23944,x23942,x23945))
% 157.55/157.24 [2395]~E(x23951,x23952)+E(f735(x23953,x23954,x23955,x23951),f735(x23953,x23954,x23955,x23952))
% 157.55/157.24 [2396]~E(x23961,x23962)+E(f521(x23961,x23963),f521(x23962,x23963))
% 157.55/157.24 [2397]~E(x23971,x23972)+E(f521(x23973,x23971),f521(x23973,x23972))
% 157.55/157.24 [2398]~E(x23981,x23982)+E(f590(x23981,x23983),f590(x23982,x23983))
% 157.55/157.24 [2399]~E(x23991,x23992)+E(f590(x23993,x23991),f590(x23993,x23992))
% 157.55/157.24 [2400]~E(x24001,x24002)+E(f476(x24001,x24003),f476(x24002,x24003))
% 157.55/157.24 [2401]~E(x24011,x24012)+E(f476(x24013,x24011),f476(x24013,x24012))
% 157.55/157.24 [2402]~E(x24021,x24022)+E(f670(x24021,x24023),f670(x24022,x24023))
% 157.55/157.24 [2403]~E(x24031,x24032)+E(f670(x24033,x24031),f670(x24033,x24032))
% 157.55/157.24 [2404]~E(x24041,x24042)+E(f231(x24041,x24043,x24044,x24045),f231(x24042,x24043,x24044,x24045))
% 157.55/157.24 [2405]~E(x24051,x24052)+E(f231(x24053,x24051,x24054,x24055),f231(x24053,x24052,x24054,x24055))
% 157.55/157.24 [2406]~E(x24061,x24062)+E(f231(x24063,x24064,x24061,x24065),f231(x24063,x24064,x24062,x24065))
% 157.55/157.24 [2407]~E(x24071,x24072)+E(f231(x24073,x24074,x24075,x24071),f231(x24073,x24074,x24075,x24072))
% 157.55/157.24 [2408]~E(x24081,x24082)+E(f424(x24081,x24083,x24084),f424(x24082,x24083,x24084))
% 157.55/157.24 [2409]~E(x24091,x24092)+E(f424(x24093,x24091,x24094),f424(x24093,x24092,x24094))
% 157.55/157.24 [2410]~E(x24101,x24102)+E(f424(x24103,x24104,x24101),f424(x24103,x24104,x24102))
% 157.55/157.24 [2411]~E(x24111,x24112)+E(f348(x24111,x24113),f348(x24112,x24113))
% 157.55/157.24 [2412]~E(x24121,x24122)+E(f348(x24123,x24121),f348(x24123,x24122))
% 157.55/157.24 [2413]~E(x24131,x24132)+E(f350(x24131,x24133,x24134),f350(x24132,x24133,x24134))
% 157.55/157.24 [2414]~E(x24141,x24142)+E(f350(x24143,x24141,x24144),f350(x24143,x24142,x24144))
% 157.55/157.24 [2415]~E(x24151,x24152)+E(f350(x24153,x24154,x24151),f350(x24153,x24154,x24152))
% 157.55/157.24 [2416]~E(x24161,x24162)+E(f644(x24161,x24163),f644(x24162,x24163))
% 157.55/157.24 [2417]~E(x24171,x24172)+E(f644(x24173,x24171),f644(x24173,x24172))
% 157.55/157.24 [2418]~E(x24181,x24182)+E(f819(x24181,x24183),f819(x24182,x24183))
% 157.55/157.24 [2419]~E(x24191,x24192)+E(f819(x24193,x24191),f819(x24193,x24192))
% 157.55/157.24 [2420]~E(x24201,x24202)+E(f21(x24201,x24203,x24204,x24205),f21(x24202,x24203,x24204,x24205))
% 157.55/157.24 [2421]~E(x24211,x24212)+E(f21(x24213,x24211,x24214,x24215),f21(x24213,x24212,x24214,x24215))
% 157.55/157.24 [2422]~E(x24221,x24222)+E(f21(x24223,x24224,x24221,x24225),f21(x24223,x24224,x24222,x24225))
% 157.55/157.24 [2423]~E(x24231,x24232)+E(f21(x24233,x24234,x24235,x24231),f21(x24233,x24234,x24235,x24232))
% 157.55/157.24 [2424]~E(x24241,x24242)+E(f486(x24241,x24243,x24244),f486(x24242,x24243,x24244))
% 157.55/157.24 [2425]~E(x24251,x24252)+E(f486(x24253,x24251,x24254),f486(x24253,x24252,x24254))
% 157.55/157.24 [2426]~E(x24261,x24262)+E(f486(x24263,x24264,x24261),f486(x24263,x24264,x24262))
% 157.55/157.24 [2427]~E(x24271,x24272)+E(f796(x24271,x24273),f796(x24272,x24273))
% 157.55/157.24 [2428]~E(x24281,x24282)+E(f796(x24283,x24281),f796(x24283,x24282))
% 157.55/157.24 [2429]~E(x24291,x24292)+E(f754(x24291,x24293,x24294),f754(x24292,x24293,x24294))
% 157.55/157.24 [2430]~E(x24301,x24302)+E(f754(x24303,x24301,x24304),f754(x24303,x24302,x24304))
% 157.55/157.24 [2431]~E(x24311,x24312)+E(f754(x24313,x24314,x24311),f754(x24313,x24314,x24312))
% 157.55/157.24 [2432]~E(x24321,x24322)+E(f811(x24321,x24323),f811(x24322,x24323))
% 157.55/157.24 [2433]~E(x24331,x24332)+E(f811(x24333,x24331),f811(x24333,x24332))
% 157.55/157.24 [2434]~E(x24341,x24342)+E(f821(x24341,x24343,x24344,x24345,x24346,x24347),f821(x24342,x24343,x24344,x24345,x24346,x24347))
% 157.55/157.24 [2435]~E(x24351,x24352)+E(f821(x24353,x24351,x24354,x24355,x24356,x24357),f821(x24353,x24352,x24354,x24355,x24356,x24357))
% 157.55/157.24 [2436]~E(x24361,x24362)+E(f821(x24363,x24364,x24361,x24365,x24366,x24367),f821(x24363,x24364,x24362,x24365,x24366,x24367))
% 157.55/157.24 [2437]~E(x24371,x24372)+E(f821(x24373,x24374,x24375,x24371,x24376,x24377),f821(x24373,x24374,x24375,x24372,x24376,x24377))
% 157.55/157.24 [2438]~E(x24381,x24382)+E(f821(x24383,x24384,x24385,x24386,x24381,x24387),f821(x24383,x24384,x24385,x24386,x24382,x24387))
% 157.55/157.24 [2439]~E(x24391,x24392)+E(f821(x24393,x24394,x24395,x24396,x24397,x24391),f821(x24393,x24394,x24395,x24396,x24397,x24392))
% 157.55/157.24 [2440]~E(x24401,x24402)+E(f276(x24401,x24403,x24404,x24405),f276(x24402,x24403,x24404,x24405))
% 157.55/157.24 [2441]~E(x24411,x24412)+E(f276(x24413,x24411,x24414,x24415),f276(x24413,x24412,x24414,x24415))
% 157.55/157.24 [2442]~E(x24421,x24422)+E(f276(x24423,x24424,x24421,x24425),f276(x24423,x24424,x24422,x24425))
% 157.55/157.24 [2443]~E(x24431,x24432)+E(f276(x24433,x24434,x24435,x24431),f276(x24433,x24434,x24435,x24432))
% 157.55/157.24 [2444]~E(x24441,x24442)+E(f93(x24441,x24443,x24444),f93(x24442,x24443,x24444))
% 157.55/157.24 [2445]~E(x24451,x24452)+E(f93(x24453,x24451,x24454),f93(x24453,x24452,x24454))
% 157.55/157.24 [2446]~E(x24461,x24462)+E(f93(x24463,x24464,x24461),f93(x24463,x24464,x24462))
% 157.55/157.24 [2447]~E(x24471,x24472)+E(f652(x24471,x24473,x24474),f652(x24472,x24473,x24474))
% 157.55/157.24 [2448]~E(x24481,x24482)+E(f652(x24483,x24481,x24484),f652(x24483,x24482,x24484))
% 157.55/157.24 [2449]~E(x24491,x24492)+E(f652(x24493,x24494,x24491),f652(x24493,x24494,x24492))
% 157.55/157.24 [2450]~E(x24501,x24502)+E(f713(x24501,x24503,x24504),f713(x24502,x24503,x24504))
% 157.55/157.24 [2451]~E(x24511,x24512)+E(f713(x24513,x24511,x24514),f713(x24513,x24512,x24514))
% 157.55/157.24 [2452]~E(x24521,x24522)+E(f713(x24523,x24524,x24521),f713(x24523,x24524,x24522))
% 157.55/157.24 [2453]~E(x24531,x24532)+E(f414(x24531,x24533,x24534,x24535),f414(x24532,x24533,x24534,x24535))
% 157.55/157.24 [2454]~E(x24541,x24542)+E(f414(x24543,x24541,x24544,x24545),f414(x24543,x24542,x24544,x24545))
% 157.55/157.24 [2455]~E(x24551,x24552)+E(f414(x24553,x24554,x24551,x24555),f414(x24553,x24554,x24552,x24555))
% 157.55/157.24 [2456]~E(x24561,x24562)+E(f414(x24563,x24564,x24565,x24561),f414(x24563,x24564,x24565,x24562))
% 157.55/157.24 [2457]~E(x24571,x24572)+E(f638(x24571,x24573,x24574,x24575,x24576),f638(x24572,x24573,x24574,x24575,x24576))
% 157.55/157.24 [2458]~E(x24581,x24582)+E(f638(x24583,x24581,x24584,x24585,x24586),f638(x24583,x24582,x24584,x24585,x24586))
% 157.55/157.24 [2459]~E(x24591,x24592)+E(f638(x24593,x24594,x24591,x24595,x24596),f638(x24593,x24594,x24592,x24595,x24596))
% 157.55/157.24 [2460]~E(x24601,x24602)+E(f638(x24603,x24604,x24605,x24601,x24606),f638(x24603,x24604,x24605,x24602,x24606))
% 157.55/157.24 [2461]~E(x24611,x24612)+E(f638(x24613,x24614,x24615,x24616,x24611),f638(x24613,x24614,x24615,x24616,x24612))
% 157.55/157.24 [2462]~E(x24621,x24622)+E(f898(x24621,x24623,x24624,x24625),f898(x24622,x24623,x24624,x24625))
% 157.55/157.24 [2463]~E(x24631,x24632)+E(f898(x24633,x24631,x24634,x24635),f898(x24633,x24632,x24634,x24635))
% 157.55/157.24 [2464]~E(x24641,x24642)+E(f898(x24643,x24644,x24641,x24645),f898(x24643,x24644,x24642,x24645))
% 157.55/157.24 [2465]~E(x24651,x24652)+E(f898(x24653,x24654,x24655,x24651),f898(x24653,x24654,x24655,x24652))
% 157.55/157.24 [2466]~E(x24661,x24662)+E(f225(x24661,x24663,x24664,x24665,x24666),f225(x24662,x24663,x24664,x24665,x24666))
% 157.55/157.24 [2467]~E(x24671,x24672)+E(f225(x24673,x24671,x24674,x24675,x24676),f225(x24673,x24672,x24674,x24675,x24676))
% 157.55/157.24 [2468]~E(x24681,x24682)+E(f225(x24683,x24684,x24681,x24685,x24686),f225(x24683,x24684,x24682,x24685,x24686))
% 157.55/157.24 [2469]~E(x24691,x24692)+E(f225(x24693,x24694,x24695,x24691,x24696),f225(x24693,x24694,x24695,x24692,x24696))
% 157.55/157.24 [2470]~E(x24701,x24702)+E(f225(x24703,x24704,x24705,x24706,x24701),f225(x24703,x24704,x24705,x24706,x24702))
% 157.55/157.24 [2471]~E(x24711,x24712)+E(f361(x24711,x24713,x24714),f361(x24712,x24713,x24714))
% 157.55/157.24 [2472]~E(x24721,x24722)+E(f361(x24723,x24721,x24724),f361(x24723,x24722,x24724))
% 157.55/157.24 [2473]~E(x24731,x24732)+E(f361(x24733,x24734,x24731),f361(x24733,x24734,x24732))
% 157.55/157.24 [2474]~E(x24741,x24742)+E(f581(x24741,x24743,x24744),f581(x24742,x24743,x24744))
% 157.55/157.24 [2475]~E(x24751,x24752)+E(f581(x24753,x24751,x24754),f581(x24753,x24752,x24754))
% 157.55/157.24 [2476]~E(x24761,x24762)+E(f581(x24763,x24764,x24761),f581(x24763,x24764,x24762))
% 157.55/157.24 [2477]~E(x24771,x24772)+E(f523(x24771,x24773,x24774,x24775,x24776),f523(x24772,x24773,x24774,x24775,x24776))
% 157.55/157.24 [2478]~E(x24781,x24782)+E(f523(x24783,x24781,x24784,x24785,x24786),f523(x24783,x24782,x24784,x24785,x24786))
% 157.55/157.24 [2479]~E(x24791,x24792)+E(f523(x24793,x24794,x24791,x24795,x24796),f523(x24793,x24794,x24792,x24795,x24796))
% 157.55/157.24 [2480]~E(x24801,x24802)+E(f523(x24803,x24804,x24805,x24801,x24806),f523(x24803,x24804,x24805,x24802,x24806))
% 157.55/157.24 [2481]~E(x24811,x24812)+E(f523(x24813,x24814,x24815,x24816,x24811),f523(x24813,x24814,x24815,x24816,x24812))
% 157.55/157.24 [2482]~E(x24821,x24822)+E(f679(x24821,x24823,x24824,x24825),f679(x24822,x24823,x24824,x24825))
% 157.55/157.24 [2483]~E(x24831,x24832)+E(f679(x24833,x24831,x24834,x24835),f679(x24833,x24832,x24834,x24835))
% 157.55/157.24 [2484]~E(x24841,x24842)+E(f679(x24843,x24844,x24841,x24845),f679(x24843,x24844,x24842,x24845))
% 157.55/157.24 [2485]~E(x24851,x24852)+E(f679(x24853,x24854,x24855,x24851),f679(x24853,x24854,x24855,x24852))
% 157.55/157.24 [2486]~E(x24861,x24862)+E(f864(x24861,x24863,x24864,x24865,x24866,x24867,x24868),f864(x24862,x24863,x24864,x24865,x24866,x24867,x24868))
% 157.55/157.24 [2487]~E(x24871,x24872)+E(f864(x24873,x24871,x24874,x24875,x24876,x24877,x24878),f864(x24873,x24872,x24874,x24875,x24876,x24877,x24878))
% 157.55/157.24 [2488]~E(x24881,x24882)+E(f864(x24883,x24884,x24881,x24885,x24886,x24887,x24888),f864(x24883,x24884,x24882,x24885,x24886,x24887,x24888))
% 157.55/157.24 [2489]~E(x24891,x24892)+E(f864(x24893,x24894,x24895,x24891,x24896,x24897,x24898),f864(x24893,x24894,x24895,x24892,x24896,x24897,x24898))
% 157.55/157.24 [2490]~E(x24901,x24902)+E(f864(x24903,x24904,x24905,x24906,x24901,x24907,x24908),f864(x24903,x24904,x24905,x24906,x24902,x24907,x24908))
% 157.55/157.24 [2491]~E(x24911,x24912)+E(f864(x24913,x24914,x24915,x24916,x24917,x24911,x24918),f864(x24913,x24914,x24915,x24916,x24917,x24912,x24918))
% 157.55/157.24 [2492]~E(x24921,x24922)+E(f864(x24923,x24924,x24925,x24926,x24927,x24928,x24921),f864(x24923,x24924,x24925,x24926,x24927,x24928,x24922))
% 157.55/157.24 [2493]~E(x24931,x24932)+E(f786(x24931),f786(x24932))
% 157.55/157.24 [2494]~E(x24941,x24942)+E(f336(x24941),f336(x24942))
% 157.55/157.24 [2495]~E(x24951,x24952)+E(f557(x24951,x24953,x24954,x24955),f557(x24952,x24953,x24954,x24955))
% 157.55/157.24 [2496]~E(x24961,x24962)+E(f557(x24963,x24961,x24964,x24965),f557(x24963,x24962,x24964,x24965))
% 157.55/157.24 [2497]~E(x24971,x24972)+E(f557(x24973,x24974,x24971,x24975),f557(x24973,x24974,x24972,x24975))
% 157.55/157.24 [2498]~E(x24981,x24982)+E(f557(x24983,x24984,x24985,x24981),f557(x24983,x24984,x24985,x24982))
% 157.55/157.24 [2499]~E(x24991,x24992)+E(f259(x24991,x24993,x24994,x24995,x24996),f259(x24992,x24993,x24994,x24995,x24996))
% 157.55/157.24 [2500]~E(x25001,x25002)+E(f259(x25003,x25001,x25004,x25005,x25006),f259(x25003,x25002,x25004,x25005,x25006))
% 157.55/157.24 [2501]~E(x25011,x25012)+E(f259(x25013,x25014,x25011,x25015,x25016),f259(x25013,x25014,x25012,x25015,x25016))
% 157.55/157.24 [2502]~E(x25021,x25022)+E(f259(x25023,x25024,x25025,x25021,x25026),f259(x25023,x25024,x25025,x25022,x25026))
% 157.55/157.24 [2503]~E(x25031,x25032)+E(f259(x25033,x25034,x25035,x25036,x25031),f259(x25033,x25034,x25035,x25036,x25032))
% 157.55/157.24 [2504]~E(x25041,x25042)+E(f430(x25041,x25043,x25044,x25045),f430(x25042,x25043,x25044,x25045))
% 157.55/157.24 [2505]~E(x25051,x25052)+E(f430(x25053,x25051,x25054,x25055),f430(x25053,x25052,x25054,x25055))
% 157.55/157.24 [2506]~E(x25061,x25062)+E(f430(x25063,x25064,x25061,x25065),f430(x25063,x25064,x25062,x25065))
% 157.55/157.24 [2507]~E(x25071,x25072)+E(f430(x25073,x25074,x25075,x25071),f430(x25073,x25074,x25075,x25072))
% 157.55/157.24 [2508]~E(x25081,x25082)+E(f474(x25081,x25083,x25084),f474(x25082,x25083,x25084))
% 157.55/157.24 [2509]~E(x25091,x25092)+E(f474(x25093,x25091,x25094),f474(x25093,x25092,x25094))
% 157.55/157.24 [2510]~E(x25101,x25102)+E(f474(x25103,x25104,x25101),f474(x25103,x25104,x25102))
% 157.55/157.24 [2511]~E(x25111,x25112)+E(f540(x25111,x25113,x25114,x25115,x25116),f540(x25112,x25113,x25114,x25115,x25116))
% 157.55/157.24 [2512]~E(x25121,x25122)+E(f540(x25123,x25121,x25124,x25125,x25126),f540(x25123,x25122,x25124,x25125,x25126))
% 157.55/157.24 [2513]~E(x25131,x25132)+E(f540(x25133,x25134,x25131,x25135,x25136),f540(x25133,x25134,x25132,x25135,x25136))
% 157.55/157.24 [2514]~E(x25141,x25142)+E(f540(x25143,x25144,x25145,x25141,x25146),f540(x25143,x25144,x25145,x25142,x25146))
% 157.55/157.24 [2515]~E(x25151,x25152)+E(f540(x25153,x25154,x25155,x25156,x25151),f540(x25153,x25154,x25155,x25156,x25152))
% 157.55/157.24 [2516]~E(x25161,x25162)+E(f692(x25161,x25163),f692(x25162,x25163))
% 157.55/157.24 [2517]~E(x25171,x25172)+E(f692(x25173,x25171),f692(x25173,x25172))
% 157.55/157.24 [2518]~E(x25181,x25182)+E(f593(x25181,x25183,x25184),f593(x25182,x25183,x25184))
% 157.55/157.24 [2519]~E(x25191,x25192)+E(f593(x25193,x25191,x25194),f593(x25193,x25192,x25194))
% 157.55/157.24 [2520]~E(x25201,x25202)+E(f593(x25203,x25204,x25201),f593(x25203,x25204,x25202))
% 157.55/157.24 [2521]~E(x25211,x25212)+E(f475(x25211,x25213,x25214),f475(x25212,x25213,x25214))
% 157.55/157.24 [2522]~E(x25221,x25222)+E(f475(x25223,x25221,x25224),f475(x25223,x25222,x25224))
% 157.55/157.24 [2523]~E(x25231,x25232)+E(f475(x25233,x25234,x25231),f475(x25233,x25234,x25232))
% 157.55/157.24 [2524]~E(x25241,x25242)+E(f292(x25241,x25243),f292(x25242,x25243))
% 157.55/157.24 [2525]~E(x25251,x25252)+E(f292(x25253,x25251),f292(x25253,x25252))
% 157.55/157.24 [2526]~E(x25261,x25262)+E(f218(x25261,x25263),f218(x25262,x25263))
% 157.55/157.24 [2527]~E(x25271,x25272)+E(f218(x25273,x25271),f218(x25273,x25272))
% 157.55/157.24 [2528]~E(x25281,x25282)+E(f485(x25281,x25283,x25284),f485(x25282,x25283,x25284))
% 157.55/157.24 [2529]~E(x25291,x25292)+E(f485(x25293,x25291,x25294),f485(x25293,x25292,x25294))
% 157.55/157.24 [2530]~E(x25301,x25302)+E(f485(x25303,x25304,x25301),f485(x25303,x25304,x25302))
% 157.55/157.24 [2531]~E(x25311,x25312)+E(f748(x25311,x25313,x25314),f748(x25312,x25313,x25314))
% 157.55/157.24 [2532]~E(x25321,x25322)+E(f748(x25323,x25321,x25324),f748(x25323,x25322,x25324))
% 157.55/157.24 [2533]~E(x25331,x25332)+E(f748(x25333,x25334,x25331),f748(x25333,x25334,x25332))
% 157.55/157.24 [2534]~E(x25341,x25342)+E(f366(x25341),f366(x25342))
% 157.55/157.24 [2535]~E(x25351,x25352)+E(f880(x25351,x25353,x25354,x25355,x25356),f880(x25352,x25353,x25354,x25355,x25356))
% 157.55/157.24 [2536]~E(x25361,x25362)+E(f880(x25363,x25361,x25364,x25365,x25366),f880(x25363,x25362,x25364,x25365,x25366))
% 157.55/157.24 [2537]~E(x25371,x25372)+E(f880(x25373,x25374,x25371,x25375,x25376),f880(x25373,x25374,x25372,x25375,x25376))
% 157.55/157.24 [2538]~E(x25381,x25382)+E(f880(x25383,x25384,x25385,x25381,x25386),f880(x25383,x25384,x25385,x25382,x25386))
% 157.55/157.24 [2539]~E(x25391,x25392)+E(f880(x25393,x25394,x25395,x25396,x25391),f880(x25393,x25394,x25395,x25396,x25392))
% 157.55/157.24 [2540]~E(x25401,x25402)+E(f641(x25401,x25403,x25404,x25405,x25406,x25407),f641(x25402,x25403,x25404,x25405,x25406,x25407))
% 157.55/157.24 [2541]~E(x25411,x25412)+E(f641(x25413,x25411,x25414,x25415,x25416,x25417),f641(x25413,x25412,x25414,x25415,x25416,x25417))
% 157.55/157.24 [2542]~E(x25421,x25422)+E(f641(x25423,x25424,x25421,x25425,x25426,x25427),f641(x25423,x25424,x25422,x25425,x25426,x25427))
% 157.55/157.24 [2543]~E(x25431,x25432)+E(f641(x25433,x25434,x25435,x25431,x25436,x25437),f641(x25433,x25434,x25435,x25432,x25436,x25437))
% 157.55/157.24 [2544]~E(x25441,x25442)+E(f641(x25443,x25444,x25445,x25446,x25441,x25447),f641(x25443,x25444,x25445,x25446,x25442,x25447))
% 157.55/157.24 [2545]~E(x25451,x25452)+E(f641(x25453,x25454,x25455,x25456,x25457,x25451),f641(x25453,x25454,x25455,x25456,x25457,x25452))
% 157.55/157.24 [2546]~E(x25461,x25462)+E(f887(x25461,x25463,x25464,x25465,x25466),f887(x25462,x25463,x25464,x25465,x25466))
% 157.55/157.24 [2547]~E(x25471,x25472)+E(f887(x25473,x25471,x25474,x25475,x25476),f887(x25473,x25472,x25474,x25475,x25476))
% 157.55/157.24 [2548]~E(x25481,x25482)+E(f887(x25483,x25484,x25481,x25485,x25486),f887(x25483,x25484,x25482,x25485,x25486))
% 157.55/157.24 [2549]~E(x25491,x25492)+E(f887(x25493,x25494,x25495,x25491,x25496),f887(x25493,x25494,x25495,x25492,x25496))
% 157.55/157.24 [2550]~E(x25501,x25502)+E(f887(x25503,x25504,x25505,x25506,x25501),f887(x25503,x25504,x25505,x25506,x25502))
% 157.55/157.24 [2551]~E(x25511,x25512)+E(f807(x25511,x25513,x25514,x25515,x25516),f807(x25512,x25513,x25514,x25515,x25516))
% 157.55/157.24 [2552]~E(x25521,x25522)+E(f807(x25523,x25521,x25524,x25525,x25526),f807(x25523,x25522,x25524,x25525,x25526))
% 157.55/157.24 [2553]~E(x25531,x25532)+E(f807(x25533,x25534,x25531,x25535,x25536),f807(x25533,x25534,x25532,x25535,x25536))
% 157.55/157.24 [2554]~E(x25541,x25542)+E(f807(x25543,x25544,x25545,x25541,x25546),f807(x25543,x25544,x25545,x25542,x25546))
% 157.55/157.24 [2555]~E(x25551,x25552)+E(f807(x25553,x25554,x25555,x25556,x25551),f807(x25553,x25554,x25555,x25556,x25552))
% 157.55/157.24 [2556]~E(x25561,x25562)+E(f585(x25561,x25563,x25564,x25565,x25566,x25567),f585(x25562,x25563,x25564,x25565,x25566,x25567))
% 157.55/157.24 [2557]~E(x25571,x25572)+E(f585(x25573,x25571,x25574,x25575,x25576,x25577),f585(x25573,x25572,x25574,x25575,x25576,x25577))
% 157.55/157.24 [2558]~E(x25581,x25582)+E(f585(x25583,x25584,x25581,x25585,x25586,x25587),f585(x25583,x25584,x25582,x25585,x25586,x25587))
% 157.55/157.24 [2559]~E(x25591,x25592)+E(f585(x25593,x25594,x25595,x25591,x25596,x25597),f585(x25593,x25594,x25595,x25592,x25596,x25597))
% 157.55/157.24 [2560]~E(x25601,x25602)+E(f585(x25603,x25604,x25605,x25606,x25601,x25607),f585(x25603,x25604,x25605,x25606,x25602,x25607))
% 157.55/157.24 [2561]~E(x25611,x25612)+E(f585(x25613,x25614,x25615,x25616,x25617,x25611),f585(x25613,x25614,x25615,x25616,x25617,x25612))
% 157.55/157.24 [2562]~E(x25621,x25622)+E(f720(x25621,x25623),f720(x25622,x25623))
% 157.55/157.24 [2563]~E(x25631,x25632)+E(f720(x25633,x25631),f720(x25633,x25632))
% 157.55/157.24 [2564]~E(x25641,x25642)+E(f208(x25641),f208(x25642))
% 157.55/157.24 [2565]~E(x25651,x25652)+E(f869(x25651,x25653,x25654),f869(x25652,x25653,x25654))
% 157.55/157.24 [2566]~E(x25661,x25662)+E(f869(x25663,x25661,x25664),f869(x25663,x25662,x25664))
% 157.55/157.24 [2567]~E(x25671,x25672)+E(f869(x25673,x25674,x25671),f869(x25673,x25674,x25672))
% 157.55/157.24 [2568]~E(x25681,x25682)+E(f427(x25681,x25683,x25684,x25685),f427(x25682,x25683,x25684,x25685))
% 157.55/157.24 [2569]~E(x25691,x25692)+E(f427(x25693,x25691,x25694,x25695),f427(x25693,x25692,x25694,x25695))
% 157.55/157.24 [2570]~E(x25701,x25702)+E(f427(x25703,x25704,x25701,x25705),f427(x25703,x25704,x25702,x25705))
% 157.55/157.24 [2571]~E(x25711,x25712)+E(f427(x25713,x25714,x25715,x25711),f427(x25713,x25714,x25715,x25712))
% 157.55/157.24 [2572]~E(x25721,x25722)+E(f268(x25721,x25723),f268(x25722,x25723))
% 157.55/157.24 [2573]~E(x25731,x25732)+E(f268(x25733,x25731),f268(x25733,x25732))
% 157.55/157.24 [2574]~E(x25741,x25742)+E(f704(x25741,x25743),f704(x25742,x25743))
% 157.55/157.24 [2575]~E(x25751,x25752)+E(f704(x25753,x25751),f704(x25753,x25752))
% 157.55/157.24 [2576]~E(x25761,x25762)+E(f750(x25761,x25763,x25764),f750(x25762,x25763,x25764))
% 157.55/157.24 [2577]~E(x25771,x25772)+E(f750(x25773,x25771,x25774),f750(x25773,x25772,x25774))
% 157.55/157.24 [2578]~E(x25781,x25782)+E(f750(x25783,x25784,x25781),f750(x25783,x25784,x25782))
% 157.55/157.24 [2579]~E(x25791,x25792)+E(f721(x25791,x25793),f721(x25792,x25793))
% 157.55/157.24 [2580]~E(x25801,x25802)+E(f721(x25803,x25801),f721(x25803,x25802))
% 157.55/157.24 [2581]~E(x25811,x25812)+E(f883(x25811,x25813),f883(x25812,x25813))
% 157.55/157.24 [2582]~E(x25821,x25822)+E(f883(x25823,x25821),f883(x25823,x25822))
% 157.55/157.24 [2583]~E(x25831,x25832)+E(f788(x25831,x25833),f788(x25832,x25833))
% 157.55/157.24 [2584]~E(x25841,x25842)+E(f788(x25843,x25841),f788(x25843,x25842))
% 157.55/157.24 [2585]~E(x25851,x25852)+E(f502(x25851,x25853,x25854,x25855),f502(x25852,x25853,x25854,x25855))
% 157.55/157.24 [2586]~E(x25861,x25862)+E(f502(x25863,x25861,x25864,x25865),f502(x25863,x25862,x25864,x25865))
% 157.55/157.24 [2587]~E(x25871,x25872)+E(f502(x25873,x25874,x25871,x25875),f502(x25873,x25874,x25872,x25875))
% 157.55/157.24 [2588]~E(x25881,x25882)+E(f502(x25883,x25884,x25885,x25881),f502(x25883,x25884,x25885,x25882))
% 157.55/157.24 [2589]~E(x25891,x25892)+E(f900(x25891,x25893,x25894),f900(x25892,x25893,x25894))
% 157.55/157.24 [2590]~E(x25901,x25902)+E(f900(x25903,x25901,x25904),f900(x25903,x25902,x25904))
% 157.55/157.24 [2591]~E(x25911,x25912)+E(f900(x25913,x25914,x25911),f900(x25913,x25914,x25912))
% 157.55/157.24 [2592]~E(x25921,x25922)+E(f625(x25921,x25923,x25924,x25925,x25926,x25927,x25928),f625(x25922,x25923,x25924,x25925,x25926,x25927,x25928))
% 157.55/157.24 [2593]~E(x25931,x25932)+E(f625(x25933,x25931,x25934,x25935,x25936,x25937,x25938),f625(x25933,x25932,x25934,x25935,x25936,x25937,x25938))
% 157.55/157.24 [2594]~E(x25941,x25942)+E(f625(x25943,x25944,x25941,x25945,x25946,x25947,x25948),f625(x25943,x25944,x25942,x25945,x25946,x25947,x25948))
% 157.55/157.24 [2595]~E(x25951,x25952)+E(f625(x25953,x25954,x25955,x25951,x25956,x25957,x25958),f625(x25953,x25954,x25955,x25952,x25956,x25957,x25958))
% 157.55/157.24 [2596]~E(x25961,x25962)+E(f625(x25963,x25964,x25965,x25966,x25961,x25967,x25968),f625(x25963,x25964,x25965,x25966,x25962,x25967,x25968))
% 157.55/157.24 [2597]~E(x25971,x25972)+E(f625(x25973,x25974,x25975,x25976,x25977,x25971,x25978),f625(x25973,x25974,x25975,x25976,x25977,x25972,x25978))
% 157.55/157.24 [2598]~E(x25981,x25982)+E(f625(x25983,x25984,x25985,x25986,x25987,x25988,x25981),f625(x25983,x25984,x25985,x25986,x25987,x25988,x25982))
% 157.55/157.24 [2599]~E(x25991,x25992)+E(f264(x25991,x25993,x25994),f264(x25992,x25993,x25994))
% 157.55/157.24 [2600]~E(x26001,x26002)+E(f264(x26003,x26001,x26004),f264(x26003,x26002,x26004))
% 157.55/157.24 [2601]~E(x26011,x26012)+E(f264(x26013,x26014,x26011),f264(x26013,x26014,x26012))
% 157.55/157.24 [2602]~E(x26021,x26022)+E(f124(x26021),f124(x26022))
% 157.55/157.24 [2603]~E(x26031,x26032)+E(f447(x26031,x26033,x26034,x26035),f447(x26032,x26033,x26034,x26035))
% 157.55/157.24 [2604]~E(x26041,x26042)+E(f447(x26043,x26041,x26044,x26045),f447(x26043,x26042,x26044,x26045))
% 157.55/157.24 [2605]~E(x26051,x26052)+E(f447(x26053,x26054,x26051,x26055),f447(x26053,x26054,x26052,x26055))
% 157.55/157.24 [2606]~E(x26061,x26062)+E(f447(x26063,x26064,x26065,x26061),f447(x26063,x26064,x26065,x26062))
% 157.55/157.24 [2607]~E(x26071,x26072)+E(f601(x26071,x26073,x26074,x26075),f601(x26072,x26073,x26074,x26075))
% 157.55/157.24 [2608]~E(x26081,x26082)+E(f601(x26083,x26081,x26084,x26085),f601(x26083,x26082,x26084,x26085))
% 157.55/157.24 [2609]~E(x26091,x26092)+E(f601(x26093,x26094,x26091,x26095),f601(x26093,x26094,x26092,x26095))
% 157.55/157.24 [2610]~E(x26101,x26102)+E(f601(x26103,x26104,x26105,x26101),f601(x26103,x26104,x26105,x26102))
% 157.55/157.24 [2611]~E(x26111,x26112)+E(f563(x26111,x26113,x26114,x26115),f563(x26112,x26113,x26114,x26115))
% 157.55/157.24 [2612]~E(x26121,x26122)+E(f563(x26123,x26121,x26124,x26125),f563(x26123,x26122,x26124,x26125))
% 157.55/157.24 [2613]~E(x26131,x26132)+E(f563(x26133,x26134,x26131,x26135),f563(x26133,x26134,x26132,x26135))
% 157.55/157.24 [2614]~E(x26141,x26142)+E(f563(x26143,x26144,x26145,x26141),f563(x26143,x26144,x26145,x26142))
% 157.55/157.24 [2615]~E(x26151,x26152)+E(f703(x26151,x26153),f703(x26152,x26153))
% 157.55/157.24 [2616]~E(x26161,x26162)+E(f703(x26163,x26161),f703(x26163,x26162))
% 157.55/157.24 [2617]~E(x26171,x26172)+E(f622(x26171,x26173,x26174,x26175),f622(x26172,x26173,x26174,x26175))
% 157.55/157.24 [2618]~E(x26181,x26182)+E(f622(x26183,x26181,x26184,x26185),f622(x26183,x26182,x26184,x26185))
% 157.55/157.24 [2619]~E(x26191,x26192)+E(f622(x26193,x26194,x26191,x26195),f622(x26193,x26194,x26192,x26195))
% 157.55/157.24 [2620]~E(x26201,x26202)+E(f622(x26203,x26204,x26205,x26201),f622(x26203,x26204,x26205,x26202))
% 157.55/157.24 [2621]~E(x26211,x26212)+E(f734(x26211,x26213),f734(x26212,x26213))
% 157.55/157.24 [2622]~E(x26221,x26222)+E(f734(x26223,x26221),f734(x26223,x26222))
% 157.55/157.24 [2623]~E(x26231,x26232)+E(f606(x26231,x26233,x26234),f606(x26232,x26233,x26234))
% 157.55/157.24 [2624]~E(x26241,x26242)+E(f606(x26243,x26241,x26244),f606(x26243,x26242,x26244))
% 157.55/157.24 [2625]~E(x26251,x26252)+E(f606(x26253,x26254,x26251),f606(x26253,x26254,x26252))
% 157.55/157.24 [2626]~E(x26261,x26262)+E(f657(x26261,x26263,x26264),f657(x26262,x26263,x26264))
% 157.55/157.24 [2627]~E(x26271,x26272)+E(f657(x26273,x26271,x26274),f657(x26273,x26272,x26274))
% 157.55/157.24 [2628]~E(x26281,x26282)+E(f657(x26283,x26284,x26281),f657(x26283,x26284,x26282))
% 157.55/157.24 [2629]~E(x26291,x26292)+E(f626(x26291,x26293,x26294,x26295,x26296),f626(x26292,x26293,x26294,x26295,x26296))
% 157.55/157.24 [2630]~E(x26301,x26302)+E(f626(x26303,x26301,x26304,x26305,x26306),f626(x26303,x26302,x26304,x26305,x26306))
% 157.55/157.24 [2631]~E(x26311,x26312)+E(f626(x26313,x26314,x26311,x26315,x26316),f626(x26313,x26314,x26312,x26315,x26316))
% 157.55/157.24 [2632]~E(x26321,x26322)+E(f626(x26323,x26324,x26325,x26321,x26326),f626(x26323,x26324,x26325,x26322,x26326))
% 157.55/157.24 [2633]~E(x26331,x26332)+E(f626(x26333,x26334,x26335,x26336,x26331),f626(x26333,x26334,x26335,x26336,x26332))
% 157.55/157.24 [2634]~E(x26341,x26342)+E(f882(x26341,x26343,x26344,x26345),f882(x26342,x26343,x26344,x26345))
% 157.55/157.24 [2635]~E(x26351,x26352)+E(f882(x26353,x26351,x26354,x26355),f882(x26353,x26352,x26354,x26355))
% 157.55/157.24 [2636]~E(x26361,x26362)+E(f882(x26363,x26364,x26361,x26365),f882(x26363,x26364,x26362,x26365))
% 157.55/157.24 [2637]~E(x26371,x26372)+E(f882(x26373,x26374,x26375,x26371),f882(x26373,x26374,x26375,x26372))
% 157.55/157.24 [2638]~E(x26381,x26382)+E(f834(x26381,x26383,x26384,x26385,x26386),f834(x26382,x26383,x26384,x26385,x26386))
% 157.55/157.24 [2639]~E(x26391,x26392)+E(f834(x26393,x26391,x26394,x26395,x26396),f834(x26393,x26392,x26394,x26395,x26396))
% 157.55/157.24 [2640]~E(x26401,x26402)+E(f834(x26403,x26404,x26401,x26405,x26406),f834(x26403,x26404,x26402,x26405,x26406))
% 157.55/157.24 [2641]~E(x26411,x26412)+E(f834(x26413,x26414,x26415,x26411,x26416),f834(x26413,x26414,x26415,x26412,x26416))
% 157.55/157.24 [2642]~E(x26421,x26422)+E(f834(x26423,x26424,x26425,x26426,x26421),f834(x26423,x26424,x26425,x26426,x26422))
% 157.55/157.24 [2643]~E(x26431,x26432)+E(f826(x26431,x26433,x26434,x26435),f826(x26432,x26433,x26434,x26435))
% 157.55/157.24 [2644]~E(x26441,x26442)+E(f826(x26443,x26441,x26444,x26445),f826(x26443,x26442,x26444,x26445))
% 157.55/157.24 [2645]~E(x26451,x26452)+E(f826(x26453,x26454,x26451,x26455),f826(x26453,x26454,x26452,x26455))
% 157.55/157.24 [2646]~E(x26461,x26462)+E(f826(x26463,x26464,x26465,x26461),f826(x26463,x26464,x26465,x26462))
% 157.55/157.24 [2647]~E(x26471,x26472)+E(f820(x26471,x26473,x26474,x26475),f820(x26472,x26473,x26474,x26475))
% 157.55/157.24 [2648]~E(x26481,x26482)+E(f820(x26483,x26481,x26484,x26485),f820(x26483,x26482,x26484,x26485))
% 157.55/157.24 [2649]~E(x26491,x26492)+E(f820(x26493,x26494,x26491,x26495),f820(x26493,x26494,x26492,x26495))
% 157.55/157.24 [2650]~E(x26501,x26502)+E(f820(x26503,x26504,x26505,x26501),f820(x26503,x26504,x26505,x26502))
% 157.55/157.24 [2651]~E(x26511,x26512)+E(f203(x26511,x26513,x26514),f203(x26512,x26513,x26514))
% 157.55/157.24 [2652]~E(x26521,x26522)+E(f203(x26523,x26521,x26524),f203(x26523,x26522,x26524))
% 157.55/157.24 [2653]~E(x26531,x26532)+E(f203(x26533,x26534,x26531),f203(x26533,x26534,x26532))
% 157.55/157.24 [2654]~E(x26541,x26542)+E(f744(x26541,x26543,x26544),f744(x26542,x26543,x26544))
% 157.55/157.24 [2655]~E(x26551,x26552)+E(f744(x26553,x26551,x26554),f744(x26553,x26552,x26554))
% 157.55/157.24 [2656]~E(x26561,x26562)+E(f744(x26563,x26564,x26561),f744(x26563,x26564,x26562))
% 157.55/157.24 [2657]~E(x26571,x26572)+E(f385(x26571,x26573,x26574),f385(x26572,x26573,x26574))
% 157.55/157.24 [2658]~E(x26581,x26582)+E(f385(x26583,x26581,x26584),f385(x26583,x26582,x26584))
% 157.55/157.24 [2659]~E(x26591,x26592)+E(f385(x26593,x26594,x26591),f385(x26593,x26594,x26592))
% 157.55/157.24 [2660]~E(x26601,x26602)+E(f123(x26601),f123(x26602))
% 157.55/157.24 [2661]~E(x26611,x26612)+E(f817(x26611,x26613),f817(x26612,x26613))
% 157.55/157.24 [2662]~E(x26621,x26622)+E(f817(x26623,x26621),f817(x26623,x26622))
% 157.55/157.24 [2663]~E(x26631,x26632)+E(f389(x26631,x26633,x26634),f389(x26632,x26633,x26634))
% 157.55/157.24 [2664]~E(x26641,x26642)+E(f389(x26643,x26641,x26644),f389(x26643,x26642,x26644))
% 157.55/157.24 [2665]~E(x26651,x26652)+E(f389(x26653,x26654,x26651),f389(x26653,x26654,x26652))
% 157.55/157.24 [2666]~E(x26661,x26662)+E(f756(x26661,x26663,x26664),f756(x26662,x26663,x26664))
% 157.55/157.24 [2667]~E(x26671,x26672)+E(f756(x26673,x26671,x26674),f756(x26673,x26672,x26674))
% 157.55/157.24 [2668]~E(x26681,x26682)+E(f756(x26683,x26684,x26681),f756(x26683,x26684,x26682))
% 157.55/157.24 [2669]~E(x26691,x26692)+E(f293(x26691,x26693,x26694),f293(x26692,x26693,x26694))
% 157.55/157.24 [2670]~E(x26701,x26702)+E(f293(x26703,x26701,x26704),f293(x26703,x26702,x26704))
% 157.55/157.24 [2671]~E(x26711,x26712)+E(f293(x26713,x26714,x26711),f293(x26713,x26714,x26712))
% 157.55/157.24 [2672]~E(x26721,x26722)+E(f896(x26721,x26723,x26724),f896(x26722,x26723,x26724))
% 157.55/157.24 [2673]~E(x26731,x26732)+E(f896(x26733,x26731,x26734),f896(x26733,x26732,x26734))
% 157.55/157.24 [2674]~E(x26741,x26742)+E(f896(x26743,x26744,x26741),f896(x26743,x26744,x26742))
% 157.55/157.24 [2675]~E(x26751,x26752)+E(f546(x26751,x26753),f546(x26752,x26753))
% 157.55/157.24 [2676]~E(x26761,x26762)+E(f546(x26763,x26761),f546(x26763,x26762))
% 157.55/157.24 [2677]~E(x26771,x26772)+E(f691(x26771,x26773),f691(x26772,x26773))
% 157.55/157.24 [2678]~E(x26781,x26782)+E(f691(x26783,x26781),f691(x26783,x26782))
% 157.55/157.24 [2679]~E(x26791,x26792)+E(f519(x26791,x26793,x26794),f519(x26792,x26793,x26794))
% 157.55/157.24 [2680]~E(x26801,x26802)+E(f519(x26803,x26801,x26804),f519(x26803,x26802,x26804))
% 157.55/157.24 [2681]~E(x26811,x26812)+E(f519(x26813,x26814,x26811),f519(x26813,x26814,x26812))
% 157.55/157.24 [2682]~E(x26821,x26822)+E(f889(x26821,x26823,x26824),f889(x26822,x26823,x26824))
% 157.55/157.24 [2683]~E(x26831,x26832)+E(f889(x26833,x26831,x26834),f889(x26833,x26832,x26834))
% 157.55/157.24 [2684]~E(x26841,x26842)+E(f889(x26843,x26844,x26841),f889(x26843,x26844,x26842))
% 157.55/157.24 [2685]~E(x26851,x26852)+E(f605(x26851,x26853,x26854,x26855,x26856,x26857,x26858,x26859),f605(x26852,x26853,x26854,x26855,x26856,x26857,x26858,x26859))
% 157.55/157.24 [2686]~E(x26861,x26862)+E(f605(x26863,x26861,x26864,x26865,x26866,x26867,x26868,x26869),f605(x26863,x26862,x26864,x26865,x26866,x26867,x26868,x26869))
% 157.55/157.24 [2687]~E(x26871,x26872)+E(f605(x26873,x26874,x26871,x26875,x26876,x26877,x26878,x26879),f605(x26873,x26874,x26872,x26875,x26876,x26877,x26878,x26879))
% 157.55/157.24 [2688]~E(x26881,x26882)+E(f605(x26883,x26884,x26885,x26881,x26886,x26887,x26888,x26889),f605(x26883,x26884,x26885,x26882,x26886,x26887,x26888,x26889))
% 157.55/157.24 [2689]~E(x26891,x26892)+E(f605(x26893,x26894,x26895,x26896,x26891,x26897,x26898,x26899),f605(x26893,x26894,x26895,x26896,x26892,x26897,x26898,x26899))
% 157.55/157.24 [2690]~E(x26901,x26902)+E(f605(x26903,x26904,x26905,x26906,x26907,x26901,x26908,x26909),f605(x26903,x26904,x26905,x26906,x26907,x26902,x26908,x26909))
% 157.55/157.24 [2691]~E(x26911,x26912)+E(f605(x26913,x26914,x26915,x26916,x26917,x26918,x26911,x26919),f605(x26913,x26914,x26915,x26916,x26917,x26918,x26912,x26919))
% 157.55/157.24 [2692]~E(x26921,x26922)+E(f605(x26923,x26924,x26925,x26926,x26927,x26928,x26929,x26921),f605(x26923,x26924,x26925,x26926,x26927,x26928,x26929,x26922))
% 157.55/157.24 [2693]~E(x26931,x26932)+E(f731(x26931,x26933,x26934,x26935,x26936),f731(x26932,x26933,x26934,x26935,x26936))
% 157.55/157.24 [2694]~E(x26941,x26942)+E(f731(x26943,x26941,x26944,x26945,x26946),f731(x26943,x26942,x26944,x26945,x26946))
% 157.55/157.24 [2695]~E(x26951,x26952)+E(f731(x26953,x26954,x26951,x26955,x26956),f731(x26953,x26954,x26952,x26955,x26956))
% 157.55/157.24 [2696]~E(x26961,x26962)+E(f731(x26963,x26964,x26965,x26961,x26966),f731(x26963,x26964,x26965,x26962,x26966))
% 157.55/157.24 [2697]~E(x26971,x26972)+E(f731(x26973,x26974,x26975,x26976,x26971),f731(x26973,x26974,x26975,x26976,x26972))
% 157.55/157.24 [2698]~E(x26981,x26982)+E(f548(x26981,x26983),f548(x26982,x26983))
% 157.55/157.24 [2699]~E(x26991,x26992)+E(f548(x26993,x26991),f548(x26993,x26992))
% 157.55/157.24 [2700]~E(x27001,x27002)+E(f531(x27001),f531(x27002))
% 157.55/157.24 [2701]~E(x27011,x27012)+E(f793(x27011,x27013),f793(x27012,x27013))
% 157.55/157.24 [2702]~E(x27021,x27022)+E(f793(x27023,x27021),f793(x27023,x27022))
% 157.55/157.24 [2703]~E(x27031,x27032)+E(f693(x27031,x27033,x27034,x27035),f693(x27032,x27033,x27034,x27035))
% 157.55/157.24 [2704]~E(x27041,x27042)+E(f693(x27043,x27041,x27044,x27045),f693(x27043,x27042,x27044,x27045))
% 157.55/157.24 [2705]~E(x27051,x27052)+E(f693(x27053,x27054,x27051,x27055),f693(x27053,x27054,x27052,x27055))
% 157.55/157.24 [2706]~E(x27061,x27062)+E(f693(x27063,x27064,x27065,x27061),f693(x27063,x27064,x27065,x27062))
% 157.55/157.24 [2707]~E(x27071,x27072)+E(f408(x27071,x27073,x27074,x27075,x27076),f408(x27072,x27073,x27074,x27075,x27076))
% 157.55/157.24 [2708]~E(x27081,x27082)+E(f408(x27083,x27081,x27084,x27085,x27086),f408(x27083,x27082,x27084,x27085,x27086))
% 157.55/157.24 [2709]~E(x27091,x27092)+E(f408(x27093,x27094,x27091,x27095,x27096),f408(x27093,x27094,x27092,x27095,x27096))
% 157.55/157.24 [2710]~E(x27101,x27102)+E(f408(x27103,x27104,x27105,x27101,x27106),f408(x27103,x27104,x27105,x27102,x27106))
% 157.55/157.24 [2711]~E(x27111,x27112)+E(f408(x27113,x27114,x27115,x27116,x27111),f408(x27113,x27114,x27115,x27116,x27112))
% 157.55/157.24 [2712]~E(x27121,x27122)+E(f560(x27121,x27123),f560(x27122,x27123))
% 157.55/157.24 [2713]~E(x27131,x27132)+E(f560(x27133,x27131),f560(x27133,x27132))
% 157.55/157.24 [2714]~E(x27141,x27142)+E(f846(x27141,x27143,x27144,x27145,x27146,x27147),f846(x27142,x27143,x27144,x27145,x27146,x27147))
% 157.55/157.24 [2715]~E(x27151,x27152)+E(f846(x27153,x27151,x27154,x27155,x27156,x27157),f846(x27153,x27152,x27154,x27155,x27156,x27157))
% 157.55/157.24 [2716]~E(x27161,x27162)+E(f846(x27163,x27164,x27161,x27165,x27166,x27167),f846(x27163,x27164,x27162,x27165,x27166,x27167))
% 157.55/157.24 [2717]~E(x27171,x27172)+E(f846(x27173,x27174,x27175,x27171,x27176,x27177),f846(x27173,x27174,x27175,x27172,x27176,x27177))
% 157.55/157.24 [2718]~E(x27181,x27182)+E(f846(x27183,x27184,x27185,x27186,x27181,x27187),f846(x27183,x27184,x27185,x27186,x27182,x27187))
% 157.55/157.24 [2719]~E(x27191,x27192)+E(f846(x27193,x27194,x27195,x27196,x27197,x27191),f846(x27193,x27194,x27195,x27196,x27197,x27192))
% 157.55/157.24 [2720]~E(x27201,x27202)+E(f549(x27201,x27203),f549(x27202,x27203))
% 157.55/157.24 [2721]~E(x27211,x27212)+E(f549(x27213,x27211),f549(x27213,x27212))
% 157.55/157.24 [2722]~E(x27221,x27222)+E(f542(x27221,x27223,x27224,x27225,x27226,x27227,x27228,x27229),f542(x27222,x27223,x27224,x27225,x27226,x27227,x27228,x27229))
% 157.55/157.24 [2723]~E(x27231,x27232)+E(f542(x27233,x27231,x27234,x27235,x27236,x27237,x27238,x27239),f542(x27233,x27232,x27234,x27235,x27236,x27237,x27238,x27239))
% 157.55/157.24 [2724]~E(x27241,x27242)+E(f542(x27243,x27244,x27241,x27245,x27246,x27247,x27248,x27249),f542(x27243,x27244,x27242,x27245,x27246,x27247,x27248,x27249))
% 157.55/157.24 [2725]~E(x27251,x27252)+E(f542(x27253,x27254,x27255,x27251,x27256,x27257,x27258,x27259),f542(x27253,x27254,x27255,x27252,x27256,x27257,x27258,x27259))
% 157.55/157.24 [2726]~E(x27261,x27262)+E(f542(x27263,x27264,x27265,x27266,x27261,x27267,x27268,x27269),f542(x27263,x27264,x27265,x27266,x27262,x27267,x27268,x27269))
% 157.55/157.24 [2727]~E(x27271,x27272)+E(f542(x27273,x27274,x27275,x27276,x27277,x27271,x27278,x27279),f542(x27273,x27274,x27275,x27276,x27277,x27272,x27278,x27279))
% 157.55/157.24 [2728]~E(x27281,x27282)+E(f542(x27283,x27284,x27285,x27286,x27287,x27288,x27281,x27289),f542(x27283,x27284,x27285,x27286,x27287,x27288,x27282,x27289))
% 157.55/157.24 [2729]~E(x27291,x27292)+E(f542(x27293,x27294,x27295,x27296,x27297,x27298,x27299,x27291),f542(x27293,x27294,x27295,x27296,x27297,x27298,x27299,x27292))
% 157.55/157.24 [2730]~E(x27301,x27302)+E(f743(x27301,x27303),f743(x27302,x27303))
% 157.55/157.24 [2731]~E(x27311,x27312)+E(f743(x27313,x27311),f743(x27313,x27312))
% 157.55/157.24 [2732]~E(x27321,x27322)+E(f488(x27321,x27323,x27324),f488(x27322,x27323,x27324))
% 157.55/157.24 [2733]~E(x27331,x27332)+E(f488(x27333,x27331,x27334),f488(x27333,x27332,x27334))
% 157.55/157.24 [2734]~E(x27341,x27342)+E(f488(x27343,x27344,x27341),f488(x27343,x27344,x27342))
% 157.55/157.24 [2735]~E(x27351,x27352)+E(f881(x27351,x27353,x27354,x27355,x27356),f881(x27352,x27353,x27354,x27355,x27356))
% 157.55/157.24 [2736]~E(x27361,x27362)+E(f881(x27363,x27361,x27364,x27365,x27366),f881(x27363,x27362,x27364,x27365,x27366))
% 157.55/157.24 [2737]~E(x27371,x27372)+E(f881(x27373,x27374,x27371,x27375,x27376),f881(x27373,x27374,x27372,x27375,x27376))
% 157.55/157.24 [2738]~E(x27381,x27382)+E(f881(x27383,x27384,x27385,x27381,x27386),f881(x27383,x27384,x27385,x27382,x27386))
% 157.55/157.24 [2739]~E(x27391,x27392)+E(f881(x27393,x27394,x27395,x27396,x27391),f881(x27393,x27394,x27395,x27396,x27392))
% 157.55/157.24 [2740]~E(x27401,x27402)+E(f831(x27401,x27403,x27404),f831(x27402,x27403,x27404))
% 157.55/157.24 [2741]~E(x27411,x27412)+E(f831(x27413,x27411,x27414),f831(x27413,x27412,x27414))
% 157.55/157.24 [2742]~E(x27421,x27422)+E(f831(x27423,x27424,x27421),f831(x27423,x27424,x27422))
% 157.55/157.24 [2743]~E(x27431,x27432)+E(f871(x27431,x27433,x27434),f871(x27432,x27433,x27434))
% 157.55/157.24 [2744]~E(x27441,x27442)+E(f871(x27443,x27441,x27444),f871(x27443,x27442,x27444))
% 157.55/157.24 [2745]~E(x27451,x27452)+E(f871(x27453,x27454,x27451),f871(x27453,x27454,x27452))
% 157.55/157.24 [2746]~E(x27461,x27462)+E(f755(x27461,x27463,x27464),f755(x27462,x27463,x27464))
% 157.55/157.24 [2747]~E(x27471,x27472)+E(f755(x27473,x27471,x27474),f755(x27473,x27472,x27474))
% 157.55/157.24 [2748]~E(x27481,x27482)+E(f755(x27483,x27484,x27481),f755(x27483,x27484,x27482))
% 157.55/157.24 [2749]~E(x27491,x27492)+E(f683(x27491,x27493,x27494,x27495,x27496),f683(x27492,x27493,x27494,x27495,x27496))
% 157.55/157.24 [2750]~E(x27501,x27502)+E(f683(x27503,x27501,x27504,x27505,x27506),f683(x27503,x27502,x27504,x27505,x27506))
% 157.55/157.24 [2751]~E(x27511,x27512)+E(f683(x27513,x27514,x27511,x27515,x27516),f683(x27513,x27514,x27512,x27515,x27516))
% 157.55/157.24 [2752]~E(x27521,x27522)+E(f683(x27523,x27524,x27525,x27521,x27526),f683(x27523,x27524,x27525,x27522,x27526))
% 157.55/157.24 [2753]~E(x27531,x27532)+E(f683(x27533,x27534,x27535,x27536,x27531),f683(x27533,x27534,x27535,x27536,x27532))
% 157.55/157.24 [2754]~E(x27541,x27542)+E(f368(x27541,x27543),f368(x27542,x27543))
% 157.55/157.24 [2755]~E(x27551,x27552)+E(f368(x27553,x27551),f368(x27553,x27552))
% 157.55/157.24 [2756]~E(x27561,x27562)+E(f805(x27561,x27563),f805(x27562,x27563))
% 157.55/157.24 [2757]~E(x27571,x27572)+E(f805(x27573,x27571),f805(x27573,x27572))
% 157.55/157.24 [2758]~E(x27581,x27582)+E(f226(x27581,x27583,x27584,x27585,x27586),f226(x27582,x27583,x27584,x27585,x27586))
% 157.55/157.24 [2759]~E(x27591,x27592)+E(f226(x27593,x27591,x27594,x27595,x27596),f226(x27593,x27592,x27594,x27595,x27596))
% 157.55/157.24 [2760]~E(x27601,x27602)+E(f226(x27603,x27604,x27601,x27605,x27606),f226(x27603,x27604,x27602,x27605,x27606))
% 157.55/157.24 [2761]~E(x27611,x27612)+E(f226(x27613,x27614,x27615,x27611,x27616),f226(x27613,x27614,x27615,x27612,x27616))
% 157.55/157.24 [2762]~E(x27621,x27622)+E(f226(x27623,x27624,x27625,x27626,x27621),f226(x27623,x27624,x27625,x27626,x27622))
% 157.55/157.24 [2763]~E(x27631,x27632)+E(f818(x27631,x27633),f818(x27632,x27633))
% 157.55/157.24 [2764]~E(x27641,x27642)+E(f818(x27643,x27641),f818(x27643,x27642))
% 157.55/157.24 [2765]~E(x27651,x27652)+E(f708(x27651,x27653,x27654),f708(x27652,x27653,x27654))
% 157.55/157.24 [2766]~E(x27661,x27662)+E(f708(x27663,x27661,x27664),f708(x27663,x27662,x27664))
% 157.55/157.24 [2767]~E(x27671,x27672)+E(f708(x27673,x27674,x27671),f708(x27673,x27674,x27672))
% 157.55/157.24 [2768]~E(x27681,x27682)+E(f868(x27681,x27683,x27684),f868(x27682,x27683,x27684))
% 157.55/157.24 [2769]~E(x27691,x27692)+E(f868(x27693,x27691,x27694),f868(x27693,x27692,x27694))
% 157.55/157.24 [2770]~E(x27701,x27702)+E(f868(x27703,x27704,x27701),f868(x27703,x27704,x27702))
% 157.55/157.24 [2771]~E(x27711,x27712)+E(f813(x27711),f813(x27712))
% 157.55/157.24 [2772]~E(x27721,x27722)+E(f556(x27721,x27723,x27724,x27725),f556(x27722,x27723,x27724,x27725))
% 157.55/157.24 [2773]~E(x27731,x27732)+E(f556(x27733,x27731,x27734,x27735),f556(x27733,x27732,x27734,x27735))
% 157.55/157.24 [2774]~E(x27741,x27742)+E(f556(x27743,x27744,x27741,x27745),f556(x27743,x27744,x27742,x27745))
% 157.55/157.24 [2775]~E(x27751,x27752)+E(f556(x27753,x27754,x27755,x27751),f556(x27753,x27754,x27755,x27752))
% 157.55/157.24 [2776]~E(x27761,x27762)+E(f877(x27761,x27763,x27764),f877(x27762,x27763,x27764))
% 157.55/157.24 [2777]~E(x27771,x27772)+E(f877(x27773,x27771,x27774),f877(x27773,x27772,x27774))
% 157.55/157.24 [2778]~E(x27781,x27782)+E(f877(x27783,x27784,x27781),f877(x27783,x27784,x27782))
% 157.55/157.24 [2779]~E(x27791,x27792)+E(f333(x27791,x27793),f333(x27792,x27793))
% 157.55/157.24 [2780]~E(x27801,x27802)+E(f333(x27803,x27801),f333(x27803,x27802))
% 157.55/157.24 [2781]~E(x27811,x27812)+E(f94(x27811,x27813,x27814,x27815),f94(x27812,x27813,x27814,x27815))
% 157.55/157.24 [2782]~E(x27821,x27822)+E(f94(x27823,x27821,x27824,x27825),f94(x27823,x27822,x27824,x27825))
% 157.55/157.24 [2783]~E(x27831,x27832)+E(f94(x27833,x27834,x27831,x27835),f94(x27833,x27834,x27832,x27835))
% 157.55/157.24 [2784]~E(x27841,x27842)+E(f94(x27843,x27844,x27845,x27841),f94(x27843,x27844,x27845,x27842))
% 157.55/157.24 [2785]~E(x27851,x27852)+E(f95(x27851,x27853,x27854,x27855),f95(x27852,x27853,x27854,x27855))
% 157.55/157.24 [2786]~E(x27861,x27862)+E(f95(x27863,x27861,x27864,x27865),f95(x27863,x27862,x27864,x27865))
% 157.55/157.24 [2787]~E(x27871,x27872)+E(f95(x27873,x27874,x27871,x27875),f95(x27873,x27874,x27872,x27875))
% 157.55/157.24 [2788]~E(x27881,x27882)+E(f95(x27883,x27884,x27885,x27881),f95(x27883,x27884,x27885,x27882))
% 157.55/157.24 [2789]~E(x27891,x27892)+E(f369(x27891,x27893),f369(x27892,x27893))
% 157.55/157.24 [2790]~E(x27901,x27902)+E(f369(x27903,x27901),f369(x27903,x27902))
% 157.55/157.24 [2791]~E(x27911,x27912)+E(f503(x27911,x27913,x27914,x27915,x27916),f503(x27912,x27913,x27914,x27915,x27916))
% 157.55/157.24 [2792]~E(x27921,x27922)+E(f503(x27923,x27921,x27924,x27925,x27926),f503(x27923,x27922,x27924,x27925,x27926))
% 157.55/157.24 [2793]~E(x27931,x27932)+E(f503(x27933,x27934,x27931,x27935,x27936),f503(x27933,x27934,x27932,x27935,x27936))
% 157.55/157.24 [2794]~E(x27941,x27942)+E(f503(x27943,x27944,x27945,x27941,x27946),f503(x27943,x27944,x27945,x27942,x27946))
% 157.55/157.24 [2795]~E(x27951,x27952)+E(f503(x27953,x27954,x27955,x27956,x27951),f503(x27953,x27954,x27955,x27956,x27952))
% 157.55/157.24 [2796]~E(x27961,x27962)+E(f260(x27961,x27963,x27964,x27965,x27966),f260(x27962,x27963,x27964,x27965,x27966))
% 157.55/157.24 [2797]~E(x27971,x27972)+E(f260(x27973,x27971,x27974,x27975,x27976),f260(x27973,x27972,x27974,x27975,x27976))
% 157.55/157.24 [2798]~E(x27981,x27982)+E(f260(x27983,x27984,x27981,x27985,x27986),f260(x27983,x27984,x27982,x27985,x27986))
% 157.55/157.24 [2799]~E(x27991,x27992)+E(f260(x27993,x27994,x27995,x27991,x27996),f260(x27993,x27994,x27995,x27992,x27996))
% 157.55/157.24 [2800]~E(x28001,x28002)+E(f260(x28003,x28004,x28005,x28006,x28001),f260(x28003,x28004,x28005,x28006,x28002))
% 157.55/157.24 [2801]~E(x28011,x28012)+E(f685(x28011,x28013,x28014),f685(x28012,x28013,x28014))
% 157.55/157.24 [2802]~E(x28021,x28022)+E(f685(x28023,x28021,x28024),f685(x28023,x28022,x28024))
% 157.55/157.24 [2803]~E(x28031,x28032)+E(f685(x28033,x28034,x28031),f685(x28033,x28034,x28032))
% 157.55/157.24 [2804]~E(x28041,x28042)+E(f816(x28041,x28043,x28044),f816(x28042,x28043,x28044))
% 157.55/157.24 [2805]~E(x28051,x28052)+E(f816(x28053,x28051,x28054),f816(x28053,x28052,x28054))
% 157.55/157.24 [2806]~E(x28061,x28062)+E(f816(x28063,x28064,x28061),f816(x28063,x28064,x28062))
% 157.55/157.24 [2807]~E(x28071,x28072)+E(f375(x28071),f375(x28072))
% 157.55/157.24 [2808]~E(x28081,x28082)+E(f749(x28081,x28083,x28084),f749(x28082,x28083,x28084))
% 157.55/157.24 [2809]~E(x28091,x28092)+E(f749(x28093,x28091,x28094),f749(x28093,x28092,x28094))
% 157.55/157.24 [2810]~E(x28101,x28102)+E(f749(x28103,x28104,x28101),f749(x28103,x28104,x28102))
% 157.55/157.24 [2811]~E(x28111,x28112)+E(f341(x28111),f341(x28112))
% 157.55/157.24 [2812]~E(x28121,x28122)+E(f335(x28121,x28123),f335(x28122,x28123))
% 157.55/157.24 [2813]~E(x28131,x28132)+E(f335(x28133,x28131),f335(x28133,x28132))
% 157.55/157.24 [2814]~E(x28141,x28142)+E(f884(x28141,x28143),f884(x28142,x28143))
% 157.55/157.24 [2815]~E(x28151,x28152)+E(f884(x28153,x28151),f884(x28153,x28152))
% 157.55/157.24 [2816]~P1(x28161)+P1(x28162)+~E(x28161,x28162)
% 157.55/157.24 [2817]~P105(x28171)+P105(x28172)+~E(x28171,x28172)
% 157.55/157.24 [2818]P11(x28182,x28183,x28184,x28185,x28186,x28187)+~E(x28181,x28182)+~P11(x28181,x28183,x28184,x28185,x28186,x28187)
% 157.55/157.24 [2819]P11(x28193,x28192,x28194,x28195,x28196,x28197)+~E(x28191,x28192)+~P11(x28193,x28191,x28194,x28195,x28196,x28197)
% 157.55/157.24 [2820]P11(x28203,x28204,x28202,x28205,x28206,x28207)+~E(x28201,x28202)+~P11(x28203,x28204,x28201,x28205,x28206,x28207)
% 157.55/157.24 [2821]P11(x28213,x28214,x28215,x28212,x28216,x28217)+~E(x28211,x28212)+~P11(x28213,x28214,x28215,x28211,x28216,x28217)
% 157.55/157.24 [2822]P11(x28223,x28224,x28225,x28226,x28222,x28227)+~E(x28221,x28222)+~P11(x28223,x28224,x28225,x28226,x28221,x28227)
% 157.55/157.24 [2823]P11(x28233,x28234,x28235,x28236,x28237,x28232)+~E(x28231,x28232)+~P11(x28233,x28234,x28235,x28236,x28237,x28231)
% 157.55/157.24 [2824]~P106(x28241)+P106(x28242)+~E(x28241,x28242)
% 157.55/157.24 [2825]~P108(x28251)+P108(x28252)+~E(x28251,x28252)
% 157.55/157.24 [2826]~P79(x28261)+P79(x28262)+~E(x28261,x28262)
% 157.55/157.24 [2827]~P4(x28271)+P4(x28272)+~E(x28271,x28272)
% 157.55/157.24 [2828]~P107(x28281)+P107(x28282)+~E(x28281,x28282)
% 157.55/157.24 [2829]~P86(x28291)+P86(x28292)+~E(x28291,x28292)
% 157.55/157.24 [2830]~P126(x28301)+P126(x28302)+~E(x28301,x28302)
% 157.55/157.24 [2831]~P94(x28311)+P94(x28312)+~E(x28311,x28312)
% 157.55/157.24 [2832]~P112(x28321)+P112(x28322)+~E(x28321,x28322)
% 157.55/157.24 [2833]~P113(x28331)+P113(x28332)+~E(x28331,x28332)
% 157.55/157.24 [2834]~P98(x28341)+P98(x28342)+~E(x28341,x28342)
% 157.55/157.24 [2835]~P109(x28351)+P109(x28352)+~E(x28351,x28352)
% 157.55/157.24 [2836]~P59(x28361)+P59(x28362)+~E(x28361,x28362)
% 157.55/157.24 [2837]P24(x28372,x28373,x28374,x28375)+~E(x28371,x28372)+~P24(x28371,x28373,x28374,x28375)
% 157.55/157.24 [2838]P24(x28383,x28382,x28384,x28385)+~E(x28381,x28382)+~P24(x28383,x28381,x28384,x28385)
% 157.55/157.24 [2839]P24(x28393,x28394,x28392,x28395)+~E(x28391,x28392)+~P24(x28393,x28394,x28391,x28395)
% 157.55/157.24 [2840]P24(x28403,x28404,x28405,x28402)+~E(x28401,x28402)+~P24(x28403,x28404,x28405,x28401)
% 157.55/157.24 [2841]~P75(x28411)+P75(x28412)+~E(x28411,x28412)
% 157.55/157.24 [2842]~P2(x28421)+P2(x28422)+~E(x28421,x28422)
% 157.55/157.24 [2843]~P63(x28431)+P63(x28432)+~E(x28431,x28432)
% 157.55/157.24 [2844]~P67(x28441)+P67(x28442)+~E(x28441,x28442)
% 157.55/157.24 [2845]~P100(x28451)+P100(x28452)+~E(x28451,x28452)
% 157.55/157.24 [2846]~P77(x28461)+P77(x28462)+~E(x28461,x28462)
% 157.55/157.24 [2847]P36(x28472,x28473)+~E(x28471,x28472)+~P36(x28471,x28473)
% 157.55/157.24 [2848]P36(x28483,x28482)+~E(x28481,x28482)+~P36(x28483,x28481)
% 157.55/157.24 [2849]~P65(x28491)+P65(x28492)+~E(x28491,x28492)
% 157.55/157.24 [2850]~P78(x28501)+P78(x28502)+~E(x28501,x28502)
% 157.55/157.24 [2851]~P124(x28511)+P124(x28512)+~E(x28511,x28512)
% 157.55/157.24 [2852]P12(x28522,x28523)+~E(x28521,x28522)+~P12(x28521,x28523)
% 157.55/157.24 [2853]P12(x28533,x28532)+~E(x28531,x28532)+~P12(x28533,x28531)
% 157.55/157.24 [2854]~P96(x28541)+P96(x28542)+~E(x28541,x28542)
% 157.55/157.24 [2855]P18(x28552,x28553,x28554,x28555)+~E(x28551,x28552)+~P18(x28551,x28553,x28554,x28555)
% 157.55/157.24 [2856]P18(x28563,x28562,x28564,x28565)+~E(x28561,x28562)+~P18(x28563,x28561,x28564,x28565)
% 157.55/157.24 [2857]P18(x28573,x28574,x28572,x28575)+~E(x28571,x28572)+~P18(x28573,x28574,x28571,x28575)
% 157.55/157.24 [2858]P18(x28583,x28584,x28585,x28582)+~E(x28581,x28582)+~P18(x28583,x28584,x28585,x28581)
% 157.55/157.24 [2859]~P3(x28591)+P3(x28592)+~E(x28591,x28592)
% 157.55/157.24 [2860]~P69(x28601)+P69(x28602)+~E(x28601,x28602)
% 157.55/157.24 [2861]~P66(x28611)+P66(x28612)+~E(x28611,x28612)
% 157.55/157.24 [2862]~P110(x28621)+P110(x28622)+~E(x28621,x28622)
% 157.55/157.24 [2863]P29(x28632,x28633,x28634)+~E(x28631,x28632)+~P29(x28631,x28633,x28634)
% 157.55/157.24 [2864]P29(x28643,x28642,x28644)+~E(x28641,x28642)+~P29(x28643,x28641,x28644)
% 157.55/157.24 [2865]P29(x28653,x28654,x28652)+~E(x28651,x28652)+~P29(x28653,x28654,x28651)
% 157.55/157.24 [2866]~P93(x28661)+P93(x28662)+~E(x28661,x28662)
% 157.55/157.24 [2867]~P39(x28671)+P39(x28672)+~E(x28671,x28672)
% 157.55/157.24 [2868]~P101(x28681)+P101(x28682)+~E(x28681,x28682)
% 157.55/157.24 [2869]P34(x28692,x28693,x28694)+~E(x28691,x28692)+~P34(x28691,x28693,x28694)
% 157.55/157.24 [2870]P34(x28703,x28702,x28704)+~E(x28701,x28702)+~P34(x28703,x28701,x28704)
% 157.55/157.24 [2871]P34(x28713,x28714,x28712)+~E(x28711,x28712)+~P34(x28713,x28714,x28711)
% 157.55/157.24 [2872]P37(x28722,x28723)+~E(x28721,x28722)+~P37(x28721,x28723)
% 157.55/157.24 [2873]P37(x28733,x28732)+~E(x28731,x28732)+~P37(x28733,x28731)
% 157.55/157.24 [2874]~P62(x28741)+P62(x28742)+~E(x28741,x28742)
% 157.55/157.24 [2875]~P64(x28751)+P64(x28752)+~E(x28751,x28752)
% 157.55/157.24 [2876]P32(x28762,x28763,x28764)+~E(x28761,x28762)+~P32(x28761,x28763,x28764)
% 157.55/157.24 [2877]P32(x28773,x28772,x28774)+~E(x28771,x28772)+~P32(x28773,x28771,x28774)
% 157.55/157.24 [2878]P32(x28783,x28784,x28782)+~E(x28781,x28782)+~P32(x28783,x28784,x28781)
% 157.55/157.24 [2879]P30(x28792,x28793,x28794)+~E(x28791,x28792)+~P30(x28791,x28793,x28794)
% 157.55/157.24 [2880]P30(x28803,x28802,x28804)+~E(x28801,x28802)+~P30(x28803,x28801,x28804)
% 157.55/157.24 [2881]P30(x28813,x28814,x28812)+~E(x28811,x28812)+~P30(x28813,x28814,x28811)
% 157.55/157.24 [2882]~P73(x28821)+P73(x28822)+~E(x28821,x28822)
% 157.55/157.24 [2883]~P5(x28831)+P5(x28832)+~E(x28831,x28832)
% 157.55/157.24 [2884]~P83(x28841)+P83(x28842)+~E(x28841,x28842)
% 157.55/157.24 [2885]P33(x28852,x28853,x28854,x28855,x28856)+~E(x28851,x28852)+~P33(x28851,x28853,x28854,x28855,x28856)
% 157.55/157.24 [2886]P33(x28863,x28862,x28864,x28865,x28866)+~E(x28861,x28862)+~P33(x28863,x28861,x28864,x28865,x28866)
% 157.55/157.24 [2887]P33(x28873,x28874,x28872,x28875,x28876)+~E(x28871,x28872)+~P33(x28873,x28874,x28871,x28875,x28876)
% 157.55/157.24 [2888]P33(x28883,x28884,x28885,x28882,x28886)+~E(x28881,x28882)+~P33(x28883,x28884,x28885,x28881,x28886)
% 157.55/157.24 [2889]P33(x28893,x28894,x28895,x28896,x28892)+~E(x28891,x28892)+~P33(x28893,x28894,x28895,x28896,x28891)
% 157.55/157.24 [2890]~P82(x28901)+P82(x28902)+~E(x28901,x28902)
% 157.55/157.24 [2891]~P70(x28911)+P70(x28912)+~E(x28911,x28912)
% 157.55/157.24 [2892]P145(x28922,x28923,x28924)+~E(x28921,x28922)+~P145(x28921,x28923,x28924)
% 157.55/157.24 [2893]P145(x28933,x28932,x28934)+~E(x28931,x28932)+~P145(x28933,x28931,x28934)
% 157.55/157.24 [2894]P145(x28943,x28944,x28942)+~E(x28941,x28942)+~P145(x28943,x28944,x28941)
% 157.55/157.24 [2895]~P74(x28951)+P74(x28952)+~E(x28951,x28952)
% 157.55/157.24 [2896]~P71(x28961)+P71(x28962)+~E(x28961,x28962)
% 157.55/157.24 [2897]P25(x28972,x28973,x28974,x28975,x28976)+~E(x28971,x28972)+~P25(x28971,x28973,x28974,x28975,x28976)
% 157.55/157.24 [2898]P25(x28983,x28982,x28984,x28985,x28986)+~E(x28981,x28982)+~P25(x28983,x28981,x28984,x28985,x28986)
% 157.55/157.24 [2899]P25(x28993,x28994,x28992,x28995,x28996)+~E(x28991,x28992)+~P25(x28993,x28994,x28991,x28995,x28996)
% 157.55/157.24 [2900]P25(x29003,x29004,x29005,x29002,x29006)+~E(x29001,x29002)+~P25(x29003,x29004,x29005,x29001,x29006)
% 157.55/157.24 [2901]P25(x29013,x29014,x29015,x29016,x29012)+~E(x29011,x29012)+~P25(x29013,x29014,x29015,x29016,x29011)
% 157.55/157.24 [2902]P51(x29022,x29023,x29024)+~E(x29021,x29022)+~P51(x29021,x29023,x29024)
% 157.55/157.24 [2903]P51(x29033,x29032,x29034)+~E(x29031,x29032)+~P51(x29033,x29031,x29034)
% 157.55/157.24 [2904]P51(x29043,x29044,x29042)+~E(x29041,x29042)+~P51(x29043,x29044,x29041)
% 157.55/157.24 [2905]~P68(x29051)+P68(x29052)+~E(x29051,x29052)
% 157.55/157.24 [2906]P22(x29062,x29063,x29064,x29065,x29066,x29067)+~E(x29061,x29062)+~P22(x29061,x29063,x29064,x29065,x29066,x29067)
% 157.55/157.24 [2907]P22(x29073,x29072,x29074,x29075,x29076,x29077)+~E(x29071,x29072)+~P22(x29073,x29071,x29074,x29075,x29076,x29077)
% 157.55/157.24 [2908]P22(x29083,x29084,x29082,x29085,x29086,x29087)+~E(x29081,x29082)+~P22(x29083,x29084,x29081,x29085,x29086,x29087)
% 157.55/157.24 [2909]P22(x29093,x29094,x29095,x29092,x29096,x29097)+~E(x29091,x29092)+~P22(x29093,x29094,x29095,x29091,x29096,x29097)
% 157.55/157.24 [2910]P22(x29103,x29104,x29105,x29106,x29102,x29107)+~E(x29101,x29102)+~P22(x29103,x29104,x29105,x29106,x29101,x29107)
% 157.55/157.24 [2911]P22(x29113,x29114,x29115,x29116,x29117,x29112)+~E(x29111,x29112)+~P22(x29113,x29114,x29115,x29116,x29117,x29111)
% 157.55/157.24 [2912]~P141(x29121)+P141(x29122)+~E(x29121,x29122)
% 157.55/157.24 [2913]~P84(x29131)+P84(x29132)+~E(x29131,x29132)
% 157.55/157.24 [2914]P31(x29142,x29143,x29144,x29145)+~E(x29141,x29142)+~P31(x29141,x29143,x29144,x29145)
% 157.55/157.24 [2915]P31(x29153,x29152,x29154,x29155)+~E(x29151,x29152)+~P31(x29153,x29151,x29154,x29155)
% 157.55/157.24 [2916]P31(x29163,x29164,x29162,x29165)+~E(x29161,x29162)+~P31(x29163,x29164,x29161,x29165)
% 157.55/157.24 [2917]P31(x29173,x29174,x29175,x29172)+~E(x29171,x29172)+~P31(x29173,x29174,x29175,x29171)
% 157.55/157.24 [2918]P146(x29182,x29183,x29184)+~E(x29181,x29182)+~P146(x29181,x29183,x29184)
% 157.55/157.24 [2919]P146(x29193,x29192,x29194)+~E(x29191,x29192)+~P146(x29193,x29191,x29194)
% 157.55/157.24 [2920]P146(x29203,x29204,x29202)+~E(x29201,x29202)+~P146(x29203,x29204,x29201)
% 157.55/157.24 [2921]~P85(x29211)+P85(x29212)+~E(x29211,x29212)
% 157.55/157.24 [2922]P38(x29222,x29223)+~E(x29221,x29222)+~P38(x29221,x29223)
% 157.55/157.24 [2923]P38(x29233,x29232)+~E(x29231,x29232)+~P38(x29233,x29231)
% 157.55/157.24 [2924]~P60(x29241)+P60(x29242)+~E(x29241,x29242)
% 157.55/157.24 [2925]~P140(x29251)+P140(x29252)+~E(x29251,x29252)
% 157.55/157.24 [2926]~P111(x29261)+P111(x29262)+~E(x29261,x29262)
% 157.55/157.24 [2927]~P118(x29271)+P118(x29272)+~E(x29271,x29272)
% 157.55/157.24 [2928]P53(x29282,x29283,x29284)+~E(x29281,x29282)+~P53(x29281,x29283,x29284)
% 157.55/157.24 [2929]P53(x29293,x29292,x29294)+~E(x29291,x29292)+~P53(x29293,x29291,x29294)
% 157.55/157.24 [2930]P53(x29303,x29304,x29302)+~E(x29301,x29302)+~P53(x29303,x29304,x29301)
% 157.55/157.24 [2931]~P88(x29311)+P88(x29312)+~E(x29311,x29312)
% 157.55/157.24 [2932]~P137(x29321)+P137(x29322)+~E(x29321,x29322)
% 157.55/157.24 [2933]~P143(x29331)+P143(x29332)+~E(x29331,x29332)
% 157.55/157.24 [2934]P58(x29342,x29343)+~E(x29341,x29342)+~P58(x29341,x29343)
% 157.55/157.24 [2935]P58(x29353,x29352)+~E(x29351,x29352)+~P58(x29353,x29351)
% 157.55/157.24 [2936]~P138(x29361)+P138(x29362)+~E(x29361,x29362)
% 157.55/157.24 [2937]P14(x29372,x29373)+~E(x29371,x29372)+~P14(x29371,x29373)
% 157.55/157.24 [2938]P14(x29383,x29382)+~E(x29381,x29382)+~P14(x29383,x29381)
% 157.55/157.24 [2939]P10(x29392,x29393,x29394,x29395)+~E(x29391,x29392)+~P10(x29391,x29393,x29394,x29395)
% 157.55/157.24 [2940]P10(x29403,x29402,x29404,x29405)+~E(x29401,x29402)+~P10(x29403,x29401,x29404,x29405)
% 157.55/157.24 [2941]P10(x29413,x29414,x29412,x29415)+~E(x29411,x29412)+~P10(x29413,x29414,x29411,x29415)
% 157.55/157.24 [2942]P10(x29423,x29424,x29425,x29422)+~E(x29421,x29422)+~P10(x29423,x29424,x29425,x29421)
% 157.55/157.24 [2943]~P81(x29431)+P81(x29432)+~E(x29431,x29432)
% 157.55/157.24 [2944]P55(x29442,x29443,x29444,x29445,x29446)+~E(x29441,x29442)+~P55(x29441,x29443,x29444,x29445,x29446)
% 157.55/157.24 [2945]P55(x29453,x29452,x29454,x29455,x29456)+~E(x29451,x29452)+~P55(x29453,x29451,x29454,x29455,x29456)
% 157.55/157.24 [2946]P55(x29463,x29464,x29462,x29465,x29466)+~E(x29461,x29462)+~P55(x29463,x29464,x29461,x29465,x29466)
% 157.55/157.24 [2947]P55(x29473,x29474,x29475,x29472,x29476)+~E(x29471,x29472)+~P55(x29473,x29474,x29475,x29471,x29476)
% 157.55/157.24 [2948]P55(x29483,x29484,x29485,x29486,x29482)+~E(x29481,x29482)+~P55(x29483,x29484,x29485,x29486,x29481)
% 157.55/157.24 [2949]P20(x29492,x29493,x29494,x29495,x29496)+~E(x29491,x29492)+~P20(x29491,x29493,x29494,x29495,x29496)
% 157.55/157.24 [2950]P20(x29503,x29502,x29504,x29505,x29506)+~E(x29501,x29502)+~P20(x29503,x29501,x29504,x29505,x29506)
% 157.55/157.24 [2951]P20(x29513,x29514,x29512,x29515,x29516)+~E(x29511,x29512)+~P20(x29513,x29514,x29511,x29515,x29516)
% 157.55/157.24 [2952]P20(x29523,x29524,x29525,x29522,x29526)+~E(x29521,x29522)+~P20(x29523,x29524,x29525,x29521,x29526)
% 157.55/157.24 [2953]P20(x29533,x29534,x29535,x29536,x29532)+~E(x29531,x29532)+~P20(x29533,x29534,x29535,x29536,x29531)
% 157.55/157.24 [2954]~P125(x29541)+P125(x29542)+~E(x29541,x29542)
% 157.55/157.24 [2955]P42(x29552,x29553)+~E(x29551,x29552)+~P42(x29551,x29553)
% 157.55/157.24 [2956]P42(x29563,x29562)+~E(x29561,x29562)+~P42(x29563,x29561)
% 157.55/157.24 [2957]P21(x29572,x29573,x29574,x29575,x29576,x29577)+~E(x29571,x29572)+~P21(x29571,x29573,x29574,x29575,x29576,x29577)
% 157.55/157.24 [2958]P21(x29583,x29582,x29584,x29585,x29586,x29587)+~E(x29581,x29582)+~P21(x29583,x29581,x29584,x29585,x29586,x29587)
% 157.55/157.24 [2959]P21(x29593,x29594,x29592,x29595,x29596,x29597)+~E(x29591,x29592)+~P21(x29593,x29594,x29591,x29595,x29596,x29597)
% 157.55/157.24 [2960]P21(x29603,x29604,x29605,x29602,x29606,x29607)+~E(x29601,x29602)+~P21(x29603,x29604,x29605,x29601,x29606,x29607)
% 157.55/157.24 [2961]P21(x29613,x29614,x29615,x29616,x29612,x29617)+~E(x29611,x29612)+~P21(x29613,x29614,x29615,x29616,x29611,x29617)
% 157.55/157.24 [2962]P21(x29623,x29624,x29625,x29626,x29627,x29622)+~E(x29621,x29622)+~P21(x29623,x29624,x29625,x29626,x29627,x29621)
% 157.55/157.24 [2963]~P130(x29631)+P130(x29632)+~E(x29631,x29632)
% 157.55/157.24 [2964]~P80(x29641)+P80(x29642)+~E(x29641,x29642)
% 157.55/157.24 [2965]~P61(x29651)+P61(x29652)+~E(x29651,x29652)
% 157.55/157.24 [2966]P45(x29662,x29663)+~E(x29661,x29662)+~P45(x29661,x29663)
% 157.55/157.24 [2967]P45(x29673,x29672)+~E(x29671,x29672)+~P45(x29673,x29671)
% 157.55/157.24 [2968]P7(x29682,x29683,x29684)+~E(x29681,x29682)+~P7(x29681,x29683,x29684)
% 157.55/157.24 [2969]P7(x29693,x29692,x29694)+~E(x29691,x29692)+~P7(x29693,x29691,x29694)
% 157.55/157.24 [2970]P7(x29703,x29704,x29702)+~E(x29701,x29702)+~P7(x29703,x29704,x29701)
% 157.55/157.24 [2971]~P139(x29711)+P139(x29712)+~E(x29711,x29712)
% 157.55/157.24 [2972]~P121(x29721)+P121(x29722)+~E(x29721,x29722)
% 157.55/157.24 [2973]P23(x29732,x29733,x29734)+~E(x29731,x29732)+~P23(x29731,x29733,x29734)
% 157.55/157.24 [2974]P23(x29743,x29742,x29744)+~E(x29741,x29742)+~P23(x29743,x29741,x29744)
% 157.55/157.24 [2975]P23(x29753,x29754,x29752)+~E(x29751,x29752)+~P23(x29753,x29754,x29751)
% 157.55/157.24 [2976]P17(x29762,x29763,x29764)+~E(x29761,x29762)+~P17(x29761,x29763,x29764)
% 157.55/157.24 [2977]P17(x29773,x29772,x29774)+~E(x29771,x29772)+~P17(x29773,x29771,x29774)
% 157.55/157.24 [2978]P17(x29783,x29784,x29782)+~E(x29781,x29782)+~P17(x29783,x29784,x29781)
% 157.55/157.24 [2979]P15(x29792,x29793,x29794)+~E(x29791,x29792)+~P15(x29791,x29793,x29794)
% 157.55/157.24 [2980]P15(x29803,x29802,x29804)+~E(x29801,x29802)+~P15(x29803,x29801,x29804)
% 157.55/157.24 [2981]P15(x29813,x29814,x29812)+~E(x29811,x29812)+~P15(x29813,x29814,x29811)
% 157.55/157.24 [2982]~P127(x29821)+P127(x29822)+~E(x29821,x29822)
% 157.55/157.24 [2983]~P87(x29831)+P87(x29832)+~E(x29831,x29832)
% 157.55/157.24 [2984]~P102(x29841)+P102(x29842)+~E(x29841,x29842)
% 157.55/157.24 [2985]P54(x29852,x29853,x29854)+~E(x29851,x29852)+~P54(x29851,x29853,x29854)
% 157.55/157.24 [2986]P54(x29863,x29862,x29864)+~E(x29861,x29862)+~P54(x29863,x29861,x29864)
% 157.55/157.24 [2987]P54(x29873,x29874,x29872)+~E(x29871,x29872)+~P54(x29873,x29874,x29871)
% 157.55/157.24 [2988]P50(x29882,x29883)+~E(x29881,x29882)+~P50(x29881,x29883)
% 157.55/157.24 [2989]P50(x29893,x29892)+~E(x29891,x29892)+~P50(x29893,x29891)
% 157.55/157.24 [2990]~P116(x29901)+P116(x29902)+~E(x29901,x29902)
% 157.55/157.24 [2991]P56(x29912,x29913)+~E(x29911,x29912)+~P56(x29911,x29913)
% 157.55/157.24 [2992]P56(x29923,x29922)+~E(x29921,x29922)+~P56(x29923,x29921)
% 157.55/157.24 [2993]P57(x29932,x29933,x29934,x29935)+~E(x29931,x29932)+~P57(x29931,x29933,x29934,x29935)
% 157.55/157.24 [2994]P57(x29943,x29942,x29944,x29945)+~E(x29941,x29942)+~P57(x29943,x29941,x29944,x29945)
% 157.55/157.24 [2995]P57(x29953,x29954,x29952,x29955)+~E(x29951,x29952)+~P57(x29953,x29954,x29951,x29955)
% 157.55/157.24 [2996]P57(x29963,x29964,x29965,x29962)+~E(x29961,x29962)+~P57(x29963,x29964,x29965,x29961)
% 157.55/157.24 [2997]P48(x29972,x29973)+~E(x29971,x29972)+~P48(x29971,x29973)
% 157.55/157.24 [2998]P48(x29983,x29982)+~E(x29981,x29982)+~P48(x29983,x29981)
% 157.55/157.24 [2999]P27(x29992,x29993)+~E(x29991,x29992)+~P27(x29991,x29993)
% 157.55/157.24 [3000]P27(x30003,x30002)+~E(x30001,x30002)+~P27(x30003,x30001)
% 157.55/157.24 [3001]P49(x30012,x30013)+~E(x30011,x30012)+~P49(x30011,x30013)
% 157.55/157.24 [3002]P49(x30023,x30022)+~E(x30021,x30022)+~P49(x30023,x30021)
% 157.55/157.24 [3003]~P142(x30031)+P142(x30032)+~E(x30031,x30032)
% 157.55/157.24 [3004]~P132(x30041)+P132(x30042)+~E(x30041,x30042)
% 157.55/157.24 [3005]P41(x30052,x30053,x30054,x30055,x30056,x30057)+~E(x30051,x30052)+~P41(x30051,x30053,x30054,x30055,x30056,x30057)
% 157.55/157.24 [3006]P41(x30063,x30062,x30064,x30065,x30066,x30067)+~E(x30061,x30062)+~P41(x30063,x30061,x30064,x30065,x30066,x30067)
% 157.55/157.24 [3007]P41(x30073,x30074,x30072,x30075,x30076,x30077)+~E(x30071,x30072)+~P41(x30073,x30074,x30071,x30075,x30076,x30077)
% 157.55/157.24 [3008]P41(x30083,x30084,x30085,x30082,x30086,x30087)+~E(x30081,x30082)+~P41(x30083,x30084,x30085,x30081,x30086,x30087)
% 157.55/157.24 [3009]P41(x30093,x30094,x30095,x30096,x30092,x30097)+~E(x30091,x30092)+~P41(x30093,x30094,x30095,x30096,x30091,x30097)
% 157.55/157.24 [3010]P41(x30103,x30104,x30105,x30106,x30107,x30102)+~E(x30101,x30102)+~P41(x30103,x30104,x30105,x30106,x30107,x30101)
% 157.55/157.24 [3011]~P131(x30111)+P131(x30112)+~E(x30111,x30112)
% 157.55/157.24 [3012]~P115(x30121)+P115(x30122)+~E(x30121,x30122)
% 157.55/157.24 [3013]~P117(x30131)+P117(x30132)+~E(x30131,x30132)
% 157.55/157.24 [3014]P6(x30142,x30143)+~E(x30141,x30142)+~P6(x30141,x30143)
% 157.55/157.24 [3015]P6(x30153,x30152)+~E(x30151,x30152)+~P6(x30153,x30151)
% 157.55/157.24 [3016]P26(x30162,x30163)+~E(x30161,x30162)+~P26(x30161,x30163)
% 157.55/157.24 [3017]P26(x30173,x30172)+~E(x30171,x30172)+~P26(x30173,x30171)
% 157.55/157.24 [3018]P28(x30182,x30183,x30184)+~E(x30181,x30182)+~P28(x30181,x30183,x30184)
% 157.55/157.24 [3019]P28(x30193,x30192,x30194)+~E(x30191,x30192)+~P28(x30193,x30191,x30194)
% 157.55/157.24 [3020]P28(x30203,x30204,x30202)+~E(x30201,x30202)+~P28(x30203,x30204,x30201)
% 157.55/157.24 [3021]~P99(x30211)+P99(x30212)+~E(x30211,x30212)
% 157.55/157.24 [3022]~P133(x30221)+P133(x30222)+~E(x30221,x30222)
% 157.55/157.24 [3023]P13(x30232,x30233,x30234)+~E(x30231,x30232)+~P13(x30231,x30233,x30234)
% 157.55/157.24 [3024]P13(x30243,x30242,x30244)+~E(x30241,x30242)+~P13(x30243,x30241,x30244)
% 157.55/157.24 [3025]P13(x30253,x30254,x30252)+~E(x30251,x30252)+~P13(x30253,x30254,x30251)
% 157.55/157.24 [3026]~P128(x30261)+P128(x30262)+~E(x30261,x30262)
% 157.55/157.24 [3027]~P135(x30271)+P135(x30272)+~E(x30271,x30272)
% 157.55/157.24 [3028]~P103(x30281)+P103(x30282)+~E(x30281,x30282)
% 157.55/157.24 [3029]P16(x30292,x30293,x30294)+~E(x30291,x30292)+~P16(x30291,x30293,x30294)
% 157.55/157.24 [3030]P16(x30303,x30302,x30304)+~E(x30301,x30302)+~P16(x30303,x30301,x30304)
% 157.55/157.24 [3031]P16(x30313,x30314,x30312)+~E(x30311,x30312)+~P16(x30313,x30314,x30311)
% 157.55/157.24 [3032]~P134(x30321)+P134(x30322)+~E(x30321,x30322)
% 157.55/157.24 [3033]~P92(x30331)+P92(x30332)+~E(x30331,x30332)
% 157.55/157.24 [3034]~P89(x30341)+P89(x30342)+~E(x30341,x30342)
% 157.55/157.24 [3035]~P144(x30351)+P144(x30352)+~E(x30351,x30352)
% 157.55/157.24 [3036]~P95(x30361)+P95(x30362)+~E(x30361,x30362)
% 157.55/157.24 [3037]P47(x30372,x30373,x30374)+~E(x30371,x30372)+~P47(x30371,x30373,x30374)
% 157.55/157.24 [3038]P47(x30383,x30382,x30384)+~E(x30381,x30382)+~P47(x30383,x30381,x30384)
% 157.55/157.24 [3039]P47(x30393,x30394,x30392)+~E(x30391,x30392)+~P47(x30393,x30394,x30391)
% 157.55/157.24 [3040]~P114(x30401)+P114(x30402)+~E(x30401,x30402)
% 157.55/157.24 [3041]~P122(x30411)+P122(x30412)+~E(x30411,x30412)
% 157.55/157.24 [3042]~P119(x30421)+P119(x30422)+~E(x30421,x30422)
% 157.55/157.24 [3043]~P97(x30431)+P97(x30432)+~E(x30431,x30432)
% 157.55/157.24 [3044]P52(x30442,x30443)+~E(x30441,x30442)+~P52(x30441,x30443)
% 157.55/157.24 [3045]P52(x30453,x30452)+~E(x30451,x30452)+~P52(x30453,x30451)
% 157.55/157.24 [3046]P43(x30462,x30463)+~E(x30461,x30462)+~P43(x30461,x30463)
% 157.55/157.24 [3047]P43(x30473,x30472)+~E(x30471,x30472)+~P43(x30473,x30471)
% 157.55/157.24 [3048]~P91(x30481)+P91(x30482)+~E(x30481,x30482)
% 157.55/157.24 [3049]~P76(x30491)+P76(x30492)+~E(x30491,x30492)
% 157.55/157.24 [3050]~P129(x30501)+P129(x30502)+~E(x30501,x30502)
% 157.55/157.24 [3051]~P136(x30511)+P136(x30512)+~E(x30511,x30512)
% 157.55/157.24 [3052]~P120(x30521)+P120(x30522)+~E(x30521,x30522)
% 157.55/157.24 [3053]~P104(x30531)+P104(x30532)+~E(x30531,x30532)
% 157.55/157.24 [3054]~P123(x30541)+P123(x30542)+~E(x30541,x30542)
% 157.55/157.24 [3055]~P90(x30551)+P90(x30552)+~E(x30551,x30552)
% 157.55/157.24 [3056]P40(x30562,x30563,x30564,x30565)+~E(x30561,x30562)+~P40(x30561,x30563,x30564,x30565)
% 157.55/157.24 [3057]P40(x30573,x30572,x30574,x30575)+~E(x30571,x30572)+~P40(x30573,x30571,x30574,x30575)
% 157.55/157.24 [3058]P40(x30583,x30584,x30582,x30585)+~E(x30581,x30582)+~P40(x30583,x30584,x30581,x30585)
% 157.55/157.24 [3059]P40(x30593,x30594,x30595,x30592)+~E(x30591,x30592)+~P40(x30593,x30594,x30595,x30591)
% 157.55/157.24 [3060]P19(x30602,x30603,x30604,x30605)+~E(x30601,x30602)+~P19(x30601,x30603,x30604,x30605)
% 157.55/157.24 [3061]P19(x30613,x30612,x30614,x30615)+~E(x30611,x30612)+~P19(x30613,x30611,x30614,x30615)
% 157.55/157.24 [3062]P19(x30623,x30624,x30622,x30625)+~E(x30621,x30622)+~P19(x30623,x30624,x30621,x30625)
% 157.55/157.24 [3063]P19(x30633,x30634,x30635,x30632)+~E(x30631,x30632)+~P19(x30633,x30634,x30635,x30631)
% 157.55/157.24 [3064]~P72(x30641)+P72(x30642)+~E(x30641,x30642)
% 157.55/157.24 [3065]~P35(x30651)+P35(x30652)+~E(x30651,x30652)
% 157.55/157.24 [3066]P9(x30662,x30663,x30664,x30665,x30666)+~E(x30661,x30662)+~P9(x30661,x30663,x30664,x30665,x30666)
% 157.55/157.24 [3067]P9(x30673,x30672,x30674,x30675,x30676)+~E(x30671,x30672)+~P9(x30673,x30671,x30674,x30675,x30676)
% 157.55/157.24 [3068]P9(x30683,x30684,x30682,x30685,x30686)+~E(x30681,x30682)+~P9(x30683,x30684,x30681,x30685,x30686)
% 157.55/157.24 [3069]P9(x30693,x30694,x30695,x30692,x30696)+~E(x30691,x30692)+~P9(x30693,x30694,x30695,x30691,x30696)
% 157.55/157.24 [3070]P9(x30703,x30704,x30705,x30706,x30702)+~E(x30701,x30702)+~P9(x30703,x30704,x30705,x30706,x30701)
% 157.55/157.24 [3071]~P44(x30711)+P44(x30712)+~E(x30711,x30712)
% 157.55/157.24 [3072]P8(x30722,x30723,x30724)+~E(x30721,x30722)+~P8(x30721,x30723,x30724)
% 157.55/157.24 [3073]P8(x30733,x30732,x30734)+~E(x30731,x30732)+~P8(x30733,x30731,x30734)
% 157.55/157.24 [3074]P8(x30743,x30744,x30742)+~E(x30741,x30742)+~P8(x30743,x30744,x30741)
% 157.55/157.24 [3075]P46(x30752,x30753,x30754)+~E(x30751,x30752)+~P46(x30751,x30753,x30754)
% 157.55/157.24 [3076]P46(x30763,x30762,x30764)+~E(x30761,x30762)+~P46(x30763,x30761,x30764)
% 157.55/157.24 [3077]P46(x30773,x30774,x30772)+~E(x30771,x30772)+~P46(x30773,x30774,x30771)
% 157.55/157.24
% 157.55/157.24 %-------------------------------------------
% 157.55/157.27 cnf(10412,plain,
% 157.55/157.27 (~E(f326(a112,x104121),x104121)),
% 157.55/157.27 inference(rename_variables,[],[4628])).
% 157.55/157.27 cnf(10422,plain,
% 157.55/157.27 (~E(f326(a112,x104221),x104221)),
% 157.55/157.27 inference(rename_variables,[],[4628])).
% 157.55/157.27 cnf(10435,plain,
% 157.55/157.27 (~E(f326(a112,x104351),x104351)),
% 157.55/157.27 inference(rename_variables,[],[4628])).
% 157.55/157.27 cnf(10440,plain,
% 157.55/157.27 (~P105(f326(f326(f172(x104401),f113(x104401)),x104402))),
% 157.55/157.27 inference(rename_variables,[],[4688])).
% 157.55/157.27 cnf(10443,plain,
% 157.55/157.27 (~P105(f326(f326(f172(x104431),f113(x104431)),x104432))),
% 157.55/157.27 inference(rename_variables,[],[4688])).
% 157.55/157.27 cnf(10446,plain,
% 157.55/157.27 (~E(f326(a112,x104461),x104461)),
% 157.55/157.27 inference(rename_variables,[],[4628])).
% 157.55/157.27 cnf(10449,plain,
% 157.55/157.27 (~P105(f326(f326(f235(a909),x104491),f2(a909)))),
% 157.55/157.27 inference(rename_variables,[],[4683])).
% 157.55/157.27 cnf(10452,plain,
% 157.55/157.27 (~P105(f326(f326(f235(a909),x104521),f2(a909)))),
% 157.55/157.27 inference(rename_variables,[],[4683])).
% 157.55/157.27 cnf(10469,plain,
% 157.55/157.27 (~P105(f326(f326(f234(a909),f326(a112,x104691)),x104691))),
% 157.55/157.27 inference(rename_variables,[],[4689])).
% 157.55/157.27 cnf(10472,plain,
% 157.55/157.27 (~E(f326(f326(f151(x104721),x104722),x104723),x104723)),
% 157.55/157.27 inference(rename_variables,[],[4647])).
% 157.55/157.27 cnf(10478,plain,
% 157.55/157.27 (~P105(f326(f326(f235(a909),x104781),f2(a909)))),
% 157.55/157.27 inference(rename_variables,[],[4683])).
% 157.55/157.27 cnf(10481,plain,
% 157.55/157.27 (E(f326(f283(x104811,x104811),f262(x104811,x104812)),x104812)),
% 157.55/157.27 inference(rename_variables,[],[3433])).
% 157.55/157.27 cnf(10484,plain,
% 157.55/157.27 (E(f326(f283(x104841,x104841),f262(x104841,x104842)),x104842)),
% 157.55/157.27 inference(rename_variables,[],[3433])).
% 157.55/157.27 cnf(10489,plain,
% 157.55/157.27 (~P105(f326(f326(f235(a909),x104891),x104891))),
% 157.55/157.27 inference(rename_variables,[],[4679])).
% 157.55/157.27 cnf(10494,plain,
% 157.55/157.27 (~P105(f326(f326(f235(a909),f326(f326(f79(a909),x104941),x104942)),x104942))),
% 157.55/157.27 inference(rename_variables,[],[4703])).
% 157.55/157.27 cnf(10497,plain,
% 157.55/157.27 (~P105(f326(f326(f235(a909),f326(f326(f79(a909),x104971),x104972)),x104972))),
% 157.55/157.27 inference(rename_variables,[],[4703])).
% 157.55/157.27 cnf(10504,plain,
% 157.55/157.27 (~E(x105041,f326(a112,x105041))),
% 157.55/157.27 inference(scs_inference,[],[4628,10412,10422,10435,3267,3433,10481,3309,3370,3305,3332,3316,4647,3540,3456,4683,10449,10452,4680,4642,4688,10440,4679,4689,4291,4686,3449,4672,4705,4703,10494,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325])).
% 157.55/157.27 cnf(10518,plain,
% 157.55/157.27 (~E(f326(a112,x105181),x105181)),
% 157.55/157.27 inference(rename_variables,[],[4628])).
% 157.55/157.27 cnf(10521,plain,
% 157.55/157.27 (~P105(f326(f326(f235(a909),x105211),x105211))),
% 157.55/157.27 inference(rename_variables,[],[4679])).
% 157.55/157.27 cnf(10524,plain,
% 157.55/157.27 (P105(f326(f326(f234(a909),f45(a909,x105241,x105242)),x105241))),
% 157.55/157.27 inference(rename_variables,[],[3927])).
% 157.55/157.27 cnf(10545,plain,
% 157.55/157.27 (E(f326(f35(a909),f326(f281(a909),x105451)),x105451)),
% 157.55/157.27 inference(rename_variables,[],[3367])).
% 157.55/157.27 cnf(10553,plain,
% 157.55/157.27 (~E(f326(a112,x105531),x105531)),
% 157.55/157.27 inference(rename_variables,[],[4628])).
% 157.55/157.27 cnf(10556,plain,
% 157.55/157.27 (~E(f326(a112,x105561),x105561)),
% 157.55/157.27 inference(rename_variables,[],[4628])).
% 157.55/157.27 cnf(10559,plain,
% 157.55/157.27 (~E(f326(a112,x105591),x105591)),
% 157.55/157.27 inference(rename_variables,[],[4628])).
% 157.55/157.27 cnf(10564,plain,
% 157.55/157.27 (P105(f326(f326(f235(a909),x105641),f326(a112,x105641)))),
% 157.55/157.27 inference(rename_variables,[],[3540])).
% 157.55/157.27 cnf(10573,plain,
% 157.55/157.27 (P105(f326(f326(f234(a909),x105731),x105731))),
% 157.55/157.27 inference(rename_variables,[],[3472])).
% 157.55/157.27 cnf(10580,plain,
% 157.55/157.27 (E(f326(f283(x105801,x105801),f262(x105801,x105802)),x105802)),
% 157.55/157.27 inference(rename_variables,[],[3433])).
% 157.55/157.27 cnf(10583,plain,
% 157.55/157.27 (E(f326(f283(x105831,x105831),f262(x105831,x105832)),x105832)),
% 157.55/157.27 inference(rename_variables,[],[3433])).
% 157.55/157.27 cnf(10600,plain,
% 157.55/157.27 (P105(f326(f326(f234(a1),x106001),x106001))),
% 157.55/157.27 inference(rename_variables,[],[3473])).
% 157.55/157.27 cnf(10605,plain,
% 157.55/157.27 (~P105(f326(f326(f235(a909),x106051),f2(a909)))),
% 157.55/157.27 inference(rename_variables,[],[4683])).
% 157.55/157.27 cnf(10608,plain,
% 157.55/157.27 (P105(f326(f326(f234(f917(x106081,a905)),x106082),f241(f917(x106081,a905))))),
% 157.55/157.27 inference(rename_variables,[],[3852])).
% 157.55/157.27 cnf(10613,plain,
% 157.55/157.27 (~P105(f326(f326(f172(x106131),f113(x106131)),x106132))),
% 157.55/157.27 inference(rename_variables,[],[4688])).
% 157.55/157.27 cnf(10642,plain,
% 157.55/157.27 (~E(f326(f326(f151(x106421),x106422),x106423),x106423)),
% 157.55/157.27 inference(rename_variables,[],[4647])).
% 157.55/157.27 cnf(10645,plain,
% 157.55/157.27 (~E(f326(a112,x106451),f2(a909))),
% 157.55/157.27 inference(rename_variables,[],[4638])).
% 157.55/157.27 cnf(10656,plain,
% 157.55/157.27 (P105(f326(f326(f234(a1),x106561),x106561))),
% 157.55/157.27 inference(rename_variables,[],[3473])).
% 157.55/157.27 cnf(10661,plain,
% 157.55/157.27 (~E(f326(a112,x106611),x106611)),
% 157.55/157.27 inference(rename_variables,[],[4628])).
% 157.55/157.27 cnf(10664,plain,
% 157.55/157.27 (~P105(f326(f326(f188(f917(x106641,f917(x106642,a905))),x106643),x106644))),
% 157.55/157.27 inference(rename_variables,[],[4706])).
% 157.55/157.27 cnf(10671,plain,
% 157.55/157.27 (P105(f326(f326(f234(a909),x106711),x106711))),
% 157.55/157.27 inference(rename_variables,[],[3472])).
% 157.55/157.27 cnf(10684,plain,
% 157.55/157.27 (P105(f326(f326(f235(a909),x106841),f326(a112,x106841)))),
% 157.55/157.27 inference(rename_variables,[],[3540])).
% 157.55/157.27 cnf(10705,plain,
% 157.55/157.27 (P105(f326(f326(f234(f917(x107051,a905)),x107052),f241(f917(x107051,a905))))),
% 157.55/157.27 inference(rename_variables,[],[3852])).
% 157.55/157.27 cnf(10708,plain,
% 157.55/157.27 (~P105(f326(f326(f172(x107081),f113(x107081)),x107082))),
% 157.55/157.27 inference(rename_variables,[],[4688])).
% 157.55/157.27 cnf(10727,plain,
% 157.55/157.27 (~P105(f326(f326(f172(x107271),f113(x107271)),x107272))),
% 157.55/157.27 inference(rename_variables,[],[4688])).
% 157.55/157.27 cnf(10734,plain,
% 157.55/157.27 (~P105(f326(f326(f172(x107341),f113(x107341)),x107342))),
% 157.55/157.27 inference(rename_variables,[],[4688])).
% 157.55/157.27 cnf(10745,plain,
% 157.55/157.27 (~E(f326(a112,x107451),f2(a909))),
% 157.55/157.27 inference(rename_variables,[],[4638])).
% 157.55/157.27 cnf(10750,plain,
% 157.55/157.27 (P105(f326(f326(f328(x107501),x107502),f241(f917(x107501,a905))))),
% 157.55/157.27 inference(rename_variables,[],[3625])).
% 157.55/157.27 cnf(10754,plain,
% 157.55/157.27 (P105(f326(f326(f235(a909),f2(a909)),f326(a104,f77(a1))))),
% 157.55/157.27 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,4638,10645,3267,3433,10481,10484,10580,3309,3370,3305,3332,3316,3942,3403,4647,10472,3367,4250,4708,3388,3834,3540,10564,10684,3456,4683,10449,10452,10478,10605,4696,3909,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,4200,3852,10608,3472,10573,10671,3473,10600,4679,10489,10521,3625,3565,3990,3927,10524,4689,10469,4291,4686,4671,3449,3453,4673,4672,4705,4706,3951,4703,10494,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065])).
% 157.55/157.27 cnf(10757,plain,
% 157.55/157.27 (~P105(f326(f326(f172(x107571),f113(x107571)),x107572))),
% 157.55/157.27 inference(rename_variables,[],[4688])).
% 157.55/157.27 cnf(10762,plain,
% 157.55/157.27 (P105(f326(f326(f235(a909),x107621),f326(a112,x107621)))),
% 157.55/157.27 inference(rename_variables,[],[3540])).
% 157.55/157.27 cnf(10765,plain,
% 157.55/157.27 (~P105(f326(f326(f172(x107651),f113(x107651)),x107652))),
% 157.55/157.27 inference(rename_variables,[],[4688])).
% 157.55/157.27 cnf(10768,plain,
% 157.55/157.27 (~P105(f326(f326(f172(x107681),f113(x107681)),x107682))),
% 157.55/157.27 inference(rename_variables,[],[4688])).
% 157.55/157.27 cnf(10771,plain,
% 157.55/157.27 (~P105(f326(f62(x107711,x107712,f188(f917(x107711,a905))),x107713))),
% 157.55/157.27 inference(rename_variables,[],[4702])).
% 157.55/157.27 cnf(10774,plain,
% 157.55/157.27 (~P105(f326(f62(x107741,x107742,f188(f917(x107741,a905))),x107743))),
% 157.55/157.27 inference(rename_variables,[],[4702])).
% 157.55/157.27 cnf(10777,plain,
% 157.55/157.27 (~P105(f326(f326(f188(f917(x107771,f917(x107772,a905))),x107773),x107774))),
% 157.55/157.27 inference(rename_variables,[],[4706])).
% 157.55/157.27 cnf(10780,plain,
% 157.55/157.27 (~P105(f326(f326(f235(a909),x107801),f2(a909)))),
% 157.55/157.27 inference(rename_variables,[],[4683])).
% 157.55/157.27 cnf(10785,plain,
% 157.55/157.27 (~P105(f326(f326(f172(x107851),f113(x107851)),x107852))),
% 157.55/157.27 inference(rename_variables,[],[4688])).
% 157.55/157.27 cnf(10796,plain,
% 157.55/157.27 (~E(f326(a112,x107961),x107961)),
% 157.55/157.27 inference(rename_variables,[],[4628])).
% 157.55/157.27 cnf(10814,plain,
% 157.55/157.27 (P105(f326(f326(f235(a99),f326(a5,x108141)),f326(a5,f326(a112,x108141))))),
% 157.55/157.27 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,4638,10645,3267,3433,10481,10484,10580,3309,3370,3305,3332,3316,3942,3403,4647,10472,3367,4250,4708,3388,3834,3540,10564,10684,10762,3922,3456,4683,10449,10452,10478,10605,4696,3909,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,4200,3852,10608,3472,10573,10671,3473,10600,4679,10489,10521,3625,3565,3990,3927,10524,4689,10469,4291,4686,4671,3449,3453,4673,4672,4702,10771,4705,4706,10664,3951,4703,10494,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261])).
% 157.55/157.27 cnf(10821,plain,
% 157.55/157.27 (P105(f326(f326(f234(a909),x108211),x108211))),
% 157.55/157.27 inference(rename_variables,[],[3472])).
% 157.55/157.27 cnf(10824,plain,
% 157.55/157.27 (P105(f326(f326(f234(a909),x108241),f326(f326(f80(a909),x108241),x108241)))),
% 157.55/157.27 inference(rename_variables,[],[3733])).
% 157.55/157.27 cnf(10826,plain,
% 157.55/157.27 (P105(f326(f326(f235(a909),x108261),f326(f326(f80(a909),f326(a112,x108261)),f326(a112,x108261))))),
% 157.55/157.27 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,4638,10645,3267,3433,10481,10484,10580,3309,3370,3305,3332,3316,3942,3403,4647,10472,3367,4250,4708,3388,3834,3540,10564,10684,10762,3922,3456,4683,10449,10452,10478,10605,4696,3909,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,4200,3852,10608,3472,10573,10671,3473,10600,4679,10489,10521,3625,3565,3990,3927,10524,4689,10469,4291,4686,4671,3449,3453,4673,4672,4702,10771,3733,10824,4705,4706,10664,3951,4703,10494,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285])).
% 157.55/157.27 cnf(10827,plain,
% 157.55/157.27 (P105(f326(f326(f234(a909),x108271),f326(f326(f80(a909),x108271),x108271)))),
% 157.55/157.27 inference(rename_variables,[],[3733])).
% 157.55/157.27 cnf(10830,plain,
% 157.55/157.27 (P105(f326(f326(f235(a909),x108301),f326(a112,f326(f326(f79(a909),x108302),x108301))))),
% 157.55/157.27 inference(rename_variables,[],[3920])).
% 157.55/157.27 cnf(10835,plain,
% 157.55/157.27 (P105(f326(f326(f235(a909),x108351),f326(a112,x108351)))),
% 157.55/157.27 inference(rename_variables,[],[3540])).
% 157.55/157.27 cnf(10838,plain,
% 157.55/157.27 (P105(f326(f326(f235(a909),x108381),f326(a112,x108381)))),
% 157.55/157.27 inference(rename_variables,[],[3540])).
% 157.55/157.27 cnf(10841,plain,
% 157.55/157.27 (P105(f326(f326(f328(x108411),x108412),f241(f917(x108411,a905))))),
% 157.55/157.27 inference(rename_variables,[],[3625])).
% 157.55/157.27 cnf(10860,plain,
% 157.55/157.27 (~P105(f326(f326(f234(a909),f326(a112,x108601)),x108601))),
% 157.55/157.27 inference(rename_variables,[],[4689])).
% 157.55/157.27 cnf(10863,plain,
% 157.55/157.27 (~P105(f326(f326(f234(a909),f326(a112,x108631)),x108631))),
% 157.55/157.27 inference(rename_variables,[],[4689])).
% 157.55/157.27 cnf(10866,plain,
% 157.55/157.27 (~P105(f326(f326(f235(a909),f326(f326(f79(a909),x108661),x108662)),x108662))),
% 157.55/157.27 inference(rename_variables,[],[4703])).
% 157.55/157.27 cnf(10869,plain,
% 157.55/157.27 (~P105(f326(f326(f235(a909),f326(f326(f79(a909),x108691),x108692)),x108692))),
% 157.55/157.27 inference(rename_variables,[],[4703])).
% 157.55/157.27 cnf(10872,plain,
% 157.55/157.27 (P105(f326(f241(f917(x108721,a905)),x108722))),
% 157.55/157.27 inference(rename_variables,[],[3533])).
% 157.55/157.27 cnf(10875,plain,
% 157.55/157.27 (E(f326(f35(a909),f326(f281(a909),x108751)),x108751)),
% 157.55/157.27 inference(rename_variables,[],[3367])).
% 157.55/157.27 cnf(10878,plain,
% 157.55/157.27 (P105(f326(f326(f235(a909),x108781),f326(a112,x108781)))),
% 157.55/157.27 inference(rename_variables,[],[3540])).
% 157.55/157.27 cnf(10885,plain,
% 157.55/157.27 (P105(f326(f326(f234(a909),x108851),x108851))),
% 157.55/157.27 inference(rename_variables,[],[3472])).
% 157.55/157.27 cnf(10890,plain,
% 157.55/157.27 (P105(f326(f326(f234(a1),x108901),x108901))),
% 157.55/157.27 inference(rename_variables,[],[3473])).
% 157.55/157.27 cnf(10899,plain,
% 157.55/157.27 (E(f326(f283(x108991,x108991),f262(x108991,x108992)),x108992)),
% 157.55/157.27 inference(rename_variables,[],[3433])).
% 157.55/157.27 cnf(10902,plain,
% 157.55/157.27 (P105(f326(f241(f917(x109021,a905)),x109022))),
% 157.55/157.27 inference(rename_variables,[],[3533])).
% 157.55/157.27 cnf(10905,plain,
% 157.55/157.27 (P105(f326(f326(f234(a909),f2(a909)),x109051))),
% 157.55/157.27 inference(rename_variables,[],[3493])).
% 157.55/157.27 cnf(10908,plain,
% 157.55/157.27 (P105(f326(f326(f234(f917(x109081,a905)),f188(f917(x109081,a905))),x109082))),
% 157.55/157.27 inference(rename_variables,[],[3919])).
% 157.55/157.27 cnf(10911,plain,
% 157.55/157.27 (P105(f326(f241(f917(x109111,a905)),x109112))),
% 157.55/157.27 inference(rename_variables,[],[3533])).
% 157.55/157.27 cnf(10914,plain,
% 157.55/157.27 (P105(f326(f241(f917(x109141,a905)),x109142))),
% 157.55/157.27 inference(rename_variables,[],[3533])).
% 157.55/157.27 cnf(10917,plain,
% 157.55/157.28 (P105(f326(f241(f917(x109171,a905)),x109172))),
% 157.55/157.28 inference(rename_variables,[],[3533])).
% 157.55/157.28 cnf(10920,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x109201),f326(f326(f80(a909),x109201),x109201)))),
% 157.55/157.28 inference(rename_variables,[],[3733])).
% 157.55/157.28 cnf(10929,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,f326(a112,f326(f326(f79(a909),x109291),x109292)))),f326(a112,x109292)))),
% 157.55/157.28 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,4638,10645,3267,3433,10481,10484,10580,10583,3410,3309,3370,3305,3332,3316,3942,3403,4647,10472,3367,10545,4250,4708,3388,3834,3770,3540,10564,10684,10762,10835,10838,10878,3922,3456,4683,10449,10452,10478,10605,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,4200,3852,10608,3472,10573,10671,10821,3473,10600,10656,4679,10489,10521,3625,10750,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,3493,4291,4686,4671,3449,3453,4673,4672,4702,10771,4707,3919,3733,10824,10827,4705,4706,10664,3951,4703,10494,10497,10866,3920,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544])).
% 157.55/157.28 cnf(10937,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a99),f326(a5,x109371)),f326(a5,f2(a909))))),
% 157.55/157.28 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,4638,10645,3267,3433,10481,10484,10580,10583,3410,3309,3370,3305,3332,3316,3942,3403,4647,10472,3367,10545,4250,4708,3388,3834,3770,3540,10564,10684,10762,10835,10838,10878,3922,3456,4683,10449,10452,10478,10605,10780,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,4200,3852,10608,3472,10573,10671,10821,3473,10600,10656,4679,10489,10521,3625,10750,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,3493,4291,4686,4671,3449,3453,4673,4672,4702,10771,4707,3919,3733,10824,10827,4705,4706,10664,3951,4703,10494,10497,10866,3920,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549])).
% 157.55/157.28 cnf(10960,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x109601),x109601))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(10971,plain,
% 157.55/157.28 (~P105(f326(f326(f172(x109711),f113(x109711)),x109712))),
% 157.55/157.28 inference(rename_variables,[],[4688])).
% 157.55/157.28 cnf(10978,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x109781),f326(a112,x109781)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(10980,plain,
% 157.55/157.28 (P105(f326(f326(f235(a1),f326(f326(f3(a1),x109801),f77(a1))),x109801))),
% 157.55/157.28 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,4638,10645,3267,3433,10481,10484,10580,10583,3410,3309,3370,3305,3332,3316,3942,3403,4647,10472,3367,10545,4250,4110,4708,3388,3834,3770,3540,10564,10684,10762,10835,10838,10878,3922,3456,4683,10449,10452,10478,10605,10780,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,4200,3852,10608,3472,10573,10671,10821,10885,10960,3473,10600,10656,10890,4679,10489,10521,3625,10750,4692,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,3493,4291,4686,4671,4674,3449,3453,4673,4672,4702,10771,4707,3919,3733,10824,10827,4705,4706,10664,3951,4703,10494,10497,10866,3920,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811])).
% 157.55/157.28 cnf(10981,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x109811),x109811))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(10986,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x109861),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(11001,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x110011),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(11004,plain,
% 157.55/157.28 (~P105(f326(f326(f235(f917(x110041,a905)),x110042),f188(f917(x110041,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4700])).
% 157.55/157.28 cnf(11007,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x110071),x110071))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(11010,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x110101),x110101))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(11025,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x110251),x110251))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(11034,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x110341),x110342),f188(f917(x110341,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11041,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x110411),x110411))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(11044,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x110441,a905)),f326(f309(x110442,x110441,x110443),f326(f310(x110442,x110441,x110443),x110444))),x110444))),
% 157.55/157.28 inference(rename_variables,[],[4349])).
% 157.55/157.28 cnf(11053,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x110531,a905)),f326(f172(x110531),f326(f136(x110531,x110532),x110533))),f326(f172(x110531),x110533)))),
% 157.55/157.28 inference(rename_variables,[],[4119])).
% 157.55/157.28 cnf(11056,plain,
% 157.55/157.28 (E(f326(f309(x110561,x110561,f7(x110561)),x110562),x110562)),
% 157.55/157.28 inference(rename_variables,[],[3529])).
% 157.55/157.28 cnf(11061,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f2(a909)),x110611))),
% 157.55/157.28 inference(rename_variables,[],[3493])).
% 157.55/157.28 cnf(11064,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x110641),x110641))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(11067,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x110671),x110671))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(11069,plain,
% 157.55/157.28 (~P32(x110691,f188(f917(x110692,a905)),x110693)),
% 157.55/157.28 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,4638,10645,3267,3433,10481,10484,10580,10583,3410,3309,3370,3305,3332,3316,3942,3529,3403,4647,10472,3367,10545,4250,4110,4708,3388,3669,3834,3770,3540,10564,10684,10762,10835,10838,10878,10978,3922,3456,4683,10449,10452,10478,10605,10780,10986,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,4212,4119,4200,3852,10608,4700,3472,10573,10671,10821,10885,10960,11007,11010,11041,3473,10600,10656,10890,3474,4679,10489,10521,11025,3625,10750,4692,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,3493,10905,4291,4686,4671,4674,3449,3453,4673,4672,4702,10771,4707,3919,3733,10824,10827,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357])).
% 157.55/157.28 cnf(11076,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x110761),x110761))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(11087,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x110871),f326(f326(f80(a909),x110871),x110871)))),
% 157.55/157.28 inference(rename_variables,[],[3733])).
% 157.55/157.28 cnf(11093,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x110931),f326(a112,f326(f326(f79(a909),x110932),x110931))))),
% 157.55/157.28 inference(rename_variables,[],[3920])).
% 157.55/157.28 cnf(11100,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x111001),x111001))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(11103,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x111031),x111031))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(11106,plain,
% 157.55/157.28 (~E(f326(a112,x111061),x111061)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11111,plain,
% 157.55/157.28 (P105(f326(f326(f328(x111111),x111112),f241(f917(x111111,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3625])).
% 157.55/157.28 cnf(11116,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x111161),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(11118,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x111181,a905)),x111182),f37(f917(x111181,a905),f326(f307(x111181),x111182))))),
% 157.55/157.28 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,4638,10645,3267,3433,10481,10484,10580,10583,3410,3309,3370,3305,3332,3316,3942,3529,3403,4647,10472,3367,10545,4250,4110,4708,3388,3669,3834,3770,3540,10564,10684,10762,10835,10838,10878,10978,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,4212,4119,11053,3835,4200,3852,10608,4700,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,4692,11034,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,3493,10905,4291,4686,4671,4674,3449,3453,4673,4672,4702,10771,4707,3919,3733,10824,10827,10920,11087,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,10830,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679])).
% 157.55/157.28 cnf(11131,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f2(a909)),x111311))),
% 157.55/157.28 inference(rename_variables,[],[3493])).
% 157.55/157.28 cnf(11138,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x111381),x111381))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(11147,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x111471),x111472),f188(f917(x111471,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11151,plain,
% 157.55/157.28 (E(f326(f326(f101(f917(x111511,a905)),f326(f326(f101(f917(x111511,a905)),x111512),f326(f78(f917(x111511,a905)),x111513))),x111513),f188(f917(x111511,a905)))),
% 157.55/157.28 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,4638,10645,3267,3433,10481,10484,10580,10583,3410,3309,3370,3305,3332,3316,3942,3529,3403,4647,10472,3367,10545,4250,4110,4708,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,4212,4119,11053,3835,4200,3852,10608,4700,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,4692,11034,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,3919,3733,10824,10827,10920,11087,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952])).
% 157.55/157.28 cnf(11155,plain,
% 157.55/157.28 (P105(f326(f326(f328(x111551),x111552),f241(f917(x111551,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3625])).
% 157.55/157.28 cnf(11158,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x111581),f910(x111581))),f326(f326(f251(f910(x111581),f910(x111581)),x111582),f113(x111581))),f145(x111581,x111583)))),
% 157.55/157.28 inference(rename_variables,[],[4708])).
% 157.55/157.28 cnf(11167,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(x111671,x111671)),x111672),f262(x111671,f188(f917(x111671,a905)))))),
% 157.55/157.28 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,4638,10645,3267,3433,10481,10484,10580,10583,3410,3309,3370,3305,3332,3316,3942,3529,3403,4647,10472,3367,10545,4250,4110,4708,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,4212,4119,11053,3835,4200,3852,10608,4700,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,4692,11034,11147,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,3919,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092])).
% 157.55/157.28 cnf(11168,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x111681),x111682),f188(f917(x111681,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11170,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x111701),x111702),f326(f310(x111701,x111703,x111704),f188(f917(x111703,a905)))))),
% 157.55/157.28 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,4638,10645,3267,3433,10481,10484,10580,10583,3410,3309,3370,3305,3332,3316,3942,3529,3403,4647,10472,3367,10545,4250,4110,4708,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,4212,4119,11053,3835,4200,3852,10608,4700,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,4692,11034,11147,11168,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,3919,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123])).
% 157.55/157.28 cnf(11171,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x111711),x111712),f188(f917(x111711,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11174,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x111741,a905)),x111742),f326(f326(f308(x111741),x111743),x111742)))),
% 157.55/157.28 inference(rename_variables,[],[3917])).
% 157.55/157.28 cnf(11177,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x111771),x111771))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(11180,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x111801,a905)),x111802),f326(f326(f308(x111801),x111803),x111802)))),
% 157.55/157.28 inference(rename_variables,[],[3917])).
% 157.55/157.28 cnf(11183,plain,
% 157.55/157.28 (E(f326(f309(x111831,x111831,f7(x111831)),x111832),x111832)),
% 157.55/157.28 inference(rename_variables,[],[3529])).
% 157.55/157.28 cnf(11198,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x111981,a905)),x111982),f326(f326(f308(x111981),x111983),x111982)))),
% 157.55/157.28 inference(rename_variables,[],[3917])).
% 157.55/157.28 cnf(11209,plain,
% 157.55/157.28 (~E(f326(a112,x112091),f2(a909))),
% 157.55/157.28 inference(rename_variables,[],[4638])).
% 157.55/157.28 cnf(11212,plain,
% 157.55/157.28 (~P105(f326(f326(f172(x112121),f113(x112121)),x112122))),
% 157.55/157.28 inference(rename_variables,[],[4688])).
% 157.55/157.28 cnf(11225,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x112251),f326(a112,x112251)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(11235,plain,
% 157.55/157.28 (~E(f326(f309(x112351,f917(x112351,a905),x112352),x112353),f326(f307(x112351),x112353))),
% 157.55/157.28 inference(rename_variables,[],[4690])).
% 157.55/157.28 cnf(11238,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x112381),x112382),f188(f917(x112381,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11241,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x112411),x112412),f188(f917(x112411,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11244,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(x112441,x112441)),f326(f326(f251(x112441,x112441),x112442),x112443)),f153(x112441,f113(f917(x112441,a909)))))),
% 157.55/157.28 inference(rename_variables,[],[4707])).
% 157.55/157.28 cnf(11247,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(x112471,x112471)),f326(f326(f251(x112471,x112471),x112472),x112473)),f153(x112471,f113(f917(x112471,a909)))))),
% 157.55/157.28 inference(rename_variables,[],[4707])).
% 157.55/157.28 cnf(11252,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x112521),x112522),f188(f917(x112521,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11255,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(x112551,x112551)),f326(f326(f251(x112551,x112551),x112552),x112552)),f306(x112551,x112553)))),
% 157.55/157.28 inference(rename_variables,[],[4110])).
% 157.55/157.28 cnf(11258,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x112581,a905)),x112582),f241(f917(x112581,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(11261,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x112611,a905)),f326(f172(x112611),f176(x112611,x112612,x112613))),f326(f172(x112611),x112612)))),
% 157.55/157.28 inference(rename_variables,[],[4166])).
% 157.55/157.28 cnf(11277,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x112771,a905)),f188(f917(x112771,a905))),x112772))),
% 157.55/157.28 inference(rename_variables,[],[3919])).
% 157.55/157.28 cnf(11288,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x112881),f910(x112881))),f326(f326(f251(f910(x112881),f910(x112881)),x112882),f113(x112881))),f147(x112881,x112883)))),
% 157.55/157.28 inference(rename_variables,[],[4709])).
% 157.55/157.28 cnf(11299,plain,
% 157.55/157.28 (~E(f326(a112,x112991),x112991)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11302,plain,
% 157.55/157.28 (~E(f326(a112,x113021),x113021)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11306,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(f910(x113061),f910(x113061))),f326(f326(f251(f910(x113061),f910(x113061)),f113(x113061)),f113(x113061))),f326(f326(f288(f910(x113061),f910(x113061),f910(x113061)),f158(x113061,x113062)),f306(f910(x113061),f158(x113061,x113062)))))),
% 157.55/157.28 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,4638,10645,10745,3267,3319,3433,10481,10484,10580,10583,3410,3929,3309,3370,3305,3332,3316,3942,3529,11056,3403,4108,4647,10472,4690,3367,10545,4250,4110,11255,4708,11158,4709,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,11116,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,4212,4119,11053,4166,3835,4200,3852,10608,10705,4700,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,11155,4692,11034,11147,11168,11171,11238,11241,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,11244,4076,3917,11174,11180,3919,10908,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770])).
% 157.55/157.28 cnf(11309,plain,
% 157.55/157.28 (~E(f326(a112,x113091),f2(a909))),
% 157.55/157.28 inference(rename_variables,[],[4638])).
% 157.55/157.28 cnf(11311,plain,
% 157.55/157.28 (E(f326(x113111,f326(f90(x113112,x113113,f241(f917(x113112,a905)),x113111),f326(x113111,x113114))),f326(x113111,x113114))),
% 157.55/157.28 inference(scs_inference,[],[4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,4638,10645,10745,11209,3267,3319,3433,10481,10484,10580,10583,3410,3929,3309,3370,3305,3332,3316,3942,3529,11056,3403,4108,4647,10472,4690,3367,10545,4250,4110,11255,4708,11158,4709,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,11116,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,4212,4119,11053,4166,3835,4200,3852,10608,10705,4700,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,11155,4692,11034,11147,11168,11171,11238,11241,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,11244,4076,3917,11174,11180,3919,10908,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784])).
% 157.55/157.28 cnf(11314,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x113141,a905)),x113142),x113142))),
% 157.55/157.28 inference(rename_variables,[],[3766])).
% 157.55/157.28 cnf(11321,plain,
% 157.55/157.28 (~E(f326(a112,x113211),x113211)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11324,plain,
% 157.55/157.28 (~E(f326(a112,x113241),x113241)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11329,plain,
% 157.55/157.28 (P24(x113291,x113291,f7(x113291),x113292)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(11334,plain,
% 157.55/157.28 (~E(f326(f309(x113341,f917(x113341,a905),x113342),x113343),f326(f307(x113341),x113343))),
% 157.55/157.28 inference(rename_variables,[],[4690])).
% 157.55/157.28 cnf(11339,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x113391,a905)),x113392),f241(f917(x113391,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(11355,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x113551),x113552),f188(f917(x113551,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11358,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x113581)),x113581))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(11363,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x113631),x113632),f188(f917(x113631,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11374,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x113741)),x113741))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(11377,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x113771),x113772),f188(f917(x113771,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11386,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(x113861,x113861)),f326(f326(f251(x113861,x113861),x113862),x113862)),f306(x113861,x113863)))),
% 157.55/157.28 inference(rename_variables,[],[4110])).
% 157.55/157.28 cnf(11389,plain,
% 157.55/157.28 (P105(f326(f326(f328(x113891),x113892),f241(f917(x113891,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3625])).
% 157.55/157.28 cnf(11392,plain,
% 157.55/157.28 (P105(f326(f326(f328(x113921),x113922),f241(f917(x113921,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3625])).
% 157.55/157.28 cnf(11399,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x113991),f910(x113991))),f326(f326(f251(f910(x113991),f910(x113991)),x113992),f113(x113991))),f145(x113991,x113993)))),
% 157.55/157.28 inference(rename_variables,[],[4708])).
% 157.55/157.28 cnf(11402,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x114021),f910(x114021))),f326(f326(f251(f910(x114021),f910(x114021)),x114022),f113(x114021))),f147(x114021,x114023)))),
% 157.55/157.28 inference(rename_variables,[],[4709])).
% 157.55/157.28 cnf(11405,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x114051),f910(x114051))),f326(f326(f251(f910(x114051),f910(x114051)),x114052),f113(x114051))),f157(x114051,x114053)))),
% 157.55/157.28 inference(rename_variables,[],[4710])).
% 157.55/157.28 cnf(11410,plain,
% 157.55/157.28 (~P105(f326(f326(f235(f917(x114101,a905)),x114102),f188(f917(x114101,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4700])).
% 157.55/157.28 cnf(11413,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x114131),x114132),f188(f917(x114131,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11417,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x114171,a905)),x114172),f326(f326(f110(f917(x114171,a905)),x114173),f241(f917(x114171,a905)))))),
% 157.55/157.28 inference(scs_inference,[],[3709,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,4638,10645,10745,11209,3267,3319,3433,10481,10484,10580,10583,3410,3929,3309,3370,3305,3332,3316,3942,3529,11056,3403,4108,4647,10472,4690,11235,3576,3367,10545,4250,4110,11255,4708,11158,11399,4709,11288,4710,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,11116,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,4212,4119,11053,4166,3835,4200,3852,10608,10705,11258,11339,4700,11004,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,11155,11389,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,11358,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,11244,4076,3917,11174,11180,3766,3919,10908,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275])).
% 157.55/157.28 cnf(11418,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x114181,a905)),x114182),f241(f917(x114181,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(11424,plain,
% 157.55/157.28 (~P105(f326(f326(f254(x114241,x114242,a905,f326(f172(x114243),f113(x114243))),x114244),x114245))),
% 157.55/157.28 inference(scs_inference,[],[3709,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,4638,10645,10745,11209,3267,3319,3433,10481,10484,10580,10583,3410,3929,3309,3370,3305,3332,3316,3942,3529,11056,3403,4108,4647,10472,4690,11235,3576,3367,10545,4250,4110,11255,4708,11158,11399,4709,11288,4710,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,11116,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,4212,4119,11053,4166,3835,4200,3852,10608,10705,11258,11339,4700,11004,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,11155,11389,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,11358,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,11244,4076,3917,11174,11180,3766,3919,10908,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380])).
% 157.55/157.28 cnf(11425,plain,
% 157.55/157.28 (~P105(f326(f326(f172(x114251),f113(x114251)),x114252))),
% 157.55/157.28 inference(rename_variables,[],[4688])).
% 157.55/157.28 cnf(11430,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x114301),x114302),f188(f917(x114301,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11433,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(x114331,x114331)),f326(f326(f251(x114331,x114331),x114332),x114333)),f153(x114331,f113(f917(x114331,a909)))))),
% 157.55/157.28 inference(rename_variables,[],[4707])).
% 157.55/157.28 cnf(11436,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x114361,a905)),x114362),x114362))),
% 157.55/157.28 inference(rename_variables,[],[3766])).
% 157.55/157.28 cnf(11439,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x114391),x114392),f188(f917(x114391,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11441,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x114411,a905)),f326(f284(x114412,x114411,f188(f917(f916(x114412,x114411),a905))),x114413)),x114414))),
% 157.55/157.28 inference(scs_inference,[],[3709,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,4638,10645,10745,11209,3267,3319,3433,10481,10484,10580,10583,3410,3929,3309,3370,3305,3332,3316,3942,3529,11056,3403,4108,4647,10472,4690,11235,3576,3367,10545,4250,4110,11255,4708,11158,11399,4709,11288,4710,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,11116,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,4212,4119,11053,4166,3835,4200,3852,10608,10705,11258,11339,4700,11004,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,11155,11389,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,11358,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,11244,11247,4076,3917,11174,11180,3766,11314,3919,10908,11277,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445])).
% 157.55/157.28 cnf(11442,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x114421,a905)),f188(f917(x114421,a905))),x114422))),
% 157.55/157.28 inference(rename_variables,[],[3919])).
% 157.55/157.28 cnf(11445,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(x114451,x114451)),f326(f326(f251(x114451,x114451),x114452),x114452)),f306(x114451,x114453)))),
% 157.55/157.28 inference(rename_variables,[],[4110])).
% 157.55/157.28 cnf(11451,plain,
% 157.55/157.28 (P33(x114511,x114512,x114513,f326(f326(f154(x114514,x114511),x114515),f114(x114514,f113(x114514))),f113(x114512))),
% 157.55/157.28 inference(scs_inference,[],[3709,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,4638,10645,10745,11209,3267,3319,3433,10481,10484,10580,10583,3410,3929,3309,3370,3305,3332,3316,3942,3529,11056,3403,4108,4647,10472,4690,11235,3576,3367,10545,4250,4110,11255,11386,4708,11158,11399,4709,11288,4710,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,11116,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,4212,4119,11053,4166,3835,4200,3852,10608,10705,11258,11339,4700,11004,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,11155,11389,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,11358,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,11244,11247,4076,3917,11174,11180,3766,11314,3919,10908,11277,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476])).
% 157.55/157.28 cnf(11456,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x114561),f910(x114561))),f326(f326(f251(f910(x114561),f910(x114561)),x114562),f113(x114561))),f157(x114561,x114563)))),
% 157.55/157.28 inference(rename_variables,[],[4710])).
% 157.55/157.28 cnf(11463,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x114631),f910(x114631))),f326(f326(f251(f910(x114631),f910(x114631)),f113(x114631)),x114632)),f145(x114631,x114633)))),
% 157.55/157.28 inference(rename_variables,[],[4711])).
% 157.55/157.28 cnf(11468,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f917(x114681,a905),f917(x114681,a905))),f326(f326(f251(f917(x114681,a905),f917(x114681,a905)),x114682),f188(f917(x114681,a905)))),f313(x114681)))),
% 157.55/157.28 inference(scs_inference,[],[3709,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,4638,10645,10745,11209,3267,3319,3433,10481,10484,10580,10583,3410,3929,3309,3370,3305,3332,3316,3942,3529,11056,3403,4108,4647,10472,4690,11235,3576,3367,10545,4250,4110,11255,11386,4708,11158,11399,4709,11288,4710,11405,4711,4712,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,11116,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,4212,4119,11053,4166,3835,4200,3852,10608,10705,11258,11339,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,11155,11389,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,11358,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,11244,11247,4076,3917,11174,11180,3766,11314,3919,10908,11277,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607])).
% 157.55/157.28 cnf(11471,plain,
% 157.55/157.28 (P105(f326(f326(f328(x114711),x114712),f241(f917(x114711,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3625])).
% 157.55/157.28 cnf(11476,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x114761,a905)),f188(f917(x114761,a905))),x114762))),
% 157.55/157.28 inference(rename_variables,[],[3919])).
% 157.55/157.28 cnf(11479,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x114791),x114792),f188(f917(x114791,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11482,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x114821,a905)),x114822),f241(f917(x114821,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(11486,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x114861,a905)),f326(f284(x114862,x114861,x114863),f188(f917(x114862,a905)))),x114864))),
% 157.55/157.28 inference(scs_inference,[],[3709,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,4638,10645,10745,11209,3267,3319,3433,10481,10484,10580,10583,3410,3929,3309,3370,3305,3332,3316,3942,3529,11056,3403,4108,4647,10472,4690,11235,3576,3367,10545,4250,4110,11255,11386,4708,11158,11399,4709,11288,4710,11405,4711,4712,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,11116,4696,3909,3678,4058,3499,3501,3475,4680,4642,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,4212,4119,11053,4166,3835,4200,3852,10608,10705,11258,11339,11418,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,11155,11389,11392,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,3533,10872,10902,10911,10914,3565,3990,3927,10524,4689,10469,10860,10863,11358,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,11244,11247,4076,3917,11174,11180,3766,11314,3919,10908,11277,11442,11476,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,4254,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712])).
% 157.55/157.28 cnf(11487,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x114871,a905)),f188(f917(x114871,a905))),x114872))),
% 157.55/157.28 inference(rename_variables,[],[3919])).
% 157.55/157.28 cnf(11500,plain,
% 157.55/157.28 (P105(f326(f241(f917(x115001,a905)),x115002))),
% 157.55/157.28 inference(rename_variables,[],[3533])).
% 157.55/157.28 cnf(11508,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x115081),f910(x115081))),f326(f326(f251(f910(x115081),f910(x115081)),x115082),f113(x115081))),f145(x115081,x115083)))),
% 157.55/157.28 inference(rename_variables,[],[4708])).
% 157.55/157.28 cnf(11511,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x115111),f910(x115111))),f326(f326(f251(f910(x115111),f910(x115111)),x115112),f113(x115111))),f147(x115111,x115113)))),
% 157.55/157.28 inference(rename_variables,[],[4709])).
% 157.55/157.28 cnf(11514,plain,
% 157.55/157.28 (~E(f326(f326(f151(x115141),x115142),x115143),x115143)),
% 157.55/157.28 inference(rename_variables,[],[4647])).
% 157.55/157.28 cnf(11517,plain,
% 157.55/157.28 (~E(f326(a112,x115171),x115171)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11520,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x115201),x115202),f188(f917(x115201,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11525,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x115251),x115252),f188(f917(x115251,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11528,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x115281),x115282),f188(f917(x115281,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11531,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(f910(x115311),f910(x115311))),f326(f326(f251(f910(x115311),f910(x115311)),x115312),x115312)),f158(x115311,f306(x115311,x115313))))),
% 157.55/157.28 inference(rename_variables,[],[4243])).
% 157.55/157.28 cnf(11534,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x115341),f910(x115341))),f326(f326(f251(f910(x115341),f910(x115341)),x115342),f113(x115341))),f145(x115341,x115343)))),
% 157.55/157.28 inference(rename_variables,[],[4708])).
% 157.55/157.28 cnf(11544,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(x115441,x115441)),f326(f326(f251(x115441,x115441),x115442),x115443)),f153(x115441,f113(f917(x115441,a909)))))),
% 157.55/157.28 inference(rename_variables,[],[4707])).
% 157.55/157.28 cnf(11547,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x115471),x115472),f188(f917(x115471,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11550,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x115501),x115502),f188(f917(x115501,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11553,plain,
% 157.55/157.28 (P105(f326(f326(f328(x115531),x115532),f241(f917(x115531,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3625])).
% 157.55/157.28 cnf(11556,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x115561),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(11561,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(x115611,x115611)),f326(f326(f251(x115611,x115611),x115612),x115613)),f153(x115611,f113(f917(x115611,a909)))))),
% 157.55/157.28 inference(rename_variables,[],[4707])).
% 157.55/157.28 cnf(11570,plain,
% 157.55/157.28 (~E(f326(f309(x115701,f917(x115701,a905),x115702),x115703),f326(f307(x115701),x115703))),
% 157.55/157.28 inference(rename_variables,[],[4690])).
% 157.55/157.28 cnf(11573,plain,
% 157.55/157.28 (~E(f326(f309(x115731,f917(x115731,a905),x115732),x115733),f326(f307(x115731),x115733))),
% 157.55/157.28 inference(rename_variables,[],[4690])).
% 157.55/157.28 cnf(11578,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x115781),f910(x115781))),f326(f326(f251(f910(x115781),f910(x115781)),x115782),f113(x115781))),f145(x115781,x115783)))),
% 157.55/157.28 inference(rename_variables,[],[4708])).
% 157.55/157.28 cnf(11584,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x115841),f910(x115841))),f326(f326(f251(f910(x115841),f910(x115841)),x115842),f113(x115841))),f145(x115841,x115843)))),
% 157.55/157.28 inference(rename_variables,[],[4708])).
% 157.55/157.28 cnf(11587,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x115871),x115872),f188(f917(x115871,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11589,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(x115891,x115892)),f326(f326(f251(x115891,x115892),f326(x115893,x115894)),f326(x115895,x115894))),f326(f309(f916(x115896,x115896),f916(x115891,x115892),f257(x115896,x115891,x115896,x115892,x115893,x115895)),f306(x115896,x115897))))),
% 157.55/157.28 inference(scs_inference,[],[3709,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,4638,10645,10745,11209,3267,3319,3433,10481,10484,10580,10583,3410,3929,3309,3370,3305,3332,3316,3942,3529,11056,3403,4108,4647,10472,10642,4690,11235,11334,11570,3576,3367,10545,4250,4110,11255,11386,11445,4708,11158,11399,11508,11534,11578,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,3834,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,3922,3456,4683,10449,10452,10478,10605,10780,10986,11001,11116,4696,3909,3678,4058,3499,3501,3475,4680,4642,4243,11531,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,4212,4119,11053,4166,3835,4200,3852,10608,10705,11258,11339,11418,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,3473,10600,10656,10890,10981,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,11155,11389,11392,11471,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,3533,10872,10902,10911,10914,10917,3565,3990,3927,10524,4689,10469,10860,10863,11358,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4702,10771,4707,11244,11247,11433,11544,4076,3917,11174,11180,3766,11314,3919,10908,11277,11442,11476,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,4254,3951,4703,10494,10497,10866,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226])).
% 157.55/157.28 cnf(11592,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x115921),x115922),f188(f917(x115921,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11595,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x115951),x115952),f188(f917(x115951,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11598,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x115981),x115982),f188(f917(x115981,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11601,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x116011),x116012),f188(f917(x116011,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11604,plain,
% 157.55/157.28 (P105(f326(f326(f328(x116041),f326(x116042,x116043)),f326(f309(x116044,x116041,x116042),f241(f917(x116044,a905)))))),
% 157.55/157.28 inference(rename_variables,[],[4076])).
% 157.55/157.28 cnf(11607,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(x116071,x116071)),f326(f326(f251(x116071,x116071),x116072),x116073)),f153(x116071,f113(f917(x116071,a909)))))),
% 157.55/157.28 inference(rename_variables,[],[4707])).
% 157.55/157.28 cnf(11615,plain,
% 157.55/157.28 (E(f114(x116151,f113(x116151)),f113(x116151))),
% 157.55/157.28 inference(rename_variables,[],[3319])).
% 157.55/157.28 cnf(11618,plain,
% 157.55/157.28 (~E(f326(a112,x116181),x116181)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11625,plain,
% 157.55/157.28 (~E(f326(a112,x116251),x116251)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11630,plain,
% 157.55/157.28 (E(f326(f283(x116301,x116301),f262(x116301,x116302)),x116302)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(11633,plain,
% 157.55/157.28 (E(f326(f283(x116331,x116331),f262(x116331,x116332)),x116332)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(11639,plain,
% 157.55/157.28 (~E(f326(a112,x116391),x116391)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11644,plain,
% 157.55/157.28 (~E(f326(f326(f79(a1),x116441),x116441),a97)),
% 157.55/157.28 inference(rename_variables,[],[4645])).
% 157.55/157.28 cnf(11651,plain,
% 157.55/157.28 (E(f326(f326(f3(a909),f2(a909)),x116511),f2(a909))),
% 157.55/157.28 inference(rename_variables,[],[3389])).
% 157.55/157.28 cnf(11654,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x116541),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(11661,plain,
% 157.55/157.28 (E(f326(f326(f79(a1),f326(f326(f80(a1),x116611),f326(f326(f36(a1),x116612),x116611))),f45(a1,x116612,x116611)),x116612)),
% 157.55/157.28 inference(rename_variables,[],[4023])).
% 157.55/157.28 cnf(11685,plain,
% 157.55/157.28 (~E(f326(a112,x116851),x116851)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11688,plain,
% 157.55/157.28 (~E(f326(a112,x116881),x116881)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11714,plain,
% 157.55/157.28 (~P105(f326(f326(f172(x117141),f113(x117141)),x117142))),
% 157.55/157.28 inference(rename_variables,[],[4688])).
% 157.55/157.28 cnf(11720,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),f2(a909)),f326(a112,x117201)))),
% 157.55/157.28 inference(rename_variables,[],[3552])).
% 157.55/157.28 cnf(11721,plain,
% 157.55/157.28 (~E(f326(a112,x117211),x117211)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11724,plain,
% 157.55/157.28 (P105(f326(f326(f328(x117241),x117242),f241(f917(x117241,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3625])).
% 157.55/157.28 cnf(11736,plain,
% 157.55/157.28 (~E(f326(a112,x117361),x117361)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11739,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x117391),x117391))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(11746,plain,
% 157.55/157.28 (P105(f326(f66(x117461,x117462,x117463,x117464,f188(f917(x117461,a905))),x117464))),
% 157.55/157.28 inference(rename_variables,[],[4388])).
% 157.55/157.28 cnf(11747,plain,
% 157.55/157.28 (E(f326(f283(x117471,x117471),f262(x117471,x117472)),x117472)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(11760,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),f326(f326(f79(a909),x117601),x117602)),x117602))),
% 157.55/157.28 inference(rename_variables,[],[4703])).
% 157.55/157.28 cnf(11763,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a1),f326(f100(a1),x117631)),f2(a1)))),
% 157.55/157.28 inference(rename_variables,[],[4696])).
% 157.55/157.28 cnf(11779,plain,
% 157.55/157.28 (~E(f326(f326(f101(a909),f326(a112,x117791)),x117791),f326(a112,x117791))),
% 157.55/157.28 inference(scs_inference,[],[3709,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,3393,4638,10645,10745,11209,3086,3092,3096,3097,3104,3108,3119,3124,3130,3145,3150,3151,3152,3160,3179,3214,3223,3224,3234,3255,3267,4626,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,3410,3929,3309,4023,11661,3370,3305,3332,3316,3942,3529,11056,3403,4108,4647,10472,10642,4690,11235,11334,11570,11573,3576,3367,10545,10875,3368,3286,3389,11651,4250,4110,11255,11386,11445,4708,11158,11399,11508,11534,11578,11584,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,3834,4645,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,3922,3456,3552,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,4696,3909,3678,4058,3499,3501,3475,4680,4642,3662,4697,4243,11531,3792,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,4212,4119,11053,4166,3835,4200,3852,10608,10705,11258,11339,11418,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,3473,10600,10656,10890,10981,11103,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,11155,11389,11392,11471,11553,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,3533,10872,10902,10911,10914,10917,3565,3990,3927,10524,4689,10469,10860,10863,11358,11374,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,4076,3917,11174,11180,3766,11314,3919,10908,11277,11442,11476,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,4254,3951,4703,10494,10497,10866,10869,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519])).
% 157.55/157.28 cnf(11786,plain,
% 157.55/157.28 (E(f326(f283(x117861,x117861),f262(x117861,x117862)),x117862)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(11791,plain,
% 157.55/157.28 (E(f326(f283(x117911,x117911),f262(x117911,x117912)),x117912)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(11794,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a1),f326(f100(a1),x117941)),f2(a1)))),
% 157.55/157.28 inference(rename_variables,[],[4696])).
% 157.55/157.28 cnf(11799,plain,
% 157.55/157.28 (~E(f326(a112,x117991),x117991)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11808,plain,
% 157.55/157.28 (~P105(f326(f326(f172(x118081),f113(x118081)),x118082))),
% 157.55/157.28 inference(rename_variables,[],[4688])).
% 157.55/157.28 cnf(11828,plain,
% 157.55/157.28 (E(f45(a909,x118281,x118281),f2(a909))),
% 157.55/157.28 inference(scs_inference,[],[3709,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,3393,4638,10645,10745,11209,3086,3092,3093,3096,3097,3104,3108,3109,3119,3120,3124,3130,3145,3150,3151,3152,3160,3179,3214,3223,3224,3234,3235,3255,3267,4626,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,3410,3929,3309,4023,11661,3370,3305,3332,3328,3316,3317,3942,3529,11056,3403,4108,4647,10472,10642,4690,11235,11334,11570,11573,3576,3367,10545,10875,3368,3286,3389,11651,4250,4110,11255,11386,11445,4708,11158,11399,11508,11534,11578,11584,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,3834,4645,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,3922,3456,3552,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,4696,11763,11794,3909,3678,4058,3499,3501,3475,4680,4642,3662,4697,4243,11531,3792,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,4212,4119,11053,4166,3835,4200,3852,10608,10705,11258,11339,11418,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,3473,10600,10656,10890,10981,11103,3474,4679,10489,10521,11025,11067,3625,10750,10841,11111,11155,11389,11392,11471,11553,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,3533,10872,10902,10911,10914,10917,3572,3565,3990,3927,10524,4689,10469,10860,10863,11358,11374,3493,10905,11061,4291,4686,3998,4671,4674,3449,3453,4673,4672,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,4076,3917,11174,11180,3766,11314,3919,10908,11277,11442,11476,3626,3733,10824,10827,10920,11087,4705,4706,10664,4349,4254,3951,4703,10494,10497,10866,10869,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677])).
% 157.55/157.28 cnf(11831,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a1),f326(f100(a1),x118311)),f2(a1)))),
% 157.55/157.28 inference(rename_variables,[],[4696])).
% 157.55/157.28 cnf(11834,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x118341),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(11835,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x118351),f326(a112,x118351)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(11838,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a1),f326(f100(a1),x118381)),f2(a1)))),
% 157.55/157.28 inference(rename_variables,[],[4696])).
% 157.55/157.28 cnf(11841,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x118411),x118412),f188(f917(x118411,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11842,plain,
% 157.55/157.28 (P105(f326(f326(f328(f917(x118421,a905)),x118422),f326(f307(x118421),x118422)))),
% 157.55/157.28 inference(rename_variables,[],[3835])).
% 157.55/157.28 cnf(11857,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x118571)),x118571))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(11858,plain,
% 157.55/157.28 (~E(f326(a112,x118581),x118581)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11861,plain,
% 157.55/157.28 (E(f326(f283(x118611,x118611),f262(x118611,x118612)),x118612)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(11871,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),f326(f326(f79(a909),x118711),x118712)),x118711))),
% 157.55/157.28 inference(rename_variables,[],[4704])).
% 157.55/157.28 cnf(11874,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a1),f326(f100(a1),x118741)),f2(a1)))),
% 157.55/157.28 inference(rename_variables,[],[4696])).
% 157.55/157.28 cnf(11877,plain,
% 157.55/157.28 (~E(f326(a112,x118771),x118771)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(11890,plain,
% 157.55/157.28 (P105(f326(f326(f328(x118901),x118902),f326(f326(f308(x118901),x118902),x118903)))),
% 157.55/157.28 inference(rename_variables,[],[3782])).
% 157.55/157.28 cnf(11891,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a1),f2(a1)),f326(f78(a1),f326(f100(a1),f326(a112,x118911)))))),
% 157.55/157.28 inference(rename_variables,[],[4705])).
% 157.55/157.28 cnf(11894,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),f326(f326(f3(a909),x118941),x118942)),f326(a112,x118941)))),
% 157.55/157.28 inference(rename_variables,[],[3922])).
% 157.55/157.28 cnf(11897,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f45(a909,x118971,x118972)),x118971))),
% 157.55/157.28 inference(rename_variables,[],[3927])).
% 157.55/157.28 cnf(11903,plain,
% 157.55/157.28 (E(f326(f283(x119031,x119031),f262(x119031,x119032)),x119032)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(11908,plain,
% 157.55/157.28 (E(f326(f326(f134(x119081),f169(x119081,x119082,x119083)),f169(x119081,x119084,x119083)),f326(f326(f134(x119081),f169(x119081,x119084,x119083)),f169(x119081,x119082,x119083)))),
% 157.55/157.28 inference(rename_variables,[],[4037])).
% 157.55/157.28 cnf(11913,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x119131)),x119131))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(11922,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x119221),x119221))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(11925,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f45(a909,x119251,x119252)),x119251))),
% 157.55/157.28 inference(rename_variables,[],[3927])).
% 157.55/157.28 cnf(11926,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f2(a909)),x119261))),
% 157.55/157.28 inference(rename_variables,[],[3493])).
% 157.55/157.28 cnf(11943,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x119431),x119431))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(11946,plain,
% 157.55/157.28 (P105(f326(f326(f328(x119461),f326(x119462,x119463)),f326(f309(x119464,x119461,x119462),f241(f917(x119464,a905)))))),
% 157.55/157.28 inference(rename_variables,[],[4076])).
% 157.55/157.28 cnf(11947,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x119471)),x119471))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(11950,plain,
% 157.55/157.28 (P105(f326(f326(f328(x119501),f326(x119502,x119503)),f326(f309(x119504,x119501,x119502),f241(f917(x119504,a905)))))),
% 157.55/157.28 inference(rename_variables,[],[4076])).
% 157.55/157.28 cnf(11951,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),f326(f326(f79(a909),x119511),x119512)),x119512))),
% 157.55/157.28 inference(rename_variables,[],[4703])).
% 157.55/157.28 cnf(11956,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),f326(f326(f79(a909),x119561),x119562)),x119561))),
% 157.55/157.28 inference(rename_variables,[],[4704])).
% 157.55/157.28 cnf(11959,plain,
% 157.55/157.28 (~P105(f326(f326(f172(x119591),f113(x119591)),x119592))),
% 157.55/157.28 inference(rename_variables,[],[4688])).
% 157.55/157.28 cnf(11962,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x119621),x119621))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(11968,plain,
% 157.55/157.28 (~P34(x119681,x119682,f113(x119681))),
% 157.55/157.28 inference(rename_variables,[],[4658])).
% 157.55/157.28 cnf(11971,plain,
% 157.55/157.28 (P105(f326(f326(f328(x119711),x119712),f241(f917(x119711,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3625])).
% 157.55/157.28 cnf(11972,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x119721)),x119721))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(11985,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x119851),x119852),f188(f917(x119851,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(11988,plain,
% 157.55/157.28 (E(f326(f326(f18(x119881,x119882),x119883),x119884),x119883)),
% 157.55/157.28 inference(rename_variables,[],[3463])).
% 157.55/157.28 cnf(11991,plain,
% 157.55/157.28 (E(f326(f326(f18(x119911,x119912),x119913),x119914),x119913)),
% 157.55/157.28 inference(rename_variables,[],[3463])).
% 157.55/157.28 cnf(12003,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),f2(a909)),f326(a112,x120031)))),
% 157.55/157.28 inference(rename_variables,[],[3552])).
% 157.55/157.28 cnf(12006,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x120061),x120061))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12009,plain,
% 157.55/157.28 (P105(f326(f61(x120091),f326(f172(x120091),x120092)))),
% 157.55/157.28 inference(rename_variables,[],[3512])).
% 157.55/157.28 cnf(12012,plain,
% 157.55/157.28 (P105(f326(f61(x120121),f326(f172(x120121),x120122)))),
% 157.55/157.28 inference(rename_variables,[],[3512])).
% 157.55/157.28 cnf(12015,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),f326(f78(a1),f326(f100(a1),x120151))),f326(f100(a1),x120152)))),
% 157.55/157.28 inference(rename_variables,[],[3952])).
% 157.55/157.28 cnf(12018,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x120181),x120182),f188(f917(x120181,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12036,plain,
% 157.55/157.28 (~P105(f326(f326(f328(a909),x120361),f326(f281(a909),f2(a909))))),
% 157.55/157.28 inference(scs_inference,[],[3709,4657,4658,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,3393,4638,10645,10745,11209,3085,3086,3089,3092,3093,3096,3097,3104,3108,3109,3119,3120,3124,3130,3145,3150,3151,3152,3159,3160,3179,3214,3223,3224,3226,3234,3235,3255,3267,4626,4037,11908,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,3410,3929,3309,3671,4023,11661,3370,3305,3332,3328,3316,3317,3942,3529,11056,3403,4108,4647,10472,10642,3463,11988,4690,11235,11334,11570,11573,3576,3367,10545,10875,3368,3630,3286,3389,11651,4250,4110,11255,11386,11445,4708,11158,11399,11508,11534,11578,11584,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,3834,4524,4525,4645,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,3922,11894,3456,3552,11720,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,4696,11763,11794,11831,11838,3909,3678,4058,3499,3501,3475,4680,4642,3662,4697,4243,11531,3792,3512,12009,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,4212,4119,11053,4166,3835,4200,3852,10608,10705,11258,11339,11418,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,3473,10600,10656,10890,10981,11103,3474,3548,4679,10489,10521,11025,11067,11076,11922,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,3533,10872,10902,10911,10914,10917,3572,3565,3990,3927,10524,11897,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,3493,10905,11061,11131,3952,4291,4686,3998,4671,4674,3449,3453,4673,4672,3782,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,4076,11604,11946,3917,11174,11180,3766,11314,3919,10908,11277,11442,11476,3626,3733,10824,10827,10920,11087,4705,11891,4706,10664,4349,4254,3951,3895,4703,10494,10497,10866,10869,11760,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677,5679,5680,5681,5683,5685,5686,5687,5688,5689,5690,5699,5700,5710,5713,5724,5740,5741,5744,5754,5757,5758,5759,5786,5796,5811,5812,5821,5822,5824,5826,5831,5866,5871,5873,5932,5967,5968,5982,5988,5991,5992,5993,5994,6013,6017,6018,6027,6049,6078,6097,6101,6102,6104,6127,6131,6134,6135,6136,6152,6163,6164,6196,6197,6201,6222,6225,6228,6249,6250,6278,6281,6289,6298,6300,6309,6313,6321,6322,6323,6324])).
% 157.55/157.28 cnf(12039,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x120391),x120391))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(12042,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x120421),x120421))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(12051,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x120511),x120511))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(12054,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x120541),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(12059,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x120591),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(12068,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f2(a909)),x120681))),
% 157.55/157.28 inference(rename_variables,[],[3493])).
% 157.55/157.28 cnf(12069,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x120691)),x120691))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(12072,plain,
% 157.55/157.28 (~P105(f326(f326(f172(x120721),f113(x120721)),x120722))),
% 157.55/157.28 inference(rename_variables,[],[4688])).
% 157.55/157.28 cnf(12075,plain,
% 157.55/157.28 (~P105(f326(f326(f172(x120751),f113(x120751)),x120752))),
% 157.55/157.28 inference(rename_variables,[],[4688])).
% 157.55/157.28 cnf(12094,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x120941)),x120941))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(12097,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x120971)),x120971))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(12100,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x121001)),x121001))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(12103,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x121031)),x121031))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(12106,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x121061),x121061))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12109,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x121091),x121091))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12112,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x121121),x121121))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12115,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x121151),x121151))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12132,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x121321),x121321))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12135,plain,
% 157.55/157.28 (P24(a909,a909,a112,x121351)),
% 157.55/157.28 inference(rename_variables,[],[3677])).
% 157.55/157.28 cnf(12138,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x121381),x121381))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(12149,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x121491),x121491))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(12152,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(f916(f910(x121521),f910(x121521)),a905)),f158(x121521,x121522)),f306(f910(x121521),f157(x121521,x121522))))),
% 157.55/157.28 inference(rename_variables,[],[4171])).
% 157.55/157.28 cnf(12159,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x121591),f326(a112,x121591)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(12162,plain,
% 157.55/157.28 (P105(f326(f326(f328(f917(x121621,a905)),x121622),f326(f307(x121621),x121622)))),
% 157.55/157.28 inference(rename_variables,[],[3835])).
% 157.55/157.28 cnf(12163,plain,
% 157.55/157.28 (~E(f326(a112,x121631),x121631)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(12168,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x121681),x121681))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(12173,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x121731),x121731))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(12184,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x121841,a905)),x121842),f326(f326(f308(x121841),x121843),x121842)))),
% 157.55/157.28 inference(rename_variables,[],[3917])).
% 157.55/157.28 cnf(12187,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x121871),x121871))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12188,plain,
% 157.55/157.28 (~E(f326(a112,x121881),x121881)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(12199,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x121991),x121991))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12200,plain,
% 157.55/157.28 (~E(f326(a112,x122001),x122001)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(12203,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x122031),x122031))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12206,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x122061),x122061))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12209,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x122091),x122091))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12212,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x122121),x122121))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12214,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),f326(a104,f2(a1))),f326(a112,x122141)))),
% 157.55/157.28 inference(scs_inference,[],[3709,4657,4658,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,3677,3393,4638,10645,10745,11209,3085,3086,3089,3092,3093,3096,3097,3104,3108,3109,3110,3119,3120,3124,3130,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3255,3267,4626,4037,11908,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,3410,3929,3309,3671,4023,11661,3370,3305,3332,3328,3316,3317,3942,3529,11056,3403,4108,4647,10472,10642,3463,11988,4690,11235,11334,11570,11573,3576,3367,10545,10875,3368,3630,3286,3389,11651,4250,4110,11255,11386,11445,4708,11158,11399,11508,11534,11578,11584,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,3834,4524,4525,4645,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,3922,11894,3456,3552,11720,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,4696,11763,11794,11831,11838,11874,3909,3678,4058,3499,3501,3475,4680,4642,3662,4697,4243,11531,3792,3512,12009,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,4212,4171,4119,11053,4166,3835,11842,4200,3852,10608,10705,11258,11339,11418,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,3474,3548,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,3533,10872,10902,10911,10914,10917,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,3493,10905,11061,11131,11926,3952,4291,4686,3998,4671,4674,3449,3453,4673,4672,3782,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,4076,11604,11946,3917,11174,11180,11198,3766,11314,3919,10908,11277,11442,11476,3626,3733,10824,10827,10920,11087,4705,11891,4706,10664,4349,4254,3951,3895,4703,10494,10497,10866,10869,11760,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677,5679,5680,5681,5683,5685,5686,5687,5688,5689,5690,5699,5700,5710,5713,5724,5740,5741,5744,5754,5757,5758,5759,5786,5796,5811,5812,5821,5822,5824,5826,5831,5866,5871,5873,5932,5967,5968,5982,5988,5991,5992,5993,5994,6013,6017,6018,6027,6049,6078,6097,6101,6102,6104,6127,6131,6134,6135,6136,6152,6163,6164,6196,6197,6201,6222,6225,6228,6249,6250,6278,6281,6289,6298,6300,6309,6313,6321,6322,6323,6324,6355,6372,6424,6461,6463,6485,6486,6493,6497,6498,6502,6516,6532,6553,6554,6559,6568,6583,6603,6609,6611,6626,6627,6630,6631,6633,6635,6636,6637,6639,6641,6645,6651,6652,6654,6655,6661,6663,6705,6711,6726,6729,6730,6731,6765,6770,6772,6777,6778,6788,6792,6806,6829,6830,6832,6833,6844,6850,6869,6872,6892,6922,6923,6924,6930,6944,6963,6965,6967,6969,6974])).
% 157.55/157.28 cnf(12215,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x122151),x122151))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(12218,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x122181),x122181))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12221,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x122211),x122211))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12222,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x122221),f326(a112,x122221)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(12229,plain,
% 157.55/157.28 (~E(f326(a112,x122291),x122291)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(12234,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x122341),x122341))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12235,plain,
% 157.55/157.28 (~E(f326(a112,x122351),x122351)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(12238,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x122381),x122381))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(12255,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x122551),x122551))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(12260,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f2(a909)),x122601))),
% 157.55/157.28 inference(rename_variables,[],[3493])).
% 157.55/157.28 cnf(12274,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x122741),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(12277,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x122771),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(12280,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x122801),x122802),f188(f917(x122801,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12283,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x122831),x122832),f188(f917(x122831,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12285,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x122851),f326(f326(f101(a909),x122852),x122851)))),
% 157.55/157.28 inference(scs_inference,[],[3709,4657,4658,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,3677,3393,4638,10645,10745,11209,3085,3086,3089,3092,3093,3096,3097,3104,3108,3109,3110,3119,3120,3124,3130,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3255,3267,4626,4037,11908,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,3410,3419,3929,4236,3309,3671,4023,11661,3370,3305,3332,3328,3316,3317,3942,3529,11056,3403,4108,4647,10472,10642,3463,11988,4690,11235,11334,11570,11573,3576,3367,10545,10875,3368,3630,3286,3389,11651,4250,4110,11255,11386,11445,4708,11158,11399,11508,11534,11578,11584,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,3834,4524,4525,4645,3770,3986,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,3922,11894,3456,3552,11720,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,4696,11763,11794,11831,11838,11874,3909,3678,4058,3499,3501,3475,4680,4642,3662,4697,4243,11531,3792,3512,12009,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,4212,4171,4119,11053,4166,3835,11842,4200,3852,10608,10705,11258,11339,11418,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,3474,3548,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,3533,10872,10902,10911,10914,10917,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,3493,10905,11061,11131,11926,12068,3952,4291,4686,3964,3998,4671,4674,3449,3453,4673,4672,3782,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,4076,11604,11946,3917,11174,11180,11198,3766,11314,3919,10908,11277,11442,11476,3626,3733,10824,10827,10920,11087,4705,11891,4706,10664,4349,4254,3951,3895,4703,10494,10497,10866,10869,11760,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677,5679,5680,5681,5683,5685,5686,5687,5688,5689,5690,5699,5700,5710,5713,5724,5740,5741,5744,5754,5757,5758,5759,5786,5796,5811,5812,5821,5822,5824,5826,5831,5866,5871,5873,5932,5967,5968,5982,5988,5991,5992,5993,5994,6013,6017,6018,6027,6049,6078,6097,6101,6102,6104,6127,6131,6134,6135,6136,6152,6163,6164,6196,6197,6201,6222,6225,6228,6249,6250,6278,6281,6289,6298,6300,6309,6313,6321,6322,6323,6324,6355,6372,6424,6461,6463,6485,6486,6493,6497,6498,6502,6516,6532,6553,6554,6559,6568,6583,6603,6609,6611,6626,6627,6630,6631,6633,6635,6636,6637,6639,6641,6645,6651,6652,6654,6655,6661,6663,6705,6711,6726,6729,6730,6731,6765,6770,6772,6777,6778,6788,6792,6806,6829,6830,6832,6833,6844,6850,6869,6872,6892,6922,6923,6924,6930,6944,6963,6965,6967,6969,6974,6980,6982,6996,7001,7002,7037,7038,7039,7053,7054,7056,7057,7076,7078,7093,7120,7144,7155,7157,7159,7161,7162,7194,7195,7199,7200,7207])).
% 157.55/157.28 cnf(12286,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x122861),x122861))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12289,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x122891),x122891))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12292,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x122921),x122921))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12295,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x122951),x122951))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12298,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x122981),f326(a112,x122981)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(12305,plain,
% 157.55/157.28 (P105(f326(f326(f328(f917(x123051,a905)),x123052),f326(f307(x123051),x123052)))),
% 157.55/157.28 inference(rename_variables,[],[3835])).
% 157.55/157.28 cnf(12310,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x123101,a905)),x123102),f326(f326(f308(x123101),x123103),x123102)))),
% 157.55/157.28 inference(rename_variables,[],[3917])).
% 157.55/157.28 cnf(12317,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x123171),x123172),f188(f917(x123171,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12326,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x123261,a905)),x123262),f241(f917(x123261,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(12327,plain,
% 157.55/157.28 (~E(f326(a112,x123271),x123271)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(12330,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x123301,a905)),f326(f172(x123301),f326(f136(x123301,x123302),x123303))),f326(f172(x123301),x123303)))),
% 157.55/157.28 inference(rename_variables,[],[4119])).
% 157.55/157.28 cnf(12336,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x123361),f326(a112,x123361)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(12344,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(x123441,x123441)),x123442),f153(x123441,f113(f917(x123441,a909)))))),
% 157.55/157.28 inference(scs_inference,[],[3709,4657,4658,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,3677,3393,4638,10645,10745,11209,3085,3086,3088,3089,3092,3093,3096,3097,3104,3108,3109,3110,3119,3120,3124,3130,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3255,3267,4626,4037,11908,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,3410,3419,3929,4236,3309,3671,4023,11661,3370,3305,3332,3328,3316,3317,3942,3529,11056,3403,4108,4647,10472,10642,3463,11988,4690,11235,11334,11570,11573,3576,3367,10545,10875,3368,3630,3286,3389,11651,4250,4110,11255,11386,11445,4708,11158,11399,11508,11534,11578,11584,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,3834,4524,4525,4645,3770,3986,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,4696,11763,11794,11831,11838,11874,3909,3678,4058,3499,3501,3475,4680,4642,3662,4697,4243,11531,3792,3512,12009,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,4212,4171,4119,11053,4166,3835,11842,12162,4200,3852,10608,10705,11258,11339,11418,11482,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,3474,3548,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,3533,10872,10902,10911,10914,10917,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,3493,10905,11061,11131,11926,12068,3952,4291,4686,3964,3998,4671,4674,3449,3453,4673,4672,3782,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,4076,11604,11946,3917,11174,11180,11198,12184,3766,11314,3919,10908,11277,11442,11476,3626,3733,10824,10827,10920,11087,4705,11891,4706,10664,4349,4254,3951,3895,4703,10494,10497,10866,10869,11760,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677,5679,5680,5681,5683,5685,5686,5687,5688,5689,5690,5699,5700,5710,5713,5724,5740,5741,5744,5754,5757,5758,5759,5786,5796,5811,5812,5821,5822,5824,5826,5831,5866,5871,5873,5932,5967,5968,5982,5988,5991,5992,5993,5994,6013,6017,6018,6027,6049,6078,6097,6101,6102,6104,6127,6131,6134,6135,6136,6152,6163,6164,6196,6197,6201,6222,6225,6228,6249,6250,6278,6281,6289,6298,6300,6309,6313,6321,6322,6323,6324,6355,6372,6424,6461,6463,6485,6486,6493,6497,6498,6502,6516,6532,6553,6554,6559,6568,6583,6603,6609,6611,6626,6627,6630,6631,6633,6635,6636,6637,6639,6641,6645,6651,6652,6654,6655,6661,6663,6705,6711,6726,6729,6730,6731,6765,6770,6772,6777,6778,6788,6792,6806,6829,6830,6832,6833,6844,6850,6869,6872,6892,6922,6923,6924,6930,6944,6963,6965,6967,6969,6974,6980,6982,6996,7001,7002,7037,7038,7039,7053,7054,7056,7057,7076,7078,7093,7120,7144,7155,7157,7159,7161,7162,7194,7195,7199,7200,7207,7208,7210,7212,7234,7243,7244,7255,7265,7305,7315,7319,7326,7337,7342,7344,7351,7359,7372,7389,7410,7412,7431])).
% 157.55/157.28 cnf(12345,plain,
% 157.55/157.28 (E(f326(f283(x123451,x123451),f262(x123451,x123452)),x123452)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12356,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x123561)),x123561))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(12357,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x123571),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(12362,plain,
% 157.55/157.28 (P105(f326(f61(x123621),f188(f917(x123621,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3548])).
% 157.55/157.28 cnf(12363,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x123631),x123632),f188(f917(x123631,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12370,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x123701,a905)),f326(f172(x123701),f176(x123701,x123702,x123703))),f326(f172(x123701),x123702)))),
% 157.55/157.28 inference(rename_variables,[],[4166])).
% 157.55/157.28 cnf(12373,plain,
% 157.55/157.28 (P24(x123731,x123731,f7(x123731),x123732)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(12380,plain,
% 157.55/157.28 (P105(f326(f326(f328(f917(x123801,a905)),x123802),f326(f307(x123801),x123802)))),
% 157.55/157.28 inference(rename_variables,[],[3835])).
% 157.55/157.28 cnf(12387,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x123871),x123871))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12390,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x123901),x123902),f188(f917(x123901,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12393,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x123931,a905)),x123932),f326(f326(f308(x123931),x123933),x123932)))),
% 157.55/157.28 inference(rename_variables,[],[3917])).
% 157.55/157.28 cnf(12394,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x123941,a905)),x123942),f241(f917(x123941,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(12401,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x124011),x124011))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12404,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x124041),x124041))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12407,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x124071),x124071))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12410,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x124101),x124101))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12413,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x124131),f326(a112,x124131)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(12416,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x124161),f326(a112,x124161)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(12419,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x124191,a905)),x124192),x124192))),
% 157.55/157.28 inference(rename_variables,[],[3766])).
% 157.55/157.28 cnf(12426,plain,
% 157.55/157.28 (P105(f326(f326(f328(f917(x124261,a905)),x124262),f326(f307(x124261),x124262)))),
% 157.55/157.28 inference(rename_variables,[],[3835])).
% 157.55/157.28 cnf(12435,plain,
% 157.55/157.28 (~E(f326(a112,x124351),x124351)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(12436,plain,
% 157.55/157.28 (E(f326(f309(x124361,x124361,f7(x124361)),x124362),x124362)),
% 157.55/157.28 inference(rename_variables,[],[3529])).
% 157.55/157.28 cnf(12439,plain,
% 157.55/157.28 (P31(x124391,x124392,f113(x124391),f113(x124391))),
% 157.55/157.28 inference(rename_variables,[],[3718])).
% 157.55/157.28 cnf(12442,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x124421,a905)),f326(f172(x124421),f176(x124421,x124422,x124423))),f326(f172(x124421),x124422)))),
% 157.55/157.28 inference(rename_variables,[],[4166])).
% 157.55/157.28 cnf(12443,plain,
% 157.55/157.28 (P105(f326(f61(x124431),f326(f172(x124431),x124432)))),
% 157.55/157.28 inference(rename_variables,[],[3512])).
% 157.55/157.28 cnf(12454,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x124541),x124541))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12457,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x124571),x124571))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12462,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f2(a909)),x124621))),
% 157.55/157.28 inference(rename_variables,[],[3493])).
% 157.55/157.28 cnf(12469,plain,
% 157.55/157.28 (P12(a909,f326(f168(a909),f326(f326(f154(f910(x124691),a909),f189(f910(x124691))),f179(x124691,x124692))))),
% 157.55/157.28 inference(rename_variables,[],[4033])).
% 157.55/157.28 cnf(12472,plain,
% 157.55/157.28 (P24(x124721,x124721,f7(x124721),x124722)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(12475,plain,
% 157.55/157.28 (P24(x124751,x124751,f7(x124751),x124752)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(12478,plain,
% 157.55/157.28 (P105(f326(f326(f328(f910(x124781)),f113(x124781)),f161(x124781,x124782)))),
% 157.55/157.28 inference(rename_variables,[],[3669])).
% 157.55/157.28 cnf(12481,plain,
% 157.55/157.28 (~P105(f326(f326(f188(f917(x124811,f917(x124812,a905))),x124813),x124814))),
% 157.55/157.28 inference(rename_variables,[],[4706])).
% 157.55/157.28 cnf(12486,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x124861),x124861))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12487,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f2(a909)),x124871))),
% 157.55/157.28 inference(rename_variables,[],[3493])).
% 157.55/157.28 cnf(12489,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),f2(a1)),f362(x124891,f188(f917(x124892,f917(x124893,a905))),f77(a1))))),
% 157.55/157.28 inference(scs_inference,[],[3709,11329,12373,12472,3718,4657,4658,4656,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,3677,3393,4638,10645,10745,11209,3085,3086,3088,3089,3092,3093,3095,3096,3097,3104,3108,3109,3110,3119,3120,3124,3130,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3255,3267,4626,4037,11908,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,3410,3419,3929,4236,3309,3671,4023,11661,3370,3305,3332,3328,3316,3317,3942,3352,3529,11056,11183,3403,4108,4647,10472,10642,3463,11988,4690,11235,11334,11570,11573,3576,3367,10545,10875,3368,3630,3286,3389,11651,4250,4110,11255,11386,11445,4708,11158,11399,11508,11534,11578,11584,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,3834,4524,4525,4645,3770,4292,3986,4033,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,4696,11763,11794,11831,11838,11874,3909,3678,4058,3499,3501,3475,4680,4642,3662,4697,4243,11531,3792,3512,12009,12012,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,4212,4171,4119,11053,4166,11261,12370,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,3474,3548,12362,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,3533,10872,10902,10911,10914,10917,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,3493,10905,11061,11131,11926,12068,12260,12462,3952,4291,4686,3964,3998,4671,4674,3449,3453,4673,4672,3782,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,4076,11604,11946,3917,11174,11180,11198,12184,12310,3766,11314,11436,3919,10908,11277,11442,11476,3626,3733,10824,10827,10920,11087,4705,11891,4706,10664,10777,12481,4349,4254,3951,3895,4703,10494,10497,10866,10869,11760,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677,5679,5680,5681,5683,5685,5686,5687,5688,5689,5690,5699,5700,5710,5713,5724,5740,5741,5744,5754,5757,5758,5759,5786,5796,5811,5812,5821,5822,5824,5826,5831,5866,5871,5873,5932,5967,5968,5982,5988,5991,5992,5993,5994,6013,6017,6018,6027,6049,6078,6097,6101,6102,6104,6127,6131,6134,6135,6136,6152,6163,6164,6196,6197,6201,6222,6225,6228,6249,6250,6278,6281,6289,6298,6300,6309,6313,6321,6322,6323,6324,6355,6372,6424,6461,6463,6485,6486,6493,6497,6498,6502,6516,6532,6553,6554,6559,6568,6583,6603,6609,6611,6626,6627,6630,6631,6633,6635,6636,6637,6639,6641,6645,6651,6652,6654,6655,6661,6663,6705,6711,6726,6729,6730,6731,6765,6770,6772,6777,6778,6788,6792,6806,6829,6830,6832,6833,6844,6850,6869,6872,6892,6922,6923,6924,6930,6944,6963,6965,6967,6969,6974,6980,6982,6996,7001,7002,7037,7038,7039,7053,7054,7056,7057,7076,7078,7093,7120,7144,7155,7157,7159,7161,7162,7194,7195,7199,7200,7207,7208,7210,7212,7234,7243,7244,7255,7265,7305,7315,7319,7326,7337,7342,7344,7351,7359,7372,7389,7410,7412,7431,7488,7489,7490,7492,7494,7498,7499,7504,7566,7595,7610,7615,7626,7657,7660,7682,7705,7723,7726,7727,7737,7757,7759,7761,7763,7764,7765,7790,7816,7817,7848,7850,7851,7852,7858,7879,7896,7901,7907,7909,7917,7929,7930,7932,7953,7959,7980,8046,8047,8048,8095,8101,8102,8125,8126])).
% 157.55/157.28 cnf(12490,plain,
% 157.55/157.28 (~P105(f326(f326(f188(f917(x124901,f917(x124902,a905))),x124903),x124904))),
% 157.55/157.28 inference(rename_variables,[],[4706])).
% 157.55/157.28 cnf(12493,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(f916(f910(x124931),f910(x124931)),a905)),f158(x124931,x124932)),f306(f910(x124931),f157(x124931,x124932))))),
% 157.55/157.28 inference(rename_variables,[],[4171])).
% 157.55/157.28 cnf(12499,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x124991,a905)),f326(f309(x124992,x124991,x124993),f326(f310(x124992,x124991,x124993),x124994))),x124994))),
% 157.55/157.28 inference(rename_variables,[],[4349])).
% 157.55/157.28 cnf(12502,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x125021,a905)),f326(f172(x125021),f176(x125021,x125022,x125023))),f326(f172(x125021),x125022)))),
% 157.55/157.28 inference(rename_variables,[],[4166])).
% 157.55/157.28 cnf(12503,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x125031,a905)),f326(f172(x125031),f326(f136(x125031,x125032),x125033))),f326(f172(x125031),x125033)))),
% 157.55/157.28 inference(rename_variables,[],[4119])).
% 157.55/157.28 cnf(12506,plain,
% 157.55/157.28 (~P105(f326(f326(f235(f917(x125061,a905)),x125062),f188(f917(x125061,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4700])).
% 157.55/157.28 cnf(12514,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x125141,a905)),f326(f309(x125142,x125141,x125143),f326(f310(x125142,x125141,x125143),x125144))),x125144))),
% 157.55/157.28 inference(rename_variables,[],[4349])).
% 157.55/157.28 cnf(12519,plain,
% 157.55/157.28 (P105(f326(f326(f328(f910(x125191)),f113(x125191)),f161(x125191,x125192)))),
% 157.55/157.28 inference(rename_variables,[],[3669])).
% 157.55/157.28 cnf(12522,plain,
% 157.55/157.28 (~P105(f326(f326(f328(f916(f910(x125221),f910(x125221))),f326(f326(f251(f910(x125221),f910(x125221)),x125222),f113(x125221))),f145(x125221,x125223)))),
% 157.55/157.28 inference(rename_variables,[],[4708])).
% 157.55/157.28 cnf(12525,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x125251),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(12527,plain,
% 157.55/157.28 (~P105(f326(f61(x125271),f241(f917(x125271,a905))))),
% 157.55/157.28 inference(scs_inference,[],[3709,11329,12373,12472,3718,3726,3443,4657,4658,3342,3345,4656,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,3677,3393,4638,10645,10745,11209,3085,3086,3088,3089,3092,3093,3095,3096,3097,3104,3108,3109,3110,3119,3120,3124,3130,3139,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3255,3267,4626,4037,11908,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,3410,3419,3929,4236,3309,3671,4023,11661,3370,3305,3332,3328,3316,3317,3942,3352,3529,11056,11183,3403,4108,4647,10472,10642,3463,11988,4690,11235,11334,11570,11573,3576,3367,10545,10875,3368,3630,3286,3389,11651,4250,4110,11255,11386,11445,4708,11158,11399,11508,11534,11578,11584,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,12478,12519,3834,4524,4525,4645,3770,4292,3986,4033,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,4696,11763,11794,11831,11838,11874,3909,3678,4058,3499,3501,3475,4680,4642,3662,4697,4243,11531,3792,3512,12009,12012,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,4212,4171,12152,12493,4119,11053,12330,4166,11261,12370,12442,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,3474,3548,12362,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,3533,10872,10902,10911,10914,10917,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,3493,10905,11061,11131,11926,12068,12260,12462,3952,4291,4686,3964,3998,4671,4674,3449,3453,4673,4672,3782,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,4076,11604,11946,3917,11174,11180,11198,12184,12310,3766,11314,11436,12419,3919,10908,11277,11442,11476,3626,3733,10824,10827,10920,11087,4705,11891,4706,10664,10777,12481,4349,11044,12499,4254,3951,3895,4703,10494,10497,10866,10869,11760,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,939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% 157.55/157.28 cnf(12528,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x125281,a905)),x125282),x125282))),
% 157.55/157.28 inference(rename_variables,[],[3766])).
% 157.55/157.28 cnf(12531,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x125311),x125312),f188(f917(x125311,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12534,plain,
% 157.55/157.28 (~P105(f326(f326(f188(f917(x125341,f917(x125342,a905))),x125343),x125344))),
% 157.55/157.28 inference(rename_variables,[],[4706])).
% 157.55/157.28 cnf(12537,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x125371,a905)),f326(f309(x125372,x125371,x125373),f326(f310(x125372,x125371,x125373),x125374))),x125374))),
% 157.55/157.28 inference(rename_variables,[],[4349])).
% 157.55/157.28 cnf(12538,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x125381,a905)),x125382),x125382))),
% 157.55/157.28 inference(rename_variables,[],[3766])).
% 157.55/157.28 cnf(12543,plain,
% 157.55/157.28 (E(f326(f283(x125431,x125431),f262(x125431,x125432)),x125432)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12546,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x125461,a905)),f326(f172(x125461),f176(x125461,x125462,x125463))),f326(f172(x125461),x125462)))),
% 157.55/157.28 inference(rename_variables,[],[4166])).
% 157.55/157.28 cnf(12547,plain,
% 157.55/157.28 (P105(f326(f61(x125471),f326(f172(x125471),x125472)))),
% 157.55/157.28 inference(rename_variables,[],[3512])).
% 157.55/157.28 cnf(12550,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x125501),x125501))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12553,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x125531),x125531))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12556,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x125561),x125561))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12567,plain,
% 157.55/157.28 (P24(x125671,x125671,f7(x125671),x125672)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(12575,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x125751),x125752),f188(f917(x125751,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12578,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(x125781,x125781)),f326(f326(f251(x125781,x125781),x125782),x125782)),f306(x125781,x125783)))),
% 157.55/157.28 inference(rename_variables,[],[4110])).
% 157.55/157.28 cnf(12581,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x125811),x125812),f188(f917(x125811,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12584,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(x125841,x125841)),f326(f326(f251(x125841,x125841),x125842),x125842)),f306(x125841,x125843)))),
% 157.55/157.28 inference(rename_variables,[],[4110])).
% 157.55/157.28 cnf(12594,plain,
% 157.55/157.28 (~E(f326(f326(f151(x125941),x125942),x125943),x125943)),
% 157.55/157.28 inference(rename_variables,[],[4647])).
% 157.55/157.28 cnf(12596,plain,
% 157.55/157.28 (~P25(a909,a909,x125961,f241(f917(a909,a905)),f302(a909,x125962,x125963))),
% 157.55/157.28 inference(scs_inference,[],[3709,11329,12373,12472,12475,3718,3726,3443,4657,4658,3342,3345,4656,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,3677,12135,3393,4638,10645,10745,11209,3085,3086,3088,3089,3092,3093,3095,3096,3097,3104,3108,3109,3110,3114,3119,3120,3124,3130,3139,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3255,3267,4626,4037,11908,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,3410,3419,3929,4236,3309,3671,4023,11661,3370,3305,3332,3787,3328,3316,3317,3942,3352,3529,11056,11183,3403,4108,4647,10472,10642,11514,3463,11988,4690,11235,11334,11570,11573,3576,4668,3367,10545,10875,3368,3630,3286,3389,11651,4250,4110,11255,11386,11445,12578,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,12478,12519,3834,3618,4524,4525,4645,11644,3770,4292,3986,4033,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,4696,11763,11794,11831,11838,11874,3909,3678,4058,3499,3501,3475,4680,4642,3662,4697,4243,11531,3792,3512,12009,12012,12443,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,4212,4171,12152,12493,4119,11053,12330,4166,11261,12370,12442,12502,12546,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,3474,3548,12362,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,3533,10872,10902,10911,10914,10917,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,3493,10905,11061,11131,11926,12068,12260,12462,3952,4291,4686,3964,3998,4671,4674,3449,3453,4673,4672,3782,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,3917,11174,11180,11198,12184,12310,3766,11314,11436,12419,12528,3919,10908,11277,11442,11476,3626,3733,10824,10827,10920,11087,4705,11891,4706,10664,10777,12481,12490,4349,11044,12499,12514,4254,3951,3895,4703,10494,10497,10866,10869,11760,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677,5679,5680,5681,5683,5685,5686,5687,5688,5689,5690,5699,5700,5710,5713,5724,5740,5741,5744,5754,5757,5758,5759,5786,5796,5811,5812,5821,5822,5824,5826,5831,5866,5871,5873,5932,5967,5968,5982,5988,5991,5992,5993,5994,6013,6017,6018,6027,6049,6078,6097,6101,6102,6104,6127,6131,6134,6135,6136,6152,6163,6164,6196,6197,6201,6222,6225,6228,6249,6250,6278,6281,6289,6298,6300,6309,6313,6321,6322,6323,6324,6355,6372,6424,6461,6463,6485,6486,6493,6497,6498,6502,6516,6532,6553,6554,6559,6568,6583,6603,6609,6611,6626,6627,6630,6631,6633,6635,6636,6637,6639,6641,6645,6651,6652,6654,6655,6661,6663,6705,6711,6726,6729,6730,6731,6765,6770,6772,6777,6778,6788,6792,6806,6829,6830,6832,6833,6844,6850,6869,6872,6892,6922,6923,6924,6930,6944,6963,6965,6967,6969,6974,6980,6982,6996,7001,7002,7037,7038,7039,7053,7054,7056,7057,7076,7078,7093,7120,7144,7155,7157,7159,7161,7162,7194,7195,7199,7200,7207,7208,7210,7212,7234,7243,7244,7255,7265,7305,7315,7319,7326,7337,7342,7344,7351,7359,7372,7389,7410,7412,7431,7488,7489,7490,7492,7494,7498,7499,7504,7566,7595,7610,7615,7626,7657,7660,7682,7705,7723,7726,7727,7737,7757,7759,7761,7763,7764,7765,7790,7816,7817,7848,7850,7851,7852,7858,7879,7896,7901,7907,7909,7917,7929,7930,7932,7953,7959,7980,8046,8047,8048,8095,8101,8102,8125,8126,8143,8144,8145,8202,8203,8232,8262,8271,8282,8295,8324,8328,8334,8346,8364,8369,8391,8436,8465,8479,8498,8501,8527,8552,8610,8611,8614,8615,8683,8717,8718,8719,8720,8747,8779,8808,8816])).
% 157.55/157.28 cnf(12601,plain,
% 157.55/157.28 (P105(f326(f326(f328(x126011),x126012),f241(f917(x126011,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3625])).
% 157.55/157.28 cnf(12602,plain,
% 157.55/157.28 (~E(f326(a112,x126021),x126021)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(12605,plain,
% 157.55/157.28 (P105(f326(f326(f328(f910(x126051)),f113(x126051)),f161(x126051,x126052)))),
% 157.55/157.28 inference(rename_variables,[],[3669])).
% 157.55/157.28 cnf(12606,plain,
% 157.55/157.28 (~E(f326(f326(f151(x126061),x126062),x126063),f113(x126061))),
% 157.55/157.28 inference(rename_variables,[],[4654])).
% 157.55/157.28 cnf(12609,plain,
% 157.55/157.28 (P24(x126091,x126091,f7(x126091),x126092)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(12612,plain,
% 157.55/157.28 (P105(f326(f326(f328(x126121),f326(x126122,x126123)),f326(f309(x126124,x126121,x126122),f241(f917(x126124,a905)))))),
% 157.55/157.28 inference(rename_variables,[],[4076])).
% 157.55/157.28 cnf(12613,plain,
% 157.55/157.28 (P24(x126131,x126131,f7(x126131),x126132)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(12616,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x126161,a905)),f188(f917(x126161,a905))),x126162))),
% 157.55/157.28 inference(rename_variables,[],[3919])).
% 157.55/157.28 cnf(12617,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x126171,a905)),x126172),x126172))),
% 157.55/157.28 inference(rename_variables,[],[3766])).
% 157.55/157.28 cnf(12620,plain,
% 157.55/157.28 (P105(f326(f326(f328(x126201),f326(x126202,x126203)),f326(f309(x126204,x126201,x126202),f241(f917(x126204,a905)))))),
% 157.55/157.28 inference(rename_variables,[],[4076])).
% 157.55/157.28 cnf(12621,plain,
% 157.55/157.28 (P24(x126211,x126211,f7(x126211),x126212)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(12624,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(f910(x126241),f910(x126241))),f326(f326(f251(f910(x126241),f910(x126241)),f113(x126241)),f113(x126241))),f158(x126241,x126242)))),
% 157.55/157.28 inference(rename_variables,[],[4250])).
% 157.55/157.28 cnf(12628,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x126281),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(12634,plain,
% 157.55/157.28 (E(f326(f326(f134(x126341),x126342),f113(x126341)),x126342)),
% 157.55/157.28 inference(rename_variables,[],[3404])).
% 157.55/157.28 cnf(12635,plain,
% 157.55/157.28 (~E(f326(f326(f151(x126351),x126352),x126353),x126353)),
% 157.55/157.28 inference(rename_variables,[],[4647])).
% 157.55/157.28 cnf(12638,plain,
% 157.55/157.28 (E(f326(f326(f134(x126381),x126382),f113(x126381)),x126382)),
% 157.55/157.28 inference(rename_variables,[],[3404])).
% 157.55/157.28 cnf(12639,plain,
% 157.55/157.28 (~E(f326(f326(f151(x126391),x126392),x126393),x126393)),
% 157.55/157.28 inference(rename_variables,[],[4647])).
% 157.55/157.28 cnf(12642,plain,
% 157.55/157.28 (E(f326(f326(f134(x126421),x126422),f113(x126421)),x126422)),
% 157.55/157.28 inference(rename_variables,[],[3404])).
% 157.55/157.28 cnf(12649,plain,
% 157.55/157.28 (P50(x126491,f262(x126491,x126492))),
% 157.55/157.28 inference(rename_variables,[],[3346])).
% 157.55/157.28 cnf(12652,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x126521,a905)),f326(f172(x126521),f326(f136(x126521,x126522),x126523))),f326(f172(x126521),x126523)))),
% 157.55/157.28 inference(rename_variables,[],[4119])).
% 157.55/157.28 cnf(12653,plain,
% 157.55/157.28 (E(f326(f309(x126531,x126531,f7(x126531)),x126532),x126532)),
% 157.55/157.28 inference(rename_variables,[],[3529])).
% 157.55/157.28 cnf(12658,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x126581,a905)),x126582),f241(f917(x126581,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(12662,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x126621),x126621))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12663,plain,
% 157.55/157.28 (~E(f326(a112,x126631),x126631)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(12666,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x126661,a905)),f188(f917(x126661,a905))),x126662))),
% 157.55/157.28 inference(rename_variables,[],[3919])).
% 157.55/157.28 cnf(12669,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x126691),x126691))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12672,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x126721,a905)),x126722),x126722))),
% 157.55/157.28 inference(rename_variables,[],[3766])).
% 157.55/157.28 cnf(12677,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x126771,a905)),x126772),f326(f326(f308(x126771),x126773),x126772)))),
% 157.55/157.28 inference(rename_variables,[],[3917])).
% 157.55/157.28 cnf(12680,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x126801,a905)),x126802),x126802))),
% 157.55/157.28 inference(rename_variables,[],[3766])).
% 157.55/157.28 cnf(12681,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x126811),x126812),f188(f917(x126811,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12684,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x126841),x126842),f188(f917(x126841,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12692,plain,
% 157.55/157.28 (~P105(f326(f326(f234(f917(f916(x126921,x126921),a905)),f326(f309(f916(x126921,x126921),f916(x126921,x126921),f7(f916(x126921,x126921))),f241(f917(f916(x126921,x126921),a905)))),f326(f309(f916(x126921,x126921),f916(x126921,x126921),f7(f916(x126921,x126921))),f188(f917(f916(x126921,x126921),a905)))))),
% 157.55/157.28 inference(scs_inference,[],[3709,11329,12373,12472,12475,12567,12609,12613,12621,3718,3726,3443,4657,4658,3342,3345,3346,4656,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,12435,12602,3528,3677,12135,3393,4638,10645,10745,11209,3085,3086,3088,3089,3092,3093,3095,3096,3097,3104,3108,3109,3110,3114,3119,3120,3124,3130,3139,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3255,3267,4626,4037,11908,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,3404,12634,12638,3410,3419,3929,4236,3309,3671,4023,11661,3370,3305,3332,3787,3328,3316,3317,3942,3352,3529,11056,11183,12436,12653,3403,4108,4647,10472,10642,11514,12594,12635,4654,12606,3463,11988,4690,11235,11334,11570,11573,3576,4668,3367,10545,10875,3368,3630,3286,3389,11651,4250,12624,4110,11255,11386,11445,12578,12584,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,12478,12519,12605,3834,3618,4524,4525,4645,11644,3770,4292,3986,4033,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,4696,11763,11794,11831,11838,11874,3909,3678,4058,3499,3501,3475,4680,4642,3860,3662,4697,4243,11531,3792,3512,12009,12012,12443,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,12075,4212,4171,12152,12493,4119,11053,12330,12503,4166,11261,12370,12442,12502,12546,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,12550,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,3474,3548,12362,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,12556,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,12581,12681,3533,10872,10902,10911,10914,10917,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,3493,10905,11061,11131,11926,12068,12260,12462,3952,4291,4686,3964,3998,4671,4674,3449,3453,4673,4672,3782,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,11950,12612,3917,11174,11180,11198,12184,12310,12393,3766,11314,11436,12419,12528,12538,12617,12672,3919,10908,11277,11442,11476,11487,12616,3626,3733,10824,10827,10920,11087,4705,11891,4706,10664,10777,12481,12490,4349,11044,12499,12514,4254,3951,3895,4703,10494,10497,10866,10869,11760,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677,5679,5680,5681,5683,5685,5686,5687,5688,5689,5690,5699,5700,5710,5713,5724,5740,5741,5744,5754,5757,5758,5759,5786,5796,5811,5812,5821,5822,5824,5826,5831,5866,5871,5873,5932,5967,5968,5982,5988,5991,5992,5993,5994,6013,6017,6018,6027,6049,6078,6097,6101,6102,6104,6127,6131,6134,6135,6136,6152,6163,6164,6196,6197,6201,6222,6225,6228,6249,6250,6278,6281,6289,6298,6300,6309,6313,6321,6322,6323,6324,6355,6372,6424,6461,6463,6485,6486,6493,6497,6498,6502,6516,6532,6553,6554,6559,6568,6583,6603,6609,6611,6626,6627,6630,6631,6633,6635,6636,6637,6639,6641,6645,6651,6652,6654,6655,6661,6663,6705,6711,6726,6729,6730,6731,6765,6770,6772,6777,6778,6788,6792,6806,6829,6830,6832,6833,6844,6850,6869,6872,6892,6922,6923,6924,6930,6944,6963,6965,6967,6969,6974,6980,6982,6996,7001,7002,7037,7038,7039,7053,7054,7056,7057,7076,7078,7093,7120,7144,7155,7157,7159,7161,7162,7194,7195,7199,7200,7207,7208,7210,7212,7234,7243,7244,7255,7265,7305,7315,7319,7326,7337,7342,7344,7351,7359,7372,7389,7410,7412,7431,7488,7489,7490,7492,7494,7498,7499,7504,7566,7595,7610,7615,7626,7657,7660,7682,7705,7723,7726,7727,7737,7757,7759,7761,7763,7764,7765,7790,7816,7817,7848,7850,7851,7852,7858,7879,7896,7901,7907,7909,7917,7929,7930,7932,7953,7959,7980,8046,8047,8048,8095,8101,8102,8125,8126,8143,8144,8145,8202,8203,8232,8262,8271,8282,8295,8324,8328,8334,8346,8364,8369,8391,8436,8465,8479,8498,8501,8527,8552,8610,8611,8614,8615,8683,8717,8718,8719,8720,8747,8779,8808,8816,8817,8858,8879,8924,8940,8986,8989,9004,9011,9053,9092,9093,9111,9112,9126,9243,9248,9252,9272,9283,9306,9308,9311,9317,9319,9320,9330,9331,9350,9356])).
% 157.55/157.28 cnf(12693,plain,
% 157.55/157.28 (P24(x126931,x126931,f7(x126931),x126932)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(12696,plain,
% 157.55/157.28 (E(f326(f189(f910(x126961)),f169(x126961,x126962,x126963)),x126962)),
% 157.55/157.28 inference(rename_variables,[],[3539])).
% 157.55/157.28 cnf(12699,plain,
% 157.55/157.28 (P25(x126991,x126991,f31(x126991),x126992,x126992)),
% 157.55/157.28 inference(rename_variables,[],[4134])).
% 157.55/157.28 cnf(12702,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x127021),x127021))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12703,plain,
% 157.55/157.28 (P105(f326(f241(f917(x127031,a905)),x127032))),
% 157.55/157.28 inference(rename_variables,[],[3533])).
% 157.55/157.28 cnf(12706,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x127061),x127062),f188(f917(x127061,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12709,plain,
% 157.55/157.28 (P105(f326(f326(f328(x127091),f326(x127092,x127093)),f326(f309(x127094,x127091,x127092),f241(f917(x127094,a905)))))),
% 157.55/157.28 inference(rename_variables,[],[4076])).
% 157.55/157.28 cnf(12710,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(x127101,x127101)),f326(f326(f251(x127101,x127101),x127102),x127102)),f306(x127101,x127103)))),
% 157.55/157.28 inference(rename_variables,[],[4110])).
% 157.55/157.28 cnf(12713,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(x127131,x127131)),f326(f326(f251(x127131,x127131),x127132),x127132)),f306(x127131,x127133)))),
% 157.55/157.28 inference(rename_variables,[],[4110])).
% 157.55/157.28 cnf(12716,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x127161),x127161))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(12717,plain,
% 157.55/157.28 (P105(f326(f241(f917(x127171,a905)),x127172))),
% 157.55/157.28 inference(rename_variables,[],[3533])).
% 157.55/157.28 cnf(12720,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x127201,a905)),x127202),f241(f917(x127201,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(12721,plain,
% 157.55/157.28 (P25(x127211,x127211,f31(x127211),x127212,x127212)),
% 157.55/157.28 inference(rename_variables,[],[4134])).
% 157.55/157.28 cnf(12724,plain,
% 157.55/157.28 (P105(f326(f61(x127241),f326(f172(x127241),x127242)))),
% 157.55/157.28 inference(rename_variables,[],[3512])).
% 157.55/157.28 cnf(12731,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(x127311,x127311)),f326(f326(f251(x127311,x127311),x127312),x127312)),f326(f326(f288(x127311,x127311,x127311),f306(x127311,x127313)),f306(x127311,f306(x127311,x127313)))))),
% 157.55/157.28 inference(scs_inference,[],[4134,12699,3709,11329,12373,12472,12475,12567,12609,12613,12621,3718,3726,3443,4657,4658,3342,3345,3346,4656,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,12435,12602,3528,3677,12135,3393,4638,10645,10745,11209,3085,3086,3088,3089,3092,3093,3095,3096,3097,3104,3108,3109,3110,3114,3119,3120,3124,3130,3139,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3255,3267,4626,4037,11908,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,3404,12634,12638,12642,3410,3419,3929,4236,3539,3309,3671,4023,11661,3370,3305,3332,3787,3328,3316,3317,3942,3352,3529,11056,11183,12436,12653,3403,4108,4647,10472,10642,11514,12594,12635,4654,12606,3463,11988,4690,11235,11334,11570,11573,3576,4668,3367,10545,10875,3368,3630,3286,3389,11651,4250,12624,4110,11255,11386,11445,12578,12584,12710,12713,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,12478,12519,12605,3834,3618,4524,4525,4645,11644,3770,4292,3986,4033,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,4696,11763,11794,11831,11838,11874,3909,3678,4058,3499,3501,3475,4680,4642,3860,3662,4697,4243,11531,3792,3512,12009,12012,12443,12547,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,12075,4212,4171,12152,12493,4119,11053,12330,12503,4166,11261,12370,12442,12502,12546,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,12658,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,12550,12669,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,3474,3548,12362,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,12556,12662,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,12581,12681,12684,3533,10872,10902,10911,10914,10917,11500,12703,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,3493,10905,11061,11131,11926,12068,12260,12462,3952,4291,4686,3964,3998,4671,4674,3449,3453,4673,4672,3782,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,11950,12612,12620,3917,11174,11180,11198,12184,12310,12393,3766,11314,11436,12419,12528,12538,12617,12672,3919,10908,11277,11442,11476,11487,12616,3626,3733,10824,10827,10920,11087,4705,11891,4706,10664,10777,12481,12490,4349,11044,12499,12514,4254,3951,3895,4703,10494,10497,10866,10869,11760,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677,5679,5680,5681,5683,5685,5686,5687,5688,5689,5690,5699,5700,5710,5713,5724,5740,5741,5744,5754,5757,5758,5759,5786,5796,5811,5812,5821,5822,5824,5826,5831,5866,5871,5873,5932,5967,5968,5982,5988,5991,5992,5993,5994,6013,6017,6018,6027,6049,6078,6097,6101,6102,6104,6127,6131,6134,6135,6136,6152,6163,6164,6196,6197,6201,6222,6225,6228,6249,6250,6278,6281,6289,6298,6300,6309,6313,6321,6322,6323,6324,6355,6372,6424,6461,6463,6485,6486,6493,6497,6498,6502,6516,6532,6553,6554,6559,6568,6583,6603,6609,6611,6626,6627,6630,6631,6633,6635,6636,6637,6639,6641,6645,6651,6652,6654,6655,6661,6663,6705,6711,6726,6729,6730,6731,6765,6770,6772,6777,6778,6788,6792,6806,6829,6830,6832,6833,6844,6850,6869,6872,6892,6922,6923,6924,6930,6944,6963,6965,6967,6969,6974,6980,6982,6996,7001,7002,7037,7038,7039,7053,7054,7056,7057,7076,7078,7093,7120,7144,7155,7157,7159,7161,7162,7194,7195,7199,7200,7207,7208,7210,7212,7234,7243,7244,7255,7265,7305,7315,7319,7326,7337,7342,7344,7351,7359,7372,7389,7410,7412,7431,7488,7489,7490,7492,7494,7498,7499,7504,7566,7595,7610,7615,7626,7657,7660,7682,7705,7723,7726,7727,7737,7757,7759,7761,7763,7764,7765,7790,7816,7817,7848,7850,7851,7852,7858,7879,7896,7901,7907,7909,7917,7929,7930,7932,7953,7959,7980,8046,8047,8048,8095,8101,8102,8125,8126,8143,8144,8145,8202,8203,8232,8262,8271,8282,8295,8324,8328,8334,8346,8364,8369,8391,8436,8465,8479,8498,8501,8527,8552,8610,8611,8614,8615,8683,8717,8718,8719,8720,8747,8779,8808,8816,8817,8858,8879,8924,8940,8986,8989,9004,9011,9053,9092,9093,9111,9112,9126,9243,9248,9252,9272,9283,9306,9308,9311,9317,9319,9320,9330,9331,9350,9356,9366,9373,9415,9433,9488,9489,9495,9534,9557,9562,9601,9611])).
% 157.55/157.28 cnf(12734,plain,
% 157.55/157.28 (~P105(f326(f326(f188(f917(x127341,f917(x127342,a905))),x127343),x127344))),
% 157.55/157.28 inference(rename_variables,[],[4706])).
% 157.55/157.28 cnf(12737,plain,
% 157.55/157.28 (~P105(f326(f326(f188(f917(x127371,f917(x127372,a905))),x127373),x127374))),
% 157.55/157.28 inference(rename_variables,[],[4706])).
% 157.55/157.28 cnf(12740,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x127401,a905)),x127402),f241(f917(x127401,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(12743,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(x127431,x127431)),f326(f326(f251(x127431,x127431),x127432),x127432)),f306(x127431,x127433)))),
% 157.55/157.28 inference(rename_variables,[],[4110])).
% 157.55/157.28 cnf(12746,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),f326(f326(f79(a909),x127461),x127462)),x127462))),
% 157.55/157.28 inference(rename_variables,[],[4703])).
% 157.55/157.28 cnf(12747,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x127471),f326(a112,x127471)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(12750,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x127501,a905)),x127502),f241(f917(x127501,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(12753,plain,
% 157.55/157.28 (E(f326(f283(x127531,x127531),f262(x127531,x127532)),x127532)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12764,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x127641),x127642),f188(f917(x127641,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12765,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(f910(x127651),f910(x127651))),f326(f326(f251(f910(x127651),f910(x127651)),f113(x127651)),f113(x127651))),f158(x127651,x127652)))),
% 157.55/157.28 inference(rename_variables,[],[4250])).
% 157.55/157.28 cnf(12767,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(a909,a909)),f326(f326(f251(a909,a909),f2(a909)),f326(a112,f2(a909)))),f326(f326(f288(a909,a909,a909),f306(a909,a316)),f306(a909,f306(a909,a316)))))),
% 157.55/157.28 inference(scs_inference,[],[4134,12699,3709,11329,12373,12472,12475,12567,12609,12613,12621,3718,3726,3443,4657,4658,3342,3345,3346,4656,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,12435,12602,3528,3677,12135,3393,4638,10645,10745,11209,3085,3086,3088,3089,3092,3093,3095,3096,3097,3104,3108,3109,3110,3114,3119,3120,3124,3130,3139,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3255,3267,4626,3807,4037,11908,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,12543,3404,12634,12638,12642,3410,3419,3929,4236,3539,3309,3671,4023,11661,3370,3305,3332,3787,3328,3316,3317,3942,3352,3529,11056,11183,12436,12653,3403,4108,4647,10472,10642,11514,12594,12635,4654,12606,3463,11988,4690,11235,11334,11570,11573,3576,4668,3367,10545,10875,3368,3630,3286,3389,11651,4250,12624,4110,11255,11386,11445,12578,12584,12710,12713,12743,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,12478,12519,12605,3834,3618,4524,4525,4645,11644,3770,4292,3986,4033,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,4696,11763,11794,11831,11838,11874,3909,3678,4058,3499,3501,3475,4680,4642,3860,3662,4697,4243,11531,3792,3512,12009,12012,12443,12547,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,12075,4212,4171,12152,12493,4119,11053,12330,12503,4166,11261,12370,12442,12502,12546,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,12658,12720,12740,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,12550,12669,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,3474,3548,12362,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,12556,12662,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,12581,12681,12684,12706,3533,10872,10902,10911,10914,10917,11500,12703,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,3493,10905,11061,11131,11926,12068,12260,12462,3952,4291,4686,3964,3998,4671,4674,3449,3453,4673,4672,3782,4388,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,11950,12612,12620,3917,11174,11180,11198,12184,12310,12393,3766,11314,11436,12419,12528,12538,12617,12672,4248,3919,10908,11277,11442,11476,11487,12616,3626,3733,10824,10827,10920,11087,4705,11891,4706,10664,10777,12481,12490,12534,12734,4349,11044,12499,12514,4254,3951,3895,4703,10494,10497,10866,10869,11760,11951,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677,5679,5680,5681,5683,5685,5686,5687,5688,5689,5690,5699,5700,5710,5713,5724,5740,5741,5744,5754,5757,5758,5759,5786,5796,5811,5812,5821,5822,5824,5826,5831,5866,5871,5873,5932,5967,5968,5982,5988,5991,5992,5993,5994,6013,6017,6018,6027,6049,6078,6097,6101,6102,6104,6127,6131,6134,6135,6136,6152,6163,6164,6196,6197,6201,6222,6225,6228,6249,6250,6278,6281,6289,6298,6300,6309,6313,6321,6322,6323,6324,6355,6372,6424,6461,6463,6485,6486,6493,6497,6498,6502,6516,6532,6553,6554,6559,6568,6583,6603,6609,6611,6626,6627,6630,6631,6633,6635,6636,6637,6639,6641,6645,6651,6652,6654,6655,6661,6663,6705,6711,6726,6729,6730,6731,6765,6770,6772,6777,6778,6788,6792,6806,6829,6830,6832,6833,6844,6850,6869,6872,6892,6922,6923,6924,6930,6944,6963,6965,6967,6969,6974,6980,6982,6996,7001,7002,7037,7038,7039,7053,7054,7056,7057,7076,7078,7093,7120,7144,7155,7157,7159,7161,7162,7194,7195,7199,7200,7207,7208,7210,7212,7234,7243,7244,7255,7265,7305,7315,7319,7326,7337,7342,7344,7351,7359,7372,7389,7410,7412,7431,7488,7489,7490,7492,7494,7498,7499,7504,7566,7595,7610,7615,7626,7657,7660,7682,7705,7723,7726,7727,7737,7757,7759,7761,7763,7764,7765,7790,7816,7817,7848,7850,7851,7852,7858,7879,7896,7901,7907,7909,7917,7929,7930,7932,7953,7959,7980,8046,8047,8048,8095,8101,8102,8125,8126,8143,8144,8145,8202,8203,8232,8262,8271,8282,8295,8324,8328,8334,8346,8364,8369,8391,8436,8465,8479,8498,8501,8527,8552,8610,8611,8614,8615,8683,8717,8718,8719,8720,8747,8779,8808,8816,8817,8858,8879,8924,8940,8986,8989,9004,9011,9053,9092,9093,9111,9112,9126,9243,9248,9252,9272,9283,9306,9308,9311,9317,9319,9320,9330,9331,9350,9356,9366,9373,9415,9433,9488,9489,9495,9534,9557,9562,9601,9611,9614,9615,9617,9618,9630,9653,9668,9677,9678,9680,9682,9711])).
% 157.55/157.28 cnf(12772,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x127721),x127722),f188(f917(x127721,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12777,plain,
% 157.55/157.28 (P30(x127771,x127772,f113(x127771))),
% 157.55/157.28 inference(rename_variables,[],[3409])).
% 157.55/157.28 cnf(12780,plain,
% 157.55/157.28 (E(f326(f189(f910(x127801)),f169(x127801,x127802,x127803)),x127802)),
% 157.55/157.28 inference(rename_variables,[],[3539])).
% 157.55/157.28 cnf(12783,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x127831),x127832),f188(f917(x127831,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12789,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x127891),x127891))),
% 157.55/157.28 inference(rename_variables,[],[4679])).
% 157.55/157.28 cnf(12791,plain,
% 157.55/157.28 (P105(f326(f326(f328(f916(f910(x127911),f910(x127911))),f326(f326(f251(f910(x127911),f910(x127911)),f169(x127911,f326(f189(f910(x127911)),x127912),x127913)),x127912)),f158(x127911,f241(f917(f916(x127911,x127911),a905)))))),
% 157.55/157.28 inference(scs_inference,[],[4134,12699,3709,11329,12373,12472,12475,12567,12609,12613,12621,3718,3726,3443,3409,4657,4658,3342,3345,3346,4656,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,12435,12602,3528,3677,12135,3393,4638,10645,10745,11209,3085,3086,3088,3089,3092,3093,3095,3096,3097,3104,3108,3109,3110,3114,3119,3120,3124,3130,3139,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3255,3267,4626,3807,4037,11908,3319,11615,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,12543,3404,12634,12638,12642,3410,3419,3929,4236,3539,12696,12780,3309,3671,4023,11661,3370,3305,3332,3787,3328,4300,3316,3317,3942,3352,3529,11056,11183,12436,12653,3403,4108,4647,10472,10642,11514,12594,12635,4654,12606,3463,11988,4690,11235,11334,11570,11573,3576,4668,3367,10545,10875,3368,3630,3286,3389,11651,4250,12624,12765,4110,11255,11386,11445,12578,12584,12710,12713,12743,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,12478,12519,12605,3834,3618,4524,4525,4645,11644,3770,4292,3986,4033,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,4696,11763,11794,11831,11838,11874,3909,3678,4058,3499,3501,3475,4680,4642,3860,3662,4697,4243,11531,3792,3512,12009,12012,12443,12547,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,12075,4212,4171,12152,12493,4119,11053,12330,12503,4166,11261,12370,12442,12502,12546,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,12658,12720,12740,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,12550,12669,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,3474,3548,12362,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,12556,12662,12702,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,12601,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,12581,12681,12684,12706,12764,12772,3533,10872,10902,10911,10914,10917,11500,12703,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,3493,10905,11061,11131,11926,12068,12260,12462,3952,4291,4686,3964,3998,4671,4674,3449,3453,4673,4672,3782,4388,11746,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,11950,12612,12620,3917,11174,11180,11198,12184,12310,12393,3766,11314,11436,12419,12528,12538,12617,12672,4248,3919,10908,11277,11442,11476,11487,12616,3626,3733,10824,10827,10920,11087,4705,11891,4706,10664,10777,12481,12490,12534,12734,4349,11044,12499,12514,4254,3951,3895,4703,10494,10497,10866,10869,11760,11951,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,79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% 157.55/157.28 cnf(12792,plain,
% 157.55/157.28 (P105(f326(f326(f328(x127921),x127922),f241(f917(x127921,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3625])).
% 157.55/157.28 cnf(12796,plain,
% 157.55/157.28 (~P105(f326(f326(f188(f917(x127961,f917(x127962,a905))),x127963),x127964))),
% 157.55/157.28 inference(rename_variables,[],[4706])).
% 157.55/157.28 cnf(12799,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x127991,a905)),x127992),x127992))),
% 157.55/157.28 inference(rename_variables,[],[3766])).
% 157.55/157.28 cnf(12802,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x128021),x128022),f188(f917(x128021,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(12805,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),f2(a1)),f326(f326(f243(a1),f326(f75(a1),x128051)),x128052)))),
% 157.55/157.28 inference(rename_variables,[],[3951])).
% 157.55/157.28 cnf(12810,plain,
% 157.55/157.28 (~E(f326(a112,x128101),x128101)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(12812,plain,
% 157.55/157.28 (E(f326(f283(x128121,x128121),f262(x128121,x128122)),x128122)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12816,plain,
% 157.55/157.28 (E(f188(f917(f916(x128161,x128161),a905)),f262(x128161,f188(f917(x128161,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3543])).
% 157.55/157.28 cnf(12818,plain,
% 157.55/157.28 (E(f188(f917(f916(x128181,x128181),a905)),f262(x128181,f188(f917(x128181,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3543])).
% 157.55/157.28 cnf(12820,plain,
% 157.55/157.28 (E(f326(f283(x128201,x128201),f262(x128201,x128202)),x128202)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12822,plain,
% 157.55/157.28 (E(f326(f283(x128221,x128221),f262(x128221,x128222)),x128222)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12824,plain,
% 157.55/157.28 (P24(x128241,x128241,f7(x128241),x128242)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(12826,plain,
% 157.55/157.28 (P24(x128261,x128261,f7(x128261),x128262)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(12833,plain,
% 157.55/157.28 (P36(x128331,f153(x128331,x128332))),
% 157.55/157.28 inference(rename_variables,[],[3342])).
% 157.55/157.28 cnf(12839,plain,
% 157.55/157.28 (E(f326(f283(x128391,x128391),f262(x128391,x128392)),x128392)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12841,plain,
% 157.55/157.28 (E(f326(f283(x128411,x128411),f262(x128411,x128412)),x128412)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12843,plain,
% 157.55/157.28 (E(f326(f283(x128431,x128431),f262(x128431,x128432)),x128432)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12849,plain,
% 157.55/157.28 (P37(x128491,f262(x128491,x128492))),
% 157.55/157.28 inference(rename_variables,[],[3343])).
% 157.55/157.28 cnf(12857,plain,
% 157.55/157.28 (E(f326(f283(x128571,x128571),f262(x128571,x128572)),x128572)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12859,plain,
% 157.55/157.28 (E(f326(f283(x128591,x128591),f262(x128591,x128592)),x128592)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12868,plain,
% 157.55/157.28 (P25(x128681,x128681,f31(x128681),x128682,x128682)),
% 157.55/157.28 inference(rename_variables,[],[4134])).
% 157.55/157.28 cnf(12870,plain,
% 157.55/157.28 (P25(x128701,x128701,f31(x128701),x128702,x128702)),
% 157.55/157.28 inference(rename_variables,[],[4134])).
% 157.55/157.28 cnf(12872,plain,
% 157.55/157.28 (P25(x128721,x128721,f31(x128721),x128722,x128722)),
% 157.55/157.28 inference(rename_variables,[],[4134])).
% 157.55/157.28 cnf(12876,plain,
% 157.55/157.28 (P51(x128761,x128762,f262(x128761,x128762))),
% 157.55/157.28 inference(rename_variables,[],[3442])).
% 157.55/157.28 cnf(12878,plain,
% 157.55/157.28 (P51(x128781,x128782,f262(x128781,x128782))),
% 157.55/157.28 inference(rename_variables,[],[3442])).
% 157.55/157.28 cnf(12880,plain,
% 157.55/157.28 (P51(x128801,x128802,f262(x128801,x128802))),
% 157.55/157.28 inference(rename_variables,[],[3442])).
% 157.55/157.28 cnf(12882,plain,
% 157.55/157.28 (P31(x128821,x128822,f113(x128821),f113(x128821))),
% 157.55/157.28 inference(rename_variables,[],[3718])).
% 157.55/157.28 cnf(12884,plain,
% 157.55/157.28 (P31(x128841,x128842,f113(x128841),f113(x128841))),
% 157.55/157.28 inference(rename_variables,[],[3718])).
% 157.55/157.28 cnf(12895,plain,
% 157.55/157.28 (E(f326(f283(x128951,x128951),f262(x128951,x128952)),x128952)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12897,plain,
% 157.55/157.28 (P53(x128971,x128971,f262(x128971,x128972))),
% 157.55/157.28 inference(rename_variables,[],[3443])).
% 157.55/157.28 cnf(12912,plain,
% 157.55/157.28 (E(f188(f917(f916(x129121,x129121),a905)),f262(x129121,f188(f917(x129121,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3543])).
% 157.55/157.28 cnf(12914,plain,
% 157.55/157.28 (P23(x129141,x129142,f188(f917(f908(x129141),a905)))),
% 157.55/157.28 inference(rename_variables,[],[3527])).
% 157.55/157.28 cnf(12920,plain,
% 157.55/157.28 (P54(x129201,f188(f917(x129201,a905)),x129202)),
% 157.55/157.28 inference(rename_variables,[],[3491])).
% 157.55/157.28 cnf(12924,plain,
% 157.55/157.28 (P50(x129241,f262(x129241,x129242))),
% 157.55/157.28 inference(rename_variables,[],[3346])).
% 157.55/157.28 cnf(12929,plain,
% 157.55/157.28 (E(f326(f283(x129291,x129291),f262(x129291,x129292)),x129292)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(12932,plain,
% 157.55/157.28 (P41(x129321,x129322,x129323,x129324,f188(f917(x129321,a905)),x129324)),
% 157.55/157.28 inference(rename_variables,[],[4410])).
% 157.55/157.28 cnf(12941,plain,
% 157.55/157.28 (P13(x129411,f917(x129411,a905),f308(x129411))),
% 157.55/157.28 inference(rename_variables,[],[3446])).
% 157.55/157.28 cnf(12957,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x129571),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(12966,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a1),f326(f100(a1),x129661)),f326(f78(a1),f326(f100(a1),x129662))))),
% 157.55/157.28 inference(rename_variables,[],[4701])).
% 157.55/157.28 cnf(12976,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x129761),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(12979,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x129791),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(12982,plain,
% 157.55/157.28 (P105(f326(f61(a909),f304(a909,x129821,x129822)))),
% 157.55/157.28 inference(rename_variables,[],[3680])).
% 157.55/157.28 cnf(12985,plain,
% 157.55/157.28 (P105(f326(f61(a909),f304(a909,x129851,x129852)))),
% 157.55/157.28 inference(rename_variables,[],[3680])).
% 157.55/157.28 cnf(12988,plain,
% 157.55/157.28 (P105(f326(f61(a909),f304(a909,x129881,x129882)))),
% 157.55/157.28 inference(rename_variables,[],[3680])).
% 157.55/157.28 cnf(12991,plain,
% 157.55/157.28 (P105(f326(f61(a909),f304(a909,x129911,x129912)))),
% 157.55/157.28 inference(rename_variables,[],[3680])).
% 157.55/157.28 cnf(12998,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),f326(f78(a1),f326(f100(a1),x129981))),f326(f100(a1),x129982)))),
% 157.55/157.28 inference(rename_variables,[],[3952])).
% 157.55/157.28 cnf(13000,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),f2(a1)),f326(f103(a1),f2(a1))))),
% 157.55/157.28 inference(scs_inference,[],[4713,4134,12699,12721,12868,12870,3709,11329,12373,12472,12475,12567,12609,12613,12621,12693,12824,3718,12439,12882,12884,3726,3442,12876,12878,12880,3443,12897,3409,12777,4657,4658,11968,4410,12932,3446,12941,3285,3342,12833,3343,12849,3344,3345,3346,12649,12924,4656,3768,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,12435,12602,12663,3528,3491,12920,3677,12135,3393,4638,10645,10745,11209,3085,3086,3088,3089,3092,3093,3095,3096,3097,3104,3108,3109,3110,3113,3114,3119,3120,3124,3130,3139,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3245,3255,4625,3267,3341,4626,3807,4037,11908,3319,11615,3454,3430,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,12543,12753,12812,12820,12822,12839,12841,12843,12857,12859,12895,3404,12634,12638,12642,3410,3419,3929,4236,3539,12696,12780,3309,3671,4023,11661,3527,12914,3370,3305,3332,3787,3328,3435,4143,4031,3850,4300,3316,3317,3295,3942,3352,3529,11056,11183,12436,12653,3403,4108,4647,10472,10642,11514,12594,12635,12639,4654,12606,3463,11988,4066,4690,11235,11334,11570,11573,3869,3576,3793,4668,3543,12816,12818,12912,3367,10545,10875,3368,3630,3360,3286,3389,11651,4250,12624,12765,4110,11255,11386,11445,12578,12584,12710,12713,12743,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,12478,12519,12605,3834,3618,4524,4525,3690,4645,11644,3811,3770,4292,3986,4033,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,12628,12957,12976,4696,11763,11794,11831,11838,11874,3909,3678,3680,12982,12985,12988,4058,3499,3501,3475,4680,4642,3860,4172,3662,4697,4243,11531,3792,3512,12009,12012,12443,12547,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,12075,4212,4171,12152,12493,4119,11053,12330,12503,4166,11261,12370,12442,12502,12546,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,12658,12720,12740,12750,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,12550,12669,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,3474,3548,12362,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,12556,12662,12702,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,12601,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,12581,12681,12684,12706,12764,12772,12783,3533,10872,10902,10911,10914,10917,11500,12703,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,3493,10905,11061,11131,11926,12068,12260,12462,3952,12015,4291,4686,3964,3998,4671,4674,4675,3449,3453,4673,4672,3782,4388,11746,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,11950,12612,12620,3917,11174,11180,11198,12184,12310,12393,3766,11314,11436,12419,12528,12538,12617,12672,12680,4248,3919,10908,11277,11442,11476,11487,12616,3626,3733,10824,10827,10920,11087,3735,4705,11891,4701,12966,4706,10664,10777,12481,12490,12534,12734,12737,4349,11044,12499,12514,4254,3951,3895,3896,4703,10494,10497,10866,10869,11760,11951,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,655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% 157.55/157.28 cnf(13003,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x130031),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(13004,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x130041),x130041))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13011,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x130111),f326(a112,x130111)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(13013,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),f2(a1)),a82))),
% 157.55/157.28 inference(scs_inference,[],[4713,4134,12699,12721,12868,12870,3709,11329,12373,12472,12475,12567,12609,12613,12621,12693,12824,3718,12439,12882,12884,3726,3442,12876,12878,12880,3443,12897,3409,12777,4657,4658,11968,4410,12932,3446,12941,3285,3342,12833,3343,12849,3344,3345,3346,12649,12924,4656,3768,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,12435,12602,12663,3528,3491,12920,3677,12135,3393,4638,10645,10745,11209,3085,3086,3088,3089,3092,3093,3095,3096,3097,3104,3108,3109,3110,3113,3114,3119,3120,3124,3130,3139,3145,3150,3151,3152,3159,3160,3169,3179,3214,3219,3223,3224,3226,3234,3235,3245,3255,4625,3267,3341,4626,3807,4037,11908,3319,11615,3454,3430,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,12543,12753,12812,12820,12822,12839,12841,12843,12857,12859,12895,3404,12634,12638,12642,3410,3419,3929,4236,3539,12696,12780,3309,3671,4023,11661,3527,12914,3370,3305,3332,3787,3328,3435,4143,4031,3850,4300,3316,3317,3295,3942,3352,3529,11056,11183,12436,12653,3403,4108,4647,10472,10642,11514,12594,12635,12639,4654,12606,3463,11988,4066,4690,11235,11334,11570,11573,3869,3576,3793,4668,3543,12816,12818,12912,3367,10545,10875,3368,3630,3360,3286,3389,11651,4250,12624,12765,4110,11255,11386,11445,12578,12584,12710,12713,12743,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,12478,12519,12605,3834,3618,4524,4525,3690,4645,11644,3811,3770,3813,4292,3986,4033,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,12747,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,12628,12957,12976,12979,4696,11763,11794,11831,11838,11874,3909,3678,3680,12982,12985,12988,4058,3499,3501,3475,4680,3366,4642,3860,4172,3662,4697,4243,11531,3792,3512,12009,12012,12443,12547,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,12075,4212,4171,12152,12493,4119,11053,12330,12503,4166,11261,12370,12442,12502,12546,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,12658,12720,12740,12750,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,12550,12669,12716,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,3474,3548,12362,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,12556,12662,12702,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,12601,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,12581,12681,12684,12706,12764,12772,12783,3533,10872,10902,10911,10914,10917,11500,12703,3572,3565,3990,3927,10524,11897,11925,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,3493,10905,11061,11131,11926,12068,12260,12462,3952,12015,4291,3684,4686,3964,3998,4671,4674,4675,3449,3453,4673,4672,3782,4388,11746,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,11950,12612,12620,3917,11174,11180,11198,12184,12310,12393,3766,11314,11436,12419,12528,12538,12617,12672,12680,4248,3919,10908,11277,11442,11476,11487,12616,3626,3733,10824,10827,10920,11087,3735,4705,11891,4701,12966,4706,10664,10777,12481,12490,12534,12734,12737,4349,11044,12499,12514,4254,3951,3895,3896,4703,10494,10497,10866,10869,11760,11951,4704,11871,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677,5679,5680,5681,5683,5685,5686,5687,5688,5689,5690,5699,5700,5710,5713,5724,5740,5741,5744,5754,5757,5758,5759,5786,5796,5811,5812,5821,5822,5824,5826,5831,5866,5871,5873,5932,5967,5968,5982,5988,5991,5992,5993,5994,6013,6017,6018,6027,6049,6078,6097,6101,6102,6104,6127,6131,6134,6135,6136,6152,6163,6164,6196,6197,6201,6222,6225,6228,6249,6250,6278,6281,6289,6298,6300,6309,6313,6321,6322,6323,6324,6355,6372,6424,6461,6463,6485,6486,6493,6497,6498,6502,6516,6532,6553,6554,6559,6568,6583,6603,6609,6611,6626,6627,6630,6631,6633,6635,6636,6637,6639,6641,6645,6651,6652,6654,6655,6661,6663,6705,6711,6726,6729,6730,6731,6765,6770,6772,6777,6778,6788,6792,6806,6829,6830,6832,6833,6844,6850,6869,6872,6892,6922,6923,6924,6930,6944,6963,6965,6967,6969,6974,6980,6982,6996,7001,7002,7037,7038,7039,7053,7054,7056,7057,7076,7078,7093,7120,7144,7155,7157,7159,7161,7162,7194,7195,7199,7200,7207,7208,7210,7212,7234,7243,7244,7255,7265,7305,7315,7319,7326,7337,7342,7344,7351,7359,7372,7389,7410,7412,7431,7488,7489,7490,7492,7494,7498,7499,7504,7566,7595,7610,7615,7626,7657,7660,7682,7705,7723,7726,7727,7737,7757,7759,7761,7763,7764,7765,7790,7816,7817,7848,7850,7851,7852,7858,7879,7896,7901,7907,7909,7917,7929,7930,7932,7953,7959,7980,8046,8047,8048,8095,8101,8102,8125,8126,8143,8144,8145,8202,8203,8232,8262,8271,8282,8295,8324,8328,8334,8346,8364,8369,8391,8436,8465,8479,8498,8501,8527,8552,8610,8611,8614,8615,8683,8717,8718,8719,8720,8747,8779,8808,8816,8817,8858,8879,8924,8940,8986,8989,9004,9011,9053,9092,9093,9111,9112,9126,9243,9248,9252,9272,9283,9306,9308,9311,9317,9319,9320,9330,9331,9350,9356,9366,9373,9415,9433,9488,9489,9495,9534,9557,9562,9601,9611,9614,9615,9617,9618,9630,9653,9668,9677,9678,9680,9682,9711,9812,9832,9833,9882,9883,9922,9957,10068,10136,10205,10287,10305,10310,10330,3,2817,2818,2819,2821,2822,2826,2827,2837,2838,2839,2840,2847,2848,2853,2859,2861,2867,2869,2870,2871,2872,2873,2879,2880,2881,2882,2883,2885,2886,2888,2889,2892,2893,2894,2897,2898,2899,2900,2901,2902,2903,2904,2914,2916,2917,2918,2919,2920,2922,2923,2927,2928,2929,2930,2934,2939,2941,2946,2947,2966,2968,2969,2970,2973,2974,2975,2985,2986,2988,2989,2990,3000,3005,3008,3009,3010,3015,3023,3025,3044,3045,5435,5476,5625,5626,5627,5711,5810,5840,5874,5890,5892,5898,5960,5961,5962,5963,5980,6015,6147,6185,6195,6219,6253,6290])).
% 157.55/157.28 cnf(13018,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x130181),x130181))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(13021,plain,
% 157.55/157.28 (P105(f326(f61(a909),f304(a909,x130211,x130212)))),
% 157.55/157.28 inference(rename_variables,[],[3680])).
% 157.55/157.28 cnf(13024,plain,
% 157.55/157.28 (P105(f326(f61(a909),f304(a909,x130241,x130242)))),
% 157.55/157.28 inference(rename_variables,[],[3680])).
% 157.55/157.28 cnf(13027,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x130271),x130271))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13028,plain,
% 157.55/157.28 (~E(f326(a112,x130281),f2(a909))),
% 157.55/157.28 inference(rename_variables,[],[4638])).
% 157.55/157.28 cnf(13045,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f45(a909,x130451,x130452)),x130451))),
% 157.55/157.28 inference(rename_variables,[],[3927])).
% 157.55/157.28 cnf(13050,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x130501),f326(a112,x130501)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(13053,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x130531),f326(a112,x130531)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(13054,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x130541),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(13063,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a1),f326(f100(a1),x130631)),f2(a1)))),
% 157.55/157.28 inference(rename_variables,[],[4696])).
% 157.55/157.28 cnf(13064,plain,
% 157.55/157.28 (P105(f326(f241(f917(x130641,a905)),x130642))),
% 157.55/157.28 inference(rename_variables,[],[3533])).
% 157.55/157.28 cnf(13067,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a1),f326(f100(a1),x130671)),f2(a1)))),
% 157.55/157.28 inference(rename_variables,[],[4696])).
% 157.55/157.28 cnf(13068,plain,
% 157.55/157.28 (P105(f326(f241(f917(x130681,a905)),x130682))),
% 157.55/157.28 inference(rename_variables,[],[3533])).
% 157.55/157.28 cnf(13071,plain,
% 157.55/157.28 (P105(f326(f241(f917(x130711,a905)),x130712))),
% 157.55/157.28 inference(rename_variables,[],[3533])).
% 157.55/157.28 cnf(13082,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x130821),x130822),f188(f917(x130821,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(13083,plain,
% 157.55/157.28 (P105(f326(f61(x130831),f188(f917(x130831,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3548])).
% 157.55/157.28 cnf(13092,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f2(a909)),x130921))),
% 157.55/157.28 inference(rename_variables,[],[3493])).
% 157.55/157.28 cnf(13095,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x130951),x130952),f188(f917(x130951,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(13098,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x130981),x130982),f188(f917(x130981,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(13103,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x131031),x131031))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13111,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x131111),f326(a112,x131111)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(13114,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x131141),x131141))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13119,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x131191),x131191))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13122,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x131221),x131221))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13125,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x131251),x131251))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13128,plain,
% 157.55/157.28 (E(f326(f326(f3(f917(x131281,a905)),f188(f917(x131281,a905))),x131282),f188(f917(x131281,a905)))),
% 157.55/157.28 inference(rename_variables,[],[3738])).
% 157.55/157.28 cnf(13129,plain,
% 157.55/157.28 (P105(f326(f61(x131291),f188(f917(x131291,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3548])).
% 157.55/157.28 cnf(13132,plain,
% 157.55/157.28 (E(f326(f326(f3(f917(x131321,a905)),f188(f917(x131321,a905))),x131322),f188(f917(x131321,a905)))),
% 157.55/157.28 inference(rename_variables,[],[3738])).
% 157.55/157.28 cnf(13133,plain,
% 157.55/157.28 (P105(f326(f61(x131331),f188(f917(x131331,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3548])).
% 157.55/157.28 cnf(13136,plain,
% 157.55/157.28 (E(f326(f326(f3(f917(x131361,a905)),f188(f917(x131361,a905))),x131362),f188(f917(x131361,a905)))),
% 157.55/157.28 inference(rename_variables,[],[3738])).
% 157.55/157.28 cnf(13137,plain,
% 157.55/157.28 (P105(f326(f61(x131371),f188(f917(x131371,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3548])).
% 157.55/157.28 cnf(13140,plain,
% 157.55/157.28 (E(f326(f326(f3(f917(x131401,a905)),f188(f917(x131401,a905))),x131402),f188(f917(x131401,a905)))),
% 157.55/157.28 inference(rename_variables,[],[3738])).
% 157.55/157.28 cnf(13141,plain,
% 157.55/157.28 (P105(f326(f61(x131411),f188(f917(x131411,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3548])).
% 157.55/157.28 cnf(13145,plain,
% 157.55/157.28 (E(f326(f283(x131451,x131451),f262(x131451,x131452)),x131452)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(13150,plain,
% 157.55/157.28 (E(f326(f326(f3(f917(x131501,a905)),f188(f917(x131501,a905))),x131502),f188(f917(x131501,a905)))),
% 157.55/157.28 inference(rename_variables,[],[3738])).
% 157.55/157.28 cnf(13151,plain,
% 157.55/157.28 (P105(f326(f61(x131511),f188(f917(x131511,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3548])).
% 157.55/157.28 cnf(13155,plain,
% 157.55/157.28 (P105(f326(f61(x131551),f188(f917(x131551,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3548])).
% 157.55/157.28 cnf(13158,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x131581),x131581))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13162,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x131621),x131621))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(13171,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x131711),x131711))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13182,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x131821),x131821))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(13193,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x131931),x131932),f188(f917(x131931,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(13204,plain,
% 157.55/157.28 (P105(f326(f326(f328(x132041),x132042),f241(f917(x132041,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3625])).
% 157.55/157.28 cnf(13205,plain,
% 157.55/157.28 (E(f326(f192(x132051,x132052),x132053),f121(x132051,x132052))),
% 157.55/157.28 inference(rename_variables,[],[3387])).
% 157.55/157.28 cnf(13208,plain,
% 157.55/157.28 (P105(f326(f326(f328(x132081),f326(x132082,x132083)),f326(f309(x132084,x132081,x132082),f241(f917(x132084,a905)))))),
% 157.55/157.28 inference(rename_variables,[],[4076])).
% 157.55/157.28 cnf(13212,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x132121,a905)),x132122),f241(f917(x132121,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(13215,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x132151,a905)),x132152),x132152))),
% 157.55/157.28 inference(rename_variables,[],[3766])).
% 157.55/157.28 cnf(13221,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x132211),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(13222,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x132221),x132221))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(13226,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x132261),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(13227,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x132271),x132271))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(13232,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x132321),x132321))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13233,plain,
% 157.55/157.28 (P105(f326(f61(a909),f302(a909,x132331,x132332)))),
% 157.55/157.28 inference(rename_variables,[],[3678])).
% 157.55/157.28 cnf(13240,plain,
% 157.55/157.28 (E(f326(f326(f18(x132401,x132402),x132403),x132404),x132403)),
% 157.55/157.28 inference(rename_variables,[],[3463])).
% 157.55/157.28 cnf(13243,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x132431,a905)),f326(f172(x132431),f176(x132431,x132432,x132433))),f326(f172(x132431),x132432)))),
% 157.55/157.28 inference(rename_variables,[],[4166])).
% 157.55/157.28 cnf(13247,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x132471),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(13248,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x132481),x132481))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(13252,plain,
% 157.55/157.28 (~P105(f326(f326(f235(a909),x132521),f2(a909)))),
% 157.55/157.28 inference(rename_variables,[],[4683])).
% 157.55/157.28 cnf(13253,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x132531),x132531))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(13257,plain,
% 157.55/157.28 (~P105(f326(f326(f234(f917(a909,a905)),f302(a909,f326(a112,x132571),f326(a112,x132571))),f302(a909,x132572,x132571)))),
% 157.55/157.28 inference(scs_inference,[],[4713,4134,12699,12721,12868,12870,3709,11329,12373,12472,12475,12567,12609,12613,12621,12693,12824,3718,12439,12882,12884,3726,3442,12876,12878,12880,3443,12897,3409,12777,4657,4658,11968,4410,12932,3446,12941,3285,3342,12833,3343,12849,3344,3345,3346,12649,12924,4656,3768,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,12435,12602,12663,3528,3491,12920,3677,12135,3393,4638,10645,10745,11209,11309,3085,3086,3088,3089,3092,3093,3095,3096,3097,3103,3104,3108,3109,3110,3113,3114,3115,3119,3120,3124,3127,3130,3139,3145,3150,3151,3152,3159,3160,3169,3179,3190,3194,3202,3205,3214,3216,3219,3223,3224,3226,3227,3234,3235,3245,3255,4625,3267,3341,4626,3807,4037,11908,3319,11615,3454,3430,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,12543,12753,12812,12820,12822,12839,12841,12843,12857,12859,12895,12929,3404,12634,12638,12642,3410,3419,3929,4236,3387,13205,3539,12696,12780,3309,3671,4023,11661,3527,12914,3370,3305,3332,3787,3328,3435,4143,4031,3850,4300,3316,3317,3295,3942,3352,3529,11056,11183,12436,12653,3403,4108,4647,10472,10642,11514,12594,12635,12639,4654,12606,3463,11988,11991,4066,4690,11235,11334,11570,11573,3869,3576,3793,4668,3543,12816,12818,12912,3367,10545,10875,3368,3630,3360,3286,3389,11651,4250,12624,12765,4110,11255,11386,11445,12578,12584,12710,12713,12743,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,4711,11463,4712,3388,3669,12478,12519,12605,3834,3618,4524,4525,3690,4645,11644,3811,3770,3813,4292,3986,3738,13128,13132,13136,13140,13150,4033,12469,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,12747,13011,13050,13053,13111,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,12628,12957,12976,12979,13003,13054,13221,13226,13247,4696,11763,11794,11831,11838,11874,13063,13067,3909,3678,13233,3680,12982,12985,12988,12991,13021,4058,3499,3501,3475,4680,3366,4642,3860,4172,3662,4697,4243,11531,3792,3512,12009,12012,12443,12547,12724,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,12075,4212,4171,12152,12493,4119,11053,12330,12503,4166,11261,12370,12442,12502,12546,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,12658,12720,12740,12750,4700,11004,11410,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,12550,12669,12716,13004,13027,13103,13114,13119,13122,13125,13158,13171,13232,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,12255,13018,13162,13182,13222,13227,13248,3474,3548,12362,13083,13129,13133,13137,13141,13151,13155,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,12556,12662,12702,12789,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,12601,12792,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,12581,12681,12684,12706,12764,12772,12783,12802,13082,13095,13098,3533,10872,10902,10911,10914,10917,11500,12703,12717,13064,13068,13071,3572,3565,3990,3927,10524,11897,11925,13045,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,3493,10905,11061,11131,11926,12068,12260,12462,12487,3952,12015,12998,4291,3684,4686,3964,3998,4671,4674,4675,3449,3453,4673,4672,3782,4388,11746,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,11950,12612,12620,12709,3917,11174,11180,11198,12184,12310,12393,3766,11314,11436,12419,12528,12538,12617,12672,12680,12799,4248,3919,10908,11277,11442,11476,11487,12616,3626,3733,10824,10827,10920,11087,3735,4705,11891,4701,12966,4706,10664,10777,12481,12490,12534,12734,12737,4349,11044,12499,12514,4254,3951,12805,3895,3896,4703,10494,10497,10866,10869,11760,11951,12746,4704,11871,11956,3920,10830,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,590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8005,8043,8044,8121,8161,8215,8237,8238,8310,8404,8475,8476,8480,8513,8574,8575,8642,8659])).
% 157.55/157.28 cnf(13258,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x132581),x132581))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13261,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x132611),x132611))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13264,plain,
% 157.55/157.28 (~P105(f326(f326(f234(a909),f326(a112,x132641)),x132641))),
% 157.55/157.28 inference(rename_variables,[],[4689])).
% 157.55/157.28 cnf(13270,plain,
% 157.55/157.28 (P105(f326(f326(f328(x132701),f326(x132702,x132703)),f326(f309(x132704,x132701,x132702),f241(f917(x132704,a905)))))),
% 157.55/157.28 inference(rename_variables,[],[4076])).
% 157.55/157.28 cnf(13271,plain,
% 157.55/157.28 (P24(x132711,x132711,f7(x132711),x132712)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(13276,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x132761,a905)),x132762),f241(f917(x132761,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(13277,plain,
% 157.55/157.28 (P24(x132771,x132771,f7(x132771),x132772)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(13281,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x132811,a905)),x132812),f241(f917(x132811,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(13282,plain,
% 157.55/157.28 (P24(x132821,x132821,f7(x132821),x132822)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(13286,plain,
% 157.55/157.28 (P24(x132861,x132861,f7(x132861),x132862)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(13289,plain,
% 157.55/157.28 (~P105(f326(f326(f235(f917(x132891,a905)),x132892),f188(f917(x132891,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4700])).
% 157.55/157.28 cnf(13292,plain,
% 157.55/157.28 (P24(x132921,x132921,f7(x132921),x132922)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(13295,plain,
% 157.55/157.28 (P24(x132951,x132951,f7(x132951),x132952)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(13301,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x133011,a905)),x133012),f241(f917(x133011,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(13306,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x133061,a905)),f188(f917(x133061,a905))),x133062))),
% 157.55/157.28 inference(rename_variables,[],[3919])).
% 157.55/157.28 cnf(13310,plain,
% 157.55/157.28 (E(f326(f283(x133101,x133101),f262(x133101,x133102)),x133102)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(13314,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x133141),x133142),f188(f917(x133141,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(13319,plain,
% 157.55/157.28 (P24(x133191,x133191,f7(x133191),x133192)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(13322,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x133221,a905)),x133222),f241(f917(x133221,a905))))),
% 157.55/157.28 inference(rename_variables,[],[3852])).
% 157.55/157.28 cnf(13330,plain,
% 157.55/157.28 (E(f326(f326(f18(x133301,x133302),x133303),x133304),x133303)),
% 157.55/157.28 inference(rename_variables,[],[3463])).
% 157.55/157.28 cnf(13333,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x133331),x133332),f188(f917(x133331,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(13336,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x133361),x133362),f188(f917(x133361,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(13340,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),x133401),x133401))),
% 157.55/157.28 inference(rename_variables,[],[3472])).
% 157.55/157.28 cnf(13343,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x133431),f326(a112,x133431)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(13344,plain,
% 157.55/157.28 (~E(f326(a112,x133441),x133441)),
% 157.55/157.28 inference(rename_variables,[],[4628])).
% 157.55/157.28 cnf(13347,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x133471),f326(a112,f326(f326(f79(a909),x133472),x133471))))),
% 157.55/157.28 inference(rename_variables,[],[3920])).
% 157.55/157.28 cnf(13348,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),x133481),f326(a112,x133481)))),
% 157.55/157.28 inference(rename_variables,[],[3540])).
% 157.55/157.28 cnf(13350,plain,
% 157.55/157.28 (~E(f326(f326(f80(a909),f326(a112,f2(a909))),f119(x133501)),f326(f326(f80(a909),f326(a112,f2(a909))),f126(x133501,x133502,x133503)))),
% 157.55/157.28 inference(scs_inference,[],[4713,4134,12699,12721,12868,12870,12872,3709,11329,12373,12472,12475,12567,12609,12613,12621,12693,12824,12826,13271,13277,13282,13286,13292,13295,3718,12439,12882,12884,3726,3442,12876,12878,12880,3443,12897,3409,12777,4657,4658,11968,4410,12932,3446,12941,3285,3342,12833,3343,12849,3344,3345,3346,12649,12924,4656,3768,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,12435,12602,12663,12810,13344,3528,3491,12920,3677,12135,3393,4638,10645,10745,11209,11309,3085,3086,3088,3089,3092,3093,3095,3096,3097,3103,3104,3108,3109,3110,3113,3114,3115,3119,3120,3124,3127,3130,3139,3145,3150,3151,3152,3159,3160,3169,3179,3190,3194,3202,3205,3214,3216,3219,3223,3224,3226,3227,3234,3235,3245,3255,4625,3267,3341,4626,3807,4037,11908,3319,11615,3454,3430,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,12543,12753,12812,12820,12822,12839,12841,12843,12857,12859,12895,12929,13145,3404,12634,12638,12642,3410,3419,3929,4236,3387,13205,3539,12696,12780,3308,3309,3671,4023,11661,3527,12914,3370,3305,3332,3787,3328,3435,4143,4031,3850,4300,3316,3317,3295,3942,3352,3529,11056,11183,12436,12653,3403,4108,4647,10472,10642,11514,12594,12635,12639,4654,12606,3463,11988,11991,13240,4066,4690,11235,11334,11570,11573,3869,3460,3576,3793,4668,3543,12816,12818,12912,3367,10545,10875,3368,4677,3630,3360,3286,3389,11651,4250,12624,12765,4110,11255,11386,11445,12578,12584,12710,12713,12743,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,11456,4711,11463,4712,3388,3669,12478,12519,12605,3834,3618,4524,4525,3690,4645,11644,3811,3770,3813,4292,3986,3738,13128,13132,13136,13140,13150,4033,12469,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,12747,13011,13050,13053,13111,13343,3922,11894,3456,3552,11720,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,12628,12957,12976,12979,13003,13054,13221,13226,13247,4696,11763,11794,11831,11838,11874,13063,13067,3909,3678,13233,3680,12982,12985,12988,12991,13021,4058,3499,3501,3475,4680,3366,4642,3860,4172,3662,4697,4243,11531,3792,3512,12009,12012,12443,12547,12724,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,12075,4212,4171,12152,12493,4119,11053,12330,12503,4166,11261,12370,12442,12502,12546,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,12658,12720,12740,12750,13212,13276,13281,13301,4700,11004,11410,12506,13289,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,12550,12669,12716,13004,13027,13103,13114,13119,13122,13125,13158,13171,13232,13258,13261,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,12255,13018,13162,13182,13222,13227,13248,3474,3548,12362,13083,13129,13133,13137,13141,13151,13155,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,12556,12662,12702,12789,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,12601,12792,13204,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,12581,12681,12684,12706,12764,12772,12783,12802,13082,13095,13098,13193,13314,13333,3533,10872,10902,10911,10914,10917,11500,12703,12717,13064,13068,13071,3572,3565,3990,3927,10524,11897,11925,13045,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,13264,3493,10905,11061,11131,11926,12068,12260,12462,12487,3952,12015,12998,4291,3684,4686,3964,3998,4671,4674,4675,3449,3453,4673,4672,3782,11890,4388,11746,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,11950,12612,12620,12709,13208,13270,3917,11174,11180,11198,12184,12310,12393,12677,3766,11314,11436,12419,12528,12538,12617,12672,12680,12799,4248,3919,10908,11277,11442,11476,11487,12616,12666,3626,3733,10824,10827,10920,11087,3735,4705,11891,4701,12966,4706,10664,10777,12481,12490,12534,12734,12737,12796,4349,11044,12499,12514,12537,4254,3951,12805,3895,3896,4703,10494,10497,10866,10869,11760,11951,12746,4704,11871,11956,3920,10830,11093,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,556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6842,6981,6995,7066,7067,7073,7094,7126,7128,7132,7177,7197,7198,7216,7217,7254,7299,7300,7396,7467,7468,7469,7470,7487,7520,7571,7572,7581,7586,7587,7598,7629,7630,7631,7632,7772,7774,7775,7776,7782,7783,7856,7988,7994,7995,8005,8043,8044,8121,8161,8215,8237,8238,8310,8404,8475,8476,8480,8513,8574,8575,8642,8659,8660,8661,8662,8812,9070,9071,9140,9154,9207,9208,9327,9359,9385,9417,9458,9651,9774,9917,10105,10161,10163,10322,6588,6589,6678])).
% 157.55/157.28 cnf(13357,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),f2(a1)),f326(f100(a1),x133571)))),
% 157.55/157.28 inference(rename_variables,[],[3572])).
% 157.55/157.28 cnf(13360,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f2(a909)),x133601))),
% 157.55/157.28 inference(rename_variables,[],[3493])).
% 157.55/157.28 cnf(13364,plain,
% 157.55/157.28 (~E(f326(a112,x133641),f2(a909))),
% 157.55/157.28 inference(rename_variables,[],[4638])).
% 157.55/157.28 cnf(13367,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),x133671),x133671))),
% 157.55/157.28 inference(rename_variables,[],[3473])).
% 157.55/157.28 cnf(13373,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x133731),x133732),f188(f917(x133731,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(13376,plain,
% 157.55/157.28 (P105(f326(f61(a909),f304(a909,x133761,x133762)))),
% 157.55/157.28 inference(rename_variables,[],[3680])).
% 157.55/157.28 cnf(13377,plain,
% 157.55/157.28 (E(f326(f326(f232(a909),f326(a112,x133771)),f326(a112,x133772)),f326(a112,f326(f326(f232(a909),x133771),x133772)))),
% 157.55/157.28 inference(rename_variables,[],[3643])).
% 157.55/157.28 cnf(13380,plain,
% 157.55/157.28 (P105(f326(f61(a909),f304(a909,x133801,x133802)))),
% 157.55/157.28 inference(rename_variables,[],[3680])).
% 157.55/157.28 cnf(13381,plain,
% 157.55/157.28 (E(f326(f326(f233(a909),f326(a112,x133811)),f326(a112,x133812)),f326(a112,f326(f326(f233(a909),x133811),x133812)))),
% 157.55/157.28 inference(rename_variables,[],[3644])).
% 157.55/157.28 cnf(13384,plain,
% 157.55/157.28 (P105(f326(f61(a909),f304(a909,x133841,x133842)))),
% 157.55/157.28 inference(rename_variables,[],[3680])).
% 157.55/157.28 cnf(13393,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x133931),x133932),f188(f917(x133931,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(13394,plain,
% 157.55/157.28 (E(f326(f326(f18(x133941,x133942),x133943),x133944),x133943)),
% 157.55/157.28 inference(rename_variables,[],[3463])).
% 157.55/157.28 cnf(13397,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x133971,a905)),f326(f172(x133971),f326(f136(x133971,x133972),x133973))),f326(f172(x133971),x133973)))),
% 157.55/157.28 inference(rename_variables,[],[4119])).
% 157.55/157.28 cnf(13398,plain,
% 157.55/157.28 (E(f326(f326(f18(x133981,x133982),x133983),x133984),x133983)),
% 157.55/157.28 inference(rename_variables,[],[3463])).
% 157.55/157.28 cnf(13401,plain,
% 157.55/157.28 (P105(f326(f326(f234(f917(x134011,a905)),f326(f172(x134011),f326(f326(f175(x134011),x134012),x134013))),f326(f172(x134011),x134013)))),
% 157.55/157.28 inference(rename_variables,[],[4161])).
% 157.55/157.28 cnf(13402,plain,
% 157.55/157.28 (E(f326(f326(f18(x134021,x134022),x134023),x134024),x134023)),
% 157.55/157.28 inference(rename_variables,[],[3463])).
% 157.55/157.28 cnf(13406,plain,
% 157.55/157.28 (E(f326(f326(f18(x134061,x134062),x134063),x134064),x134063)),
% 157.55/157.28 inference(rename_variables,[],[3463])).
% 157.55/157.28 cnf(13419,plain,
% 157.55/157.28 (P105(f326(f326(f234(a1),f2(a1)),f326(f100(a1),x134191)))),
% 157.55/157.28 inference(rename_variables,[],[3572])).
% 157.55/157.28 cnf(13424,plain,
% 157.55/157.28 (P24(x134241,x134241,f7(x134241),x134242)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(13427,plain,
% 157.55/157.28 (~P105(f326(f326(f328(x134271),x134272),f188(f917(x134271,a905))))),
% 157.55/157.28 inference(rename_variables,[],[4692])).
% 157.55/157.28 cnf(13428,plain,
% 157.55/157.28 (E(f326(f283(x134281,x134281),f262(x134281,x134282)),x134282)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(13429,plain,
% 157.55/157.28 (P24(x134291,x134291,f7(x134291),x134292)),
% 157.55/157.28 inference(rename_variables,[],[3709])).
% 157.55/157.28 cnf(13433,plain,
% 157.55/157.28 (E(f326(f283(x134331,x134331),f262(x134331,x134332)),x134332)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(13447,plain,
% 157.55/157.28 (P105(f326(f326(f234(a909),f2(a909)),x134471))),
% 157.55/157.28 inference(rename_variables,[],[3493])).
% 157.55/157.28 cnf(13448,plain,
% 157.55/157.28 (P105(f326(f326(f235(a909),f2(a909)),f326(a112,x134481)))),
% 157.55/157.28 inference(rename_variables,[],[3552])).
% 157.55/157.28 cnf(13449,plain,
% 157.55/157.28 (E(f326(f283(x134491,x134491),f262(x134491,x134492)),x134492)),
% 157.55/157.28 inference(rename_variables,[],[3433])).
% 157.55/157.28 cnf(13528,plain,
% 157.55/157.28 (P105(f326(f326(f235(a1),f2(a1)),f326(f75(a1),f77(a1))))),
% 157.55/157.28 inference(scs_inference,[],[4713,4134,12699,12721,12868,12870,12872,3709,11329,12373,12472,12475,12567,12609,12613,12621,12693,12824,12826,13271,13277,13282,13286,13292,13295,13319,13424,13429,3718,12439,12882,12884,3726,3442,12876,12878,12880,3443,12897,3409,12777,4657,4658,11968,4410,12932,3446,12941,3285,3342,12833,3343,12849,3344,3345,3346,12649,12924,4656,3768,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,12435,12602,12663,12810,13344,3528,3491,12920,3677,12135,3393,4638,10645,10745,11209,11309,13028,13364,3085,3086,3088,3089,3092,3093,3095,3096,3097,3103,3104,3108,3109,3110,3113,3114,3115,3119,3120,3124,3125,3127,3130,3139,3143,3145,3147,3150,3151,3152,3159,3160,3169,3179,3184,3190,3191,3194,3202,3205,3214,3216,3219,3223,3224,3226,3227,3234,3235,3245,3255,4625,3267,3341,4626,3807,4037,11908,3319,11615,3454,3430,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,12543,12753,12812,12820,12822,12839,12841,12843,12857,12859,12895,12929,13145,13310,13428,13433,13449,3404,12634,12638,12642,3410,3419,3929,4236,3387,13205,3539,12696,12780,3308,3309,3671,4023,11661,3527,12914,3370,3305,3332,3787,3328,3435,4143,4031,3850,4300,3316,3317,3295,3942,3352,3529,11056,11183,12436,12653,3403,4108,4647,10472,10642,11514,12594,12635,12639,4654,12606,3463,11988,11991,13240,13330,13394,13398,13402,13406,4066,4690,11235,11334,11570,11573,3869,3460,3576,3793,3568,4668,3543,12816,12818,12912,3367,10545,10875,3368,4677,3630,3360,3286,3389,11651,4250,12624,12765,4110,11255,11386,11445,12578,12584,12710,12713,12743,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,11456,4711,11463,4712,3388,3669,12478,12519,12605,3834,3618,4524,4525,3653,3690,4645,11644,3811,3770,3813,4292,3986,3738,13128,13132,13136,13140,13150,4033,12469,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,12747,13011,13050,13053,13111,13343,13348,3922,11894,3456,3552,11720,12003,13448,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,12628,12957,12976,12979,13003,13054,13221,13226,13247,13252,4696,11763,11794,11831,11838,11874,13063,13067,3909,3678,13233,3680,12982,12985,12988,12991,13021,13024,13376,13380,13384,3681,4058,3643,13377,3644,13381,3499,3501,3475,4680,3366,4642,3860,4172,3662,4697,4243,11531,3792,3512,12009,12012,12443,12547,12724,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,12075,4212,4171,12152,12493,4119,11053,12330,12503,12652,13397,4161,13401,4166,11261,12370,12442,12502,12546,13243,4167,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,12658,12720,12740,12750,13212,13276,13281,13301,13322,4700,11004,11410,12506,13289,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,12550,12669,12716,13004,13027,13103,13114,13119,13122,13125,13158,13171,13232,13258,13261,13340,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,12255,13018,13162,13182,13222,13227,13248,13253,13367,3474,3548,12362,13083,13129,13133,13137,13141,13151,13155,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,12556,12662,12702,12789,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,12601,12792,13204,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,12581,12681,12684,12706,12764,12772,12783,12802,13082,13095,13098,13193,13314,13333,13336,13373,13393,13427,3533,10872,10902,10911,10914,10917,11500,12703,12717,13064,13068,13071,3572,13357,13419,3565,3990,3927,10524,11897,11925,13045,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,13264,3493,10905,11061,11131,11926,12068,12260,12462,12487,13092,13360,13447,3952,12015,12998,4291,3684,4686,3964,3998,4671,4674,4675,3449,3453,4673,4672,4461,3782,11890,4388,11746,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,11950,12612,12620,12709,13208,13270,3917,11174,11180,11198,12184,12310,12393,12677,3766,11314,11436,12419,12528,12538,12617,12672,12680,12799,13215,4248,3919,10908,11277,11442,11476,11487,12616,12666,13306,3626,3733,10824,10827,10920,11087,3735,4705,11891,4701,12966,4706,10664,10777,12481,12490,12534,12734,12737,12796,4349,11044,12499,12514,12537,4254,3951,12805,3895,3896,4703,10494,10497,10866,10869,11760,11951,12746,4704,11871,11956,3920,10830,11093,13347,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045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969,2970,2973,2974,2975,2985,2986,2988,2989,2990,3000,3005,3008,3009,3010,3015,3023,3025,3044,3045,5435,5476,5625,5626,5627,5711,5810,5840,5874,5890,5892,5898,5960,5961,5962,5963,5980,6015,6147,6185,6195,6219,6253,6290,6440,6445,6483,6484,6507,6509,6511,6518,6519,6520,6521,6522,6523,6524,6525,6604,6675,6676,6764,6801,6802,6841,6842,6981,6995,7066,7067,7073,7094,7126,7128,7132,7177,7197,7198,7216,7217,7254,7299,7300,7396,7467,7468,7469,7470,7487,7520,7571,7572,7581,7586,7587,7598,7629,7630,7631,7632,7772,7774,7775,7776,7782,7783,7856,7988,7994,7995,8005,8043,8044,8121,8161,8215,8237,8238,8310,8404,8475,8476,8480,8513,8574,8575,8642,8659,8660,8661,8662,8812,9070,9071,9140,9154,9207,9208,9327,9359,9385,9417,9458,9651,9774,9917,10105,10161,10163,10322,6588,6589,6678,6698,6699,7117,7335,8460,8733,8980,9165,9166,9234,9235,9412,9506,9507,9508,9509,9714,9980,9994,10364,10365,6660,8566,8567,9036,9054,9981,10363,4767,4799,4800,4803,4849,4853,4858,4899,4996,5013,5043,5044,5075,5138,5141,5201,5333,5373,5374,5376,5383,5384,5408,5453,5484,5506,5641,5716,5717,5718,5836,5837])).
% 157.55/157.28 cnf(13550,plain,
% 157.55/157.28 (~P105(f326(f61(x135501),f37(f917(x135501,a905),f241(f917(f917(x135501,a905),a905)))))),
% 157.55/157.28 inference(scs_inference,[],[4713,4134,12699,12721,12868,12870,12872,3709,11329,12373,12472,12475,12567,12609,12613,12621,12693,12824,12826,13271,13277,13282,13286,13292,13295,13319,13424,13429,3718,12439,12882,12884,3726,3442,12876,12878,12880,3443,12897,3409,12777,4657,4658,11968,4410,12932,3446,12941,3285,3342,12833,3343,12849,3344,3345,3346,12649,12924,4656,3768,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,12435,12602,12663,12810,13344,3528,3491,12920,3677,12135,3393,4638,10645,10745,11209,11309,13028,13364,3085,3086,3088,3089,3092,3093,3095,3096,3097,3103,3104,3108,3109,3110,3113,3114,3115,3119,3120,3124,3125,3127,3130,3139,3143,3145,3147,3150,3151,3152,3159,3160,3169,3179,3184,3190,3191,3194,3202,3205,3214,3216,3219,3223,3224,3226,3227,3234,3235,3245,3255,4625,3267,3341,4626,3807,4037,11908,3319,11615,3454,3430,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,12543,12753,12812,12820,12822,12839,12841,12843,12857,12859,12895,12929,13145,13310,13428,13433,13449,3404,12634,12638,12642,3410,3419,3929,4236,3387,13205,3539,12696,12780,3308,3309,3671,4023,11661,3527,12914,3370,3305,3332,3787,3328,3435,4143,4031,3850,4300,3316,3317,3295,3942,3352,3529,11056,11183,12436,12653,3403,4108,4647,10472,10642,11514,12594,12635,12639,4654,12606,3463,11988,11991,13240,13330,13394,13398,13402,13406,4066,4690,11235,11334,11570,11573,3869,3460,3576,3793,3568,4668,3543,12816,12818,12912,3367,10545,10875,3368,4677,3630,3360,3286,3389,11651,4250,12624,12765,4110,11255,11386,11445,12578,12584,12710,12713,12743,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,11456,4711,11463,4712,3388,3669,12478,12519,12605,3834,3618,4524,4525,3653,3690,4645,11644,3811,3770,3813,4292,3986,3738,13128,13132,13136,13140,13150,4033,12469,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,12747,13011,13050,13053,13111,13343,13348,3922,11894,3456,3552,11720,12003,13448,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,12628,12957,12976,12979,13003,13054,13221,13226,13247,13252,4696,11763,11794,11831,11838,11874,13063,13067,3909,3678,13233,3680,12982,12985,12988,12991,13021,13024,13376,13380,13384,3681,4058,3643,13377,3644,13381,3499,3501,3475,4680,3366,4642,3860,4172,3662,4697,4243,11531,3792,3512,12009,12012,12443,12547,12724,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,12075,4212,4171,12152,12493,4119,11053,12330,12503,12652,13397,4161,13401,4166,11261,12370,12442,12502,12546,13243,4167,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,12658,12720,12740,12750,13212,13276,13281,13301,13322,4700,11004,11410,12506,13289,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,12550,12669,12716,13004,13027,13103,13114,13119,13122,13125,13158,13171,13232,13258,13261,13340,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,12255,13018,13162,13182,13222,13227,13248,13253,13367,3474,3548,12362,13083,13129,13133,13137,13141,13151,13155,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,12556,12662,12702,12789,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,12601,12792,13204,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,12581,12681,12684,12706,12764,12772,12783,12802,13082,13095,13098,13193,13314,13333,13336,13373,13393,13427,3533,10872,10902,10911,10914,10917,11500,12703,12717,13064,13068,13071,3572,13357,13419,3565,3990,3927,10524,11897,11925,13045,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,13264,3493,10905,11061,11131,11926,12068,12260,12462,12487,13092,13360,13447,3952,12015,12998,4291,3684,4686,3964,3998,4671,4674,4675,3449,3453,4673,4672,4461,3782,11890,4388,11746,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,11950,12612,12620,12709,13208,13270,3917,11174,11180,11198,12184,12310,12393,12677,3766,11314,11436,12419,12528,12538,12617,12672,12680,12799,13215,4248,3919,10908,11277,11442,11476,11487,12616,12666,13306,3626,3733,10824,10827,10920,11087,3735,4705,11891,4701,12966,4706,10664,10777,12481,12490,12534,12734,12737,12796,4349,11044,12499,12514,12537,4254,3951,12805,3895,3896,4703,10494,10497,10866,10869,11760,11951,12746,4704,11871,11956,3920,10830,11093,13347,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045,5046,5061,5115,5116,5139,5140,5154,5158,5183,5189,5205,5209,5210,5211,5216,5217,5240,5265,5267,5268,5278,5283,5289,5325,5326,5334,5342,5346,5348,5351,5363,5366,5372,5377,5378,5391,5397,5400,5401,5405,5439,5454,5463,5465,5466,5469,5470,5471,5481,5483,5489,5490,5491,5497,5501,5502,5503,5511,5516,5517,5522,5535,5543,5556,5558,5566,5568,5569,5572,5576,5603,5617,5618,5633,5645,5667,5673,5697,5698,5702,5721,5729,5730,5735,5736,5746,5748,5761,5765,5774,5775,5777,5778,5794,5799,5808,5809,5820,5827,5841,5845,5848,5854,5855,5856,5859,5864,5900,5901,5904,5906,5908,5910,5911,5912,5914,5916,5918,5923,5930,5945,5959,5965,5966,5978,5989,5990,5997,6001,6003,6008,6016,6052,6065,6074,6077,6086,6090,6091,6092,6093,6094,6098,6103,6113,6119,6137,6141,6150,6179,6194,6220,6237,6238,6241,6255,6257,6259,6261,6276,6277,6280,6282,6285,6286,6302,6310,6311,6312,6314,6316,6352,6353,6358,6361,6367,6371,6405,6407,6409,6411,6421,6423,6425,6431,6433,6438,6441,6449,6457,6459,6460,6466,6488,6489,6490,6491,6492,6494,6501,6506,6540,6541,6544,6545,6546,6548,6549,6550,6551,6558,6590,6591,6600,6621,6622,6644,6646,6658,6659,6665,6695,6697,6712,6751,6754,6755,6811,6834,6877,6891,6899,6908,6909,6910,6911,6928,6929,6936,6948,6951,6953,6955,6956,6957,6959,6973,6984,6985,6986,6999,7051,7062,7064,7086,7087,7122,7129,7136,7166,7196,7252,7281,7336,7357,7365,7368,7428,7441,7503,7505,7519,7528,7529,7530,7547,7551,7553,7599,7609,7612,7627,7674,7676,7679,7721,7722,7740,7808,7826,7849,7873,7885,7899,7910,7921,7922,7948,7950,7952,7961,7997,8008,8033,8060,8092,8123,8156,8195,8211,8213,8229,8230,8292,8303,8368,8392,8411,8438,8477,8478,8495,8534,8536,8538,8544,8559,8563,8578,8599,8607,8609,8619,8624,8628,8629,8630,8631,8632,8633,8652,8666,8667,8685,8687,8691,8692,8693,8694,8695,8713,8714,8715,8725,8738,8741,8752,8757,8759,8761,8762,8763,8770,8776,8784,8787,8804,8805,8814,8815,8823,8842,8855,8859,8880,8902,8903,8906,8907,8913,8922,8923,8946,8957,8967,8968,8969,8972,8995,8996,9007,9056,9066,9068,9084,9096,9097,9098,9109,9173,9204,9205,9206,9221,9238,9246,9274,9275,9343,9374,9380,9390,9391,9392,9401,9429,9445,9449,9453,9475,9476,9503,9565,9570,9573,9605,9606,9607,9631,9632,9648,9669,9675,9687,9712,9733,9742,9743,9744,9745,9760,9762,9767,9797,9798,9804,9805,9850,9851,9862,9863,9887,9905,9907,9908,9916,9921,9928,9952,9986,9988,9992,10043,10077,10087,10089,10093,10094,10096,10106,10107,10127,10132,10226,10313,10314,10315,10316,10378,10396,2,8,9,4733,4734,4752,4794,4796,4797,4820,4826,4827,4837,4882,4884,4932,5062,5063,5080,5104,5161,5162,5168,5169,5171,5173,5182,5185,5186,5194,5207,5208,5214,5235,5236,5254,5259,5260,5261,5262,5266,5274,5277,5284,5339,5344,5345,5350,5357,5388,5398,5403,5419,5436,5438,5445,5446,5448,5459,5477,5479,5480,5487,5494,5495,5507,5508,5509,5510,5513,5514,5518,5519,5520,5521,5552,5553,5554,5562,5563,5564,5565,5609,5614,5616,5652,5654,5655,5657,5658,5660,5661,5663,5672,5677,5679,5680,5681,5683,5685,5686,5687,5688,5689,5690,5699,5700,5710,5713,5724,5740,5741,5744,5754,5757,5758,5759,5786,5796,5811,5812,5821,5822,5824,5826,5831,5866,5871,5873,5932,5967,5968,5982,5988,5991,5992,5993,5994,6013,6017,6018,6027,6049,6078,6097,6101,6102,6104,6127,6131,6134,6135,6136,6152,6163,6164,6196,6197,6201,6222,6225,6228,6249,6250,6278,6281,6289,6298,6300,6309,6313,6321,6322,6323,6324,6355,6372,6424,6461,6463,6485,6486,6493,6497,6498,6502,6516,6532,6553,6554,6559,6568,6583,6603,6609,6611,6626,6627,6630,6631,6633,6635,6636,6637,6639,6641,6645,6651,6652,6654,6655,6661,6663,6705,6711,6726,6729,6730,6731,6765,6770,6772,6777,6778,6788,6792,6806,6829,6830,6832,6833,6844,6850,6869,6872,6892,6922,6923,6924,6930,6944,6963,6965,6967,6969,6974,6980,6982,6996,7001,7002,7037,7038,7039,7053,7054,7056,7057,7076,7078,7093,7120,7144,7155,7157,7159,7161,7162,7194,7195,7199,7200,7207,7208,7210,7212,7234,7243,7244,7255,7265,7305,7315,7319,7326,7337,7342,7344,7351,7359,7372,7389,7410,7412,7431,7488,7489,7490,7492,7494,7498,7499,7504,7566,7595,7610,7615,7626,7657,7660,7682,7705,7723,7726,7727,7737,7757,7759,7761,7763,7764,7765,7790,7816,7817,7848,7850,7851,7852,7858,7879,7896,7901,7907,7909,7917,7929,7930,7932,7953,7959,7980,8046,8047,8048,8095,8101,8102,8125,8126,8143,8144,8145,8202,8203,8232,8262,8271,8282,8295,8324,8328,8334,8346,8364,8369,8391,8436,8465,8479,8498,8501,8527,8552,8610,8611,8614,8615,8683,8717,8718,8719,8720,8747,8779,8808,8816,8817,8858,8879,8924,8940,8986,8989,9004,9011,9053,9092,9093,9111,9112,9126,9243,9248,9252,9272,9283,9306,9308,9311,9317,9319,9320,9330,9331,9350,9356,9366,9373,9415,9433,9488,9489,9495,9534,9557,9562,9601,9611,9614,9615,9617,9618,9630,9653,9668,9677,9678,9680,9682,9711,9812,9832,9833,9882,9883,9922,9957,10068,10136,10205,10287,10305,10310,10330,3,2817,2818,2819,2821,2822,2826,2827,2837,2838,2839,2840,2847,2848,2853,2859,2861,2867,2869,2870,2871,2872,2873,2879,2880,2881,2882,2883,2885,2886,2888,2889,2892,2893,2894,2897,2898,2899,2900,2901,2902,2903,2904,2914,2916,2917,2918,2919,2920,2922,2923,2927,2928,2929,2930,2934,2939,2941,2946,2947,2966,2968,2969,2970,2973,2974,2975,2985,2986,2988,2989,2990,3000,3005,3008,3009,3010,3015,3023,3025,3044,3045,5435,5476,5625,5626,5627,5711,5810,5840,5874,5890,5892,5898,5960,5961,5962,5963,5980,6015,6147,6185,6195,6219,6253,6290,6440,6445,6483,6484,6507,6509,6511,6518,6519,6520,6521,6522,6523,6524,6525,6604,6675,6676,6764,6801,6802,6841,6842,6981,6995,7066,7067,7073,7094,7126,7128,7132,7177,7197,7198,7216,7217,7254,7299,7300,7396,7467,7468,7469,7470,7487,7520,7571,7572,7581,7586,7587,7598,7629,7630,7631,7632,7772,7774,7775,7776,7782,7783,7856,7988,7994,7995,8005,8043,8044,8121,8161,8215,8237,8238,8310,8404,8475,8476,8480,8513,8574,8575,8642,8659,8660,8661,8662,8812,9070,9071,9140,9154,9207,9208,9327,9359,9385,9417,9458,9651,9774,9917,10105,10161,10163,10322,6588,6589,6678,6698,6699,7117,7335,8460,8733,8980,9165,9166,9234,9235,9412,9506,9507,9508,9509,9714,9980,9994,10364,10365,6660,8566,8567,9036,9054,9981,10363,4767,4799,4800,4803,4849,4853,4858,4899,4996,5013,5043,5044,5075,5138,5141,5201,5333,5373,5374,5376,5383,5384,5408,5453,5484,5506,5641,5716,5717,5718,5836,5837,5863,5867,5926,5928,5937,5943,6031,6111,6260,6317,6427])).
% 157.55/157.29 cnf(13558,plain,
% 157.55/157.29 (~P105(f326(f326(f235(a909),f2(a909)),f188(a909)))),
% 157.55/157.29 inference(scs_inference,[],[4713,4134,12699,12721,12868,12870,12872,3709,11329,12373,12472,12475,12567,12609,12613,12621,12693,12824,12826,13271,13277,13282,13286,13292,13295,13319,13424,13429,3718,12439,12882,12884,3726,3442,12876,12878,12880,3443,12897,3409,12777,4657,4658,11968,4410,12932,3446,12941,3285,3342,12833,3343,12849,3344,3345,3346,12649,12924,4656,3768,4628,10412,10422,10435,10446,10518,10553,10556,10559,10661,10796,11106,11299,11302,11321,11324,11517,11618,11625,11639,11685,11688,11721,11736,11799,11858,11877,12163,12188,12200,12229,12235,12327,12435,12602,12663,12810,13344,3528,3491,12920,3677,12135,3393,4638,10645,10745,11209,11309,13028,13364,3085,3086,3088,3089,3092,3093,3095,3096,3097,3103,3104,3108,3109,3110,3113,3114,3115,3119,3120,3124,3125,3127,3130,3139,3143,3145,3147,3150,3151,3152,3159,3160,3169,3179,3184,3190,3191,3194,3202,3205,3214,3216,3219,3223,3224,3226,3227,3234,3235,3245,3255,4625,3267,3341,4626,3807,4037,11908,3319,11615,3454,3430,3433,10481,10484,10580,10583,10899,11630,11633,11747,11786,11791,11861,11903,12345,12543,12753,12812,12820,12822,12839,12841,12843,12857,12859,12895,12929,13145,13310,13428,13433,13449,3404,12634,12638,12642,3410,3419,3929,4236,3387,13205,3539,12696,12780,3308,3309,3671,4023,11661,3527,12914,3370,3305,3332,3787,3328,3435,4143,4031,3850,4300,3316,3317,3295,3942,3352,3529,11056,11183,12436,12653,3403,4108,4647,10472,10642,11514,12594,12635,12639,4654,12606,3463,11988,11991,13240,13330,13394,13398,13402,13406,4066,4690,11235,11334,11570,11573,3869,3460,3576,3793,3568,4668,3543,12816,12818,12912,3367,10545,10875,3368,4677,3630,3360,3286,3389,11651,4250,12624,12765,4110,11255,11386,11445,12578,12584,12710,12713,12743,4708,11158,11399,11508,11534,11578,11584,12522,4709,11288,11402,11511,4710,11405,11456,4711,11463,4712,3388,3669,12478,12519,12605,3834,3618,4524,4525,3653,3690,4645,11644,3811,3770,3813,4292,3986,3738,13128,13132,13136,13140,13150,4033,12469,3655,3912,3540,10564,10684,10762,10835,10838,10878,10978,11225,11835,12159,12222,12298,12336,12413,12416,12747,13011,13050,13053,13111,13343,13348,3922,11894,3456,3552,11720,12003,13448,3732,4683,10449,10452,10478,10605,10780,10986,11001,11116,11556,11654,11834,12054,12059,12274,12277,12357,12525,12628,12957,12976,12979,13003,13054,13221,13226,13247,13252,4696,11763,11794,11831,11838,11874,13063,13067,3909,3678,13233,3680,12982,12985,12988,12991,13021,13024,13376,13380,13384,3681,4058,3643,13377,3644,13381,3499,3501,3475,4680,3366,4642,3860,4172,3662,4697,4243,11531,3792,3512,12009,12012,12443,12547,12724,4688,10440,10443,10613,10708,10727,10734,10757,10765,10768,10785,10971,11212,11425,11714,11808,11959,12072,12075,4212,4171,12152,12493,4119,11053,12330,12503,12652,13397,4161,13401,4166,11261,12370,12442,12502,12546,13243,4167,3835,11842,12162,12305,12380,12426,4200,3852,10608,10705,11258,11339,11418,11482,12326,12394,12658,12720,12740,12750,13212,13276,13281,13301,13322,4700,11004,11410,12506,13289,3472,10573,10671,10821,10885,10960,11007,11010,11041,11064,11100,11138,11177,11962,12006,12132,12187,12203,12206,12209,12212,12387,12401,12404,12407,12410,12486,12550,12669,12716,13004,13027,13103,13114,13119,13122,13125,13158,13171,13232,13258,13261,13340,3473,10600,10656,10890,10981,11103,11739,12039,12042,12051,12138,12149,12168,12173,12215,12238,12255,13018,13162,13182,13222,13227,13248,13253,13367,3474,3548,12362,13083,13129,13133,13137,13141,13151,13155,4679,10489,10521,11025,11067,11076,11922,11943,12106,12109,12112,12115,12199,12218,12221,12234,12286,12289,12292,12295,12454,12457,12553,12556,12662,12702,12789,3625,10750,10841,11111,11155,11389,11392,11471,11553,11724,11971,12601,12792,13204,4692,11034,11147,11168,11171,11238,11241,11252,11355,11363,11377,11413,11430,11439,11479,11520,11525,11528,11547,11550,11587,11592,11595,11598,11601,11841,11985,12018,12280,12283,12317,12363,12390,12531,12575,12581,12681,12684,12706,12764,12772,12783,12802,13082,13095,13098,13193,13314,13333,13336,13373,13393,13427,3533,10872,10902,10911,10914,10917,11500,12703,12717,13064,13068,13071,3572,13357,13419,3565,3990,3927,10524,11897,11925,13045,4689,10469,10860,10863,11358,11374,11857,11913,11947,11972,12069,12094,12097,12100,12103,12356,13264,3493,10905,11061,11131,11926,12068,12260,12462,12487,13092,13360,13447,3952,12015,12998,4291,3684,4686,3964,3998,4671,4674,4675,3449,3453,4673,4672,4461,3782,11890,4388,11746,4702,10771,10774,4707,11244,11247,11433,11544,11561,11607,4076,11604,11946,11950,12612,12620,12709,13208,13270,3917,11174,11180,11198,12184,12310,12393,12677,3766,11314,11436,12419,12528,12538,12617,12672,12680,12799,13215,4248,3919,10908,11277,11442,11476,11487,12616,12666,13306,3626,3733,10824,10827,10920,11087,3735,4705,11891,4701,12966,4706,10664,10777,12481,12490,12534,12734,12737,12796,4349,11044,12499,12514,12537,4254,3951,12805,3895,3896,4703,10494,10497,10866,10869,11760,11951,12746,4704,11871,11956,3920,10830,11093,13347,4186,4720,4746,4801,4805,4833,4848,4855,4857,4893,4898,4927,4933,5019,5045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% 157.55/157.29 cnf(13682,plain,
% 157.55/157.29 (E(f326(f326(f134(x136821),x136822),f113(x136821)),x136822)),
% 157.55/157.29 inference(rename_variables,[],[3404])).
% 157.55/157.29 cnf(13687,plain,
% 157.55/157.29 (~P105(f326(f326(f328(a909),x136871),f326(f281(a909),f2(a909))))),
% 157.55/157.29 inference(rename_variables,[],[12036])).
% 157.55/157.29 cnf(13715,plain,
% 157.55/157.29 (~P105(f326(f326(f235(a909),x137151),x137151))),
% 157.55/157.29 inference(rename_variables,[],[4679])).
% 157.55/157.29 cnf(13726,plain,
% 157.55/157.29 (E(f326(f283(x137261,x137261),f262(x137261,x137262)),x137262)),
% 157.55/157.29 inference(rename_variables,[],[3433])).
% 157.55/157.29 cnf(13729,plain,
% 157.55/157.29 (P105(f326(f326(f234(f917(x137291,a905)),f326(f284(x137292,x137291,x137293),f188(f917(x137292,a905)))),x137294))),
% 157.55/157.29 inference(rename_variables,[],[11486])).
% 157.55/157.29 cnf(13735,plain,
% 157.55/157.29 (~E(f326(f326(f151(x137351),x137352),x137353),x137353)),
% 157.55/157.29 inference(rename_variables,[],[4647])).
% 157.55/157.29 cnf(13740,plain,
% 157.55/157.29 (~E(f326(f326(f101(a909),f326(a112,x137401)),x137401),f326(a112,x137401))),
% 157.55/157.29 inference(rename_variables,[],[11779])).
% 157.55/157.29 cnf(13743,plain,
% 157.55/157.29 (~E(f326(f326(f151(x137431),x137432),x137433),x137433)),
% 157.55/157.29 inference(rename_variables,[],[4647])).
% 157.55/157.29 cnf(13754,plain,
% 157.55/157.29 (~P105(f326(f326(f328(x137541),x137542),f188(f917(x137541,a905))))),
% 157.55/157.29 inference(rename_variables,[],[4692])).
% 157.55/157.29 cnf(13771,plain,
% 157.55/157.29 (~E(f326(f326(f151(x137711),x137712),x137713),x137713)),
% 157.55/157.29 inference(rename_variables,[],[4647])).
% 157.55/157.29 cnf(13787,plain,
% 157.55/157.29 (~P105(f326(f326(f235(a909),f326(f326(f79(a909),x137871),x137872)),x137871))),
% 157.55/157.29 inference(rename_variables,[],[4704])).
% 157.55/157.29 cnf(13794,plain,
% 157.55/157.29 (P105(f326(f326(f235(a1),f326(f326(f3(a1),x137941),f77(a1))),x137941))),
% 157.55/157.29 inference(rename_variables,[],[10980])).
% 157.55/157.29 cnf(13805,plain,
% 157.55/157.29 (~P105(f326(f326(f328(x138051),x138052),f188(f917(x138051,a905))))),
% 157.55/157.29 inference(rename_variables,[],[4692])).
% 157.55/157.29 cnf(13815,plain,
% 157.55/157.29 (~P105(f326(f326(f328(a909),x138151),f326(f281(a909),f2(a909))))),
% 157.55/157.29 inference(rename_variables,[],[12036])).
% 157.55/157.29 cnf(13818,plain,
% 157.55/157.29 (~P105(f326(f326(f328(f916(x138181,x138181)),x138182),f262(x138181,f188(f917(x138181,a905)))))),
% 157.55/157.29 inference(rename_variables,[],[11167])).
% 157.55/157.29 cnf(13825,plain,
% 157.55/157.29 (P105(f326(f326(f234(a909),x138251),f326(f326(f80(a909),x138251),x138251)))),
% 157.55/157.29 inference(rename_variables,[],[3733])).
% 157.55/157.29 cnf(13838,plain,
% 157.55/157.29 (P105(f326(f326(f234(a909),f2(a909)),x138381))),
% 157.55/157.29 inference(rename_variables,[],[3493])).
% 157.55/157.29 cnf(13841,plain,
% 157.55/157.29 (~P105(f326(f326(f328(f916(x138411,x138411)),x138412),f262(x138411,f188(f917(x138411,a905)))))),
% 157.55/157.29 inference(rename_variables,[],[11167])).
% 157.55/157.29 cnf(13869,plain,
% 157.55/157.29 (P105(f326(f326(f234(a909),x138691),f326(f326(f80(a909),x138691),x138691)))),
% 157.55/157.29 inference(rename_variables,[],[3733])).
% 157.55/157.29 cnf(13882,plain,
% 157.55/157.29 (~P105(f326(f326(f328(a909),x138821),f326(f281(a909),f2(a909))))),
% 157.55/157.29 inference(rename_variables,[],[12036])).
% 157.55/157.29 cnf(13885,plain,
% 157.55/157.29 (~P105(f326(f326(f328(a909),x138851),f326(f281(a909),f2(a909))))),
% 157.55/157.29 inference(rename_variables,[],[12036])).
% 157.55/157.29 cnf(13898,plain,
% 157.55/157.29 (~P105(f326(f326(f328(x138981),x138982),f188(f917(x138981,a905))))),
% 157.55/157.29 inference(rename_variables,[],[4692])).
% 157.55/157.29 cnf(13903,plain,
% 157.55/157.29 (P105(f326(f326(f234(f917(x139031,a905)),x139032),f326(f326(f110(f917(x139031,a905)),x139033),f241(f917(x139031,a905)))))),
% 157.55/157.29 inference(rename_variables,[],[11417])).
% 157.55/157.29 cnf(13915,plain,
% 157.55/157.29 (P105(f326(f326(f328(x139151),f326(x139152,x139153)),f326(f309(x139154,x139151,x139152),f241(f917(x139154,a905)))))),
% 157.55/157.29 inference(rename_variables,[],[4076])).
% 157.55/157.29 cnf(13918,plain,
% 157.55/157.29 (~E(f326(f326(f151(x139181),x139182),x139183),x139183)),
% 157.55/157.29 inference(rename_variables,[],[4647])).
% 157.55/157.29 cnf(13931,plain,
% 157.55/157.29 (~E(f326(f326(f151(x139311),x139312),x139313),x139313)),
% 157.55/157.29 inference(rename_variables,[],[4647])).
% 157.55/157.29 cnf(13958,plain,
% 157.55/157.29 (P105(f326(f326(f234(f917(x139581,a905)),f326(f172(x139581),f176(x139581,x139582,x139583))),f326(f172(x139581),x139582)))),
% 157.55/157.29 inference(rename_variables,[],[4166])).
% 157.55/157.29 cnf(13961,plain,
% 157.55/157.29 (~E(f326(f326(f151(x139611),x139612),x139613),x139613)),
% 157.55/157.29 inference(rename_variables,[],[4647])).
% 157.55/157.29 cnf(13971,plain,
% 157.55/157.29 (~P105(f326(f326(f328(f916(x139711,x139711)),x139712),f262(x139711,f188(f917(x139711,a905)))))),
% 157.55/157.29 inference(rename_variables,[],[11167])).
% 157.55/157.29 cnf(13994,plain,
% 157.55/157.29 (P105(f326(f326(f234(f917(x139941,a905)),x139942),x139942))),
% 157.55/157.29 inference(rename_variables,[],[3766])).
% 157.55/157.29 cnf(13999,plain,
% 157.55/157.29 (~P105(f326(f326(f328(f916(x139991,x139991)),x139992),f262(x139991,f188(f917(x139991,a905)))))),
% 157.55/157.29 inference(rename_variables,[],[11167])).
% 157.55/157.29 cnf(14012,plain,
% 157.55/157.29 (~P105(f326(f326(f328(f916(x140121,x140121)),x140122),f262(x140121,f188(f917(x140121,a905)))))),
% 157.55/157.29 inference(rename_variables,[],[11167])).
% 157.55/157.29 cnf(14076,plain,
% 157.55/157.29 ($false),
% 157.55/157.29 inference(scs_inference,[],[3501,4212,4250,4058,3267,4705,3475,3474,4671,4110,3548,4673,3565,3922,4708,3572,4076,13915,4692,13754,13805,13898,4166,13958,4638,4647,13735,13743,13771,13918,13931,13961,3456,3552,3927,3493,13838,3782,3917,3766,13994,3626,3733,13825,13869,3735,4349,3920,3433,13726,3404,13682,3317,3428,4712,4679,13715,4689,4702,4706,4703,4704,13787,11779,13740,10504,13350,12214,11589,13528,10754,12489,10826,13000,10814,13013,11306,12731,12767,11417,13903,11118,10980,13794,4466,12791,11486,13729,11441,11311,11828,11151,3530,3504,3418,11468,13257,10929,13558,12527,12036,13687,13815,13882,13885,10937,11167,13818,13841,13971,13999,14012,12344,11170,12285,11424,12692,13550,11451,12596,11069,3111,2,10077,9392,4805,5217,6545,8092,9675,4803,5566,7530,5061,6086,6659,7721,8823,5746,6074,6098,6834,5377,5391,6540,8695,7428,4933,6141,10093,5777,5809,5997,6103,6665,6877,9476,5138,7573,5400,8759,5348,5470,6312,6709,8495,5702,9,8633,6409,5211,5572,5989,6466,5761,8411,6929,5641,8218,5673,9851,10315,6908,6984,7064,7166,8787,6621,8691,6494,10314,6911,5618,6541,7087,7368,6111,6411,9907,4927,5603,6237,6457,6948,7553,6255,5568,5748,6985,8946,6999,7676,10089,6712,5558,9205,6352,8211,5569,6441,9887,10226,9449,4848,5378,6052,6220,6449,5189,6179,7062,9565,6488,9204,5333,5045,5325,6314,7505,8693,8741,5351,7503,8694,9862,10396,5775,6427,8,6910,8292,7627,8060,6959,9648,9743,9921,8902,5808,8123,6361,9952,8762,9475,8628,9797,8229,8715,8392,5439,5855,6957,6544,9503,5141,5265,6423,7826,10094,5075,9712,5901,6622,7674,8195,8784,6282,8855,4833]),
% 157.55/157.29 ['proof']).
% 157.55/157.29 % SZS output end Proof
% 157.55/157.29 % Total time :142.890000s
%------------------------------------------------------------------------------