TSTP Solution File: SWW389+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW389+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:09:07 EDT 2024
% Result : Theorem 179.72s 179.57s
% Output : CNFRefutation 179.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW389+1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jun 19 08:22:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.52/0.57 start to proof:theBenchmark
% 179.23/179.40 %-------------------------------------------
% 179.23/179.40 % File :CSE---1.7
% 179.23/179.40 % Problem :theBenchmark
% 179.23/179.40 % Transform :cnf
% 179.23/179.40 % Format :tptp:raw
% 179.23/179.40 % Command :java -jar mcs_scs.jar %d %s
% 179.23/179.40
% 179.23/179.40 % Result :Theorem 164.460000s
% 179.23/179.40 % Output :CNFRefutation 164.460000s
% 179.23/179.40 %-------------------------------------------
% 179.23/179.41 %------------------------------------------------------------------------------
% 179.23/179.41 % File : SWW389+1 : TPTP v8.2.0. Released v5.2.0.
% 179.23/179.41 % Domain : Software Verification
% 179.23/179.41 % Problem : Hoare's Logic with Procedures 435715, 5000 axioms selected
% 179.23/179.41 % Version : Especial.
% 179.23/179.41 % English :
% 179.23/179.41
% 179.23/179.41 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 179.23/179.41 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 179.23/179.41 % Source : [Bla11]
% 179.23/179.41 % Names : hoare_435715.5000.p [Bla11]
% 179.23/179.41
% 179.23/179.41 % Status : ContradictoryAxioms
% 179.23/179.41 % Rating : 0.72 v8.1.0, 0.81 v7.5.0, 0.78 v7.4.0, 0.83 v7.3.0, 0.79 v7.1.0, 0.74 v7.0.0, 0.87 v6.4.0, 0.85 v6.3.0, 0.83 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.93 v5.4.0, 0.96 v5.3.0, 1.00 v5.2.0
% 179.23/179.41 % Syntax : Number of formulae : 5241 (1737 unt; 0 def)
% 179.23/179.41 % Number of atoms : 12574 (4581 equ)
% 179.23/179.41 % Maximal formula atoms : 13 ( 2 avg)
% 179.23/179.41 % Number of connectives : 8321 ( 988 ~; 149 |; 702 &)
% 179.23/179.41 % ( 887 <=>;5595 =>; 0 <=; 0 <~>)
% 179.23/179.41 % Maximal formula depth : 22 ( 6 avg)
% 179.23/179.41 % Maximal term depth : 19 ( 2 avg)
% 179.23/179.41 % Number of predicates : 143 ( 142 usr; 0 prp; 1-6 aty)
% 179.23/179.41 % Number of functors : 379 ( 379 usr; 52 con; 0-10 aty)
% 179.23/179.41 % Number of variables : 16786 (16644 !; 142 ?)
% 179.23/179.41 % SPC : FOF_CAX_RFO_SEQ
% 179.23/179.41
% 179.23/179.41 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 179.23/179.41 % 2011-03-01 13:04:54
% 179.23/179.41 %------------------------------------------------------------------------------
% 179.23/179.41 %----Relevant facts (4987)
% 179.23/179.41 fof(fact_ext,axiom,
% 179.23/179.41 ! [V_g_2,V_f_2] :
% 179.23/179.41 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 179.23/179.41 => V_f_2 = V_g_2 ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_empty,axiom,
% 179.23/179.41 ! [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))) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 179.23/179.41 ! [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))) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_triple_Oinject,axiom,
% 179.23/179.41 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
% 179.23/179.41 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_H_2),V_com_H_2),V_fun2_H_2)
% 179.23/179.41 <=> ( V_fun1_2 = V_fun1_H_2
% 179.23/179.41 & V_com_2 = V_com_H_2
% 179.23/179.41 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_cut,axiom,
% 179.23/179.41 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 179.23/179.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 179.23/179.41 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 179.23/179.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_hoare__derivs_Oinsert,axiom,
% 179.23/179.41 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 179.23/179.41 ( 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))))
% 179.23/179.41 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
% 179.23/179.41 => 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)) ) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_derivs__insertD,axiom,
% 179.23/179.41 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 179.23/179.41 ( 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))
% 179.23/179.41 => ( 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))))
% 179.23/179.41 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_bot__fun__def,axiom,
% 179.23/179.41 ! [V_x_2,T_c,T_b] :
% 179.23/179.41 ( class_Orderings_Obot(T_b)
% 179.23/179.41 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_triple_Orecs,axiom,
% 179.23/179.41 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_triple_Osimps_I2_J,axiom,
% 179.23/179.41 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_empty__not__insert,axiom,
% 179.23/179.41 ! [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) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_insert__not__empty,axiom,
% 179.23/179.41 ! [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)) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_doubleton__eq__iff,axiom,
% 179.23/179.41 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.23/179.41 ( 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))))
% 179.23/179.41 <=> ( ( V_a_2 = V_ca_2
% 179.23/179.41 & V_b_2 = V_d_2 )
% 179.23/179.41 | ( V_a_2 = V_d_2
% 179.23/179.41 & V_b_2 = V_ca_2 ) ) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_singleton__inject,axiom,
% 179.23/179.41 ! [V_b_2,V_a_2,T_b] :
% 179.23/179.41 ( 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)))
% 179.23/179.41 => V_a_2 = V_b_2 ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_bot__apply,axiom,
% 179.23/179.41 ! [V_x_2,T_c,T_b] :
% 179.23/179.41 ( class_Orderings_Obot(T_b)
% 179.23/179.41 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_escape,axiom,
% 179.23/179.41 ! [V_Qa_2,V_ca_2,V_Ga_2,T_b,V_P_2] :
% 179.23/179.41 ( ! [B_Z,B_s] :
% 179.23/179.41 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 179.23/179.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Qa_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
% 179.23/179.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_hoare__derivs_OSkip,axiom,
% 179.23/179.41 ! [V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 179.23/179.41 ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_conseq2,axiom,
% 179.23/179.41 ! [V_Qa_2,V_Q_H_2,V_ca_2,V_P_2,V_Ga_2,T_b] :
% 179.23/179.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 179.23/179.41 => ( ! [B_Z,B_s] :
% 179.23/179.41 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 179.23/179.41 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s)) )
% 179.23/179.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_insert__code,axiom,
% 179.23/179.41 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 179.23/179.41 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 179.23/179.41 <=> ( V_y_2 = V_x_2
% 179.23/179.41 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_insert__commute,axiom,
% 179.23/179.41 ! [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)) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_insert__absorb2,axiom,
% 179.23/179.41 ! [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) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_the__elem__eq,axiom,
% 179.23/179.41 ! [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 ).
% 179.23/179.41
% 179.23/179.41 fof(fact_conseq1,axiom,
% 179.23/179.41 ! [V_P_2,V_Qa_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] :
% 179.23/179.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 179.23/179.41 => ( ! [B_Z,B_s] :
% 179.23/179.41 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 179.23/179.41 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 179.23/179.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_Comp,axiom,
% 179.23/179.41 ! [V_R_2,V_d_2,V_Qa_2,V_ca_2,V_P_2,V_Ga_2,T_b] :
% 179.23/179.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 179.23/179.41 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Qa_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 179.23/179.41 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_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)))) ) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_LoopF,axiom,
% 179.23/179.41 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_hoare__sound,axiom,
% 179.23/179.41 ! [V_ts_2,V_Ga_2,T_b] :
% 179.23/179.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
% 179.23/179.41 => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_ts_2) ) ).
% 179.23/179.41
% 179.23/179.41 fof(fact_conseq12,axiom,
% 179.23/179.41 ! [V_Qa_2,V_P_2,V_Q_H_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] :
% 179.23/179.41 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 179.23/179.41 => ( ! [B_Z,B_s] :
% 179.23/179.41 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 179.23/179.41 => ! [B_s_H] :
% 179.23/179.41 ( ! [B_Z_H] :
% 179.23/179.41 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s))
% 179.23/179.41 => hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)) )
% 179.23/179.41 => hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) )
% 179.23/179.42 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),V_ca_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_hoare__derivs_Oequations_I8_J,axiom,
% 179.23/179.42 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_a2_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_a3_2)),V_a4_2))),c_Com_Ocom_OAss(V_a3_2,V_a4_2)),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Ass,axiom,
% 179.23/179.42 ! [V_a_2,V_X_2,V_P_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_P_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_the__elem__def,axiom,
% 179.23/179.42 ! [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))))) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Collect__conv__if,axiom,
% 179.23/179.42 ! [T_b,V_a_2,V_P_2] :
% 179.23/179.42 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 179.23/179.42 => 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_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 179.23/179.42 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 179.23/179.42 => 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_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Collect__conv__if2,axiom,
% 179.23/179.42 ! [T_b,V_a_2,V_P_2] :
% 179.23/179.42 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 179.23/179.42 => 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_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 179.23/179.42 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 179.23/179.42 => 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_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_singleton__conv,axiom,
% 179.23/179.42 ! [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))) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Collect__def,axiom,
% 179.23/179.42 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2 ).
% 179.23/179.42
% 179.23/179.42 fof(fact_empty__Collect__eq,axiom,
% 179.23/179.42 ! [V_P_2,T_b] :
% 179.23/179.42 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
% 179.23/179.42 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Collect__empty__eq,axiom,
% 179.23/179.42 ! [V_P_2,T_b] :
% 179.23/179.42 ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.42 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_empty__def,axiom,
% 179.23/179.42 ! [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)) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_insert__Collect,axiom,
% 179.23/179.42 ! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_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_P_2)) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_singleton__conv2,axiom,
% 179.23/179.42 ! [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))) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I13_J,axiom,
% 179.23/179.42 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I12_J,axiom,
% 179.23/179.42 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I9_J,axiom,
% 179.23/179.42 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I8_J,axiom,
% 179.23/179.42 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I25_J,axiom,
% 179.23/179.42 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I24_J,axiom,
% 179.23/179.42 ! [V_com2_H_2,V_com1_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I17_J,axiom,
% 179.23/179.42 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I16_J,axiom,
% 179.23/179.42 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I47_J,axiom,
% 179.23/179.42 ! [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) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I46_J,axiom,
% 179.23/179.42 ! [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) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I29_J,axiom,
% 179.23/179.42 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I28_J,axiom,
% 179.23/179.42 ! [V_com_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I5_J,axiom,
% 179.23/179.42 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 179.23/179.42 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 179.23/179.42 <=> ( V_fun_2 = V_fun_H_2
% 179.23/179.42 & V_com_2 = V_com_H_2 ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I1_J,axiom,
% 179.23/179.42 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
% 179.23/179.42 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
% 179.23/179.42 <=> ( V_vname_2 = V_vname_H_2
% 179.23/179.42 & V_fun_2 = V_fun_H_2 ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I3_J,axiom,
% 179.23/179.42 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 179.23/179.42 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 179.23/179.42 <=> ( V_com1_2 = V_com1_H_2
% 179.23/179.42 & V_com2_2 = V_com2_H_2 ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_the__sym__eq__trivial,axiom,
% 179.23/179.42 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 179.23/179.42
% 179.23/179.42 fof(fact_the__eq__trivial,axiom,
% 179.23/179.42 ! [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 ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Loop__sound__lemma,axiom,
% 179.23/179.42 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 179.23/179.42 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 179.23/179.42 => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_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)))) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Loop,axiom,
% 179.23/179.42 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 179.23/179.42 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 179.23/179.42 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_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)))) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_insert__compr__raw,axiom,
% 179.23/179.42 ! [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))) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_insert__compr,axiom,
% 179.23/179.42 ! [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))) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_enum__the__def,axiom,
% 179.23/179.42 ! [V_P_2,T_b] : c_Enum_Oenum__the(T_b,V_P_2) = c_HOL_OThe(T_b,V_P_2) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I64_J,axiom,
% 179.23/179.42 ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2 ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I67_J,axiom,
% 179.23/179.42 ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I65_J,axiom,
% 179.23/179.42 ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_insert__def,axiom,
% 179.23/179.42 ! [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) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_com_Osimps_I69_J,axiom,
% 179.23/179.42 ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(V_f6_2,V_fun_2),V_com_2) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_equalityCE,axiom,
% 179.23/179.42 ! [V_ca_2,T_b,V_B_2,V_A_2] :
% 179.23/179.42 ( V_A_2 = V_B_2
% 179.23/179.42 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.42 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) )
% 179.23/179.42 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_emptyE,axiom,
% 179.23/179.42 ! [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)))) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_insertE,axiom,
% 179.23/179.42 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 179.23/179.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 179.23/179.42 => ( V_a_2 != V_b_2
% 179.23/179.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_insertCI,axiom,
% 179.23/179.42 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 179.23/179.42 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 179.23/179.42 => V_a_2 = V_b_2 )
% 179.23/179.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_UnE,axiom,
% 179.23/179.42 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.42 ( 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)))
% 179.23/179.42 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_UnCI,axiom,
% 179.23/179.42 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 179.23/179.42 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 179.23/179.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
% 179.23/179.42 => 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))) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_CollectI,axiom,
% 179.23/179.42 ! [T_b,V_a_2,V_P_2] :
% 179.23/179.42 ( hBOOL(hAPP(V_P_2,V_a_2))
% 179.23/179.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__absorb,axiom,
% 179.23/179.42 ! [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 ).
% 179.23/179.42
% 179.23/179.42 fof(fact_mem__def,axiom,
% 179.23/179.42 ! [V_A_2,V_x_2,T_b] :
% 179.23/179.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.42 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__commute,axiom,
% 179.23/179.42 ! [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) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__left__absorb,axiom,
% 179.23/179.42 ! [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) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__left__commute,axiom,
% 179.23/179.42 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__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)) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__iff,axiom,
% 179.23/179.42 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.42 ( 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)))
% 179.23/179.42 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.42 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__assoc,axiom,
% 179.23/179.42 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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)) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_bex__Un,axiom,
% 179.23/179.42 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 179.23/179.42 ( ? [B_x] :
% 179.23/179.42 ( 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)))
% 179.23/179.42 & hBOOL(hAPP(V_P_2,B_x)) )
% 179.23/179.42 <=> ( ? [B_x] :
% 179.23/179.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.23/179.42 & hBOOL(hAPP(V_P_2,B_x)) )
% 179.23/179.42 | ? [B_x] :
% 179.23/179.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 179.23/179.42 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_ball__Un,axiom,
% 179.23/179.42 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 179.23/179.42 ( ! [B_x] :
% 179.23/179.42 ( 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)))
% 179.23/179.42 => hBOOL(hAPP(V_P_2,B_x)) )
% 179.23/179.42 <=> ( ! [B_x] :
% 179.23/179.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.23/179.42 => hBOOL(hAPP(V_P_2,B_x)) )
% 179.23/179.42 & ! [B_x] :
% 179.23/179.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 179.23/179.42 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_UnI1,axiom,
% 179.23/179.42 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.42 => 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))) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_UnI2,axiom,
% 179.23/179.42 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 179.23/179.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 179.23/179.42 => 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))) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_eqset__imp__iff,axiom,
% 179.23/179.42 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 179.23/179.42 ( V_A_2 = V_B_2
% 179.23/179.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.42 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_eqelem__imp__iff,axiom,
% 179.23/179.42 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 179.23/179.42 ( V_x_2 = V_y_2
% 179.23/179.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.42 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_eq__mem__trans,axiom,
% 179.23/179.42 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 179.23/179.42 ( V_a_2 = V_b_2
% 179.23/179.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 179.23/179.42 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__def,axiom,
% 179.23/179.42 ! [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))) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__empty__left,axiom,
% 179.23/179.42 ! [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 ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__empty__right,axiom,
% 179.23/179.42 ! [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 ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__empty,axiom,
% 179.23/179.42 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.42 ( 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))
% 179.23/179.42 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.42 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__insert__right,axiom,
% 179.23/179.42 ! [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)) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_Un__insert__left,axiom,
% 179.23/179.42 ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_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)) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_all__not__in__conv,axiom,
% 179.23/179.42 ! [V_A_2,T_b] :
% 179.23/179.42 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.23/179.42 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_ex__in__conv,axiom,
% 179.23/179.42 ! [V_A_2,T_b] :
% 179.23/179.42 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.23/179.42 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_empty__iff,axiom,
% 179.23/179.42 ! [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)))) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_equals0D,axiom,
% 179.23/179.42 ! [V_a_2,T_b,V_A_2] :
% 179.23/179.42 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.42 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_insertI1,axiom,
% 179.23/179.42 ! [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))) ).
% 179.23/179.42
% 179.23/179.42 fof(fact_insert__iff,axiom,
% 179.23/179.42 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 179.23/179.43 <=> ( V_a_2 = V_b_2
% 179.23/179.43 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_insert__ident,axiom,
% 179.23/179.43 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 179.23/179.43 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 179.23/179.43 => ( 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)
% 179.23/179.43 <=> V_A_2 = V_B_2 ) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_insertI2,axiom,
% 179.23/179.43 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 179.23/179.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_insert__absorb,axiom,
% 179.23/179.43 ! [V_A_2,V_a_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.43 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_peek__and__def,axiom,
% 179.23/179.43 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_p_2),V_Z_2),V_s_2))
% 179.23/179.43 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2))
% 179.23/179.43 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Collect__disj__eq,axiom,
% 179.23/179.43 ! [V_Qa_2,V_P_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_P_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_P_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Collect__mem__eq,axiom,
% 179.23/179.43 ! [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 ).
% 179.23/179.43
% 179.23/179.43 fof(fact_mem__Collect__eq,axiom,
% 179.23/179.43 ! [V_P_2,V_a_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 179.23/179.43 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_CollectD,axiom,
% 179.23/179.43 ! [V_P_2,V_a_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 179.23/179.43 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_CollectE,axiom,
% 179.23/179.43 ! [V_P_2,V_a_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 179.23/179.43 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_insert__is__Un,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_singleton__iff,axiom,
% 179.23/179.43 ! [V_a_2,V_b_2,T_b] :
% 179.23/179.43 ( 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)))))
% 179.23/179.43 <=> V_b_2 = V_a_2 ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_singletonE,axiom,
% 179.23/179.43 ! [V_a_2,V_b_2,T_b] :
% 179.23/179.43 ( 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)))))
% 179.23/179.43 => V_b_2 = V_a_2 ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_hoare__derivs_OIf,axiom,
% 179.23/179.43 ! [V_d_2,V_Qa_2,V_ca_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 179.23/179.43 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_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))))
% 179.23/179.43 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_P_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))))
% 179.23/179.43 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_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)))) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup1CI,axiom,
% 179.23/179.43 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 179.23/179.43 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 179.23/179.43 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup1E,axiom,
% 179.23/179.43 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 179.23/179.43 ( 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))
% 179.23/179.43 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 179.23/179.43 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup__fun__def,axiom,
% 179.23/179.43 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 179.23/179.43 ( class_Lattices_Olattice(T_b)
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup__Un__eq,axiom,
% 179.23/179.43 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 179.23/179.43 ( 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))
% 179.23/179.43 <=> 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))) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_bot__empty__eq,axiom,
% 179.23/179.43 ! [V_x_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 179.23/179.43 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup__apply,axiom,
% 179.23/179.43 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 179.23/179.43 ( class_Lattices_Olattice(T_b)
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup__bot__left,axiom,
% 179.23/179.43 ! [V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Obounded__lattice__bot(T_a)
% 179.23/179.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup__bot__right,axiom,
% 179.23/179.43 ! [V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Obounded__lattice__bot(T_a)
% 179.23/179.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup__eq__bot__iff,axiom,
% 179.23/179.43 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.43 ( class_Lattices_Obounded__lattice__bot(T_b)
% 179.23/179.43 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 179.23/179.43 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 179.23/179.43 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_K__record__comp,axiom,
% 179.23/179.43 ! [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 ).
% 179.23/179.43
% 179.23/179.43 fof(fact_o__def,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_com_Osimps_I4_J,axiom,
% 179.23/179.43 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 179.23/179.43 ( 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)
% 179.23/179.43 <=> ( V_fun_2 = V_fun_H_2
% 179.23/179.43 & V_com1_2 = V_com1_H_2
% 179.23/179.43 & V_com2_2 = V_com2_H_2 ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_com_Osimps_I53_J,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_com_Osimps_I52_J,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_com_Osimps_I26_J,axiom,
% 179.23/179.43 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_com_Osimps_I27_J,axiom,
% 179.23/179.43 ! [V_fun_2,V_vname_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_com_Osimps_I44_J,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_com_Osimps_I45_J,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_com_Osimps_I14_J,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_com_Osimps_I15_J,axiom,
% 179.23/179.43 ! [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 ).
% 179.23/179.43
% 179.23/179.43 fof(fact_com_Osimps_I68_J,axiom,
% 179.23/179.43 ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_eq__mem,axiom,
% 179.23/179.43 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 179.23/179.43 <=> V_x_2 = V_y_2 ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup_Oidem,axiom,
% 179.23/179.43 ! [V_a,T_a] :
% 179.23/179.43 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup__idem,axiom,
% 179.23/179.43 ! [V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup_Ocommute,axiom,
% 179.23/179.43 ! [V_b,V_a,T_a] :
% 179.23/179.43 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.43 => 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) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_inf__sup__aci_I5_J,axiom,
% 179.23/179.43 ! [V_y,V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Olattice(T_a)
% 179.23/179.43 => 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) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup__commute,axiom,
% 179.23/179.43 ! [V_y,V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.43 => 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) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup_Oleft__idem,axiom,
% 179.23/179.43 ! [V_b,V_a,T_a] :
% 179.23/179.43 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.43 => 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) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_inf__sup__aci_I8_J,axiom,
% 179.23/179.43 ! [V_y,V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Olattice(T_a)
% 179.23/179.43 => 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) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup__left__idem,axiom,
% 179.23/179.43 ! [V_y,V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.43 => 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) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup_Oleft__commute,axiom,
% 179.23/179.43 ! [V_c,V_a,V_b,T_a] :
% 179.23/179.43 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_inf__sup__aci_I7_J,axiom,
% 179.23/179.43 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Olattice(T_a)
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup__left__commute,axiom,
% 179.23/179.43 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup_Oassoc,axiom,
% 179.23/179.43 ! [V_c,V_b,V_a,T_a] :
% 179.23/179.43 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_inf__sup__aci_I6_J,axiom,
% 179.23/179.43 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Olattice(T_a)
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup__assoc,axiom,
% 179.23/179.43 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup1I1,axiom,
% 179.23/179.43 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 179.23/179.43 ( hBOOL(hAPP(V_A_2,V_x_2))
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_sup1I2,axiom,
% 179.23/179.43 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 179.23/179.43 ( hBOOL(hAPP(V_B_2,V_x_2))
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_o__assoc,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_o__apply,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_o__eq__dest__lhs,axiom,
% 179.23/179.43 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 179.23/179.43 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_ca_2
% 179.23/179.43 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_o__eq__dest,axiom,
% 179.23/179.43 ! [V_v_2,V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 179.23/179.43 ( 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)
% 179.23/179.43 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_o__eq__elim,axiom,
% 179.23/179.43 ! [V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 179.23/179.43 ( 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)
% 179.23/179.43 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_pred__equals__eq,axiom,
% 179.23/179.43 ! [V_S_2,V_R_2,T_b] :
% 179.23/179.43 ( 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)
% 179.23/179.43 <=> V_R_2 = V_S_2 ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_the__inv__into__def,axiom,
% 179.23/179.43 ! [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))) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_override__on__def,axiom,
% 179.23/179.43 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 179.23/179.43 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.43 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) )
% 179.23/179.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.43 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_comp__cong,axiom,
% 179.23/179.43 ! [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] :
% 179.23/179.43 ( 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))
% 179.23/179.43 => 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) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Sup__fin_Oidem,axiom,
% 179.23/179.43 ! [V_x,T_a] :
% 179.23/179.43 ( class_Lattices_Olattice(T_a)
% 179.23/179.43 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_override__on__emptyset,axiom,
% 179.23/179.43 ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2 ).
% 179.23/179.43
% 179.23/179.43 fof(fact_image__constant,axiom,
% 179.23/179.43 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.43 => 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))) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_override__on__apply__notin,axiom,
% 179.23/179.43 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 179.23/179.43 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.43 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_override__on__apply__in,axiom,
% 179.23/179.43 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.43 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimage__insert,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimage__singleton__eq,axiom,
% 179.23/179.43 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 179.23/179.43 ( 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))))))
% 179.23/179.43 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_insert__Diff,axiom,
% 179.23/179.43 ! [V_A_2,V_a_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.43 => 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 ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_image__eqI,axiom,
% 179.23/179.43 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 179.23/179.43 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 179.23/179.43 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 179.23/179.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_DiffI,axiom,
% 179.23/179.43 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 179.23/179.43 => 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))) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_DiffE,axiom,
% 179.23/179.43 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.43 ( 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)))
% 179.23/179.43 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimageI,axiom,
% 179.23/179.43 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 179.23/179.43 ( hAPP(V_f_2,V_a_2) = V_b_2
% 179.23/179.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 179.23/179.43 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_fun__diff__def,axiom,
% 179.23/179.43 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 179.23/179.43 ( class_Groups_Ominus(T_b)
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_minus__apply,axiom,
% 179.23/179.43 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 179.23/179.43 ( class_Groups_Ominus(T_b)
% 179.23/179.43 => 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)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimage__Diff,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Diff__idemp,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimage__code,axiom,
% 179.23/179.43 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 179.23/179.43 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_image__image,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_image__ident,axiom,
% 179.23/179.43 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimage__ident,axiom,
% 179.23/179.43 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 179.23/179.43
% 179.23/179.43 fof(fact_image__iff,axiom,
% 179.23/179.43 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 179.23/179.43 <=> ? [B_x] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.23/179.43 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_imageI,axiom,
% 179.23/179.43 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.43 => 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))) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_rev__image__eqI,axiom,
% 179.23/179.43 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.43 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 179.23/179.43 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_empty__is__image,axiom,
% 179.23/179.43 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.43 ( 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)
% 179.23/179.43 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_image__empty,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_image__is__empty,axiom,
% 179.23/179.43 ! [V_A_2,V_f_2,T_b,T_c] :
% 179.23/179.43 ( 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))
% 179.23/179.43 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_image__insert,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_image__Un,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_image__compose,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Diff__iff,axiom,
% 179.23/179.43 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.43 ( 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)))
% 179.23/179.43 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.43 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_DiffD1,axiom,
% 179.23/179.43 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.43 ( 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)))
% 179.23/179.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_DiffD2,axiom,
% 179.23/179.43 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.43 ( 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)))
% 179.23/179.43 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimage__eq,axiom,
% 179.23/179.43 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 179.23/179.43 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimageD,axiom,
% 179.23/179.43 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 179.23/179.43 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimageI2,axiom,
% 179.23/179.43 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 179.23/179.43 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_empty__Diff,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Diff__empty,axiom,
% 179.23/179.43 ! [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 ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Diff__cancel,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimage__empty,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Un__Diff__cancel,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Un__Diff__cancel2,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Un__Diff,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimage__Un,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimage__compose,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimage__Collect__eq,axiom,
% 179.23/179.43 ! [V_P_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_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_insert__image,axiom,
% 179.23/179.43 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.43 => 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) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_insert__Diff1,axiom,
% 179.23/179.43 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 179.23/179.43 => 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) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_insert__Diff__if,axiom,
% 179.23/179.43 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 179.23/179.43 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 179.23/179.43 => 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) )
% 179.23/179.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 179.23/179.43 => 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)) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Diff__insert,axiom,
% 179.23/179.43 ! [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)))) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Diff__insert2,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_insert__Diff__single,axiom,
% 179.23/179.43 ! [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) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_image__constant__conv,axiom,
% 179.23/179.43 ! [V_ca_2,T_c,T_b,V_A_2] :
% 179.23/179.43 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.43 => 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)) )
% 179.23/179.43 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.43 => 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))) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_set__diff__eq,axiom,
% 179.23/179.43 ! [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)))) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_vimage__def,axiom,
% 179.23/179.43 ! [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)) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_Diff__insert__absorb,axiom,
% 179.23/179.43 ! [V_A_2,V_x_2,T_b] :
% 179.23/179.43 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.43 => 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 ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_fun__upd__image,axiom,
% 179.23/179.43 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 179.23/179.43 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.43 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
% 179.23/179.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.43 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ) ).
% 179.23/179.43
% 179.23/179.43 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 179.23/179.43 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 179.23/179.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.44 => ( 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)
% 179.23/179.44 => 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)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__insert,axiom,
% 179.23/179.44 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 179.23/179.44 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.44 & ~ 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))))))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_subset__insert__iff,axiom,
% 179.23/179.44 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 179.23/179.44 ( 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)))
% 179.23/179.44 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.44 => 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)) )
% 179.23/179.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_diff__single__insert,axiom,
% 179.23/179.44 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 179.23/179.44 ( 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))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.44 => 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))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_the__inv__into__comp,axiom,
% 179.23/179.44 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 179.23/179.44 ( 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))
% 179.23/179.44 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 179.23/179.44 => ( 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))))
% 179.23/179.44 => 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) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_imageE,axiom,
% 179.23/179.44 ! [V_A_2,V_f_2,T_c,V_b_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 179.23/179.44 => ~ ! [B_x] :
% 179.23/179.44 ( V_b_2 = hAPP(V_f_2,B_x)
% 179.23/179.44 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_vimage__const,axiom,
% 179.23/179.44 ! [T_c,V_A_2,V_ca_2,T_b] :
% 179.23/179.44 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.44 => 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)) )
% 179.23/179.44 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.44 => 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)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_vimageE,axiom,
% 179.23/179.44 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_if__image__distrib,axiom,
% 179.23/179.44 ! [V_S_2,V_g_2,V_f_2,V_P_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_P_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_P_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_P_2))))) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__left__comm__idem__remove,axiom,
% 179.23/179.44 ! [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))))) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_order__refl,axiom,
% 179.23/179.44 ! [V_x,T_a] :
% 179.23/179.44 ( class_Orderings_Opreorder(T_a)
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_equalityI,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.23/179.44 => V_A_2 = V_B_2 ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_top1I,axiom,
% 179.23/179.44 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf1E,axiom,
% 179.23/179.44 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 179.23/179.44 ( 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))
% 179.23/179.44 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 179.23/179.44 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf1I,axiom,
% 179.23/179.44 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 179.23/179.44 ( hBOOL(hAPP(V_A_2,V_x_2))
% 179.23/179.44 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 179.23/179.44 => 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)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__upd__triv,axiom,
% 179.23/179.44 ! [V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ).
% 179.23/179.44
% 179.23/179.44 fof(fact_subsetD,axiom,
% 179.23/179.44 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_UNIV__I,axiom,
% 179.23/179.44 ! [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)))) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_IntE,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.44 ( 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)))
% 179.23/179.44 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.44 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_IntI,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 179.23/179.44 => 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))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_empty__subsetI,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__empty,axiom,
% 179.23/179.44 ! [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))) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_image__Int,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__image__subset__iff,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => ( 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)))
% 179.23/179.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__image__Int,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 179.23/179.44 => 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)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Inf__fin_Oidem,axiom,
% 179.23/179.44 ! [V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__left__comm__idem__inf,axiom,
% 179.23/179.44 ! [T_b] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_b)
% 179.23/179.44 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 179.23/179.44 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 179.23/179.44 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 179.23/179.44 => 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) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_linorder__le__cases,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Orderings_Olinorder(T_a)
% 179.23/179.44 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__funE,axiom,
% 179.23/179.44 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 179.23/179.44 ( class_Orderings_Oord(T_c)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 179.23/179.44 => 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))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_equalityE,axiom,
% 179.23/179.44 ! [T_b,V_B_2,V_A_2] :
% 179.23/179.44 ( V_A_2 = V_B_2
% 179.23/179.44 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__mono,axiom,
% 179.23/179.44 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 179.23/179.44 => 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))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__greatest,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 179.23/179.44 => 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))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_xt1_I6_J,axiom,
% 179.23/179.44 ! [V_z,V_x,V_y,T_a] :
% 179.23/179.44 ( class_Orderings_Oorder(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_xt1_I5_J,axiom,
% 179.23/179.44 ! [V_x,V_y,T_a] :
% 179.23/179.44 ( class_Orderings_Oorder(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.44 => V_x = V_y ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_order__trans,axiom,
% 179.23/179.44 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.44 ( class_Orderings_Opreorder(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_order__antisym,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Orderings_Oorder(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.23/179.44 => V_x = V_y ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_xt1_I4_J,axiom,
% 179.23/179.44 ! [V_c,V_a,V_b,T_a] :
% 179.23/179.44 ( class_Orderings_Oorder(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 179.23/179.44 => ( V_b = V_c
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_ord__le__eq__trans,axiom,
% 179.23/179.44 ! [V_c,V_b,V_a,T_a] :
% 179.23/179.44 ( class_Orderings_Oord(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.23/179.44 => ( V_b = V_c
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_subset__trans,axiom,
% 179.23/179.44 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_xt1_I3_J,axiom,
% 179.23/179.44 ! [V_c,V_b,V_a,T_a] :
% 179.23/179.44 ( class_Orderings_Oorder(T_a)
% 179.23/179.44 => ( V_a = V_b
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_ord__eq__le__trans,axiom,
% 179.23/179.44 ! [V_c,V_b,V_a,T_a] :
% 179.23/179.44 ( class_Orderings_Oord(T_a)
% 179.23/179.44 => ( V_a = V_b
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_order__antisym__conv,axiom,
% 179.23/179.44 ! [V_x_2,V_y_2,T_b] :
% 179.23/179.44 ( class_Orderings_Oorder(T_b)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.23/179.44 <=> V_x_2 = V_y_2 ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__absorb1,axiom,
% 179.23/179.44 ! [V_A_2,V_B_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.23/179.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__absorb2,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__funD,axiom,
% 179.23/179.44 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 179.23/179.44 ( class_Orderings_Oord(T_c)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 179.23/179.44 => 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))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_order__eq__refl,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Orderings_Opreorder(T_a)
% 179.23/179.44 => ( V_x = V_y
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_equalityD2,axiom,
% 179.23/179.44 ! [T_b,V_B_2,V_A_2] :
% 179.23/179.44 ( V_A_2 = V_B_2
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_equalityD1,axiom,
% 179.23/179.44 ! [T_b,V_B_2,V_A_2] :
% 179.23/179.44 ( V_A_2 = V_B_2
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__assoc,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__left__commute,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__left__absorb,axiom,
% 179.23/179.44 ! [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) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_order__eq__iff,axiom,
% 179.23/179.44 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.44 ( class_Orderings_Oorder(T_b)
% 179.23/179.44 => ( V_x_2 = V_y_2
% 179.23/179.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.23/179.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_set__eq__subset,axiom,
% 179.23/179.44 ! [T_b,V_B_2,V_A_2] :
% 179.23/179.44 ( V_A_2 = V_B_2
% 179.23/179.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_linorder__linear,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Orderings_Olinorder(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__commute,axiom,
% 179.23/179.44 ! [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) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__fun__def,axiom,
% 179.23/179.44 ! [V_g_2,V_f_2,T_b,T_c] :
% 179.23/179.44 ( class_Orderings_Oord(T_c)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 179.23/179.44 <=> ! [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))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__lower2,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__lower1,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__absorb,axiom,
% 179.23/179.44 ! [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 ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__UNIV__right,axiom,
% 179.23/179.44 ! [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 ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__UNIV__left,axiom,
% 179.23/179.44 ! [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 ).
% 179.23/179.44
% 179.23/179.44 fof(fact_top__apply,axiom,
% 179.23/179.44 ! [V_x_2,T_c,T_b] :
% 179.23/179.44 ( class_Orderings_Otop(T_b)
% 179.23/179.44 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_subset__refl,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_top__greatest,axiom,
% 179.23/179.44 ! [V_x,T_a] :
% 179.23/179.44 ( class_Orderings_Otop(T_a)
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_subset__UNIV,axiom,
% 179.23/179.44 ! [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)))) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf1D2,axiom,
% 179.23/179.44 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 179.23/179.44 ( 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))
% 179.23/179.44 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf1D1,axiom,
% 179.23/179.44 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 179.23/179.44 ( 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))
% 179.23/179.44 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__upd__idem,axiom,
% 179.23/179.44 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 179.23/179.44 ( hAPP(V_f_2,V_x_2) = V_y_2
% 179.23/179.44 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__infE,axiom,
% 179.23/179.44 ! [V_b,V_a,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => ( 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)))
% 179.23/179.44 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 179.23/179.44 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__mono,axiom,
% 179.23/179.44 ! [V_d,V_b,V_c,V_a,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 179.23/179.44 => 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))) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__greatest,axiom,
% 179.23/179.44 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 179.23/179.44 => 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))) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__infI,axiom,
% 179.23/179.44 ! [V_b,V_a,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 179.23/179.44 => 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))) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__Int,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.44 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 179.23/179.44 => 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)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_subset__inj__on,axiom,
% 179.23/179.44 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.44 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_predicate1D,axiom,
% 179.23/179.44 ! [V_x_2,V_Qa_2,V_P_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Qa_2))
% 179.23/179.44 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.23/179.44 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__absorb2,axiom,
% 179.23/179.44 ! [V_x,V_y,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.23/179.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__absorb1,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__infI2,axiom,
% 179.23/179.44 ! [V_a,V_x,V_b,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 179.23/179.44 => 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)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__infI1,axiom,
% 179.23/179.44 ! [V_b,V_x,V_a,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 179.23/179.44 => 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)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_injD,axiom,
% 179.23/179.44 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 179.23/179.44 => V_x_2 = V_y_2 ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__eq,axiom,
% 179.23/179.44 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 179.23/179.44 <=> V_x_2 = V_y_2 ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__fun,axiom,
% 179.23/179.44 ! [T_d,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => 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))) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_rev__predicate1D,axiom,
% 179.23/179.44 ! [V_Qa_2,T_b,V_x_2,V_P_2] :
% 179.23/179.44 ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Qa_2))
% 179.23/179.44 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__upd__other,axiom,
% 179.23/179.44 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 179.23/179.44 ( V_z_2 != V_x_2
% 179.23/179.44 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__upd__twist,axiom,
% 179.23/179.44 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] :
% 179.23/179.44 ( V_a_2 != V_ca_2
% 179.23/179.44 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_a_2),V_b_2)),V_ca_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_ca_2),V_d_2)),V_a_2),V_b_2) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__upd__apply,axiom,
% 179.23/179.44 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 179.23/179.44 ( ( V_z_2 = V_x_2
% 179.23/179.44 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 )
% 179.23/179.44 & ( V_z_2 != V_x_2
% 179.23/179.44 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__upd__same,axiom,
% 179.23/179.44 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__upd__upd,axiom,
% 179.23/179.44 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_z_2) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__apply,axiom,
% 179.23/179.44 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( class_Lattices_Olattice(T_b)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__upd__idem__iff,axiom,
% 179.23/179.44 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
% 179.23/179.44 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__assoc,axiom,
% 179.23/179.44 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__sup__aci_I2_J,axiom,
% 179.23/179.44 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf_Oassoc,axiom,
% 179.23/179.44 ! [V_c,V_b,V_a,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__eq__top__iff,axiom,
% 179.23/179.44 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.44 ( class_Lattices_Obounded__lattice__top(T_b)
% 179.23/179.44 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 179.23/179.44 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 179.23/179.44 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__inf__iff,axiom,
% 179.23/179.44 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_b)
% 179.23/179.44 => ( 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)))
% 179.23/179.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.23/179.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__left__commute,axiom,
% 179.23/179.44 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__sup__aci_I3_J,axiom,
% 179.23/179.44 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf_Oleft__commute,axiom,
% 179.23/179.44 ! [V_c,V_a,V_b,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__left__idem,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => 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) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__sup__aci_I4_J,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf_Oleft__idem,axiom,
% 179.23/179.44 ! [V_b,V_a,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => 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) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__iff__inf,axiom,
% 179.23/179.44 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_b)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.23/179.44 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__def,axiom,
% 179.23/179.44 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.44 <=> ! [B_x] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.23/179.44 => ! [B_xa] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 179.23/179.44 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 179.23/179.44 => B_x = B_xa ) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__commute,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => 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) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__sup__aci_I1_J,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf_Ocommute,axiom,
% 179.23/179.44 ! [V_b,V_a,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => 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) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__fun__def,axiom,
% 179.23/179.44 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( class_Lattices_Olattice(T_b)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__le2,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__sup__ord_I2_J,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__le1,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__sup__ord_I1_J,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__idem,axiom,
% 179.23/179.44 ! [V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf_Oidem,axiom,
% 179.23/179.44 ! [V_a,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__top__right,axiom,
% 179.23/179.44 ! [V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Obounded__lattice__top(T_a)
% 179.23/179.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__top__left,axiom,
% 179.23/179.44 ! [V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Obounded__lattice__top(T_a)
% 179.23/179.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__image__eq__iff,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => ( 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)
% 179.23/179.44 <=> V_A_2 = V_B_2 ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__comp,axiom,
% 179.23/179.44 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 179.23/179.44 => 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))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_distrib__inf__le,axiom,
% 179.23/179.44 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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)))) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_distrib__sup__le,axiom,
% 179.23/179.44 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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)))) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__id2,axiom,
% 179.23/179.44 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_image__Int__subset,axiom,
% 179.23/179.44 ! [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)))) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Un__Int__assoc__eq,axiom,
% 179.23/179.44 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 179.23/179.44 ( 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))
% 179.23/179.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_vimage__subsetI,axiom,
% 179.23/179.44 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => ( 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)))
% 179.23/179.44 => 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)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_the__inv__f__f,axiom,
% 179.23/179.44 ! [V_x_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => 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 ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__upd__def,axiom,
% 179.23/179.44 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 179.23/179.44 ( ( V_x_2 = V_a_2
% 179.23/179.44 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 )
% 179.23/179.44 & ( V_x_2 != V_a_2
% 179.23/179.44 => hAPP(hAPP(hAPP(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) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__left__comm__idem__insert,axiom,
% 179.23/179.44 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_range__ex1__eq,axiom,
% 179.23/179.44 ! [V_b_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => ( 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)))))
% 179.23/179.44 <=> ? [B_x] :
% 179.23/179.44 ( V_b_2 = hAPP(V_f_2,B_x)
% 179.23/179.44 & ! [B_y] :
% 179.23/179.44 ( V_b_2 = hAPP(V_f_2,B_y)
% 179.23/179.44 => B_y = B_x ) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__image__mem__iff,axiom,
% 179.23/179.44 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => ( 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)))
% 179.23/179.44 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__left__comm__idem__sup,axiom,
% 179.23/179.44 ! [T_b] :
% 179.23/179.44 ( class_Lattices_Osemilattice__sup(T_b)
% 179.23/179.44 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__image__set__diff,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 179.23/179.44 => 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)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_image__set__diff,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 179.23/179.44 ! [V_x_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 179.23/179.44 => 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) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__contraD,axiom,
% 179.23/179.44 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.44 => ( V_x_2 != V_y_2
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 179.23/179.44 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__iff,axiom,
% 179.23/179.44 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 179.23/179.44 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 179.23/179.44 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__onD,axiom,
% 179.23/179.44 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.44 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 179.23/179.44 => V_x_2 = V_y_2 ) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__vimage__image__eq,axiom,
% 179.23/179.44 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.44 => 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 ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__fun__updI,axiom,
% 179.23/179.44 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 179.23/179.44 => c_Fun_Oinj__on(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__imageI2,axiom,
% 179.23/179.44 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 179.23/179.44 ( 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)
% 179.23/179.44 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_image__vimage__eq,axiom,
% 179.23/179.44 ! [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)))) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__on__diff,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.44 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__bot__right,axiom,
% 179.23/179.44 ! [V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Obounded__lattice__bot(T_a)
% 179.23/179.44 => 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) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__bot__left,axiom,
% 179.23/179.44 ! [V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Obounded__lattice__bot(T_a)
% 179.23/179.44 => 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) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_vimage__subsetD,axiom,
% 179.23/179.44 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 179.23/179.44 ( 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))
% 179.23/179.44 => ( 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))
% 179.23/179.44 => 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))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__sup__absorb,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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 ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_sup__inf__absorb,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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 ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__sup__distrib1,axiom,
% 179.23/179.44 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Odistrib__lattice(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_sup__inf__distrib1,axiom,
% 179.23/179.44 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Odistrib__lattice(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__sup__distrib2,axiom,
% 179.23/179.44 ! [V_x,V_z,V_y,T_a] :
% 179.23/179.44 ( class_Lattices_Odistrib__lattice(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_sup__inf__distrib2,axiom,
% 179.23/179.44 ! [V_x,V_z,V_y,T_a] :
% 179.23/179.44 ( class_Lattices_Odistrib__lattice(T_a)
% 179.23/179.44 => 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)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 179.23/179.44 ! [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) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 179.23/179.44 ! [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) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inj__singleton,axiom,
% 179.23/179.44 ! [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))) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_IntD2,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.44 ( 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)))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_IntD1,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.44 ( 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)))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__iff,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.44 ( 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)))
% 179.23/179.44 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.44 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_disjoint__iff__not__equal,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.44 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.44 <=> ! [B_x] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.23/179.44 => ! [B_xa] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 179.23/179.44 => B_x != B_xa ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__empty__right,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__empty__left,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_insert__inter__insert,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_set__mp,axiom,
% 179.23/179.44 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_set__rev__mp,axiom,
% 179.23/179.44 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_in__mono,axiom,
% 179.23/179.44 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 179.23/179.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_iso__tuple__UNIV__I,axiom,
% 179.23/179.44 ! [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)))) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_bot__least,axiom,
% 179.23/179.44 ! [V_x,T_a] :
% 179.23/179.44 ( class_Orderings_Obot(T_a)
% 179.23/179.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Un__Int__crazy,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Un__Int__distrib2,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__Un__distrib2,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Un__Int__distrib,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_Int__Un__distrib,axiom,
% 179.23/179.44 ! [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)) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_subset__empty,axiom,
% 179.23/179.44 ! [V_A_2,T_b] :
% 179.23/179.44 ( 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))))
% 179.23/179.44 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__sup__ord_I3_J,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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))) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_sup__ge1,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.44 => 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))) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_inf__sup__ord_I4_J,axiom,
% 179.23/179.44 ! [V_x,V_y,T_a] :
% 179.23/179.44 ( class_Lattices_Olattice(T_a)
% 179.23/179.44 => 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))) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_sup__ge2,axiom,
% 179.23/179.44 ! [V_x,V_y,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.44 => 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))) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__iff__sup,axiom,
% 179.23/179.44 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.44 ( class_Lattices_Osemilattice__sup(T_b)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.23/179.44 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__sup__iff,axiom,
% 179.23/179.44 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 179.23/179.44 ( class_Lattices_Osemilattice__sup(T_b)
% 179.23/179.44 => ( 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))
% 179.23/179.44 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 179.23/179.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__supI1,axiom,
% 179.23/179.44 ! [V_b,V_a,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 179.23/179.44 => 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))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__supI2,axiom,
% 179.23/179.44 ! [V_a,V_b,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 179.23/179.44 => 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))) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_sup__absorb2,axiom,
% 179.23/179.44 ! [V_y,V_x,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_sup__absorb1,axiom,
% 179.23/179.44 ! [V_x,V_y,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.23/179.44 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_le__supI,axiom,
% 179.23/179.44 ! [V_b,V_x,V_a,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 179.23/179.44 => 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)) ) ) ) ).
% 179.23/179.44
% 179.23/179.44 fof(fact_sup__least,axiom,
% 179.23/179.44 ! [V_z,V_x,V_y,T_a] :
% 179.23/179.44 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.23/179.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 179.23/179.45 => 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)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_sup__mono,axiom,
% 179.23/179.45 ! [V_d,V_b,V_c,V_a,T_a] :
% 179.23/179.45 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 179.23/179.45 => 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))) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_le__supE,axiom,
% 179.23/179.45 ! [V_x,V_b,V_a,T_a] :
% 179.23/179.45 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.45 => ( 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))
% 179.23/179.45 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 179.23/179.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_UNIV__not__empty,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__Int2,axiom,
% 179.23/179.45 ! [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) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__Int__distrib2,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Int__Diff,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__Int__distrib,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_insert__mono,axiom,
% 179.23/179.45 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 179.23/179.45 => 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))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_subset__insertI2,axiom,
% 179.23/179.45 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => 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))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_subset__insertI,axiom,
% 179.23/179.45 ! [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))) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_image__mono,axiom,
% 179.23/179.45 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_subset__image__iff,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 <=> ? [B_AA] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 179.23/179.45 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Un__mono,axiom,
% 179.23/179.45 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 179.23/179.45 => 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))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Un__least,axiom,
% 179.23/179.45 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 179.23/179.45 => 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)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Un__absorb2,axiom,
% 179.23/179.45 ! [V_A_2,V_B_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.23/179.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Un__absorb1,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_subset__Un__eq,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Un__upper2,axiom,
% 179.23/179.45 ! [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))) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Un__upper1,axiom,
% 179.23/179.45 ! [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))) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Un__UNIV__right,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Un__UNIV__left,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_double__diff,axiom,
% 179.23/179.45 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 179.23/179.45 => 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 ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__mono,axiom,
% 179.23/179.45 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 179.23/179.45 => 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))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__subset,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_vimage__Int,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_thin,axiom,
% 179.23/179.45 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 179.23/179.45 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
% 179.23/179.45 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_weaken,axiom,
% 179.23/179.45 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] :
% 179.23/179.45 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 179.23/179.45 => ( 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))
% 179.23/179.45 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_asm,axiom,
% 179.23/179.45 ! [V_Ga_2,V_ts_2,T_b] :
% 179.23/179.45 ( 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))
% 179.23/179.45 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_vimage__mono,axiom,
% 179.23/179.45 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => 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))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_vimage__UNIV,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inj__vimage__singleton,axiom,
% 179.23/179.45 ! [V_a_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.45 => 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))))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inf__Int__eq,axiom,
% 179.23/179.45 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 179.23/179.45 ( 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))
% 179.23/179.45 <=> 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))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Collect__conj__eq,axiom,
% 179.23/179.45 ! [V_Qa_2,V_P_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_P_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_P_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_pred__subset__eq,axiom,
% 179.23/179.45 ! [V_S_2,V_R_2,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_the__inv__into__into,axiom,
% 179.23/179.45 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => 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)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_UNIV__def,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_range__composition,axiom,
% 179.23/179.45 ! [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)))) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fun__upd__comp,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_d),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_sup__top__left,axiom,
% 179.23/179.45 ! [V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Obounded__lattice__top(T_a)
% 179.23/179.45 => 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) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_sup__top__right,axiom,
% 179.23/179.45 ! [V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Obounded__lattice__top(T_a)
% 179.23/179.45 => 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) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inj__on__Un,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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))
% 179.23/179.45 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 179.23/179.45 & 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)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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))
% 179.23/179.45 => ( 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)
% 179.23/179.45 <=> V_A_2 = V_B_2 ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inj__on__imageI,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 179.23/179.45 ( 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)
% 179.23/179.45 => 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)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_comp__inj__on,axiom,
% 179.23/179.45 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 => ( 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))
% 179.23/179.45 => 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) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_comp__inj__on__iff,axiom,
% 179.23/179.45 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 => ( 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))
% 179.23/179.45 <=> 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) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Int__insert__right,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 179.23/179.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.45 => 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)) )
% 179.23/179.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.45 => 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) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Int__insert__left,axiom,
% 179.23/179.45 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 179.23/179.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 179.23/179.45 => 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)) )
% 179.23/179.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 179.23/179.45 => 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) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Int__insert__right__if0,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 179.23/179.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.45 => 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) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Int__insert__left__if0,axiom,
% 179.23/179.45 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 179.23/179.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 179.23/179.45 => 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) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Int__insert__right__if1,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.45 => 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)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Int__insert__left__if1,axiom,
% 179.23/179.45 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 179.23/179.45 => 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)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__disjoint,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__triv,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_insert__subset,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 179.23/179.45 ( 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))
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 179.23/179.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_subset__insert,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 179.23/179.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => ( 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)))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_the__inv__into__f__eq,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_the__inv__into__f__f,axiom,
% 179.23/179.45 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => 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 ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_range__eqI,axiom,
% 179.23/179.45 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 179.23/179.45 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 179.23/179.45 => 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))))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_rangeI,axiom,
% 179.23/179.45 ! [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))))) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Un__Diff__Int,axiom,
% 179.23/179.45 ! [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 ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__Un,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__Int,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_subset__singletonD,axiom,
% 179.23/179.45 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.45 ( 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)))))
% 179.23/179.45 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.45 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_the__inv__into__onto,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 => 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 ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inj__on__the__inv__into,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 => 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)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__UNIV,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_comp__surj,axiom,
% 179.23/179.45 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 179.23/179.45 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.45 => ( 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))
% 179.23/179.45 => 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)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_image__diff__subset,axiom,
% 179.23/179.45 ! [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)))) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__partition,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => 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 ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__subset__conv,axiom,
% 179.23/179.45 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( 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))
% 179.23/179.45 <=> 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))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_image__vimage__subset,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_surj__image__vimage__eq,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_b,T_c] :
% 179.23/179.45 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.45 => 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 ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Int__Collect,axiom,
% 179.23/179.45 ! [V_P_2,V_A_2,V_x_2,T_b] :
% 179.23/179.45 ( 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_P_2))))
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Int__def,axiom,
% 179.23/179.45 ! [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))) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_f__the__inv__into__f,axiom,
% 179.23/179.45 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 179.23/179.45 => 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 ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inj__on__iff__surj,axiom,
% 179.23/179.45 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 179.23/179.45 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.45 => ( ? [B_f] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 179.23/179.45 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2)) )
% 179.23/179.45 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_flat__lub__def,axiom,
% 179.23/179.45 ! [V_b_2,V_A_2,T_b] :
% 179.23/179.45 ( ( 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)))))
% 179.23/179.45 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 179.23/179.45 & ( ~ 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)))))
% 179.23/179.45 => 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)))))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 179.23/179.45 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 179.23/179.45 ( 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))
% 179.23/179.45 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.45 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 179.23/179.45 | ? [B_x,B_y] :
% 179.23/179.45 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 179.23/179.45 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 179.23/179.45 & 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) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_diff__eq__diff__less__eq,axiom,
% 179.23/179.45 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.23/179.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.23/179.45 => ( 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)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__fun_I1_J,axiom,
% 179.23/179.45 ! [V_g_2,V_f_2,T_b,T_c] :
% 179.23/179.45 ( ( class_Orderings_Oorder(T_c)
% 179.23/179.45 & class_Enum_Oenum(T_b) )
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 179.23/179.45 <=> 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))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_psubset__insert__iff,axiom,
% 179.23/179.45 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 179.23/179.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 179.23/179.45 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => 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)) )
% 179.23/179.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Int__Collect__mono,axiom,
% 179.23/179.45 ! [V_Qa_2,V_P_2,V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => ( ! [B_x] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.23/179.45 => ( hBOOL(hAPP(V_P_2,B_x))
% 179.23/179.45 => hBOOL(hAPP(V_Qa_2,B_x)) ) )
% 179.23/179.45 => 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_P_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)))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff1__fold__graph,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => 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))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_vimage__if,axiom,
% 179.23/179.45 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] :
% 179.23/179.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.45 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 179.23/179.45 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 179.23/179.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 179.23/179.45 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 179.23/179.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.45 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 179.23/179.45 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) )
% 179.23/179.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 179.23/179.45 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_rangeE,axiom,
% 179.23/179.45 ! [V_f_2,T_c,V_b_2,T_b] :
% 179.23/179.45 ( 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)))))
% 179.23/179.45 => ~ ! [B_x] : V_b_2 != hAPP(V_f_2,B_x) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_dom__override__on,axiom,
% 179.23/179.45 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Fun_Ooverride__on(T_b,tc_Option_Ooption(T_c),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2)))))),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_b,T_c,V_g_2))))) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inj__uminus,axiom,
% 179.23/179.45 ! [V_A_2,T_b] :
% 179.23/179.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.23/179.45 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_ComplI,axiom,
% 179.23/179.45 ! [V_A_2,V_ca_2,T_b] :
% 179.23/179.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fun__Compl__def,axiom,
% 179.23/179.45 ! [V_x_2,V_A_2,T_c,T_b] :
% 179.23/179.45 ( class_Groups_Ouminus(T_b)
% 179.23/179.45 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_double__compl,axiom,
% 179.23/179.45 ! [V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_uminus__apply,axiom,
% 179.23/179.45 ! [V_x_2,V_A_2,T_c,T_b] :
% 179.23/179.45 ( class_Groups_Ouminus(T_b)
% 179.23/179.45 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_compl__eq__compl__iff,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_b)
% 179.23/179.45 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 179.23/179.45 <=> V_x_2 = V_y_2 ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__less__irrefl,axiom,
% 179.23/179.45 ! [V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Opreorder(T_a)
% 179.23/179.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_double__complement,axiom,
% 179.23/179.45 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2 ).
% 179.23/179.45
% 179.23/179.45 fof(fact_linorder__neq__iff,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_b)
% 179.23/179.45 => ( V_x_2 != V_y_2
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 179.23/179.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_not__less__iff__gr__or__eq,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_b)
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 179.23/179.45 | V_x_2 = V_y_2 ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_linorder__less__linear,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 | V_x = V_y
% 179.23/179.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__eq__Compl__iff,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
% 179.23/179.45 <=> V_A_2 = V_B_2 ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_linorder__antisym__conv3,axiom,
% 179.23/179.45 ! [V_x_2,V_y_2,T_b] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_b)
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 179.23/179.45 <=> V_x_2 = V_y_2 ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_linorder__neqE,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_a)
% 179.23/179.45 => ( V_x != V_y
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_less__imp__neq,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => V_x != V_y ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__less__not__sym,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Opreorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__less__imp__not__less,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Opreorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__less__imp__not__eq,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => V_x != V_y ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__less__imp__not__eq2,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => V_y != V_x ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__less__asym_H,axiom,
% 179.23/179.45 ! [V_b,V_a,T_a] :
% 179.23/179.45 ( class_Orderings_Opreorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.23/179.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_xt1_I9_J,axiom,
% 179.23/179.45 ! [V_a,V_b,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 179.23/179.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_ord__eq__less__trans,axiom,
% 179.23/179.45 ! [V_c,V_b,V_a,T_a] :
% 179.23/179.45 ( class_Orderings_Oord(T_a)
% 179.23/179.45 => ( V_a = V_b
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_xt1_I1_J,axiom,
% 179.23/179.45 ! [V_c,V_b,V_a,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( V_a = V_b
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_psubset__trans,axiom,
% 179.23/179.45 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_ord__less__eq__trans,axiom,
% 179.23/179.45 ! [V_c,V_b,V_a,T_a] :
% 179.23/179.45 ( class_Orderings_Oord(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.23/179.45 => ( V_b = V_c
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_xt1_I2_J,axiom,
% 179.23/179.45 ! [V_c,V_a,V_b,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 179.23/179.45 => ( V_b = V_c
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__less__trans,axiom,
% 179.23/179.45 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Opreorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_xt1_I10_J,axiom,
% 179.23/179.45 ! [V_z,V_x,V_y,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__less__asym,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Opreorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_linorder__cases,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_a)
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => ( V_x != V_y
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_neg__less__iff__less,axiom,
% 179.23/179.45 ! [V_a_2,V_b_2,T_b] :
% 179.23/179.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_neg__equal__iff__equal,axiom,
% 179.23/179.45 ! [V_b_2,V_a_2,T_b] :
% 179.23/179.45 ( class_Groups_Ogroup__add(T_b)
% 179.23/179.45 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 179.23/179.45 <=> V_a_2 = V_b_2 ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_minus__less__iff,axiom,
% 179.23/179.45 ! [V_b_2,V_a_2,T_b] :
% 179.23/179.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_minus__equation__iff,axiom,
% 179.23/179.45 ! [V_b_2,V_a_2,T_b] :
% 179.23/179.45 ( class_Groups_Ogroup__add(T_b)
% 179.23/179.45 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 179.23/179.45 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_less__minus__iff,axiom,
% 179.23/179.45 ! [V_b_2,V_a_2,T_b] :
% 179.23/179.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_equation__minus__iff,axiom,
% 179.23/179.45 ! [V_b_2,V_a_2,T_b] :
% 179.23/179.45 ( class_Groups_Ogroup__add(T_b)
% 179.23/179.45 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 179.23/179.45 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_minus__minus,axiom,
% 179.23/179.45 ! [V_a,T_a] :
% 179.23/179.45 ( class_Groups_Ogroup__add(T_a)
% 179.23/179.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_le__imp__neg__le,axiom,
% 179.23/179.45 ! [V_b,V_a,T_a] :
% 179.23/179.45 ( class_Groups_Oordered__ab__group__add(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_neg__le__iff__le,axiom,
% 179.23/179.45 ! [V_a_2,V_b_2,T_b] :
% 179.23/179.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_minus__le__iff,axiom,
% 179.23/179.45 ! [V_b_2,V_a_2,T_b] :
% 179.23/179.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_le__minus__iff,axiom,
% 179.23/179.45 ! [V_b_2,V_a_2,T_b] :
% 179.23/179.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_minus__diff__eq,axiom,
% 179.23/179.45 ! [V_b,V_a,T_a] :
% 179.23/179.45 ( class_Groups_Oab__group__add(T_a)
% 179.23/179.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_all__code,axiom,
% 179.23/179.45 ! [V_P_2,T_b] :
% 179.23/179.45 ( class_Enum_Oenum(T_b)
% 179.23/179.45 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 179.23/179.45 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_enum__all,axiom,
% 179.23/179.45 ! [V_P_2,T_b] :
% 179.23/179.45 ( class_Enum_Oenum(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
% 179.23/179.45 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_diff__eq__diff__less,axiom,
% 179.23/179.45 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.23/179.45 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.23/179.45 => ( 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)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_compl__le__compl__iff,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_compl__mono,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__iff,axiom,
% 179.23/179.45 ! [V_A_2,V_ca_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 179.23/179.45 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_ComplD,axiom,
% 179.23/179.45 ! [V_A_2,V_ca_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 179.23/179.45 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_ComplE,axiom,
% 179.23/179.45 ! [V_A_2,V_ca_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 179.23/179.45 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_less__fun__def,axiom,
% 179.23/179.45 ! [V_g_2,V_f_2,T_b,T_c] :
% 179.23/179.45 ( class_Orderings_Oord(T_c)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 179.23/179.45 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__subset__Compl__iff,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__anti__mono,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_linorder__not__less,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_b)
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_linorder__not__le,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_b)
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_linorder__le__less__linear,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.45 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__less__le,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.45 ( class_Orderings_Oorder(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.23/179.45 & V_x_2 != V_y_2 ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_less__le__not__le,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.45 ( class_Orderings_Opreorder(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.23/179.45 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__le__less,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.45 ( class_Orderings_Oorder(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 179.23/179.45 | V_x_2 = V_y_2 ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_leI,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_a)
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_not__leE,axiom,
% 179.23/179.45 ! [V_x,V_y,T_a] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_a)
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_linorder__antisym__conv1,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_b)
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.23/179.45 <=> V_x_2 = V_y_2 ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__neq__le__trans,axiom,
% 179.23/179.45 ! [V_b,V_a,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( V_a != V_b
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_xt1_I12_J,axiom,
% 179.23/179.45 ! [V_b,V_a,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( V_a != V_b
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_leD,axiom,
% 179.23/179.45 ! [V_x,V_y,T_a] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.23/179.45 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__less__imp__le,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Opreorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_linorder__antisym__conv2,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,T_b] :
% 179.23/179.45 ( class_Orderings_Olinorder(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 179.23/179.45 <=> V_x_2 = V_y_2 ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__le__imp__less__or__eq,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 | V_x = V_y ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__le__neq__trans,axiom,
% 179.23/179.45 ! [V_b,V_a,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.23/179.45 => ( V_a != V_b
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_xt1_I11_J,axiom,
% 179.23/179.45 ! [V_a,V_b,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 179.23/179.45 => ( V_a != V_b
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__less__le__trans,axiom,
% 179.23/179.45 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Opreorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_xt1_I7_J,axiom,
% 179.23/179.45 ! [V_z,V_x,V_y,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__le__less__trans,axiom,
% 179.23/179.45 ! [V_z,V_y,V_x,T_a] :
% 179.23/179.45 ( class_Orderings_Opreorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_xt1_I8_J,axiom,
% 179.23/179.45 ! [V_z,V_x,V_y,T_a] :
% 179.23/179.45 ( class_Orderings_Oorder(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_psubsetD,axiom,
% 179.23/179.45 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_not__psubset__empty,axiom,
% 179.23/179.45 ! [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)))) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_less__supI2,axiom,
% 179.23/179.45 ! [V_a,V_b,V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 179.23/179.45 => 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))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_less__supI1,axiom,
% 179.23/179.45 ! [V_b,V_a,V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Osemilattice__sup(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 179.23/179.45 => 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))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_less__infI1,axiom,
% 179.23/179.45 ! [V_b,V_x,V_a,T_a] :
% 179.23/179.45 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 179.23/179.45 => 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)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_less__infI2,axiom,
% 179.23/179.45 ! [V_a,V_x,V_b,T_a] :
% 179.23/179.45 ( class_Lattices_Osemilattice__inf(T_a)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 179.23/179.45 => 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)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_psubset__eq,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 & V_A_2 != V_B_2 ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_subset__iff__psubset__eq,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 | V_A_2 = V_B_2 ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_psubset__imp__subset,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_psubset__subset__trans,axiom,
% 179.23/179.45 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_subset__psubset__trans,axiom,
% 179.23/179.45 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_vimage__Compl,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fold__graph_OemptyI,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_empty__fold__graphE,axiom,
% 179.23/179.45 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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))
% 179.23/179.45 => V_x_2 = V_z_2 ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Collect__neg__eq,axiom,
% 179.23/179.45 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inf__compl__bot,axiom,
% 179.23/179.45 ! [V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_compl__inf__bot,axiom,
% 179.23/179.45 ! [V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_diff__eq,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_compl__bot__eq,axiom,
% 179.23/179.45 ! [T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_compl__top__eq,axiom,
% 179.23/179.45 ! [T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_compl__inf,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_compl__sup,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_sup__compl__top,axiom,
% 179.23/179.45 ! [V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_compl__sup__top,axiom,
% 179.23/179.45 ! [V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_subset__Compl__self__eq,axiom,
% 179.23/179.45 ! [V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 179.23/179.45 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__UNIV__eq,axiom,
% 179.23/179.45 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__empty__eq,axiom,
% 179.23/179.45 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__disjoint2,axiom,
% 179.23/179.45 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__disjoint,axiom,
% 179.23/179.45 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__partition,axiom,
% 179.23/179.45 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__partition2,axiom,
% 179.23/179.45 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__Int,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__Un,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 179.23/179.45 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__Diff__eq,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__eq,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Diff__Compl,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inj__on__strict__subset,axiom,
% 179.23/179.45 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => 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))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Compl__eq,axiom,
% 179.23/179.45 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_Collect__imp__eq,axiom,
% 179.23/179.45 ! [V_Qa_2,V_P_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_P_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_P_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fold__graph_OinsertI,axiom,
% 179.23/179.45 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 179.23/179.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 179.23/179.45 => 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))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_dom__if,axiom,
% 179.23/179.45 ! [V_g_2,V_f_2,V_P_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),T_b),c_If(tc_Option_Ooption(T_c))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_g_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)))) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_disjoint__eq__subset__Compl,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_surj__Compl__image__subset,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_b,T_c] :
% 179.23/179.45 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_diff__eq__diff__eq,axiom,
% 179.23/179.45 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.23/179.45 ( class_Groups_Oab__group__add(T_b)
% 179.23/179.45 => ( 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)
% 179.23/179.45 => ( V_a_2 = V_b_2
% 179.23/179.45 <=> V_ca_2 = V_d_2 ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_compl__unique,axiom,
% 179.23/179.45 ! [V_y,V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Oboolean__algebra(T_a)
% 179.23/179.45 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 179.23/179.45 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 179.23/179.45 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inj__image__Compl__subset,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fold1Set_Ointros,axiom,
% 179.23/179.45 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.45 => 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)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_order__fun_I2_J,axiom,
% 179.23/179.45 ! [V_g_2,V_f_2,T_b,T_c] :
% 179.23/179.45 ( ( class_Orderings_Oorder(T_c)
% 179.23/179.45 & class_Enum_Oenum(T_b) )
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 179.23/179.45 & 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)))) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fold__graph__permute__diff,axiom,
% 179.23/179.45 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 179.23/179.45 ( class_Groups_Oab__semigroup__mult(T_b)
% 179.23/179.45 => ( 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))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 179.23/179.45 => 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)) ) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_restrict__fun__upd,axiom,
% 179.23/179.45 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 179.23/179.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 179.23/179.45 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) )
% 179.23/179.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 179.23/179.45 => c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fun__upd__restrict__conv,axiom,
% 179.23/179.45 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 179.23/179.45 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inv__into__comp,axiom,
% 179.23/179.45 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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))
% 179.23/179.45 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 179.23/179.45 => ( 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))))
% 179.23/179.45 => 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) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_mk__less__def,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 179.23/179.45 ( c_Partial__Function_Omk__less(T_b,V_R_2,V_x_2,V_y_2)
% 179.23/179.45 <=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 179.23/179.45 & ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_dom__fun__upd,axiom,
% 179.23/179.45 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] :
% 179.23/179.45 ( ( V_y_2 = c_Option_Ooption_ONone(T_b)
% 179.23/179.45 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) )
% 179.23/179.45 & ( V_y_2 != c_Option_Ooption_ONone(T_b)
% 179.23/179.45 => c_Map_Odom(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_vimage__subset__eq,axiom,
% 179.23/179.45 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 => ( 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))
% 179.23/179.45 <=> 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))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_psubset__imp__ex__mem,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.45 => ? [B_b] : hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_empty__upd__none,axiom,
% 179.23/179.45 ! [V_xa_2,V_x_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2),c_Option_Ooption_ONone(T_b)),V_xa_2) = c_Option_Ooption_ONone(T_b) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inv__inv__eq,axiom,
% 179.23/179.45 ! [V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 => 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 ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__imp__bij__inv,axiom,
% 179.23/179.45 ! [V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 => 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))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__betw__inv__into,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 179.23/179.45 => 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) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 179.23/179.45 ! [V_c,V_b,V_a,T_a] :
% 179.23/179.45 ( class_Groups_Oab__semigroup__mult(T_a)
% 179.23/179.45 => 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)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_restrict__map__empty,axiom,
% 179.23/179.45 ! [V_x_2,V_D_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_restrict__out,axiom,
% 179.23/179.45 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 179.23/179.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inv__into__inv__into__eq,axiom,
% 179.23/179.45 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.45 => 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) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_mult__left__idem,axiom,
% 179.23/179.45 ! [V_b,V_a,T_a] :
% 179.23/179.45 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 179.23/179.45 => 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) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_mult__idem,axiom,
% 179.23/179.45 ! [V_x,T_a] :
% 179.23/179.45 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 179.23/179.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_times_Oidem,axiom,
% 179.23/179.45 ! [V_a,T_a] :
% 179.23/179.45 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 179.23/179.45 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_enum__ex,axiom,
% 179.23/179.45 ! [V_P_2,T_b] :
% 179.23/179.45 ( class_Enum_Oenum(T_b)
% 179.23/179.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
% 179.23/179.45 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_exists__code,axiom,
% 179.23/179.45 ! [V_P_2,T_b] :
% 179.23/179.45 ( class_Enum_Oenum(T_b)
% 179.23/179.45 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 179.23/179.45 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_restrict__map__def,axiom,
% 179.23/179.45 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 179.23/179.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) )
% 179.23/179.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_restrict__map__to__empty,axiom,
% 179.23/179.45 ! [V_x_2,V_m_2,T_b,T_c] : hAPP(c_Map_Orestrict__map(T_c,T_b,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_o__inv__distrib,axiom,
% 179.23/179.45 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 => ( 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)))
% 179.23/179.45 => 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)) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__betw__empty2,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__betw__empty1,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)
% 179.23/179.45 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__betw__comp__iff,axiom,
% 179.23/179.45 ! [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] :
% 179.23/179.45 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 179.23/179.45 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 179.23/179.45 <=> 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) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__betw__trans,axiom,
% 179.23/179.45 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 179.23/179.45 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 179.23/179.45 => 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) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__betw__imp__inj__on,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 179.23/179.45 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_restrict__in,axiom,
% 179.23/179.45 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_restrict__map__insert,axiom,
% 179.23/179.45 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__betw__the__inv__into,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 179.23/179.45 => 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) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_restrict__restrict,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fun__left__comm__idem,axiom,
% 179.23/179.45 ! [T_b] :
% 179.23/179.45 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 179.23/179.45 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__vimage__eq__inv__image,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 => 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) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_restrict__complement__singleton__eq,axiom,
% 179.23/179.45 ! [V_x_2,V_f_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_c)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__image__Collect__eq,axiom,
% 179.23/179.45 ! [V_P_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_P_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))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__betw__subset,axiom,
% 179.23/179.45 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.23/179.45 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 179.23/179.45 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__betw__imp__surj,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 => 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)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__is__surj,axiom,
% 179.23/179.45 ! [V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 => 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)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__comp,axiom,
% 179.23/179.45 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 => ( 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)))
% 179.23/179.45 => 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))) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fun__upd__None__restrict,axiom,
% 179.23/179.45 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 179.23/179.45 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 179.23/179.45 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) )
% 179.23/179.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 179.23/179.45 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_c)) = c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inj__on__imp__bij__betw,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 => 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)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__betw__def,axiom,
% 179.23/179.45 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 179.23/179.45 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_bij__is__inj,axiom,
% 179.23/179.45 ! [V_f_2,T_c,T_b] :
% 179.23/179.45 ( 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)))
% 179.23/179.45 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_fold1Set__nonempty,axiom,
% 179.23/179.45 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 179.23/179.45 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_empty__fold1SetE,axiom,
% 179.23/179.45 ! [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)) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_domIff,axiom,
% 179.23/179.45 ! [V_m_2,T_c,V_a_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2)))
% 179.23/179.45 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inv__into__injective,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 179.23/179.45 ( 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)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 179.23/179.45 => V_x_2 = V_y_2 ) ) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inv__into__into,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 179.23/179.45 => 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)) ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_f__inv__into__f,axiom,
% 179.23/179.45 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 179.23/179.45 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 179.23/179.45 => 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 ) ).
% 179.23/179.45
% 179.23/179.45 fof(fact_inv__into__f__eq,axiom,
% 179.23/179.45 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.45 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.45 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.45 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 179.23/179.45 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 179.23/179.45
% 179.23/179.46 fof(fact_inv__into__f__f,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => 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 ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_image__inv__into__cancel,axiom,
% 179.23/179.46 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 179.23/179.46 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 179.23/179.46 => 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 ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_image__surj__f__inv__f,axiom,
% 179.23/179.46 ! [V_A_2,V_f_2,T_b,T_c] :
% 179.23/179.46 ( 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))
% 179.23/179.46 => 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 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_surj__f__inv__f,axiom,
% 179.23/179.46 ! [V_y_2,V_f_2,T_b,T_c] :
% 179.23/179.46 ( 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))
% 179.23/179.46 => 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 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_surj__iff__all,axiom,
% 179.23/179.46 ! [V_f_2,T_b,T_c] :
% 179.23/179.46 ( 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))
% 179.23/179.46 <=> ! [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 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inv__f__f,axiom,
% 179.23/179.46 ! [V_x_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.46 => 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 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inv__f__eq,axiom,
% 179.23/179.46 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.46 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 179.23/179.46 => 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 ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_dom__empty,axiom,
% 179.23/179.46 ! [T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_dom__eq__empty__conv,axiom,
% 179.23/179.46 ! [V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_dom__def,axiom,
% 179.23/179.46 ! [V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_c)))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_dom__restrict,axiom,
% 179.23/179.46 ! [V_A_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m_2)),V_A_2) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_bij__betw__combine,axiom,
% 179.23/179.46 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 179.23/179.46 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 179.23/179.46 => ( 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))
% 179.23/179.46 => 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)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_bij__betw__Disj__Un,axiom,
% 179.23/179.46 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( 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))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 179.23/179.46 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 179.23/179.46 => 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)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_bij__betw__comp__iff2,axiom,
% 179.23/179.46 ! [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] :
% 179.23/179.46 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 179.23/179.46 => ( 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))
% 179.23/179.46 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 179.23/179.46 <=> 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) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_bij__def,axiom,
% 179.23/179.46 ! [V_f_2,T_c,T_b] :
% 179.23/179.46 ( 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)))
% 179.23/179.46 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.46 & 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)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_bijI,axiom,
% 179.23/179.46 ! [V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => 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))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_bij__image__Compl__eq,axiom,
% 179.23/179.46 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( 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)))
% 179.23/179.46 => 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)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_dom__minus,axiom,
% 179.23/179.46 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] :
% 179.23/179.46 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b)
% 179.23/179.46 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Map_Odom(T_c,T_b,V_f_2)),V_A_2) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_fold__graph__insert__swap,axiom,
% 179.23/179.46 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 179.23/179.46 ( class_Groups_Oab__semigroup__mult(T_b)
% 179.23/179.46 => ( 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))
% 179.23/179.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 179.23/179.46 => 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))) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inj__on__inv__into,axiom,
% 179.23/179.46 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 179.23/179.46 ( 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)))
% 179.23/179.46 => 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) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inv__into__image__cancel,axiom,
% 179.23/179.46 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 179.23/179.46 => 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 ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_surj__imp__inj__inv,axiom,
% 179.23/179.46 ! [V_f_2,T_b,T_c] :
% 179.23/179.46 ( 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))
% 179.23/179.46 => 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))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inv__image__comp,axiom,
% 179.23/179.46 ! [V_X_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.46 => 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 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_image__inv__f__f,axiom,
% 179.23/179.46 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.46 => 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 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inj__imp__surj__inv,axiom,
% 179.23/179.46 ! [V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.46 => 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)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_o__inv__o__cancel,axiom,
% 179.23/179.46 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.46 => 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 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_fun__upd__restrict,axiom,
% 179.23/179.46 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2),V_y_2) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_fold1Set__sing,axiom,
% 179.23/179.46 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 179.23/179.46 ( 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))
% 179.23/179.46 <=> V_a_2 = V_b_2 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_minus__mult__right,axiom,
% 179.23/179.46 ! [V_b,V_a,T_a] :
% 179.23/179.46 ( class_Rings_Oring(T_a)
% 179.23/179.46 => 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)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_minus__mult__left,axiom,
% 179.23/179.46 ! [V_b,V_a,T_a] :
% 179.23/179.46 ( class_Rings_Oring(T_a)
% 179.23/179.46 => 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) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_minus__mult__commute,axiom,
% 179.23/179.46 ! [V_b,V_a,T_a] :
% 179.23/179.46 ( class_Rings_Oring(T_a)
% 179.23/179.46 => 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)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_minus__mult__minus,axiom,
% 179.23/179.46 ! [V_b,V_a,T_a] :
% 179.23/179.46 ( class_Rings_Oring(T_a)
% 179.23/179.46 => 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) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_square__eq__iff,axiom,
% 179.23/179.46 ! [V_b_2,V_a_2,T_b] :
% 179.23/179.46 ( class_Rings_Oidom(T_b)
% 179.23/179.46 => ( 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)
% 179.23/179.46 <=> ( V_a_2 = V_b_2
% 179.23/179.46 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inj__transfer,axiom,
% 179.23/179.46 ! [V_x_2,V_P_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.46 => ( ! [B_y] :
% 179.23/179.46 ( 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)))))
% 179.23/179.46 => hBOOL(hAPP(V_P_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))) )
% 179.23/179.46 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_insert__fold1SetE,axiom,
% 179.23/179.46 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 179.23/179.46 ( 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))
% 179.23/179.46 => ~ ! [B_a,B_A] :
% 179.23/179.46 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_fold1Set_Oequations,axiom,
% 179.23/179.46 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 179.23/179.46 ( 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))
% 179.23/179.46 <=> ? [B_a,B_A] :
% 179.23/179.46 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 179.23/179.46 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 179.23/179.46 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_dom__eq__singleton__conv,axiom,
% 179.23/179.46 ! [V_x_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Map_Odom(T_b,T_c,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.46 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),B_v)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__upd__eqD1,axiom,
% 179.23/179.46 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
% 179.23/179.46 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))
% 179.23/179.46 => V_x_2 = V_y_2 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__upd__triv,axiom,
% 179.23/179.46 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
% 179.23/179.46 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 179.23/179.46 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = V_t_2 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__upd__Some__unfold,axiom,
% 179.23/179.46 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] :
% 179.23/179.46 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 179.23/179.46 <=> ( ( V_x_2 = V_a_2
% 179.23/179.46 & V_b_2 = V_y_2 )
% 179.23/179.46 | ( V_x_2 != V_a_2
% 179.23/179.46 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_domI,axiom,
% 179.23/179.46 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 179.23/179.46 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_image__map__upd,axiom,
% 179.23/179.46 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 179.23/179.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_c),V_m_2),V_A_2) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_insert__dom,axiom,
% 179.23/179.46 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] :
% 179.23/179.46 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 179.23/179.46 => hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Map_Odom(T_c,T_b,V_f_2)) = c_Map_Odom(T_c,T_b,V_f_2) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_dom__const,axiom,
% 179.23/179.46 ! [V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__upd__nonempty,axiom,
% 179.23/179.46 ! [V_x_2,V_k_2,V_t_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_enum__all__option__def,axiom,
% 179.23/179.46 ! [V_P_2,T_b] :
% 179.23/179.46 ( class_Enum_Oenum(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_b)),V_P_2))
% 179.23/179.46 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_b)))
% 179.23/179.46 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b),V_P_2),c_Option_Ooption_OSome(T_b)))) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_enum__ex__option__def,axiom,
% 179.23/179.46 ! [V_P_2,T_b] :
% 179.23/179.46 ( class_Enum_Oenum(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_b)),V_P_2))
% 179.23/179.46 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_b)))
% 179.23/179.46 | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b),V_P_2),c_Option_Ooption_OSome(T_b)))) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_linorder__neqE__linordered__idom,axiom,
% 179.23/179.46 ! [V_y,V_x,T_a] :
% 179.23/179.46 ( class_Rings_Olinordered__idom(T_a)
% 179.23/179.46 => ( V_x != V_y
% 179.23/179.46 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_restrict__upd__same,axiom,
% 179.23/179.46 ! [V_y_2,V_x_2,V_m_2,T_c,T_b] : c_Map_Orestrict__map(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_UNIV__option__conv,axiom,
% 179.23/179.46 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_b)),c_Option_Ooption_ONone(T_b)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ran__map__upd,axiom,
% 179.23/179.46 ! [V_b_2,T_c,T_b,V_a_2,V_m_2] :
% 179.23/179.46 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b)
% 179.23/179.46 => c_Map_Oran(T_c,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_not__None__eq,axiom,
% 179.23/179.46 ! [T_b,V_x_2] :
% 179.23/179.46 ( V_x_2 != c_Option_Ooption_ONone(T_b)
% 179.23/179.46 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_not__Some__eq,axiom,
% 179.23/179.46 ! [T_b,V_x_2] :
% 179.23/179.46 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y)
% 179.23/179.46 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_option_Osimps_I3_J,axiom,
% 179.23/179.46 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_option_Osimps_I2_J,axiom,
% 179.23/179.46 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Cantor__Bernstein,axiom,
% 179.23/179.46 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.23/179.46 => ( 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))
% 179.23/179.46 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 179.23/179.46 => ( 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))
% 179.23/179.46 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ran__empty,axiom,
% 179.23/179.46 ! [T_b,T_c] : c_Map_Oran(T_c,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__upd__left,axiom,
% 179.23/179.46 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] :
% 179.23/179.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2)))
% 179.23/179.46 => c_Map_Omap__add(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_c),V_u1_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__assoc,axiom,
% 179.23/179.46 ! [V_m3_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__add(T_b,T_c,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_m3_2) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__None,axiom,
% 179.23/179.46 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 179.23/179.46 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b)
% 179.23/179.46 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 179.23/179.46 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__find__right,axiom,
% 179.23/179.46 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] :
% 179.23/179.46 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2)
% 179.23/179.46 => hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inj__on__map__add__dom,axiom,
% 179.23/179.46 ! [V_m_H_2,V_m_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),c_Map_Omap__add(T_b,T_c,V_m_2,V_m_H_2),c_Map_Odom(T_b,T_c,V_m_H_2))
% 179.23/179.46 <=> c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_c),V_m_H_2,c_Map_Odom(T_b,T_c,V_m_H_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_empty__map__add,axiom,
% 179.23/179.46 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)),V_m_2) = V_m_2 ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__empty,axiom,
% 179.23/179.46 ! [V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c))) = V_m_2 ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 179.23/179.46 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 179.23/179.46 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 179.23/179.46 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 179.23/179.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 179.23/179.46 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 179.23/179.46 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
% 179.23/179.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2)))
% 179.23/179.46 => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__Some__iff,axiom,
% 179.23/179.46 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 179.23/179.46 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 179.23/179.46 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 179.23/179.46 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 179.23/179.46 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__SomeD,axiom,
% 179.23/179.46 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 179.23/179.46 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 179.23/179.46 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 179.23/179.46 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 179.23/179.46 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_dom__map__add,axiom,
% 179.23/179.46 ! [V_n_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_n_2)),c_Map_Odom(T_b,T_c,V_m_2)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__upd,axiom,
% 179.23/179.46 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__comm,axiom,
% 179.23/179.46 ! [V_m2_2,V_m1_2,T_c,T_b] :
% 179.23/179.46 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_m1_2)),c_Map_Odom(T_b,T_c,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2) = c_Map_Omap__add(T_b,T_c,V_m2_2,V_m1_2) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inj__Some,axiom,
% 179.23/179.46 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,tc_Option_Ooption(T_b),c_Option_Ooption_OSome(T_b),V_A_2) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_option_Oinject,axiom,
% 179.23/179.46 ! [V_a_H_2,V_a_2,T_b] :
% 179.23/179.46 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2)
% 179.23/179.46 <=> V_a_2 = V_a_H_2 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ranI,axiom,
% 179.23/179.46 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 179.23/179.46 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 179.23/179.46 ! [V_x_2,T_b] : c_Option_Oset(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ran__restrictD,axiom,
% 179.23/179.46 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Map_Oran(T_c,T_b,c_Map_Orestrict__map(T_c,T_b,V_m_2,V_A_2))))
% 179.23/179.46 => ? [B_x] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.23/179.46 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_map__add__def,axiom,
% 179.23/179.46 ! [V_x_2,V_m2_2,V_m1_2,T_b,T_c] : hAPP(c_Map_Omap__add(T_c,T_b,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_b)),hAPP(V_m2_2,V_x_2)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 179.23/179.46 ! [T_b] : c_Option_Oset(T_b,c_Option_Ooption_ONone(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_set__empty__eq,axiom,
% 179.23/179.46 ! [V_xo_2,T_b] :
% 179.23/179.46 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_elem__set,axiom,
% 179.23/179.46 ! [V_xo_2,V_x_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2)))
% 179.23/179.46 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__range__updI,axiom,
% 179.23/179.46 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_option_Orecs_I2_J,axiom,
% 179.23/179.46 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_option_Osimps_I5_J,axiom,
% 179.23/179.46 ! [V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_c),V_a_2)) = hAPP(V_f2_2,V_a_2) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite_OemptyI,axiom,
% 179.23/179.46 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite_OinsertI,axiom,
% 179.23/179.46 ! [V_a_2,V_A_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__imageI,axiom,
% 179.23/179.46 ! [V_h_2,T_c,V_F_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Int,axiom,
% 179.23/179.46 ! [V_Ga_2,V_F_2,T_b] :
% 179.23/179.46 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 179.23/179.46 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 179.23/179.46 => 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))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Diff,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => 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))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Collect__conjI,axiom,
% 179.23/179.46 ! [V_Qa_2,V_P_2,T_b] :
% 179.23/179.46 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 179.23/179.46 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) )
% 179.23/179.46 => 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_P_2)),V_Qa_2)))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Collect__subsets,axiom,
% 179.23/179.46 ! [V_A_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => 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)))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_nat__seg__image__imp__finite,axiom,
% 179.23/179.46 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 179.23/179.46 ( 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)))
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__fun__UNIVD2,axiom,
% 179.23/179.46 ! [T_c,T_b] :
% 179.23/179.46 ( 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))))
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Plus__UNIV__iff,axiom,
% 179.23/179.46 ! [T_c,T_b] :
% 179.23/179.46 ( 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))))
% 179.23/179.46 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 179.23/179.46 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Prod__UNIV,axiom,
% 179.23/179.46 ! [T_c,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 179.23/179.46 => 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)))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite,axiom,
% 179.23/179.46 ! [V_A_2,T_b] :
% 179.23/179.46 ( class_Finite__Set_Ofinite(T_b)
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__code,axiom,
% 179.23/179.46 ! [V_A_2,T_b] :
% 179.23/179.46 ( class_Finite__Set_Ofinite(T_b)
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite_Oequations_I1_J,axiom,
% 179.23/179.46 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__insert,axiom,
% 179.23/179.46 ! [V_A_2,V_a_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 179.23/179.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__subset,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_rev__finite__subset,axiom,
% 179.23/179.46 ! [V_A_2,V_B_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__UNIV,axiom,
% 179.23/179.46 ! [T_b] :
% 179.23/179.46 ( class_Finite__Set_Ofinite(T_b)
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__UnI,axiom,
% 179.23/179.46 ! [V_Ga_2,V_F_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 179.23/179.46 => 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))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Un,axiom,
% 179.23/179.46 ! [V_Ga_2,V_F_2,T_b] :
% 179.23/179.46 ( 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)))
% 179.23/179.46 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 179.23/179.46 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Diff2,axiom,
% 179.23/179.46 ! [V_A_2,V_B_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( 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)))
% 179.23/179.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_bij__betw__finite,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_fold__graph__imp__finite,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__option__UNIV,axiom,
% 179.23/179.46 ! [T_b] :
% 179.23/179.46 ( 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))))
% 179.23/179.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Collect__disjI,axiom,
% 179.23/179.46 ! [V_Qa_2,V_P_2,T_b] :
% 179.23/179.46 ( 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_P_2)),V_Qa_2))))
% 179.23/179.46 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 179.23/179.46 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__surj,axiom,
% 179.23/179.46 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( 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)))
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Diff__insert,axiom,
% 179.23/179.46 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 179.23/179.46 ( 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))))
% 179.23/179.46 <=> 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))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__imageD,axiom,
% 179.23/179.46 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 179.23/179.46 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__compl,axiom,
% 179.23/179.46 ! [V_A_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 179.23/179.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Collect__not,axiom,
% 179.23/179.46 ! [V_P_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 179.23/179.46 => ( 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_P_2))))
% 179.23/179.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__range__imageI,axiom,
% 179.23/179.46 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 179.23/179.46 ( 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)))))
% 179.23/179.46 => 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))))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__surj__inj,axiom,
% 179.23/179.46 ! [V_f_2,V_A_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( 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)))
% 179.23/179.46 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_endo__inj__surj,axiom,
% 179.23/179.46 ! [V_f_2,V_A_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 179.23/179.46 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__UNIV__inj__surj,axiom,
% 179.23/179.46 ! [V_f_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 179.23/179.46 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.23/179.46 => 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)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__UNIV__surj__inj,axiom,
% 179.23/179.46 ! [V_f_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__vimageD,axiom,
% 179.23/179.46 ! [V_F_2,V_h_2,T_c,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__vimageI,axiom,
% 179.23/179.46 ! [V_h_2,T_c,V_F_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 179.23/179.46 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 179.23/179.46 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__vimage__iff,axiom,
% 179.23/179.46 ! [V_F_2,V_h_2,T_c,T_b] :
% 179.23/179.46 ( 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)))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 179.23/179.46 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_option_Osimps_I4_J,axiom,
% 179.23/179.46 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_Option_Ooption_Ooption__case(T_b,T_c,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_c)) = V_f1_2 ).
% 179.23/179.46
% 179.23/179.46 fof(fact_option_Orecs_I1_J,axiom,
% 179.23/179.46 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Option_Ooption_Ooption__rec(T_b,T_c,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_c)) = V_f1_2 ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Oremove,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => 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)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__one_Oremove,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 179.23/179.46 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => 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)))))) ) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__image__simple_Oremove,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 179.23/179.46 => 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)))))) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__image_Oreindex,axiom,
% 179.23/179.46 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.23/179.46 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 179.23/179.46 => 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) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Ounion,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => 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)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Oinsert__remove,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => 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)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__one_Ounion__inter,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => 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)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__one_Ounion__disjoint,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => 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)) ) ) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Collect__le__nat,axiom,
% 179.23/179.46 ! [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)))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__Collect__less__nat,axiom,
% 179.23/179.46 ! [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)))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_termination__basic__simps_I5_J,axiom,
% 179.23/179.46 ! [V_y,V_x] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 179.23/179.46 ! [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] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 179.23/179.46 => 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) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Ocommute__comp,axiom,
% 179.23/179.46 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => 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)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Ocommute__left__comp,axiom,
% 179.23/179.46 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => 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)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__image__simple_Oempty,axiom,
% 179.23/179.46 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.23/179.46 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__image_Odistrib,axiom,
% 179.23/179.46 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.23/179.46 => 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)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Ocommute__comp_H,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => 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)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 179.23/179.46 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => 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)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => 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)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 179.23/179.46 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => 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)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__one_Osingleton,axiom,
% 179.23/179.46 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 179.23/179.46 => 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 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__image__simple_Oinsert,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.23/179.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 179.23/179.46 => 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)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 179.23/179.46 => 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)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Oinsert,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => 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)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding_Ounion__inter,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => 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)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__one_Oinsert,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.23/179.46 => 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)))))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__one_Oinsert__remove,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 179.23/179.46 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => 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)))))) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => 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)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__M__bounded__by__nat,axiom,
% 179.23/179.46 ! [V_i_2,V_P_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_P_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))))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__pointwise,axiom,
% 179.23/179.46 ! [V_Qa_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_c,V_U_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2))
% 179.23/179.46 => ( ! [B_p] :
% 179.23/179.46 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
% 179.23/179.46 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Qa_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) )
% 179.23/179.46 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2))
% 179.23/179.46 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_2)),V_c0_2)),V_Qa_2)),V_U_2)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Oremove,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 179.23/179.46 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => 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)))))) ) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Oremove,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 179.23/179.46 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => 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)))))) ) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__idem_Ounion__idem,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => 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)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.23/179.46 => 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) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__idem_Oinsert__idem,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => 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)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__one_Oclosed,axiom,
% 179.23/179.46 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( ! [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))))))
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_infinite__UNIV__nat,axiom,
% 179.23/179.46 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 179.23/179.46 ! [V_N_2] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 179.23/179.46 <=> ? [B_m] :
% 179.23/179.46 ! [B_x] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__le__Sup,axiom,
% 179.23/179.46 ! [V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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))) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Osingleton,axiom,
% 179.23/179.46 ! [V_x_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => 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 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Osingleton,axiom,
% 179.23/179.46 ! [V_x_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => 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 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 179.23/179.46 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => 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) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__idem_Oidem__comp,axiom,
% 179.23/179.46 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => 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) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__nat__set__iff__bounded,axiom,
% 179.23/179.46 ! [V_N_2] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 179.23/179.46 <=> ? [B_m] :
% 179.23/179.46 ! [B_x] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Oin__idem,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => 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) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_sup__Inf__absorb,axiom,
% 179.23/179.46 ! [V_a_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.46 => 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 ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Oin__idem,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => 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) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inf__Sup__absorb,axiom,
% 179.23/179.46 ! [V_a_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.46 => 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 ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Osubset__idem,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.23/179.46 => 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) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Osubset__idem,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.23/179.46 => 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) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Ounion__idem,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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)) ) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Ounion__idem,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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)) ) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Oinsert,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Oinsert,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => 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 )
% 179.23/179.46 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => 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)))))) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => 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 )
% 179.23/179.46 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.23/179.46 => 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)))))) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Ounion__inter,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => 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)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => 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)) ) ) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => 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)) ) ) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Ounion__inter,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( 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))
% 179.23/179.46 => 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)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.23/179.46 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.46 => 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) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Oclosed,axiom,
% 179.23/179.46 ! [V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( ! [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))))))
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Oclosed,axiom,
% 179.23/179.46 ! [V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( ! [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))))))
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 179.23/179.46 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 179.23/179.46 ( 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)))
% 179.23/179.46 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 179.23/179.46 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 179.23/179.46 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 179.23/179.46 ( 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)))
% 179.23/179.46 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 179.23/179.46 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 179.23/179.46 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 179.23/179.46 ( 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)))
% 179.23/179.46 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 179.23/179.46 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 179.23/179.46 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 179.23/179.46 ( 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)))
% 179.23/179.46 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 179.23/179.46 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ord_OgreaterThan__iff,axiom,
% 179.23/179.46 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 179.23/179.46 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ord_OlessThan__iff,axiom,
% 179.23/179.46 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 179.23/179.46 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ord_OatMost__iff,axiom,
% 179.23/179.46 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 179.23/179.46 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_ord_OatLeast__iff,axiom,
% 179.23/179.46 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 179.23/179.46 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_less__or__eq__imp__le,axiom,
% 179.23/179.46 ! [V_n,V_m] :
% 179.23/179.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.23/179.46 | V_m = V_n )
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_le__neq__implies__less,axiom,
% 179.23/179.46 ! [V_n,V_m] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.23/179.46 => ( V_m != V_n
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_less__imp__le__nat,axiom,
% 179.23/179.46 ! [V_n,V_m] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_le__eq__less__or__eq,axiom,
% 179.23/179.46 ! [V_n_2,V_m_2] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.23/179.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 179.23/179.46 | V_m_2 = V_n_2 ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_nat__less__le,axiom,
% 179.23/179.46 ! [V_n_2,V_m_2] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 179.23/179.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.23/179.46 & V_m_2 != V_n_2 ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_diff__less__mono,axiom,
% 179.23/179.46 ! [V_c,V_b,V_a] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 179.23/179.46 => 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))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_diff__mult__distrib2,axiom,
% 179.23/179.46 ! [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)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_diff__mult__distrib,axiom,
% 179.23/179.46 ! [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)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_diff__commute,axiom,
% 179.23/179.46 ! [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) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_diff__less__mono2,axiom,
% 179.23/179.46 ! [V_l,V_n,V_m] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 179.23/179.46 => 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))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_less__imp__diff__less,axiom,
% 179.23/179.46 ! [V_n,V_k,V_j] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 179.23/179.46 => 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)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_nat__less__cases,axiom,
% 179.23/179.46 ! [V_P_2,V_n_2,V_m_2] :
% 179.23/179.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 179.23/179.46 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 179.23/179.46 => ( ( V_m_2 = V_n_2
% 179.23/179.46 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 179.23/179.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 179.23/179.46 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 179.23/179.46 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_less__not__refl3,axiom,
% 179.23/179.46 ! [V_t,V_s] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 179.23/179.46 => V_s != V_t ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_less__not__refl2,axiom,
% 179.23/179.46 ! [V_m,V_n] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 179.23/179.46 => V_m != V_n ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_less__irrefl__nat,axiom,
% 179.23/179.46 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_linorder__neqE__nat,axiom,
% 179.23/179.46 ! [V_y,V_x] :
% 179.23/179.46 ( V_x != V_y
% 179.23/179.46 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_nat__neq__iff,axiom,
% 179.23/179.46 ! [V_n_2,V_m_2] :
% 179.23/179.46 ( V_m_2 != V_n_2
% 179.23/179.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 179.23/179.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_less__not__refl,axiom,
% 179.23/179.46 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_le__square,axiom,
% 179.23/179.46 ! [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))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_le__cube,axiom,
% 179.23/179.46 ! [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)))) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_mult__le__mono1,axiom,
% 179.23/179.46 ! [V_k,V_j,V_i] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.23/179.46 => 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))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_mult__le__mono2,axiom,
% 179.23/179.46 ! [V_k,V_j,V_i] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.23/179.46 => 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))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_mult__le__mono,axiom,
% 179.23/179.46 ! [V_l,V_k,V_j,V_i] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 179.23/179.46 => 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))) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_le__antisym,axiom,
% 179.23/179.46 ! [V_n,V_m] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 179.23/179.46 => V_m = V_n ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_le__trans,axiom,
% 179.23/179.46 ! [V_k,V_j,V_i] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_eq__imp__le,axiom,
% 179.23/179.46 ! [V_n,V_m] :
% 179.23/179.46 ( V_m = V_n
% 179.23/179.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_nat__le__linear,axiom,
% 179.23/179.46 ! [V_n,V_m] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.23/179.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_le__refl,axiom,
% 179.23/179.46 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_diff__le__self,axiom,
% 179.23/179.46 ! [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)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_diff__le__mono2,axiom,
% 179.23/179.46 ! [V_l,V_n,V_m] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.23/179.46 => 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))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_diff__le__mono,axiom,
% 179.23/179.46 ! [V_l,V_n,V_m] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.23/179.46 => 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))) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_diff__diff__cancel,axiom,
% 179.23/179.46 ! [V_n,V_i] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 179.23/179.46 => 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 ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_eq__diff__iff,axiom,
% 179.23/179.46 ! [V_n_2,V_m_2,V_k_2] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 179.23/179.46 => ( 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)
% 179.23/179.46 <=> V_m_2 = V_n_2 ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Nat_Odiff__diff__eq,axiom,
% 179.23/179.46 ! [V_n,V_m,V_k] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 179.23/179.46 => 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) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_le__diff__iff,axiom,
% 179.23/179.46 ! [V_n_2,V_m_2,V_k_2] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 179.23/179.46 => ( 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)))
% 179.23/179.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_less__diff__iff,axiom,
% 179.23/179.46 ! [V_n_2,V_m_2,V_k_2] :
% 179.23/179.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 179.23/179.46 => ( 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)))
% 179.23/179.46 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inf__Sup2__distrib,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Odistrib__lattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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))))))) ) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_inf__Sup1__distrib,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Odistrib__lattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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))))) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_sup__Inf2__distrib,axiom,
% 179.23/179.46 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Odistrib__lattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.46 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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))))))) ) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_sup__Inf1__distrib,axiom,
% 179.23/179.46 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.46 ( class_Lattices_Odistrib__lattice(T_b)
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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))))) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_,axiom,
% 179.23/179.46 ! [V_y_2,V_x_2,T_b] : c_Smallcheck_Oorelse(T_b,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_b,V_y_2,c_Option_Ooption_OSome(T_b)),V_x_2) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Inf__fin_Ohom__commute,axiom,
% 179.23/179.46 ! [V_N_2,V_h_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( ! [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))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.23/179.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_Sup__fin_Ohom__commute,axiom,
% 179.23/179.46 ! [V_N_2,V_h_2,T_b] :
% 179.23/179.46 ( class_Lattices_Olattice(T_b)
% 179.23/179.46 => ( ! [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))
% 179.23/179.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.23/179.46 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.46 => 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)) ) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__empty__induct,axiom,
% 179.23/179.46 ! [V_P_2,V_A_2,T_b] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.46 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 179.23/179.46 => ( ! [B_a,B_A] :
% 179.23/179.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 179.23/179.46 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 179.23/179.46 => ( hBOOL(hAPP(V_P_2,B_A))
% 179.23/179.46 => hBOOL(hAPP(V_P_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)))))) ) ) )
% 179.23/179.46 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_nat__mult__commute,axiom,
% 179.23/179.46 ! [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) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_nat__mult__assoc,axiom,
% 179.23/179.46 ! [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)) ).
% 179.23/179.46
% 179.23/179.46 fof(fact_finite__image__set,axiom,
% 179.23/179.47 ! [V_f_2,T_c,V_P_2,T_b] :
% 179.23/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 179.23/179.47 => 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_P_2))))) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_finite__Collect__bounded__ex,axiom,
% 179.23/179.47 ! [V_Qa_2,T_c,V_P_2,T_b] :
% 179.23/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 179.23/179.47 => ( 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_P_2))),V_Qa_2)))))
% 179.23/179.47 <=> ! [B_y] :
% 179.23/179.47 ( hBOOL(hAPP(V_P_2,B_y))
% 179.23/179.47 => 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)))) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_ran__def,axiom,
% 179.23/179.47 ! [V_m_2,T_b,T_c] : c_Map_Oran(T_c,T_b,V_m_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_b)))) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 179.23/179.47 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.47 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => 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)) ) ) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_map__comp__def,axiom,
% 179.23/179.47 ! [V_k_2,V_g_2,V_f_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_c,c_Option_Ooption_ONone(T_b),V_f_2),hAPP(V_g_2,V_k_2)) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 179.23/179.47 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.47 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.23/179.47 => 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) ) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_finite__subset__induct,axiom,
% 179.23/179.47 ! [V_P_2,V_A_2,V_F_2,T_b] :
% 179.23/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 179.23/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 179.23/179.47 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 179.23/179.47 => ( ! [B_a,B_F] :
% 179.23/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 179.23/179.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 179.23/179.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 179.23/179.47 => ( hBOOL(hAPP(V_P_2,B_F))
% 179.23/179.47 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 179.23/179.47 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 179.23/179.47 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.47 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => 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)) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_finite__conv__nat__seg__image,axiom,
% 179.23/179.47 ! [V_A_2,T_b] :
% 179.23/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 <=> ? [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))) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_image__eq__fold__image,axiom,
% 179.23/179.47 ! [V_f_2,T_c,V_A_2,T_b] :
% 179.23/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => 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) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold1__Un,axiom,
% 179.23/179.47 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.47 ( class_Groups_Oab__semigroup__mult(T_b)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => ( 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))
% 179.23/179.47 => 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)) ) ) ) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_folding__one__idem_Oidem,axiom,
% 179.23/179.47 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 179.23/179.47 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 179.23/179.47 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold__image__empty,axiom,
% 179.23/179.47 ! [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 ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold1__singleton,axiom,
% 179.23/179.47 ! [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 ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold1__singleton__def,axiom,
% 179.23/179.47 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 179.23/179.47 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 179.23/179.47 => 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 ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_map__comp__simps_I1_J,axiom,
% 179.23/179.47 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] :
% 179.23/179.47 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 179.23/179.47 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_d) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_map__comp__Some__iff,axiom,
% 179.23/179.47 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 179.23/179.47 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2)
% 179.23/179.47 <=> ? [B_k_H] :
% 179.23/179.47 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 179.23/179.47 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_map__comp__simps_I2_J,axiom,
% 179.23/179.47 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] :
% 179.23/179.47 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2)
% 179.23/179.47 => c_Map_Omap__comp(T_b,T_d,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 179.23/179.47 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.47 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.23/179.47 => 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) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_folding__image_Oeq__fold,axiom,
% 179.23/179.47 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.47 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.23/179.47 => 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) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_folding__one_Oeq__fold,axiom,
% 179.23/179.47 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.47 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_map__comp__empty_I1_J,axiom,
% 179.23/179.47 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c)),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_map__comp__empty_I2_J,axiom,
% 179.23/179.47 ! [V_x_2,V_m_2,T_d,T_b,T_c] : c_Map_Omap__comp(T_c,T_b,T_d,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold1__def,axiom,
% 179.23/179.47 ! [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)) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_Sup__fin_OF__eq,axiom,
% 179.23/179.47 ! [V_A_2,T_b] :
% 179.23/179.47 ( class_Lattices_Olattice(T_b)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => 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) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_Inf__fin_OF__eq,axiom,
% 179.23/179.47 ! [V_A_2,T_b] :
% 179.23/179.47 ( class_Lattices_Olattice(T_b)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => 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) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_folding__one__idem_Oin__idem,axiom,
% 179.23/179.47 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.47 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.47 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold__image__insert,axiom,
% 179.23/179.47 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 179.23/179.47 ( class_Groups_Oab__semigroup__mult(T_c)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.47 => 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)) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold1__belowI,axiom,
% 179.23/179.47 ! [V_a_2,V_A_2,T_b] :
% 179.23/179.47 ( class_Lattices_Osemilattice__inf(T_b)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.23/179.47 => 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)) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_below__fold1__iff,axiom,
% 179.23/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.47 ( class_Lattices_Osemilattice__inf(T_b)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => ( 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)))
% 179.23/179.47 <=> ! [B_x] :
% 179.23/179.47 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.23/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold1__insert__idem,axiom,
% 179.23/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.47 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 179.23/179.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => 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)) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold1__Un2,axiom,
% 179.23/179.47 ! [V_B_2,V_A_2,T_b] :
% 179.23/179.47 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.47 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => 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)) ) ) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_map__comp__None__iff,axiom,
% 179.23/179.47 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 179.23/179.47 ( c_Map_Omap__comp(T_c,T_b,T_d,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 179.23/179.47 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c)
% 179.23/179.47 | ? [B_k_H] :
% 179.23/179.47 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 179.23/179.47 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold__image__reindex,axiom,
% 179.23/179.47 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 179.23/179.47 ( class_Groups_Oab__semigroup__mult(T_d)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 179.23/179.47 => 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) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold1__insert,axiom,
% 179.23/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.47 ( class_Groups_Oab__semigroup__mult(T_b)
% 179.23/179.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.47 => 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)) ) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_semilattice__big_OF__eq,axiom,
% 179.23/179.47 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 179.23/179.47 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_comm__monoid__big_OF__eq,axiom,
% 179.23/179.47 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 179.23/179.47 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 179.23/179.47 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.23/179.47 => 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) )
% 179.23/179.47 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.23/179.47 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold1__in,axiom,
% 179.23/179.47 ! [V_A_2,T_b] :
% 179.23/179.47 ( class_Groups_Oab__semigroup__mult(T_b)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => ( ! [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))))))
% 179.23/179.47 => 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)) ) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_hom__fold1__commute,axiom,
% 179.23/179.47 ! [V_N_2,V_h_2,T_b] :
% 179.23/179.47 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 179.23/179.47 => ( ! [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))
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.23/179.47 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.23/179.47 => 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)) ) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_fold__Un__disjoint,axiom,
% 179.23/179.47 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 179.23/179.47 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.23/179.47 => ( 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))
% 179.23/179.47 => 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)) ) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_Option_Omap__def,axiom,
% 179.23/179.47 ! [V_f_2,T_c,T_b] : hAPP(c_Option_Omap(T_b,T_c),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_c),T_b,c_Option_Ooption_ONone(T_c),hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_card__Diff1__less,axiom,
% 179.23/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.23/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.47 => 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))) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_card__Diff2__less,axiom,
% 179.23/179.47 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 179.23/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.23/179.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.23/179.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 179.23/179.47 => 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))) ) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_one__reorient,axiom,
% 179.23/179.47 ! [V_x_2,T_b] :
% 179.23/179.47 ( class_Groups_Oone(T_b)
% 179.23/179.47 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 179.23/179.47 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_mult_Ocomm__neutral,axiom,
% 179.23/179.47 ! [V_a,T_a] :
% 179.23/179.47 ( class_Groups_Ocomm__monoid__mult(T_a)
% 179.23/179.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_mult__1__right,axiom,
% 179.23/179.47 ! [V_a,T_a] :
% 179.23/179.47 ( class_Groups_Omonoid__mult(T_a)
% 179.23/179.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_mult__1,axiom,
% 179.23/179.47 ! [V_a,T_a] :
% 179.23/179.47 ( class_Groups_Ocomm__monoid__mult(T_a)
% 179.23/179.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_mult__1__left,axiom,
% 179.23/179.47 ! [V_a,T_a] :
% 179.23/179.47 ( class_Groups_Omonoid__mult(T_a)
% 179.23/179.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_bij__betw__same__card,axiom,
% 179.23/179.47 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.23/179.47 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 179.23/179.47 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_nat__mult__1,axiom,
% 179.23/179.47 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 179.23/179.47
% 179.23/179.47 fof(fact_nat__1__eq__mult__iff,axiom,
% 179.23/179.47 ! [V_n_2,V_m_2] :
% 179.23/179.47 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 179.23/179.47 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 179.23/179.47 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_nat__mult__1__right,axiom,
% 179.23/179.47 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 179.23/179.47
% 179.23/179.47 fof(fact_nat__mult__eq__1__iff,axiom,
% 179.23/179.47 ! [V_n_2,V_m_2] :
% 179.23/179.47 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 179.23/179.47 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 179.23/179.47 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_option__map__comp,axiom,
% 179.23/179.47 ! [V_opt_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_opt_2) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_Option_Omap_Ocompositionality,axiom,
% 179.23/179.47 ! [V_option_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_Option_Omap(T_d,T_c),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_option_2) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_Option_Omap_Ocomp,axiom,
% 179.23/179.47 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(c_Option_Omap(T_b,T_d),V_g_2)) = hAPP(c_Option_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_option__map__None,axiom,
% 179.23/179.47 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),c_Option_Ooption_ONone(T_c)) = c_Option_Ooption_ONone(T_b) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_option__map__is__None,axiom,
% 179.23/179.47 ! [V_opt_2,V_f_2,T_b,T_c] :
% 179.23/179.47 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b)
% 179.23/179.47 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_option__map__Some,axiom,
% 179.23/179.47 ! [V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_option__map__eq__Some,axiom,
% 179.23/179.47 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] :
% 179.23/179.47 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 179.23/179.47 <=> ? [B_z] :
% 179.23/179.47 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z)
% 179.23/179.47 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 179.23/179.47 ! [V_A_2,T_b] :
% 179.23/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 179.23/179.47 => ( 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)))
% 179.23/179.47 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 179.23/179.47
% 179.23/179.47 fof(fact_option__map__o__empty,axiom,
% 179.23/179.47 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_d,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_c),T_d),c_Option_Ooption_ONone(T_c))),V_x_2) = c_Option_Ooption_ONone(T_b) ).
% 179.23/179.47
% 179.48/179.47 fof(fact_card__image,axiom,
% 179.48/179.47 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.48/179.47 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_BIJ,axiom,
% 179.48/179.47 ! [V_B_2,T_c,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 179.48/179.47 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 179.48/179.47 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__1__mult,axiom,
% 179.48/179.47 ! [V_n,V_m,T_a] :
% 179.48/179.47 ( class_Rings_Olinordered__semidom(T_a)
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 179.48/179.47 => 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))) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_dom__option__map,axiom,
% 179.48/179.47 ! [V_m_2,V_f_2,T_d,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c)),T_b),c_Option_Omap(T_d,T_c)),V_f_2)),V_m_2)) = c_Map_Odom(T_b,T_d,V_m_2) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_square__eq__1__iff,axiom,
% 179.48/179.47 ! [V_x_2,T_b] :
% 179.48/179.47 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 179.48/179.47 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 179.48/179.47 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 179.48/179.47 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__Diff__insert,axiom,
% 179.48/179.47 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.48/179.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 179.48/179.47 => 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)) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__Diff__singleton__if,axiom,
% 179.48/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.47 => 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)) )
% 179.48/179.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.47 => 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) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__Diff__singleton,axiom,
% 179.48/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.47 => 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)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__insert__le,axiom,
% 179.48/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => 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)))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__mono,axiom,
% 179.48/179.47 ! [V_A_2,V_B_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.48/179.47 => 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))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__seteq,axiom,
% 179.48/179.47 ! [V_A_2,V_B_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.48/179.47 => ( 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)))
% 179.48/179.47 => V_A_2 = V_B_2 ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__image__le,axiom,
% 179.48/179.47 ! [V_f_2,T_c,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_eq__card__imp__inj__on,axiom,
% 179.48/179.47 ! [V_f_2,T_c,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( 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)
% 179.48/179.47 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_inj__on__iff__eq__card,axiom,
% 179.48/179.47 ! [V_f_2,T_c,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.48/179.47 <=> 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) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_pigeonhole,axiom,
% 179.48/179.47 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.48/179.47 ( 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)))
% 179.48/179.47 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_option__map__o__map__upd,axiom,
% 179.48/179.47 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_d)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_d),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_b_2))) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_psubset__card__mono,axiom,
% 179.48/179.47 ! [V_A_2,V_B_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.48/179.47 => 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))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_fold__image__distrib,axiom,
% 179.48/179.47 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 179.48/179.47 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => 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)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__bij__eq,axiom,
% 179.48/179.47 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.48/179.47 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.48/179.47 => ( 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))
% 179.48/179.47 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 179.48/179.47 => ( 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))
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 179.48/179.47 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__Diff__subset,axiom,
% 179.48/179.47 ! [V_A_2,V_B_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.48/179.47 => 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)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__Diff__subset__Int,axiom,
% 179.48/179.47 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.47 ( 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)))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__card__le__card__Diff,axiom,
% 179.48/179.47 ! [V_A_2,V_B_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.47 => 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)))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__psubset,axiom,
% 179.48/179.47 ! [V_A_2,V_B_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.48/179.47 => ( 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)))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 179.48/179.47 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 179.48/179.47 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 179.48/179.47 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.48/179.47 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__Diff1__le,axiom,
% 179.48/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__inj__on__le,axiom,
% 179.48/179.47 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.48/179.47 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.48/179.47 => ( 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))
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 179.48/179.47 => 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))) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_inj__on__iff__card__le,axiom,
% 179.48/179.47 ! [V_B_2,T_c,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 179.48/179.47 => ( ? [B_f] :
% 179.48/179.47 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 179.48/179.47 & 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)) )
% 179.48/179.47 <=> 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))) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_fold__image__Un__Int,axiom,
% 179.48/179.47 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 179.48/179.47 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.47 => 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))) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 179.48/179.47 ! [V_x,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__ring__1(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_fold__image__Un__one,axiom,
% 179.48/179.47 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 179.48/179.47 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 179.48/179.47 => ( ! [B_x] :
% 179.48/179.47 ( 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)))
% 179.48/179.47 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 179.48/179.47 => 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)) ) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 179.48/179.47 ! [V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 179.48/179.47 ! [V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card_Oremove,axiom,
% 179.48/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.47 => 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)))))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__Suc__Diff1,axiom,
% 179.48/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.47 => 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) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 179.48/179.47 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 179.48/179.47 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 179.48/179.47 => ( ! [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))
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.48/179.47 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.47 => 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)) ) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 179.48/179.47 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.48/179.47 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 179.48/179.47 => ( ! [B_x] :
% 179.48/179.47 ( 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)))
% 179.48/179.47 => hAPP(V_g_2,B_x) = V_z_2 )
% 179.48/179.47 => 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)) ) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__mono,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_lessI,axiom,
% 179.48/179.47 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_inj__on__add__nat,axiom,
% 179.48/179.47 ! [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) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__UNIV__unit,axiom,
% 179.48/179.47 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) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_mult__Suc__right,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_mult__Suc,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_crossproduct__eq,axiom,
% 179.48/179.47 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 179.48/179.47 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 179.48/179.47 => ( 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))
% 179.48/179.47 <=> ( V_w_2 = V_x_2
% 179.48/179.47 | V_y_2 = V_z_2 ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 179.48/179.47 ! [V_b,V_m,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 179.48/179.47 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_crossproduct__noteq,axiom,
% 179.48/179.47 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.48/179.47 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 179.48/179.47 => ( ( V_a_2 != V_b_2
% 179.48/179.47 & V_ca_2 != V_d_2 )
% 179.48/179.47 <=> 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)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 179.48/179.47 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 179.48/179.47 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 179.48/179.47 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 179.48/179.47 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 179.48/179.47 ! [V_d,V_c,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 179.48/179.47 ! [V_d,V_c,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 179.48/179.47 ! [V_c,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 179.48/179.47 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oab__semigroup__add(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__left__cancel,axiom,
% 179.48/179.47 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 179.48/179.47 ( class_Groups_Ocancel__semigroup__add(T_b)
% 179.48/179.47 => ( 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)
% 179.48/179.47 <=> V_b_2 = V_ca_2 ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__right__cancel,axiom,
% 179.48/179.47 ! [V_ca_2,V_a_2,V_b_2,T_b] :
% 179.48/179.47 ( class_Groups_Ocancel__semigroup__add(T_b)
% 179.48/179.47 => ( 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)
% 179.48/179.47 <=> V_b_2 = V_ca_2 ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__left__imp__eq,axiom,
% 179.48/179.47 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Ocancel__semigroup__add(T_a)
% 179.48/179.47 => ( 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)
% 179.48/179.47 => V_b = V_c ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__imp__eq,axiom,
% 179.48/179.47 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 179.48/179.47 => ( 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)
% 179.48/179.47 => V_b = V_c ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__right__imp__eq,axiom,
% 179.48/179.47 ! [V_c,V_a,V_b,T_a] :
% 179.48/179.47 ( class_Groups_Ocancel__semigroup__add(T_a)
% 179.48/179.47 => ( 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)
% 179.48/179.47 => V_b = V_c ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_inj__Suc,axiom,
% 179.48/179.47 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_n__not__Suc__n,axiom,
% 179.48/179.47 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__n__not__n,axiom,
% 179.48/179.47 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 179.48/179.47
% 179.48/179.47 fof(fact_nat__add__commute,axiom,
% 179.48/179.47 ! [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) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__Suc__right,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_nat__add__left__commute,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__Suc,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__Suc__shift,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_nat_Oinject,axiom,
% 179.48/179.47 ! [V_nat_H_2,V_nat_2] :
% 179.48/179.47 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 179.48/179.47 <=> V_nat_2 = V_nat_H_2 ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_nat__add__assoc,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_nat__add__left__cancel,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.47 ( 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)
% 179.48/179.47 <=> V_m_2 = V_n_2 ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_nat__add__right__cancel,axiom,
% 179.48/179.47 ! [V_n_2,V_k_2,V_m_2] :
% 179.48/179.47 ( 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)
% 179.48/179.47 <=> V_m_2 = V_n_2 ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__inject,axiom,
% 179.48/179.47 ! [V_y,V_x] :
% 179.48/179.47 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 179.48/179.47 => V_x = V_y ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__iff__Suc__add,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 179.48/179.47 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__add__Suc2,axiom,
% 179.48/179.47 ! [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)))) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__add__Suc1,axiom,
% 179.48/179.47 ! [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)))) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__Suc__diff__eq2,axiom,
% 179.48/179.47 ! [V_m,V_j,V_k] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__Suc__diff__eq1,axiom,
% 179.48/179.47 ! [V_m,V_j,V_k] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__le__imp__le__left,axiom,
% 179.48/179.47 ! [V_b,V_a,V_c,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__le__imp__le__right,axiom,
% 179.48/179.47 ! [V_b,V_c,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__mono,axiom,
% 179.48/179.47 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 179.48/179.47 => 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))) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__left__mono,axiom,
% 179.48/179.47 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.48/179.47 => 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))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__right__mono,axiom,
% 179.48/179.47 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.48/179.47 => 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))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__le__cancel__left,axiom,
% 179.48/179.47 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.48/179.47 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__le__cancel__right,axiom,
% 179.48/179.47 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 179.48/179.47 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__less__imp__less__left,axiom,
% 179.48/179.47 ! [V_b,V_a,V_c,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__less__imp__less__right,axiom,
% 179.48/179.47 ! [V_b,V_c,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__strict__mono,axiom,
% 179.48/179.47 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 179.48/179.47 => 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))) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__strict__left__mono,axiom,
% 179.48/179.47 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.48/179.47 => 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))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__strict__right__mono,axiom,
% 179.48/179.47 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.48/179.47 => 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))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__less__cancel__left,axiom,
% 179.48/179.47 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.48/179.47 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__less__cancel__right,axiom,
% 179.48/179.47 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 179.48/179.47 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__class_Odistrib,axiom,
% 179.48/179.47 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_combine__common__factor,axiom,
% 179.48/179.47 ! [V_c,V_b,V_e,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Osemiring(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__diff__cancel,axiom,
% 179.48/179.47 ! [V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.47 => 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 ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__add__cancel,axiom,
% 179.48/179.47 ! [V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.47 => 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 ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_minus__add__cancel,axiom,
% 179.48/179.47 ! [V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.47 => 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 ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__minus__cancel,axiom,
% 179.48/179.47 ! [V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.47 => 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 ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_minus__add,axiom,
% 179.48/179.47 ! [V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_minus__add__distrib,axiom,
% 179.48/179.47 ! [V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oab__group__add(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_not__less__eq,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2] :
% 179.48/179.47 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__Suc__eq,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 179.48/179.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 179.48/179.47 | V_m_2 = V_n_2 ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__less__eq,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2] :
% 179.48/179.47 ( 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)))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_not__less__less__Suc__eq,axiom,
% 179.48/179.47 ! [V_m_2,V_n_2] :
% 179.48/179.47 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 179.48/179.47 <=> V_n_2 = V_m_2 ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__antisym,axiom,
% 179.48/179.47 ! [V_m,V_n] :
% 179.48/179.47 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 179.48/179.47 => V_m = V_n ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__SucI,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__lessI,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.48/179.47 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__trans__Suc,axiom,
% 179.48/179.47 ! [V_k,V_j,V_i] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__SucE,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 179.48/179.47 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.48/179.47 => V_m = V_n ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__lessD,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__less__SucD,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__n__not__le__n,axiom,
% 179.48/179.47 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_not__less__eq__eq,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2] :
% 179.48/179.47 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__Suc__eq,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 179.48/179.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.48/179.47 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__le__mono,axiom,
% 179.48/179.47 ! [V_m_2,V_n_2] :
% 179.48/179.47 ( 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)))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__SucI,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__SucE,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 179.48/179.47 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.48/179.47 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__leD,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_not__add__less1,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_not__add__less2,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_nat__add__left__cancel__less,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.47 ( 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)))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_trans__less__add1,axiom,
% 179.48/179.47 ! [V_m,V_j,V_i] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_trans__less__add2,axiom,
% 179.48/179.47 ! [V_m,V_j,V_i] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__less__mono1,axiom,
% 179.48/179.47 ! [V_k,V_j,V_i] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__less__mono,axiom,
% 179.48/179.47 ! [V_l,V_k,V_j,V_i] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 179.48/179.47 => 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))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__add__eq__less,axiom,
% 179.48/179.47 ! [V_n,V_m,V_l,V_k] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 179.48/179.47 => ( 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)
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__lessD1,axiom,
% 179.48/179.47 ! [V_k,V_j,V_i] :
% 179.48/179.47 ( 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))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_termination__basic__simps_I1_J,axiom,
% 179.48/179.47 ! [V_z,V_y,V_x] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_termination__basic__simps_I2_J,axiom,
% 179.48/179.47 ! [V_y,V_z,V_x] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__diff__diff,axiom,
% 179.48/179.47 ! [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) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__Suc__Suc,axiom,
% 179.48/179.47 ! [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) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__Suc__1,axiom,
% 179.48/179.47 ! [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 ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__mult__cancel1,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.47 ( 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)
% 179.48/179.47 <=> V_m_2 = V_n_2 ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__add2,axiom,
% 179.48/179.47 ! [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))) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__add1,axiom,
% 179.48/179.47 ! [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))) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__iff__add,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.48/179.47 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_nat__add__left__cancel__le,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.47 ( 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)))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_trans__le__add1,axiom,
% 179.48/179.47 ! [V_m,V_j,V_i] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_trans__le__add2,axiom,
% 179.48/179.47 ! [V_m,V_j,V_i] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__le__mono1,axiom,
% 179.48/179.47 ! [V_k,V_j,V_i] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__le__mono,axiom,
% 179.48/179.47 ! [V_l,V_k,V_j,V_i] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 179.48/179.47 => 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))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__leD2,axiom,
% 179.48/179.47 ! [V_n,V_k,V_m] :
% 179.48/179.47 ( 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))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__leD1,axiom,
% 179.48/179.47 ! [V_n,V_k,V_m] :
% 179.48/179.47 ( 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))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__leE,axiom,
% 179.48/179.47 ! [V_n,V_k,V_m] :
% 179.48/179.47 ( 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))
% 179.48/179.47 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.48/179.47 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_termination__basic__simps_I3_J,axiom,
% 179.48/179.47 ! [V_z,V_y,V_x] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_termination__basic__simps_I4_J,axiom,
% 179.48/179.47 ! [V_y,V_z,V_x] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__cancel2,axiom,
% 179.48/179.47 ! [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) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__cancel,axiom,
% 179.48/179.47 ! [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) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__diff__left,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__add__inverse,axiom,
% 179.48/179.47 ! [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 ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__add__inverse2,axiom,
% 179.48/179.47 ! [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 ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__mult__distrib,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__mult__distrib2,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 179.48/179.47 ! [V_m,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 179.48/179.47 ! [V_a,V_m,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 179.48/179.47 ! [V_m,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 179.48/179.47 ! [V_y,V_x,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__ring__1(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__less__le__mono,axiom,
% 179.48/179.47 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 179.48/179.47 => 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))) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__le__less__mono,axiom,
% 179.48/179.47 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 179.48/179.47 => 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))) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__add__one,axiom,
% 179.48/179.47 ! [V_a,T_a] :
% 179.48/179.47 ( class_Rings_Olinordered__semidom(T_a)
% 179.48/179.47 => 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)))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_eq__add__iff1,axiom,
% 179.48/179.47 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 179.48/179.47 ( class_Rings_Oring(T_b)
% 179.48/179.47 => ( 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)
% 179.48/179.47 <=> 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 ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_eq__add__iff2,axiom,
% 179.48/179.47 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 179.48/179.47 ( class_Rings_Oring(T_b)
% 179.48/179.47 => ( 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)
% 179.48/179.47 <=> 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) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__minus__eq__add,axiom,
% 179.48/179.47 ! [V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_ab__diff__minus,axiom,
% 179.48/179.47 ! [V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Oab__group__add(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__def,axiom,
% 179.48/179.47 ! [V_b,V_a,T_a] :
% 179.48/179.47 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__le__lessD,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__less__Suc__eq,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.48/179.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 179.48/179.47 <=> V_n_2 = V_m_2 ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__leI,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__imp__less__Suc,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.48/179.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__le__eq,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__Suc__eq__le,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__eq__Suc__le,axiom,
% 179.48/179.47 ! [V_m_2,V_n_2] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__less__Suc,axiom,
% 179.48/179.47 ! [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))) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__mult__less__cancel1,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.47 ( 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)))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__diff__le,axiom,
% 179.48/179.47 ! [V_m,V_n] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_Suc__mult__le__cancel1,axiom,
% 179.48/179.47 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.47 ( 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)))
% 179.48/179.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__diff__conv,axiom,
% 179.48/179.47 ! [V_k_2,V_j_2,V_i_2] :
% 179.48/179.47 ( 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)))
% 179.48/179.47 <=> 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__diff__inverse,axiom,
% 179.48/179.47 ! [V_n,V_m] :
% 179.48/179.47 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.48/179.47 => 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 ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__add__assoc2,axiom,
% 179.48/179.47 ! [V_i,V_j,V_k] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__diff__assoc2,axiom,
% 179.48/179.47 ! [V_i,V_j,V_k] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__add__assoc,axiom,
% 179.48/179.47 ! [V_i,V_j,V_k] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__imp__diff__is__add,axiom,
% 179.48/179.47 ! [V_k_2,V_j_2,V_i_2] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 179.48/179.47 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 179.48/179.47 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__add__diff__inverse2,axiom,
% 179.48/179.47 ! [V_m,V_n] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 179.48/179.47 => 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 ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__diff__conv2,axiom,
% 179.48/179.47 ! [V_i_2,V_j_2,V_k_2] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 179.48/179.47 => ( 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)))
% 179.48/179.47 <=> 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)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_add__diff__assoc,axiom,
% 179.48/179.47 ! [V_i,V_j,V_k] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__add__diff__inverse,axiom,
% 179.48/179.47 ! [V_m,V_n] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 179.48/179.47 => 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 ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__add__diff,axiom,
% 179.48/179.47 ! [V_m,V_n,V_k] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__diff__conv,axiom,
% 179.48/179.47 ! [V_i_2,V_k_2,V_j_2] :
% 179.48/179.47 ( 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))
% 179.48/179.47 <=> 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_diff__diff__right,axiom,
% 179.48/179.47 ! [V_i,V_j,V_k] :
% 179.48/179.47 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__eq__Suc__le__raw,axiom,
% 179.48/179.47 ! [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)) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__add__iff2,axiom,
% 179.48/179.47 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 179.48/179.47 ( class_Rings_Oordered__ring(T_b)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 <=> 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))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_le__add__iff1,axiom,
% 179.48/179.47 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 179.48/179.47 ( class_Rings_Oordered__ring(T_b)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 <=> 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)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__add__iff1,axiom,
% 179.48/179.47 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 179.48/179.47 ( class_Rings_Oordered__ring(T_b)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 <=> 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)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_less__add__iff2,axiom,
% 179.48/179.47 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 179.48/179.47 ( class_Rings_Oordered__ring(T_b)
% 179.48/179.47 => ( 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)))
% 179.48/179.47 <=> 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))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 179.48/179.47 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 179.48/179.47 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 179.48/179.47 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 179.48/179.47 ! [V_rx,V_ly,V_lx,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 179.48/179.47 ! [V_rx,V_ly,V_lx,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 179.48/179.47 ! [V_ry,V_rx,V_lx,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 179.48/179.47 ! [V_ry,V_rx,V_lx,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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)) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 179.48/179.47 ! [V_b,V_a,T_a] :
% 179.48/179.47 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.47 => 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) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__insert__disjoint,axiom,
% 179.48/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.47 => 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)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__insert__if,axiom,
% 179.48/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.47 => 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) )
% 179.48/179.47 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.47 => 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)) ) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card_Oinsert,axiom,
% 179.48/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.47 => 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)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__Un__Int,axiom,
% 179.48/179.47 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.47 => 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))) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card_Ounion__inter,axiom,
% 179.48/179.47 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.47 => 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)) ) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__insert,axiom,
% 179.48/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => 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)))))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card_Oinsert__remove,axiom,
% 179.48/179.47 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.47 => 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)))))) ) ).
% 179.48/179.47
% 179.48/179.47 fof(fact_card__Un__disjoint,axiom,
% 179.48/179.47 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.47 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.48 => ( 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))
% 179.48/179.48 => 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)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__less__add__iff2,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__less__add__iff1,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> 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)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__eq__add__iff2,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 179.48/179.48 => ( 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)
% 179.48/179.48 <=> 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) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__diff__add__eq2,axiom,
% 179.48/179.48 ! [V_n,V_m,V_u,V_j,V_i] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.48/179.48 => 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)) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__le__add__iff2,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__eq__add__iff1,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 179.48/179.48 => ( 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)
% 179.48/179.48 <=> 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 ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__diff__add__eq1,axiom,
% 179.48/179.48 ! [V_n,V_m,V_u,V_i,V_j] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 179.48/179.48 => 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) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__le__add__iff1,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> 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)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_left__add__mult__distrib,axiom,
% 179.48/179.48 ! [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) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 179.48/179.48 ! [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) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Suc__eq__plus1,axiom,
% 179.48/179.48 ! [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)) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Suc__eq__plus1__left,axiom,
% 179.48/179.48 ! [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) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_finite__fun__UNIVD1,axiom,
% 179.48/179.48 ! [T_c,T_b] :
% 179.48/179.48 ( 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))))
% 179.48/179.48 => ( 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))
% 179.48/179.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__Max__commute,axiom,
% 179.48/179.48 ! [V_k_2,V_N_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.48/179.48 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.48 => 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))))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__Min__commute,axiom,
% 179.48/179.48 ! [V_k_2,V_N_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.48/179.48 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.48 => 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))))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_less__zeroE,axiom,
% 179.48/179.48 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_le0,axiom,
% 179.48/179.48 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__less__Suc,axiom,
% 179.48/179.48 ! [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))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__reorient,axiom,
% 179.48/179.48 ! [V_x_2,T_b] :
% 179.48/179.48 ( class_Groups_Ozero(T_b)
% 179.48/179.48 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 179.48/179.48 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_bot__nat__def,axiom,
% 179.48/179.48 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__0__iff,axiom,
% 179.48/179.48 ! [V_a_2,V_b_2,T_b] :
% 179.48/179.48 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 179.48/179.48 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 179.48/179.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__0__left,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Groups_Omonoid__add(T_a)
% 179.48/179.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__0,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Groups_Ocomm__monoid__add(T_a)
% 179.48/179.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_double__zero__sym,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 179.48/179.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__0__right,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Groups_Omonoid__add(T_a)
% 179.48/179.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add_Ocomm__neutral,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Groups_Ocomm__monoid__add(T_a)
% 179.48/179.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.48 => 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) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.48/179.48 => 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) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_divisors__zero,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Ono__zero__divisors(T_a)
% 179.48/179.48 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 179.48/179.48 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 179.48/179.48 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_no__zero__divisors,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Ono__zero__divisors(T_a)
% 179.48/179.48 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 179.48/179.48 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 179.48/179.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__eq__0__iff,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Rings_Oring__no__zero__divisors(T_b)
% 179.48/179.48 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.48 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.48 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__zero__right,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Rings_Omult__zero(T_a)
% 179.48/179.48 => 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) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__zero__left,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Rings_Omult__zero(T_a)
% 179.48/179.48 => 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) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_right__minus__eq,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Ogroup__add(T_b)
% 179.48/179.48 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.48 <=> V_a_2 = V_b_2 ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_eq__iff__diff__eq__0,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Oab__group__add(T_b)
% 179.48/179.48 => ( V_a_2 = V_b_2
% 179.48/179.48 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diff__self,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.48 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diff__0__right,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.48 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_one__neq__zero,axiom,
% 179.48/179.48 ! [T_a] :
% 179.48/179.48 ( class_Rings_Ozero__neq__one(T_a)
% 179.48/179.48 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__neq__one,axiom,
% 179.48/179.48 ! [T_a] :
% 179.48/179.48 ( class_Rings_Ozero__neq__one(T_a)
% 179.48/179.48 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_neg__equal__zero,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 179.48/179.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_neg__equal__0__iff__equal,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Ogroup__add(T_b)
% 179.48/179.48 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_equal__neg__zero,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 179.48/179.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_neg__0__equal__iff__equal,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Ogroup__add(T_b)
% 179.48/179.48 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 179.48/179.48 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_minus__zero,axiom,
% 179.48/179.48 ! [T_a] :
% 179.48/179.48 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.48 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Zero__not__Suc,axiom,
% 179.48/179.48 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat_Osimps_I2_J,axiom,
% 179.48/179.48 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Suc__not__Zero,axiom,
% 179.48/179.48 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat_Osimps_I3_J,axiom,
% 179.48/179.48 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Zero__neq__Suc,axiom,
% 179.48/179.48 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Suc__neq__Zero,axiom,
% 179.48/179.48 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_not__less0,axiom,
% 179.48/179.48 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_neq0__conv,axiom,
% 179.48/179.48 ! [V_n_2] :
% 179.48/179.48 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_less__nat__zero__code,axiom,
% 179.48/179.48 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_gr__implies__not0,axiom,
% 179.48/179.48 ! [V_n,V_m] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.48/179.48 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_gr0I,axiom,
% 179.48/179.48 ! [V_n] :
% 179.48/179.48 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_plus__nat_Oadd__0,axiom,
% 179.48/179.48 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Nat_Oadd__0__right,axiom,
% 179.48/179.48 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__is__0,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2] :
% 179.48/179.48 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__eq__self__zero,axiom,
% 179.48/179.48 ! [V_n,V_m] :
% 179.48/179.48 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 179.48/179.48 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 179.48/179.48 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_le__0__eq,axiom,
% 179.48/179.48 ! [V_n_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 179.48/179.48 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diffs0__imp__equal,axiom,
% 179.48/179.48 ! [V_n,V_m] :
% 179.48/179.48 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 => V_m = V_n ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diff__self__eq__0,axiom,
% 179.48/179.48 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_minus__nat_Odiff__0,axiom,
% 179.48/179.48 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diff__0__eq__0,axiom,
% 179.48/179.48 ! [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) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__cancel2,axiom,
% 179.48/179.48 ! [V_n_2,V_k_2,V_m_2] :
% 179.48/179.48 ( 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)
% 179.48/179.48 <=> ( V_m_2 = V_n_2
% 179.48/179.48 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__cancel1,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.48 ( 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)
% 179.48/179.48 <=> ( V_m_2 = V_n_2
% 179.48/179.48 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__is__0,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2] :
% 179.48/179.48 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__0__right,axiom,
% 179.48/179.48 ! [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) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__0,axiom,
% 179.48/179.48 ! [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) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.48 ( 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)
% 179.48/179.48 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 | V_m_2 = V_n_2 ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_sum__squares__eq__zero__iff,axiom,
% 179.48/179.48 ! [V_y_2,V_x_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_b)
% 179.48/179.48 => ( 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)
% 179.48/179.48 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.48 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_sum__squares__le__zero__iff,axiom,
% 179.48/179.48 ! [V_y_2,V_x_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.48 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_sum__squares__ge__zero,axiom,
% 179.48/179.48 ! [V_y,V_x,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__ring(T_a)
% 179.48/179.48 => 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)))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_not__sum__squares__lt__zero,axiom,
% 179.48/179.48 ! [V_y,V_x,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__ring(T_a)
% 179.48/179.48 => ~ 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))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_sum__squares__gt__zero__iff,axiom,
% 179.48/179.48 ! [V_y_2,V_x_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_b)
% 179.48/179.48 => ( 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))))
% 179.48/179.48 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.48 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__nonneg__nonneg,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__nonneg__eq__0__iff,axiom,
% 179.48/179.48 ! [V_y_2,V_x_2,T_b] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 179.48/179.48 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.48 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.48 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__increasing,axiom,
% 179.48/179.48 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__increasing2,axiom,
% 179.48/179.48 ! [V_a,V_b,V_c,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__nonpos__nonpos,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_split__mult__neg__le,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 179.48/179.48 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 179.48/179.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 179.48/179.48 => 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_split__mult__pos__le,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__ring(T_a)
% 179.48/179.48 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 179.48/179.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 179.48/179.48 => 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__mono,axiom,
% 179.48/179.48 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__semiring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__mono_H,axiom,
% 179.48/179.48 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__semiring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__left__mono__neg,axiom,
% 179.48/179.48 ! [V_c,V_a,V_b,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__ring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__right__mono__neg,axiom,
% 179.48/179.48 ! [V_c,V_a,V_b,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__ring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_comm__mult__left__mono,axiom,
% 179.48/179.48 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__comm__semiring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__left__mono,axiom,
% 179.48/179.48 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__semiring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__right__mono,axiom,
% 179.48/179.48 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__semiring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__nonpos__nonpos,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__ring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__nonpos__nonneg,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__nonneg__nonpos2,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__nonneg__nonpos,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__nonneg__nonneg,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__le__0__iff,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 179.48/179.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__le__mult__iff,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 179.48/179.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__le__square,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__ring(T_a)
% 179.48/179.48 => 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))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_pos__add__strict,axiom,
% 179.48/179.48 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semidom(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__pos__pos,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__neg__neg,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_not__square__less__zero,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__ring(T_a)
% 179.48/179.48 => ~ 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))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__less__cancel__right__disj,axiom,
% 179.48/179.48 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 179.48/179.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__less__cancel__left__disj,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 179.48/179.48 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__less__cancel__left__pos,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__pos__pos,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__pos__neg,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__pos__neg2,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__less__mult__pos,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__less__mult__pos2,axiom,
% 179.48/179.48 ! [V_a,V_b,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__less__cancel__left__neg,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__neg__pos,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__neg__neg,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__strict__right__mono,axiom,
% 179.48/179.48 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__strict__left__mono,axiom,
% 179.48/179.48 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_comm__mult__strict__left__mono,axiom,
% 179.48/179.48 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__strict__right__mono__neg,axiom,
% 179.48/179.48 ! [V_c,V_a,V_b,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__strict__left__mono__neg,axiom,
% 179.48/179.48 ! [V_c,V_a,V_b,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_le__iff__diff__le__0,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 179.48/179.48 <=> 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_less__iff__diff__less__0,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 179.48/179.48 <=> 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__scale__eq__noteq,axiom,
% 179.48/179.48 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 179.48/179.48 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 179.48/179.48 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 179.48/179.48 => ( ( V_a = V_b
% 179.48/179.48 & V_c != V_d )
% 179.48/179.48 => 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)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__le__one,axiom,
% 179.48/179.48 ! [T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semidom(T_a)
% 179.48/179.48 => 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))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_not__one__le__zero,axiom,
% 179.48/179.48 ! [T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semidom(T_a)
% 179.48/179.48 => ~ 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))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__less__one,axiom,
% 179.48/179.48 ! [T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semidom(T_a)
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_not__one__less__zero,axiom,
% 179.48/179.48 ! [T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semidom(T_a)
% 179.48/179.48 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_neg__0__le__iff__le,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_le__minus__self__iff,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_neg__le__0__iff__le,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_minus__le__self__iff,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( 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))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_less__minus__self__iff,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__idom(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_neg__less__nonneg,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_neg__less__0__iff__less,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_neg__0__less__iff__less,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_minus__Min__eq__Max,axiom,
% 179.48/179.48 ! [V_S_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.48/179.48 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.48 => 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)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_minus__Max__eq__Min,axiom,
% 179.48/179.48 ! [V_S_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.48/179.48 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.48 => 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)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_minus__unique,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.48 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 179.48/179.48 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_ab__left__minus,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oab__group__add(T_a)
% 179.48/179.48 => 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) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_left__minus,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.48 => 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) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Ogroup__add(T_b)
% 179.48/179.48 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 179.48/179.48 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_right__minus,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.48 => 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) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diff__0,axiom,
% 179.48/179.48 ! [V_a,T_a] :
% 179.48/179.48 ( class_Groups_Ogroup__add(T_a)
% 179.48/179.48 => 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) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_less__Suc__eq__0__disj,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 179.48/179.48 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 | ? [B_j] :
% 179.48/179.48 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_less__Suc0,axiom,
% 179.48/179.48 ! [V_n_2] :
% 179.48/179.48 ( 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))))
% 179.48/179.48 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_gr0__conv__Suc,axiom,
% 179.48/179.48 ! [V_n_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 179.48/179.48 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_one__is__add,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2] :
% 179.48/179.48 ( 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)
% 179.48/179.48 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 179.48/179.48 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 179.48/179.48 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__is__1,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2] :
% 179.48/179.48 ( 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))
% 179.48/179.48 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 179.48/179.48 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 179.48/179.48 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__gr__0,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 179.48/179.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card_Oempty,axiom,
% 179.48/179.48 ! [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) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card__infinite,axiom,
% 179.48/179.48 ! [V_A_2,T_b] :
% 179.48/179.48 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__eq__1__iff,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2] :
% 179.48/179.48 ( 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))
% 179.48/179.48 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 179.48/179.48 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__less__diff,axiom,
% 179.48/179.48 ! [V_m_2,V_n_2] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diff__less,axiom,
% 179.48/179.48 ! [V_m,V_n] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 179.48/179.48 => 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)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__0__less__mult__iff,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__less__cancel1,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__less__cancel2,axiom,
% 179.48/179.48 ! [V_n_2,V_k_2,V_m_2] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 179.48/179.48 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__less__mono1,axiom,
% 179.48/179.48 ! [V_k,V_j,V_i] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 179.48/179.48 => 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__less__mono2,axiom,
% 179.48/179.48 ! [V_k,V_j,V_i] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 179.48/179.48 => 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__mult__eq__cancel1,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 179.48/179.48 => ( 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)
% 179.48/179.48 <=> V_m_2 = V_n_2 ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__mult__less__cancel1,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diff__add__0,axiom,
% 179.48/179.48 ! [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) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diff__is__0__eq_H,axiom,
% 179.48/179.48 ! [V_n,V_m] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.48/179.48 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diff__is__0__eq,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2] :
% 179.48/179.48 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_One__nat__def,axiom,
% 179.48/179.48 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Max_Osingleton,axiom,
% 179.48/179.48 ! [V_x_2,T_b] :
% 179.48/179.48 ( class_Orderings_Olinorder(T_b)
% 179.48/179.48 => 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 ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Min_Osingleton,axiom,
% 179.48/179.48 ! [V_x_2,T_b] :
% 179.48/179.48 ( class_Orderings_Olinorder(T_b)
% 179.48/179.48 => 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 ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__eq__self__implies__10,axiom,
% 179.48/179.48 ! [V_n,V_m] :
% 179.48/179.48 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 179.48/179.48 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 179.48/179.48 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Suc__pred_H,axiom,
% 179.48/179.48 ! [V_n] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.48/179.48 => 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))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__eq__if,axiom,
% 179.48/179.48 ! [V_n,V_m] :
% 179.48/179.48 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 179.48/179.48 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 => 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)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__pos__nonneg,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__nonneg__pos,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__strict__increasing,axiom,
% 179.48/179.48 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__strict__increasing2,axiom,
% 179.48/179.48 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__neg__nonpos,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_add__nonpos__neg,axiom,
% 179.48/179.48 ! [V_b,V_a,T_a] :
% 179.48/179.48 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__le__cancel__left__pos,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__le__cancel__left__neg,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__ring__strict(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__strict__mono,axiom,
% 179.48/179.48 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__strict__mono_H,axiom,
% 179.48/179.48 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__less__le__imp__less,axiom,
% 179.48/179.48 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__le__less__imp__less,axiom,
% 179.48/179.48 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => 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))) ) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__right__less__imp__less,axiom,
% 179.48/179.48 ! [V_b,V_c,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring(T_a)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__less__imp__less__right,axiom,
% 179.48/179.48 ! [V_b,V_c,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__left__less__imp__less,axiom,
% 179.48/179.48 ! [V_b,V_a,V_c,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring(T_a)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__less__imp__less__left,axiom,
% 179.48/179.48 ! [V_b,V_a,V_c,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__right__le__imp__le,axiom,
% 179.48/179.48 ! [V_b,V_c,V_a,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__left__le__imp__le,axiom,
% 179.48/179.48 ! [V_b,V_a,V_c,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__strict(T_a)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__eq__if,axiom,
% 179.48/179.48 ! [V_n,V_m] :
% 179.48/179.48 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 179.48/179.48 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 => 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)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__left__le__one__le,axiom,
% 179.48/179.48 ! [V_y,V_x,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__idom(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 179.48/179.48 => 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)) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__right__le__one__le,axiom,
% 179.48/179.48 ! [V_y,V_x,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__idom(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 179.48/179.48 => 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)) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_zero__less__two,axiom,
% 179.48/179.48 ! [T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semidom(T_a)
% 179.48/179.48 => 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)))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card__eq__0__iff,axiom,
% 179.48/179.48 ! [V_A_2,T_b] :
% 179.48/179.48 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.48 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card__ge__0__finite,axiom,
% 179.48/179.48 ! [V_A_2,T_b] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Suc__pred,axiom,
% 179.48/179.48 ! [V_n] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.48/179.48 => 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 ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_diff__Suc__less,axiom,
% 179.48/179.48 ! [V_i,V_n] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.48/179.48 => 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)) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_one__less__mult,axiom,
% 179.48/179.48 ! [V_m,V_n] :
% 179.48/179.48 ( 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))
% 179.48/179.48 => ( 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))
% 179.48/179.48 => 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_n__less__n__mult__m,axiom,
% 179.48/179.48 ! [V_m,V_n] :
% 179.48/179.48 ( 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))
% 179.48/179.48 => ( 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))
% 179.48/179.48 => 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_n__less__m__mult__n,axiom,
% 179.48/179.48 ! [V_m,V_n] :
% 179.48/179.48 ( 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))
% 179.48/179.48 => ( 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))
% 179.48/179.48 => 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__diff__split__asm,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,V_P_2] :
% 179.48/179.48 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 179.48/179.48 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 179.48/179.48 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 179.48/179.48 | ? [B_d] :
% 179.48/179.48 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 179.48/179.48 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__diff__split,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,V_P_2] :
% 179.48/179.48 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 179.48/179.48 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 179.48/179.48 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 179.48/179.48 & ! [B_d] :
% 179.48/179.48 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 179.48/179.48 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_one__le__mult__iff,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 <=> ( 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))
% 179.48/179.48 & 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)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__le__cancel2,axiom,
% 179.48/179.48 ! [V_n_2,V_k_2,V_m_2] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_mult__le__cancel1,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__mult__le__cancel1,axiom,
% 179.48/179.48 ! [V_n_2,V_m_2,V_k_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Min__le,axiom,
% 179.48/179.48 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.48 ( class_Orderings_Olinorder(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.48 => 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)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Max__ge,axiom,
% 179.48/179.48 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.48 ( class_Orderings_Olinorder(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Max__in,axiom,
% 179.48/179.48 ! [V_A_2,T_b] :
% 179.48/179.48 ( class_Orderings_Olinorder(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Min__in,axiom,
% 179.48/179.48 ! [V_A_2,T_b] :
% 179.48/179.48 ( class_Orderings_Olinorder(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card__less__Suc2,axiom,
% 179.48/179.48 ! [V_i_2,V_M_2] :
% 179.48/179.48 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 179.48/179.48 => 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))))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card__less,axiom,
% 179.48/179.48 ! [V_i_2,V_M_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 179.48/179.48 => 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) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card__less__Suc,axiom,
% 179.48/179.48 ! [V_i_2,V_M_2] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 179.48/179.48 => 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))))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_convex__bound__le,axiom,
% 179.48/179.48 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__1(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 179.48/179.48 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 179.48/179.48 => 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)) ) ) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card__gt__0__iff,axiom,
% 179.48/179.48 ! [V_A_2,T_b] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.48 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_finite__UNIV__card__ge__0,axiom,
% 179.48/179.48 ! [T_b] :
% 179.48/179.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 179.48/179.48 => 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))))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Suc__diff__1,axiom,
% 179.48/179.48 ! [V_n] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.48/179.48 => 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 ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Min__antimono,axiom,
% 179.48/179.48 ! [V_N_2,V_M_2,T_b] :
% 179.48/179.48 ( class_Orderings_Olinorder(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 179.48/179.48 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.48/179.48 => 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))) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Max__mono,axiom,
% 179.48/179.48 ! [V_N_2,V_M_2,T_b] :
% 179.48/179.48 ( class_Orderings_Olinorder(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 179.48/179.48 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.48/179.48 => 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))) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card__def,axiom,
% 179.48/179.48 ! [V_A_2,T_b] :
% 179.48/179.48 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => 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) )
% 179.48/179.48 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card_Oeq__fold__g,axiom,
% 179.48/179.48 ! [V_A_2,T_b] :
% 179.48/179.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => 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) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_convex__bound__lt,axiom,
% 179.48/179.48 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 179.48/179.48 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 179.48/179.48 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 179.48/179.48 => 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)) ) ) ) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_triple_Osize_I1_J,axiom,
% 179.48/179.48 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_even__less__0__iff,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__idom(T_b)
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_triple_Osize_I2_J,axiom,
% 179.48/179.48 ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card_Ounion__inter__neutral,axiom,
% 179.48/179.48 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.48 => ( ( ? [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)))
% 179.48/179.48 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 179.48/179.48 => 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)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card__Suc__eq,axiom,
% 179.48/179.48 ! [V_k_2,V_A_2,T_b] :
% 179.48/179.48 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 179.48/179.48 <=> ? [B_b,B_B] :
% 179.48/179.48 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 179.48/179.48 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 179.48/179.48 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 179.48/179.48 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.48/179.48 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_option_Osize_I2_J,axiom,
% 179.48/179.48 ! [V_a_2,V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_com_Osize_I4_J,axiom,
% 179.48/179.48 ! [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))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_option_Osize_I1_J,axiom,
% 179.48/179.48 ! [V_fa_2,T_b] : c_Option_Ooption_Ooption__size(T_b,V_fa_2,c_Option_Ooption_ONone(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_com_Osize_I2_J,axiom,
% 179.48/179.48 ! [V_fun_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_com_Osize_I1_J,axiom,
% 179.48/179.48 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_com_Osize_I6_J,axiom,
% 179.48/179.48 ! [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))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_double__eq__0__iff,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Groups_Olinordered__ab__group__add(T_b)
% 179.48/179.48 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_com_Osize_I5_J,axiom,
% 179.48/179.48 ! [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))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat_Osize_I2_J,axiom,
% 179.48/179.48 ! [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))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat_Osize_I4_J,axiom,
% 179.48/179.48 ! [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))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_option_Osize_I4_J,axiom,
% 179.48/179.48 ! [V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),hAPP(c_Option_Ooption_OSome(T_a),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_option_Osize_I3_J,axiom,
% 179.48/179.48 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Ints__odd__less__0,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Rings_Olinordered__idom(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 179.48/179.48 => ( 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)))
% 179.48/179.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card__Plus__conv__if,axiom,
% 179.48/179.48 ! [V_B_2,T_c,V_A_2,T_b] :
% 179.48/179.48 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 179.48/179.48 => 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)) )
% 179.48/179.48 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 179.48/179.48 => 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) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat__size,axiom,
% 179.48/179.48 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Ints__0,axiom,
% 179.48/179.48 ! [T_b] :
% 179.48/179.48 ( class_Rings_Oring__1(T_b)
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Ints__add,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Rings_Oring__1(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Ints__mult,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Rings_Oring__1(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat_Osize_I3_J,axiom,
% 179.48/179.48 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) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Ints__diff,axiom,
% 179.48/179.48 ! [V_b_2,V_a_2,T_b] :
% 179.48/179.48 ( class_Rings_Oring__1(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 179.48/179.48 => 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))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Ints__1,axiom,
% 179.48/179.48 ! [T_b] :
% 179.48/179.48 ( class_Rings_Oring__1(T_b)
% 179.48/179.48 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Ints__minus,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Rings_Oring__1(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 179.48/179.48 => 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_nat_Osize_I1_J,axiom,
% 179.48/179.48 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Ints__double__eq__0__iff,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Int_Oring__char__0(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 179.48/179.48 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.48 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_finite__Plus__iff,axiom,
% 179.48/179.48 ! [V_B_2,V_A_2,T_c,T_b] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_finite__Plus,axiom,
% 179.48/179.48 ! [V_B_2,T_c,V_A_2,T_b] :
% 179.48/179.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 179.48/179.48 => 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))) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_finite__PlusD_I1_J,axiom,
% 179.48/179.48 ! [V_B_2,V_A_2,T_c,T_b] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_finite__PlusD_I2_J,axiom,
% 179.48/179.48 ! [V_B_2,V_A_2,T_c,T_b] :
% 179.48/179.48 ( 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)))
% 179.48/179.48 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_card__Plus,axiom,
% 179.48/179.48 ! [V_B_2,T_c,V_A_2,T_b] :
% 179.48/179.48 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.48 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 179.48/179.48 => 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)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Ints__odd__nonzero,axiom,
% 179.48/179.48 ! [V_a_2,T_b] :
% 179.48/179.48 ( class_Int_Oring__char__0(T_b)
% 179.48/179.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 179.48/179.48 => 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) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_UNIV__Plus__UNIV,axiom,
% 179.48/179.48 ! [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)) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_Plus__eq__empty__conv,axiom,
% 179.48/179.48 ! [V_B_2,V_A_2,T_c,T_b] :
% 179.48/179.48 ( 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))
% 179.48/179.48 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.48 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_com_Osize_I12_J,axiom,
% 179.48/179.48 ! [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))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_com_Osize_I13_J,axiom,
% 179.48/179.48 ! [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))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_com_Osize_I14_J,axiom,
% 179.48/179.48 ! [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))) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_ex__least__nat__less,axiom,
% 179.48/179.48 ! [V_n_2,V_P_2] :
% 179.48/179.48 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 179.48/179.48 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 179.48/179.48 => ? [B_k] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 179.48/179.48 & ! [B_i] :
% 179.48/179.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 179.48/179.48 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 179.48/179.48 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 179.48/179.48
% 179.48/179.48 fof(fact_com_Osize_I10_J,axiom,
% 179.48/179.48 ! [V_fun_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.48
% 179.48/179.49 fof(fact_com_Osize_I9_J,axiom,
% 179.48/179.49 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sgn__neg,axiom,
% 179.48/179.49 ! [V_a,T_a] :
% 179.48/179.49 ( class_Rings_Olinordered__idom(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.48/179.49 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sgn__1__neg,axiom,
% 179.48/179.49 ! [V_a_2,T_b] :
% 179.48/179.49 ( class_Rings_Olinordered__idom(T_b)
% 179.48/179.49 => ( 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))
% 179.48/179.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sgn__if,axiom,
% 179.48/179.49 ! [V_x,T_a] :
% 179.48/179.49 ( class_Groups_Osgn__if(T_a)
% 179.48/179.49 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 179.48/179.49 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 179.48/179.49 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 179.48/179.49 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.48/179.49 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 179.48/179.49 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.48/179.49 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Min_Oremove,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.49 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 179.48/179.49 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => 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)))))) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Max_Oremove,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.49 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 179.48/179.49 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => 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)))))) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_diff__Suc,axiom,
% 179.48/179.49 ! [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)) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_max__Suc2,axiom,
% 179.48/179.49 ! [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) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_max__Suc1,axiom,
% 179.48/179.49 ! [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) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_minus__min__eq__max,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Groups_Olinordered__ab__group__add(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_minus__max__eq__min,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Groups_Olinordered__ab__group__add(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup_Oidem,axiom,
% 179.48/179.49 ! [V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf_Oidem,axiom,
% 179.48/179.49 ! [V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup_Ocommute,axiom,
% 179.48/179.49 ! [V_b,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__commute,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf_Ocommute,axiom,
% 179.48/179.49 ! [V_b,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__commute,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__inf__absorb,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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 ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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 ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 179.48/179.49 ! [V_b,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__left__idem,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 179.48/179.49 ! [V_b,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__left__idem,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 179.48/179.49 ! [V_c,V_a,V_b,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__left__commute,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 179.48/179.49 ! [V_c,V_a,V_b,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__left__commute,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup_Oassoc,axiom,
% 179.48/179.49 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__assoc,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf_Oassoc,axiom,
% 179.48/179.49 ! [V_c,V_b,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__assoc,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 179.48/179.49 ! [V_x,V_z,V_y,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 179.48/179.49 ! [V_x,V_z,V_y,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Max_Oidem,axiom,
% 179.48/179.49 ! [V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Min_Oidem,axiom,
% 179.48/179.49 ! [V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sgn__sgn,axiom,
% 179.48/179.49 ! [V_a,T_a] :
% 179.48/179.49 ( class_Rings_Olinordered__idom(T_a)
% 179.48/179.49 => 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) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Odistrib__inf__le,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)))) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Odistrib__sup__le,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)))) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_le__maxI1,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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))) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_le__maxI2,axiom,
% 179.48/179.49 ! [V_x,V_y,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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))) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__iff__sup,axiom,
% 179.48/179.49 ! [V_y_2,V_x_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.48/179.49 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__sup__iff,axiom,
% 179.48/179.49 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( 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))
% 179.48/179.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 179.48/179.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__supI1,axiom,
% 179.48/179.49 ! [V_b,V_a,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 179.48/179.49 => 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))) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__supI2,axiom,
% 179.48/179.49 ! [V_a,V_b,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 179.48/179.49 => 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))) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__absorb2,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.48/179.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__absorb1,axiom,
% 179.48/179.49 ! [V_x,V_y,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.48/179.49 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__supI,axiom,
% 179.48/179.49 ! [V_b,V_x,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 179.48/179.49 => 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)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__least,axiom,
% 179.48/179.49 ! [V_z,V_x,V_y,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 179.48/179.49 => 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)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__mono,axiom,
% 179.48/179.49 ! [V_d,V_b,V_c,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 179.48/179.49 => 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))) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__supE,axiom,
% 179.48/179.49 ! [V_x,V_b,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( 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))
% 179.48/179.49 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 179.48/179.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_le__max__iff__disj,axiom,
% 179.48/179.49 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( 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)))
% 179.48/179.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 179.48/179.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__le1,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__le2,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__iff__inf,axiom,
% 179.48/179.49 ! [V_y_2,V_x_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.48/179.49 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__inf__iff,axiom,
% 179.48/179.49 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( 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)))
% 179.48/179.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.48/179.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__infI1,axiom,
% 179.48/179.49 ! [V_b,V_x,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 179.48/179.49 => 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)) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__infI2,axiom,
% 179.48/179.49 ! [V_a,V_x,V_b,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 179.48/179.49 => 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)) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__absorb1,axiom,
% 179.48/179.49 ! [V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.48/179.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__absorb2,axiom,
% 179.48/179.49 ! [V_x,V_y,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 179.48/179.49 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__infI,axiom,
% 179.48/179.49 ! [V_b,V_a,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 179.48/179.49 => 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))) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__greatest,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 179.48/179.49 => 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))) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__mono,axiom,
% 179.48/179.49 ! [V_d,V_b,V_c,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 179.48/179.49 => 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))) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ole__infE,axiom,
% 179.48/179.49 ! [V_b,V_a,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( 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)))
% 179.48/179.49 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 179.48/179.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__le__iff__disj,axiom,
% 179.48/179.49 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( 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))
% 179.48/179.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 179.48/179.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oless__supI1,axiom,
% 179.48/179.49 ! [V_b,V_a,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 179.48/179.49 => 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))) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oless__supI2,axiom,
% 179.48/179.49 ! [V_a,V_b,V_x,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 179.48/179.49 => 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))) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_less__max__iff__disj,axiom,
% 179.48/179.49 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( 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)))
% 179.48/179.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 179.48/179.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_max__less__iff__conj,axiom,
% 179.48/179.49 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( 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))
% 179.48/179.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 179.48/179.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oless__infI1,axiom,
% 179.48/179.49 ! [V_b,V_x,V_a,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 179.48/179.49 => 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)) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oless__infI2,axiom,
% 179.48/179.49 ! [V_a,V_x,V_b,T_a] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 179.48/179.49 => 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)) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__less__iff__conj,axiom,
% 179.48/179.49 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( 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)))
% 179.48/179.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 179.48/179.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__less__iff__disj,axiom,
% 179.48/179.49 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( 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))
% 179.48/179.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 179.48/179.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_max__add__distrib__left,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__add__distrib__left,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_max__diff__distrib__left,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Groups_Oordered__ab__group__add(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__diff__distrib__left,axiom,
% 179.48/179.49 ! [V_z,V_y,V_x,T_a] :
% 179.48/179.49 ( class_Groups_Oordered__ab__group__add(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sup__max,axiom,
% 179.48/179.49 ! [T_b] :
% 179.48/179.49 ( ( class_Lattices_Osemilattice__sup(T_b)
% 179.48/179.49 & class_Orderings_Olinorder(T_b) )
% 179.48/179.49 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_max__0L,axiom,
% 179.48/179.49 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 179.48/179.49
% 179.48/179.49 fof(fact_max__0R,axiom,
% 179.48/179.49 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 179.48/179.49
% 179.48/179.49 fof(fact_inf__min,axiom,
% 179.48/179.49 ! [T_b] :
% 179.48/179.49 ( ( class_Lattices_Osemilattice__inf(T_b)
% 179.48/179.49 & class_Orderings_Olinorder(T_b) )
% 179.48/179.49 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__0L,axiom,
% 179.48/179.49 ! [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) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__0R,axiom,
% 179.48/179.49 ! [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) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_max__Suc__Suc,axiom,
% 179.48/179.49 ! [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)) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__Suc__Suc,axiom,
% 179.48/179.49 ! [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)) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__diff,axiom,
% 179.48/179.49 ! [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) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 179.48/179.49 ! [T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 179.48/179.49 ! [T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__Suc2,axiom,
% 179.48/179.49 ! [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) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__Suc1,axiom,
% 179.48/179.49 ! [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) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sgn0,axiom,
% 179.48/179.49 ! [T_a] :
% 179.48/179.49 ( class_Groups_Osgn__if(T_a)
% 179.48/179.49 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sgn__0__0,axiom,
% 179.48/179.49 ! [V_a_2,T_b] :
% 179.48/179.49 ( class_Rings_Olinordered__idom(T_b)
% 179.48/179.49 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.48/179.49 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sgn__times,axiom,
% 179.48/179.49 ! [V_b,V_a,T_a] :
% 179.48/179.49 ( class_Rings_Olinordered__idom(T_a)
% 179.48/179.49 => 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_nat__minus__add__max,axiom,
% 179.48/179.49 ! [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) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_nat__case__0,axiom,
% 179.48/179.49 ! [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 ).
% 179.48/179.49
% 179.48/179.49 fof(fact_nat__case__Suc,axiom,
% 179.48/179.49 ! [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) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Max_Oin__idem,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.49 => 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) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Min_Oin__idem,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.49 => 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) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sgn__less,axiom,
% 179.48/179.49 ! [V_a_2,T_b] :
% 179.48/179.49 ( class_Rings_Olinordered__idom(T_b)
% 179.48/179.49 => ( 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)))
% 179.48/179.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sgn__greater,axiom,
% 179.48/179.49 ! [V_a_2,T_b] :
% 179.48/179.49 ( class_Rings_Olinordered__idom(T_b)
% 179.48/179.49 => ( 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)))
% 179.48/179.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Max_OF__eq,axiom,
% 179.48/179.49 ! [V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => 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) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Min_OF__eq,axiom,
% 179.48/179.49 ! [V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => 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) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Ofold1__belowI,axiom,
% 179.48/179.49 ! [V_a_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.48/179.49 => 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)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( 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)))
% 179.48/179.49 <=> ! [B_x] :
% 179.48/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.48/179.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_fold1__below__iff,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( 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))
% 179.48/179.49 <=> ? [B_x] :
% 179.48/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.48/179.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_strict__below__fold1__iff,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( 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)))
% 179.48/179.49 <=> ! [B_x] :
% 179.48/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.48/179.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_fold1__strict__below__iff,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( 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))
% 179.48/179.49 <=> ? [B_x] :
% 179.48/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.48/179.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Max__insert,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Min__insert,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Max_Osubset__idem,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.48/179.49 => 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) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Min_Osubset__idem,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.48/179.49 => 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) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Max__Un,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Min__Un,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sgn__pos,axiom,
% 179.48/179.49 ! [V_a,T_a] :
% 179.48/179.49 ( class_Rings_Olinordered__idom(T_a)
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.48/179.49 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sgn__1__pos,axiom,
% 179.48/179.49 ! [V_a_2,T_b] :
% 179.48/179.49 ( class_Rings_Olinordered__idom(T_b)
% 179.48/179.49 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 179.48/179.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Max_Oinsert,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Min_Oinsert,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_fold1__antimono,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => 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))) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Max_Oinsert__remove,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 179.48/179.49 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => 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)))))) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Max_Ounion__disjoint,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Max_Ounion__inter,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Min_Oinsert__remove,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 179.48/179.49 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => 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)))))) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Min_Ounion__disjoint,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_Min_Ounion__inter,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_dual__min,axiom,
% 179.48/179.49 ! [T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => 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) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_dual__max,axiom,
% 179.48/179.49 ! [T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => 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) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_max__ord__max,axiom,
% 179.48/179.49 ! [T_b] :
% 179.48/179.49 ( class_Orderings_Oord(T_b)
% 179.48/179.49 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__ord__min,axiom,
% 179.48/179.49 ! [T_b] :
% 179.48/179.49 ( class_Orderings_Oord(T_b)
% 179.48/179.49 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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))))) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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))))) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_inf__nat__def,axiom,
% 179.48/179.49 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_sup__nat__def,axiom,
% 179.48/179.49 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OInf__le__Sup,axiom,
% 179.48/179.49 ! [V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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))) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.49 => 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) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.49 => 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) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 179.48/179.49 ! [V_x_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => 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 ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 179.48/179.49 ! [V_x_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => 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 ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 179.48/179.49 ! [V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => 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) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 179.48/179.49 ! [V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => 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) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.48/179.49 => 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) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.48/179.49 => 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) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 179.48/179.49 ! [V_a_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.48/179.49 => 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 ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 179.48/179.49 ! [V_a_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.48/179.49 => 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 ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 179.48/179.49 ! [V_n_2,V_m_2] :
% 179.48/179.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 179.48/179.49 <=> 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)) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => 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 )
% 179.48/179.49 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => 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)))))) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 179.48/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => 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 )
% 179.48/179.49 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.48/179.49 => 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)))))) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.48/179.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => 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)) ) ) ) ) ).
% 179.48/179.49
% 179.48/179.49 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 179.48/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.48/179.49 ( class_Orderings_Olinorder(T_b)
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.48/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.48/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => 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)) ) ) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 179.58/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.58/179.49 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.58/179.49 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 179.58/179.49 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.58/179.49 => 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)))))) ) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 179.58/179.49 ! [V_x_2,V_A_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.58/179.49 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.58/179.49 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 179.58/179.49 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 179.58/179.49 => 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)))))) ) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 179.58/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => 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))))))) ) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 179.58/179.49 ! [V_B_2,V_A_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.49 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => 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))))))) ) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 179.58/179.49 ! [V_A_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => ( ! [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))))))
% 179.58/179.49 => 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)) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 179.58/179.49 ! [V_A_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => ( ! [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))))))
% 179.58/179.49 => 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)) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_Max_Oclosed,axiom,
% 179.58/179.49 ! [V_A_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => ( ! [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))))))
% 179.58/179.49 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_Min_Oclosed,axiom,
% 179.58/179.49 ! [V_A_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => ( ! [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))))))
% 179.58/179.49 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 179.58/179.49 ! [V_N_2,V_h_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( ! [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))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.58/179.49 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => 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)) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 179.58/179.49 ! [V_N_2,V_h_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( ! [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))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.58/179.49 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => 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)) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_Max_Ohom__commute,axiom,
% 179.58/179.49 ! [V_N_2,V_h_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( ! [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))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.58/179.49 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => 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)) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_Min_Ohom__commute,axiom,
% 179.58/179.49 ! [V_N_2,V_h_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( ! [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))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 179.58/179.49 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => 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)) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_pigeonhole__infinite,axiom,
% 179.58/179.49 ! [V_f_2,T_c,V_A_2,T_b] :
% 179.58/179.49 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 179.58/179.49 => ? [B_x] :
% 179.58/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.49 & ~ 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)))))) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_finite__range__map__of__map__add,axiom,
% 179.58/179.49 ! [V_l_2,V_f_2,T_c,T_b] :
% 179.58/179.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 179.58/179.49 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),c_Map_Omap__add(T_c,T_b,V_f_2,hAPP(c_Map_Omap__of(T_c,T_b),V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_inj__on__diff__nat,axiom,
% 179.58/179.49 ! [V_k_2,V_N_2] :
% 179.58/179.49 ( ! [B_x] :
% 179.58/179.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 179.58/179.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 179.58/179.49 => 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) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__diff1,axiom,
% 179.58/179.49 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Oab__group__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.49 => 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)) )
% 179.58/179.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.49 => 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) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__commute,axiom,
% 179.58/179.49 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.49 => 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) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__0,axiom,
% 179.58/179.49 ! [V_A_2,T_c,T_b] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.49 => 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) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__addf,axiom,
% 179.58/179.49 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.49 => 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)) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__product,axiom,
% 179.58/179.49 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.49 ( class_Rings_Osemiring__0(T_b)
% 179.58/179.49 => 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) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__left__distrib,axiom,
% 179.58/179.49 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.49 ( class_Rings_Osemiring__0(T_b)
% 179.58/179.49 => 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) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__right__distrib,axiom,
% 179.58/179.49 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 179.58/179.49 ( class_Rings_Osemiring__0(T_b)
% 179.58/179.49 => 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) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__subtractf,axiom,
% 179.58/179.49 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 179.58/179.49 ( class_Groups_Oab__group__add(T_b)
% 179.58/179.49 => 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)) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__negf,axiom,
% 179.58/179.49 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.49 ( class_Groups_Oab__group__add(T_b)
% 179.58/179.49 => 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)) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__empty,axiom,
% 179.58/179.49 ! [V_f_2,T_c,T_b] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.49 => 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) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum_Oempty,axiom,
% 179.58/179.49 ! [V_g_2,T_c,T_b] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.49 => 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) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__infinite,axiom,
% 179.58/179.49 ! [V_f_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => 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) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum_Oinfinite,axiom,
% 179.58/179.49 ! [V_g_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => 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) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__eq__0__iff,axiom,
% 179.58/179.49 ! [V_f_2,V_F_2,T_b] :
% 179.58/179.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 179.58/179.49 => ( 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)
% 179.58/179.49 <=> ! [B_x] :
% 179.58/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 179.58/179.49 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum_Odistrib,axiom,
% 179.58/179.49 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => 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)) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_finite__dom__map__of,axiom,
% 179.58/179.49 ! [V_l_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_l_2)))) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_card__eq__setsum,axiom,
% 179.58/179.49 ! [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) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__eq__Suc0__iff,axiom,
% 179.58/179.49 ! [V_f_2,V_A_2,T_b] :
% 179.58/179.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( 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))
% 179.58/179.49 <=> ? [B_x] :
% 179.58/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.49 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 179.58/179.49 & ! [B_xa] :
% 179.58/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 179.58/179.49 => ( B_x != B_xa
% 179.58/179.49 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__reindex,axiom,
% 179.58/179.49 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_d)
% 179.58/179.49 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 179.58/179.49 => 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) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__eq__1__iff,axiom,
% 179.58/179.49 ! [V_f_2,V_A_2,T_b] :
% 179.58/179.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( 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)
% 179.58/179.49 <=> ? [B_x] :
% 179.58/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.49 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 179.58/179.49 & ! [B_xa] :
% 179.58/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 179.58/179.49 => ( B_x != B_xa
% 179.58/179.49 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__delta_H,axiom,
% 179.58/179.49 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.49 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 179.58/179.49 => 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) )
% 179.58/179.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 179.58/179.49 => 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) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__delta,axiom,
% 179.58/179.49 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.49 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 179.58/179.49 => 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) )
% 179.58/179.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 179.58/179.49 => 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) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__setsum__restrict,axiom,
% 179.58/179.49 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_d)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 179.58/179.49 => 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) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum_Oinsert,axiom,
% 179.58/179.49 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.58/179.49 => 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)) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__insert,axiom,
% 179.58/179.49 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 179.58/179.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 179.58/179.49 => 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)) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__Un__Int,axiom,
% 179.58/179.49 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.49 => 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)) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__diff,axiom,
% 179.58/179.49 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Oab__group__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.58/179.49 => 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)) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum_Oreindex,axiom,
% 179.58/179.49 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 179.58/179.49 => 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) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum_OF__eq,axiom,
% 179.58/179.49 ! [V_g_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => 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) )
% 179.58/179.49 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => 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) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum_Oeq__fold,axiom,
% 179.58/179.49 ! [V_g_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => 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) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__diff__nat,axiom,
% 179.58/179.49 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 179.58/179.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.58/179.49 => 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)) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__restrict__set_H,axiom,
% 179.58/179.49 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => 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) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__restrict__set,axiom,
% 179.58/179.49 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => 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) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__image__gen,axiom,
% 179.58/179.49 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.49 => 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)) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_finite__range__map__of,axiom,
% 179.58/179.49 ! [V_xys_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),hAPP(c_Set_Oimage(T_c,tc_Option_Ooption(T_b),hAPP(c_Map_Omap__of(T_c,T_b),V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum_Oinsert__remove,axiom,
% 179.58/179.49 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => 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)))))) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__Un__disjoint,axiom,
% 179.58/179.49 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.49 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.49 => 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)) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__Un,axiom,
% 179.58/179.49 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Oab__group__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.49 => 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))) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__diff1__nat,axiom,
% 179.58/179.49 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 179.58/179.49 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.49 => 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)) )
% 179.58/179.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.49 => 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) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__Un__nat,axiom,
% 179.58/179.49 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 179.58/179.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.49 => 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))) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__cases,axiom,
% 179.58/179.49 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => 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_P_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_P_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_P_2))))) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum_Oremove,axiom,
% 179.58/179.49 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.58/179.49 => 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)))))) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__diff1_H,axiom,
% 179.58/179.49 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.49 => 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)))))) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__diff1__ring,axiom,
% 179.58/179.49 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Rings_Oring(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.49 => 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)) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__mono2,axiom,
% 179.58/179.49 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.58/179.49 => ( ! [B_b] :
% 179.58/179.49 ( 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)))
% 179.58/179.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 179.58/179.49 => 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))) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_arith__series__nat,axiom,
% 179.58/179.49 ! [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)))) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 179.58/179.49 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.49 => ( ! [B_x] :
% 179.58/179.49 ( 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)))
% 179.58/179.49 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 179.58/179.49 => 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)) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__Un__zero,axiom,
% 179.58/179.49 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 179.58/179.49 => ( ! [B_x] :
% 179.58/179.49 ( 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)))
% 179.58/179.49 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 179.58/179.49 => 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)) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__mono3,axiom,
% 179.58/179.49 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 179.58/179.49 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.49 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.58/179.49 => ( ! [B_x] :
% 179.58/179.49 ( 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)))
% 179.58/179.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 179.58/179.49 => 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))) ) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__reindex__nonzero,axiom,
% 179.58/179.49 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_d)
% 179.58/179.49 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.49 => ( ! [B_x] :
% 179.58/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 179.58/179.49 => ! [B_y] :
% 179.58/179.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 179.58/179.49 => ( B_x != B_y
% 179.58/179.49 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 179.58/179.49 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 179.58/179.49 => 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) ) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_finite__lessThan,axiom,
% 179.58/179.49 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_lessThan__eq__iff,axiom,
% 179.58/179.49 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 179.58/179.49 <=> V_x_2 = V_y_2 ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_lessThan__0,axiom,
% 179.58/179.49 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)) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_lessThan__Suc,axiom,
% 179.58/179.49 ! [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)) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_card__lessThan,axiom,
% 179.58/179.49 ! [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 ).
% 179.58/179.49
% 179.58/179.49 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 179.58/179.49 ! [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))) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_setsum__lessThan__Suc,axiom,
% 179.58/179.49 ! [V_n_2,V_f_2,T_b] :
% 179.58/179.49 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.49 => 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)) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_lessThan__iff,axiom,
% 179.58/179.49 ! [V_k_2,V_i_2,T_b] :
% 179.58/179.49 ( class_Orderings_Oord(T_b)
% 179.58/179.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 179.58/179.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_lessThan__subset__iff,axiom,
% 179.58/179.49 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.49 => ( 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)))
% 179.58/179.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 179.58/179.49
% 179.58/179.49 fof(fact_lessThan__strict__subset__iff,axiom,
% 179.58/179.49 ! [V_n_2,V_m_2,T_b] :
% 179.58/179.49 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_single__Diff__lessThan,axiom,
% 179.58/179.50 ! [V_k_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__multicount,axiom,
% 179.58/179.50 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 179.58/179.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 179.58/179.50 => ( ! [B_x] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 179.58/179.50 => 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 )
% 179.58/179.50 => 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)) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_arith__series__general,axiom,
% 179.58/179.50 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Rings_Ocomm__semiring__1(T_b)
% 179.58/179.50 => 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)))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__multicount__gen,axiom,
% 179.58/179.50 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 179.58/179.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 179.58/179.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 179.58/179.50 => ( ! [B_x] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 179.58/179.50 => 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) )
% 179.58/179.50 => 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) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__nonneg__0,axiom,
% 179.58/179.50 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 179.58/179.50 ( class_Groups_Oordered__ab__group__add(T_c)
% 179.58/179.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 179.58/179.50 => ( ! [B_i] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 179.58/179.50 => ( 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)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 179.58/179.50 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__nonneg__leq__bound,axiom,
% 179.58/179.50 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 179.58/179.50 ( class_Groups_Oordered__ab__group__add(T_c)
% 179.58/179.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 179.58/179.50 => ( ! [B_i] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 179.58/179.50 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_sum__diff__distrib,axiom,
% 179.58/179.50 ! [V_n_2,V_P_2,V_Qa_2] :
% 179.58/179.50 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Qa_2,B_x)),hAPP(V_P_2,B_x)))
% 179.58/179.50 => 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_P_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_P_2)),V_Qa_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_negative__zless,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__eq__iff,axiom,
% 179.58/179.50 ! [V_n_2,V_m_2,T_b] :
% 179.58/179.50 ( class_Nat_Osemiring__char__0(T_b)
% 179.58/179.50 => ( 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)
% 179.58/179.50 <=> V_m_2 = V_n_2 ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_negative__eq__positive,axiom,
% 179.58/179.50 ! [V_m_2,V_n_2] :
% 179.58/179.50 ( 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)
% 179.58/179.50 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.50 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__eq__0__conv,axiom,
% 179.58/179.50 ! [V_n_2] :
% 179.58/179.50 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.58/179.50 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__0,axiom,
% 179.58/179.50 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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__le__0__conv,axiom,
% 179.58/179.50 ! [V_n_2] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__zle__neg,axiom,
% 179.58/179.50 ! [V_m_2,V_n_2] :
% 179.58/179.50 ( 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))))
% 179.58/179.50 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.50 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_not__zle__0__negative,axiom,
% 179.58/179.50 ! [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))))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_negative__zless__0,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zless__iff__Suc__zadd,axiom,
% 179.58/179.50 ! [V_z_2,V_w_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 179.58/179.50 <=> ? [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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__Suc,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zless__int,axiom,
% 179.58/179.50 ! [V_n_2,V_m_2] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__int,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__int__left,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zle__int,axiom,
% 179.58/179.50 ! [V_n_2,V_m_2] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__mult,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zmult__int,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__1,axiom,
% 179.58/179.50 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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_inj__int,axiom,
% 179.58/179.50 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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__setsum,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__Suc0__eq__1,axiom,
% 179.58/179.50 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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zero__less__int__conv,axiom,
% 179.58/179.50 ! [V_n_2] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zmult__zless__mono2__lemma,axiom,
% 179.58/179.50 ! [V_k,V_j,V_i] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 179.58/179.50 => 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))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zero__le__imp__of__nat,axiom,
% 179.58/179.50 ! [V_m,T_a] :
% 179.58/179.50 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__0__le__iff,axiom,
% 179.58/179.50 ! [V_n,T_a] :
% 179.58/179.50 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zdiff__int,axiom,
% 179.58/179.50 ! [V_m,V_n] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__less__0__iff,axiom,
% 179.58/179.50 ! [V_m,T_a] :
% 179.58/179.50 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.50 => ~ 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__0,axiom,
% 179.58/179.50 ! [T_a] :
% 179.58/179.50 ( class_Rings_Osemiring__1(T_a)
% 179.58/179.50 => 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) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__less__imp__less,axiom,
% 179.58/179.50 ! [V_n,V_m,T_a] :
% 179.58/179.50 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_less__imp__of__nat__less,axiom,
% 179.58/179.50 ! [V_n,V_m,T_a] :
% 179.58/179.50 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.58/179.50 => 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))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__less__iff,axiom,
% 179.58/179.50 ! [V_n_2,V_m_2,T_b] :
% 179.58/179.50 ( class_Rings_Olinordered__semidom(T_b)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__le__iff,axiom,
% 179.58/179.50 ! [V_n_2,V_m_2,T_b] :
% 179.58/179.50 ( class_Rings_Olinordered__semidom(T_b)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__add,axiom,
% 179.58/179.50 ! [V_n,V_m,T_a] :
% 179.58/179.50 ( class_Rings_Osemiring__1(T_a)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__mult,axiom,
% 179.58/179.50 ! [V_n,V_m,T_a] :
% 179.58/179.50 ( class_Rings_Osemiring__1(T_a)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__1,axiom,
% 179.58/179.50 ! [T_a] :
% 179.58/179.50 ( class_Rings_Osemiring__1(T_a)
% 179.58/179.50 => 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) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Ints__of__nat,axiom,
% 179.58/179.50 ! [V_n_2,T_b] :
% 179.58/179.50 ( class_Rings_Oring__1(T_b)
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__setsum,axiom,
% 179.58/179.50 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.50 ( class_Rings_Osemiring__1(T_b)
% 179.58/179.50 => 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) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_inj__of__nat,axiom,
% 179.58/179.50 ! [T_b] :
% 179.58/179.50 ( class_Nat_Osemiring__char__0(T_b)
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__Suc,axiom,
% 179.58/179.50 ! [V_m,T_a] :
% 179.58/179.50 ( class_Rings_Osemiring__1(T_a)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__diff,axiom,
% 179.58/179.50 ! [V_m,V_n,T_a] :
% 179.58/179.50 ( class_Rings_Oring__1(T_a)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 179.58/179.50 => 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)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__constant,axiom,
% 179.58/179.50 ! [V_A_2,V_y_2,T_c,T_b] :
% 179.58/179.50 ( class_Rings_Osemiring__1(T_b)
% 179.58/179.50 => 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) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__0__less__iff,axiom,
% 179.58/179.50 ! [V_n_2,T_b] :
% 179.58/179.50 ( class_Rings_Olinordered__semidom(T_b)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 179.58/179.50 ! [V_n_2,T_b] :
% 179.58/179.50 ( class_Rings_Osemiring__1(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zdiff__int__split,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2,V_P_2] :
% 179.58/179.50 ( hBOOL(hAPP(V_P_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))))
% 179.58/179.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 179.58/179.50 => hBOOL(hAPP(V_P_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)))) )
% 179.58/179.50 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 179.58/179.50 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__bounded,axiom,
% 179.58/179.50 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 179.58/179.50 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 179.58/179.50 & class_Rings_Osemiring__1(T_c) )
% 179.58/179.50 => ( ! [B_i] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 179.58/179.50 => 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))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 179.58/179.50 ! [V_x_2,V_y_2,V_ca_2] :
% 179.58/179.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 179.58/179.50 => 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)) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 179.58/179.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 179.58/179.50 => 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))) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 179.58/179.50 => 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)) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_greaterThan__0,axiom,
% 179.58/179.50 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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__natinterval__difff,axiom,
% 179.58/179.50 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 179.58/179.50 ( class_Groups_Oab__group__add(T_b)
% 179.58/179.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.58/179.50 => 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)))) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.58/179.50 => 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) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_finite__atLeastLessThan,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_finite__atLeastAtMost,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_negative__zle,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zle__iff__zadd,axiom,
% 179.58/179.50 ! [V_z_2,V_w_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 179.58/179.50 <=> ? [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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_not__int__zless__negative,axiom,
% 179.58/179.50 ! [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)))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__int__eq,axiom,
% 179.58/179.50 ! [V_n_2,V_m_2] :
% 179.58/179.50 ( 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)
% 179.58/179.50 <=> V_m_2 = V_n_2 ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_negative__zle__0,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zero__zle__int,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__less__0__conv,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_le__imp__0__less,axiom,
% 179.58/179.50 ! [V_z] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_odd__nonzero,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_odd__less__0,axiom,
% 179.58/179.50 ! [V_z_2] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__zminus__inverse2,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__0__right,axiom,
% 179.58/179.50 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__0,axiom,
% 179.58/179.50 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zmult__zless__mono2,axiom,
% 179.58/179.50 ! [V_k,V_j,V_i] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 179.58/179.50 => 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))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zminus__0,axiom,
% 179.58/179.50 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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_less__bin__lemma,axiom,
% 179.58/179.50 ! [V_l_2,V_k_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 179.58/179.50 <=> 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_pos__zmult__eq__1__iff,axiom,
% 179.58/179.50 ! [V_n_2,V_m_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 179.58/179.50 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 179.58/179.50 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 179.58/179.50 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__0__less__1,axiom,
% 179.58/179.50 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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__0__neq__1,axiom,
% 179.58/179.50 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__one__le__iff__zero__less,axiom,
% 179.58/179.50 ! [V_z_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zle__diff1__eq,axiom,
% 179.58/179.50 ! [V_z_2,V_w_2] :
% 179.58/179.50 ( 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))))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zmult__1,axiom,
% 179.58/179.50 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zmult__1__right,axiom,
% 179.58/179.50 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zless__le,axiom,
% 179.58/179.50 ! [V_w_2,V_z_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 179.58/179.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 179.58/179.50 & V_z_2 != V_w_2 ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zle__antisym,axiom,
% 179.58/179.50 ! [V_w,V_z] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 179.58/179.50 => V_z = V_w ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zle__trans,axiom,
% 179.58/179.50 ! [V_k,V_j,V_i] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zle__linear,axiom,
% 179.58/179.50 ! [V_w,V_z] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 179.58/179.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zle__refl,axiom,
% 179.58/179.50 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zminus__zminus,axiom,
% 179.58/179.50 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zless__linear,axiom,
% 179.58/179.50 ! [V_y,V_x] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 179.58/179.50 | V_x = V_y
% 179.58/179.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zmult__zminus,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zmult__commute,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zmult__assoc,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zdiff__zmult__distrib,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zdiff__zmult__distrib2,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_diff__int__def__symmetric,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_diff__int__def,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__zless__mono,axiom,
% 179.58/179.50 ! [V_z,V_z_H,V_w,V_w_H] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 179.58/179.50 => 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))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__left__mono,axiom,
% 179.58/179.50 ! [V_k,V_j,V_i] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__commute,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__left__commute,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__assoc,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zminus__zadd__distrib,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__strict__right__mono,axiom,
% 179.58/179.50 ! [V_k,V_j,V_i] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__zmult__distrib2,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zadd__zmult__distrib,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zless__add1__eq,axiom,
% 179.58/179.50 ! [V_z_2,V_w_2] :
% 179.58/179.50 ( 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))))
% 179.58/179.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 179.58/179.50 | V_w_2 = V_z_2 ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zle__add1__eq__le,axiom,
% 179.58/179.50 ! [V_z_2,V_w_2] :
% 179.58/179.50 ( 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))))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_add1__zle__eq,axiom,
% 179.58/179.50 ! [V_z_2,V_w_2] :
% 179.58/179.50 ( 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))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zless__imp__add1__zle,axiom,
% 179.58/179.50 ! [V_z,V_w] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_greaterThan__eq__iff,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 179.58/179.50 <=> V_x_2 = V_y_2 ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zsgn__def,axiom,
% 179.58/179.50 ! [V_i] :
% 179.58/179.50 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.58/179.50 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 179.58/179.50 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.58/179.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 179.58/179.50 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 179.58/179.50 => 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)) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I21_J,axiom,
% 179.58/179.50 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 179.58/179.50 => 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) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__int_I15_J,axiom,
% 179.58/179.50 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__int_I7_J,axiom,
% 179.58/179.50 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThan__eq__iff,axiom,
% 179.58/179.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 179.58/179.50 => ( 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)
% 179.58/179.50 <=> ( V_a_2 = V_ca_2
% 179.58/179.50 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 179.58/179.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( 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)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 179.58/179.50 => V_a_2 = V_ca_2 ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 179.58/179.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( 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)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 179.58/179.50 => V_b_2 = V_d_2 ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThan__add__Un,axiom,
% 179.58/179.50 ! [V_k_2,V_j_2,V_i_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThan0,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeast0LessThan,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I6_J,axiom,
% 179.58/179.50 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 179.58/179.50 => 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) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_subset__card__intvl__is__intvl,axiom,
% 179.58/179.50 ! [V_k_2,V_A_2] :
% 179.58/179.50 ( 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)))))
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_card__atLeastLessThan,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastatMost__empty__iff2,axiom,
% 179.58/179.50 ! [V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( 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)
% 179.58/179.50 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastatMost__empty__iff,axiom,
% 179.58/179.50 ! [V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( 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))
% 179.58/179.50 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastatMost__empty,axiom,
% 179.58/179.50 ! [V_a_2,V_b_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 179.58/179.50 => 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)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastatMost__subset__iff,axiom,
% 179.58/179.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 179.58/179.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 179.58/179.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_image__Suc__atLeastLessThan,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThan__empty,axiom,
% 179.58/179.50 ! [V_a_2,V_b_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 179.58/179.50 => 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)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastAtMost__singleton,axiom,
% 179.58/179.50 ! [V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 179.58/179.50 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> ( V_a_2 = V_b_2
% 179.58/179.50 & V_b_2 = V_ca_2 ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastAtMost__singleton_H,axiom,
% 179.58/179.50 ! [V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( V_a_2 = V_b_2
% 179.58/179.50 => 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))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 179.58/179.50 ! [V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( 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)
% 179.58/179.50 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThan__empty__iff,axiom,
% 179.58/179.50 ! [V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( 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))
% 179.58/179.50 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThan__subset__iff,axiom,
% 179.58/179.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 179.58/179.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 179.58/179.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 179.58/179.50 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 179.58/179.50 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I17_J,axiom,
% 179.58/179.50 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 179.58/179.50 => 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) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 179.58/179.50 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 179.58/179.50 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_image__uminus__atLeastAtMost,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.50 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__diff,axiom,
% 179.58/179.50 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 179.58/179.50 => 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) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__int_I11_J,axiom,
% 179.58/179.50 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_image__Suc__atLeastAtMost,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 179.58/179.50 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 179.58/179.50 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 179.58/179.50 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 179.58/179.50 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_image__add__atLeastLessThan,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_image__add__atLeastAtMost,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__add__nat__ivl,axiom,
% 179.58/179.50 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 179.58/179.50 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 179.58/179.50 => 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)) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__diff__nat__ivl,axiom,
% 179.58/179.50 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 179.58/179.50 ( class_Groups_Oab__group__add(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 179.58/179.50 => 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)) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_greaterThan__iff,axiom,
% 179.58/179.50 ! [V_k_2,V_i_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oord(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 179.58/179.50 ! [V_i_2,V_inc_2,T_b] :
% 179.58/179.50 ( class_Rings_Osemiring__1(T_b)
% 179.58/179.50 => 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 ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 179.58/179.50 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 179.58/179.50 ( class_Rings_Osemiring__1(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_greaterThan__subset__iff,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_card__atLeastAtMost,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastAtMostSuc__conv,axiom,
% 179.58/179.50 ! [V_n_2,V_m_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThan__singleton,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 179.58/179.50 ! [V_k_2,V_f_2] :
% 179.58/179.50 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Int__atLeastAtMost,axiom,
% 179.58/179.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastatMost__psubset__iff,axiom,
% 179.58/179.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 179.58/179.50 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 179.58/179.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 179.58/179.50 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2))
% 179.58/179.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 179.58/179.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Int__atLeastLessThan,axiom,
% 179.58/179.50 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__int_I4_J,axiom,
% 179.58/179.50 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I8_J,axiom,
% 179.58/179.50 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 179.58/179.50 => 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) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__int_I2_J,axiom,
% 179.58/179.50 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 179.58/179.50 ! [V_k_2,V_f_2,T_b] :
% 179.58/179.50 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.50 => 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)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__head__upt__Suc,axiom,
% 179.58/179.50 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 179.58/179.50 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 179.58/179.50 => 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))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__head__Suc,axiom,
% 179.58/179.50 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 179.58/179.50 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.58/179.50 => 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))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThanSuc,axiom,
% 179.58/179.50 ! [V_n_2,V_m_2] :
% 179.58/179.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.58/179.50 => 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)) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.58/179.50 => 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)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__op__ivl__Suc,axiom,
% 179.58/179.50 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 179.58/179.50 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 179.58/179.50 => 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) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 179.58/179.50 => 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)) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_image__uminus__lessThan,axiom,
% 179.58/179.50 ! [V_x_2,T_b] :
% 179.58/179.50 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_image__uminus__greaterThan,axiom,
% 179.58/179.50 ! [V_x_2,T_b] :
% 179.58/179.50 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_greaterThan__Suc,axiom,
% 179.58/179.50 ! [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)))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__cl__ivl__Suc,axiom,
% 179.58/179.50 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 179.58/179.50 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 179.58/179.50 => 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) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 179.58/179.50 => 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))) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_setsum__ub__add__nat,axiom,
% 179.58/179.50 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 179.58/179.50 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 => ( 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))))
% 179.58/179.50 => 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)))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_gauss__sum,axiom,
% 179.58/179.50 ! [V_n_2,T_b] :
% 179.58/179.50 ( class_Rings_Ocomm__semiring__1(T_b)
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_self__quotient__aux2,axiom,
% 179.58/179.50 ! [V_q,V_r,V_a] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.58/179.50 => ( 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))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_self__quotient__aux1,axiom,
% 179.58/179.50 ! [V_q,V_r,V_a] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.58/179.50 => ( 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))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 179.58/179.50 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 179.58/179.50 ( 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)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_unique__quotient__lemma__neg,axiom,
% 179.58/179.50 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zdiv__mono2__lemma,axiom,
% 179.58/179.50 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 179.58/179.50 ( 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)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_simp__from__to,axiom,
% 179.58/179.50 ! [V_i_2,V_j_2] :
% 179.58/179.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 179.58/179.50 => 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)) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 179.58/179.50 => 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)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_image__add__int__atLeastLessThan,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_q__pos__lemma,axiom,
% 179.58/179.50 ! [V_r_H,V_q_H,V_b_H] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_q__neg__lemma,axiom,
% 179.58/179.50 ! [V_r_H,V_q_H,V_b_H] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_unique__quotient__lemma,axiom,
% 179.58/179.50 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 179.58/179.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 179.58/179.50 ! [V_P_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_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_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_all__nat__less,axiom,
% 179.58/179.50 ! [V_P_2,V_n_2] :
% 179.58/179.50 ( ! [B_m] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 179.58/179.50 => hBOOL(hAPP(V_P_2,B_m)) )
% 179.58/179.50 <=> ! [B_x] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ex__nat__less,axiom,
% 179.58/179.50 ! [V_P_2,V_n_2] :
% 179.58/179.50 ( ? [B_m] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 179.58/179.50 & hBOOL(hAPP(V_P_2,B_m)) )
% 179.58/179.50 <=> ? [B_x] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 179.58/179.50 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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_finite__atLeastAtMost__int,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_finite__atLeastLessThan__int,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_infinite__UNIV__int,axiom,
% 179.58/179.50 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 179.58/179.50 ! [V_B_2,V_A_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.58/179.50 <=> 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 179.58/179.50 ! [V_B_2,V_A_2] :
% 179.58/179.50 ( V_A_2 = V_B_2
% 179.58/179.50 <=> 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) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2] :
% 179.58/179.50 ( 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)
% 179.58/179.50 <=> V_x_2 = V_y_2 ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 179.58/179.50 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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 179.58/179.50 ! [V_A_2,V_x_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 179.58/179.50 <=> 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 179.58/179.50 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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 179.58/179.50 ! [V_A_2] :
% 179.58/179.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 179.58/179.50 <=> 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 179.58/179.50 ! [V_B_2,V_A_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.58/179.50 <=> 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 179.58/179.50 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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 179.58/179.50 ! [V_y,V_x] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.58/179.50 => 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))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 179.58/179.50 ! [V_P_2] :
% 179.58/179.50 ( ! [B_x] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 179.58/179.50 => hBOOL(hAPP(V_P_2,B_x)) )
% 179.58/179.50 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 179.58/179.50 ! [V_P_2] :
% 179.58/179.50 ( ? [B_x] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 179.58/179.50 & hBOOL(hAPP(V_P_2,B_x)) )
% 179.58/179.50 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 179.58/179.50 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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 179.58/179.50 ! [V_y,V_x] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.58/179.50 => 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))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ex__nat__less__eq,axiom,
% 179.58/179.50 ! [V_P_2,V_n_2] :
% 179.58/179.50 ( ? [B_m] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 179.58/179.50 & hBOOL(hAPP(V_P_2,B_m)) )
% 179.58/179.50 <=> ? [B_x] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_all__nat__less__eq,axiom,
% 179.58/179.50 ! [V_P_2,V_n_2] :
% 179.58/179.50 ( ! [B_m] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 179.58/179.50 => hBOOL(hAPP(V_P_2,B_m)) )
% 179.58/179.50 <=> ! [B_x] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_bset_I6_J,axiom,
% 179.58/179.50 ! [V_t_2,V_B_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ! [B_x] :
% 179.58/179.50 ( ! [B_xa] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xb] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 179.58/179.50 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 179.58/179.50 => 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)) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_aset_I8_J,axiom,
% 179.58/179.50 ! [V_t_2,V_A_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ! [B_x] :
% 179.58/179.50 ( ! [B_xa] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xb] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 179.58/179.50 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 179.58/179.50 => 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))) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_bset_I8_J,axiom,
% 179.58/179.50 ! [V_B_2,V_t_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ( 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))
% 179.58/179.50 => ! [B_x] :
% 179.58/179.50 ( ! [B_xa] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xb] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 179.58/179.50 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 179.58/179.50 => 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))) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_aset_I6_J,axiom,
% 179.58/179.50 ! [V_A_2,V_t_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ( 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))
% 179.58/179.50 => ! [B_x] :
% 179.58/179.50 ( ! [B_xa] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xb] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 179.58/179.50 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 179.58/179.50 => 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)) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_periodic__finite__ex,axiom,
% 179.58/179.50 ! [V_P_2,V_d_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 179.58/179.50 => ( ! [B_x,B_k] :
% 179.58/179.50 ( hBOOL(hAPP(V_P_2,B_x))
% 179.58/179.50 <=> hBOOL(hAPP(V_P_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)))) )
% 179.58/179.50 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 179.58/179.50 <=> ? [B_x] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_aset_I4_J,axiom,
% 179.58/179.50 ! [V_A_2,V_t_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 179.58/179.50 => ! [B_x] :
% 179.58/179.50 ( ! [B_xa] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xb] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 179.58/179.50 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 179.58/179.50 => ( B_x != V_t_2
% 179.58/179.50 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_bset_I4_J,axiom,
% 179.58/179.50 ! [V_B_2,V_t_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 179.58/179.50 => ! [B_x] :
% 179.58/179.50 ( ! [B_xa] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xb] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 179.58/179.50 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 179.58/179.50 => ( B_x != V_t_2
% 179.58/179.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_bset_I7_J,axiom,
% 179.58/179.50 ! [V_B_2,V_t_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 179.58/179.50 => ! [B_x] :
% 179.58/179.50 ( ! [B_xa] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xb] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 179.58/179.50 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 179.58/179.50 => 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))) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_aset_I5_J,axiom,
% 179.58/179.50 ! [V_A_2,V_t_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 179.58/179.50 => ! [B_x] :
% 179.58/179.50 ( ! [B_xa] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xb] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 179.58/179.50 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 179.58/179.50 => 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)) ) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_aset_I3_J,axiom,
% 179.58/179.50 ! [V_A_2,V_t_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ( 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))
% 179.58/179.50 => ( ! [B_x] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xa] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 179.58/179.50 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 179.58/179.50 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_bset_I3_J,axiom,
% 179.58/179.50 ! [V_B_2,V_t_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ( 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))
% 179.58/179.50 => ( ! [B_x] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xa] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 179.58/179.50 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 179.58/179.50 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_aset_I7_J,axiom,
% 179.58/179.50 ! [V_t_2,V_A_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ! [B_x] :
% 179.58/179.50 ( ! [B_xa] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xb] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 179.58/179.50 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 179.58/179.50 => 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))) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_bset_I5_J,axiom,
% 179.58/179.50 ! [V_t_2,V_B_2,V_D_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 179.58/179.50 => ! [B_x] :
% 179.58/179.50 ( ! [B_xa] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 => ! [B_xb] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 179.58/179.50 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 179.58/179.50 => 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)) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeast__Suc,axiom,
% 179.58/179.50 ! [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)))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_small_H_Osimps,axiom,
% 179.58/179.50 ! [V_f_2,V_i_2,V_d_2] :
% 179.58/179.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 179.58/179.50 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 179.58/179.50 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeast__eq__iff,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 179.58/179.50 <=> V_x_2 = V_y_2 ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeast__iff,axiom,
% 179.58/179.50 ! [V_k_2,V_i_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oord(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeast__subset__iff,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeast__0,axiom,
% 179.58/179.50 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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Compl__lessThan,axiom,
% 179.58/179.50 ! [V_k_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => 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) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Compl__atLeast,axiom,
% 179.58/179.50 ! [V_k_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => 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) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeast__Suc__greaterThan,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I14_J,axiom,
% 179.58/179.50 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 179.58/179.50 => 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) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__int_I8_J,axiom,
% 179.58/179.50 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Int__atLeastAtMostL2,axiom,
% 179.58/179.50 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => 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) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Int__atLeastAtMostR2,axiom,
% 179.58/179.50 ! [V_d_2,V_ca_2,V_a_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => 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) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I1_J,axiom,
% 179.58/179.50 ! [V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => 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) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I13_J,axiom,
% 179.58/179.50 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 179.58/179.50 => 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) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_tsub__def,axiom,
% 179.58/179.50 ! [V_x,V_y] :
% 179.58/179.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 179.58/179.50 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 179.58/179.50 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I18_J,axiom,
% 179.58/179.50 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 179.58/179.50 => 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) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I3_J,axiom,
% 179.58/179.50 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 179.58/179.50 => 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) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I5_J,axiom,
% 179.58/179.50 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 179.58/179.50 => 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) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 179.58/179.50 ! [V_u_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 179.58/179.50 => 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))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_finite__greaterThanAtMost,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_finite__greaterThanLessThan,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_finite__greaterThanAtMost__int,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_finite__greaterThanLessThan__int,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__int,axiom,
% 179.58/179.50 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 179.58/179.50
% 179.58/179.50 fof(fact_card__greaterThanAtMost__int,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__int_I10_J,axiom,
% 179.58/179.50 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I16_J,axiom,
% 179.58/179.50 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 179.58/179.50 => 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) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 179.58/179.50 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__0,axiom,
% 179.58/179.50 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 179.58/179.50 ! [V_y,V_x] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.58/179.50 => 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)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ex__nat,axiom,
% 179.58/179.50 ! [V_P_2] :
% 179.58/179.50 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 179.58/179.50 <=> ? [B_x] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 179.58/179.50 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_all__nat,axiom,
% 179.58/179.50 ! [V_P_2] :
% 179.58/179.50 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 179.58/179.50 <=> ! [B_x] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 179.58/179.50 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 179.58/179.50 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 179.58/179.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_eq__nat__nat__iff,axiom,
% 179.58/179.50 ! [V_z_H_2,V_z_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 179.58/179.50 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 179.58/179.50 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 179.58/179.50 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 179.58/179.50 ! [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 ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_card__greaterThanLessThan__int,axiom,
% 179.58/179.50 ! [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)))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I4_J,axiom,
% 179.58/179.50 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 179.58/179.50 => 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) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I19_J,axiom,
% 179.58/179.50 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 179.58/179.50 => 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) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_greaterThanAtMost__empty,axiom,
% 179.58/179.50 ! [V_k_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 179.58/179.50 => 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)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 179.58/179.50 ! [V_l_2,V_k_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( 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)
% 179.58/179.50 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 179.58/179.50 ! [V_l_2,V_k_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( 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))
% 179.58/179.50 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__un_I20_J,axiom,
% 179.58/179.50 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Olinorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 179.58/179.50 => 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) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 179.58/179.50 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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_greaterThanLessThan__empty,axiom,
% 179.58/179.50 ! [V_k_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 179.58/179.50 => 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)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_ivl__disj__int_I14_J,axiom,
% 179.58/179.50 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.50 ( class_Orderings_Oorder(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__le__0,axiom,
% 179.58/179.50 ! [V_z] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.50 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__0__iff,axiom,
% 179.58/179.50 ! [V_i_2] :
% 179.58/179.50 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__mono__iff,axiom,
% 179.58/179.50 ! [V_w_2,V_z_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zless__nat__conj,axiom,
% 179.58/179.50 ! [V_z_2,V_w_2] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 179.58/179.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.50 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__1,axiom,
% 179.58/179.50 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__0__le,axiom,
% 179.58/179.50 ! [V_z] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 179.58/179.50 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__eq__iff,axiom,
% 179.58/179.50 ! [V_z_2,V_m_2] :
% 179.58/179.50 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 179.58/179.50 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 179.58/179.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_int__nat__eq,axiom,
% 179.58/179.50 ! [V_z] :
% 179.58/179.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 179.58/179.50 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 179.58/179.50 => 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) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zless__nat__eq__int__zless,axiom,
% 179.58/179.50 ! [V_z_2,V_m_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 179.58/179.50 <=> 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__zminus__int,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_card__greaterThanAtMost,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 179.58/179.50 ! [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))) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 179.58/179.50 ! [V_A_2,V_f_2,T_b] :
% 179.58/179.50 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.50 & class_Groups_Ocomm__monoid__mult(T_b) )
% 179.58/179.50 => 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)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 179.58/179.50 ! [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) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_card__atLeastLessThan__int,axiom,
% 179.58/179.50 ! [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)) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_zero__less__nat__eq,axiom,
% 179.58/179.50 ! [V_z_2] :
% 179.58/179.50 ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 179.58/179.50 ! [V_y_2,V_x_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 179.58/179.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__less__eq__zless,axiom,
% 179.58/179.50 ! [V_z_2,V_w_2] :
% 179.58/179.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__eq__iff2,axiom,
% 179.58/179.50 ! [V_w_2,V_m_2] :
% 179.58/179.50 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 179.58/179.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 179.58/179.50 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 179.58/179.50 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__eq__iff,axiom,
% 179.58/179.50 ! [V_m_2,V_w_2] :
% 179.58/179.50 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 179.58/179.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 179.58/179.50 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 179.58/179.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 179.58/179.50 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_nat__le__eq__zle,axiom,
% 179.58/179.50 ! [V_z_2,V_w_2] :
% 179.58/179.50 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 179.58/179.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 179.58/179.50 => ( 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)))
% 179.58/179.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 179.58/179.50
% 179.58/179.50 fof(fact_split__nat,axiom,
% 179.58/179.51 ! [V_i_2,V_P_2] :
% 179.58/179.51 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 179.58/179.51 <=> ( ! [B_n] :
% 179.58/179.51 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 179.58/179.51 => hBOOL(hAPP(V_P_2,B_n)) )
% 179.58/179.51 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.51 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 179.58/179.51 ! [V_y,V_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nat__add__distrib,axiom,
% 179.58/179.51 ! [V_z_H,V_z] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 179.58/179.51 ! [V_y,V_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nat__mult__distrib,axiom,
% 179.58/179.51 ! [V_z_H,V_z] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 179.58/179.51 ! [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))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nat__diff__distrib,axiom,
% 179.58/179.51 ! [V_z,V_z_H] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__un_I22_J,axiom,
% 179.58/179.51 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 179.58/179.51 => 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) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__int_I16_J,axiom,
% 179.58/179.51 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Oorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Int__greaterThanAtMost,axiom,
% 179.58/179.51 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_image__uminus__atLeastLessThan,axiom,
% 179.58/179.51 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 179.58/179.51 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__int_I12_J,axiom,
% 179.58/179.51 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Oorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__int_I13_J,axiom,
% 179.58/179.51 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Oorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__int_I9_J,axiom,
% 179.58/179.51 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Oorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Int__greaterThanLessThan,axiom,
% 179.58/179.51 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__un_I11_J,axiom,
% 179.58/179.51 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_card__greaterThanLessThan,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__int_I5_J,axiom,
% 179.58/179.51 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Oorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__int_I6_J,axiom,
% 179.58/179.51 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Oorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_one__less__nat__eq,axiom,
% 179.58/179.51 ! [V_z_2] :
% 179.58/179.51 ( 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)))
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nat__less__iff,axiom,
% 179.58/179.51 ! [V_m_2,V_w_2] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 179.58/179.51 <=> 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))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 179.58/179.51 ! [V_z] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 179.58/179.51 ! [V_y,V_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.58/179.51 => 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))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nat__mult__distrib__neg,axiom,
% 179.58/179.51 ! [V_z_H,V_z] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 179.58/179.51 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_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_P_2),c_Int_Onat)))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_tsub__eq,axiom,
% 179.58/179.51 ! [V_x,V_y] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 179.58/179.51 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_card__atLeastAtMost__int,axiom,
% 179.58/179.51 ! [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))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__un_I15_J,axiom,
% 179.58/179.51 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 179.58/179.51 => 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) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setsum__head,axiom,
% 179.58/179.51 ! [V_P_2,V_n_2,V_m_2,T_b] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.58/179.51 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_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_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__un_I12_J,axiom,
% 179.58/179.51 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nat__aux__def,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__morphism__nat__int,axiom,
% 179.58/179.51 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))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 179.58/179.51 ! [V_n_2,V_m_2] :
% 179.58/179.51 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 179.58/179.51 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 179.58/179.51 => 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))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__of__nat,axiom,
% 179.58/179.51 ! [V_k,T_a] :
% 179.58/179.51 ( class_Rings_Oring__1(T_a)
% 179.58/179.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.51 => 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)))) )
% 179.58/179.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.51 => 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)) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 179.58/179.51 => 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))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 179.58/179.51 ! [V_y_2,V_x_2] :
% 179.58/179.51 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 179.58/179.51 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__eq__iff,axiom,
% 179.58/179.51 ! [V_z_2,V_w_2,T_b] :
% 179.58/179.51 ( class_Int_Oring__char__0(T_b)
% 179.58/179.51 => ( 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)
% 179.58/179.51 <=> V_w_2 = V_z_2 ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 179.58/179.51 ! [V_x_2,V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 179.58/179.51 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__int__eq,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 179.58/179.51 => ( V_A_2 = V_B_2
% 179.58/179.51 <=> 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) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 179.58/179.51 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 179.58/179.51 ! [V_y,V_x] :
% 179.58/179.51 ( c_Nat__Transfer_Ois__nat(V_x)
% 179.58/179.51 => ( c_Nat__Transfer_Ois__nat(V_y)
% 179.58/179.51 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 179.58/179.51 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 179.58/179.51 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 179.58/179.51 ! [V_y,V_x] :
% 179.58/179.51 ( c_Nat__Transfer_Ois__nat(V_x)
% 179.58/179.51 => ( c_Nat__Transfer_Ois__nat(V_y)
% 179.58/179.51 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 179.58/179.51 ! [V_y,V_x] :
% 179.58/179.51 ( c_Nat__Transfer_Ois__nat(V_x)
% 179.58/179.51 => ( c_Nat__Transfer_Ois__nat(V_y)
% 179.58/179.51 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 179.58/179.51 ! [V_A_2,V_x_2] :
% 179.58/179.51 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 179.58/179.51 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 179.58/179.51 <=> 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))) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__eq__0__iff,axiom,
% 179.58/179.51 ! [V_z_2,T_b] :
% 179.58/179.51 ( class_Int_Oring__char__0(T_b)
% 179.58/179.51 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.51 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__0__eq__iff,axiom,
% 179.58/179.51 ! [V_z_2,T_b] :
% 179.58/179.51 ( class_Int_Oring__char__0(T_b)
% 179.58/179.51 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 179.58/179.51 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__0,axiom,
% 179.58/179.51 ! [T_a] :
% 179.58/179.51 ( class_Rings_Oring__1(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 179.58/179.51 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__le__iff,axiom,
% 179.58/179.51 ! [V_z_2,V_w_2,T_b] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_b)
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__less__iff,axiom,
% 179.58/179.51 ! [V_z_2,V_w_2,T_b] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_b)
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__add,axiom,
% 179.58/179.51 ! [V_z,V_w,T_a] :
% 179.58/179.51 ( class_Rings_Oring__1(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__mult,axiom,
% 179.58/179.51 ! [V_z,V_w,T_a] :
% 179.58/179.51 ( class_Rings_Oring__1(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__1,axiom,
% 179.58/179.51 ! [T_a] :
% 179.58/179.51 ( class_Rings_Oring__1(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__diff,axiom,
% 179.58/179.51 ! [V_z,V_w,T_a] :
% 179.58/179.51 ( class_Rings_Oring__1(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__of__nat__eq,axiom,
% 179.58/179.51 ! [V_n,T_a] :
% 179.58/179.51 ( class_Rings_Oring__1(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__minus,axiom,
% 179.58/179.51 ! [V_z,T_a] :
% 179.58/179.51 ( class_Rings_Oring__1(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Ints__of__int,axiom,
% 179.58/179.51 ! [V_z_2,T_b] :
% 179.58/179.51 ( class_Rings_Oring__1(T_b)
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nat__set__def,axiom,
% 179.58/179.51 ! [V_S_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_S_2)
% 179.58/179.51 <=> ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 179.58/179.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_is__nat__def,axiom,
% 179.58/179.51 ! [V_x_2] :
% 179.58/179.51 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__setsum,axiom,
% 179.58/179.51 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.51 ( class_Rings_Oring__1(T_b)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 179.58/179.51 ! [V_y_2,V_x_2] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 179.58/179.51 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 179.58/179.51 => 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))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 179.58/179.51 ! [V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => 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 ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 179.58/179.51 ! [V_x_2,V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 179.58/179.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__le__0__iff,axiom,
% 179.58/179.51 ! [V_z_2,T_b] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_b)
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__0__le__iff,axiom,
% 179.58/179.51 ! [V_z_2,T_b] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_b)
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__less__0__iff,axiom,
% 179.58/179.51 ! [V_z_2,T_b] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_b)
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__0__less__iff,axiom,
% 179.58/179.51 ! [V_z_2,T_b] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_b)
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__nat__nat,axiom,
% 179.58/179.51 ! [V_z,T_a] :
% 179.58/179.51 ( class_Rings_Oring__1(T_a)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 179.58/179.51 ! [V_f_2,V_A_2,T_b] :
% 179.58/179.51 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.51 & class_Groups_Ocomm__monoid__mult(T_b) )
% 179.58/179.51 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 179.58/179.51 ! [V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 179.58/179.51 <=> 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))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 179.58/179.51 ! [V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 179.58/179.51 ! [V_P_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_P_2))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.58/179.51 <=> 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))) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2] :
% 179.58/179.51 ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.58/179.51 <=> 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))) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 179.58/179.51 ! [V_f_2,V_A_2,T_b] :
% 179.58/179.51 ( ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.51 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 179.58/179.51 ! [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))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_decr__mult__lemma,axiom,
% 179.58/179.51 ! [V_k_2,V_P_2,V_d_2] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 179.58/179.51 => ( ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(V_P_2,B_x))
% 179.58/179.51 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 179.58/179.51 => ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(V_P_2,B_x))
% 179.58/179.51 => hBOOL(hAPP(V_P_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)))) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_negD,axiom,
% 179.58/179.51 ! [V_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.51 => ? [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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_incr__mult__lemma,axiom,
% 179.58/179.51 ! [V_k_2,V_P_2,V_d_2] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 179.58/179.51 => ( ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(V_P_2,B_x))
% 179.58/179.51 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 179.58/179.51 => ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(V_P_2,B_x))
% 179.58/179.51 => hBOOL(hAPP(V_P_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)))) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_finite__atMost,axiom,
% 179.58/179.51 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_atMost__eq__iff,axiom,
% 179.58/179.51 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 179.58/179.51 <=> V_x_2 = V_y_2 ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_atLeast0AtMost,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_lessThan__Suc__atMost,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_card__atMost,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_atMost__Suc,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_atMost__iff,axiom,
% 179.58/179.51 ! [V_k_2,V_i_2,T_b] :
% 179.58/179.51 ( class_Orderings_Oord(T_b)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_atMost__subset__iff,axiom,
% 179.58/179.51 ! [V_y_2,V_x_2,T_b] :
% 179.58/179.51 ( class_Orderings_Oorder(T_b)
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Compl__atMost,axiom,
% 179.58/179.51 ! [V_k_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Compl__greaterThan,axiom,
% 179.58/179.51 ! [V_k_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setsum__atMost__Suc,axiom,
% 179.58/179.51 ! [V_n_2,V_f_2,T_b] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_atMost__0,axiom,
% 179.58/179.51 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))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Int__atLeastAtMostR1,axiom,
% 179.58/179.51 ! [V_d_2,V_ca_2,V_b_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Int__atLeastAtMostL1,axiom,
% 179.58/179.51 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__un_I9_J,axiom,
% 179.58/179.51 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__int_I3_J,axiom,
% 179.58/179.51 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Oorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__int_I1_J,axiom,
% 179.58/179.51 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Oorder(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_image__uminus__atMost,axiom,
% 179.58/179.51 ! [V_x_2,T_b] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_image__uminus__atLeast,axiom,
% 179.58/179.51 ! [V_x_2,T_b] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__un_I2_J,axiom,
% 179.58/179.51 ! [V_u_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__un_I10_J,axiom,
% 179.58/179.51 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_atMost__Int__atLeast,axiom,
% 179.58/179.51 ! [V_n_2,T_b] :
% 179.58/179.51 ( class_Orderings_Oorder(T_b)
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ivl__disj__un_I7_J,axiom,
% 179.58/179.51 ! [V_u_2,V_l_2,T_b] :
% 179.58/179.51 ( class_Orderings_Olinorder(T_b)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_zero__less__imp__eq__int,axiom,
% 179.58/179.51 ! [V_k] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 179.58/179.51 => ? [B_n] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 179.58/179.51 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setsum__mono__zero__left,axiom,
% 179.58/179.51 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 179.58/179.51 => ( ! [B_x] :
% 179.58/179.51 ( 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)))
% 179.58/179.51 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 179.58/179.51 => 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) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setsum__mono__zero__right,axiom,
% 179.58/179.51 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 179.58/179.51 => ( ! [B_x] :
% 179.58/179.51 ( 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)))
% 179.58/179.51 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 179.58/179.51 => 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) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setsum__strict__mono,axiom,
% 179.58/179.51 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 179.58/179.51 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => ( ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 179.58/179.51 => 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))) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_decr__lemma,axiom,
% 179.58/179.51 ! [V_z,V_x,V_d] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setsum__abs,axiom,
% 179.58/179.51 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setsum__abs__ge__zero,axiom,
% 179.58/179.51 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__eq__0,axiom,
% 179.58/179.51 ! [V_a_2,T_b] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 179.58/179.51 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.51 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__zero,axiom,
% 179.58/179.51 ! [T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__mult__self,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__mult,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__add__abs,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__one,axiom,
% 179.58/179.51 ! [T_a] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_a)
% 179.58/179.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__minus__cancel,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__idempotent,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__int__eq,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__of__nat,axiom,
% 179.58/179.51 ! [V_n,T_a] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__minus__commute,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__ge__self,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__le__D1,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 179.58/179.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__setsum__abs,axiom,
% 179.58/179.51 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__of__nonneg,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__le__zero__iff,axiom,
% 179.58/179.51 ! [V_a_2,T_b] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__ge__zero,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__of__pos,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_zero__less__abs__iff,axiom,
% 179.58/179.51 ! [V_a_2,T_b] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__not__less__zero,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => ~ 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__triangle__ineq,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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)))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__mult__less,axiom,
% 179.58/179.51 ! [V_d,V_b,V_c,V_a,T_a] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_a)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 179.58/179.51 => 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))) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__triangle__ineq2__sym,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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)))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__triangle__ineq2,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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)))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__triangle__ineq3,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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)))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__le__D2,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 179.58/179.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__leI,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 179.58/179.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__le__iff,axiom,
% 179.58/179.51 ! [V_b_2,V_a_2,T_b] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 179.58/179.51 => ( 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))
% 179.58/179.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 179.58/179.51 & 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)) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__ge__minus__self,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__less__iff,axiom,
% 179.58/179.51 ! [V_b_2,V_a_2,T_b] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_b)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 179.58/179.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 179.58/179.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__zmult__eq__1,axiom,
% 179.58/179.51 ! [V_n,V_m] :
% 179.58/179.51 ( 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)
% 179.58/179.51 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_mult__sgn__abs,axiom,
% 179.58/179.51 ! [V_x,T_a] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_a)
% 179.58/179.51 => 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 ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__sgn,axiom,
% 179.58/179.51 ! [V_k,T_a] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__mult__pos,axiom,
% 179.58/179.51 ! [V_y,V_x,T_a] :
% 179.58/179.51 ( class_Rings_Olinordered__idom(T_a)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__eq__mult,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Rings_Oordered__ring__abs(T_a)
% 179.58/179.51 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 179.58/179.51 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.58/179.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__diff__triangle__ineq,axiom,
% 179.58/179.51 ! [V_d,V_c,V_b,V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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))))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__triangle__ineq4,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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)))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__of__nonpos,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__minus__le__zero,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__if,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oabs__if(T_a)
% 179.58/179.51 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 179.58/179.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__of__neg,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.51 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_zabs__less__one__iff,axiom,
% 179.58/179.51 ! [V_z_2] :
% 179.58/179.51 ( 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)))
% 179.58/179.51 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_zabs__def,axiom,
% 179.58/179.51 ! [V_i] :
% 179.58/179.51 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.51 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 179.58/179.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.51 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nat__abs__mult__distrib,axiom,
% 179.58/179.51 ! [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))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_incr__lemma,axiom,
% 179.58/179.51 ! [V_x,V_z,V_d] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 179.58/179.51 => 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)))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 179.58/179.51 ! [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)))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 179.58/179.51 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 179.58/179.51 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.51 & class_Groups_Ocomm__monoid__mult(T_b) )
% 179.58/179.51 => ( V_A_2 = V_B_2
% 179.58/179.51 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 179.58/179.51 => ( ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 179.58/179.51 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 179.58/179.51 => 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) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_int__val__lemma,axiom,
% 179.58/179.51 ! [V_k_2,V_f_2,V_n_2] :
% 179.58/179.51 ( ! [B_i] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 179.58/179.51 => 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))) )
% 179.58/179.51 => ( 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))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 179.58/179.51 => ? [B_i] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 179.58/179.51 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nat0__intermed__int__val,axiom,
% 179.58/179.51 ! [V_k_2,V_f_2,V_n_2] :
% 179.58/179.51 ( ! [B_i] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 179.58/179.51 => 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))) )
% 179.58/179.51 => ( 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))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 179.58/179.51 => ? [B_i] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 179.58/179.51 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__le__eq__Un0,axiom,
% 179.58/179.51 ! [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))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SUP1__I,axiom,
% 179.58/179.51 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__o,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SUP1__iff,axiom,
% 179.58/179.51 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 179.58/179.51 ( 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))
% 179.58/179.51 <=> ? [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.51 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_finite__UN,axiom,
% 179.58/179.51 ! [V_B_2,T_c,V_A_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SUP__UN__eq,axiom,
% 179.58/179.51 ! [V_x_2,V_r_2,T_c,T_b] :
% 179.58/179.51 ( 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))
% 179.58/179.51 <=> 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__lessThan__UNIV,axiom,
% 179.58/179.51 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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__atMost__UNIV,axiom,
% 179.58/179.51 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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__atLeast__UNIV,axiom,
% 179.58/179.51 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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__UN__finite__eq,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__le__add__shift,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__I,axiom,
% 179.58/179.51 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 179.58/179.51 => 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))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_vimage__eq__UN,axiom,
% 179.58/179.51 ! [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))))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_image__eq__UN,axiom,
% 179.58/179.51 ! [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)))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__insert,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__simps_I3_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.58/179.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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)) )
% 179.58/179.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ball__UN,axiom,
% 179.58/179.51 ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
% 179.58/179.51 ( ! [B_x] :
% 179.58/179.51 ( 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)))
% 179.58/179.51 => hBOOL(hAPP(V_P_2,B_x)) )
% 179.58/179.51 <=> ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.58/179.51 => ! [B_xa] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 179.58/179.51 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SUP__commute,axiom,
% 179.58/179.51 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 179.58/179.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__UN__flatten,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__simps_I9_J,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__extend__simps_I9_J,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SUP__le__iff,axiom,
% 179.58/179.51 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 179.58/179.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.58/179.51 => ( 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))
% 179.58/179.51 <=> ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.58/179.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_less__SUP__iff,axiom,
% 179.58/179.51 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 179.58/179.51 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.58/179.51 & class_Orderings_Olinorder(T_b) )
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> ? [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.58/179.51 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__iff,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 179.58/179.51 ( 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)))
% 179.58/179.51 <=> ? [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.58/179.51 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SUP__const,axiom,
% 179.58/179.51 ! [V_M_2,T_b,V_A_2,T_c] :
% 179.58/179.51 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 179.58/179.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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 ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UNION__empty__conv_I1_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2,T_c,T_b] :
% 179.58/179.51 ( 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)
% 179.58/179.51 <=> ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.58/179.51 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__empty2,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__constant,axiom,
% 179.58/179.51 ! [V_ca_2,T_c,T_b,V_A_2] :
% 179.58/179.51 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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)) )
% 179.58/179.51 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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 ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UNION__empty__conv_I2_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( 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))
% 179.58/179.51 <=> ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.58/179.51 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__subset__iff,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 179.58/179.51 ( 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))
% 179.58/179.51 <=> ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__extend__simps_I10_J,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_image__UN,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__simps_I10_J,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__Un__distrib,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__Un,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Int__UN__distrib2,axiom,
% 179.58/179.51 ! [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))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__extend__simps_I4_J,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Int__UN__distrib,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__extend__simps_I5_J,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__simps_I4_J,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__simps_I5_J,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SUPR__apply,axiom,
% 179.58/179.51 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 179.58/179.51 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__extend__simps_I6_J,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__simps_I6_J,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_vimage__UN,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SUP__subset,axiom,
% 179.58/179.51 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.58/179.51 => 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))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_le__SUPI,axiom,
% 179.58/179.51 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 179.58/179.51 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 179.58/179.51 => 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))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__insert__distrib,axiom,
% 179.58/179.51 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__upper,axiom,
% 179.58/179.51 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__absorb,axiom,
% 179.58/179.51 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__extend__simps_I1_J,axiom,
% 179.58/179.51 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 179.58/179.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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))) )
% 179.58/179.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__singleton,axiom,
% 179.58/179.51 ! [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 ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__simps_I1_J,axiom,
% 179.58/179.51 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 179.58/179.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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)) )
% 179.58/179.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__extend__simps_I2_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.58/179.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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 )
% 179.58/179.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__extend__simps_I3_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.58/179.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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 )
% 179.58/179.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__simps_I2_J,axiom,
% 179.58/179.51 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.58/179.51 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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)) )
% 179.58/179.51 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__finite2__subset,axiom,
% 179.58/179.51 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 179.58/179.51 ( ! [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)))
% 179.58/179.51 => 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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__finite2__eq,axiom,
% 179.58/179.51 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 179.58/179.51 ( ! [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)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_UN__finite__subset,axiom,
% 179.58/179.51 ! [V_C_2,V_A_2,T_b] :
% 179.58/179.51 ( ! [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))
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_finite__UN__I,axiom,
% 179.58/179.51 ! [V_B_2,T_c,V_A_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( ! [B_a] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 179.58/179.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 179.58/179.51 => 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))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SUP2__I,axiom,
% 179.58/179.51 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 179.58/179.51 ! [V_M_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 179.58/179.51 => ? [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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_finite__map__freshness,axiom,
% 179.58/179.51 ! [V_f_2,T_c,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2)))
% 179.58/179.51 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 179.58/179.51 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_diff__nat__eq__if,axiom,
% 179.58/179.51 ! [V_z_2,V_z_H_2] :
% 179.58/179.51 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 179.58/179.51 => 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) )
% 179.58/179.51 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setsum__SucD,axiom,
% 179.58/179.51 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 179.58/179.51 ( 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)
% 179.58/179.51 => ? [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.51 & 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))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_SUP2__iff,axiom,
% 179.58/179.51 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 179.58/179.51 ( 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))
% 179.58/179.51 <=> ? [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.51 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_not__neg__0,axiom,
% 179.58/179.51 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_not__neg__int,axiom,
% 179.58/179.51 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_not__neg__1,axiom,
% 179.58/179.51 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_not__neg__eq__ge__0,axiom,
% 179.58/179.51 ! [V_x_2] :
% 179.58/179.51 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_neg__def,axiom,
% 179.58/179.51 ! [V_Z_2] :
% 179.58/179.51 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 179.58/179.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_neg__nat,axiom,
% 179.58/179.51 ! [V_z] :
% 179.58/179.51 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 179.58/179.51 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_not__neg__nat,axiom,
% 179.58/179.51 ! [V_z] :
% 179.58/179.51 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 179.58/179.51 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_neg__zminus__int,axiom,
% 179.58/179.51 ! [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))))) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ex__bij__betw__nat__finite,axiom,
% 179.58/179.51 ! [V_M_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 179.58/179.51 => ? [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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_Oremove,axiom,
% 179.58/179.51 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.58/179.51 => 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)))))) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_ex__bij__betw__finite__nat,axiom,
% 179.58/179.51 ! [V_M_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 179.58/179.51 => ? [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))) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_fold__image__1,axiom,
% 179.58/179.51 ! [V_f_2,V_S_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.51 => ( ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 179.58/179.51 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 179.58/179.51 => 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) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_int__setprod,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__nat__setprod,axiom,
% 179.58/179.51 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.51 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 179.58/179.51 & class_Rings_Osemiring__1(T_b) )
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__setprod,axiom,
% 179.58/179.51 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.51 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 179.58/179.51 & class_Rings_Oring__1(T_b) )
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__1,axiom,
% 179.58/179.51 ! [V_A_2,T_c,T_b] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_b)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__timesf,axiom,
% 179.58/179.51 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_b)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_abs__setprod,axiom,
% 179.58/179.51 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.51 ( class_Fields_Olinordered__field(T_b)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 179.58/179.51 ! [V_A_2,V_f_2,T_b] :
% 179.58/179.51 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.51 & class_Groups_Ocomm__monoid__mult(T_b) )
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__zero,axiom,
% 179.58/179.51 ! [V_f_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Rings_Ocomm__semiring__1(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( ? [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.51 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 179.58/179.51 => 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) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__zero__iff,axiom,
% 179.58/179.51 ! [V_f_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 179.58/179.51 & class_Rings_Ono__zero__divisors(T_c) )
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( 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)
% 179.58/179.51 <=> ? [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.51 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_Oempty,axiom,
% 179.58/179.51 ! [V_g_2,T_c,T_b] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_b)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__empty,axiom,
% 179.58/179.51 ! [V_f_2,T_c,T_b] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_b)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_Oinfinite,axiom,
% 179.58/179.51 ! [V_g_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__infinite,axiom,
% 179.58/179.51 ! [V_f_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__eq__1__iff,axiom,
% 179.58/179.51 ! [V_f_2,V_F_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 179.58/179.51 => ( 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)
% 179.58/179.51 <=> ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 179.58/179.51 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 179.58/179.51 ! [V_f_2,V_A_2,T_b] :
% 179.58/179.51 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.51 & class_Groups_Ocomm__monoid__mult(T_b) )
% 179.58/179.51 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_Odistrib,axiom,
% 179.58/179.51 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__pos__nat__iff,axiom,
% 179.58/179.51 ! [V_f_2,V_S_2,T_b] :
% 179.58/179.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.51 => ( 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)))
% 179.58/179.51 <=> ! [B_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 179.58/179.51 => 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))) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__reindex__cong,axiom,
% 179.58/179.51 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_d)
% 179.58/179.51 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.58/179.51 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 179.58/179.51 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 179.58/179.51 => 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) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__reindex,axiom,
% 179.58/179.51 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_d)
% 179.58/179.51 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__delta,axiom,
% 179.58/179.51 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 179.58/179.51 => 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) )
% 179.58/179.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 179.58/179.51 => 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) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__delta_H,axiom,
% 179.58/179.51 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 179.58/179.51 => 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) )
% 179.58/179.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 179.58/179.51 => 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) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_Oinsert,axiom,
% 179.58/179.51 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.58/179.51 => 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)) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__insert,axiom,
% 179.58/179.51 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.51 => 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)) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__Un__Int,axiom,
% 179.58/179.51 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.51 => 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)) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_Ounion__inter,axiom,
% 179.58/179.51 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.51 => 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)) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_Oreindex,axiom,
% 179.58/179.51 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 179.58/179.51 => 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) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_Oeq__fold,axiom,
% 179.58/179.51 ! [V_g_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_OF__eq,axiom,
% 179.58/179.51 ! [V_g_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => 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) )
% 179.58/179.51 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => 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) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_Oinsert__remove,axiom,
% 179.58/179.51 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => 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)))))) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_Ounion__disjoint,axiom,
% 179.58/179.51 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.51 => ( 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))
% 179.58/179.51 => 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)) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__Un__disjoint,axiom,
% 179.58/179.51 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.51 => ( 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))
% 179.58/179.51 => 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)) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 179.58/179.51 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.51 => ( ! [B_x] :
% 179.58/179.51 ( 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)))
% 179.58/179.51 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 179.58/179.51 => 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)) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__Un__one,axiom,
% 179.58/179.51 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 179.58/179.51 => ( ! [B_x] :
% 179.58/179.51 ( 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)))
% 179.58/179.51 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 179.58/179.51 => 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)) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__gen__delta,axiom,
% 179.58/179.51 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 179.58/179.51 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.58/179.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 179.58/179.51 => 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)))) )
% 179.58/179.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 179.58/179.51 => 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)) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setprod__diff1,axiom,
% 179.58/179.51 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 179.58/179.51 ( class_Fields_Ofield(T_c)
% 179.58/179.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.51 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 179.58/179.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.51 => 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)) )
% 179.58/179.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.58/179.51 => 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) ) ) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 179.58/179.51 ! [V_n,V_x] :
% 179.58/179.51 ( c_Nat__Transfer_Ois__nat(V_x)
% 179.58/179.51 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_of__int__power,axiom,
% 179.58/179.51 ! [V_n,V_z,T_a] :
% 179.58/179.51 ( class_Rings_Oring__1(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 179.58/179.51 ! [V_x,T_a] :
% 179.58/179.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.58/179.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 179.58/179.51 ! [V_q,V_p,V_x,T_a] :
% 179.58/179.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_zpower__int,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_int__power,axiom,
% 179.58/179.51 ! [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) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_divide__zero,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_divide__zero__left,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_add__divide__distrib,axiom,
% 179.58/179.51 ! [V_c,V_b,V_a,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_times__divide__eq__right,axiom,
% 179.58/179.51 ! [V_c,V_b,V_a,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_minus__divide__left,axiom,
% 179.58/179.51 ! [V_b,V_a,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_divide__1,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_a)
% 179.58/179.51 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 179.58/179.51 ! [V_q,V_y,V_x,T_a] :
% 179.58/179.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_diff__divide__distrib,axiom,
% 179.58/179.51 ! [V_c,V_b,V_a,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_zpower__zpower,axiom,
% 179.58/179.51 ! [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)) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nat__power__eq,axiom,
% 179.58/179.51 ! [V_n,V_z] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 179.58/179.51 ! [V_n,V_x] :
% 179.58/179.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_setsum__divide__distrib,axiom,
% 179.58/179.51 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 179.58/179.51 ( class_Fields_Ofield(T_b)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_eq__divide__imp,axiom,
% 179.58/179.51 ! [V_b,V_a,V_c,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_a)
% 179.58/179.51 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.51 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 179.58/179.51 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_divide__eq__imp,axiom,
% 179.58/179.51 ! [V_a,V_b,V_c,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_a)
% 179.58/179.51 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.51 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 179.58/179.51 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nonzero__divide__eq__eq,axiom,
% 179.58/179.51 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_b)
% 179.58/179.51 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.51 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 179.58/179.51 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nonzero__eq__divide__eq,axiom,
% 179.58/179.51 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_b)
% 179.58/179.51 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.51 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 179.58/179.51 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_right__inverse__eq,axiom,
% 179.58/179.51 ! [V_a_2,V_b_2,T_b] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_b)
% 179.58/179.51 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.51 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 179.58/179.51 <=> V_a_2 = V_b_2 ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_divide__self,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_a)
% 179.58/179.51 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.51 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_divide__self__if,axiom,
% 179.58/179.51 ! [V_a,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 179.58/179.51 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.51 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 179.58/179.51 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.51 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nonzero__minus__divide__divide,axiom,
% 179.58/179.51 ! [V_a,V_b,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_a)
% 179.58/179.51 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.51 => 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) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_nonzero__minus__divide__right,axiom,
% 179.58/179.51 ! [V_a,V_b,T_a] :
% 179.58/179.51 ( class_Rings_Odivision__ring(T_a)
% 179.58/179.51 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.51 => 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)) ) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 179.58/179.51 ! [V_q,V_x,T_a] :
% 179.58/179.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 179.58/179.51 ! [V_q,V_x,T_a] :
% 179.58/179.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 179.58/179.51 ! [V_q,V_x,T_a] :
% 179.58/179.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.58/179.51 => 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)) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 179.58/179.51 ! [V_x,T_a] :
% 179.58/179.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.58/179.51 => 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) ) ).
% 179.58/179.51
% 179.58/179.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 179.58/179.51 ! [V_q,V_p,V_x,T_a] :
% 179.58/179.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 179.58/179.52 ! [V_n,V_x] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.52 => 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))) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zpower__zadd__distrib,axiom,
% 179.58/179.52 ! [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)) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Ints__power,axiom,
% 179.58/179.52 ! [V_n_2,V_a_2,T_b] :
% 179.58/179.52 ( class_Rings_Oring__1(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_setprod__dividef,axiom,
% 179.58/179.52 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_c)
% 179.58/179.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_geometric__sum,axiom,
% 179.58/179.52 ! [V_n_2,V_x_2,T_b] :
% 179.58/179.52 ( class_Fields_Ofield(T_b)
% 179.58/179.52 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zero__le__zpower__abs,axiom,
% 179.58/179.52 ! [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))) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_setprod__constant,axiom,
% 179.58/179.52 ! [V_y_2,V_A_2,T_b,T_c] :
% 179.58/179.52 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__eq__if,axiom,
% 179.58/179.52 ! [V_p,V_m] :
% 179.58/179.52 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.52 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 179.58/179.52 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.52 => 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)))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zero__less__zpower__abs__iff,axiom,
% 179.58/179.52 ! [V_n_2,V_x_2] :
% 179.58/179.52 ( 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)))
% 179.58/179.52 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.58/179.52 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__strict__mono,axiom,
% 179.58/179.52 ! [V_n,V_b,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.58/179.52 => 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))) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__diff,axiom,
% 179.58/179.52 ! [V_m,V_n,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Ofield(T_a)
% 179.58/179.52 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 179.58/179.52 => 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)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_one__less__power,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__le__imp__le__exp,axiom,
% 179.58/179.52 ! [V_n,V_m,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_field__power__not__zero,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 179.58/179.52 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 179.58/179.52 ! [V_m_2,V_x_2] :
% 179.58/179.52 ( 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))
% 179.58/179.52 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.52 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__Suc__0,axiom,
% 179.58/179.52 ! [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)) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_nat__power__less__imp__less,axiom,
% 179.58/179.52 ! [V_n,V_m,V_i] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_nat__zero__less__power__iff,axiom,
% 179.58/179.52 ! [V_n_2,V_x_2] :
% 179.58/179.52 ( 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)))
% 179.58/179.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 179.58/179.52 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__commutes,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Groups_Omonoid__mult(T_a)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__mult__distrib,axiom,
% 179.58/179.52 ! [V_n,V_b,V_a,T_a] :
% 179.58/179.52 ( class_Groups_Ocomm__monoid__mult(T_a)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__one,axiom,
% 179.58/179.52 ! [V_n,T_a] :
% 179.58/179.52 ( class_Groups_Omonoid__mult(T_a)
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_of__nat__power,axiom,
% 179.58/179.52 ! [V_n,V_m,T_a] :
% 179.58/179.52 ( class_Rings_Osemiring__1(T_a)
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__mult,axiom,
% 179.58/179.52 ! [V_n,V_m,V_a,T_a] :
% 179.58/179.52 ( class_Groups_Omonoid__mult(T_a)
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__divide,axiom,
% 179.58/179.52 ! [V_n,V_b,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_a)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__abs,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__idom(T_a)
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__one__right,axiom,
% 179.58/179.52 ! [V_a,T_a] :
% 179.58/179.52 ( class_Groups_Omonoid__mult(T_a)
% 179.58/179.52 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__mono,axiom,
% 179.58/179.52 ! [V_n,V_b,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zero__le__power,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zero__less__power,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__eq__0__iff,axiom,
% 179.58/179.52 ! [V_n_2,V_a_2,T_b] :
% 179.58/179.52 ( ( class_Power_Opower(T_b)
% 179.58/179.52 & class_Rings_Omult__zero(T_b)
% 179.58/179.52 & class_Rings_Ono__zero__divisors(T_b)
% 179.58/179.52 & class_Rings_Ozero__neq__one(T_b) )
% 179.58/179.52 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.52 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.52 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_one__le__power,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__0__Suc,axiom,
% 179.58/179.52 ! [V_n,T_a] :
% 179.58/179.52 ( ( class_Power_Opower(T_a)
% 179.58/179.52 & class_Rings_Osemiring__0(T_a) )
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__inject__exp,axiom,
% 179.58/179.52 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 179.58/179.52 => ( 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)
% 179.58/179.52 <=> V_m_2 = V_n_2 ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__Suc,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Power_Opower(T_a)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__Suc2,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Groups_Omonoid__mult(T_a)
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_nat__one__le__power,axiom,
% 179.58/179.52 ! [V_n,V_i] :
% 179.58/179.52 ( 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))
% 179.58/179.52 => 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))) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__0,axiom,
% 179.58/179.52 ! [V_a,T_a] :
% 179.58/179.52 ( class_Power_Opower(T_a)
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__add,axiom,
% 179.58/179.52 ! [V_n,V_m,V_a,T_a] :
% 179.58/179.52 ( class_Groups_Omonoid__mult(T_a)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_nonzero__power__divide,axiom,
% 179.58/179.52 ! [V_n,V_a,V_b,T_a] :
% 179.58/179.52 ( class_Fields_Ofield(T_a)
% 179.58/179.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__one__over,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_a)
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_abs__power__minus,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__idom(T_a)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__less__imp__less__base,axiom,
% 179.58/179.52 ! [V_b,V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( 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)))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__inject__base,axiom,
% 179.58/179.52 ! [V_b,V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( 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))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.58/179.52 => V_a = V_b ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__le__imp__le__base,axiom,
% 179.58/179.52 ! [V_b,V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( 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))))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__less__power__Suc,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 179.58/179.52 => 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)))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__gt1__lemma,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 179.58/179.52 => 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)))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__0__left,axiom,
% 179.58/179.52 ! [V_n,T_a] :
% 179.58/179.52 ( ( class_Power_Opower(T_a)
% 179.58/179.52 & class_Rings_Osemiring__0(T_a) )
% 179.58/179.52 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.52 => 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) )
% 179.58/179.52 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.52 => 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) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__gt1,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 179.58/179.52 => 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)))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__strict__increasing__iff,axiom,
% 179.58/179.52 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__less__imp__less__exp,axiom,
% 179.58/179.52 ! [V_n,V_m,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__strict__increasing,axiom,
% 179.58/179.52 ! [V_a,V_N,V_n,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zero__le__power__abs,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__idom(T_a)
% 179.58/179.52 => 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))) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__increasing,axiom,
% 179.58/179.52 ! [V_a,V_N,V_n,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__minus,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Oring__1(T_a)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__Suc__less,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__eq__imp__eq__base,axiom,
% 179.58/179.52 ! [V_b,V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( 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)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.58/179.52 => V_a = V_b ) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__Suc__less__one,axiom,
% 179.58/179.52 ! [V_n,V_a,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__strict__decreasing,axiom,
% 179.58/179.52 ! [V_a,V_N,V_n,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 179.58/179.52 => 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))) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__decreasing,axiom,
% 179.58/179.52 ! [V_a,V_N,V_n,T_a] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 179.58/179.52 => 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))) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__increasing__iff,axiom,
% 179.58/179.52 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 179.58/179.52 ( class_Rings_Olinordered__semidom(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__left__mono__neg,axiom,
% 179.58/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 => 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))) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__left__mono,axiom,
% 179.58/179.52 ! [V_c,V_a,V_b,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 => 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))) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_neg__divide__le__eq,axiom,
% 179.58/179.52 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => ( 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))
% 179.58/179.52 <=> 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)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_neg__le__divide__eq,axiom,
% 179.58/179.52 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_times__divide__times__eq,axiom,
% 179.58/179.52 ! [V_w,V_z,V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_a)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_minus__divide__right,axiom,
% 179.58/179.52 ! [V_b,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_a)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_minus__divide__divide,axiom,
% 179.58/179.52 ! [V_b,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_a)
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_abs__divide,axiom,
% 179.58/179.52 ! [V_b,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zero__le__divide__iff,axiom,
% 179.58/179.52 ! [V_b_2,V_a_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 179.58/179.52 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__le__0__iff,axiom,
% 179.58/179.52 ! [V_b_2,V_a_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 179.58/179.52 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__right__mono,axiom,
% 179.58/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__right__mono__neg,axiom,
% 179.58/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zero__less__divide__iff,axiom,
% 179.58/179.52 ! [V_b_2,V_a_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 179.58/179.52 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__less__0__iff,axiom,
% 179.58/179.52 ! [V_b_2,V_a_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 179.58/179.52 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__pos__pos,axiom,
% 179.58/179.52 ! [V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__pos__neg,axiom,
% 179.58/179.52 ! [V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__neg__pos,axiom,
% 179.58/179.52 ! [V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__neg__neg,axiom,
% 179.58/179.52 ! [V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__strict__right__mono,axiom,
% 179.58/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__strict__right__mono__neg,axiom,
% 179.58/179.52 ! [V_c,V_a,V_b,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_frac__eq__eq,axiom,
% 179.58/179.52 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 179.58/179.52 ( class_Fields_Ofield(T_b)
% 179.58/179.52 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.52 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.52 => ( 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)
% 179.58/179.52 <=> 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) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_mult__divide__mult__cancel__left,axiom,
% 179.58/179.52 ! [V_b,V_a,V_c,T_a] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_a)
% 179.58/179.52 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_mult__divide__mult__cancel__right,axiom,
% 179.58/179.52 ! [V_b,V_a,V_c,T_a] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_a)
% 179.58/179.52 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__eq__eq,axiom,
% 179.58/179.52 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_b)
% 179.58/179.52 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 179.58/179.52 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.52 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) )
% 179.58/179.52 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.52 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_eq__divide__eq,axiom,
% 179.58/179.52 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_b)
% 179.58/179.52 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 179.58/179.52 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 )
% 179.58/179.52 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 179.58/179.52 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_nonzero__abs__divide,axiom,
% 179.58/179.52 ! [V_a,V_b,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__nonpos__neg,axiom,
% 179.58/179.52 ! [V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__nonpos__pos,axiom,
% 179.58/179.52 ! [V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_frac__le,axiom,
% 179.58/179.52 ! [V_z,V_w,V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 179.58/179.52 => 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))) ) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_frac__less,axiom,
% 179.58/179.52 ! [V_z,V_w,V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 179.58/179.52 => 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))) ) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_frac__less2,axiom,
% 179.58/179.52 ! [V_z,V_w,V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 179.58/179.52 => 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))) ) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__nonneg__neg,axiom,
% 179.58/179.52 ! [V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__nonneg__pos,axiom,
% 179.58/179.52 ! [V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__strict__left__mono__neg,axiom,
% 179.58/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 => 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))) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__strict__left__mono,axiom,
% 179.58/179.52 ! [V_c,V_a,V_b,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 => 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))) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_neg__divide__less__eq,axiom,
% 179.58/179.52 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => ( 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))
% 179.58/179.52 <=> 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)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_neg__less__divide__eq,axiom,
% 179.58/179.52 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_mult__imp__less__div__pos,axiom,
% 179.58/179.52 ! [V_x,V_z,V_y,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.58/179.52 => ( 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))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_mult__imp__div__pos__less,axiom,
% 179.58/179.52 ! [V_z,V_x,V_y,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 => 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)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_pos__divide__less__eq,axiom,
% 179.58/179.52 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => ( 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))
% 179.58/179.52 <=> 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_pos__less__divide__eq,axiom,
% 179.58/179.52 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> 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)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__less__eq,axiom,
% 179.58/179.52 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.58/179.52 => ( 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))
% 179.58/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => 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))) )
% 179.58/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => 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)) )
% 179.58/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_less__divide__eq,axiom,
% 179.58/179.52 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => 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)) )
% 179.58/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => 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))) )
% 179.58/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_add__num__frac,axiom,
% 179.58/179.52 ! [V_x,V_z,V_y,T_a] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_a)
% 179.58/179.52 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_add__divide__eq__iff,axiom,
% 179.58/179.52 ! [V_y,V_x,V_z,T_a] :
% 179.58/179.52 ( class_Fields_Ofield(T_a)
% 179.58/179.52 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_add__frac__num,axiom,
% 179.58/179.52 ! [V_z,V_x,V_y,T_a] :
% 179.58/179.52 ( class_Fields_Ofield__inverse__zero(T_a)
% 179.58/179.52 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__add__eq__iff,axiom,
% 179.58/179.52 ! [V_y,V_x,V_z,T_a] :
% 179.58/179.52 ( class_Fields_Ofield(T_a)
% 179.58/179.52 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_add__frac__eq,axiom,
% 179.58/179.52 ! [V_w,V_x,V_z,V_y,T_a] :
% 179.58/179.52 ( class_Fields_Ofield(T_a)
% 179.58/179.52 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_diff__frac__eq,axiom,
% 179.58/179.52 ! [V_w,V_x,V_z,V_y,T_a] :
% 179.58/179.52 ( class_Fields_Ofield(T_a)
% 179.58/179.52 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__diff__eq__iff,axiom,
% 179.58/179.52 ! [V_y,V_x,V_z,T_a] :
% 179.58/179.52 ( class_Fields_Ofield(T_a)
% 179.58/179.52 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_diff__divide__eq__iff,axiom,
% 179.58/179.52 ! [V_y,V_x,V_z,T_a] :
% 179.58/179.52 ( class_Fields_Ofield(T_a)
% 179.58/179.52 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_less__half__sum,axiom,
% 179.58/179.52 ! [V_b,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.58/179.52 => 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))))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_gt__half__sum,axiom,
% 179.58/179.52 ! [V_b,V_a,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_abs__div__pos,axiom,
% 179.58/179.52 ! [V_x,V_y,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_le__divide__eq,axiom,
% 179.58/179.52 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => 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)) )
% 179.58/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => 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))) )
% 179.58/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divide__le__eq,axiom,
% 179.58/179.52 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.58/179.52 => ( 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))
% 179.58/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => 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))) )
% 179.58/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => 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)) )
% 179.58/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_pos__le__divide__eq,axiom,
% 179.58/179.52 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> 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)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_pos__divide__le__eq,axiom,
% 179.58/179.52 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_b)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.58/179.52 => ( 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))
% 179.58/179.52 <=> 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_mult__imp__div__pos__le,axiom,
% 179.58/179.52 ! [V_z,V_x,V_y,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 => 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)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_mult__imp__le__div__pos,axiom,
% 179.58/179.52 ! [V_x,V_z,V_y,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field(T_a)
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.58/179.52 => ( 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))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 179.58/179.52 ! [V_f_2,V_A_2,T_b] :
% 179.58/179.52 ( ! [B_x] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.52 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_setprod__Un,axiom,
% 179.58/179.52 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 179.58/179.52 ( class_Fields_Ofield(T_c)
% 179.58/179.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 179.58/179.52 => ( ! [B_x] :
% 179.58/179.52 ( 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)))
% 179.58/179.52 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 179.58/179.52 => 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))) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power__power__power,axiom,
% 179.58/179.52 ! [T_b] :
% 179.58/179.52 ( class_Power_Opower(T_b)
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_int__power__div__base,axiom,
% 179.58/179.52 ! [V_k,V_m] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 179.58/179.52 => 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)))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__by__1,axiom,
% 179.58/179.52 ! [V_a,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 179.58/179.52 ! [V_y,V_x] :
% 179.58/179.52 ( c_Nat__Transfer_Ois__nat(V_x)
% 179.58/179.52 => ( c_Nat__Transfer_Ois__nat(V_y)
% 179.58/179.52 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__by__0,axiom,
% 179.58/179.52 ! [V_a,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__0,axiom,
% 179.58/179.52 ! [V_a,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zdiv__zminus__zminus,axiom,
% 179.58/179.52 ! [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) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zdiv__zminus2,axiom,
% 179.58/179.52 ! [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) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zdiv__zero,axiom,
% 179.58/179.52 ! [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) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 179.58/179.52 ! [V_y,V_x] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 179.58/179.52 ! [V_a_2,V_b_2] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 179.58/179.52 ! [V_a_2,V_b_2] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__neg__pos__less0,axiom,
% 179.58/179.52 ! [V_b,V_a] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zdiv__self,axiom,
% 179.58/179.52 ! [V_a] :
% 179.58/179.52 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.58/179.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__mult__mult1,axiom,
% 179.58/179.52 ! [V_b,V_a,V_c,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__mult__mult2,axiom,
% 179.58/179.52 ! [V_b,V_a,V_c,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__mult__self1__is__id,axiom,
% 179.58/179.52 ! [V_a,V_b,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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 ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__mult__self2__is__id,axiom,
% 179.58/179.52 ! [V_a,V_b,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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 ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__mult__mult1__if,axiom,
% 179.58/179.52 ! [V_b,V_a,V_c,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) )
% 179.58/179.52 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__self,axiom,
% 179.58/179.52 ! [V_a,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zdiv__eq__0__iff,axiom,
% 179.58/179.52 ! [V_k_2,V_i_2] :
% 179.58/179.52 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.58/179.52 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.58/179.52 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 179.58/179.52 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 179.58/179.52 ! [V_a_2,V_b_2] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 179.58/179.52 ! [V_i_2,V_k_2] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 179.58/179.52 ! [V_b_2,V_a_2] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zdiv__mono2,axiom,
% 179.58/179.52 ! [V_b,V_b_H,V_a] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__nonneg__neg__le0,axiom,
% 179.58/179.52 ! [V_b,V_a] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__pos__pos__trivial,axiom,
% 179.58/179.52 ! [V_b,V_a] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 179.58/179.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 179.58/179.52 ! [V_a_2,V_b_2] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.52 => ( 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)))
% 179.58/179.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__nonpos__pos__le0,axiom,
% 179.58/179.52 ! [V_b,V_a] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zdiv__mono2__neg,axiom,
% 179.58/179.52 ! [V_b,V_b_H,V_a] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 179.58/179.52 => 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))) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__neg__neg__trivial,axiom,
% 179.58/179.52 ! [V_b,V_a] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 179.58/179.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zdiv__mono1,axiom,
% 179.58/179.52 ! [V_b,V_a_H,V_a] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zdiv__mono1__neg,axiom,
% 179.58/179.52 ! [V_b,V_a_H,V_a] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_int__div__less__self,axiom,
% 179.58/179.52 ! [V_k,V_x] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zdiv__zmult2__eq,axiom,
% 179.58/179.52 ! [V_b,V_a,V_c] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power_Opower_Opower__0,axiom,
% 179.58/179.52 ! [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 ).
% 179.58/179.52
% 179.58/179.52 fof(fact_power_Opower_Opower__Suc,axiom,
% 179.58/179.52 ! [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)) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__mult__self1,axiom,
% 179.58/179.52 ! [V_c,V_a,V_b,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__mult__self2,axiom,
% 179.58/179.52 ! [V_c,V_a,V_b,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__add__self2,axiom,
% 179.58/179.52 ! [V_a,V_b,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__add__self1,axiom,
% 179.58/179.52 ! [V_a,V_b,T_a] :
% 179.58/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.58/179.52 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_divmod__int__rel__div__eq,axiom,
% 179.58/179.52 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 179.58/179.52 ( 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)
% 179.58/179.52 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 179.58/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 179.58/179.52 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.58/179.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_split__zdiv,axiom,
% 179.58/179.52 ! [V_k_2,V_n_2,V_P_2] :
% 179.58/179.52 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 179.58/179.52 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.58/179.52 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 179.58/179.52 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 179.58/179.52 => ! [B_i] :
% 179.58/179.52 ( ? [B_j] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 179.58/179.52 & 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) )
% 179.58/179.52 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 179.58/179.52 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.52 => ! [B_i] :
% 179.58/179.52 ( ? [B_j] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 179.58/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.58/179.52 & 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) )
% 179.58/179.52 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_z3div__def,axiom,
% 179.58/179.52 ! [V_k,V_l] :
% 179.58/179.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 179.58/179.52 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 179.58/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_strong__setprod__reindex__cong,axiom,
% 179.58/179.52 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 179.58/179.52 ( class_Groups_Ocomm__monoid__mult(T_d)
% 179.58/179.52 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.58/179.52 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 179.58/179.52 => ( ! [B_x] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.58/179.52 => 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) )
% 179.58/179.52 => 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) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_setprod__mono__one__left,axiom,
% 179.58/179.52 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 179.58/179.52 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 179.58/179.52 => ( ! [B_x] :
% 179.58/179.52 ( 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)))
% 179.58/179.52 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 179.58/179.52 => 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) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_setprod__mono__one__right,axiom,
% 179.58/179.52 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 179.58/179.52 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.58/179.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 179.58/179.52 => ( ! [B_x] :
% 179.58/179.52 ( 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)))
% 179.58/179.52 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 179.58/179.52 => 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) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__le__mono,axiom,
% 179.58/179.52 ! [V_k,V_n,V_m] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.58/179.52 => 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))) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__le__dividend,axiom,
% 179.58/179.52 ! [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)) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__mult2__eq,axiom,
% 179.58/179.52 ! [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) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__1,axiom,
% 179.58/179.52 ! [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 ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__less,axiom,
% 179.58/179.52 ! [V_n,V_m] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.58/179.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_nat__mult__div__cancel__disj,axiom,
% 179.58/179.52 ! [V_n,V_m,V_k] :
% 179.58/179.52 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.52 => 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) )
% 179.58/179.52 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.52 => 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) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 179.58/179.52 ! [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)) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_zdiv__int,axiom,
% 179.58/179.52 ! [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)) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__le__mono2,axiom,
% 179.58/179.52 ! [V_k,V_n,V_m] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 179.58/179.52 => 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))) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__mult__self__is__m,axiom,
% 179.58/179.52 ! [V_m,V_n] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.58/179.52 => 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 ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__mult__self1__is__m,axiom,
% 179.58/179.52 ! [V_m,V_n] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.58/179.52 => 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 ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_nat__mult__div__cancel1,axiom,
% 179.58/179.52 ! [V_n,V_m,V_k] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__less__dividend,axiom,
% 179.58/179.52 ! [V_m,V_n] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__if,axiom,
% 179.58/179.52 ! [V_m,V_n] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.58/179.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.58/179.52 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 179.58/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.58/179.52 => 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)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_div__geq,axiom,
% 179.58/179.52 ! [V_m,V_n] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.58/179.52 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_split__div,axiom,
% 179.58/179.52 ! [V_k_2,V_n_2,V_P_2] :
% 179.58/179.52 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 179.58/179.52 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.52 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 179.58/179.52 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.52 => ! [B_i,B_j] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 179.58/179.52 => ( 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)
% 179.58/179.52 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 179.58/179.52 ! [V_y,V_x] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_nat__div__distrib,axiom,
% 179.58/179.52 ! [V_y,V_x] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_le__div__geq,axiom,
% 179.58/179.52 ! [V_m,V_n] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 179.58/179.52 => 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)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_split__div__lemma,axiom,
% 179.58/179.52 ! [V_m_2,V_q_2,V_n_2] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 179.58/179.52 => ( ( 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))
% 179.58/179.52 & 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)))) )
% 179.58/179.52 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_split__div_H,axiom,
% 179.58/179.52 ! [V_n_2,V_m_2,V_P_2] :
% 179.58/179.52 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 179.58/179.52 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.58/179.52 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 179.58/179.52 | ? [B_q] :
% 179.58/179.52 ( 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))
% 179.58/179.52 & 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))))
% 179.58/179.52 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 179.58/179.52 ! [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)) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_card__Pow,axiom,
% 179.58/179.52 ! [V_A_2,T_b] :
% 179.58/179.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.58/179.52 => 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)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_field__le__mult__one__interval,axiom,
% 179.58/179.52 ! [V_y,V_x,T_a] :
% 179.58/179.52 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 179.58/179.52 => ( ! [B_z] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 179.58/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 179.58/179.52 => 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)) ) )
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 179.58/179.52 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 179.58/179.52 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 179.58/179.52 & class_Groups_Ocomm__monoid__mult(T_b) )
% 179.58/179.52 => ( V_A_2 = V_B_2
% 179.58/179.52 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 179.58/179.52 => ( ! [B_x] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 179.58/179.52 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 179.58/179.52 => 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) ) ) ) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_PowI,axiom,
% 179.58/179.52 ! [V_B_2,V_A_2,T_b] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Pow__iff,axiom,
% 179.58/179.52 ! [V_B_2,V_A_2,T_b] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 179.58/179.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_PowD,axiom,
% 179.58/179.52 ! [V_B_2,V_A_2,T_b] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 179.58/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Pow__mono,axiom,
% 179.58/179.52 ! [V_B_2,V_A_2,T_b] :
% 179.58/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.58/179.52 => 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))) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_image__Pow__surj,axiom,
% 179.58/179.52 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 179.58/179.52 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 179.58/179.52 => 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) ) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Pow__UNIV,axiom,
% 179.58/179.52 ! [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)) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Un__Pow__subset,axiom,
% 179.58/179.52 ! [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)))) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Pow__Int__eq,axiom,
% 179.58/179.52 ! [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)) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Cantors__paradox,axiom,
% 179.58/179.52 ! [V_A_2,T_b] :
% 179.58/179.52 ~ ? [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) ).
% 179.58/179.52
% 179.58/179.52 fof(fact_Pow__top,axiom,
% 179.58/179.52 ! [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))) ).
% 179.58/179.52
% 179.70/179.52 fof(fact_Pow__not__empty,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Pow__insert,axiom,
% 179.70/179.52 ! [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))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Pow__empty,axiom,
% 179.70/179.52 ! [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))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Pow__bottom,axiom,
% 179.70/179.52 ! [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))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_UN__Pow__subset,axiom,
% 179.70/179.52 ! [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)))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_image__Pow__mono,axiom,
% 179.70/179.52 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 179.70/179.52 ( 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))
% 179.70/179.52 => 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))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Pow__def,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_finite__Pow__iff,axiom,
% 179.70/179.52 ! [V_A_2,T_b] :
% 179.70/179.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 179.70/179.52 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Pow__Compl,axiom,
% 179.70/179.52 ! [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))))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 179.70/179.52 ! [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)))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Powp__Pow__eq,axiom,
% 179.70/179.52 ! [V_x_2,V_A_2,T_b] :
% 179.70/179.52 ( 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))
% 179.70/179.52 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_split__neg__lemma,axiom,
% 179.70/179.52 ! [V_n_2,V_P_2,V_k_2] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(V_P_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)))
% 179.70/179.52 <=> ! [B_i,B_j] :
% 179.70/179.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 179.70/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.70/179.52 & 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) )
% 179.70/179.52 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_split__pos__lemma,axiom,
% 179.70/179.52 ! [V_n_2,V_P_2,V_k_2] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(V_P_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)))
% 179.70/179.52 <=> ! [B_i,B_j] :
% 179.70/179.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 179.70/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 179.70/179.52 & 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) )
% 179.70/179.52 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zpower__zmod,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 179.70/179.52 ! [V_y,V_x] :
% 179.70/179.52 ( c_Nat__Transfer_Ois__nat(V_x)
% 179.70/179.52 => ( c_Nat__Transfer_Ois__nat(V_y)
% 179.70/179.52 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zdiff__zmod__left,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zdiff__zmod__right,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zminus2,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zminus__zminus,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zminus__zmod,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mod__trivial,axiom,
% 179.70/179.52 ! [V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__diff__right__eq,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Oring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__diff__left__eq,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Oring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__diff__eq,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Oring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__diff__cong,axiom,
% 179.70/179.52 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Oring__div(T_a)
% 179.70/179.52 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 179.70/179.52 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 179.70/179.52 => 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) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__minus__cong,axiom,
% 179.70/179.52 ! [V_a_H,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Oring__div(T_a)
% 179.70/179.52 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 179.70/179.52 => 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) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__minus__eq,axiom,
% 179.70/179.52 ! [V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Oring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__right__eq,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__left__eq,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__eq,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__mult1,axiom,
% 179.70/179.52 ! [V_b,V_a,V_c,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__mult2,axiom,
% 179.70/179.52 ! [V_b,V_c,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__simps_I4_J,axiom,
% 179.70/179.52 ! [V_b,V_c,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__cong,axiom,
% 179.70/179.52 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 179.70/179.52 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 179.70/179.52 => 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) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__add__self2,axiom,
% 179.70/179.52 ! [V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__add__self1,axiom,
% 179.70/179.52 ! [V_a,V_b,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__add__right__eq,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__add__left__eq,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__add__eq,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__simps_I2_J,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__simps_I1_J,axiom,
% 179.70/179.52 ! [V_b,V_c,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__add__cong,axiom,
% 179.70/179.52 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 179.70/179.52 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 179.70/179.52 => 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) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__0,axiom,
% 179.70/179.52 ! [V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zero,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__by__0,axiom,
% 179.70/179.52 ! [V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__self,axiom,
% 179.70/179.52 ! [V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__self,axiom,
% 179.70/179.52 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zmult1__eq,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__simps_I3_J,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__self2__is__0,axiom,
% 179.70/179.52 ! [V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__self1__is__0,axiom,
% 179.70/179.52 ! [V_a,V_b,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__self2,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__self1,axiom,
% 179.70/179.52 ! [V_b,V_c,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__by__1,axiom,
% 179.70/179.52 ! [V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__div__trivial,axiom,
% 179.70/179.52 ! [V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 179.70/179.52 ! [V_y,V_x] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.70/179.52 => 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))) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__le__nonneg__dividend,axiom,
% 179.70/179.52 ! [V_k,V_m] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_neg__mod__bound,axiom,
% 179.70/179.52 ! [V_a,V_b] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.70/179.52 => 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))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_pos__mod__bound,axiom,
% 179.70/179.52 ! [V_a,V_b] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__eq__0__iff,axiom,
% 179.70/179.52 ! [V_d_2,V_m_2] :
% 179.70/179.52 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zminus2__not__zero,axiom,
% 179.70/179.52 ! [V_l,V_k] :
% 179.70/179.52 ( 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)
% 179.70/179.52 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zminus1__not__zero,axiom,
% 179.70/179.52 ! [V_l,V_k] :
% 179.70/179.52 ( 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)
% 179.70/179.52 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_DIVISION__BY__ZERO,axiom,
% 179.70/179.52 ! [V_a] :
% 179.70/179.52 ( 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)
% 179.70/179.52 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zdiv__trivial,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zdiv__zadd1__eq,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 179.70/179.52 ! [V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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 ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__div__equality2,axiom,
% 179.70/179.52 ! [V_a,V_b,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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 ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__div__equality,axiom,
% 179.70/179.52 ! [V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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 ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_div__mod__equality2,axiom,
% 179.70/179.52 ! [V_c,V_a,V_b,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_div__mod__equality,axiom,
% 179.70/179.52 ! [V_c,V_b,V_a,T_a] :
% 179.70/179.52 ( class_Divides_Osemiring__div(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__neg__neg__trivial,axiom,
% 179.70/179.52 ! [V_b,V_a] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 179.70/179.52 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_neg__mod__conj,axiom,
% 179.70/179.52 ! [V_a,V_b] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.70/179.52 => ( 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)))
% 179.70/179.52 & 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))) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_neg__mod__sign,axiom,
% 179.70/179.52 ! [V_a,V_b] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.70/179.52 => 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))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__pos__pos__trivial,axiom,
% 179.70/179.52 ! [V_b,V_a] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 179.70/179.52 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_pos__mod__conj,axiom,
% 179.70/179.52 ! [V_a,V_b] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.70/179.52 => ( 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)))
% 179.70/179.52 & 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)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_pos__mod__sign,axiom,
% 179.70/179.52 ! [V_a,V_b] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.70/179.52 => 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))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zminus1__eq__if,axiom,
% 179.70/179.52 ! [V_b,V_a] :
% 179.70/179.52 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => 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) )
% 179.70/179.52 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => 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)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zminus2__eq__if,axiom,
% 179.70/179.52 ! [V_b,V_a] :
% 179.70/179.52 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => 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) )
% 179.70/179.52 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => 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) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zdiv__equality,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zdiv__zmult1__eq,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zdiv__zmod__equality,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zdiv__zmod__equality2,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmult__div__cancel,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zdiv__equality_H,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Powp__mono,axiom,
% 179.70/179.52 ! [V_B_2,V_A_2,T_b] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.70/179.52 => 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))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__pos__neg__trivial,axiom,
% 179.70/179.52 ! [V_b,V_a] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.70/179.52 => ( 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)))
% 179.70/179.52 => 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) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_split__zmod,axiom,
% 179.70/179.52 ! [V_k_2,V_n_2,V_P_2] :
% 179.70/179.52 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 179.70/179.52 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 179.70/179.52 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 179.70/179.52 => ! [B_i,B_j] :
% 179.70/179.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 179.70/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 179.70/179.52 & 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) )
% 179.70/179.52 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 179.70/179.52 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.70/179.52 => ! [B_i,B_j] :
% 179.70/179.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 179.70/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.70/179.52 & 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) )
% 179.70/179.52 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmult2__lemma__aux3,axiom,
% 179.70/179.52 ! [V_q,V_b,V_r,V_c] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 179.70/179.52 => 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))) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmult2__lemma__aux4,axiom,
% 179.70/179.52 ! [V_q,V_b,V_r,V_c] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 179.70/179.52 => 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))) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmult2__lemma__aux1,axiom,
% 179.70/179.52 ! [V_q,V_r,V_b,V_c] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.70/179.52 => 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))) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmult2__lemma__aux2,axiom,
% 179.70/179.52 ! [V_q,V_r,V_b,V_c] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.70/179.52 => 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))) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_divmod__int__rel__mod__eq,axiom,
% 179.70/179.52 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 179.70/179.52 ( 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)
% 179.70/179.52 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.70/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 179.70/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 179.70/179.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 179.70/179.52 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__zmult2__eq,axiom,
% 179.70/179.52 ! [V_b,V_a,V_c] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zdiv__zminus1__eq__if,axiom,
% 179.70/179.52 ! [V_a,V_b] :
% 179.70/179.52 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => 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)) )
% 179.70/179.52 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => 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)) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zdiv__zminus2__eq__if,axiom,
% 179.70/179.52 ! [V_a,V_b] :
% 179.70/179.52 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => 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)) )
% 179.70/179.52 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.70/179.52 => 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)) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_z3mod__def,axiom,
% 179.70/179.52 ! [V_k,V_l] :
% 179.70/179.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 179.70/179.52 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 179.70/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 179.70/179.52 => 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)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_setprod__pos__nat,axiom,
% 179.70/179.52 ! [V_f_2,V_S_2,T_b] :
% 179.70/179.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 179.70/179.52 => ( ! [B_x] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 179.70/179.52 => 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))) )
% 179.70/179.52 => 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))) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_card__quotient__disjoint,axiom,
% 179.70/179.52 ! [V_r_2,V_A_2,T_b] :
% 179.70/179.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.70/179.52 => ( 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)
% 179.70/179.52 => 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) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_card_Oneutral,axiom,
% 179.70/179.52 ! [V_A_2,T_b] :
% 179.70/179.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.70/179.52 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.70/179.52 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 179.70/179.52 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__distrib2,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__distrib,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__less,axiom,
% 179.70/179.52 ! [V_n,V_m] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.70/179.52 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__less__eq__dividend,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_quotient__is__empty,axiom,
% 179.70/179.52 ! [V_r_2,V_A_2,T_b] :
% 179.70/179.52 ( 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))
% 179.70/179.52 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_quotient__is__empty2,axiom,
% 179.70/179.52 ! [V_r_2,V_A_2,T_b] :
% 179.70/179.52 ( 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)
% 179.70/179.52 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_quotient__empty,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__1,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__Suc,axiom,
% 179.70/179.52 ! [V_n,V_m] :
% 179.70/179.52 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 179.70/179.52 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 179.70/179.52 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 179.70/179.52 => 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)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__less__divisor,axiom,
% 179.70/179.52 ! [V_m,V_n] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__eq__0__iff,axiom,
% 179.70/179.52 ! [V_d_2,V_m_2] :
% 179.70/179.52 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.70/179.52 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__if,axiom,
% 179.70/179.52 ! [V_n,V_m] :
% 179.70/179.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.70/179.52 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 179.70/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.70/179.52 => 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) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__geq,axiom,
% 179.70/179.52 ! [V_n,V_m] :
% 179.70/179.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__self3,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_le__mod__geq,axiom,
% 179.70/179.52 ! [V_m,V_n] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_zmod__int,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_div__add1__eq,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_nat__gcd_Osimps,axiom,
% 179.70/179.52 ! [V_x,V_y] :
% 179.70/179.52 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.70/179.52 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 179.70/179.52 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.70/179.52 => 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)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__le__divisor,axiom,
% 179.70/179.52 ! [V_m,V_n] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult__self4,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__mult2__eq,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_div__mult1__eq,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_div__mod__equality_H,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mult__div__cancel,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Divides_Omod__div__equality_H,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_quotient__diff1,axiom,
% 179.70/179.52 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 179.70/179.52 ( 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)
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.70/179.52 => 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)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__lemma,axiom,
% 179.70/179.52 ! [V_q,V_b,V_r,V_c] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 179.70/179.52 => 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))) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_split__mod,axiom,
% 179.70/179.52 ! [V_k_2,V_n_2,V_P_2] :
% 179.70/179.52 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 179.70/179.52 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.70/179.52 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 179.70/179.52 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.70/179.52 => ! [B_i,B_j] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 179.70/179.52 => ( 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)
% 179.70/179.52 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Suc__times__mod__eq,axiom,
% 179.70/179.52 ! [V_m,V_k] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_nat__mod__distrib,axiom,
% 179.70/179.52 ! [V_y,V_x] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.70/179.52 => 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)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 179.70/179.52 ! [V_y,V_x] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 179.70/179.52 => 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)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_quotient__def,axiom,
% 179.70/179.52 ! [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)))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_singleton__quotient,axiom,
% 179.70/179.52 ! [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))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_quotientI,axiom,
% 179.70/179.52 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.70/179.52 => 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))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_fold__image__cong,axiom,
% 179.70/179.52 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 179.70/179.52 ( class_Groups_Oab__semigroup__mult(T_c)
% 179.70/179.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.70/179.52 => ( ! [B_x] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.70/179.52 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 179.70/179.52 => 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) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Image__eq__UN,axiom,
% 179.70/179.52 ! [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))))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Image__Int__subset,axiom,
% 179.70/179.52 ! [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)))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Image__UN,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_quotientE,axiom,
% 179.70/179.52 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 179.70/179.52 ( 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)))
% 179.70/179.52 => ~ ! [B_x] :
% 179.70/179.52 ( 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))))
% 179.70/179.52 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Image__empty,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Image__mono,axiom,
% 179.70/179.52 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 179.70/179.52 ( 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))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 179.70/179.52 => 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))) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Image__Un,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Un__Image,axiom,
% 179.70/179.52 ! [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)) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_nat__mod__eq__lemma,axiom,
% 179.70/179.52 ! [V_y,V_n,V_x] :
% 179.70/179.52 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 179.70/179.52 => ? [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)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mod__induct__0,axiom,
% 179.70/179.52 ! [V_i_2,V_P_2,V_p_2] :
% 179.70/179.52 ( ! [B_i] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 179.70/179.52 => ( hBOOL(hAPP(V_P_2,B_i))
% 179.70/179.52 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 179.70/179.52 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 179.70/179.52 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Max__eqI,axiom,
% 179.70/179.52 ! [V_x_2,V_A_2,T_b] :
% 179.70/179.52 ( class_Orderings_Olinorder(T_b)
% 179.70/179.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.70/179.52 => ( ! [B_y] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 179.70/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.70/179.52 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Min__eqI,axiom,
% 179.70/179.52 ! [V_x_2,V_A_2,T_b] :
% 179.70/179.52 ( class_Orderings_Olinorder(T_b)
% 179.70/179.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.70/179.52 => ( ! [B_y] :
% 179.70/179.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 179.70/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 179.70/179.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.70/179.52 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_less__by__empty,axiom,
% 179.70/179.52 ! [V_B_2,T_b,V_A_2] :
% 179.70/179.52 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_expand__Suc,axiom,
% 179.70/179.52 ! [V_v] :
% 179.70/179.52 ( 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)))
% 179.70/179.52 => 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))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_quotient__disj,axiom,
% 179.70/179.52 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 179.70/179.52 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.70/179.52 => ( 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)))
% 179.70/179.52 => ( 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)))
% 179.70/179.52 => ( V_X_2 = V_Y_2
% 179.70/179.52 | 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)) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osize_I11_J,axiom,
% 179.70/179.52 ! [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))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osize_I3_J,axiom,
% 179.70/179.52 ! [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))) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_of__nat__number__of__lemma,axiom,
% 179.70/179.52 ! [V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => ( ( 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)))
% 179.70/179.52 => 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) )
% 179.70/179.52 & ( ~ 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)))
% 179.70/179.52 => 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) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I36_J,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I37_J,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I22_J,axiom,
% 179.70/179.52 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_fun_2,V_vname_2] : c_Com_Ocom_OAss(V_vname_2,V_fun_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I23_J,axiom,
% 179.70/179.52 ! [V_fun_2,V_vname_2,V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OAss(V_vname_2,V_fun_2) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I35_J,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I34_J,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I10_J,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I11_J,axiom,
% 179.70/179.52 ! [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 ).
% 179.70/179.52
% 179.70/179.52 fof(fact_of__nat__number__of__eq,axiom,
% 179.70/179.52 ! [V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.52 => 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) )
% 179.70/179.52 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.52 => 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) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_number__of__reorient,axiom,
% 179.70/179.52 ! [V_x_2,V_w_2,T_b] :
% 179.70/179.52 ( class_Int_Onumber(T_b)
% 179.70/179.52 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 179.70/179.52 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_eq__number__of,axiom,
% 179.70/179.52 ! [V_y_2,V_x_2,T_b] :
% 179.70/179.52 ( ( class_Int_Onumber__ring(T_b)
% 179.70/179.52 & class_Int_Oring__char__0(T_b) )
% 179.70/179.52 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 179.70/179.52 <=> V_x_2 = V_y_2 ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I2_J,axiom,
% 179.70/179.52 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 179.70/179.52 ( 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)
% 179.70/179.52 <=> ( V_loc_2 = V_loc_H_2
% 179.70/179.52 & V_fun_2 = V_fun_H_2
% 179.70/179.52 & V_com_2 = V_com_H_2 ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_number__of__eq,axiom,
% 179.70/179.52 ! [V_k,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_of__int__number__of__eq,axiom,
% 179.70/179.52 ! [V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I39_J,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I38_J,axiom,
% 179.70/179.52 ! [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) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_com_Osimps_I66_J,axiom,
% 179.70/179.52 ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_le__number__of__eq__not__less,axiom,
% 179.70/179.52 ! [V_w_2,V_v_2,T_b] :
% 179.70/179.52 ( ( class_Int_Onumber(T_b)
% 179.70/179.52 & class_Orderings_Olinorder(T_b) )
% 179.70/179.52 => ( 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)))
% 179.70/179.52 <=> ~ 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))) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_left__distrib__number__of,axiom,
% 179.70/179.52 ! [V_v,V_b,V_a,T_b] :
% 179.70/179.52 ( ( class_Int_Onumber(T_b)
% 179.70/179.52 & class_Rings_Osemiring(T_b) )
% 179.70/179.52 => 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))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_right__distrib__number__of,axiom,
% 179.70/179.52 ! [V_c,V_b,V_v,T_b] :
% 179.70/179.52 ( ( class_Int_Onumber(T_b)
% 179.70/179.52 & class_Rings_Osemiring(T_b) )
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_left__diff__distrib__number__of,axiom,
% 179.70/179.52 ! [V_v,V_b,V_a,T_b] :
% 179.70/179.52 ( ( class_Int_Onumber(T_b)
% 179.70/179.52 & class_Rings_Oring(T_b) )
% 179.70/179.52 => 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))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_right__diff__distrib__number__of,axiom,
% 179.70/179.52 ! [V_c,V_b,V_v,T_b] :
% 179.70/179.52 ( ( class_Int_Onumber(T_b)
% 179.70/179.52 & class_Rings_Oring(T_b) )
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_le__number__of,axiom,
% 179.70/179.52 ! [V_y_2,V_x_2,T_b] :
% 179.70/179.52 ( ( class_Int_Onumber__ring(T_b)
% 179.70/179.52 & class_Rings_Olinordered__idom(T_b) )
% 179.70/179.52 => ( 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)))
% 179.70/179.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_less__number__of,axiom,
% 179.70/179.52 ! [V_y_2,V_x_2,T_b] :
% 179.70/179.52 ( ( class_Int_Onumber__ring(T_b)
% 179.70/179.52 & class_Rings_Olinordered__idom(T_b) )
% 179.70/179.52 => ( 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)))
% 179.70/179.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_min__number__of,axiom,
% 179.70/179.52 ! [V_v,V_u,T_b] :
% 179.70/179.52 ( ( class_Int_Onumber(T_b)
% 179.70/179.52 & class_Orderings_Oord(T_b) )
% 179.70/179.52 => ( ( 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)))
% 179.70/179.52 => 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) )
% 179.70/179.52 & ( ~ 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)))
% 179.70/179.52 => 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) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_max__number__of,axiom,
% 179.70/179.52 ! [V_v,V_u,T_b] :
% 179.70/179.52 ( ( class_Int_Onumber(T_b)
% 179.70/179.52 & class_Orderings_Oord(T_b) )
% 179.70/179.52 => ( ( 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)))
% 179.70/179.52 => 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) )
% 179.70/179.52 & ( ~ 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)))
% 179.70/179.52 => 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) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_add__number__of__left,axiom,
% 179.70/179.52 ! [V_z,V_w,V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_add__number__of__eq,axiom,
% 179.70/179.52 ! [V_w,V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_number__of__add,axiom,
% 179.70/179.52 ! [V_w,V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_mult__number__of__left,axiom,
% 179.70/179.52 ! [V_z,V_w,V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_arith__simps_I32_J,axiom,
% 179.70/179.52 ! [V_w,V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_number__of__mult,axiom,
% 179.70/179.52 ! [V_w,V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_number__of__diff,axiom,
% 179.70/179.52 ! [V_w,V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_arith__simps_I30_J,axiom,
% 179.70/179.52 ! [V_w,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_number__of__minus,axiom,
% 179.70/179.52 ! [V_w,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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)) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_Ints__number__of,axiom,
% 179.70/179.52 ! [V_w_2,T_b] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_b)
% 179.70/179.52 => 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))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_eq__divide__eq__number__of1,axiom,
% 179.70/179.52 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 179.70/179.52 & class_Int_Onumber(T_b) )
% 179.70/179.52 => ( 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))
% 179.70/179.52 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 179.70/179.52 => 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 )
% 179.70/179.52 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.70/179.52 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_eq__divide__eq__number__of,axiom,
% 179.70/179.52 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 179.70/179.52 & class_Int_Onumber(T_b) )
% 179.70/179.52 => ( 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)
% 179.70/179.52 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 179.70/179.52 => 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 )
% 179.70/179.52 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 179.70/179.52 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_divide__eq__eq__number__of,axiom,
% 179.70/179.52 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 179.70/179.52 & class_Int_Onumber(T_b) )
% 179.70/179.52 => ( 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)
% 179.70/179.52 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 179.70/179.52 => 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) )
% 179.70/179.52 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 179.70/179.52 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_divide__eq__eq__number__of1,axiom,
% 179.70/179.52 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 179.70/179.52 & class_Int_Onumber(T_b) )
% 179.70/179.52 => ( 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
% 179.70/179.52 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 179.70/179.52 => 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)) )
% 179.70/179.52 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.70/179.52 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_add__number__of__diff1,axiom,
% 179.70/179.52 ! [V_c,V_w,V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_minus__number__of__mult,axiom,
% 179.70/179.52 ! [V_z,V_w,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_diff__number__of__eq,axiom,
% 179.70/179.52 ! [V_w,V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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))) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_divide__less__eq__number__of1,axiom,
% 179.70/179.52 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.70/179.52 & class_Int_Onumber(T_b) )
% 179.70/179.52 => ( 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))
% 179.70/179.52 <=> ( ( 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)))
% 179.70/179.52 => 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)))) )
% 179.70/179.52 & ( ~ 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)))
% 179.70/179.52 => ( ( 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)))
% 179.70/179.52 => 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)) )
% 179.70/179.52 & ( ~ 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)))
% 179.70/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_divide__less__eq__number__of,axiom,
% 179.70/179.52 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.70/179.52 & class_Int_Onumber(T_b) )
% 179.70/179.52 => ( 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)))
% 179.70/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.70/179.52 => 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))) )
% 179.70/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.70/179.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.70/179.52 => 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)) )
% 179.70/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.70/179.52 => 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))) ) ) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_less__divide__eq__number__of,axiom,
% 179.70/179.52 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.70/179.52 & class_Int_Onumber(T_b) )
% 179.70/179.52 => ( 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)))
% 179.70/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.70/179.52 => 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)) )
% 179.70/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.70/179.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.70/179.52 => 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))) )
% 179.70/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.70/179.52 => 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))) ) ) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_less__divide__eq__number__of1,axiom,
% 179.70/179.52 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.70/179.52 & class_Int_Onumber(T_b) )
% 179.70/179.52 => ( 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))))
% 179.70/179.52 <=> ( ( 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)))
% 179.70/179.52 => 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)) )
% 179.70/179.52 & ( ~ 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)))
% 179.70/179.52 => ( ( 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)))
% 179.70/179.52 => 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)))) )
% 179.70/179.52 & ( ~ 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)))
% 179.70/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_abs__number__of,axiom,
% 179.70/179.52 ! [V_x,T_a] :
% 179.70/179.52 ( ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 & class_Rings_Olinordered__idom(T_a) )
% 179.70/179.52 => ( ( 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)))
% 179.70/179.52 => 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)) )
% 179.70/179.52 & ( ~ 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)))
% 179.70/179.52 => 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) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_add__number__of__diff2,axiom,
% 179.70/179.52 ! [V_w,V_c,V_v,T_a] :
% 179.70/179.52 ( class_Int_Onumber__ring(T_a)
% 179.70/179.52 => 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) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_divide__le__eq__number__of1,axiom,
% 179.70/179.52 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.70/179.52 & class_Int_Onumber(T_b) )
% 179.70/179.52 => ( 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))
% 179.70/179.52 <=> ( ( 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)))
% 179.70/179.52 => 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)))) )
% 179.70/179.52 & ( ~ 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)))
% 179.70/179.52 => ( ( 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)))
% 179.70/179.52 => 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)) )
% 179.70/179.52 & ( ~ 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)))
% 179.70/179.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_divide__le__eq__number__of,axiom,
% 179.70/179.52 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.70/179.52 & class_Int_Onumber(T_b) )
% 179.70/179.52 => ( 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)))
% 179.70/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.70/179.52 => 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))) )
% 179.70/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.70/179.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.70/179.52 => 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)) )
% 179.70/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.70/179.52 => 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))) ) ) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_le__divide__eq__number__of,axiom,
% 179.70/179.52 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.70/179.52 & class_Int_Onumber(T_b) )
% 179.70/179.52 => ( 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)))
% 179.70/179.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.70/179.52 => 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)) )
% 179.70/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 179.70/179.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.70/179.52 => 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))) )
% 179.70/179.52 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 179.70/179.52 => 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))) ) ) ) ) ) ) ).
% 179.70/179.52
% 179.70/179.52 fof(fact_le__divide__eq__number__of1,axiom,
% 179.70/179.52 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 179.70/179.52 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.70/179.53 & class_Int_Onumber(T_b) )
% 179.70/179.53 => ( 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))))
% 179.70/179.53 <=> ( ( 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)))
% 179.70/179.53 => 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)) )
% 179.70/179.53 & ( ~ 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)))
% 179.70/179.53 => ( ( 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)))
% 179.70/179.53 => 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)))) )
% 179.70/179.53 & ( ~ 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)))
% 179.70/179.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_equiv__class__self,axiom,
% 179.70/179.53 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 179.70/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.70/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.70/179.53 => 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)))))) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_UN__equiv__class2,axiom,
% 179.70/179.53 ! [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] :
% 179.70/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 179.70/179.53 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 179.70/179.53 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 179.70/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 179.70/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 179.70/179.53 => 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) ) ) ) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_UN__equiv__class,axiom,
% 179.70/179.53 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 179.70/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.70/179.53 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 179.70/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.70/179.53 => 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) ) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_one__mod__nat__number__of,axiom,
% 179.70/179.53 ! [V_v_H] :
% 179.70/179.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 179.70/179.53 => 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)) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 179.70/179.53 => 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))) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_one__div__nat__number__of,axiom,
% 179.70/179.53 ! [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))) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_less__eq__number__of__int__code,axiom,
% 179.70/179.53 ! [V_l_2,V_k_2] :
% 179.70/179.53 ( 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)))
% 179.70/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_plus__numeral__code_I9_J,axiom,
% 179.70/179.53 ! [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)) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_times__numeral__code_I5_J,axiom,
% 179.70/179.53 ! [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)) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_minus__numeral__code_I5_J,axiom,
% 179.70/179.53 ! [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)) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_number__of__is__id,axiom,
% 179.70/179.53 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 179.70/179.53
% 179.70/179.53 fof(fact_less__number__of__int__code,axiom,
% 179.70/179.53 ! [V_l_2,V_k_2] :
% 179.70/179.53 ( 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)))
% 179.70/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_int__number__of__def,axiom,
% 179.70/179.53 ! [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) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_nat__number__of__def,axiom,
% 179.70/179.53 ! [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)) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_nat__number__of,axiom,
% 179.70/179.53 ! [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) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_congruent2__implies__congruent,axiom,
% 179.70/179.53 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 179.70/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 179.70/179.53 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 179.70/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.70/179.53 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_minus__numeral__code_I6_J,axiom,
% 179.70/179.53 ! [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))) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_neg__imp__number__of__eq__0,axiom,
% 179.70/179.53 ! [V_v] :
% 179.70/179.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_int__eq__iff__number__of,axiom,
% 179.70/179.53 ! [V_v_2,V_m_2] :
% 179.70/179.53 ( 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)
% 179.70/179.53 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 179.70/179.53 & 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))) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_eq__nat__number__of,axiom,
% 179.70/179.53 ! [V_v_H_2,V_v_2] :
% 179.70/179.53 ( 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)
% 179.70/179.53 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 179.70/179.53 => 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))) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 179.70/179.53 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 179.70/179.53 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 179.70/179.53 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_nat__number__of__add__left,axiom,
% 179.70/179.53 ! [V_k,V_v_H,V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 179.70/179.53 => 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) ) ) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_int__nat__number__of,axiom,
% 179.70/179.53 ! [V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_mod__nat__number__of,axiom,
% 179.70/179.53 ! [V_v_H,V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 179.70/179.53 => 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))) ) ) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_congruent2__implies__congruent__UN,axiom,
% 179.70/179.53 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 179.70/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 179.70/179.53 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 179.70/179.53 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 179.70/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 179.70/179.53 => 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)) ) ) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_div__nat__number__of,axiom,
% 179.70/179.53 ! [V_v_H,V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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))) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_power__nat__number__of__number__of,axiom,
% 179.70/179.53 ! [V_w,V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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)) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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))) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_power__nat__number__of,axiom,
% 179.70/179.53 ! [V_n,V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_Suc__nat__number__of__add,axiom,
% 179.70/179.53 ! [V_n,V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.70/179.53 => 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) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_diff__nat__number__of,axiom,
% 179.70/179.53 ! [V_v_2,V_v_H_2] :
% 179.70/179.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 179.70/179.53 => 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)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_min__number__of__Suc,axiom,
% 179.70/179.53 ! [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)))) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_min__Suc__number__of,axiom,
% 179.70/179.53 ! [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)))) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_rel__simps_I19_J,axiom,
% 179.70/179.53 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_diff__bin__simps_I1_J,axiom,
% 179.70/179.53 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 179.70/179.53
% 179.70/179.53 fof(fact_minus__Pls,axiom,
% 179.70/179.53 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 179.70/179.53
% 179.70/179.53 fof(fact_Pls__def,axiom,
% 179.70/179.53 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_rel__simps_I2_J,axiom,
% 179.70/179.53 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_add__Pls__right,axiom,
% 179.70/179.53 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 179.70/179.53
% 179.70/179.53 fof(fact_add__Pls,axiom,
% 179.70/179.53 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 179.70/179.53
% 179.70/179.53 fof(fact_succ__pred,axiom,
% 179.70/179.53 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 179.70/179.53
% 179.70/179.53 fof(fact_mult__Pls,axiom,
% 179.70/179.53 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 179.70/179.53
% 179.70/179.53 fof(fact_semiring__norm_I112_J,axiom,
% 179.70/179.53 ! [T_a] :
% 179.70/179.53 ( class_Int_Onumber__ring(T_a)
% 179.70/179.53 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_number__of__Pls,axiom,
% 179.70/179.53 ! [T_a] :
% 179.70/179.53 ( class_Int_Onumber__ring(T_a)
% 179.70/179.53 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_add__numeral__0,axiom,
% 179.70/179.53 ! [V_a,T_a] :
% 179.70/179.53 ( class_Int_Onumber__ring(T_a)
% 179.70/179.53 => 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 ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_add__numeral__0__right,axiom,
% 179.70/179.53 ! [V_a,T_a] :
% 179.70/179.53 ( class_Int_Onumber__ring(T_a)
% 179.70/179.53 => 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 ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_bin__less__0__simps_I1_J,axiom,
% 179.70/179.53 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_semiring__norm_I113_J,axiom,
% 179.70/179.53 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_nat__number__of__Pls,axiom,
% 179.70/179.53 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_zero__is__num__zero,axiom,
% 179.70/179.53 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_Suc__diff__number__of,axiom,
% 179.70/179.53 ! [V_m,V_v] :
% 179.70/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 179.70/179.53 => 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))) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_not__neg__number__of__Pls,axiom,
% 179.70/179.53 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_nat__1__add__number__of,axiom,
% 179.70/179.53 ! [V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => 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)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_nat__number__of__add__1,axiom,
% 179.70/179.53 ! [V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => 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)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_le__iff__pred__less,axiom,
% 179.70/179.53 ! [V_l_2,V_k_2] :
% 179.70/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 179.70/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_pred__def,axiom,
% 179.70/179.53 ! [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)) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_nat__number__of__diff__1,axiom,
% 179.70/179.53 ! [V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => 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)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_divide__Numeral0,axiom,
% 179.70/179.53 ! [V_x,T_a] :
% 179.70/179.53 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 179.70/179.53 & class_Int_Onumber__ring(T_a) )
% 179.70/179.53 => 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) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_eq__number__of__0,axiom,
% 179.70/179.53 ! [V_v_2] :
% 179.70/179.53 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.70/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_eq__0__number__of,axiom,
% 179.70/179.53 ! [V_v_2] :
% 179.70/179.53 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 179.70/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_number__of2,axiom,
% 179.70/179.53 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))) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_less__nat__number__of,axiom,
% 179.70/179.53 ! [V_v_H_2,V_v_2] :
% 179.70/179.53 ( 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)))
% 179.70/179.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 179.70/179.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 179.70/179.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_le__nat__number__of,axiom,
% 179.70/179.53 ! [V_v_H_2,V_v_2] :
% 179.70/179.53 ( 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)))
% 179.70/179.53 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 179.70/179.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_succ__def,axiom,
% 179.70/179.53 ! [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)) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_le__special_I3_J,axiom,
% 179.70/179.53 ! [V_x_2,T_b] :
% 179.70/179.53 ( ( class_Int_Onumber__ring(T_b)
% 179.70/179.53 & class_Rings_Olinordered__idom(T_b) )
% 179.70/179.53 => ( 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)))
% 179.70/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_le__special_I1_J,axiom,
% 179.70/179.53 ! [V_y_2,T_b] :
% 179.70/179.53 ( ( class_Int_Onumber__ring(T_b)
% 179.70/179.53 & class_Rings_Olinordered__idom(T_b) )
% 179.70/179.53 => ( 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)))
% 179.70/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_less__special_I3_J,axiom,
% 179.70/179.53 ! [V_x_2,T_b] :
% 179.70/179.53 ( ( class_Int_Onumber__ring(T_b)
% 179.70/179.53 & class_Rings_Olinordered__idom(T_b) )
% 179.70/179.53 => ( 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)))
% 179.70/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_less__special_I1_J,axiom,
% 179.70/179.53 ! [V_y_2,T_b] :
% 179.70/179.53 ( ( class_Int_Onumber__ring(T_b)
% 179.70/179.53 & class_Rings_Olinordered__idom(T_b) )
% 179.70/179.53 => ( 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)))
% 179.70/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_less__0__number__of,axiom,
% 179.70/179.53 ! [V_v_2] :
% 179.70/179.53 ( 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)))
% 179.70/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_add__nat__number__of,axiom,
% 179.70/179.53 ! [V_v_H,V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 179.70/179.53 => 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)) ) ) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_number__of__succ,axiom,
% 179.70/179.53 ! [V_k,T_a] :
% 179.70/179.53 ( class_Int_Onumber__ring(T_a)
% 179.70/179.53 => 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)) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_number__of__pred,axiom,
% 179.70/179.53 ! [V_w,T_a] :
% 179.70/179.53 ( class_Int_Onumber__ring(T_a)
% 179.70/179.53 => 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)) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_mult__nat__number__of,axiom,
% 179.70/179.53 ! [V_v_H,V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => 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)) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_nat__number__of__mult__left,axiom,
% 179.70/179.53 ! [V_k,V_v_H,V_v] :
% 179.70/179.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => 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) )
% 179.70/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 179.70/179.53 => 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) ) ) ).
% 179.70/179.53
% 179.70/179.53 fof(fact_neg__number__of__pred__iff__0,axiom,
% 179.70/179.53 ! [V_v_2] :
% 179.70/179.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 179.70/179.53 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Suc__eq__number__of,axiom,
% 179.72/179.53 ! [V_v_2,V_n_2] :
% 179.72/179.53 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 179.72/179.53 <=> 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))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_eq__number__of__Suc,axiom,
% 179.72/179.53 ! [V_n_2,V_v_2] :
% 179.72/179.53 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 179.72/179.53 <=> 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))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__case__number__of,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__number__of__Suc,axiom,
% 179.72/179.53 ! [V_n_2,V_v_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 <=> 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__Suc__number__of,axiom,
% 179.72/179.53 ! [V_v_2,V_n_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 <=> 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))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_le__number__of__Suc,axiom,
% 179.72/179.53 ! [V_n_2,V_v_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 <=> 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_le__Suc__number__of,axiom,
% 179.72/179.53 ! [V_v_2,V_n_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 <=> 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))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Suc__nat__number__of,axiom,
% 179.72/179.53 ! [V_v] :
% 179.72/179.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.72/179.53 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_max__Suc__number__of,axiom,
% 179.72/179.53 ! [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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_max__number__of__Suc,axiom,
% 179.72/179.53 ! [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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__case__add__eq__if,axiom,
% 179.72/179.53 ! [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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__rec__add__eq__if,axiom,
% 179.72/179.53 ! [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))))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__rec__number__of,axiom,
% 179.72/179.53 ! [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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_UN__equiv__class__type2,axiom,
% 179.72/179.53 ! [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] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 179.72/179.53 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 179.72/179.53 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( ! [B_x1] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 179.72/179.53 => ! [B_x2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 179.72/179.53 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 179.72/179.53 => 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)) ) ) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_UN__equiv__class__type,axiom,
% 179.72/179.53 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( ! [B_x] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.53 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 179.72/179.53 => 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)) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__rec__0,axiom,
% 179.72/179.53 ! [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 ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__rec__Suc,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_eq__special_I3_J,axiom,
% 179.72/179.53 ! [V_x_2,T_b] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 179.72/179.53 <=> 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_eq__special_I1_J,axiom,
% 179.72/179.53 ! [V_y_2,T_b] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 179.72/179.53 <=> 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power__number__of__odd__number__of,axiom,
% 179.72/179.53 ! [V_v_2,V_w_2,T_b] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 => ( ( 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)))
% 179.72/179.53 => 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))) )
% 179.72/179.53 & ( ~ 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)))
% 179.72/179.53 => 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) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_iszero__number__of__Bit1,axiom,
% 179.72/179.53 ! [V_w,T_a] :
% 179.72/179.53 ( ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 & class_Int_Oring__char__0(T_a) )
% 179.72/179.53 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__eq__int__code_I16_J,axiom,
% 179.72/179.53 ! [V_k2_2,V_k1_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I34_J,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__int__code_I16_J,axiom,
% 179.72/179.53 ! [V_k2_2,V_k1_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I17_J,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I51_J,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 179.72/179.53 <=> V_k_2 = V_l_2 ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I46_J,axiom,
% 179.72/179.53 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I39_J,axiom,
% 179.72/179.53 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_not__iszero__Numeral1,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_iszero__def,axiom,
% 179.72/179.53 ! [V_z_2,T_b] :
% 179.72/179.53 ( class_Rings_Osemiring__1(T_b)
% 179.72/179.53 => ( c_Int_Oiszero(T_b,V_z_2)
% 179.72/179.53 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_iszero__0,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Rings_Osemiring__1(T_a)
% 179.72/179.53 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_not__iszero__1,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Rings_Osemiring__1(T_a)
% 179.72/179.53 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_bin__less__0__simps_I4_J,axiom,
% 179.72/179.53 ! [V_w_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I22_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I12_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Bit1__def,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_neg__number__of__Bit1,axiom,
% 179.72/179.53 ! [V_w_2] :
% 179.72/179.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 179.72/179.53 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_minus__Bit1,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_succ__Pls,axiom,
% 179.72/179.53 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_number__of__Bit1,axiom,
% 179.72/179.53 ! [V_w,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mult__numeral__1,axiom,
% 179.72/179.53 ! [V_a,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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 ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mult__numeral__1__right,axiom,
% 179.72/179.53 ! [V_a,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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 ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_semiring__norm_I110_J,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_numeral__1__eq__1,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I5_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I29_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divide__Numeral1,axiom,
% 179.72/179.53 ! [V_x,T_a] :
% 179.72/179.53 ( ( class_Fields_Ofield(T_a)
% 179.72/179.53 & class_Int_Onumber__ring(T_a) )
% 179.72/179.53 => 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 ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divide__numeral__1,axiom,
% 179.72/179.53 ! [V_a,T_a] :
% 179.72/179.53 ( ( class_Fields_Ofield(T_a)
% 179.72/179.53 & class_Int_Onumber__ring(T_a) )
% 179.72/179.53 => 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 ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_eq__special_I2_J,axiom,
% 179.72/179.53 ! [V_y_2,T_b] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 179.72/179.53 <=> 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_eq__special_I4_J,axiom,
% 179.72/179.53 ! [V_x_2,T_b] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 179.72/179.53 <=> 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))))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_one__is__num__one,axiom,
% 179.72/179.53 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__numeral__1__eq__1,axiom,
% 179.72/179.53 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Numeral1__eq1__nat,axiom,
% 179.72/179.53 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 179.72/179.53 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_iszero__Numeral0,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_numeral__3__eq__3,axiom,
% 179.72/179.53 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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_numeral__1__eq__Suc__0,axiom,
% 179.72/179.53 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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power3__eq__cube,axiom,
% 179.72/179.53 ! [V_a,T_a] :
% 179.72/179.53 ( class_Groups_Omonoid__mult(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 179.72/179.53 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))))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Suc3__eq__add__3,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 179.72/179.53 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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 179.72/179.53 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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_le__special_I2_J,axiom,
% 179.72/179.53 ! [V_y_2,T_b] :
% 179.72/179.53 ( ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 & class_Rings_Olinordered__idom(T_b) )
% 179.72/179.53 => ( 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)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_le__special_I4_J,axiom,
% 179.72/179.53 ! [V_x_2,T_b] :
% 179.72/179.53 ( ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 & class_Rings_Olinordered__idom(T_b) )
% 179.72/179.53 => ( 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)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__special_I4_J,axiom,
% 179.72/179.53 ! [V_x_2,T_b] :
% 179.72/179.53 ( ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 & class_Rings_Olinordered__idom(T_b) )
% 179.72/179.53 => ( 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)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__special_I2_J,axiom,
% 179.72/179.53 ! [V_y_2,T_b] :
% 179.72/179.53 ( ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 & class_Rings_Olinordered__idom(T_b) )
% 179.72/179.53 => ( 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)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_add__special_I2_J,axiom,
% 179.72/179.53 ! [V_w,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_add__special_I3_J,axiom,
% 179.72/179.53 ! [V_v,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 179.72/179.53 ! [V_m,V_n] :
% 179.72/179.53 ( 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))
% 179.72/179.53 => 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__Suc__eq__div__add3,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Suc__div__eq__add3__div,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_eq__number__of__eq,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,T_b] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 179.72/179.53 <=> 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_diff__special_I1_J,axiom,
% 179.72/179.53 ! [V_w,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_diff__special_I2_J,axiom,
% 179.72/179.53 ! [V_v,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__number__of__Bit1,axiom,
% 179.72/179.53 ! [V_w_2] :
% 179.72/179.53 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 179.72/179.53 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 179.72/179.53 => 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power__number__of__odd,axiom,
% 179.72/179.53 ! [V_z_2,V_w_2,T_b] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 => ( ( 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)))
% 179.72/179.53 => 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))) )
% 179.72/179.53 & ( ~ 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)))
% 179.72/179.53 => 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) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zpower__number__of__odd,axiom,
% 179.72/179.53 ! [V_z_2,V_w_2] :
% 179.72/179.53 ( ( 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)))
% 179.72/179.53 => 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))) )
% 179.72/179.53 & ( ~ 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)))
% 179.72/179.53 => 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) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zmod__number__of__Bit1,axiom,
% 179.72/179.53 ! [V_v,V_w] :
% 179.72/179.53 ( ( 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)))
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( ~ 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)))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_neg__zmod__mult__2,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_arith__series__int,axiom,
% 179.72/179.53 ! [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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I49_J,axiom,
% 179.72/179.53 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I50_J,axiom,
% 179.72/179.53 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Bit0__Pls,axiom,
% 179.72/179.53 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I38_J,axiom,
% 179.72/179.53 ! [V_l_2] :
% 179.72/179.53 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 179.72/179.53 <=> c_Int_OPls = V_l_2 ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I44_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 179.72/179.53 <=> V_k_2 = c_Int_OPls ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_minus__Bit0,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I48_J,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 179.72/179.53 <=> V_k_2 = V_l_2 ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Bit0__def,axiom,
% 179.72/179.53 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_add__Bit0__Bit0,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mult__Bit0,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I14_J,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__int__code_I13_J,axiom,
% 179.72/179.53 ! [V_k2_2,V_k1_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_diff__bin__simps_I7_J,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I31_J,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__eq__int__code_I13_J,axiom,
% 179.72/179.53 ! [V_k2_2,V_k1_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_bin__less__0__simps_I3_J,axiom,
% 179.72/179.53 ! [V_w_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I27_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I21_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__eq__int__code_I14_J,axiom,
% 179.72/179.53 ! [V_k2_2,V_k1_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I32_J,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I4_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I10_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I16_J,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__int__code_I15_J,axiom,
% 179.72/179.53 ! [V_k2_2,V_k1_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_add__Bit0__Bit1,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_add__Bit1__Bit0,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_diff__bin__simps_I3_J,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_diff__bin__simps_I10_J,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_diff__bin__simps_I9_J,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zdiv__number__of__Bit0,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_neg__number__of__Bit0,axiom,
% 179.72/179.53 ! [V_w_2] :
% 179.72/179.53 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 179.72/179.53 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pred__Bit1,axiom,
% 179.72/179.53 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pred__Bit0,axiom,
% 179.72/179.53 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_iszero__number__of__Bit0,axiom,
% 179.72/179.53 ! [V_w_2,T_b] :
% 179.72/179.53 ( ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 & class_Int_Oring__char__0(T_b) )
% 179.72/179.53 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 179.72/179.53 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_succ__Bit0,axiom,
% 179.72/179.53 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_succ__Bit1,axiom,
% 179.72/179.53 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__number__of__Bit0,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_number__of__Bit0,axiom,
% 179.72/179.53 ! [V_w,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__eq__int__code_I15_J,axiom,
% 179.72/179.53 ! [V_k2_2,V_k1_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I33_J,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__int__code_I14_J,axiom,
% 179.72/179.53 ! [V_k2_2,V_k1_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I15_J,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_card__UNIV__bool,axiom,
% 179.72/179.53 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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mult__Bit1,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_diff__bin__simps_I8_J,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_add__Bit1__Bit1,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power__number__of__even,axiom,
% 179.72/179.53 ! [V_w_2,V_z_2,T_b] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zpower__number__of__even,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_double__number__of__Bit0,axiom,
% 179.72/179.53 ! [V_w,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_number__of1,axiom,
% 179.72/179.53 ! [V_n] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( 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))))
% 179.72/179.53 & 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 179.72/179.53 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power__number__of__even__number__of,axiom,
% 179.72/179.53 ! [V_w_2,V_v_2,T_b] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mult__2__right,axiom,
% 179.72/179.53 ! [V_z,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mult__2,axiom,
% 179.72/179.53 ! [V_z,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_one__add__one__is__two,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zero__eq__power2,axiom,
% 179.72/179.53 ! [V_a_2,T_b] :
% 179.72/179.53 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 179.72/179.53 => ( 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)
% 179.72/179.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zero__power2,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Rings_Osemiring__1(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_semiring__norm_I115_J,axiom,
% 179.72/179.53 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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_numeral__2__eq__2,axiom,
% 179.72/179.53 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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 179.72/179.53 ! [V_x,T_a] :
% 179.72/179.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.72/179.53 => 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power2__eq__square,axiom,
% 179.72/179.53 ! [V_a,T_a] :
% 179.72/179.53 ( class_Groups_Omonoid__mult(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 179.72/179.53 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))))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_add__2__eq__Suc_H,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_add__2__eq__Suc,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_one__power2,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Rings_Osemiring__1(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power2__minus,axiom,
% 179.72/179.53 ! [V_a,T_a] :
% 179.72/179.53 ( class_Rings_Oring__1(T_a)
% 179.72/179.53 => 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__mult__2__right,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__mult__2,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power__even__eq,axiom,
% 179.72/179.53 ! [V_n,V_a,T_a] :
% 179.72/179.53 ( class_Groups_Omonoid__mult(T_a)
% 179.72/179.53 => 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 179.72/179.53 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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 179.72/179.53 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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power2__abs,axiom,
% 179.72/179.53 ! [V_a,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_a)
% 179.72/179.53 => 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_abs__power2,axiom,
% 179.72/179.53 ! [V_a,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_a)
% 179.72/179.53 => 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__1__add__1,axiom,
% 179.72/179.53 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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod2__Suc__Suc,axiom,
% 179.72/179.53 ! [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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div2__Suc__Suc,axiom,
% 179.72/179.53 ! [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))))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zmod__number__of__Bit0,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_add__self__div__2,axiom,
% 179.72/179.53 ! [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 ).
% 179.72/179.53
% 179.72/179.53 fof(fact_half__gt__zero__iff,axiom,
% 179.72/179.53 ! [V_r_2,T_b] :
% 179.72/179.53 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 179.72/179.53 & class_Int_Onumber__ring(T_b) )
% 179.72/179.53 => ( 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))))))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_half__gt__zero,axiom,
% 179.72/179.53 ! [V_r,T_a] :
% 179.72/179.53 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 179.72/179.53 & class_Int_Onumber__ring(T_a) )
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 179.72/179.53 => 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)))))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zero__le__power2,axiom,
% 179.72/179.53 ! [V_a,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_a)
% 179.72/179.53 => 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)))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power2__le__imp__le,axiom,
% 179.72/179.53 ! [V_y,V_x,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__semidom(T_a)
% 179.72/179.53 => ( 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))))))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.72/179.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power2__eq__imp__eq,axiom,
% 179.72/179.53 ! [V_y,V_x,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__semidom(T_a)
% 179.72/179.53 => ( 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))))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.72/179.53 => V_x = V_y ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zero__less__power2,axiom,
% 179.72/179.53 ! [V_a_2,T_b] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_b)
% 179.72/179.53 => ( 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))))))
% 179.72/179.53 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power2__less__0,axiom,
% 179.72/179.53 ! [V_a,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_a)
% 179.72/179.53 => ~ 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_sum__power2__eq__zero__iff,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,T_b] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_b)
% 179.72/179.53 => ( 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)
% 179.72/179.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 179.72/179.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power2__eq__square__number__of,axiom,
% 179.72/179.53 ! [V_w,T_b] :
% 179.72/179.53 ( ( class_Groups_Omonoid__mult(T_b)
% 179.72/179.53 & class_Int_Onumber(T_b) )
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_less__2__cases,axiom,
% 179.72/179.53 ! [V_n] :
% 179.72/179.53 ( 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)))))
% 179.72/179.53 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.53 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__2,axiom,
% 179.72/179.53 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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power2__eq__1__iff,axiom,
% 179.72/179.53 ! [V_a_2,T_b] :
% 179.72/179.53 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 179.72/179.53 => ( 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)
% 179.72/179.53 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 179.72/179.53 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 179.72/179.53 ! [V_n,V_x,T_a] :
% 179.72/179.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power__minus__even,axiom,
% 179.72/179.53 ! [V_n,V_a,T_a] :
% 179.72/179.53 ( class_Rings_Oring__1(T_a)
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power2__less__imp__less,axiom,
% 179.72/179.53 ! [V_y,V_x,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__semidom(T_a)
% 179.72/179.53 => ( 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))))))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 179.72/179.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_sum__power2__ge__zero,axiom,
% 179.72/179.53 ! [V_y,V_x,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_a)
% 179.72/179.53 => 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))))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_sum__power2__le__zero__iff,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,T_b] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_b)
% 179.72/179.53 => ( 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)))
% 179.72/179.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 179.72/179.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_sum__power2__gt__zero__iff,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,T_b] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_b)
% 179.72/179.53 => ( 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)))))))
% 179.72/179.53 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 179.72/179.53 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_not__sum__power2__lt__zero,axiom,
% 179.72/179.53 ! [V_y,V_x,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_a)
% 179.72/179.53 => ~ 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power2__sum,axiom,
% 179.72/179.53 ! [V_y,V_x,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zero__le__even__power_H,axiom,
% 179.72/179.53 ! [V_n,V_a,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_a)
% 179.72/179.53 => 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 179.72/179.53 ! [V_n,V_x,T_a] :
% 179.72/179.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power__odd__eq,axiom,
% 179.72/179.53 ! [V_n,V_a,T_a] :
% 179.72/179.53 ( class_Groups_Omonoid__mult(T_a)
% 179.72/179.53 => 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))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power__minus1__even,axiom,
% 179.72/179.53 ! [V_n,T_a] :
% 179.72/179.53 ( class_Rings_Oring__1(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zdiv__number__of__Bit1,axiom,
% 179.72/179.53 ! [V_v,V_w] :
% 179.72/179.53 ( ( 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)))
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( ~ 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)))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod2__gr__0,axiom,
% 179.72/179.53 ! [V_m_2] :
% 179.72/179.53 ( 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))))))
% 179.72/179.53 <=> 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__2__gt__zero,axiom,
% 179.72/179.53 ! [V_n] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 179.72/179.53 => 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)))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power2__diff,axiom,
% 179.72/179.53 ! [V_y,V_x,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 179.72/179.53 ! [V_n,V_a,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_a)
% 179.72/179.53 => ( 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)))))
% 179.72/179.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_odd__power__less__zero,axiom,
% 179.72/179.53 ! [V_n,V_a,T_a] :
% 179.72/179.53 ( class_Rings_Olinordered__idom(T_a)
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 179.72/179.53 => 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))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power__minus1__odd,axiom,
% 179.72/179.53 ! [V_n,T_a] :
% 179.72/179.53 ( class_Rings_Oring__1(T_a)
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 179.72/179.53 ! [V_n] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.72/179.53 => 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)))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_of__nat__double,axiom,
% 179.72/179.53 ! [V_x,T_a] :
% 179.72/179.53 ( class_Rings_Osemiring__1(T_a)
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 179.72/179.53 => 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))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pos__zmod__mult__2,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_neg__zdiv__mult__2,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pos__zdiv__mult__2,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_int__of__code,axiom,
% 179.72/179.53 ! [V_k] :
% 179.72/179.53 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.53 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 179.72/179.53 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.53 => ( ( 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)
% 179.72/179.53 => 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)))))) )
% 179.72/179.53 & ( 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)
% 179.72/179.53 => 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)) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_of__int__num,axiom,
% 179.72/179.53 ! [V_k_2,T_b] :
% 179.72/179.53 ( class_Rings_Oring__1(T_b)
% 179.72/179.53 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 179.72/179.53 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => 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))) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => 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))))) ) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power__m1__odd,axiom,
% 179.72/179.53 ! [V_n,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I45_J,axiom,
% 179.72/179.53 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I42_J,axiom,
% 179.72/179.53 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I24_J,axiom,
% 179.72/179.53 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_code__numeral__zero__minus__one,axiom,
% 179.72/179.53 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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I7_J,axiom,
% 179.72/179.53 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I37_J,axiom,
% 179.72/179.53 c_Int_OPls != c_Int_OMin ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I40_J,axiom,
% 179.72/179.53 c_Int_OMin != c_Int_OPls ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I47_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 179.72/179.53 <=> V_k_2 = c_Int_OMin ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I43_J,axiom,
% 179.72/179.53 ! [V_l_2] :
% 179.72/179.53 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 179.72/179.53 <=> c_Int_OMin = V_l_2 ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Bit1__Min,axiom,
% 179.72/179.53 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 179.72/179.53
% 179.72/179.53 fof(fact_bin__less__0__simps_I2_J,axiom,
% 179.72/179.53 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I23_J,axiom,
% 179.72/179.53 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I20_J,axiom,
% 179.72/179.53 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I26_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I30_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I3_J,axiom,
% 179.72/179.53 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I6_J,axiom,
% 179.72/179.53 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I13_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I9_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I28_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I8_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_eq__number__of__Pls__Min,axiom,
% 179.72/179.53 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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Int_OMin__def,axiom,
% 179.72/179.53 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mult__Min,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_neg__number__of__Min,axiom,
% 179.72/179.53 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pred__Pls,axiom,
% 179.72/179.53 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 179.72/179.53
% 179.72/179.53 fof(fact_add__Min__right,axiom,
% 179.72/179.53 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_add__Min,axiom,
% 179.72/179.53 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pred__Min,axiom,
% 179.72/179.53 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nonzero__number__of__Min,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_succ__Min,axiom,
% 179.72/179.53 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 179.72/179.53
% 179.72/179.53 fof(fact_diff__bin__simps_I2_J,axiom,
% 179.72/179.53 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mult__minus1__right,axiom,
% 179.72/179.53 ! [V_z,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mult__minus1,axiom,
% 179.72/179.53 ! [V_z,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_number__of__Min,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_arith__simps_I31_J,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_abs__minus__one,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 & class_Rings_Olinordered__idom(T_a) )
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divide__minus1,axiom,
% 179.72/179.53 ! [V_x,T_a] :
% 179.72/179.53 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 179.72/179.53 & class_Int_Onumber__ring(T_a) )
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I25_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rel__simps_I11_J,axiom,
% 179.72/179.53 ! [V_k_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 179.72/179.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zmod__minus1__right,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_diff__bin__simps_I4_J,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_minus__Min,axiom,
% 179.72/179.53 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zmult__eq__1__iff,axiom,
% 179.72/179.53 ! [V_n_2,V_m_2] :
% 179.72/179.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 179.72/179.53 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 179.72/179.53 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 179.72/179.53 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 179.72/179.53 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 179.72/179.53 ! [V_n,V_m] :
% 179.72/179.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 179.72/179.53 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 179.72/179.53 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_diff__bin__simps_I6_J,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_diff__bin__simps_I5_J,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_of__int__m1,axiom,
% 179.72/179.53 ! [T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zdiv__minus1__right,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zero__code__numeral__code,axiom,
% 179.72/179.53 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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_minus1__divide,axiom,
% 179.72/179.53 ! [V_x,T_a] :
% 179.72/179.53 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 179.72/179.53 & class_Int_Onumber__ring(T_a) )
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_abs__power__minus__one,axiom,
% 179.72/179.53 ! [V_n,T_a] :
% 179.72/179.53 ( ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 & class_Rings_Olinordered__idom(T_a) )
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__eq__minus1,axiom,
% 179.72/179.53 ! [V_b] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__pos__neg__trivial,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => 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) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zmod__minus1,axiom,
% 179.72/179.53 ! [V_b] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_one__code__numeral__code,axiom,
% 179.72/179.53 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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_power__m1__even,axiom,
% 179.72/179.53 ! [V_n,T_a] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_a)
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nitpick_OFrac__def,axiom,
% 179.72/179.53 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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_small__int__def,axiom,
% 179.72/179.53 ! [V_d_2,V_f_2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),V_f_2),V_d_2) = c_Smallcheck_Osmall_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_int__ge__less__than2__def,axiom,
% 179.72/179.53 ! [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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_inj__graph,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_int__ge__less__than__def,axiom,
% 179.72/179.53 ! [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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nitpick_Oprod__def,axiom,
% 179.72/179.53 ! [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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__of__aux__code,axiom,
% 179.72/179.53 ! [V_n,V_i] :
% 179.72/179.53 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.53 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 179.72/179.53 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__rel__def,axiom,
% 179.72/179.53 ! [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))))))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_finite__psubset__def,axiom,
% 179.72/179.53 ! [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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_full__small__int__def,axiom,
% 179.72/179.53 ! [V_d_2,V_f_2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,V_f_2,V_d_2) = c_Smallcheck_Ofull__small_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__correct,axiom,
% 179.72/179.53 ! [V_a,V_b] :
% 179.72/179.53 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zmult2__lemma,axiom,
% 179.72/179.53 ! [V_c,V_r,V_q,V_b,V_a] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 179.72/179.53 => 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)))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_code__numeral_Osize_I1_J,axiom,
% 179.72/179.53 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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nats__number__of,axiom,
% 179.72/179.53 ! [V_w_2,T_b] :
% 179.72/179.53 ( class_Int_Onumber__ring(T_b)
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 179.72/179.53 => 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))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_sup__Un__eq2,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 179.72/179.53 ( 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))
% 179.72/179.53 <=> 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pred__subset__eq2,axiom,
% 179.72/179.53 ! [V_S_2,V_R_2,T_c,T_b] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 <=> 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pred__equals__eq2,axiom,
% 179.72/179.53 ! [V_S_2,V_R_2,T_c,T_b] :
% 179.72/179.53 ( 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)
% 179.72/179.53 <=> V_R_2 = V_S_2 ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_inf__Int__eq2,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 179.72/179.53 ( 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))
% 179.72/179.53 <=> 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_bot__empty__eq2,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,T_c,T_b] :
% 179.72/179.53 ( 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))
% 179.72/179.53 <=> 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_congruentD,axiom,
% 179.72/179.53 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 179.72/179.53 => ( 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))
% 179.72/179.53 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_congruent2D,axiom,
% 179.72/179.53 ! [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] :
% 179.72/179.53 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 179.72/179.53 => ( 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))
% 179.72/179.53 => ( 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))
% 179.72/179.53 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_enum__ex__prod__def,axiom,
% 179.72/179.53 ! [V_P_2,T_b,T_c] :
% 179.72/179.53 ( ( class_Enum_Oenum(T_c)
% 179.72/179.53 & class_Enum_Oenum(T_b) )
% 179.72/179.53 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2))
% 179.72/179.53 <=> 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_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_enum__all__prod__def,axiom,
% 179.72/179.53 ! [V_P_2,T_b,T_c] :
% 179.72/179.53 ( ( class_Enum_Oenum(T_c)
% 179.72/179.53 & class_Enum_Oenum(T_b) )
% 179.72/179.53 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2))
% 179.72/179.53 <=> 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_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_small__prod__def,axiom,
% 179.72/179.53 ! [V_d_2,V_f_2,T_b,T_c] :
% 179.72/179.53 ( ( class_Smallcheck_Osmall(T_c)
% 179.72/179.53 & class_Smallcheck_Osmall(T_b) )
% 179.72/179.53 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_b,T_c)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_b),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),c_Smallcheck_Osmall__class_Osmall(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c)))),V_d_2)),V_d_2) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Image__iff,axiom,
% 179.72/179.53 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 179.72/179.53 <=> ? [B_x] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.72/179.53 & 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rev__ImageI,axiom,
% 179.72/179.53 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.53 => ( 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))
% 179.72/179.53 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__rel__0,axiom,
% 179.72/179.53 ! [V_b] :
% 179.72/179.53 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_self__remainder,axiom,
% 179.72/179.53 ! [V_r,V_q,V_a] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_unique__quotient,axiom,
% 179.72/179.53 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => V_q = V_q_H ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_unique__remainder,axiom,
% 179.72/179.53 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => V_r = V_r_H ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_SUP__UN__eq2,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 179.72/179.53 ( 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))
% 179.72/179.53 <=> 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_self__quotient,axiom,
% 179.72/179.53 ! [V_r,V_q,V_a] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__rel__mod,axiom,
% 179.72/179.53 ! [V_r,V_q,V_b,V_a] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__rel__div,axiom,
% 179.72/179.53 ! [V_r,V_q,V_b,V_a] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nats__0,axiom,
% 179.72/179.53 ! [T_b] :
% 179.72/179.53 ( class_Rings_Osemiring__1(T_b)
% 179.72/179.53 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__mod__div,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nats__add,axiom,
% 179.72/179.53 ! [V_b_2,V_a_2,T_b] :
% 179.72/179.53 ( class_Rings_Osemiring__1(T_b)
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 179.72/179.53 => 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))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nats__mult,axiom,
% 179.72/179.53 ! [V_b_2,V_a_2,T_b] :
% 179.72/179.53 ( class_Rings_Osemiring__1(T_b)
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 179.72/179.53 => 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))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nats__1,axiom,
% 179.72/179.53 ! [T_b] :
% 179.72/179.53 ( class_Rings_Osemiring__1(T_b)
% 179.72/179.53 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_of__nat__in__Nats,axiom,
% 179.72/179.53 ! [V_n_2,T_b] :
% 179.72/179.53 ( class_Rings_Osemiring__1(T_b)
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Image__singleton__iff,axiom,
% 179.72/179.53 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 179.72/179.53 ( 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))))))
% 179.72/179.53 <=> 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_equiv__class__eq,axiom,
% 179.72/179.53 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( 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))
% 179.72/179.53 => 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_quotient__eqI,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 179.72/179.53 => ( 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))
% 179.72/179.53 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_quotient__eq__iff,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 179.72/179.53 => ( V_X_2 = V_Y_2
% 179.72/179.53 <=> 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)) ) ) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__rel__div__mod,axiom,
% 179.72/179.53 ! [V_a,V_b] :
% 179.72/179.53 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Image__singleton,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_equiv__class__eq__iff,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( 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))
% 179.72/179.53 <=> ( 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))))
% 179.72/179.53 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.53 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_eq__equiv__class__iff,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 179.72/179.53 => ( 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))))
% 179.72/179.53 <=> 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)) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_eq__equiv__class,axiom,
% 179.72/179.53 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 179.72/179.53 ( 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))))
% 179.72/179.53 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 179.72/179.53 => 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)) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_equiv__class__subset,axiom,
% 179.72/179.53 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( 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))
% 179.72/179.53 => 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)))))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_eq__equiv__class__iff2,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 179.72/179.53 => ( 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)
% 179.72/179.53 <=> 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)) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zadd1__lemma,axiom,
% 179.72/179.53 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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)))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zminus1__lemma,axiom,
% 179.72/179.53 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => 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))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_subset__equiv__class,axiom,
% 179.72/179.53 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( 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))))))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 179.72/179.53 => 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)) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_equiv__class__nondisjoint,axiom,
% 179.72/179.53 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( 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)))))))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__relI,axiom,
% 179.72/179.53 ! [V_r,V_q,V_b,V_a] :
% 179.72/179.53 ( 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)
% 179.72/179.53 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 179.72/179.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 179.72/179.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 179.72/179.53 => 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))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_zmult1__lemma,axiom,
% 179.72/179.53 ! [V_a,V_r,V_q,V_c,V_b] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pair__imageI,axiom,
% 179.72/179.53 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.53 ( 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))
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_norm__frac_Osimps,axiom,
% 179.72/179.53 ! [V_a_2,V_b_2] :
% 179.72/179.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 179.72/179.53 => 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))) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_adjust__def,axiom,
% 179.72/179.53 ! [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))))))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_sup2CI,axiom,
% 179.72/179.53 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 179.72/179.53 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_sup2E,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 179.72/179.53 ( 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))
% 179.72/179.53 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_inf2I,axiom,
% 179.72/179.53 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_inf2E,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 179.72/179.53 ( 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))
% 179.72/179.53 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 179.72/179.53 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mem__splitI,axiom,
% 179.72/179.53 ! [T_d,T_c,V_b_2,V_a_2,V_ca_2,V_z_2,T_b] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2)))
% 179.72/179.53 => 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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_splitI,axiom,
% 179.72/179.53 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_prod__caseI,axiom,
% 179.72/179.53 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_bot2E,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_splitD_H,axiom,
% 179.72/179.53 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 179.72/179.53 ( 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))
% 179.72/179.53 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_swap__inj__on,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_inf2D1,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 179.72/179.53 ( 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))
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_inf2D2,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 179.72/179.53 ( 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))
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rev__predicate2D,axiom,
% 179.72/179.53 ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Qa_2))
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_predicate2D,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_Qa_2,V_P_2,T_c,T_b] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Qa_2))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_sup2I2,axiom,
% 179.72/179.53 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_sup2I1,axiom,
% 179.72/179.53 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 179.72/179.53 => 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_split__paired__All,axiom,
% 179.72/179.53 ! [T_c,T_b,V_P_2] :
% 179.72/179.53 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 179.72/179.53 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Pair__eq,axiom,
% 179.72/179.53 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.53 ( 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)
% 179.72/179.53 <=> ( V_a_2 = V_a_H_2
% 179.72/179.53 & V_b_2 = V_b_H_2 ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Pair__inject,axiom,
% 179.72/179.53 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 179.72/179.53 ( 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)
% 179.72/179.53 => ~ ( V_a = V_a_H
% 179.72/179.53 => V_b != V_b_H ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_split__weak__cong,axiom,
% 179.72/179.53 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 179.72/179.53 ( V_p_2 = V_q_2
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_in__finite__psubset,axiom,
% 179.72/179.53 ! [V_B_2,V_A_2,T_b] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.72/179.53 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_split__twice,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_split__conv,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_prod_Osimps_I2_J,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_splitD,axiom,
% 179.72/179.53 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_split__eta,axiom,
% 179.72/179.53 ! [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 ).
% 179.72/179.53
% 179.72/179.53 fof(fact_split__paired__The,axiom,
% 179.72/179.53 ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_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_P_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_The__split__eq,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_adjust__eq,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_in__rel__def,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 179.72/179.53 <=> 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__mod__code__numeral__def,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 179.72/179.53 ! [V_w] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( 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))))
% 179.72/179.53 => 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))) )
% 179.72/179.53 & ( ~ 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))))
% 179.72/179.53 => 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)))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_negDivAlg__correct,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_negDivAlg__div__mod,axiom,
% 179.72/179.53 ! [V_l,V_k] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_negDivAlg__minus1,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_negDivAlg_Osimps,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( ( ( 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)))
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( ~ ( 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)))
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 179.72/179.53 => 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))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_negDivAlg__eqn__number__of,axiom,
% 179.72/179.53 ! [V_w,V_v] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( 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))))
% 179.72/179.53 => 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))) )
% 179.72/179.53 & ( ~ 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))))
% 179.72/179.53 => 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)))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_negDivAlg__eqn,axiom,
% 179.72/179.53 ! [V_a,V_b] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => ( ( 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)))
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( ~ 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)))
% 179.72/179.53 => 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))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Nitpick_Orefl_H__def,axiom,
% 179.72/179.53 ! [V_r_2,T_b] :
% 179.72/179.53 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 179.72/179.53 <=> ! [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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 179.72/179.53 ! [V_w] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( 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)))
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( ~ 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)))
% 179.72/179.53 => 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)))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_posDivAlg_Osimps,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 179.72/179.53 => 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) )
% 179.72/179.53 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 179.72/179.53 => 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))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_posDivAlg__0,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_posDivAlg__correct,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_posDivAlg__div__mod,axiom,
% 179.72/179.53 ! [V_l,V_k] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_posDivAlg__eqn,axiom,
% 179.72/179.53 ! [V_a,V_b] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 179.72/179.53 => 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) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 179.72/179.53 => 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))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_posDivAlg__eqn__number__of,axiom,
% 179.72/179.53 ! [V_w,V_v] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( 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)))
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( ~ 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)))
% 179.72/179.53 => 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)))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__def,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.72/179.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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))) ) ) ) ) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.72/179.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => 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))) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__step,axiom,
% 179.72/179.53 ! [V_m,V_n] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__pdivmod,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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) )
% 179.72/179.53 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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)))) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_apsnd__compose,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_negateSnd__def,axiom,
% 179.72/179.53 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_apsnd__conv,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__zero,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__base,axiom,
% 179.72/179.53 ! [V_n,V_m] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 179.72/179.53 => 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) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_negateSnd__eq,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__div__mod,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__rel__neg,axiom,
% 179.72/179.53 ! [V_qr,V_b,V_a] :
% 179.72/179.53 ( 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))
% 179.72/179.53 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__if,axiom,
% 179.72/179.53 ! [V_m_2,V_n_2] :
% 179.72/179.53 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 179.72/179.53 => 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) )
% 179.72/179.53 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pdivmod__def,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pdivmod__posDivAlg,axiom,
% 179.72/179.53 ! [V_k,V_l] :
% 179.72/179.53 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__int__code,axiom,
% 179.72/179.53 ! [V_l_2,V_k_2] :
% 179.72/179.53 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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) )
% 179.72/179.53 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 => 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)))) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_UN__equiv__class__inject,axiom,
% 179.72/179.53 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.53 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 179.72/179.53 => ( 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)
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( ! [B_x] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.53 => ! [B_y] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 179.72/179.53 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 179.72/179.53 => 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)) ) ) )
% 179.72/179.53 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 179.72/179.53 ! [V_a,V_r,V_q,V_c,V_b] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 179.72/179.53 => 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 179.72/179.53 ! [V_c,V_r,V_q,V_b,V_a] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 179.72/179.53 => 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)))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__rel__unique,axiom,
% 179.72/179.53 ! [V_qr_H,V_qr,V_n,V_m] :
% 179.72/179.53 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 179.72/179.53 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 179.72/179.53 => V_qr = V_qr_H ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__eq,axiom,
% 179.72/179.53 ! [V_qr,V_n,V_m] :
% 179.72/179.53 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 179.72/179.53 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 179.72/179.53 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__def,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod__eq,axiom,
% 179.72/179.53 ! [V_r,V_q,V_n,V_m] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__eq,axiom,
% 179.72/179.53 ! [V_r,V_q,V_n,V_m] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__rel,axiom,
% 179.72/179.53 ! [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)))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 179.72/179.53 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 179.72/179.53 => 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)))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_negDivAlg_Opsimps,axiom,
% 179.72/179.53 ! [V_b_2,V_a_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( ( 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)))
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( ~ ( 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)))
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 179.72/179.53 => 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))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_small_H_Opsimps,axiom,
% 179.72/179.53 ! [V_i_2,V_d_2,V_f_2] :
% 179.72/179.53 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_f_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2))))
% 179.72/179.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 179.72/179.53 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 179.72/179.53 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_posDivAlg_Opsimps,axiom,
% 179.72/179.53 ! [V_b_2,V_a_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 179.72/179.53 => 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) )
% 179.72/179.53 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 179.72/179.53 => 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))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_accp_Osimps,axiom,
% 179.72/179.53 ! [V_a_2,V_r_2,T_b] :
% 179.72/179.53 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 179.72/179.53 <=> ! [B_x] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 179.72/179.53 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_accp_Oequations,axiom,
% 179.72/179.53 ! [V_a_2,V_r_2,T_b] :
% 179.72/179.53 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 179.72/179.53 <=> ! [B_x] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 179.72/179.53 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_accp__downward,axiom,
% 179.72/179.53 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 179.72/179.53 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 179.72/179.53 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_accp__subset,axiom,
% 179.72/179.53 ! [V_R2_2,V_R1_2,T_b] :
% 179.72/179.53 ( 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))
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_norm__frac_Opsimps,axiom,
% 179.72/179.53 ! [V_b_2,V_a_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 179.72/179.53 => 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)) )
% 179.72/179.53 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 179.72/179.53 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 179.72/179.53 => 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))) ) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_negDivAlg_Opinduct,axiom,
% 179.72/179.53 ! [V_P_2,V_a1_2,V_a0_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ! [B_a,B_b] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( ~ ( 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)))
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_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))) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_posDivAlg_Opinduct,axiom,
% 179.72/179.53 ! [V_P_2,V_a1_2,V_a0_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ! [B_a,B_b] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 179.72/179.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_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))) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__gcd_Opsimps,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.53 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 179.72/179.53 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.53 => 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)) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_small_H_Opinduct,axiom,
% 179.72/179.53 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
% 179.72/179.53 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2))))
% 179.72/179.53 => ( ! [B_f,B_d,B_i] :
% 179.72/179.53 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i))))
% 179.72/179.53 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 179.72/179.53 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 179.72/179.53 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod__pos__neg__1__number__of,axiom,
% 179.72/179.53 ! [V_w] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => 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))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_snd__apsnd,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_apsnd__eq__conv,axiom,
% 179.72/179.53 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 179.72/179.53 ( 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)
% 179.72/179.53 <=> 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_snd__def,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_snd__conv,axiom,
% 179.72/179.53 ! [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 ).
% 179.72/179.53
% 179.72/179.53 fof(fact_snd__eqD,axiom,
% 179.72/179.53 ! [V_a,V_y,V_x,T_a,T_b] :
% 179.72/179.53 ( 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
% 179.72/179.53 => V_y = V_a ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod__int__def,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod__neg__pos,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod__pos__pos,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod__pos__pos__1__number__of,axiom,
% 179.72/179.53 ! [V_w] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod__pos__neg,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod__neg__neg,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_in__measure,axiom,
% 179.72/179.53 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 <=> 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_irrefl__def,axiom,
% 179.72/179.53 ! [V_r_2,T_b] :
% 179.72/179.53 ( c_Relation_Oirrefl(T_b,V_r_2)
% 179.72/179.53 <=> ! [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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_norm__frac_Opinduct,axiom,
% 179.72/179.53 ! [V_P_2,V_a1_2,V_a0_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ! [B_a,B_b] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mod__nat__def,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__pos__neg__1__number__of,axiom,
% 179.72/179.53 ! [V_w] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => 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))))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__def,axiom,
% 179.72/179.53 ! [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)))))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_nat__gcd_Opinduct,axiom,
% 179.72/179.53 ! [V_P_2,V_a1_2,V_a0_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ! [B_x,B_y] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Pair__fst__snd__eq,axiom,
% 179.72/179.53 ! [T_c,T_b,V_t_2,V_s_2] :
% 179.72/179.53 ( V_s_2 = V_t_2
% 179.72/179.53 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 179.72/179.53 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_prod__eqI,axiom,
% 179.72/179.53 ! [V_q,V_p,T_b,T_a] :
% 179.72/179.53 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 179.72/179.53 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 179.72/179.53 => V_p = V_q ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_fst__apsnd,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_fst__def,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Rep__Integ__inject,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2] :
% 179.72/179.53 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 179.72/179.53 <=> V_x_2 = V_y_2 ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_fst__conv,axiom,
% 179.72/179.53 ! [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 ).
% 179.72/179.53
% 179.72/179.53 fof(fact_fst__eqD,axiom,
% 179.72/179.53 ! [V_a,V_y,V_x,T_b,T_a] :
% 179.72/179.53 ( 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
% 179.72/179.53 => V_x = V_a ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_surjective__pairing,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pair__collapse,axiom,
% 179.72/179.53 ! [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 ).
% 179.72/179.53
% 179.72/179.53 fof(fact_prod__case__beta,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__int__def,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_split__beta,axiom,
% 179.72/179.53 ! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_split__comp__eq,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_split__def,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_split__comp,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_The__split,axiom,
% 179.72/179.53 ! [V_P_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_P_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_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__neg__pos,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__pos__pos,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__pos__pos__1__number__of,axiom,
% 179.72/179.53 ! [V_w] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__pos__neg,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__neg__neg,axiom,
% 179.72/179.53 ! [V_b,V_a] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 179.72/179.53 => 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)))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_prod__size__simp,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_conjI__realizer,axiom,
% 179.72/179.53 ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_P_2] :
% 179.72/179.53 ( hBOOL(hAPP(V_P_2,V_p_2))
% 179.72/179.53 => ( hBOOL(hAPP(V_Qa_2,V_q_2))
% 179.72/179.53 => ( hBOOL(hAPP(V_P_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))))
% 179.72/179.53 & 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)))) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_exI__realizer,axiom,
% 179.72/179.53 ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_P_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)))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_div__nat__def,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_divmod__nat__rel__def,axiom,
% 179.72/179.53 ! [V_qr_2,V_n_2,V_m_2] :
% 179.72/179.53 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 179.72/179.53 <=> ( 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))
% 179.72/179.53 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.53 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 179.72/179.53 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 & 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)) ) )
% 179.72/179.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 & 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))) ) ) ) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_inv__image__def,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mlex__leq,axiom,
% 179.72/179.53 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => ( 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))
% 179.72/179.53 => 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))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_code__numeral_Osize_I2_J,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_code__numeral_Oinject,axiom,
% 179.72/179.53 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 179.72/179.53 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 179.72/179.53 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 179.72/179.53 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_in__inv__image,axiom,
% 179.72/179.53 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 <=> 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_Suc__code__numeral__minus__one,axiom,
% 179.72/179.53 ! [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 ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mlex__less,axiom,
% 179.72/179.53 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 => 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))) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_code__numeral_Osize_I4_J,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_rp__inv__image__def,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_prod_Orecs,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_code__numeral_Osize_I3_J,axiom,
% 179.72/179.53 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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_map__add__map__of__foldr,axiom,
% 179.72/179.53 ! [V_ps_2,V_m_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_Map_Omap__of(T_b,T_c),V_ps_2)) = c_List_Ofoldr(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c))),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)))))),c_Option_Ooption_OSome(T_c))),V_ps_2,V_m_2) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_in__lex__prod,axiom,
% 179.72/179.53 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.53 ( 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)))
% 179.72/179.53 <=> ( 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))
% 179.72/179.53 | ( V_a_2 = V_a_H_2
% 179.72/179.53 & 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)) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_equivp__equiv,axiom,
% 179.72/179.53 ! [V_A_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 179.72/179.53 <=> 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_identity__equivp,axiom,
% 179.72/179.53 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_equivp__def,axiom,
% 179.72/179.53 ! [V_R_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 179.72/179.53 <=> ! [B_x,B_y] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 179.72/179.53 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_equivp__reflp,axiom,
% 179.72/179.53 ! [V_x_2,V_R_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_equivp__symp,axiom,
% 179.72/179.53 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_equivp__transp,axiom,
% 179.72/179.53 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 179.72/179.53 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 179.72/179.53 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_same__fstI,axiom,
% 179.72/179.53 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
% 179.72/179.53 ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.53 => ( 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)))
% 179.72/179.53 => 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_P_2,V_R_2))) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_apsnd__apfst,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_apfst__apsnd,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_apfst__conv,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_fst__apfst,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_apfst__eq__conv,axiom,
% 179.72/179.53 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 179.72/179.53 ( 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)
% 179.72/179.53 <=> 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)) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_snd__apfst,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_apfst__compose,axiom,
% 179.72/179.53 ! [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) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_apsnd__apfst__commute,axiom,
% 179.72/179.53 ! [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)) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pair__lessI2,axiom,
% 179.72/179.53 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 179.72/179.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 179.72/179.53 => 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)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_ImageE,axiom,
% 179.72/179.53 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 179.72/179.53 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 179.72/179.53 => ~ ! [B_x] :
% 179.72/179.53 ( 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))
% 179.72/179.53 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_mlex__prod__def,axiom,
% 179.72/179.53 ! [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))) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_pair__less__def,axiom,
% 179.72/179.53 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 179.72/179.53
% 179.72/179.53 fof(fact_measure__def,axiom,
% 179.72/179.54 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_less__than__iff,axiom,
% 179.72/179.54 ! [V_y_2,V_x_2] :
% 179.72/179.54 ( 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))
% 179.72/179.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_pair__lessI1,axiom,
% 179.72/179.54 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_pair__leqI2,axiom,
% 179.72/179.54 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_smax__insertI,axiom,
% 179.72/179.54 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 179.72/179.54 => ( 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))
% 179.72/179.54 => ( 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))
% 179.72/179.54 => 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)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_smin__insertI,axiom,
% 179.72/179.54 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 179.72/179.54 => ( 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))
% 179.72/179.54 => ( 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))
% 179.72/179.54 => 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)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_smin__emptyI,axiom,
% 179.72/179.54 ! [V_X_2] :
% 179.72/179.54 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_smax__emptyI,axiom,
% 179.72/179.54 ! [V_Y_2] :
% 179.72/179.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 179.72/179.54 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_pair__leqI1,axiom,
% 179.72/179.54 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_wmin__insertI,axiom,
% 179.72/179.54 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 179.72/179.54 => ( 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))
% 179.72/179.54 => ( 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))
% 179.72/179.54 => 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)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_wmax__insertI,axiom,
% 179.72/179.54 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 179.72/179.54 => ( 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))
% 179.72/179.54 => ( 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))
% 179.72/179.54 => 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)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Field__insert,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Field__empty,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_mono__Field,axiom,
% 179.72/179.54 ! [V_s_2,V_r_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Field__Un,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_finite__Field,axiom,
% 179.72/179.54 ! [V_r_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 179.72/179.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_wmax__emptyI,axiom,
% 179.72/179.54 ! [V_X_2] :
% 179.72/179.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_wmin__emptyI,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_min__weak__def,axiom,
% 179.72/179.54 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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_max__weak__def,axiom,
% 179.72/179.54 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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Id__on__def,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Id__on__def_H,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Id__on__empty,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Image__Id__on,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Id__on__eqI,axiom,
% 179.72/179.54 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 179.72/179.54 ( V_a_2 = V_b_2
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.54 => 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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Id__on__iff,axiom,
% 179.72/179.54 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 <=> ( V_x_2 = V_y_2
% 179.72/179.54 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_max__strict__def,axiom,
% 179.72/179.54 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_max__ext__additive,axiom,
% 179.72/179.54 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ( 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)))
% 179.72/179.54 => 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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_min__strict__def,axiom,
% 179.72/179.54 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_max__extp__max__ext__eq,axiom,
% 179.72/179.54 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 <=> 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_min__rpair__set,axiom,
% 179.72/179.54 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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_max__rpair__set,axiom,
% 179.72/179.54 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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_rp__inv__image__rp,axiom,
% 179.72/179.54 ! [V_f_2,T_c,V_P_2,T_b] :
% 179.72/179.54 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 179.72/179.54 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_equiv__intrel__iff,axiom,
% 179.72/179.54 ! [V_y_2,V_x_2] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 <=> 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_intrel__iff,axiom,
% 179.72/179.54 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 179.72/179.54 ( 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))
% 179.72/179.54 <=> 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Id__onE,axiom,
% 179.72/179.54 ! [V_A_2,V_ca_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2)))
% 179.72/179.54 => ~ ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.54 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_equiv__intrel,axiom,
% 179.72/179.54 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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_of__int,axiom,
% 179.72/179.54 ! [V_j_2,V_i_2,T_b] :
% 179.72/179.54 ( class_Rings_Oring__1(T_b)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_One__int__def,axiom,
% 179.72/179.54 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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_mult,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Rep__Integ__inverse,axiom,
% 179.72/179.54 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_minus,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Zero__int__def,axiom,
% 179.72/179.54 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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_int__def,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_add,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nat,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_minus__int__def,axiom,
% 179.72/179.54 ! [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))))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_less,axiom,
% 179.72/179.54 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 179.72/179.54 ( 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)))))))
% 179.72/179.54 <=> 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_le,axiom,
% 179.72/179.54 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 179.72/179.54 ( 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)))))))
% 179.72/179.54 <=> 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_eq__Abs__Integ,axiom,
% 179.72/179.54 ! [V_z_2] :
% 179.72/179.54 ~ ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Integ__def,axiom,
% 179.72/179.54 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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__mapk__SomeI,axiom,
% 179.72/179.54 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] :
% 179.72/179.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.72/179.54 => ( hAPP(hAPP(c_Map_Omap__of(T_b,T_d),V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2)
% 179.72/179.54 => hAPP(hAPP(c_Map_Omap__of(T_c,T_d),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_b),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_d),V_x_2) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_inj__mapI,axiom,
% 179.72/179.54 ! [V_f_2,T_c,T_b] :
% 179.72/179.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_inj__map,axiom,
% 179.72/179.54 ! [V_f_2,T_c,T_b] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_inj__map__eq__map,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 179.72/179.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.72/179.54 => ( 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)
% 179.72/179.54 <=> V_xs_2 = V_ys_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_inj__mapD,axiom,
% 179.72/179.54 ! [V_f_2,T_c,T_b] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__injective,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 179.72/179.54 => V_xs_2 = V_ys_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__ident,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_List_Omap_Ocomp,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__comp__map,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_List_Omap_Ocompositionality,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__map,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_foldr__map,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Rep__Integ,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__map,axiom,
% 179.72/179.54 ! [V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_d),tc_Option_Ooption(T_c),T_b,hAPP(c_Option_Omap(T_d,T_c),V_f_2)),hAPP(c_Map_Omap__of(T_b,T_d),V_xs_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__map__restrict,axiom,
% 179.72/179.54 ! [V_ks_2,V_f_2,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_b,T_c,hAPP(c_Fun_Ocomp(T_c,tc_Option_Ooption(T_c),T_b,c_Option_Ooption_OSome(T_c)),V_f_2),hAPP(c_List_Oset(T_b),V_ks_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_type__definition__Integ,axiom,
% 179.72/179.54 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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_finite__set,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__eq__conv,axiom,
% 179.72/179.54 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 179.72/179.54 ( 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)
% 179.72/179.54 <=> ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 179.72/179.54 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_infinite__UNIV__listI,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__map,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__inj__on,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => ( 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)))
% 179.72/179.54 => V_xs_2 = V_ys_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_inj__on__map__eq__map,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ( 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)
% 179.72/179.54 <=> V_xs_2 = V_ys_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__fun__upd,axiom,
% 179.72/179.54 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 179.72/179.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => hAPP(hAPP(c_List_Omap(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__eq__dom,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 179.72/179.54 ( hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2)
% 179.72/179.54 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__is__SomeD,axiom,
% 179.72/179.54 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] :
% 179.72/179.54 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__SomeD,axiom,
% 179.72/179.54 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] :
% 179.72/179.54 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xs_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_dom__map__of__conv__image__fst,axiom,
% 179.72/179.54 ! [V_xys_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__eq__None__iff,axiom,
% 179.72/179.54 ! [V_x_2,V_xys_2,T_b,T_c] :
% 179.72/179.54 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b)
% 179.72/179.54 <=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(c_List_Oset(tc_prod(T_c,T_b)),V_xys_2)))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 179.72/179.54 ! [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 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_type__definition_ORep__range,axiom,
% 179.72/179.54 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 179.72/179.54 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 179.72/179.54 => 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 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_type__definition_OAbs__image,axiom,
% 179.72/179.54 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 179.72/179.54 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__map__keys,axiom,
% 179.72/179.54 ! [V_m_2,T_c,V_xs_2,T_b] :
% 179.72/179.54 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2)
% 179.72/179.54 => hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),T_c,T_b),c_Option_Othe(T_c)),V_m_2))),V_xs_2)) = V_m_2 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_the_Osimps,axiom,
% 179.72/179.54 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 179.72/179.54
% 179.72/179.54 fof(fact_type__definition_ORep__inverse,axiom,
% 179.72/179.54 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 179.72/179.54 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 179.72/179.54 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_type__definition_ORep__inject,axiom,
% 179.72/179.54 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 179.72/179.54 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 179.72/179.54 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 179.72/179.54 <=> V_x_2 = V_y_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_type__definition_ORep,axiom,
% 179.72/179.54 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 179.72/179.54 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_type__definition_OAbs__inverse,axiom,
% 179.72/179.54 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 179.72/179.54 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 179.72/179.54 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_type__definition_OAbs__inject,axiom,
% 179.72/179.54 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 179.72/179.54 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 179.72/179.54 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 179.72/179.54 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_ran__distinct,axiom,
% 179.72/179.54 ! [V_al_2,T_c,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_al_2)))
% 179.72/179.54 => c_Map_Oran(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_al_2)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__map__of__compr,axiom,
% 179.72/179.54 ! [V_xs_2,T_c,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)))
% 179.72/179.54 => hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool),T_b),c_fequal),hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2)))),c_Option_Ooption_OSome(T_c)))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__is__SomeI,axiom,
% 179.72/179.54 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2)))
% 179.72/179.54 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__map,axiom,
% 179.72/179.54 ! [V_xs_2,V_f_2,T_c,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 179.72/179.54 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 179.72/179.54 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__inject__set,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)))
% 179.72/179.54 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_ys_2)))
% 179.72/179.54 => ( hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2)
% 179.72/179.54 <=> hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_ys_2) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Some__eq__map__of__iff,axiom,
% 179.72/179.54 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 179.72/179.54 => ( hAPP(c_Option_Ooption_OSome(T_c),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2),V_x_2)
% 179.72/179.54 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__eq__Some__iff,axiom,
% 179.72/179.54 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xys_2)))
% 179.72/179.54 => ( hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),V_y_2)
% 179.72/179.54 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_xys_2))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_greaterThanLessThan__upto,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_weak__map__of__SomeI,axiom,
% 179.72/179.54 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),V_l_2)))
% 179.72/179.54 => ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_x) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__remove1__eq,axiom,
% 179.72/179.54 ! [V_x_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => 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)))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__upto,axiom,
% 179.72/179.54 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__remove1,axiom,
% 179.72/179.54 ! [V_x,V_xs,T_a] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_remove1__commute,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_atLeastAtMost__upto,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__upto,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_in__set__remove1,axiom,
% 179.72/179.54 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 179.72/179.54 ( V_a_2 != V_b_2
% 179.72/179.54 => ( 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))))
% 179.72/179.54 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_notin__set__remove1,axiom,
% 179.72/179.54 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => ~ 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)))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_remove1__idem,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__remove1__subset,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_atLeastLessThan__upto,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_greaterThanAtMost__upto,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nat__list__def,axiom,
% 179.72/179.54 ! [V_l_2] :
% 179.72/179.54 ( c_List_Onat__list(V_l_2)
% 179.72/179.54 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sorted__list__of__set__remove,axiom,
% 179.72/179.54 ! [V_x_2,V_A_2,T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__zip__map,axiom,
% 179.72/179.54 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),hAPP(V_f_2,V_x_2)) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__zipI2,axiom,
% 179.72/179.54 ! [V_xs,T_b,V_ys,T_a] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__zipI1,axiom,
% 179.72/179.54 ! [V_ys,T_b,V_xs,T_a] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__same__conv__map,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__map__fst__snd,axiom,
% 179.72/179.54 ! [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 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__zip__map,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__zip__map2,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__same,axiom,
% 179.72/179.54 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 & V_a_2 = V_b_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__zip__leftD,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__zip__rightD,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_in__set__zipE,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__map__map,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__map1,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__map2,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sorted__list__of__set__insert,axiom,
% 179.72/179.54 ! [V_x_2,V_A_2,T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.54 => 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)))))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__zip__upd,axiom,
% 179.72/179.54 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 179.72/179.54 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 179.72/179.54 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 179.72/179.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
% 179.72/179.54 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_z_2))
% 179.72/179.54 => hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2)) ) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__removeAll__inj__on,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__zip,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__removeAll,axiom,
% 179.72/179.54 ! [V_x,V_xs,T_a] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__map,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__eq__imp__length__eq,axiom,
% 179.72/179.54 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_insort__left__comm,axiom,
% 179.72/179.54 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_insort__key__left__comm,axiom,
% 179.72/179.54 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_neq__if__length__neq,axiom,
% 179.72/179.54 ! [V_ys,V_xs,T_a] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => V_xs != V_ys ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__insort,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_c)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_remove1__insort,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => 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 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__insort,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_c)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_card__length,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_removeAll__id,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__card,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_card__distinct,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__zip__inject,axiom,
% 179.72/179.54 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 179.72/179.54 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 179.72/179.54 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
% 179.72/179.54 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 179.72/179.54 => ( hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))
% 179.72/179.54 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__fst__zip,axiom,
% 179.72/179.54 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => 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 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__snd__zip,axiom,
% 179.72/179.54 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => 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 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__remove1__removeAll,axiom,
% 179.72/179.54 ! [V_x,V_xs,T_a] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.54 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__insort,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_c)
% 179.72/179.54 => ( 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)))
% 179.72/179.54 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__pos__if__in__set,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__eq__conv,axiom,
% 179.72/179.54 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 179.72/179.54 <=> ( 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
% 179.72/179.54 & 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 ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__removeAll__inj,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 179.72/179.54 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_finite__lists__length__eq,axiom,
% 179.72/179.54 ! [V_n_2,V_A_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.54 => 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))))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__zip__is__None,axiom,
% 179.72/179.54 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => ( hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_c)
% 179.72/179.54 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__zip__is__Some,axiom,
% 179.72/179.54 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 <=> ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),B_y) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__remove1,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => 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)) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => 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) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_dom__map__of__zip,axiom,
% 179.72/179.54 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => c_Map_Odom(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_b),V_xs_2) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_finite__lists__length__le,axiom,
% 179.72/179.54 ! [V_n_2,V_A_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.54 => 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))))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__removeAll,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__sublists,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__sublist,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_insort__insert__insort__key,axiom,
% 179.72/179.54 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => ( ~ 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))))
% 179.72/179.54 => 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) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__sublistI,axiom,
% 179.72/179.54 ! [V_I_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__insort__insert,axiom,
% 179.72/179.54 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_c)
% 179.72/179.54 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => 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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_in__set__sublistD,axiom,
% 179.72/179.54 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_notin__set__sublistI,axiom,
% 179.72/179.54 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => ~ 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)))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__sublist__subset,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_insort__insert__triv,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__insort__insert,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__set__sublists,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => 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)))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublists__powset,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_insort__insert__key__triv,axiom,
% 179.72/179.54 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => ( 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))))
% 179.72/179.54 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_insort__insert__insort,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => 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) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__n__lists,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__zip,axiom,
% 179.72/179.54 ! [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)))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__zip__enum__inject,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,T_b,T_c] :
% 179.72/179.54 ( ( class_Enum_Oenum(T_c)
% 179.72/179.54 & class_Enum_Oenum(T_b) )
% 179.72/179.54 => ( 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)),c_Enum_Oenum__class_Oenum(T_c))
% 179.72/179.54 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_Enum_Oenum__class_Oenum(T_c))
% 179.72/179.54 => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),c_Enum_Oenum__class_Oenum(T_c)),V_xs_2))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),hAPP(c_Map_Omap__of(T_c,T_b),hAPP(hAPP(c_List_Ozip(T_c,T_b),c_Enum_Oenum__class_Oenum(T_c)),V_ys_2)))
% 179.72/179.54 => V_xs_2 = V_ys_2 ) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__zip,axiom,
% 179.72/179.54 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ( 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)))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__eq__iff__nth__eq,axiom,
% 179.72/179.54 ! [T_b,V_ys_2,V_xs_2] :
% 179.72/179.54 ( V_xs_2 = V_ys_2
% 179.72/179.54 <=> ( 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)
% 179.72/179.54 & ! [B_i] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__n__lists__elem,axiom,
% 179.72/179.54 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_enum__distinct,axiom,
% 179.72/179.54 ! [T_a] :
% 179.72/179.54 ( class_Enum_Oenum(T_a)
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__n__lists,axiom,
% 179.72/179.54 ! [V_n,V_xs,T_a] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_enum__fun__code,axiom,
% 179.72/179.54 ! [T_c,T_b] :
% 179.72/179.54 ( ( class_Enum_Oenum(T_b)
% 179.72/179.54 & class_HOL_Oequal(T_b)
% 179.72/179.54 & class_Enum_Oenum(T_c) )
% 179.72/179.54 => c_Enum_Oenum__class_Oenum(tc_fun(T_b,T_c)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),c_Enum_On__lists(T_c,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)),c_Enum_Oenum__class_Oenum(T_c))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_enum__fun__def,axiom,
% 179.72/179.54 ! [T_c,T_b] :
% 179.72/179.54 ( ( class_Enum_Oenum(T_b)
% 179.72/179.54 & class_Enum_Oenum(T_c) )
% 179.72/179.54 => c_Enum_Oenum__class_Oenum(tc_fun(T_b,T_c)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),c_Enum_On__lists(T_c,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)),c_Enum_Oenum__class_Oenum(T_c))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_in__enum,axiom,
% 179.72/179.54 ! [V_x_2,T_b] :
% 179.72/179.54 ( class_Enum_Oenum(T_b)
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b)))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_UNIV__enum,axiom,
% 179.72/179.54 ! [T_b] :
% 179.72/179.54 ( class_Enum_Oenum(T_b)
% 179.72/179.54 => c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_enum__UNIV,axiom,
% 179.72/179.54 ! [T_b] :
% 179.72/179.54 ( class_Enum_Oenum(T_b)
% 179.72/179.54 => hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_all__set__conv__all__nth,axiom,
% 179.72/179.54 ! [V_P_2,V_xs_2,T_b] :
% 179.72/179.54 ( ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => hBOOL(hAPP(V_P_2,B_x)) )
% 179.72/179.54 <=> ! [B_i] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__map,axiom,
% 179.72/179.54 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__conv__nth,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 <=> ! [B_i] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ! [B_j] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ( B_i != B_j
% 179.72/179.54 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__eq__iff__index__eq,axiom,
% 179.72/179.54 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => ( 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)))
% 179.72/179.54 => ( 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)))
% 179.72/179.54 => ( 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)
% 179.72/179.54 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_in__set__conv__nth,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 <=> ? [B_i] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__mem,axiom,
% 179.72/179.54 ! [V_xs_2,T_b,V_n_2] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__conv__nth,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__n__lists,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__sublist,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_enum__ex__fun__code,axiom,
% 179.72/179.54 ! [V_P_2,T_b,T_c] :
% 179.72/179.54 ( ( class_Enum_Oenum(T_c)
% 179.72/179.54 & class_Enum_Oenum(T_b)
% 179.72/179.54 & class_HOL_Oequal(T_b) )
% 179.72/179.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_b,T_c)),V_P_2))
% 179.72/179.54 <=> c_Enum_Oex__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_enum__ex__fun__def,axiom,
% 179.72/179.54 ! [V_P_2,T_b,T_c] :
% 179.72/179.54 ( ( class_Enum_Oenum(T_c)
% 179.72/179.54 & class_Enum_Oenum(T_b) )
% 179.72/179.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_b,T_c)),V_P_2))
% 179.72/179.54 <=> c_Enum_Oex__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_enum__all__fun__code,axiom,
% 179.72/179.54 ! [V_P_2,T_b,T_c] :
% 179.72/179.54 ( ( class_Enum_Oenum(T_c)
% 179.72/179.54 & class_Enum_Oenum(T_b)
% 179.72/179.54 & class_HOL_Oequal(T_b) )
% 179.72/179.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_b,T_c)),V_P_2))
% 179.72/179.54 <=> c_Enum_Oall__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_all__n__lists__def,axiom,
% 179.72/179.54 ! [V_n_2,V_P_2,T_b] :
% 179.72/179.54 ( class_Enum_Oenum(T_b)
% 179.72/179.54 => ( c_Enum_Oall__n__lists(T_b,V_P_2,V_n_2)
% 179.72/179.54 <=> ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,c_Enum_Oenum__class_Oenum(T_b)))))
% 179.72/179.54 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_ex__n__lists__def,axiom,
% 179.72/179.54 ! [V_n_2,V_P_2,T_b] :
% 179.72/179.54 ( class_Enum_Oenum(T_b)
% 179.72/179.54 => ( c_Enum_Oex__n__lists(T_b,V_P_2,V_n_2)
% 179.72/179.54 <=> ? [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,c_Enum_Oenum__class_Oenum(T_b)))))
% 179.72/179.54 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_enum__all__fun__def,axiom,
% 179.72/179.54 ! [V_P_2,T_b,T_c] :
% 179.72/179.54 ( ( class_Enum_Oenum(T_c)
% 179.72/179.54 & class_Enum_Oenum(T_b) )
% 179.72/179.54 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_b,T_c)),V_P_2))
% 179.72/179.54 <=> c_Enum_Oall__n__lists(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_HOL_Obool,tc_List_Olist(T_c)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_b,T_c),tc_List_Olist(T_c)),c_Fun_Ocomp(tc_Option_Ooption(T_c),T_c,T_b,c_Option_Othe(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_fun(T_b,tc_Option_Ooption(T_c)),tc_List_Olist(T_c)),c_Map_Omap__of(T_b,T_c)),hAPP(c_List_Ozip(T_b,T_c),c_Enum_Oenum__class_Oenum(T_b))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__list__update,axiom,
% 179.72/179.54 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => ( ~ 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))))))
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__product,axiom,
% 179.72/179.54 ! [V_ys,T_b,V_xs,T_a] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.54 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__zip__enum__is__Some,axiom,
% 179.72/179.54 ! [V_x,V_ys,T_b,T_a] :
% 179.72/179.54 ( class_Enum_Oenum(T_a)
% 179.72/179.54 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))
% 179.72/179.54 => ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a)),V_ys)),V_x) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__update,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__list__update__neq,axiom,
% 179.72/179.54 ! [V_x,V_xs,T_a,V_j,V_i] :
% 179.72/179.54 ( V_i != V_j
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__id,axiom,
% 179.72/179.54 ! [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 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__list__update,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_update__zip,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__update,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__swap,axiom,
% 179.72/179.54 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 179.72/179.54 ( V_i != V_i_H
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__overwrite,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__beyond,axiom,
% 179.72/179.54 ! [V_x,V_i,V_xs,T_a] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_enum__prod__def,axiom,
% 179.72/179.54 ! [T_b,T_a] :
% 179.72/179.54 ( ( class_Enum_Oenum(T_a)
% 179.72/179.54 & class_Enum_Oenum(T_b) )
% 179.72/179.54 => c_Enum_Oenum__class_Oenum(tc_prod(T_a,T_b)) = c_Enum_Oproduct(T_a,T_b,c_Enum_Oenum__class_Oenum(T_a),c_Enum_Oenum__class_Oenum(T_b)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__update__subsetI,axiom,
% 179.72/179.54 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__update__subset__insert,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__list__update__eq,axiom,
% 179.72/179.54 ! [V_x,V_xs,T_a,V_i] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__same__conv,axiom,
% 179.72/179.54 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 179.72/179.54 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__list__update,axiom,
% 179.72/179.54 ! [V_x,V_j,V_xs,T_a,V_i] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ( ( V_i = V_j
% 179.72/179.54 => 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 )
% 179.72/179.54 & ( V_i != V_j
% 179.72/179.54 => 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) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__update__memI,axiom,
% 179.72/179.54 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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)))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_inj__on__mapI,axiom,
% 179.72/179.54 ! [V_A_2,V_f_2,T_c,T_b] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__setsum__nth,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_restrict__map__upds,axiom,
% 179.72/179.54 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_D_2))
% 179.72/179.54 => c_Map_Orestrict__map(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_b),V_xs_2))),V_xs_2,V_ys_2) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_UnionI,axiom,
% 179.72/179.54 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 179.72/179.54 => 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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Field__Union,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_image__Union,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 179.72/179.54 ! [V_ns_2] :
% 179.72/179.54 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 <=> ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 179.72/179.54 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__disjoint,axiom,
% 179.72/179.54 ! [V_A_2,V_C_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 <=> ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Int__Union2,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Int__Union,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_UN__simps_I8_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_UN__extend__simps_I8_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__def,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_vimage__Union,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Sup__le__iff,axiom,
% 179.72/179.54 ! [V_b_2,V_A_2,T_b] :
% 179.72/179.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.54 => ( 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))
% 179.72/179.54 <=> ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__add__upds,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__upds(T_b,T_c,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_less__Sup__iff,axiom,
% 179.72/179.54 ! [V_S_2,V_a_2,T_b] :
% 179.72/179.54 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.54 & class_Orderings_Olinorder(T_b) )
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 179.72/179.54 <=> ? [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 179.72/179.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__Pow__eq,axiom,
% 179.72/179.54 ! [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 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__upper,axiom,
% 179.72/179.54 ! [V_A_2,V_B_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__empty,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__mono,axiom,
% 179.72/179.54 ! [V_B_2,V_A_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_elem__le__listsum__nat,axiom,
% 179.72/179.54 ! [V_ns,V_k] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__insert,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__quotient,axiom,
% 179.72/179.54 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.54 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.54 => 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 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_finite__UnionD,axiom,
% 179.72/179.54 ! [V_A_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 179.72/179.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_subset__Pow__Union,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__upds__apply__nontin,axiom,
% 179.72/179.54 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => hAPP(c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__UNIV,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__Un__distrib,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__image__eq,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_UNION__eq__Union__image,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Sup__upper,axiom,
% 179.72/179.54 ! [V_A_2,V_x_2,T_b] :
% 179.72/179.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.54 => 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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__0,axiom,
% 179.72/179.54 ! [V_xs_2,T_c,T_b] :
% 179.72/179.54 ( class_Groups_Omonoid__add(T_b)
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__addf,axiom,
% 179.72/179.54 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 179.72/179.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__const__mult,axiom,
% 179.72/179.54 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] :
% 179.72/179.54 ( class_Rings_Osemiring__0(T_b)
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__mult__const,axiom,
% 179.72/179.54 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] :
% 179.72/179.54 ( class_Rings_Osemiring__0(T_b)
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__subtractf,axiom,
% 179.72/179.54 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 179.72/179.54 ( class_Groups_Oab__group__add(T_b)
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Sup__empty,axiom,
% 179.72/179.54 ! [T_b] :
% 179.72/179.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Sup__singleton,axiom,
% 179.72/179.54 ! [V_a_2,T_b] :
% 179.72/179.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.54 => 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 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Sup__insert,axiom,
% 179.72/179.54 ! [V_A_2,V_a_2,T_b] :
% 179.72/179.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Sup__UNIV,axiom,
% 179.72/179.54 ! [T_b] :
% 179.72/179.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__update__nat,axiom,
% 179.72/179.54 ! [V_n,V_ns,V_k] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__abs,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 179.72/179.54 => 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)))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_uminus__listsum__map,axiom,
% 179.72/179.54 ! [V_xs_2,V_f_2,T_c,T_b] :
% 179.72/179.54 ( class_Groups_Oab__group__add(T_b)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Un__eq__Union,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Un__Union__image,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Union__Int__subset,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.72/179.54 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Sup__binary,axiom,
% 179.72/179.54 ! [V_b_2,V_a_2,T_b] :
% 179.72/179.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Sup__fin__Sup,axiom,
% 179.72/179.54 ! [V_A_2,T_b] :
% 179.72/179.54 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.54 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 179.72/179.54 ! [V_f_2,V_xs_2,T_b,T_c] :
% 179.72/179.54 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.72/179.54 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 179.72/179.54 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 179.72/179.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 179.72/179.54 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 179.72/179.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__upds__list__update2__drop,axiom,
% 179.72/179.54 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_i_2))
% 179.72/179.54 => ( 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)))
% 179.72/179.54 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__triv,axiom,
% 179.72/179.54 ! [V_xs_2,V_r_2,T_c,T_b] :
% 179.72/179.54 ( class_Rings_Osemiring__1(T_b)
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__upds__twist,axiom,
% 179.72/179.54 ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
% 179.72/179.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2)))
% 179.72/179.54 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__map__remove1,axiom,
% 179.72/179.54 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 179.72/179.54 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => 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)))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 179.72/179.54 ! [V_f_2,V_A_2,T_b,T_c] :
% 179.72/179.54 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.72/179.54 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.54 => 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))))) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.54 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_finite__Union,axiom,
% 179.72/179.54 ! [V_A_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 179.72/179.54 => ( ! [B_M] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 179.72/179.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 179.72/179.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_insert__partition,axiom,
% 179.72/179.54 ! [V_F_2,V_x_2,T_b] :
% 179.72/179.54 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 179.72/179.54 => ( ! [B_x] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ! [B_xa] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ( B_x != B_xa
% 179.72/179.54 => 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)) ) ) )
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_someI,axiom,
% 179.72/179.54 ! [T_b,V_x_2,V_P_2] :
% 179.72/179.54 ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.54 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_tfl__some,axiom,
% 179.72/179.54 ! [T_b,B_P] :
% 179.72/179.54 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 179.72/179.54 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_someI__ex,axiom,
% 179.72/179.54 ! [T_b,V_P_2] :
% 179.72/179.54 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 179.72/179.54 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_some__eq__ex,axiom,
% 179.72/179.54 ! [T_b,V_P_2] :
% 179.72/179.54 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
% 179.72/179.54 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_some__eq__trivial,axiom,
% 179.72/179.54 ! [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 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_some__sym__eq__trivial,axiom,
% 179.72/179.54 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_exE__some,axiom,
% 179.72/179.54 ! [T_b,V_ca_2,V_P_2] :
% 179.72/179.54 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 179.72/179.54 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
% 179.72/179.54 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_inv__into__def,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_inv__def,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Nitpick_Ocard_H__def,axiom,
% 179.72/179.54 ! [V_A_2,T_b] :
% 179.72/179.54 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.54 => 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)))) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.54 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__mono,axiom,
% 179.72/179.54 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 179.72/179.54 ( ( class_Groups_Omonoid__add(T_c)
% 179.72/179.54 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 179.72/179.54 => ( ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 179.72/179.54 => 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)))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__transpose,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transpose__map__map,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Eps__split__eq,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_split__paired__Eps,axiom,
% 179.72/179.54 ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_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_P_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Eps__split,axiom,
% 179.72/179.54 ! [V_P_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_P_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_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__transpose,axiom,
% 179.72/179.54 ! [V_xs_2,T_b,V_i_2] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_card__partition,axiom,
% 179.72/179.54 ! [V_k_2,V_C_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 179.72/179.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 179.72/179.54 => ( ! [B_c] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 179.72/179.54 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 179.72/179.54 => ( ! [B_c1] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 179.72/179.54 => ! [B_c2] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 179.72/179.54 => ( B_c1 != B_c2
% 179.72/179.54 => 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)) ) ) )
% 179.72/179.54 => 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)) ) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_all__nth__imp__all__set,axiom,
% 179.72/179.54 ! [V_x_2,V_P_2,V_xs_2,T_b] :
% 179.72/179.54 ( ! [B_i] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__filter,axiom,
% 179.72/179.54 ! [V_P_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_filter__filter,axiom,
% 179.72/179.54 ! [V_xs_2,V_Qa_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_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_P_2)),V_xs_2) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_filter__remove1,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_remove1__filter__not,axiom,
% 179.72/179.54 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 179.72/179.54 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.54 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_removeAll__filter__not,axiom,
% 179.72/179.54 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 179.72/179.54 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.54 => hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_filter__insort__triv,axiom,
% 179.72/179.54 ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_c)
% 179.72/179.54 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.54 => hAPP(c_List_Ofilter(T_b,V_P_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_P_2),V_xs_2) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_removeAll__filter__not__eq,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_filter__is__subset,axiom,
% 179.72/179.54 ! [V_xs_2,V_P_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_P_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_filter__id__conv,axiom,
% 179.72/179.54 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.54 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
% 179.72/179.54 <=> ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__filter__le,axiom,
% 179.72/179.54 ! [V_xs_2,V_P_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_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_filter__map,axiom,
% 179.72/179.54 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_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_P_2),V_f_2)),V_xs_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sum__length__filter__compl,axiom,
% 179.72/179.54 ! [V_xs_2,V_P_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_P_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_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__filter,axiom,
% 179.72/179.54 ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_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_P_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__filter__map,axiom,
% 179.72/179.54 ! [V_xs_2,V_f_2,T_c,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),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_P_2),V_f_2)),V_xs_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__filter__less,axiom,
% 179.72/179.54 ! [V_P_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.54 => 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_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__minus__filter__out,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_filter__in__sublist,axiom,
% 179.72/179.54 ! [V_s_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__filter__conv__card,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__filter__def,axiom,
% 179.72/179.54 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_c,c_Option_Othe(T_b)),V_f_2)),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_c),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_b)))),V_xs_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__filter__map__filter,axiom,
% 179.72/179.54 ! [V_xs_2,V_P_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) = c_List_Omap__filter(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_c,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_c),c_If(tc_Option_Ooption(T_b))),V_P_2)),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_c),c_Option_Ooption_OSome(T_b)),V_f_2))),c_Option_Ooption_ONone(T_b)),V_xs_2) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transpose__max__length,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_filter_Osimps_I1_J,axiom,
% 179.72/179.54 ! [V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__is__Nil__conv,axiom,
% 179.72/179.54 ! [V_xs_2,V_f_2,T_b,T_c] :
% 179.72/179.54 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 179.72/179.54 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map_Osimps_I1_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Nil__is__map__conv,axiom,
% 179.72/179.54 ! [V_xs_2,V_f_2,T_c,T_b] :
% 179.72/179.54 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 179.72/179.54 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__code_I1_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update_Osimps_I1_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__nonempty,axiom,
% 179.72/179.54 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 179.72/179.54 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 179.72/179.54 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__empty,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.54 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__empty2,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 179.72/179.54 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list_Osize_I3_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__0__conv,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_product_Osimps_I1_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_removeAll_Osimps_I1_J,axiom,
% 179.72/179.54 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_insort__not__Nil,axiom,
% 179.72/179.54 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_c)
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_remove1_Osimps_I1_J,axiom,
% 179.72/179.54 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__filter__simps_I2_J,axiom,
% 179.72/179.54 ! [V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip_Osimps_I1_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__Nil,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublist__nil,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct_Osimps_I1_J,axiom,
% 179.72/179.54 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__upds__Nil2,axiom,
% 179.72/179.54 ! [V_as_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,c_List_Olist_ONil(T_c)) = V_m_2 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__upds__Nil1,axiom,
% 179.72/179.54 ! [V_bs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,c_List_Olist_ONil(T_b),V_bs_2) = V_m_2 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_foldr_Osimps_I1_J,axiom,
% 179.72/179.54 ! [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 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transpose_Osimps_I1_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transpose__empty,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 179.72/179.54 <=> ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 179.72/179.54 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__simps_I1_J,axiom,
% 179.72/179.54 ! [T_a] :
% 179.72/179.54 ( class_Groups_Omonoid__add(T_a)
% 179.72/179.54 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_filter__empty__conv,axiom,
% 179.72/179.54 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.54 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 179.72/179.54 <=> ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__Cons__code_I1_J,axiom,
% 179.72/179.54 ! [V_k,T_a,T_b] : hAPP(hAPP(c_Map_Omap__of(T_b,T_a),c_List_Olist_ONil(tc_prod(T_b,T_a))),V_k) = c_Option_Ooption_ONone(T_a) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upto__empty,axiom,
% 179.72/179.54 ! [V_i,V_j] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 179.72/179.54 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sorted__list__of__set__empty,axiom,
% 179.72/179.54 ! [T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublist__empty,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of_Osimps_I1_J,axiom,
% 179.72/179.54 ! [V_x_1,T_b,T_a] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),c_List_Olist_ONil(tc_prod(T_a,T_b))),V_x_1) = c_Option_Ooption_ONone(T_b) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__greater__0__conv,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__filter__in,axiom,
% 179.72/179.54 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] :
% 179.72/179.54 ( hAPP(hAPP(c_Map_Omap__of(T_c,T_b),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2)
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
% 179.72/179.54 => hAPP(hAPP(c_Map_Omap__of(T_c,T_b),hAPP(c_List_Ofilter(tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublist__shift__lemma__Suc,axiom,
% 179.72/179.54 ! [V_is_2,V_xs_2,V_P_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_P_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_P_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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transpose__aux__max,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublist__def,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublist__shift__lemma,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upt__conv__Nil,axiom,
% 179.72/179.54 ! [V_i,V_j] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 179.72/179.54 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upt__0,axiom,
% 179.72/179.54 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__upt,axiom,
% 179.72/179.54 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sorted__list__of__set__range,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__Suc__upt,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upt__eq__Nil__conv,axiom,
% 179.72/179.54 ! [V_j_2,V_i_2] :
% 179.72/179.54 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 179.72/179.54 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_atLeastLessThan__upt,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__upt,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__upt,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__nth,axiom,
% 179.72/179.54 ! [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 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_atLeastAtMost__upt,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_atLeast__upt,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 179.72/179.54 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 179.72/179.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 179.72/179.54 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 179.72/179.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__upt,axiom,
% 179.72/179.54 ! [V_j,V_k,V_i] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_greaterThanAtMost__upt,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_greaterThanLessThan__upt,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__map__upt,axiom,
% 179.72/179.54 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_atMost__upto,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transpose__rectangle,axiom,
% 179.72/179.54 ! [V_n_2,T_b,V_xs_2] :
% 179.72/179.54 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 179.72/179.54 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 179.72/179.54 => ( ! [B_i] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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 )
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__size__conv__listsum,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__size__map,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list_Osize_I1_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__size__estimation,axiom,
% 179.72/179.54 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 179.72/179.54 => 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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__size__estimation_H,axiom,
% 179.72/179.54 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 179.72/179.54 => 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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 179.72/179.54 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transpose_Opsimps_I1_J,axiom,
% 179.72/179.54 ! [T_b] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_return__list__def,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 179.72/179.54 ! [V_l] :
% 179.72/179.54 ( c_List_Onat__list(V_l)
% 179.72/179.54 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__map__filter,axiom,
% 179.72/179.54 ! [V_f_2,V_P_2,V_xs_2,T_b,T_c] :
% 179.72/179.54 ( class_Groups_Omonoid__add(T_c)
% 179.72/179.54 => ( ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 179.72/179.54 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 179.72/179.54 => 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_P_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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_embed__list__def,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upto__rec__number__of,axiom,
% 179.72/179.54 ! [V_n,V_m] :
% 179.72/179.54 ( ( 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)))
% 179.72/179.54 => 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))) )
% 179.72/179.54 & ( ~ 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)))
% 179.72/179.54 => 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) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last__list__update,axiom,
% 179.72/179.54 ! [V_x,V_k,T_a,V_xs] :
% 179.72/179.54 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.54 => ( ( 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))
% 179.72/179.54 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 179.72/179.54 & ( 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))
% 179.72/179.54 => 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) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map_Osimps_I2_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list_Osimps_I2_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list_Osimps_I3_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last_Osimps,axiom,
% 179.72/179.54 ! [V_x,T_a,V_xs] :
% 179.72/179.54 ( ( V_xs = c_List_Olist_ONil(T_a)
% 179.72/179.54 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 179.72/179.54 & ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.54 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last__ConsR,axiom,
% 179.72/179.54 ! [V_x,T_a,V_xs] :
% 179.72/179.54 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.54 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last__ConsL,axiom,
% 179.72/179.54 ! [V_x,T_a,V_xs] :
% 179.72/179.54 ( V_xs = c_List_Olist_ONil(T_a)
% 179.72/179.54 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_insort__key_Osimps_I1_J,axiom,
% 179.72/179.54 ! [V_x_2,V_f_2,T_b,T_c] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_c)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__filter__simps_I1_J,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omap__filter(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_b),T_b,c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Omap__filter(T_c,T_b,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_foldr_Osimps_I2_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list_Oinject,axiom,
% 179.72/179.54 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 <=> ( V_a_2 = V_a_H_2
% 179.72/179.54 & V_list_2 = V_list_H_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_not__Cons__self2,axiom,
% 179.72/179.54 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 179.72/179.54
% 179.72/179.54 fof(fact_not__Cons__self,axiom,
% 179.72/179.54 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_remove1_Osimps_I2_J,axiom,
% 179.72/179.54 ! [V_xs,T_a,V_y,V_x] :
% 179.72/179.54 ( ( V_x = V_y
% 179.72/179.54 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 179.72/179.54 & ( V_x != V_y
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_removeAll_Osimps_I2_J,axiom,
% 179.72/179.54 ! [V_xs,T_a,V_y,V_x] :
% 179.72/179.54 ( ( V_x = V_y
% 179.72/179.54 => 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) )
% 179.72/179.54 & ( V_x != V_y
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_insort__key_Osimps_I2_J,axiom,
% 179.72/179.54 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 179.72/179.54 ( class_Orderings_Olinorder(T_b)
% 179.72/179.54 => ( ( 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)))
% 179.72/179.54 => 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)) )
% 179.72/179.54 & ( ~ 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)))
% 179.72/179.54 => 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)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__code_I3_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__code_I2_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__simps_I2_J,axiom,
% 179.72/179.54 ! [V_xs,V_x,T_a] :
% 179.72/179.54 ( class_Groups_Omonoid__add(T_a)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__subset__Cons,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_impossible__Cons,axiom,
% 179.72/179.54 ! [V_x,V_ys,V_xs,T_a] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__ConsD,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 => ( V_y_2 = V_x_2
% 179.72/179.54 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update_Osimps_I2_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__Cons__0,axiom,
% 179.72/179.54 ! [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 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__Cons__Suc,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__Cons__Cons,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_filter_Osimps_I2_J,axiom,
% 179.72/179.54 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 179.72/179.54 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.54 => hAPP(c_List_Ofilter(T_b,V_P_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_P_2),V_xs_2)) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.54 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth_Osimps,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last__map,axiom,
% 179.72/179.54 ! [V_f_2,T_c,T_b,V_xs_2] :
% 179.72/179.54 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct_Osimps_I2_J,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 179.72/179.54 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__upds__Cons,axiom,
% 179.72/179.54 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last__in__set,axiom,
% 179.72/179.54 ! [T_b,V_as_2] :
% 179.72/179.54 ( V_as_2 != c_List_Olist_ONil(T_b)
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list_Osize_I4_J,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__Cons_H,axiom,
% 179.72/179.54 ! [V_xs,V_x,T_a,V_n] :
% 179.72/179.54 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 179.72/179.54 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 => 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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list_Osize_I2_J,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublist__singleton,axiom,
% 179.72/179.54 ! [V_x_2,T_b,V_A_2] :
% 179.72/179.54 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 179.72/179.54 => 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)) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 179.72/179.54 => 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) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__Cons__number__of,axiom,
% 179.72/179.54 ! [V_xs,V_x,T_a,V_v] :
% 179.72/179.54 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 => 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 )
% 179.72/179.54 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 => 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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last__upt,axiom,
% 179.72/179.54 ! [V_j,V_i] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upto_Osimps,axiom,
% 179.72/179.54 ! [V_j,V_i] :
% 179.72/179.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 179.72/179.54 => 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)) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 179.72/179.54 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last__conv__nth,axiom,
% 179.72/179.54 ! [T_a,V_xs] :
% 179.72/179.54 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upto_Opsimps,axiom,
% 179.72/179.54 ! [V_j_2,V_i_2] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 179.72/179.54 => 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)) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 179.72/179.54 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__Cons__def,axiom,
% 179.72/179.54 ! [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)))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transpose_Osimps_I2_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upt__conv__Cons,axiom,
% 179.72/179.54 ! [V_j,V_i] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__Cons__code_I2_J,axiom,
% 179.72/179.54 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 179.72/179.54 ( ( V_l = V_k
% 179.72/179.54 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v) )
% 179.72/179.54 & ( V_l != V_k
% 179.72/179.54 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_ps),V_k) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_enum__option__def,axiom,
% 179.72/179.54 ! [T_b] :
% 179.72/179.54 ( class_Enum_Oenum(T_b)
% 179.72/179.54 => c_Enum_Oenum__class_Oenum(tc_Option_Ooption(T_b)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(T_b)),c_Option_Ooption_ONone(T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_Option_Ooption(T_b)),c_Option_Ooption_OSome(T_b)),c_Enum_Oenum__class_Oenum(T_b))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublists_Osimps_I1_J,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upt__eq__Cons__conv,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 179.72/179.54 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 179.72/179.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 179.72/179.54 & V_i_2 = V_x_2
% 179.72/179.54 & 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 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upt__rec,axiom,
% 179.72/179.54 ! [V_j,V_i] :
% 179.72/179.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.72/179.54 => 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)) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.72/179.54 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_n__lists__Nil,axiom,
% 179.72/179.54 ! [T_a,V_n] :
% 179.72/179.54 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 => 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))) )
% 179.72/179.54 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_n__lists_Osimps_I1_J,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of_Osimps_I2_J,axiom,
% 179.72/179.54 ! [V_ps_2,V_p_2,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),hAPP(c_Map_Omap__of(T_b,T_c),V_ps_2)),hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Option_Ooption_OSome(T_c),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upt__rec__number__of,axiom,
% 179.72/179.54 ! [V_n,V_m] :
% 179.72/179.54 ( ( 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)))
% 179.72/179.54 => 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))) )
% 179.72/179.54 & ( ~ 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)))
% 179.72/179.54 => 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) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transpose_Opsimps_I2_J,axiom,
% 179.72/179.54 ! [V_xss_2,T_b] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__Cons__sing__Nil,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__Cons1,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__Cons,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list_Osimps_I5_J,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list_Osimps_I4_J,axiom,
% 179.72/179.54 ! [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 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listset_Osimps_I1_J,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_anamorph_Osimps,axiom,
% 179.72/179.54 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 179.72/179.54 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.54 => 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) )
% 179.72/179.54 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.54 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listset_Osimps_I2_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel__Cons,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upto_Opinduct,axiom,
% 179.72/179.54 ! [V_P_2,V_a1_2,V_a0_2] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ( ! [B_i,B_j] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 179.72/179.54 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
% 179.72/179.54 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 179.72/179.54 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel__Nil2,axiom,
% 179.72/179.54 ! [V_r_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel__Nil1,axiom,
% 179.72/179.54 ! [V_r_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel__eq__len,axiom,
% 179.72/179.54 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel_ONil,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel__mono,axiom,
% 179.72/179.54 ! [V_s_2,V_r_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel_OCons,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel__Nil,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel__iff__nth,axiom,
% 179.72/179.54 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 <=> ( 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)
% 179.72/179.54 & ! [B_n] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__upds__append1,axiom,
% 179.72/179.54 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 179.72/179.54 => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublist__Cons,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__eq__Cons__conv,axiom,
% 179.72/179.54 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 179.72/179.54 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 179.72/179.54 | ? [B_ys_H] :
% 179.72/179.54 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 179.72/179.54 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Cons__eq__append__conv,axiom,
% 179.72/179.54 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 179.72/179.54 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 179.72/179.54 | ? [B_ys_H] :
% 179.72/179.54 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 179.72/179.54 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append1__eq__conv,axiom,
% 179.72/179.54 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 <=> ( V_xs_2 = V_ys_2
% 179.72/179.54 & V_x_2 = V_y_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__Cons,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Cons__eq__appendI,axiom,
% 179.72/179.54 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 179.72/179.54 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 179.72/179.54 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 179.72/179.54 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__append,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_filter__append,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_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_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_zip__append,axiom,
% 179.72/179.54 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => ( 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)
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listsum__append,axiom,
% 179.72/179.54 ! [V_ys,V_xs,T_a] :
% 179.72/179.54 ( class_Groups_Omonoid__add(T_a)
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__append,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__append,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_fun__upds__append__drop,axiom,
% 179.72/179.54 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_fun__upds__append2__drop,axiom,
% 179.72/179.54 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_removeAll__append,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__assoc,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__eq__append__conv2,axiom,
% 179.72/179.54 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 <=> ? [B_us] :
% 179.72/179.54 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 179.72/179.54 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 )
% 179.72/179.54 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 179.72/179.54 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_same__append__eq,axiom,
% 179.72/179.54 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 <=> V_ys_2 = V_zs_2 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__same__eq,axiom,
% 179.72/179.54 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 <=> V_ys_2 = V_zs_2 ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__eq__appendI,axiom,
% 179.72/179.54 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 179.72/179.54 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 179.72/179.54 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 179.72/179.54 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_foldr__append,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__of__append,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_b,T_c,hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2),hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last__append,axiom,
% 179.72/179.54 ! [V_xs,T_a,V_ys] :
% 179.72/179.54 ( ( V_ys = c_List_Olist_ONil(T_a)
% 179.72/179.54 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 179.72/179.54 & ( V_ys != c_List_Olist_ONil(T_a)
% 179.72/179.54 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last__appendR,axiom,
% 179.72/179.54 ! [V_xs,T_a,V_ys] :
% 179.72/179.54 ( V_ys != c_List_Olist_ONil(T_a)
% 179.72/179.54 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last__appendL,axiom,
% 179.72/179.54 ! [V_xs,T_a,V_ys] :
% 179.72/179.54 ( V_ys = c_List_Olist_ONil(T_a)
% 179.72/179.54 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__Nil,axiom,
% 179.72/179.54 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Nil__is__append__conv,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 179.72/179.54 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 179.72/179.54 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__Nil2,axiom,
% 179.72/179.54 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 179.72/179.54
% 179.72/179.54 fof(fact_self__append__conv,axiom,
% 179.72/179.54 ! [V_ys_2,T_b,V_xs_2] :
% 179.72/179.54 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 179.72/179.54 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_self__append__conv2,axiom,
% 179.72/179.54 ! [V_xs_2,T_b,V_ys_2] :
% 179.72/179.54 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 179.72/179.54 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__is__Nil__conv,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 179.72/179.54 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 179.72/179.54 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__self__conv,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 179.72/179.54 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__self__conv2,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 179.72/179.54 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_eq__Nil__appendI,axiom,
% 179.72/179.54 ! [T_a,V_ys,V_xs] :
% 179.72/179.54 ( V_xs = V_ys
% 179.72/179.54 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__append__length,axiom,
% 179.72/179.54 ! [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 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__append__length__plus,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__append1,axiom,
% 179.72/179.54 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__length,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_remove1__append,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => 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) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upt__add__eq__append,axiom,
% 179.72/179.54 ! [V_k,V_j,V_i] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_last__snoc,axiom,
% 179.72/179.54 ! [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 ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__append,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 179.72/179.54 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.54 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 179.72/179.54 & 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__append,axiom,
% 179.72/179.54 ! [V_ys,V_xs,T_a,V_n] :
% 179.72/179.54 ( ( 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)))
% 179.72/179.54 => 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) )
% 179.72/179.54 & ( ~ 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)))
% 179.72/179.54 => 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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__update__append,axiom,
% 179.72/179.54 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 179.72/179.54 ( ( 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)))
% 179.72/179.54 => 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) )
% 179.72/179.54 & ( ~ 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)))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublists_Osimps_I2_J,axiom,
% 179.72/179.54 ! [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))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_product_Osimps_I2_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublist__append,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upt__Suc,axiom,
% 179.72/179.54 ! [V_j,V_i] :
% 179.72/179.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.72/179.54 => 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))) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.72/179.54 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_upt__Suc__append,axiom,
% 179.72/179.54 ! [V_j,V_i] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Cons__in__lex,axiom,
% 179.72/179.54 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 <=> ( ( 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))
% 179.72/179.54 & 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) )
% 179.72/179.54 | ( V_x_2 = V_y_2
% 179.72/179.54 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrelp__listrel__eq,axiom,
% 179.72/179.54 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 179.72/179.54 ( 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)
% 179.72/179.54 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrelp_ONil,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrelp_Oequations_I1_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrelp_OCons,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 179.72/179.54 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrelp_Oequations_I2_J,axiom,
% 179.72/179.54 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 179.72/179.54 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Nil2__notin__lex,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Nil__notin__lex,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_lenlex__conv,axiom,
% 179.72/179.54 ! [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)))))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_lenlex__def,axiom,
% 179.72/179.54 ! [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)))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel__Cons2,axiom,
% 179.72/179.54 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => ~ ! [B_x,B_xs] :
% 179.72/179.54 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 179.72/179.54 => ( 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))
% 179.72/179.54 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel__Cons1,axiom,
% 179.72/179.54 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => ~ ! [B_y,B_ys] :
% 179.72/179.54 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 179.72/179.54 => ( 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))
% 179.72/179.54 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel__iff__zip,axiom,
% 179.72/179.54 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 <=> ( 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)
% 179.72/179.54 & ! [B_x] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 => 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)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_lexord__append__left__rightI,axiom,
% 179.72/179.54 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_ball__empty,axiom,
% 179.72/179.54 ! [V_P_2,T_b,B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 179.72/179.54 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Powp__def,axiom,
% 179.72/179.54 ! [V_B_2,V_A_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 179.72/179.54 <=> ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 179.72/179.54 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_congruent__def,axiom,
% 179.72/179.54 ! [V_f_2,V_r_2,T_c,T_b] :
% 179.72/179.54 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 179.72/179.54 <=> ! [B_x] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_list__eq__iff__zip__eq,axiom,
% 179.72/179.54 ! [T_b,V_ys_2,V_xs_2] :
% 179.72/179.54 ( V_xs_2 = V_ys_2
% 179.72/179.54 <=> ( 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)
% 179.72/179.54 & ! [B_x] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_lexord__Nil__right,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_lexord__append__leftI,axiom,
% 179.72/179.54 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_lexord__lex,axiom,
% 179.72/179.54 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 & 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) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_lexord__cons__cons,axiom,
% 179.72/179.54 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 <=> ( 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))
% 179.72/179.54 | ( V_a_2 = V_b_2
% 179.72/179.54 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_lexord__take__index__conv,axiom,
% 179.72/179.54 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 <=> ( ( 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)))
% 179.72/179.54 & 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 )
% 179.72/179.54 | ? [B_i] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 179.72/179.54 & 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)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 179.72/179.54 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 & V_x_2 = V_y_2 )
% 179.72/179.54 | ( V_xs_2 = V_ys_2
% 179.72/179.54 & 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)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_in__set__takeD,axiom,
% 179.72/179.54 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 179.72/179.54 ( 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))))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__all,axiom,
% 179.72/179.54 ! [V_n,V_xs,T_a] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__take__subset,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__eq__Nil,axiom,
% 179.72/179.54 ! [V_xs_2,V_n_2,T_b] :
% 179.72/179.54 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 179.72/179.54 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__0,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__Nil,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct__take,axiom,
% 179.72/179.54 ! [V_i,V_xs,T_a] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.54 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__take,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_nth__take,axiom,
% 179.72/179.54 ! [V_xs,T_a,V_n,V_i] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__take,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__zip,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__map,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__Suc__Cons,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_sublist__upt__eq__take,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__take__subset__set__take,axiom,
% 179.72/179.54 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.72/179.54 => 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)))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__append,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__1__Cons,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel1__mono,axiom,
% 179.72/179.54 ! [V_s_2,V_r_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__upt,axiom,
% 179.72/179.54 ! [V_n,V_m,V_i] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => 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)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel1I2,axiom,
% 179.72/179.54 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel1__eq__len,axiom,
% 179.72/179.54 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => 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) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_not__listrel1__Nil,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_not__Nil__listrel1,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_append__listrel1I,axiom,
% 179.72/179.54 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 & V_us_2 = V_vs_2 )
% 179.72/179.54 | ( V_xs_2 = V_ys_2
% 179.72/179.54 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) )
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__Cons,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__Cons_H,axiom,
% 179.72/179.54 ! [V_xs,V_x,T_a,V_n] :
% 179.72/179.54 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 => 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) )
% 179.72/179.54 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_dom__map__upds,axiom,
% 179.72/179.54 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))),c_Map_Odom(T_b,T_c,V_m_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel1I1,axiom,
% 179.72/179.54 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_Cons__listrel1__Cons,axiom,
% 179.72/179.54 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 <=> ( ( 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))
% 179.72/179.54 & V_xs_2 = V_ys_2 )
% 179.72/179.54 | ( V_x_2 = V_y_2
% 179.72/179.54 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__Cons__number__of,axiom,
% 179.72/179.54 ! [V_xs,V_x,T_a,V_v] :
% 179.72/179.54 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 => 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) )
% 179.72/179.54 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_map__upd__upds__conv__if,axiom,
% 179.72/179.54 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
% 179.72/179.54 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
% 179.72/179.54 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2) )
% 179.72/179.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
% 179.72/179.54 => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_take__Suc__conv__app__nth,axiom,
% 179.72/179.54 ! [V_xs,T_a,V_i] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel1I,axiom,
% 179.72/179.54 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => ( 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))
% 179.72/179.54 => ( 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))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel1__iff__update,axiom,
% 179.72/179.54 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 <=> ? [B_y,B_n] :
% 179.72/179.54 ( 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))
% 179.72/179.54 & 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)))
% 179.72/179.54 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel1E,axiom,
% 179.72/179.54 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => ~ ! [B_x,B_y] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => ! [B_us,B_vs] :
% 179.72/179.54 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 179.72/179.54 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_lexord__append__leftD,axiom,
% 179.72/179.54 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => ( ! [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))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_rotate1__def,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_rotate1__is__Nil__conv,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 179.72/179.54 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_distinct1__rotate,axiom,
% 179.72/179.54 ! [V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 179.72/179.54 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_set__rotate1,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_length__rotate1,axiom,
% 179.72/179.54 ! [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) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_rotate__simps,axiom,
% 179.72/179.54 ! [V_xs,V_x,T_b,T_a] :
% 179.72/179.54 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 179.72/179.54 & 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))) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_rotate1__length01,axiom,
% 179.72/179.54 ! [V_xs,T_a] :
% 179.72/179.54 ( 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)))
% 179.72/179.54 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_listrel1__subset__listrel,axiom,
% 179.72/179.54 ! [V_r_H_2,V_r_2,T_b] :
% 179.72/179.54 ( 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))
% 179.72/179.54 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 179.72/179.54 => 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))) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_lexn__length,axiom,
% 179.72/179.54 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.54 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.54 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 179.72/179.54 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_refl__on__Id__on,axiom,
% 179.72/179.54 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_lexn_Osimps_I1_J,axiom,
% 179.72/179.54 ! [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)) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_refl__on__empty,axiom,
% 179.72/179.54 ! [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))) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_refl__on__Un,axiom,
% 179.72/179.54 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 179.72/179.54 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 179.72/179.54 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_refl__on__Int,axiom,
% 179.72/179.54 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 179.72/179.54 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 179.72/179.54 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_refl__onD,axiom,
% 179.72/179.54 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 179.72/179.54 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 179.72/179.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.54 => 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)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_refl__onD1,axiom,
% 179.72/179.54 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 179.72/179.54 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 179.72/179.54 => ( 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))
% 179.72/179.54 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 179.72/179.54
% 179.72/179.54 fof(fact_refl__onD2,axiom,
% 179.72/179.54 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 179.72/179.54 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 179.72/179.55 => ( 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))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lex__def,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_refl__on__def_H,axiom,
% 179.72/179.55 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.55 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 179.72/179.55 <=> ( ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 179.72/179.55 => 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)) )
% 179.72/179.55 & ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.55 => 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)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lexn_Osimps_I2_J,axiom,
% 179.72/179.55 ! [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)))))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_reflp__def,axiom,
% 179.72/179.55 ! [V_r_2,T_b] :
% 179.72/179.55 ( c_Predicate_Oreflp(T_b,V_r_2)
% 179.72/179.55 <=> 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair__imageI,axiom,
% 179.72/179.55 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair__simp,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_reflpE,axiom,
% 179.72/179.55 ! [V_x_2,V_r_2,T_b] :
% 179.72/179.55 ( c_Predicate_Oreflp(T_b,V_r_2)
% 179.72/179.55 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair__ident,axiom,
% 179.72/179.55 ! [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 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_snd__prod__fun,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_fst__map__pair,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_snd__comp__map__pair,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_fst__comp__map__pair,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair_Ocomp,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair__compose,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair_Ocompositionality,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair__def,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair__surj,axiom,
% 179.72/179.55 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => ( 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))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_partition__filter__conv,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_transpose_Opsimps_I3_J,axiom,
% 179.72/179.55 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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))))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_partition__filter1,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_concat_Osimps_I1_J,axiom,
% 179.72/179.55 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_concat_Osimps_I2_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_concat__eq__Nil__conv,axiom,
% 179.72/179.55 ! [V_xss_2,T_b] :
% 179.72/179.55 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 179.72/179.55 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Nil__eq__concat__conv,axiom,
% 179.72/179.55 ! [V_xss_2,T_b] :
% 179.72/179.55 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 179.72/179.55 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__concat,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_filter__concat,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__concat,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_set__concat,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_concat__append,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_partition__P,axiom,
% 179.72/179.55 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 179.72/179.55 ( c_List_Opartition(T_b,V_P_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)
% 179.72/179.55 => ( ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 179.72/179.55 => hBOOL(hAPP(V_P_2,B_x)) )
% 179.72/179.55 & ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 179.72/179.55 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_partition_Osimps_I1_J,axiom,
% 179.72/179.55 ! [V_P_2,T_b] : c_List_Opartition(T_b,V_P_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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_partition_Osimps_I2_J,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,V_P_2,T_b] : c_List_Opartition(T_b,V_P_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_P_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_P_2,V_xs_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_transpose_Osimps_I3_J,axiom,
% 179.72/179.55 ! [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))))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_partition__filter2,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_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_P_2)),V_xs_2) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_concat__injective,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,T_b] :
% 179.72/179.55 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 179.72/179.55 => ( 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)
% 179.72/179.55 => ( ! [B_x] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => 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)) )
% 179.72/179.55 => V_xs_2 = V_ys_2 ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_concat__eq__concat__iff,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,T_b] :
% 179.72/179.55 ( ! [B_x] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => 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)) )
% 179.72/179.55 => ( 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)
% 179.72/179.55 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 179.72/179.55 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_concat__map__singleton,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_n__lists_Osimps_I2_J,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_partition__set,axiom,
% 179.72/179.55 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 179.72/179.55 ( c_List_Opartition(T_b,V_P_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)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_transpose__aux__filter__tail,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_transpose__aux__filter__head,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__tl,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_tl_Osimps_I1_J,axiom,
% 179.72/179.55 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__tl,axiom,
% 179.72/179.55 ! [V_xs,T_a] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.55 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_tl_Osimps_I2_J,axiom,
% 179.72/179.55 ! [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 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_hd_Osimps,axiom,
% 179.72/179.55 ! [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 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_take__Suc,axiom,
% 179.72/179.55 ! [V_n,T_a,V_xs] :
% 179.72/179.55 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_tl__append2,axiom,
% 179.72/179.55 ! [V_ys,T_a,V_xs] :
% 179.72/179.55 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate1__hd__tl,axiom,
% 179.72/179.55 ! [T_a,V_xs] :
% 179.72/179.55 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_take__tl,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_hd__map,axiom,
% 179.72/179.55 ! [V_f_2,T_c,T_b,V_xs_2] :
% 179.72/179.55 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_hd__append2,axiom,
% 179.72/179.55 ! [V_ys,T_a,V_xs] :
% 179.72/179.55 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_hd__append,axiom,
% 179.72/179.55 ! [V_ys,T_a,V_xs] :
% 179.72/179.55 ( ( V_xs = c_List_Olist_ONil(T_a)
% 179.72/179.55 => 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) )
% 179.72/179.55 & ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_hd__upt,axiom,
% 179.72/179.55 ! [V_j,V_i] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 179.72/179.55 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_tl__append,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__tl,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_hd__in__set,axiom,
% 179.72/179.55 ! [T_b,V_xs_2] :
% 179.72/179.55 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_tl__take,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_hd__conv__nth,axiom,
% 179.72/179.55 ! [T_a,V_xs] :
% 179.72/179.55 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__remdups__concat,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_insort__key__remove1,axiom,
% 179.72/179.55 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_c)
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 179.72/179.55 => ( 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
% 179.72/179.55 => 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 ) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted_ONil,axiom,
% 179.72/179.55 ! [T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__remdups,axiom,
% 179.72/179.55 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__single,axiom,
% 179.72/179.55 ! [V_x,T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__remdups__leq,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__filter,axiom,
% 179.72/179.55 ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 179.72/179.55 => 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_P_2),V_xs_2))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_remdups__map__remdups,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__map__remove1,axiom,
% 179.72/179.55 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__insort__key,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( 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)))
% 179.72/179.55 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__distinct__set__unique,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 179.72/179.55 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 179.72/179.55 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 179.72/179.55 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 179.72/179.55 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__tl,axiom,
% 179.72/179.55 ! [V_xs,T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_set__remdups,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__same,axiom,
% 179.72/179.55 ! [V_xs_2,V_g_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_remdups__filter,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oremdups(T_b,V_xs_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__upt,axiom,
% 179.72/179.55 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__remdups__eq,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( 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)
% 179.72/179.55 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__insort,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( 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))
% 179.72/179.55 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__remove1,axiom,
% 179.72/179.55 ! [V_a,V_xs,T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__upto,axiom,
% 179.72/179.55 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_remdups__remdups,axiom,
% 179.72/179.55 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__remdups,axiom,
% 179.72/179.55 ! [V_l,T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__insort__insert,axiom,
% 179.72/179.55 ! [V_x_2,V_xs_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_remdups__id__iff__distinct,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 179.72/179.55 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__remdups__id,axiom,
% 179.72/179.55 ! [V_xs,T_a] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.55 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_remdups_Osimps_I1_J,axiom,
% 179.72/179.55 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted_Oequations_I1_J,axiom,
% 179.72/179.55 ! [T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_remdups__eq__nil__right__iff,axiom,
% 179.72/179.55 ! [V_x_2,T_b] :
% 179.72/179.55 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 179.72/179.55 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_remdups__eq__nil__iff,axiom,
% 179.72/179.55 ! [V_x_2,T_b] :
% 179.72/179.55 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 179.72/179.55 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__many__eq,axiom,
% 179.72/179.55 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( 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)))
% 179.72/179.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 179.72/179.55 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__many,axiom,
% 179.72/179.55 ! [V_zs,V_y,V_x,T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 179.72/179.55 => 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))) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__take,axiom,
% 179.72/179.55 ! [V_n,V_xs,T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__insort__insert__key,axiom,
% 179.72/179.55 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__map__same,axiom,
% 179.72/179.55 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_remove1__remdups,axiom,
% 179.72/179.55 ! [V_x,V_xs,T_a] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__Cons,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 179.72/179.55 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 179.72/179.55 & ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__append,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 179.72/179.55 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 179.72/179.55 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 179.72/179.55 & ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => ! [B_xa] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_filter__insort,axiom,
% 179.72/179.55 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 179.72/179.55 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.55 => hAPP(c_List_Ofilter(T_c,V_P_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_P_2),V_xs_2)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_remdups_Osimps_I2_J,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => 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) )
% 179.72/179.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__remdups__card__conv,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted_Oequations_I2_J,axiom,
% 179.72/179.55 ! [V_a1_2,V_a2_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 179.72/179.55 <=> ( ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 179.72/179.55 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__list__of__set,axiom,
% 179.72/179.55 ! [V_A_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.55 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 179.72/179.55 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 179.72/179.55 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_insort__remove1,axiom,
% 179.72/179.55 ! [V_xs_2,V_a_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 179.72/179.55 => 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 ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__nth__mono,axiom,
% 179.72/179.55 ! [V_j,V_i,V_xs,T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => 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))) ) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__equals__nth__mono,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 179.72/179.55 <=> ! [B_j] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ! [B_i] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 179.72/179.55 => 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))) ) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__sorted__distinct__set__unique,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_c)
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 179.72/179.55 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 179.72/179.55 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 179.72/179.55 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 179.72/179.55 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_transpose__column,axiom,
% 179.72/179.55 ! [V_i_2,V_xs_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_nth__nth__transpose__sorted,axiom,
% 179.72/179.55 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ( 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))))
% 179.72/179.55 => ( 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))))
% 179.72/179.55 => 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) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_inj__on__rev,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__is__Nil__conv,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 179.72/179.55 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Nil__is__rev__conv,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 179.72/179.55 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev_Osimps_I1_J,axiom,
% 179.72/179.55 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__rev,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 179.72/179.55 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__is__rev__conv,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,T_b] :
% 179.72/179.55 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 179.72/179.55 <=> V_xs_2 = V_ys_2 ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__swap,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,T_b] :
% 179.72/179.55 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 179.72/179.55 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__rev__ident,axiom,
% 179.72/179.55 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__rev,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listsum__rev,axiom,
% 179.72/179.55 ! [V_xs,T_a] :
% 179.72/179.55 ( class_Groups_Ocomm__monoid__add(T_a)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__filter,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_singleton__rev__conv,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( 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)
% 179.72/179.55 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__singleton__conv,axiom,
% 179.72/179.55 ! [V_x_2,V_xs_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__append,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_zip__rev,axiom,
% 179.72/179.55 ! [V_ys,T_b,V_xs,T_a] :
% 179.72/179.55 ( 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)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_set__rev,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__map,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__concat,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__eq__Cons__iff,axiom,
% 179.72/179.55 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 179.72/179.55 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 179.72/179.55 <=> 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev_Osimps_I2_J,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_last__rev,axiom,
% 179.72/179.55 ! [T_a,V_xs] :
% 179.72/179.55 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_hd__rev,axiom,
% 179.72/179.55 ! [T_a,V_xs] :
% 179.72/179.55 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__transpose,axiom,
% 179.72/179.55 ! [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)))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__nth,axiom,
% 179.72/179.55 ! [V_xs,T_a,V_n] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__update,axiom,
% 179.72/179.55 ! [V_y,V_xs,T_a,V_k] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__rev__nth__mono,axiom,
% 179.72/179.55 ! [V_j,V_i,V_xs,T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => 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))) ) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldr__max__sorted,axiom,
% 179.72/179.55 ! [V_y_2,V_xs_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 179.72/179.55 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 179.72/179.55 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 179.72/179.55 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 179.72/179.55 => 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) ) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__transpose__sorted,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 179.72/179.55 => 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) )
% 179.72/179.55 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 179.72/179.55 => 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))) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_transpose__column__length,axiom,
% 179.72/179.55 ! [V_i_2,V_xs_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_transpose__transpose,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_take__hd__drop,axiom,
% 179.72/179.55 ! [V_xs,T_a,V_n] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__drop,axiom,
% 179.72/179.55 ! [V_n,V_xs,T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__takeWhile,axiom,
% 179.72/179.55 ! [V_P_2,V_xs_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__takeWhile__le,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_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_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile__tail,axiom,
% 179.72/179.55 ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
% 179.72/179.55 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.55 => c_List_OtakeWhile(T_b,V_P_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_P_2,V_xs_2) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__map,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_zip__takeWhile__snd,axiom,
% 179.72/179.55 ! [V_ys_2,V_P_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_P_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_P_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_zip__takeWhile__fst,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_P_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_P_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_in__set__dropD,axiom,
% 179.72/179.55 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_set__drop__subset,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__tl,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_tl__drop,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__Suc,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile__eq__all__conv,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.55 ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__zip,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_set__takeWhileD,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,V_x_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_nth__via__drop,axiom,
% 179.72/179.55 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 179.72/179.55 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 179.72/179.55 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__1__Cons,axiom,
% 179.72/179.55 ! [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 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__Suc__Cons,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__upt,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__drop,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__drop,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__0,axiom,
% 179.72/179.55 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__drop,axiom,
% 179.72/179.55 ! [V_i,V_xs,T_a] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.55 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__takeWhile,axiom,
% 179.72/179.55 ! [V_P_2,V_xs_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.55 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__Nil,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 179.72/179.55 ! [V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_append__take__drop__id,axiom,
% 179.72/179.55 ! [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 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__take,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_take__drop,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 179.72/179.55 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 179.72/179.55 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.55 => c_List_OtakeWhile(T_b,V_P_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_P_2,V_xs_2)) )
% 179.72/179.55 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.55 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile__eq__take,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_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_P_2,V_xs_2))),V_xs_2) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile__map,axiom,
% 179.72/179.55 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_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_P_2),V_f_2),V_xs_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_set__drop__subset__set__drop,axiom,
% 179.72/179.55 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 179.72/179.55 => 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)))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__eq__Nil,axiom,
% 179.72/179.55 ! [V_xs_2,V_n_2,T_b] :
% 179.72/179.55 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 179.72/179.55 <=> 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__all,axiom,
% 179.72/179.55 ! [V_n,V_xs,T_a] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__append,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_append__eq__conv__conj,axiom,
% 179.72/179.55 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.55 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 179.72/179.55 <=> ( 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)
% 179.72/179.55 & 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_last__drop,axiom,
% 179.72/179.55 ! [V_xs,T_a,V_n] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__Cons,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile__append1,axiom,
% 179.72/179.55 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.55 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_nth__length__takeWhile,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.55 ( 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_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 179.72/179.55 => ~ hBOOL(hAPP(V_P_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_P_2,V_xs_2))))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile__nth,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 179.72/179.55 ( 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_P_2,V_xs_2))))
% 179.72/179.55 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__Cons_H,axiom,
% 179.72/179.55 ! [V_xs,V_x,T_a,V_n] :
% 179.72/179.55 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.55 => 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) )
% 179.72/179.55 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_nth__drop,axiom,
% 179.72/179.55 ! [V_xs,T_a,V_i,V_n] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_append__eq__append__conv__if,axiom,
% 179.72/179.55 ! [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] :
% 179.72/179.55 ( 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)
% 179.72/179.55 <=> ( ( 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)))
% 179.72/179.55 => ( 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)
% 179.72/179.55 & 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) ) )
% 179.72/179.55 & ( ~ 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)))
% 179.72/179.55 => ( 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
% 179.72/179.55 & 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 ) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__drop,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__take,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__upds__def,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_b,T_c,V_m_2,hAPP(c_Map_Omap__of(T_b,T_c),hAPP(c_List_Orev(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_nth__drop_H,axiom,
% 179.72/179.55 ! [V_xs,T_a,V_i] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__Cons__number__of,axiom,
% 179.72/179.55 ! [V_xs,V_x,T_a,V_v] :
% 179.72/179.55 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.55 => 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) )
% 179.72/179.55 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_take__add,axiom,
% 179.72/179.55 ! [V_xs,T_a,V_j,V_i] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_hd__drop__conv__nth,axiom,
% 179.72/179.55 ! [V_n,T_a,V_xs] :
% 179.72/179.55 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_zip__append1,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_zip__append2,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 179.72/179.55 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_id__take__nth__drop,axiom,
% 179.72/179.55 ! [V_xs,T_a,V_i] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_upd__conv__take__nth__drop,axiom,
% 179.72/179.55 ! [V_a,V_xs,T_a,V_i] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile__neq__rev,axiom,
% 179.72/179.55 ! [V_x_2,V_xs_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_dropWhile__neq__rev,axiom,
% 179.72/179.55 ! [V_x_2,V_xs_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 179.72/179.55 ! [V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__dropWhile,axiom,
% 179.72/179.55 ! [V_P_2,V_xs_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.55 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 179.72/179.55 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 179.72/179.55 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.55 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_P_2,V_xs_2) )
% 179.72/179.55 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.55 => c_List_OdropWhile(T_b,V_P_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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__dropWhile,axiom,
% 179.72/179.55 ! [V_P_2,V_xs_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.55 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__dropWhile__le,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_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_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile__dropWhile__id,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),c_List_OdropWhile(T_b,V_P_2,V_xs_2)) = V_xs_2 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_hd__dropWhile,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.55 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 179.72/179.55 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_dropWhile__map,axiom,
% 179.72/179.55 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_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_P_2),V_f_2),V_xs_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_dropWhile__append1,axiom,
% 179.72/179.55 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.55 => c_List_OdropWhile(T_b,V_P_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_P_2,V_xs_2)),V_ys_2) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 179.72/179.55 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_b] :
% 179.72/179.55 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 179.72/179.55 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
% 179.72/179.55 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_dropWhile__eq__drop,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_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_P_2,V_xs_2))),V_xs_2) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_dropWhile__nth,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 179.72/179.55 ( 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_P_2,V_xs_2))))
% 179.72/179.55 => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_P_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_P_2,V_xs_2)))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__nth__monoI,axiom,
% 179.72/179.55 ! [V_xs,T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => ( ! [B_i,B_j] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => 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))) ) )
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_prod__fun__imageE,axiom,
% 179.72/179.55 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ~ ! [B_x,B_y] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => ~ 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_fold1__set,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 179.72/179.55 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_hd__rotate__conv__nth,axiom,
% 179.72/179.55 ! [V_n,T_a,V_xs] :
% 179.72/179.55 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldr__conv__foldl,axiom,
% 179.72/179.55 ! [V_a_2,V_xs_2,T_b] :
% 179.72/179.55 ( class_Groups_Oab__semigroup__add(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldl__conv__concat,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_start__le__sum,axiom,
% 179.72/179.55 ! [V_ns_2,V_n_2,V_m_2] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldl__Nil,axiom,
% 179.72/179.55 ! [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 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate__is__Nil__conv,axiom,
% 179.72/179.55 ! [V_xs_2,V_n_2,T_b] :
% 179.72/179.55 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 179.72/179.55 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__rotate,axiom,
% 179.72/179.55 ! [V_xs_2,V_n_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 179.72/179.55 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate__rotate,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldl__assoc,axiom,
% 179.72/179.55 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Groups_Osemigroup__add(T_b)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__rotate,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldl__absorb0,axiom,
% 179.72/179.55 ! [V_zs_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Groups_Omonoid__add(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldl__Cons,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldl__append,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate1__rotate__swap,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_set__rotate,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldl__map,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate__map,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate__conv__mod,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldl__foldr,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldr__foldl,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate__Suc,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listsum__foldl,axiom,
% 179.72/179.55 ! [T_b] :
% 179.72/179.55 ( class_Groups_Omonoid__add(T_b)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_concat__conv__foldl,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldl__foldr1__lemma,axiom,
% 179.72/179.55 ! [V_xs_2,V_a_2,T_b] :
% 179.72/179.55 ( class_Groups_Omonoid__add(T_b)
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_foldl__foldr1,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( class_Groups_Omonoid__add(T_b)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sum__eq__0__conv,axiom,
% 179.72/179.55 ! [V_ns_2,V_m_2] :
% 179.72/179.55 ( 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)
% 179.72/179.55 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.55 & ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 179.72/179.55 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rev__foldl__cons,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate__add,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate__id,axiom,
% 179.72/179.55 ! [V_xs,T_a,V_n] :
% 179.72/179.55 ( 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)
% 179.72/179.55 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate__length01,axiom,
% 179.72/179.55 ! [V_n,V_xs,T_a] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sup__set__fold,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sup__fin__set__fold,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Lattices_Olattice(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inf__fin__set__fold,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Lattices_Olattice(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Min__fin__set__fold,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Max__fin__set__fold,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_SUPR__set__fold,axiom,
% 179.72/179.55 ! [V_f_2,V_xs_2,T_c,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__upds__fold__map__upd,axiom,
% 179.72/179.55 ! [V_vs_2,V_ks_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(tc_prod(T_b,T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_b,tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),c_COMBC(T_b,tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c))))),tc_fun(T_b,tc_Option_Ooption(T_c))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c))),tc_fun(tc_fun(T_c,tc_Option_Ooption(T_c)),tc_fun(T_c,tc_fun(T_b,tc_Option_Ooption(T_c)))),T_b),c_COMBB(tc_Option_Ooption(T_c),tc_fun(T_b,tc_Option_Ooption(T_c)),T_c))),c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c))))),c_Option_Ooption_OSome(T_c))),V_m_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_ks_2),V_vs_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate__rev,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_elem__le__sum,axiom,
% 179.72/179.55 ! [V_ns_2,V_n_2] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate__drop__take,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_image__split__eq__Sigma,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lexord__append__rightI,axiom,
% 179.72/179.55 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 179.72/179.55 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_SigmaI,axiom,
% 179.72/179.55 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_UNIV__Times__UNIV,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_SigmaE2,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.55 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_SigmaD2,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_SigmaD1,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_mem__Sigma__iff,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.55 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sigma__Union,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_setprod__cartesian__product,axiom,
% 179.72/179.55 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 179.72/179.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_setsum__cartesian__product,axiom,
% 179.72/179.55 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 179.72/179.55 ( class_Groups_Ocomm__monoid__add(T_b)
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sigma__empty1,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sigma__empty2,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Times__empty,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sigma__Int__distrib1,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Times__Int__distrib1,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sigma__Int__distrib2,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_equiv__type,axiom,
% 179.72/179.55 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.55 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.55 => 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)))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Compl__Times__UNIV2,axiom,
% 179.72/179.55 ! [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)))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Compl__Times__UNIV1,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_card__cartesian__product,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sigma__Diff__distrib1,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Times__Diff__distrib1,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sigma__Diff__distrib2,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sigma__Un__distrib2,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Times__Un__distrib1,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sigma__Un__distrib1,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_finite__cartesian__product,axiom,
% 179.72/179.55 ! [V_B_2,T_c,V_A_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 179.72/179.55 => 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)))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Times__eq__cancel2,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 179.72/179.55 => ( 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))
% 179.72/179.55 <=> V_A_2 = V_B_2 ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Id__on__subset__Times,axiom,
% 179.72/179.55 ! [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)))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_card__cartesian__product__singleton,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Times__subset__cancel2,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 179.72/179.55 => ( 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))))
% 179.72/179.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Image__subset,axiom,
% 179.72/179.55 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_finite__cartesian__productD1,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 179.72/179.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_finite__cartesian__productD2,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Collect__split,axiom,
% 179.72/179.55 ! [V_Qa_2,V_P_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_P_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_SetCompr__Sigma__eq,axiom,
% 179.72/179.55 ! [V_Qa_2,V_P_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_P_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_fst__image__times,axiom,
% 179.72/179.55 ! [V_A_2,T_c,T_b,V_B_2] :
% 179.72/179.55 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) )
% 179.72/179.55 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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 ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_snd__image__times,axiom,
% 179.72/179.55 ! [V_B_2,T_c,T_b,V_A_2] :
% 179.72/179.55 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) )
% 179.72/179.55 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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 ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair__surj__on,axiom,
% 179.72/179.55 ! [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] :
% 179.72/179.55 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 179.72/179.55 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_product__list__set,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_swap__product,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_refl__on__def,axiom,
% 179.72/179.55 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.55 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 179.72/179.55 <=> ( 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))))
% 179.72/179.55 & ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.55 => 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)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_insert__times__insert,axiom,
% 179.72/179.55 ! [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)))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_finite__equiv__class,axiom,
% 179.72/179.55 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.55 => ( 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))))
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair__inj__on,axiom,
% 179.72/179.55 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 179.72/179.55 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.72/179.55 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_UN__Times__distrib,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sigma__def,axiom,
% 179.72/179.55 ! [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))))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_finite__quotient,axiom,
% 179.72/179.55 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.55 => ( 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))))
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_vimage__Times,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 179.72/179.55 ( class_Rings_Osemiring__0(T_d)
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => 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))))))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 179.72/179.55 ! [V_A_2,V_I_2,T_c,T_b] :
% 179.72/179.55 ? [B_f] :
% 179.72/179.55 ( 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))
% 179.72/179.55 & 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_bij__betw__id,axiom,
% 179.72/179.55 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_image__id,axiom,
% 179.72/179.55 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_surj__id,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair_Oidentity,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__pair_Oid,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_inv__id,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_of__int__eq__id,axiom,
% 179.72/179.55 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_inj__on__id,axiom,
% 179.72/179.55 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_vimage__id,axiom,
% 179.72/179.55 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_id__apply,axiom,
% 179.72/179.55 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Option_Omap_Oid,axiom,
% 179.72/179.55 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_id__def,axiom,
% 179.72/179.55 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_bij__betw__id__iff,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_b] :
% 179.72/179.55 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 179.72/179.55 <=> V_A_2 = V_B_2 ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Option_Omap_Oidentity,axiom,
% 179.72/179.55 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_apsnd__id,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_apfst__id,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_bij__id,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_List_Omap_Oidentity,axiom,
% 179.72/179.55 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_List_Omap_Oid,axiom,
% 179.72/179.55 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_folding_Oempty,axiom,
% 179.72/179.55 ! [V_F_2,V_f_2,T_c,T_b] :
% 179.72/179.55 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.72/179.55 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_o__eq__id__dest,axiom,
% 179.72/179.55 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 179.72/179.55 ( 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)
% 179.72/179.55 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_o__id,axiom,
% 179.72/179.55 ! [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 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_id__o,axiom,
% 179.72/179.55 ! [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 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rotate0,axiom,
% 179.72/179.55 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_apsnd__def,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_apfst__def,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_split__Pair,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_setsum__reindex__id,axiom,
% 179.72/179.55 ! [V_B_2,V_f_2,T_b,T_c] :
% 179.72/179.55 ( class_Groups_Ocomm__monoid__add(T_c)
% 179.72/179.55 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_setprod__reindex__id,axiom,
% 179.72/179.55 ! [V_B_2,V_f_2,T_b,T_c] :
% 179.72/179.55 ( class_Groups_Ocomm__monoid__mult(T_c)
% 179.72/179.55 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_surj__iff,axiom,
% 179.72/179.55 ! [V_f_2,T_b,T_c] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_inj__iff,axiom,
% 179.72/179.55 ! [V_f_2,T_c,T_b] :
% 179.72/179.55 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.72/179.55 <=> 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_inv__o__cancel,axiom,
% 179.72/179.55 ! [V_f_2,T_c,T_b] :
% 179.72/179.55 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_setprod__Sigma,axiom,
% 179.72/179.55 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 179.72/179.55 ( class_Groups_Ocomm__monoid__mult(T_d)
% 179.72/179.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.55 => ( ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 179.72/179.55 => 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)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_refl__onI,axiom,
% 179.72/179.55 ! [V_A_2,V_r_2,T_b] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => ( ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.55 => 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)) )
% 179.72/179.55 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_setsum__Sigma,axiom,
% 179.72/179.55 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 179.72/179.55 ( class_Groups_Ocomm__monoid__add(T_d)
% 179.72/179.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.55 => ( ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 179.72/179.55 => 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)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_fold__image__Sigma,axiom,
% 179.72/179.55 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 179.72/179.55 ( class_Groups_Ocomm__monoid__mult(T_d)
% 179.72/179.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.55 => ( ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 179.72/179.55 => 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)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_card__SigmaI,axiom,
% 179.72/179.55 ! [V_B_2,T_c,V_A_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.55 => ( ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_finite__SigmaI,axiom,
% 179.72/179.55 ! [V_B_2,T_c,V_A_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.55 => ( ! [B_a] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listrel__subset,axiom,
% 179.72/179.55 ! [V_A_2,V_r_2,T_b] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => 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))))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sort__foldl__insort,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lists_ONil,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lists__mono,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sort__key__simps_I1_J,axiom,
% 179.72/179.55 ! [V_f_2,T_b,T_c] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_c)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__sort,axiom,
% 179.72/179.55 ! [V_xs_2,V_f_2,T_b,T_c] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_c)
% 179.72/179.55 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 179.72/179.55 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__sort,axiom,
% 179.72/179.55 ! [V_xs_2,V_f_2,T_b,T_c] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_c)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_filter__sort,axiom,
% 179.72/179.55 ! [V_xs_2,V_f_2,V_P_2,T_b,T_c] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_c)
% 179.72/179.55 => hAPP(c_List_Ofilter(T_b,V_P_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_P_2),V_xs_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_set__sort,axiom,
% 179.72/179.55 ! [V_xs_2,V_f_2,T_b,T_c] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_c)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__sort,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_append__in__lists__conv,axiom,
% 179.72/179.55 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 179.72/179.55 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lists__UNIV,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_equiv__listrel,axiom,
% 179.72/179.55 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.55 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listrel__refl__on,axiom,
% 179.72/179.55 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.55 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__sort__key,axiom,
% 179.72/179.55 ! [V_xs_2,V_f_2,T_c,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sort__key__simps_I2_J,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_c)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Cons__in__lists__iff,axiom,
% 179.72/179.55 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.55 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_in__lists__conv__set,axiom,
% 179.72/179.55 ! [V_A_2,V_xs_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lists__eq__set,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lists__empty,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lexord__Nil__left,axiom,
% 179.72/179.55 ! [V_r_2,V_y_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.55 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile__eq__filter,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.55 ( ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
% 179.72/179.55 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 179.72/179.55 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lexord__irreflexive,axiom,
% 179.72/179.55 ! [V_y_2,V_r_2,T_b] :
% 179.72/179.55 ( ! [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))
% 179.72/179.55 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lexord__linear,axiom,
% 179.72/179.55 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 179.72/179.55 ( ! [B_a,B_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 | B_a = B_b
% 179.72/179.55 | 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)) )
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.55 | V_x_2 = V_y_2
% 179.72/179.55 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lists_Osimps,axiom,
% 179.72/179.55 ! [V_A_2,V_a_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 179.72/179.55 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 179.72/179.55 | ? [B_a,B_l] :
% 179.72/179.55 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 179.72/179.55 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 179.72/179.55 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 179.72/179.55 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 179.72/179.55 ( ! [B_i] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 179.72/179.55 => ( ( 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)))
% 179.72/179.55 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 179.72/179.55 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__size__pointwise,axiom,
% 179.72/179.55 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 179.72/179.55 ( ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_butlast__take,axiom,
% 179.72/179.55 ! [V_xs,T_a,V_n] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__butlast,axiom,
% 179.72/179.55 ! [T_a,V_xs] :
% 179.72/179.55 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.55 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_butlast_Osimps_I2_J,axiom,
% 179.72/179.55 ! [V_x,T_a,V_xs] :
% 179.72/179.55 ( ( V_xs = c_List_Olist_ONil(T_a)
% 179.72/179.55 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 179.72/179.55 & ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_butlast_Osimps_I1_J,axiom,
% 179.72/179.55 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_map__butlast,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_in__set__butlastD,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_drop__butlast,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_butlast__drop,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_butlast__append,axiom,
% 179.72/179.55 ! [V_xs,T_a,V_ys] :
% 179.72/179.55 ( ( V_ys = c_List_Olist_ONil(T_a)
% 179.72/179.55 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 179.72/179.55 & ( V_ys != c_List_Olist_ONil(T_a)
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted__butlast,axiom,
% 179.72/179.55 ! [V_xs,T_a] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_a)
% 179.72/179.55 => ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 179.72/179.55 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_in__set__butlast__appendI,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 179.72/179.55 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 179.72/179.55 => 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))))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_butlast__snoc,axiom,
% 179.72/179.55 ! [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 ).
% 179.72/179.55
% 179.72/179.55 fof(fact_take__butlast,axiom,
% 179.72/179.55 ! [V_xs,T_a,V_n] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__butlast,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_butlast__conv__take,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_butlast__list__update,axiom,
% 179.72/179.55 ! [V_x,V_xs,T_a,V_k] :
% 179.72/179.55 ( ( 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))
% 179.72/179.55 => 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) )
% 179.72/179.55 & ( 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))
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_append__butlast__last__id,axiom,
% 179.72/179.55 ! [T_a,V_xs] :
% 179.72/179.55 ( V_xs != c_List_Olist_ONil(T_a)
% 179.72/179.55 => 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 ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_snoc__eq__iff__butlast,axiom,
% 179.72/179.55 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 179.72/179.55 ( 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
% 179.72/179.55 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 179.72/179.55 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 179.72/179.55 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_takeWhile__not__last,axiom,
% 179.72/179.55 ! [T_b,V_xs_2] :
% 179.72/179.55 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 179.72/179.55 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_length__takeWhile__less__P__nth,axiom,
% 179.72/179.55 ! [V_xs_2,T_b,V_P_2,V_j_2] :
% 179.72/179.55 ( ! [B_i] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 179.72/179.55 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => 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_P_2,V_xs_2)))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INFI__set__fold,axiom,
% 179.72/179.55 ! [V_f_2,V_xs_2,T_c,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__D,axiom,
% 179.72/179.55 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__E,axiom,
% 179.72/179.55 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 179.72/179.55 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF1__D,axiom,
% 179.72/179.55 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF1__E,axiom,
% 179.72/179.55 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 179.72/179.55 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF2__D,axiom,
% 179.72/179.55 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF2__E,axiom,
% 179.72/179.55 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 179.72/179.55 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_finite__INT,axiom,
% 179.72/179.55 ! [V_A_2,T_c,V_I_2,T_b] :
% 179.72/179.55 ( ? [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 179.72/179.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_vimage__INT,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Compl__UN,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Compl__INT,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_UN__extend__simps_I7_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_UN__simps_I7_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__extend__simps_I9_J,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__simps_I9_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Collect__ball__eq,axiom,
% 179.72/179.55 ! [V_P_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_P_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_P_2))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INFI__bool__eq,axiom,
% 179.72/179.55 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__absorb,axiom,
% 179.72/179.55 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__Int__distrib,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__Un,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__empty,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__constant,axiom,
% 179.72/179.55 ! [V_ca_2,T_c,T_b,V_A_2] :
% 179.72/179.55 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) )
% 179.72/179.55 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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 ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__extend__simps_I1_J,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.72/179.55 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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 )
% 179.72/179.55 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__extend__simps_I2_J,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.72/179.55 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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 )
% 179.72/179.55 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__insert,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF__const,axiom,
% 179.72/179.55 ! [V_M_2,T_b,V_A_2,T_c] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 179.72/179.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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 ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__extend__simps_I5_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__simps_I5_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__simps_I8_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__extend__simps_I8_J,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__simps_I7_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__simps_I6_J,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__extend__simps_I7_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Un__INT__distrib,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__extend__simps_I6_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Un__INT__distrib2,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INFI__apply,axiom,
% 179.72/179.55 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF__commute,axiom,
% 179.72/179.55 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Pow__INT__eq,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b] :
% 179.72/179.55 ( 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)
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.72/179.55 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_b,T_c] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.72/179.55 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF__less__iff,axiom,
% 179.72/179.55 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 179.72/179.55 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 & class_Orderings_Olinorder(T_b) )
% 179.72/179.55 => ( 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))
% 179.72/179.55 <=> ? [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.72/179.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__iff,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF__INT__eq,axiom,
% 179.72/179.55 ! [V_x_2,V_r_2,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__insert__distrib,axiom,
% 179.72/179.55 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF__INT__eq2,axiom,
% 179.72/179.55 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__extend__simps_I10_J,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__simps_I10_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Image__INT__subset,axiom,
% 179.72/179.55 ! [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)))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__lower,axiom,
% 179.72/179.55 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_le__INF__iff,axiom,
% 179.72/179.55 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => ( 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)))
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__subset__iff,axiom,
% 179.72/179.55 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF__subset,axiom,
% 179.72/179.55 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INTER__def,axiom,
% 179.72/179.55 ! [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)))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__simps_I2_J,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.72/179.55 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) )
% 179.72/179.55 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__simps_I1_J,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.72/179.55 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) )
% 179.72/179.55 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__simps_I3_J,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.72/179.55 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) )
% 179.72/179.55 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__extend__simps_I3_J,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.72/179.55 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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) )
% 179.72/179.55 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__extend__simps_I4_J,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.72/179.55 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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 )
% 179.72/179.55 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_bij__image__INT,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF__leI,axiom,
% 179.72/179.55 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__greaterThan__UNIV,axiom,
% 179.72/179.55 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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INT__simps_I4_J,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 179.72/179.55 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) )
% 179.72/179.55 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_nth__take__lemma,axiom,
% 179.72/179.55 ! [V_ys,V_xs,T_a,V_k] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => ( ! [B_i] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 179.72/179.55 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 179.72/179.55 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lists__IntI,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listsp_ONil,axiom,
% 179.72/179.55 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF2__iff,axiom,
% 179.72/179.55 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INF1__iff,axiom,
% 179.72/179.55 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listsp_Oequations_I1_J,axiom,
% 179.72/179.55 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listsp__conj__eq,axiom,
% 179.72/179.55 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 179.72/179.55 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listsp_Oequations_I2_J,axiom,
% 179.72/179.55 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 179.72/179.55 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 179.72/179.55 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_append__in__listsp__conv,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 179.72/179.55 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 179.72/179.55 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listsp__infI,axiom,
% 179.72/179.55 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 179.72/179.55 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listsp__inf__eq,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_in__listsp__conv__set,axiom,
% 179.72/179.55 ! [V_xs_2,V_A_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listsp__mono,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_listsp__lists__eq,axiom,
% 179.72/179.55 ! [V_x_2,V_A_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lists__Int__eq,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_image__INT,axiom,
% 179.72/179.55 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 179.72/179.55 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 179.72/179.55 => ( ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 179.72/179.55 => 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)) )
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 179.72/179.55 => 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)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inf__Sup,axiom,
% 179.72/179.55 ! [V_A_2,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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))))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_finite__Inter,axiom,
% 179.72/179.55 ! [V_M_2,T_b] :
% 179.72/179.55 ( ? [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 179.72/179.55 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 179.72/179.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_InterE,axiom,
% 179.72/179.55 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_InterD,axiom,
% 179.72/179.55 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inter__def,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inter__UNIV,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inter__empty,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inter__eq,axiom,
% 179.72/179.55 ! [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)))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inf__less__iff,axiom,
% 179.72/179.55 ! [V_a_2,V_S_2,T_b] :
% 179.72/179.55 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 & class_Orderings_Olinorder(T_b) )
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 179.72/179.55 <=> ? [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 179.72/179.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inter__insert,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_le__Inf__iff,axiom,
% 179.72/179.55 ! [V_A_2,V_b_2,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => ( 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)))
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inter__lower,axiom,
% 179.72/179.55 ! [V_A_2,V_B_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inter__anti__mono,axiom,
% 179.72/179.55 ! [V_A_2,V_B_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inf__lower,axiom,
% 179.72/179.55 ! [V_A_2,V_x_2,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inter__Un__distrib,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inf__singleton,axiom,
% 179.72/179.55 ! [V_a_2,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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 ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inf__empty,axiom,
% 179.72/179.55 ! [T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inf__UNIV,axiom,
% 179.72/179.55 ! [T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inf__insert,axiom,
% 179.72/179.55 ! [V_A_2,V_a_2,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_INTER__eq__Inter__image,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inter__image__eq,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Un__Inter,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Int__eq__Inter,axiom,
% 179.72/179.55 ! [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))))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Int__Inter__image,axiom,
% 179.72/179.55 ! [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))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inter__Un__subset,axiom,
% 179.72/179.55 ! [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)))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inf__binary,axiom,
% 179.72/179.55 ! [V_b_2,V_a_2,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inf__fin__Inf,axiom,
% 179.72/179.55 ! [V_A_2,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.55 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Inf__set__fold,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Sup__Inf,axiom,
% 179.72/179.55 ! [V_A_2,T_b] :
% 179.72/179.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.55 => 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)))))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__def,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 179.72/179.55 <=> ( 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)
% 179.72/179.55 & ! [B_x] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_sorted_Osimps,axiom,
% 179.72/179.55 ! [V_a_2,T_b] :
% 179.72/179.55 ( class_Orderings_Olinorder(T_b)
% 179.72/179.55 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 179.72/179.55 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 179.72/179.55 | ? [B_xs,B_x] :
% 179.72/179.55 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 179.72/179.55 & ! [B_xa] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 179.72/179.55 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__rev,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
% 179.72/179.55 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__rev1,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 179.72/179.55 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__takeI,axiom,
% 179.72/179.55 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 179.72/179.55 => c_List_Olist__all2(T_b,T_c,V_P_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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__Nil2,axiom,
% 179.72/179.55 ! [V_xs_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c))
% 179.72/179.55 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__Nil,axiom,
% 179.72/179.55 ! [V_ys_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2)
% 179.72/179.55 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__eq,axiom,
% 179.72/179.55 ! [T_b,V_ys_2,V_xs_2] :
% 179.72/179.55 ( V_xs_2 = V_ys_2
% 179.72/179.55 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__lengthD,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__Cons,axiom,
% 179.72/179.55 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_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))
% 179.72/179.55 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 179.72/179.55 & c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__appendI,axiom,
% 179.72/179.55 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
% 179.72/179.55 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_ca_2,V_d_2)
% 179.72/179.55 => c_List_Olist__all2(T_b,T_c,V_P_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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__append,axiom,
% 179.72/179.55 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.55 ( 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)
% 179.72/179.55 => ( c_List_Olist__all2(T_b,T_c,V_P_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))
% 179.72/179.55 <=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 179.72/179.55 & c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__map2,axiom,
% 179.72/179.55 ! [V_bs_2,V_f_2,T_d,V_as_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
% 179.72/179.55 <=> 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_P_2)),V_f_2),V_as_2,V_bs_2) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__map1,axiom,
% 179.72/179.55 ! [V_bs_2,V_as_2,V_f_2,T_d,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
% 179.72/179.55 <=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_P_2),V_f_2),V_as_2,V_bs_2) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__dropI,axiom,
% 179.72/179.55 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,V_bs_2)
% 179.72/179.55 => c_List_Olist__all2(T_b,T_c,V_P_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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__conv__all__nth,axiom,
% 179.72/179.55 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 179.72/179.55 <=> ( 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)
% 179.72/179.55 & ! [B_i] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => hBOOL(hAPP(hAPP(V_P_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))) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__nthD,axiom,
% 179.72/179.55 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => hBOOL(hAPP(hAPP(V_P_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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__nthD2,axiom,
% 179.72/179.55 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => hBOOL(hAPP(hAPP(V_P_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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__update__cong,axiom,
% 179.72/179.55 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_c,V_xs_2,T_b,V_i_2] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 179.72/179.55 => c_List_Olist__all2(T_b,T_c,V_P_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)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2__update__cong2,axiom,
% 179.72/179.55 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 179.72/179.55 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => c_List_Olist__all2(T_b,T_c,V_P_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)) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_list__all2I,axiom,
% 179.72/179.55 ! [V_P_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.55 ( ! [B_x] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
% 179.72/179.55 => ( 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)
% 179.72/179.55 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_SigmaE,axiom,
% 179.72/179.55 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ~ ! [B_x] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.55 => ! [B_y] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 179.72/179.55 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_not__in__set__insert,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => 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) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_List_Oinsert__def,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 179.72/179.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => 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) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__insert,axiom,
% 179.72/179.55 ! [V_x,V_xs,T_a] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 179.72/179.55 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_insert__remdups,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_in__set__insert,axiom,
% 179.72/179.55 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.55 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_List_Oset__insert,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_insert__Nil,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_maps__def,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_concat__map__maps,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_maps__simps_I2_J,axiom,
% 179.72/179.55 ! [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) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_maps__simps_I1_J,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_distinct__concat,axiom,
% 179.72/179.55 ! [V_xs_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 179.72/179.55 => ( ! [B_ys] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 179.72/179.55 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 179.72/179.55 => ( ! [B_ys] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 179.72/179.55 => ! [B_zs] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 179.72/179.55 => ( B_ys != B_zs
% 179.72/179.55 => 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)) ) ) )
% 179.72/179.55 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_accp__acc__eq,axiom,
% 179.72/179.55 ! [V_x_2,V_r_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_Cons__acc__listrel1I,axiom,
% 179.72/179.55 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 179.72/179.55 => ( 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))))
% 179.72/179.55 => 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)))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_acc__subset,axiom,
% 179.72/179.55 ! [V_R2_2,V_R1_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lists__accI,axiom,
% 179.72/179.55 ! [V_r_2,V_xs_2,T_b] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => 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)))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_lists__accD,axiom,
% 179.72/179.55 ! [V_r_2,V_xs_2,T_b] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => 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)))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_acc_Osimps,axiom,
% 179.72/179.55 ! [V_r_2,V_a_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 179.72/179.55 <=> ! [B_x] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_acc__downward,axiom,
% 179.72/179.55 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 179.72/179.55 => ( 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))
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_measures__lesseq,axiom,
% 179.72/179.55 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => ( 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)))
% 179.72/179.55 => 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)))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rel__comp__def,axiom,
% 179.72/179.55 ! [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))))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rel__compI,axiom,
% 179.72/179.55 ! [V_s_2,V_ca_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => ( 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))
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rel__comp__UNION__distrib2,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rel__comp__UNION__distrib,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_union__comp__emptyR,axiom,
% 179.72/179.55 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => ( 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))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_union__comp__emptyL,axiom,
% 179.72/179.55 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => ( 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))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rel__comp__empty1,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rel__comp__empty2,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rel__comp__distrib2,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rel__comp__distrib,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_O__assoc,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rel__comp__mono,axiom,
% 179.72/179.55 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => ( 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))
% 179.72/179.55 => 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))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_rel__comp__subset__Sigma,axiom,
% 179.72/179.55 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 => ( 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))))
% 179.72/179.55 => 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)))) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_in__measures_I1_J,axiom,
% 179.72/179.55 ! [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))))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_measures__def,axiom,
% 179.72/179.55 ! [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)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_max__ext__compat,axiom,
% 179.72/179.55 ! [V_S_2,V_R_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_min__ext__compat,axiom,
% 179.72/179.55 ! [V_S_2,V_R_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_measures__less,axiom,
% 179.72/179.55 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 179.72/179.55 ( 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)))
% 179.72/179.55 => 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)))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_in__measures_I2_J,axiom,
% 179.72/179.55 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 179.72/179.55 ( 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))))
% 179.72/179.55 <=> ( 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)))
% 179.72/179.55 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 179.72/179.55 & 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))) ) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_pred__comp__rel__comp__eq,axiom,
% 179.72/179.55 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> 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))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_reduction__pairI,axiom,
% 179.72/179.55 ! [V_S_2,V_R_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_R_2)
% 179.72/179.55 => ( 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))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__less__than,axiom,
% 179.72/179.55 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_pred__comp_Ointros,axiom,
% 179.72/179.55 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 179.72/179.55 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
% 179.72/179.55 => 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__empty,axiom,
% 179.72/179.55 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__inv__image,axiom,
% 179.72/179.55 ! [V_f_2,T_c,V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__lex,axiom,
% 179.72/179.55 ! [V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__lex__prod,axiom,
% 179.72/179.55 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 179.72/179.55 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 179.72/179.55 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__lenlex,axiom,
% 179.72/179.55 ! [V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__measure,axiom,
% 179.72/179.55 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__acc__iff,axiom,
% 179.72/179.55 ! [V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_acc__wfD,axiom,
% 179.72/179.55 ! [V_x_2,V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__no__loop,axiom,
% 179.72/179.55 ! [V_R_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__union__merge,axiom,
% 179.72/179.55 ! [V_S_2,V_R_2,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__comp__self,axiom,
% 179.72/179.55 ! [V_R_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_R_2)
% 179.72/179.55 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__measures,axiom,
% 179.72/179.55 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__Int2,axiom,
% 179.72/179.55 ! [V_r_H_2,V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__Int1,axiom,
% 179.72/179.55 ! [V_r_H_2,V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__subset,axiom,
% 179.72/179.55 ! [V_p_2,V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => ( 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))
% 179.72/179.55 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__lexn,axiom,
% 179.72/179.55 ! [V_n_2,V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__not__refl,axiom,
% 179.72/179.55 ! [V_a_2,V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => ~ 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__not__sym,axiom,
% 179.72/179.55 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => ( 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))
% 179.72/179.55 => ~ 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__asym,axiom,
% 179.72/179.55 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => ( 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))
% 179.72/179.55 => ~ 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)) ) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__irrefl,axiom,
% 179.72/179.55 ! [V_a_2,V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => ~ 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)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__int__ge__less__than,axiom,
% 179.72/179.55 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__int__ge__less__than2,axiom,
% 179.72/179.55 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_max__ext__wf,axiom,
% 179.72/179.55 ! [V_r_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.55 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__pair__less,axiom,
% 179.72/179.55 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_wf__mlex,axiom,
% 179.72/179.55 ! [V_f_2,V_R_2,T_b] :
% 179.72/179.55 ( c_Wellfounded_Owf(T_b,V_R_2)
% 179.72/179.55 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 179.72/179.55
% 179.72/179.55 fof(fact_pred__comp_Oequations,axiom,
% 179.72/179.55 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 179.72/179.55 ( 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))
% 179.72/179.55 <=> ? [B_b] :
% 179.72/179.55 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 179.72/179.55 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__finite__psubset,axiom,
% 179.72/179.56 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_min__ext__wf,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.56 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__less,axiom,
% 179.72/179.56 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)))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.56 <=> ~ ? [B_f] :
% 179.72/179.56 ! [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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wfE__pf,axiom,
% 179.72/179.56 ! [V_A_2,V_R_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,V_R_2)
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__union__compatible,axiom,
% 179.72/179.56 ! [V_S_2,V_R_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,V_R_2)
% 179.72/179.56 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 179.72/179.56 => ( 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))
% 179.72/179.56 => 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)) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf,axiom,
% 179.72/179.56 ! [T_b] :
% 179.72/179.56 ( class_Orderings_Owellorder(T_b)
% 179.72/179.56 => 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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_reduction__pair__def,axiom,
% 179.72/179.56 ! [V_P_2,T_b] :
% 179.72/179.56 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 179.72/179.56 <=> ( 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_P_2))
% 179.72/179.56 & 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_P_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_P_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_P_2))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_reduction__pair__lemma,axiom,
% 179.72/179.56 ! [V_S_2,V_R_2,V_P_2,T_b] :
% 179.72/179.56 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 179.72/179.56 => ( 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_P_2)))
% 179.72/179.56 => ( 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_P_2)))
% 179.72/179.56 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 179.72/179.56 => 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)) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__map__pair__image,axiom,
% 179.72/179.56 ! [V_f_2,T_c,V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.56 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__if__measure,axiom,
% 179.72/179.56 ! [T_b,V_g_2,V_f_2,V_P_2] :
% 179.72/179.56 ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(V_P_2,B_x))
% 179.72/179.56 => 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))) )
% 179.72/179.56 => 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_P_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))))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_max__extp_Oequations,axiom,
% 179.72/179.56 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 179.72/179.56 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 179.72/179.56 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 179.72/179.56 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.56 & ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 179.72/179.56 => ? [B_xa] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 179.72/179.56 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pred__nat__def,axiom,
% 179.72/179.56 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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__same__fst,axiom,
% 179.72/179.56 ! [T_b,V_R_2,T_c,V_P_2] :
% 179.72/179.56 ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(V_P_2,B_x))
% 179.72/179.56 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 179.72/179.56 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__pred__nat,axiom,
% 179.72/179.56 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_max__ext_Ointros,axiom,
% 179.72/179.56 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 179.72/179.56 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 179.72/179.56 => ? [B_xa] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 179.72/179.56 & 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)) ) )
% 179.72/179.56 => 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))) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Oone__frac__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Ofrac__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_inj__on__Inter,axiom,
% 179.72/179.56 ! [V_f_2,T_c,T_b,V_S_2] :
% 179.72/179.56 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 179.72/179.56 => ( ! [B_A] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 179.72/179.56 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__Collect__split,axiom,
% 179.72/179.56 ! [V_P_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_P_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_P_2))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Inter__subset,axiom,
% 179.72/179.56 ! [V_B_2,V_A_2,T_b] :
% 179.72/179.56 ( ! [B_X] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 179.72/179.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_RangeI,axiom,
% 179.72/179.56 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_snd__eq__Range,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__Id__on,axiom,
% 179.72/179.56 ! [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 ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__Union,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_finite__Range,axiom,
% 179.72/179.56 ! [V_r_2,T_c,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 179.72/179.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__Un__eq,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__empty,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__empty__iff,axiom,
% 179.72/179.56 ! [V_r_2,T_b,T_c] :
% 179.72/179.56 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.56 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__iff,axiom,
% 179.72/179.56 ! [V_r_2,T_c,V_a_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 179.72/179.56 <=> ? [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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__insert,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__Int__subset,axiom,
% 179.72/179.56 ! [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)))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__Diff__subset,axiom,
% 179.72/179.56 ! [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)))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_RangeP__Range__eq,axiom,
% 179.72/179.56 ! [V_x_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_RangeE,axiom,
% 179.72/179.56 ! [V_r_2,T_c,V_b_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 179.72/179.56 => ~ ! [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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_RangeP_Ointros,axiom,
% 179.72/179.56 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 179.72/179.56 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_RangeP_Oequations,axiom,
% 179.72/179.56 ! [V_a2_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 179.72/179.56 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__Un,axiom,
% 179.72/179.56 ! [V_s_2,V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.56 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 179.72/179.56 => ( 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))
% 179.72/179.56 => 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)) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_foldl__apply,axiom,
% 179.72/179.56 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 179.72/179.56 ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 => 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)) )
% 179.72/179.56 => 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_DomainI,axiom,
% 179.72/179.56 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fst__eq__Domain,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_finite__Domain,axiom,
% 179.72/179.56 ! [V_r_2,T_c,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 179.72/179.56 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__Id__on,axiom,
% 179.72/179.56 ! [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 ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__empty,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__empty__iff,axiom,
% 179.72/179.56 ! [V_r_2,T_c,T_b] :
% 179.72/179.56 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.56 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__Un__eq,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__mono,axiom,
% 179.72/179.56 ! [V_s_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__iff,axiom,
% 179.72/179.56 ! [V_r_2,T_c,V_a_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 179.72/179.56 <=> ? [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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__insert,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__Int__subset,axiom,
% 179.72/179.56 ! [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)))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__Diff__subset,axiom,
% 179.72/179.56 ! [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)))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Field__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__Union,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__Collect__split,axiom,
% 179.72/179.56 ! [V_P_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_P_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_P_2)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_DomainP__Domain__eq,axiom,
% 179.72/179.56 ! [V_x_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_DomainE,axiom,
% 179.72/179.56 ! [V_r_2,T_c,V_a_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 179.72/179.56 => ~ ! [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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_DomainP_Ointros,axiom,
% 179.72/179.56 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 179.72/179.56 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_DomainP_Oequations,axiom,
% 179.72/179.56 ! [V_a1_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 179.72/179.56 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wfP__def,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 179.72/179.56 <=> 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Rep__Integ__cases,axiom,
% 179.72/179.56 ! [V_y_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 179.72/179.56 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wfP__empty,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_accp__wfPD,axiom,
% 179.72/179.56 ! [V_x_2,V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 179.72/179.56 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wfP__accp__iff,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 179.72/179.56 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wfP__subset,axiom,
% 179.72/179.56 ! [V_p_2,V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 179.72/179.56 => ( 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))
% 179.72/179.56 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__in__rel,axiom,
% 179.72/179.56 ! [V_R_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,V_R_2)
% 179.72/179.56 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wfP__wf__eq,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wfP__acyclicP,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Rep__Integ__induct,axiom,
% 179.72/179.56 ! [V_P_2,V_y_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 179.72/179.56 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 179.72/179.56 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_acyclic__subset,axiom,
% 179.72/179.56 ! [V_r_2,V_s_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 179.72/179.56 => ( 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))
% 179.72/179.56 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__acyclic,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.56 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 179.72/179.56 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.56 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_finite__acyclic__wf,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 179.72/179.56 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 179.72/179.56 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Owf_H__def,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 179.72/179.56 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 179.72/179.56 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 179.72/179.56 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_inj__on__INTER,axiom,
% 179.72/179.56 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 179.72/179.56 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.56 => ( ! [B_i] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 179.72/179.56 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_zip__obtain__same__length,axiom,
% 179.72/179.56 ! [V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 179.72/179.56 ( ( 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))
% 179.72/179.56 => hBOOL(hAPP(V_P_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)))) )
% 179.72/179.56 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_map__of__eqI,axiom,
% 179.72/179.56 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 179.72/179.56 ( hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2)) = hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_ys_2))
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_xs_2))))
% 179.72/179.56 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2),B_x) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2),B_x) )
% 179.72/179.56 => hAPP(c_Map_Omap__of(T_b,T_c),V_xs_2) = hAPP(c_Map_Omap__of(T_b,T_c),V_ys_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Abs__Integ__induct,axiom,
% 179.72/179.56 ! [V_x_2,V_P_2] :
% 179.72/179.56 ( ! [B_y] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 179.72/179.56 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 179.72/179.56 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Abs__Integ__cases,axiom,
% 179.72/179.56 ! [V_x_2] :
% 179.72/179.56 ~ ! [B_y] :
% 179.72/179.56 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 179.72/179.56 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wfP__SUP,axiom,
% 179.72/179.56 ! [T_b,V_r_2,T_c] :
% 179.72/179.56 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 179.72/179.56 => ( ! [B_i,B_j] :
% 179.72/179.56 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 179.72/179.56 => 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)) )
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_dropWhile__append2,axiom,
% 179.72/179.56 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 179.72/179.56 ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 => hBOOL(hAPP(V_P_2,B_x)) )
% 179.72/179.56 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_P_2,V_ys_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__all2__all__nthI,axiom,
% 179.72/179.56 ! [V_P_2,V_b_2,T_c,V_a_2,T_b] :
% 179.72/179.56 ( 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)
% 179.72/179.56 => ( ! [B_n] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => hBOOL(hAPP(hAPP(V_P_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))) )
% 179.72/179.56 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_mem__splitI2,axiom,
% 179.72/179.56 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 179.72/179.56 ( ! [B_a,B_b] :
% 179.72/179.56 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_mem__splitE,axiom,
% 179.72/179.56 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ~ ! [B_x,B_y] :
% 179.72/179.56 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 179.72/179.56 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_finite__sorted__distinct__unique,axiom,
% 179.72/179.56 ! [V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ? [B_x] :
% 179.72/179.56 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 179.72/179.56 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 179.72/179.56 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 179.72/179.56 & ! [B_y] :
% 179.72/179.56 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 179.72/179.56 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 179.72/179.56 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 179.72/179.56 => B_y = B_x ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_takeWhile__append2,axiom,
% 179.72/179.56 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 179.72/179.56 ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 => hBOOL(hAPP(V_P_2,B_x)) )
% 179.72/179.56 => c_List_OtakeWhile(T_b,V_P_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_P_2,V_ys_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_insort__is__Cons,axiom,
% 179.72/179.56 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_c)
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wfI__pf,axiom,
% 179.72/179.56 ! [V_R_2,T_b] :
% 179.72/179.56 ( ! [B_A] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 179.72/179.56 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Cons__eq__filter__iff,axiom,
% 179.72/179.56 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 179.72/179.56 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)
% 179.72/179.56 <=> ? [B_us,B_vs] :
% 179.72/179.56 ( 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))
% 179.72/179.56 & ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 179.72/179.56 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 179.72/179.56 & hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.56 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_filter__eq__Cons__iff,axiom,
% 179.72/179.56 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_b] :
% 179.72/179.56 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 179.72/179.56 <=> ? [B_us,B_vs] :
% 179.72/179.56 ( 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))
% 179.72/179.56 & ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 179.72/179.56 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 179.72/179.56 & hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.56 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Sigma__mono,axiom,
% 179.72/179.56 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.56 => 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))) )
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_not__acc__down,axiom,
% 179.72/179.56 ! [V_R_2,V_x_2,T_b] :
% 179.72/179.56 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 179.72/179.56 => ~ ! [B_z] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_acc_OaccI,axiom,
% 179.72/179.56 ! [V_r_2,V_x_2,T_b] :
% 179.72/179.56 ( ! [B_y] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__ball__nth,axiom,
% 179.72/179.56 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 => hBOOL(hAPP(V_P_2,B_x)) )
% 179.72/179.56 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_max__ext_Osimps,axiom,
% 179.72/179.56 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 179.72/179.56 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 179.72/179.56 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 179.72/179.56 & ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 179.72/179.56 => ? [B_xa] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 179.72/179.56 & 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)) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_sorted_OCons,axiom,
% 179.72/179.56 ! [V_x_2,V_xs_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 179.72/179.56 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 179.72/179.56 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_InterI,axiom,
% 179.72/179.56 ! [V_A_2,V_C_2,T_b] :
% 179.72/179.56 ( ! [B_X] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__no__infinite__down__chainE,axiom,
% 179.72/179.56 ! [V_f_2,V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.56 => ~ ! [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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__ex__length,axiom,
% 179.72/179.56 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 179.72/179.56 <=> ? [B_n] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__ex__simps_I1_J,axiom,
% 179.72/179.56 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 179.72/179.56 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.56 | c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__ex__rev,axiom,
% 179.72/179.56 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 179.72/179.56 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__ex__append,axiom,
% 179.72/179.56 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 179.72/179.56 <=> ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 179.72/179.56 | c_List_Olist__ex(T_b,V_P_2,V_ys_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__ex__iff,axiom,
% 179.72/179.56 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 179.72/179.56 <=> ? [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__ex__simps_I2_J,axiom,
% 179.72/179.56 ! [V_P_2,T_b] : ~ c_List_Olist__ex(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_setsum__reindex__cong,axiom,
% 179.72/179.56 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 179.72/179.56 ( class_Groups_Ocomm__monoid__add(T_d)
% 179.72/179.56 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 179.72/179.56 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 179.72/179.56 => ( ! [B_a] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 179.72/179.56 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 179.72/179.56 => 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) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_scomp__unfold,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_scomp__scomp,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Pair__scomp,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_scomp__Pair,axiom,
% 179.72/179.56 ! [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 ).
% 179.72/179.56
% 179.72/179.56 fof(fact_scomp__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_scomp__apply,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_iterate_Osimps,axiom,
% 179.72/179.56 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 179.72/179.56 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.56 => 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) )
% 179.72/179.56 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_setsum__ivl__cong,axiom,
% 179.72/179.56 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_b,T_c] :
% 179.72/179.56 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 179.72/179.56 & class_Orderings_Oord(T_b) )
% 179.72/179.56 => ( V_a_2 = V_ca_2
% 179.72/179.56 => ( V_b_2 = V_d_2
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 179.72/179.56 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 179.72/179.56 => 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)) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_log_Osimps,axiom,
% 179.72/179.56 ! [V_i,V_b] :
% 179.72/179.56 ( ( ( 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)))
% 179.72/179.56 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 179.72/179.56 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 179.72/179.56 & ( ~ ( 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)))
% 179.72/179.56 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_minus__shift__def,axiom,
% 179.72/179.56 ! [V_r,V_l,V_k] :
% 179.72/179.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 179.72/179.56 => 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) )
% 179.72/179.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_inc__shift__def,axiom,
% 179.72/179.56 ! [V_k,V_v] :
% 179.72/179.56 ( ( V_v = V_k
% 179.72/179.56 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 179.72/179.56 & ( V_v != V_k
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_select,axiom,
% 179.72/179.56 ! [V_s_2,T_b,V_xs_2] :
% 179.72/179.56 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_select__weight__member,axiom,
% 179.72/179.56 ! [V_s_2,V_xs_2,T_b] :
% 179.72/179.56 ( 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))))
% 179.72/179.56 => 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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_select__weigth__select,axiom,
% 179.72/179.56 ! [T_b,V_xs_2] :
% 179.72/179.56 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 179.72/179.56 => 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) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_select__weight__cons__zero,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_select__weigth__drop__zero,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pick__member,axiom,
% 179.72/179.56 ! [V_xs_2,T_b,V_i_2] :
% 179.72/179.56 ( 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))))
% 179.72/179.56 => 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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pick_Osimps,axiom,
% 179.72/179.56 ! [V_xs,V_x,T_a,V_i] :
% 179.72/179.56 ( ( 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)))
% 179.72/179.56 => 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) )
% 179.72/179.56 & ( ~ 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)))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pick__drop__zero,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_select__weight__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pick__same,axiom,
% 179.72/179.56 ! [V_xs_2,T_b,V_l_2] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => 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) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_number__of__code__numeral__def,axiom,
% 179.72/179.56 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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_zero__code__numeral__def,axiom,
% 179.72/179.56 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 179.72/179.56 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_times__code__numeral__code,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 179.72/179.56 ! [V_m_2,V_n_2] :
% 179.72/179.56 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 179.72/179.56 <=> V_n_2 = V_m_2 ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_one__code__numeral__def,axiom,
% 179.72/179.56 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 179.72/179.56 ! [V_y_2,V_x_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 179.72/179.56 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 179.72/179.56 <=> V_x_2 = V_y_2 ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_less__code__numeral__code,axiom,
% 179.72/179.56 ! [V_m_2,V_n_2] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_plus__code__numeral__code,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_less__eq__code__numeral__code,axiom,
% 179.72/179.56 ! [V_m_2,V_n_2] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_code__numeral__not__eq__zero,axiom,
% 179.72/179.56 ! [V_i_2] :
% 179.72/179.56 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 179.72/179.56 <=> 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_range,axiom,
% 179.72/179.56 ! [V_s,V_k] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_select__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_subtract__code__numeral__code,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_type__definition__code__numeral,axiom,
% 179.72/179.56 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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_times__code__numeral__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_nat__of__of__nat,axiom,
% 179.72/179.56 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 179.72/179.56
% 179.72/179.56 fof(fact_of__nat__nat__of,axiom,
% 179.72/179.56 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 179.72/179.56
% 179.72/179.56 fof(fact_nat__of__inverse,axiom,
% 179.72/179.56 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 179.72/179.56
% 179.72/179.56 fof(fact_less__code__numeral__def,axiom,
% 179.72/179.56 ! [V_m_2,V_n_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 179.72/179.56 <=> 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_int__of__def,axiom,
% 179.72/179.56 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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_nat__of__number,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_code__numeral_Onat__of__inject,axiom,
% 179.72/179.56 ! [V_y_2,V_x_2] :
% 179.72/179.56 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 179.72/179.56 <=> V_x_2 = V_y_2 ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 179.72/179.56 ! [V_l_2,V_k_2] :
% 179.72/179.56 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 179.72/179.56 <=> V_k_2 = V_l_2 ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_nat__of,axiom,
% 179.72/179.56 ! [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)))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_less__eq__code__numeral__def,axiom,
% 179.72/179.56 ! [V_m_2,V_n_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 179.72/179.56 <=> 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_nat__of__code,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_nat__of__aux__def,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Suc__code__numeral__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_minus__code__numeral__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_of__nat__inverse,axiom,
% 179.72/179.56 ! [V_y_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 179.72/179.56 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_plus__code__numeral__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_div__code__numeral__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_minus__code__numeral__code,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_subtract__code__numeral__def,axiom,
% 179.72/179.56 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_mod__code__numeral__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_code__numeral__decr,axiom,
% 179.72/179.56 ! [V_k] :
% 179.72/179.56 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_less__eq,axiom,
% 179.72/179.56 ! [V_n_2,V_m_2] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_less__than__def,axiom,
% 179.72/179.56 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__trancl,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.56 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_acyclic__def,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 179.72/179.56 <=> ! [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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl_Or__into__trancl,axiom,
% 179.72/179.56 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__subset__Field2,axiom,
% 179.72/179.56 ! [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))))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_r__into__trancl_H,axiom,
% 179.72/179.56 ! [V_r_2,V_p_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__empty,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__domain,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__range,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_finite__trancl,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 179.72/179.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__trans,axiom,
% 179.72/179.56 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 179.72/179.56 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( 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))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__into__trancl2,axiom,
% 179.72/179.56 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_r__r__into__trancl,axiom,
% 179.72/179.56 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ( 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))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__mono,axiom,
% 179.72/179.56 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 179.72/179.56 => ( 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))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__unfold,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__subset__Sigma,axiom,
% 179.72/179.56 ! [V_A_2,V_r_2,T_b] :
% 179.72/179.56 ( 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))))
% 179.72/179.56 => 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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__Int__subset,axiom,
% 179.72/179.56 ! [V_s_2,V_r_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ( 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))
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__insert,axiom,
% 179.72/179.56 ! [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)))))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_reflcl__set__eq,axiom,
% 179.72/179.56 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 <=> 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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_r__into__rtrancl,axiom,
% 179.72/179.56 ! [V_r_2,V_p_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_IdI,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__into__rtrancl,axiom,
% 179.72/179.56 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_listrel__rtrancl__refl,axiom,
% 179.72/179.56 ! [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)))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__unfold__right,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__unfold__left,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_reflcl__trancl,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__reflcl,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__rtrancl__absorb,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__trancl__absorb,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__eq__or__trancl,axiom,
% 179.72/179.56 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 <=> ( V_x_2 = V_y_2
% 179.72/179.56 | ( V_x_2 != V_y_2
% 179.72/179.56 & 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))) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__into__trancl2,axiom,
% 179.72/179.56 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtranclD,axiom,
% 179.72/179.56 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( V_a_2 = V_b_2
% 179.72/179.56 | ( V_a_2 != V_b_2
% 179.72/179.56 & 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))) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__into__trancl1,axiom,
% 179.72/179.56 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( 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))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__rtrancl__trancl,axiom,
% 179.72/179.56 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__trancl__trancl,axiom,
% 179.72/179.56 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__trans,axiom,
% 179.72/179.56 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 179.72/179.56 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( 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))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 179.72/179.56 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__Int__subset,axiom,
% 179.72/179.56 ! [V_r_2,V_s_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ( 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))
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__subset__rtrancl,axiom,
% 179.72/179.56 ! [V_s_2,V_r_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__subset,axiom,
% 179.72/179.56 ! [V_S_2,V_R_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__mono,axiom,
% 179.72/179.56 ! [V_s_2,V_r_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__Un__subset,axiom,
% 179.72/179.56 ! [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)))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Image__closed__trancl,axiom,
% 179.72/179.56 ! [V_X_2,V_r_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_refl__rtrancl,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__idemp,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__r__diff__Id,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__empty,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__reflcl,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__Un__rtrancl,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__reflcl__absorb,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_in__rtrancl__UnI,axiom,
% 179.72/179.56 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 179.72/179.56 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 179.72/179.56 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 179.72/179.56 => 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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_r__comp__rtrancl__eq,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__idemp__self__comp,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__unfold,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__rtrancl,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__rtrancl,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__Id,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__Id,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Id__O__R,axiom,
% 179.72/179.56 ! [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 ).
% 179.72/179.56
% 179.72/179.56 fof(fact_R__O__Id,axiom,
% 179.72/179.56 ! [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 ).
% 179.72/179.56
% 179.72/179.56 fof(fact_refl__Id,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Image__Id,axiom,
% 179.72/179.56 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 179.72/179.56
% 179.72/179.56 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 179.72/179.56 ! [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)))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pair__in__Id__conv,axiom,
% 179.72/179.56 ! [V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 <=> V_a_2 = V_b_2 ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 179.72/179.56 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_listrel__rtrancl__trans,axiom,
% 179.72/179.56 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 179.72/179.56 ! [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)))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pair__leq__def,axiom,
% 179.72/179.56 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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Not__Domain__rtrancl,axiom,
% 179.72/179.56 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 179.72/179.56 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 <=> V_x_2 = V_y_2 ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_acc__downwards,axiom,
% 179.72/179.56 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_acc__downwards__aux,axiom,
% 179.72/179.56 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__insert,axiom,
% 179.72/179.56 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.56 & ~ 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 179.72/179.56 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 179.72/179.56 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 179.72/179.56 => 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) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_acyclic__insert,axiom,
% 179.72/179.56 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 179.72/179.56 & ~ 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 179.72/179.56 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 179.72/179.56 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_refl__reflcl,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Id__def,axiom,
% 179.72/179.56 ! [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))))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_irrefl__diff__Id,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pred__nat__trancl__eq__le,axiom,
% 179.72/179.56 ! [V_n_2,V_m_2] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__subset__Sigma__aux,axiom,
% 179.72/179.56 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( 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))))
% 179.72/179.56 => ( V_a_2 = V_b_2
% 179.72/179.56 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_irrefl__tranclI,axiom,
% 179.72/179.56 ! [V_x_2,V_r_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ~ 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_sequence__trans,axiom,
% 179.72/179.56 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 179.72/179.56 ( ! [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)))
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__converseD,axiom,
% 179.72/179.56 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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))))
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__converseI,axiom,
% 179.72/179.56 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => 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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__converse,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__Id,axiom,
% 179.72/179.56 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converseD,axiom,
% 179.72/179.56 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converseI,axiom,
% 179.72/179.56 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__iff,axiom,
% 179.72/179.56 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 <=> 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_in__listrel1__converse,axiom,
% 179.72/179.56 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_acyclic__converse,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 179.72/179.56 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__UNION,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__Int,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_refl__on__converse,axiom,
% 179.72/179.56 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.56 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 179.72/179.56 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Field__converse,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__converse,axiom,
% 179.72/179.56 ! [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 ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__Id__on,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_finite__converse,axiom,
% 179.72/179.56 ! [V_r_2,T_c,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 179.72/179.56 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_listrel1__converse,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__INTER,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__Un,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__inv__image,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_equiv__comp__eq,axiom,
% 179.72/179.56 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.56 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 179.72/179.56 => 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 ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__rel__comp,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Domain__converse,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Range__converse,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__converse__trancl,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 179.72/179.56 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__converse,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__converseI,axiom,
% 179.72/179.56 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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))))
% 179.72/179.56 => 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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__converseD,axiom,
% 179.72/179.56 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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))))
% 179.72/179.56 => 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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Image__subset__eq,axiom,
% 179.72/179.56 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 <=> 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))))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_refl__on__comp__subset,axiom,
% 179.72/179.56 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.56 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_comp__equivI,axiom,
% 179.72/179.56 ! [V_A_2,V_r_2,T_b] :
% 179.72/179.56 ( 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
% 179.72/179.56 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 179.72/179.56 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_finite__acyclic__wf__converse,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 179.72/179.56 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 179.72/179.56 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Image__INT__eq,axiom,
% 179.72/179.56 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 179.72/179.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_total__on__diff__Id,axiom,
% 179.72/179.56 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_single__valued__Id,axiom,
% 179.72/179.56 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_total__on__converse,axiom,
% 179.72/179.56 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.56 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 179.72/179.56 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_single__valued__rel__comp,axiom,
% 179.72/179.56 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 179.72/179.56 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 179.72/179.56 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_total__on__empty,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_single__valued__Id__on,axiom,
% 179.72/179.56 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_single__valued__subset,axiom,
% 179.72/179.56 ! [V_s_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 179.72/179.56 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_single__valued__def,axiom,
% 179.72/179.56 ! [V_r_2,T_c,T_b] :
% 179.72/179.56 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 179.72/179.56 <=> ! [B_x,B_y] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ! [B_z] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => B_y = B_z ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_single__valuedD,axiom,
% 179.72/179.56 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 179.72/179.56 => ( 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))
% 179.72/179.56 => ( 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))
% 179.72/179.56 => V_y_2 = V_z_2 ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_total__on__def,axiom,
% 179.72/179.56 ! [V_r_2,V_A_2,T_b] :
% 179.72/179.56 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 179.72/179.56 <=> ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.56 => ! [B_xa] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 179.72/179.56 => ( B_x != B_xa
% 179.72/179.56 => ( 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))
% 179.72/179.56 | 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)) ) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_single__valued__confluent,axiom,
% 179.72/179.56 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 179.72/179.56 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 | 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))) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Image__Int__eq,axiom,
% 179.72/179.56 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 179.72/179.56 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 179.72/179.56 => 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 179.72/179.56 ! [V_R_2,V_p_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 179.72/179.56 => 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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_acyclicI,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( ! [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)))
% 179.72/179.56 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_single__valued__rel__pow,axiom,
% 179.72/179.56 ! [V_n_2,V_R_2,T_b] :
% 179.72/179.56 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 179.72/179.56 => 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__0__E,axiom,
% 179.72/179.56 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => V_x_2 = V_y_2 ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__0__I,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_comp__funpow,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__exp,axiom,
% 179.72/179.56 ! [V_R_2,V_n_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_funpow__swap1,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_funpow__mult,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__commute,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_relpow_Osimps_I2_J,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__1,axiom,
% 179.72/179.56 ! [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 ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__add,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_relpow_Osimps_I1_J,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__imp__rtrancl,axiom,
% 179.72/179.56 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__power,axiom,
% 179.72/179.56 ! [V_R_2,V_p_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 179.72/179.56 <=> ? [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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__Suc__I2,axiom,
% 179.72/179.56 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__Suc__I,axiom,
% 179.72/179.56 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( 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))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_funpow_Osimps_I2_J,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_funpow__add,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_funpow_Osimps_I1_J,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_trancl__power,axiom,
% 179.72/179.56 ! [V_R_2,V_p_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 179.72/179.56 <=> ? [B_n] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 179.72/179.56 & 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_funpow__code__def,axiom,
% 179.72/179.56 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__E2,axiom,
% 179.72/179.56 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.56 => V_x_2 != V_z_2 )
% 179.72/179.56 => ~ ! [B_y,B_m] :
% 179.72/179.56 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 179.72/179.56 => ( 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))
% 179.72/179.56 => ~ 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))) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rotate__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__E,axiom,
% 179.72/179.56 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.56 => V_x_2 != V_z_2 )
% 179.72/179.56 => ~ ! [B_y,B_m] :
% 179.72/179.56 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 179.72/179.56 => ( 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)))
% 179.72/179.56 => ~ 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)) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pos__not__random__dseq__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 179.72/179.56 ! [V_Qa_2,V_P_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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_P_2),V_Qa_2))))
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( 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_P_2)))
% 179.72/179.56 => ! [B_y] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => B_y = B_x ) )
% 179.72/179.56 => 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_P_2))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rtrancl__Un__separatorE,axiom,
% 179.72/179.56 ! [V_Qa_2,V_P_2,V_b_2,V_a_2,T_b] :
% 179.72/179.56 ( 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_P_2),V_Qa_2))))
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( 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_P_2)))
% 179.72/179.56 => ! [B_y] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => B_x = B_y ) )
% 179.72/179.56 => 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_P_2))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__Suc__D2,axiom,
% 179.72/179.56 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ? [B_y] :
% 179.72/179.56 ( 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))
% 179.72/179.56 & 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__Suc__E2,axiom,
% 179.72/179.56 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ~ ! [B_y] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ~ 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__pow__Suc__E,axiom,
% 179.72/179.56 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ~ ! [B_y] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ~ 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_tranclD2,axiom,
% 179.72/179.56 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ? [B_z] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 & 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_tranclD,axiom,
% 179.72/179.56 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ? [B_z] :
% 179.72/179.56 ( 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))
% 179.72/179.56 & 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_IdE,axiom,
% 179.72/179.56 ! [V_p_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 179.72/179.56 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_nat__intermed__int__val,axiom,
% 179.72/179.56 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 179.72/179.56 ( ! [B_i] :
% 179.72/179.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 179.72/179.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 179.72/179.56 => 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))) )
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 179.72/179.56 => ? [B_i] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 179.72/179.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 179.72/179.56 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_in__set__conv__decomp,axiom,
% 179.72/179.56 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 <=> ? [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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_in__set__conv__decomp__first,axiom,
% 179.72/179.56 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 <=> ? [B_ys] :
% 179.72/179.56 ( ? [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))
% 179.72/179.56 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_in__set__conv__decomp__last,axiom,
% 179.72/179.56 ! [V_xs_2,V_x_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 <=> ? [B_ys,B_zs] :
% 179.72/179.56 ( 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))
% 179.72/179.56 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_mod__div__decomp,axiom,
% 179.72/179.56 ! [V_b,V_a,T_a] :
% 179.72/179.56 ( class_Divides_Osemiring__div(T_a)
% 179.72/179.56 => 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 179.72/179.56 ! [V_x_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.56 => 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) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_sup__Sup__fold__sup,axiom,
% 179.72/179.56 ! [V_B_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_union__fold__insert,axiom,
% 179.72/179.56 ! [V_B_2,V_A_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fold__sup__insert,axiom,
% 179.72/179.56 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Lattices_Osemilattice__sup(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 179.72/179.56 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 179.72/179.56 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fold__inf__insert,axiom,
% 179.72/179.56 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Lattices_Osemilattice__inf(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fold__empty,axiom,
% 179.72/179.56 ! [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 ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fold__image__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_folding_Oeq__fold,axiom,
% 179.72/179.56 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fold__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_min__max_Ofold__sup__insert,axiom,
% 179.72/179.56 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_min__max_Ofold__inf__insert,axiom,
% 179.72/179.56 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_inf__Inf__fold__inf,axiom,
% 179.72/179.56 ! [V_B_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_sup__SUPR__fold__sup,axiom,
% 179.72/179.56 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 179.72/179.56 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_inf__INFI__fold__inf,axiom,
% 179.72/179.56 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 179.72/179.56 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 179.72/179.56 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 179.72/179.56 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 179.72/179.56 => 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) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_sup__le__fold__sup,axiom,
% 179.72/179.56 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Lattices_Osemilattice__sup(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.56 => 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))) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fold__inf__le__inf,axiom,
% 179.72/179.56 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Lattices_Osemilattice__inf(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.56 => 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))) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 179.72/179.56 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.56 => 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))) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 179.72/179.56 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.56 => 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))) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Sup__fold__sup,axiom,
% 179.72/179.56 ! [V_A_2,T_b] :
% 179.72/179.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Inf__fold__inf,axiom,
% 179.72/179.56 ! [V_A_2,T_b] :
% 179.72/179.56 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fold1__eq__fold__idem,axiom,
% 179.72/179.56 ! [V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 179.72/179.56 ! [V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Lattices_Olattice(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 179.72/179.56 ! [V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Lattices_Olattice(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 179.72/179.56 ! [V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 179.72/179.56 ! [V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 179.72/179.56 ! [V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 179.72/179.56 ! [V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_minus__fold__remove,axiom,
% 179.72/179.56 ! [V_B_2,V_A_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_folding__one_Oeq__fold_H,axiom,
% 179.72/179.56 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.56 => 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) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_SUPR__fold__sup,axiom,
% 179.72/179.56 ! [V_f_2,V_A_2,T_b,T_c] :
% 179.72/179.56 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_INFI__fold__inf,axiom,
% 179.72/179.56 ! [V_f_2,V_A_2,T_b,T_c] :
% 179.72/179.56 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fold1__eq__fold,axiom,
% 179.72/179.56 ! [V_a_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Groups_Oab__semigroup__mult(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.56 => 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) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 179.72/179.56 ! [V_x_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Lattices_Olattice(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.56 => 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) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 179.72/179.56 ! [V_x_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Lattices_Olattice(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.56 => 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) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Min_Oeq__fold_H,axiom,
% 179.72/179.56 ! [V_x_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.56 => 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) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Max_Oeq__fold_H,axiom,
% 179.72/179.56 ! [V_x_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.56 => 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) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 179.72/179.56 ! [V_x_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.56 => 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) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 179.72/179.56 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.56 => 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)))))) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 179.72/179.56 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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)))))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 179.72/179.56 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm__insort,axiom,
% 179.72/179.56 ! [T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 179.72/179.56 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 179.72/179.56 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 179.72/179.56 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 179.72/179.56 => V_y_2 = V_x_2 ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm,axiom,
% 179.72/179.56 ! [T_b] :
% 179.72/179.56 ( class_Groups_Oab__semigroup__mult(T_b)
% 179.72/179.56 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 179.72/179.56 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 179.72/179.56 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 179.72/179.56 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 179.72/179.56 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 179.72/179.56 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.56 => 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) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 179.72/179.56 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.56 => 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)) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 179.72/179.56 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => 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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 179.72/179.56 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 179.72/179.56 => ? [B_y_H] :
% 179.72/179.56 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 179.72/179.56 & 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)) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 179.72/179.56 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 179.72/179.56 => ( 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))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 179.72/179.56 => ~ ! [B_y] :
% 179.72/179.56 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 179.72/179.56 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 179.72/179.56 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 179.72/179.56 => 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))) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 179.72/179.56 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Orderings_Olinorder(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 179.72/179.56 => 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))) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_inf__le__fold__inf,axiom,
% 179.72/179.56 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Lattices_Osemilattice__inf(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 179.72/179.56 => 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))) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_fold__sup__le__sup,axiom,
% 179.72/179.56 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 179.72/179.56 ( class_Lattices_Osemilattice__sup(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 179.72/179.56 => 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))) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_wf__eq__minimal,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( c_Wellfounded_Owf(T_b,V_r_2)
% 179.72/179.56 <=> ! [B_Q] :
% 179.72/179.56 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 179.72/179.56 => ? [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 179.72/179.56 & ! [B_y] :
% 179.72/179.56 ( 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))
% 179.72/179.56 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 179.72/179.56 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 179.72/179.56 => 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)) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 179.72/179.56 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.72/179.56 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 179.72/179.56 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 179.72/179.56 => 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) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 179.72/179.56 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 179.72/179.56 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 179.72/179.56 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 179.72/179.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 179.72/179.56 => 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) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_transfer__nat__int__set__cong,axiom,
% 179.72/179.56 ! [V_P_H_2,V_P_2] :
% 179.72/179.56 ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 179.72/179.56 => ( hBOOL(hAPP(V_P_2,B_x))
% 179.72/179.56 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 179.72/179.56 => 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_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)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_UnionE,axiom,
% 179.72/179.56 ! [V_C_2,V_A_2,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ~ ! [B_X] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 179.72/179.56 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rel__compE,axiom,
% 179.72/179.56 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ~ ! [B_x,B_y,B_z] :
% 179.72/179.56 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 179.72/179.56 => ( 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))
% 179.72/179.56 => ~ 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)) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converseE,axiom,
% 179.72/179.56 ! [V_r_2,V_yx_2,T_c,T_b] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => ~ ! [B_x,B_y] :
% 179.72/179.56 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 179.72/179.56 => ~ 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_setprod__pos,axiom,
% 179.72/179.56 ! [V_f_2,V_A_2,T_b,T_c] :
% 179.72/179.56 ( class_Rings_Olinordered__semidom(T_c)
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Oof__frac__def,axiom,
% 179.72/179.56 ! [V_q,T_a,T_b] :
% 179.72/179.56 ( ( class_Rings_Oinverse(T_b)
% 179.72/179.56 & class_Rings_Oring__1(T_b) )
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Oless__frac__def,axiom,
% 179.72/179.56 ! [V_r_2,V_q_2,T_b] :
% 179.72/179.56 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 179.72/179.56 <=> 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 179.72/179.56 ! [V_r_2,V_q_2,T_b] :
% 179.72/179.56 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 179.72/179.56 <=> 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Onum__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Nitpick_Odenom__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__all__length,axiom,
% 179.72/179.56 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 179.72/179.56 <=> ! [B_n] :
% 179.72/179.56 ( 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)))
% 179.72/179.56 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_internal__split__def,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Ball__set__list__all,axiom,
% 179.72/179.56 ! [V_P_2,V_xs_2,T_b] :
% 179.72/179.56 ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 => hBOOL(hAPP(V_P_2,B_x)) )
% 179.72/179.56 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__all__rev,axiom,
% 179.72/179.56 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 179.72/179.56 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__all__append,axiom,
% 179.72/179.56 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 179.72/179.56 <=> ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 179.72/179.56 & c_List_Olist__all(T_b,V_P_2,V_ys_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__all__iff,axiom,
% 179.72/179.56 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 179.72/179.56 <=> ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__all__simps_I2_J,axiom,
% 179.72/179.56 ! [V_P_2,T_b] : c_List_Olist__all(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__all__simps_I1_J,axiom,
% 179.72/179.56 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 179.72/179.56 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.56 & c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__all__iff__raw,axiom,
% 179.72/179.56 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 179.72/179.56 <=> ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_internal__split__conv,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__ex1__simps_I2_J,axiom,
% 179.72/179.56 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 179.72/179.56 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.56 => 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_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) )
% 179.72/179.56 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.56 => c_List_Olist__ex1(T_b,V_P_2,V_xs_2) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_setprod__nonneg,axiom,
% 179.72/179.56 ! [V_f_2,V_A_2,T_b,T_c] :
% 179.72/179.56 ( class_Rings_Olinordered__semidom(T_c)
% 179.72/179.56 => ( ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__ex1__simps_I1_J,axiom,
% 179.72/179.56 ! [V_P_2,T_b] : ~ c_List_Olist__ex1(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_exists1__code,axiom,
% 179.72/179.56 ! [V_P_2,T_b] :
% 179.72/179.56 ( class_Enum_Oenum(T_b)
% 179.72/179.56 => ( ? [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(V_P_2,B_x))
% 179.72/179.56 & ! [B_y] :
% 179.72/179.56 ( hBOOL(hAPP(V_P_2,B_y))
% 179.72/179.56 => B_y = B_x ) )
% 179.72/179.56 <=> c_List_Olist__ex1(T_b,V_P_2,c_Enum_Oenum__class_Oenum(T_b)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_list__ex1__iff,axiom,
% 179.72/179.56 ! [V_xs_2,V_P_2,T_b] :
% 179.72/179.56 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 179.72/179.56 <=> ? [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 & hBOOL(hAPP(V_P_2,B_x))
% 179.72/179.56 & ! [B_y] :
% 179.72/179.56 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 179.72/179.56 & hBOOL(hAPP(V_P_2,B_y)) )
% 179.72/179.56 => B_y = B_x ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_bool_Osize_I2_J,axiom,
% 179.72/179.56 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_bool_Osize_I1_J,axiom,
% 179.72/179.56 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_finite__less__ub,axiom,
% 179.72/179.56 ! [V_u_2,V_f_2] :
% 179.72/179.56 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 179.72/179.56 => 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)))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_measure__function__int,axiom,
% 179.72/179.56 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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_measure__fst,axiom,
% 179.72/179.56 ! [T_c,V_f_2,T_b] :
% 179.72/179.56 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_measure__size,axiom,
% 179.72/179.56 ! [T_b] :
% 179.72/179.56 ( class_Nat_Osize(T_b)
% 179.72/179.56 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_is__measure_Ointros,axiom,
% 179.72/179.56 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_is__measure_Oequations,axiom,
% 179.72/179.56 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_is__measure_Osimps,axiom,
% 179.72/179.56 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_measure__snd,axiom,
% 179.72/179.56 ! [T_c,V_f_2,T_b] :
% 179.72/179.56 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 179.72/179.56 => 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_finite__induct,axiom,
% 179.72/179.56 ! [V_P_2,V_F_2,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 179.72/179.56 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 179.72/179.56 => ( ! [B_x,B_F] :
% 179.72/179.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 179.72/179.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 179.72/179.56 => ( hBOOL(hAPP(V_P_2,B_F))
% 179.72/179.56 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 179.72/179.56 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_equal__fun__def,axiom,
% 179.72/179.56 ! [V_g_2,V_f_2,T_b,T_c] :
% 179.72/179.56 ( ( class_HOL_Oequal(T_c)
% 179.72/179.56 & class_Enum_Oenum(T_b) )
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 179.72/179.56 <=> ! [B_x] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_Enum_Oenum__class_Oenum(T_b))))
% 179.72/179.56 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__equal,axiom,
% 179.72/179.56 ! [T_b] :
% 179.72/179.56 ( class_HOL_Oequal(T_b)
% 179.72/179.56 => c_fequal = c_HOL_Oequal__class_Oequal(T_b) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_equal__eq,axiom,
% 179.72/179.56 ! [V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( class_HOL_Oequal(T_b)
% 179.72/179.56 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_b),V_x_2),V_y_2))
% 179.72/179.56 <=> V_x_2 = V_y_2 ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_equal__refl,axiom,
% 179.72/179.56 ! [V_x,T_a] :
% 179.72/179.56 ( class_HOL_Oequal(T_a)
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_equal,axiom,
% 179.72/179.56 ! [T_b] :
% 179.72/179.56 ( class_HOL_Oequal(T_b)
% 179.72/179.56 => c_HOL_Oequal__class_Oequal(T_b) = c_fequal ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_bool_Osize_I3_J,axiom,
% 179.72/179.56 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_bool_Osize_I4_J,axiom,
% 179.72/179.56 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_size__code,axiom,
% 179.72/179.56 ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = hAPP(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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_transfer__morphism__int__nat,axiom,
% 179.72/179.56 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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I2_J,axiom,
% 179.72/179.56 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I5_J,axiom,
% 179.72/179.56 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I12_J,axiom,
% 179.72/179.56 ! [V_k1_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I8_J,axiom,
% 179.72/179.56 ! [V_k2_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I11_J,axiom,
% 179.72/179.56 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I7_J,axiom,
% 179.72/179.56 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I10_J,axiom,
% 179.72/179.56 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I4_J,axiom,
% 179.72/179.56 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I9_J,axiom,
% 179.72/179.56 ! [V_k1_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I3_J,axiom,
% 179.72/179.56 ! [V_k2_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__number__of__int__code,axiom,
% 179.72/179.56 ! [V_l_2,V_k_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(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)))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I6_J,axiom,
% 179.72/179.56 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I16_J,axiom,
% 179.72/179.56 ! [V_k2_2,V_k1_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I1_J,axiom,
% 179.72/179.56 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I13_J,axiom,
% 179.72/179.56 ! [V_k2_2,V_k1_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_equal__int__def,axiom,
% 179.72/179.56 ! [V_l_2,V_k_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
% 179.72/179.56 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I15_J,axiom,
% 179.72/179.56 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OBit0(V_k2))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__code_I14_J,axiom,
% 179.72/179.56 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OBit1(V_k2))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_lazy__sequence__size__code,axiom,
% 179.72/179.56 ! [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) = hAPP(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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_seq__case,axiom,
% 179.72/179.56 ! [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) = hAPP(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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_eq__int__refl,axiom,
% 179.72/179.56 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_yieldn__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_lazy__sequence_Oinject,axiom,
% 179.72/179.56 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 179.72/179.56 ( 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)
% 179.72/179.56 <=> ( V_a_2 = V_a_H_2
% 179.72/179.56 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact__01,axiom,
% 179.72/179.56 ! [V_xq,V_x,T_a] : hAPP(c_Lazy__Sequence_Oyield(T_a),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq)) = hAPP(c_Option_Ooption_OSome(tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_Product__Type_OPair(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_x),V_xq)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 179.72/179.56 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 179.72/179.56 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.56 => 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) )
% 179.72/179.56 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 179.72/179.56 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 179.72/179.56 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.56 => 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) )
% 179.72/179.56 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 179.72/179.56 => 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)) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 179.72/179.56 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pos__empty__def,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_neg__bind__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_neg__map__def,axiom,
% 179.72/179.56 ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_neg__single__def,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pos__bind__def,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pos__map__def,axiom,
% 179.72/179.56 ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_pos__single__def,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_length__splice,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_splice_Osimps_I3_J,axiom,
% 179.72/179.56 ! [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))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_splice_Osimps_I1_J,axiom,
% 179.72/179.56 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 179.72/179.56
% 179.72/179.56 fof(fact_splice__Nil2,axiom,
% 179.72/179.56 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 179.72/179.56
% 179.72/179.56 fof(fact_splice_Osimps_I2_J,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_New__DSequence_Opos__single__def,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_acyclicP__converse,axiom,
% 179.72/179.56 ! [V_r_2,T_b] :
% 179.72/179.56 ( 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))))
% 179.72/179.56 <=> 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__meet,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_conversepD,axiom,
% 179.72/179.56 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_conversep_Ointros,axiom,
% 179.72/179.56 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 179.72/179.56 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_conversep_Oequations,axiom,
% 179.72/179.56 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_conversep__iff,axiom,
% 179.72/179.56 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 179.72/179.56 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_conversep__conversep,axiom,
% 179.72/179.56 ! [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 ).
% 179.72/179.56
% 179.72/179.56 fof(fact_conversep__eq,axiom,
% 179.72/179.56 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 179.72/179.56
% 179.72/179.56 fof(fact_conversep__noteq,axiom,
% 179.72/179.56 ! [V_y_2,V_x_2,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 <=> V_x_2 != V_y_2 ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__pred__comp,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_converse__join,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_conversep__converse__eq,axiom,
% 179.72/179.56 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 179.72/179.56 ( 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))
% 179.72/179.56 <=> 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))) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact__02,axiom,
% 179.72/179.56 ! [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)))) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_tl__replicate,axiom,
% 179.72/179.56 ! [V_x,T_a,V_n] :
% 179.72/179.56 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.56 => 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) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_zip__replicate,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_replicate__append__same,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_replicate__app__Cons__same,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_replicate__Suc,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_filter__replicate,axiom,
% 179.72/179.56 ! [V_n_2,T_b,V_x_2,V_P_2] :
% 179.72/179.56 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.56 => hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) )
% 179.72/179.56 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 179.72/179.56 => hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_replicate__0,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_empty__replicate,axiom,
% 179.72/179.56 ! [V_x_2,V_n_2,T_b] :
% 179.72/179.56 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 179.72/179.56 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_replicate__empty,axiom,
% 179.72/179.56 ! [V_x_2,V_n_2,T_b] :
% 179.72/179.56 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 179.72/179.56 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_concat__replicate__trivial,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_drop__replicate,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_take__replicate,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_hd__replicate,axiom,
% 179.72/179.56 ! [V_x,T_a,V_n] :
% 179.72/179.56 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.56 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Bex__set__replicate,axiom,
% 179.72/179.56 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 179.72/179.56 ( ? [B_x] :
% 179.72/179.56 ( 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))))
% 179.72/179.56 & hBOOL(hAPP(V_P_2,B_x)) )
% 179.72/179.56 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 179.72/179.56 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_Ball__set__replicate,axiom,
% 179.72/179.56 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 179.72/179.56 ( ! [B_x] :
% 179.72/179.56 ( 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))))
% 179.72/179.56 => hBOOL(hAPP(V_P_2,B_x)) )
% 179.72/179.56 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 179.72/179.56 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_append__replicate__commute,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_replicate__eq__replicate,axiom,
% 179.72/179.56 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 179.72/179.56 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 179.72/179.56 <=> ( V_m_2 = V_n_2
% 179.72/179.56 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.56 => V_x_2 = V_y_2 ) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_last__replicate,axiom,
% 179.72/179.56 ! [V_x,T_a,V_n] :
% 179.72/179.56 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.56 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_rev__replicate,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_nth__replicate,axiom,
% 179.72/179.56 ! [V_x,T_a,V_n,V_i] :
% 179.72/179.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 179.72/179.56 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_replicate__add,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_map__replicate,axiom,
% 179.72/179.56 ! [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)) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_in__set__replicate,axiom,
% 179.72/179.56 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 179.72/179.56 ( 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))))
% 179.72/179.56 <=> ( V_x_2 = V_y_2
% 179.72/179.56 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_replicate__length__filter,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_length__replicate,axiom,
% 179.72/179.56 ! [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 ).
% 179.72/179.56
% 179.72/179.56 fof(fact_map__replicate__const,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_map__replicate__trivial,axiom,
% 179.72/179.56 ! [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) ).
% 179.72/179.56
% 179.72/179.56 fof(fact_set__replicate__conv__if,axiom,
% 179.72/179.56 ! [V_x_2,T_b,V_n_2] :
% 179.72/179.56 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.56 => 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)) )
% 179.72/179.56 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 179.72/179.56 => 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))) ) ) ).
% 179.72/179.56
% 179.72/179.56 %----Arity declarations (233)
% 179.72/179.56 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 179.72/179.56 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Lattices_Obounded__lattice(T_1)
% 179.72/179.56 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 179.72/179.56 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Lattices_Obounded__lattice(T_1)
% 179.72/179.56 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Lattices_Obounded__lattice(T_1)
% 179.72/179.56 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Lattices_Olattice(T_1)
% 179.72/179.56 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Lattices_Olattice(T_1)
% 179.72/179.56 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Lattices_Odistrib__lattice(T_1)
% 179.72/179.56 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Lattices_Oboolean__algebra(T_1)
% 179.72/179.56 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Orderings_Opreorder,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Orderings_Opreorder(T_1)
% 179.72/179.56 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 179.72/179.56 ! [T_1,T_2] :
% 179.72/179.56 ( ( class_Finite__Set_Ofinite(T_2)
% 179.72/179.56 & class_Finite__Set_Ofinite(T_1) )
% 179.72/179.56 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Lattices_Olattice,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Lattices_Olattice(T_1)
% 179.72/179.56 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Orderings_Oorder,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Orderings_Oorder(T_1)
% 179.72/179.56 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Orderings_Otop,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Orderings_Otop(T_1)
% 179.72/179.56 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Orderings_Oord,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Orderings_Oord(T_1)
% 179.72/179.56 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Orderings_Obot,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Orderings_Obot(T_1)
% 179.72/179.56 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Groups_Ouminus,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Groups_Ouminus(T_1)
% 179.72/179.56 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Groups_Ominus,axiom,
% 179.72/179.56 ! [T_2,T_1] :
% 179.72/179.56 ( class_Groups_Ominus(T_1)
% 179.72/179.56 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__HOL_Oequal,axiom,
% 179.72/179.56 ! [T_1,T_2] :
% 179.72/179.56 ( ( class_Enum_Oenum(T_2)
% 179.72/179.56 & class_HOL_Oequal(T_1) )
% 179.72/179.56 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_fun__Enum_Oenum,axiom,
% 179.72/179.56 ! [T_1,T_2] :
% 179.72/179.56 ( ( class_Enum_Oenum(T_2)
% 179.72/179.56 & class_Enum_Oenum(T_1) )
% 179.72/179.56 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Com__Ocom__HOL_Oequal,axiom,
% 179.72/179.56 class_HOL_Oequal(tc_Com_Ocom) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Com__Ocom__Nat_Osize,axiom,
% 179.72/179.56 class_Nat_Osize(tc_Com_Ocom) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 179.72/179.56 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 179.72/179.56 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 179.72/179.56 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 179.72/179.56 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 179.72/179.56 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 179.72/179.56 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 179.72/179.56 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 179.72/179.56 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 179.72/179.56 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 179.72/179.56 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 179.72/179.56 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 179.72/179.56 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 179.72/179.56 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 179.72/179.56 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 179.72/179.56 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 179.72/179.56 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 179.72/179.56 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 179.72/179.56 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 179.72/179.56 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 179.72/179.56 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 179.72/179.56 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 179.72/179.56 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 179.72/179.56 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 179.72/179.56 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 179.72/179.56 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 179.72/179.56 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 179.72/179.56 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 179.72/179.56 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 179.72/179.56 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 179.72/179.56 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 179.72/179.56 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 179.72/179.56 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 179.72/179.56 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 179.72/179.56 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 179.72/179.56 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 179.72/179.56 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 179.72/179.56 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 179.72/179.56 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 179.72/179.56 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 179.72/179.56 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 179.72/179.56 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 179.72/179.56 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 179.72/179.56 class_Orderings_Opreorder(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 179.72/179.56 class_Orderings_Olinorder(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 179.72/179.56 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 179.72/179.56 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 179.72/179.56 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 179.72/179.56 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 179.72/179.56 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 179.72/179.56 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 179.72/179.56 class_Lattices_Olattice(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 179.72/179.56 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 179.72/179.56 class_Divides_Oring__div(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 179.72/179.56 class_Rings_Omult__zero(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 179.72/179.56 class_Orderings_Oorder(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 179.72/179.56 class_Int_Oring__char__0(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 179.72/179.56 class_Int_Onumber__ring(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 179.72/179.56 class_Rings_Osemiring(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 179.72/179.56 class_Orderings_Oord(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 179.72/179.56 class_Groups_Ouminus(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 179.72/179.56 class_Groups_Osgn__if(tc_Int_Oint) ).
% 179.72/179.56
% 179.72/179.56 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 179.72/179.56 class_Groups_Oabs__if(tc_Int_Oint) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 179.72/179.57 class_Rings_Oring__1(tc_Int_Oint) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 179.72/179.57 class_Groups_Ominus(tc_Int_Oint) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Int__Oint__Power_Opower,axiom,
% 179.72/179.57 class_Power_Opower(tc_Int_Oint) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 179.72/179.57 class_Groups_Ozero(tc_Int_Oint) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Int__Oint__Rings_Oring,axiom,
% 179.72/179.57 class_Rings_Oring(tc_Int_Oint) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 179.72/179.57 class_Rings_Oidom(tc_Int_Oint) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Int__Oint__Int_Onumber,axiom,
% 179.72/179.57 class_Int_Onumber(tc_Int_Oint) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Int__Oint__Groups_Oone,axiom,
% 179.72/179.57 class_Groups_Oone(tc_Int_Oint) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Int__Oint__HOL_Oequal,axiom,
% 179.72/179.57 class_HOL_Oequal(tc_Int_Oint) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 179.72/179.57 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 179.72/179.57 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 179.72/179.57 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 179.72/179.57 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 179.72/179.57 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 179.72/179.57 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 179.72/179.57 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 179.72/179.57 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 179.72/179.57 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 179.72/179.57 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 179.72/179.57 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 179.72/179.57 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 179.72/179.57 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 179.72/179.57 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 179.72/179.57 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 179.72/179.57 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 179.72/179.57 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 179.72/179.57 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 179.72/179.57 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 179.72/179.57 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 179.72/179.57 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 179.72/179.57 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 179.72/179.57 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 179.72/179.57 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 179.72/179.57 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 179.72/179.57 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 179.72/179.57 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 179.72/179.57 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 179.72/179.57 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 179.72/179.57 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 179.72/179.57 class_Lattices_Olattice(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 179.72/179.57 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 179.72/179.57 class_Orderings_Oorder(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 179.72/179.57 class_Rings_Osemiring(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 179.72/179.57 class_Orderings_Oord(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 179.72/179.57 class_Orderings_Obot(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 179.72/179.57 class_Groups_Ominus(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Power_Opower,axiom,
% 179.72/179.57 class_Power_Opower(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 179.72/179.57 class_Groups_Ozero(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 179.72/179.57 class_Int_Onumber(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 179.72/179.57 class_Groups_Oone(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__HOL_Oequal,axiom,
% 179.72/179.57 class_HOL_Oequal(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 179.72/179.57 class_Nat_Osize(tc_Nat_Onat) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 179.72/179.57 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 179.72/179.57 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 179.72/179.57 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 179.72/179.57 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 179.72/179.57 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 179.72/179.57 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 179.72/179.57 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 179.72/179.57 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 179.72/179.57 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 179.72/179.57 class_Lattices_Olattice(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 179.72/179.57 class_Orderings_Oorder(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 179.72/179.57 class_Orderings_Otop(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 179.72/179.57 class_Orderings_Oord(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 179.72/179.57 class_Orderings_Obot(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 179.72/179.57 class_Groups_Ouminus(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 179.72/179.57 class_Groups_Ominus(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__HOL_Oequal,axiom,
% 179.72/179.57 class_HOL_Oequal(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 179.72/179.57 class_Enum_Oenum(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 179.72/179.57 class_Nat_Osize(tc_HOL_Obool) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Com__Ostate__HOL_Oequal,axiom,
% 179.72/179.57 class_HOL_Oequal(tc_Com_Ostate) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Com__Ostate__Nat_Osize,axiom,
% 179.72/179.57 class_Nat_Osize(tc_Com_Ostate) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Com__Ovname__HOL_Oequal,axiom,
% 179.72/179.57 class_HOL_Oequal(tc_Com_Ovname) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Com__Ovname__Nat_Osize,axiom,
% 179.72/179.57 class_Nat_Osize(tc_Com_Ovname) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_List__Olist__HOL_Oequal,axiom,
% 179.72/179.57 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_List__Olist__Nat_Osize,axiom,
% 179.72/179.57 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 179.72/179.57 ! [T_1,T_2] :
% 179.72/179.57 ( ( class_Finite__Set_Ofinite(T_2)
% 179.72/179.57 & class_Finite__Set_Ofinite(T_1) )
% 179.72/179.57 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_sum__HOL_Oequal,axiom,
% 179.72/179.57 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_sum__Enum_Oenum,axiom,
% 179.72/179.57 ! [T_1,T_2] :
% 179.72/179.57 ( ( class_Enum_Oenum(T_2)
% 179.72/179.57 & class_Enum_Oenum(T_1) )
% 179.72/179.57 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_sum__Nat_Osize,axiom,
% 179.72/179.57 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 179.72/179.57 ! [T_1] :
% 179.72/179.57 ( class_Finite__Set_Ofinite(T_1)
% 179.72/179.57 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Option__Ooption__HOL_Oequal,axiom,
% 179.72/179.57 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 179.72/179.57 ! [T_1] :
% 179.72/179.57 ( class_Enum_Oenum(T_1)
% 179.72/179.57 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 179.72/179.57 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 179.72/179.57 ! [T_1,T_2] :
% 179.72/179.57 ( ( class_Finite__Set_Ofinite(T_2)
% 179.72/179.57 & class_Finite__Set_Ofinite(T_1) )
% 179.72/179.57 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_prod__Smallcheck_Osmall,axiom,
% 179.72/179.57 ! [T_1,T_2] :
% 179.72/179.57 ( ( class_Smallcheck_Osmall(T_2)
% 179.72/179.57 & class_Smallcheck_Osmall(T_1) )
% 179.72/179.57 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_prod__HOL_Oequal,axiom,
% 179.72/179.57 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_prod__Enum_Oenum,axiom,
% 179.72/179.57 ! [T_1,T_2] :
% 179.72/179.57 ( ( class_Enum_Oenum(T_2)
% 179.72/179.57 & class_Enum_Oenum(T_1) )
% 179.72/179.57 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_prod__Nat_Osize,axiom,
% 179.72/179.57 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 179.72/179.57 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 179.72/179.57 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
% 179.72/179.57 class_HOL_Oequal(tc_Product__Type_Ounit) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 179.72/179.57 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 179.72/179.57 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
% 179.72/179.57 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 179.72/179.57 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
% 179.72/179.57 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 179.72/179.57 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 179.72/179.57 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 179.72/179.57 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 179.72/179.57 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 179.72/179.57 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 179.72/179.57 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 179.72/179.57 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 179.72/179.57 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 179.72/179.57 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 179.72/179.57 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 179.72/179.57 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 179.72/179.57 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 179.72/179.57 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 179.72/179.57 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 179.72/179.57 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 179.72/179.57 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 179.72/179.57 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 179.72/179.57 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 179.72/179.57 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 179.72/179.57 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 179.72/179.57 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 179.72/179.57 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 179.72/179.57 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 179.72/179.57 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 179.72/179.57 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 179.72/179.57 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 179.72/179.57 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 179.72/179.57 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 179.72/179.57 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 179.72/179.57 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 179.72/179.57 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 179.72/179.57 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 179.72/179.57 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 179.72/179.57 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 179.72/179.57 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 179.72/179.57 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
% 179.72/179.57 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 179.72/179.57 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
% 179.72/179.57 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 179.72/179.57
% 179.72/179.57 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 179.72/179.57 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 179.72/179.57
% 179.72/179.57 %----Helper facts (20)
% 179.72/179.57 fof(help_c__COMBI__1,axiom,
% 179.72/179.57 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__COMBK__1,axiom,
% 179.72/179.57 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__COMBB__1,axiom,
% 179.72/179.57 ! [V_R_2,V_Qa_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Qa_2),V_R_2) = hAPP(V_P_2,hAPP(V_Qa_2,V_R_2)) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__COMBC__1,axiom,
% 179.72/179.57 ! [V_R_2,V_Qa_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_P_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Qa_2) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__COMBS__1,axiom,
% 179.72/179.57 ! [V_R_2,V_Qa_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Qa_2,V_R_2)) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fequal__1,axiom,
% 179.72/179.57 ! [V_y_2,V_x_2] :
% 179.72/179.57 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 179.72/179.57 | V_x_2 = V_y_2 ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fequal__2,axiom,
% 179.72/179.57 ! [V_y_2,V_x_2] :
% 179.72/179.57 ( V_x_2 != V_y_2
% 179.72/179.57 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fFalse__1,axiom,
% 179.72/179.57 ~ hBOOL(c_fFalse) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fTrue__1,axiom,
% 179.72/179.57 hBOOL(c_fTrue) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fNot__1,axiom,
% 179.72/179.57 ! [V_P_2] :
% 179.72/179.57 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 179.72/179.57 | ~ hBOOL(V_P_2) ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fNot__2,axiom,
% 179.72/179.57 ! [V_P_2] :
% 179.72/179.57 ( ~ ~ hBOOL(V_P_2)
% 179.72/179.57 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fconj__1,axiom,
% 179.72/179.57 ! [V_Qa_2,V_P_2] :
% 179.72/179.57 ( ~ hBOOL(V_P_2)
% 179.72/179.57 | ~ hBOOL(V_Qa_2)
% 179.72/179.57 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Qa_2)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fconj__2,axiom,
% 179.72/179.57 ! [V_Qa_2,V_P_2] :
% 179.72/179.57 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Qa_2))
% 179.72/179.57 | hBOOL(V_P_2) ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fconj__3,axiom,
% 179.72/179.57 ! [V_Qa_2,V_P_2] :
% 179.72/179.57 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Qa_2))
% 179.72/179.57 | hBOOL(V_Qa_2) ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fdisj__1,axiom,
% 179.72/179.57 ! [V_Qa_2,V_P_2] :
% 179.72/179.57 ( ~ hBOOL(V_P_2)
% 179.72/179.57 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Qa_2)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fdisj__2,axiom,
% 179.72/179.57 ! [V_P_2,V_Qa_2] :
% 179.72/179.57 ( ~ hBOOL(V_Qa_2)
% 179.72/179.57 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Qa_2)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fdisj__3,axiom,
% 179.72/179.57 ! [V_Qa_2,V_P_2] :
% 179.72/179.57 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Qa_2))
% 179.72/179.57 | hBOOL(V_P_2)
% 179.72/179.57 | hBOOL(V_Qa_2) ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fimplies__1,axiom,
% 179.72/179.57 ! [V_Qa_2,V_P_2] :
% 179.72/179.57 ( hBOOL(V_P_2)
% 179.72/179.57 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Qa_2)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fimplies__2,axiom,
% 179.72/179.57 ! [V_P_2,V_Qa_2] :
% 179.72/179.57 ( ~ hBOOL(V_Qa_2)
% 179.72/179.57 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Qa_2)) ) ).
% 179.72/179.57
% 179.72/179.57 fof(help_c__fimplies__3,axiom,
% 179.72/179.57 ! [V_Qa_2,V_P_2] :
% 179.72/179.57 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Qa_2))
% 179.72/179.57 | ~ hBOOL(V_P_2)
% 179.72/179.57 | hBOOL(V_Qa_2) ) ).
% 179.72/179.57
% 179.72/179.57 %----Conjectures (1)
% 179.72/179.57 fof(conj_0,conjecture,
% 179.72/179.57 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),v_c),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ).
% 179.72/179.57
% 179.72/179.57 %------------------------------------------------------------------------------
% 179.72/179.57 %-------------------------------------------
% 179.72/179.57 % Proof found
% 179.72/179.57 % SZS status Theorem for theBenchmark
% 179.72/179.57 % SZS output start Proof
% 179.72/179.57 %ClaNum:10151(EqnAxiom:2862)
% 179.72/179.57 %VarNum:70217(SingletonVarNum:20509)
% 179.72/179.57 %MaxLitNum:8
% 179.72/179.57 %MaxfuncDepth:13
% 179.72/179.57 %SharedTerms:1035
% 179.72/179.57 %goalClause: 4565
% 179.72/179.57 %singleGoalClaCount:1
% 179.72/179.57 [2866]P1(a855)
% 179.72/179.57 [2867]P1(a860)
% 179.72/179.57 [2868]P101(a187)
% 179.72/179.57 [2869]P2(a855)
% 179.72/179.57 [2870]P2(a860)
% 179.72/179.57 [2871]P2(a1)
% 179.72/179.57 [2872]P3(a855)
% 179.72/179.57 [2873]P97(a855)
% 179.72/179.57 [2874]P97(a860)
% 179.72/179.57 [2875]P97(a1)
% 179.72/179.57 [2876]P4(a855)
% 179.72/179.57 [2877]P4(a860)
% 179.72/179.57 [2878]P4(a1)
% 179.72/179.57 [2879]P4(a99)
% 179.72/179.57 [2880]P102(a855)
% 179.72/179.57 [2881]P102(a860)
% 179.72/179.57 [2882]P102(a1)
% 179.72/179.57 [2883]P102(a99)
% 179.72/179.57 [2884]P98(a855)
% 179.72/179.57 [2885]P98(a860)
% 179.72/179.57 [2886]P98(a1)
% 179.72/179.57 [2887]P103(a860)
% 179.72/179.57 [2888]P103(a1)
% 179.72/179.57 [2889]P103(a99)
% 179.72/179.57 [2890]P104(a855)
% 179.72/179.57 [2891]P104(a860)
% 179.72/179.57 [2892]P104(a1)
% 179.72/179.57 [2893]P104(a99)
% 179.72/179.57 [2894]P105(a855)
% 179.72/179.57 [2895]P105(a860)
% 179.72/179.57 [2896]P105(a1)
% 179.72/179.57 [2897]P105(a99)
% 179.72/179.57 [2898]P106(a855)
% 179.72/179.57 [2899]P95(a855)
% 179.72/179.57 [2900]P96(a855)
% 179.72/179.57 [2901]P96(a860)
% 179.72/179.57 [2902]P96(a1)
% 179.72/179.57 [2903]P75(a1)
% 179.72/179.57 [2904]P5(a855)
% 179.72/179.57 [2905]P5(a863)
% 179.72/179.57 [2906]P79(a855)
% 179.72/179.57 [2907]P79(a1)
% 179.72/179.57 [2908]P87(a855)
% 179.72/179.57 [2909]P59(a1)
% 179.72/179.57 [2910]P60(a1)
% 179.72/179.57 [2911]P66(a860)
% 179.72/179.57 [2912]P66(a1)
% 179.72/179.57 [2913]P66(a99)
% 179.72/179.57 [2914]P107(a1)
% 179.72/179.57 [2915]P108(a1)
% 179.72/179.57 [2916]P116(a1)
% 179.72/179.57 [2917]P61(a855)
% 179.72/179.57 [2918]P61(a863)
% 179.72/179.57 [2919]P68(a860)
% 179.72/179.57 [2920]P68(a1)
% 179.72/179.57 [2921]P68(a99)
% 179.72/179.57 [2922]P76(a860)
% 179.72/179.57 [2923]P76(a1)
% 179.72/179.57 [2924]P76(a99)
% 179.72/179.57 [2925]P77(a860)
% 179.72/179.57 [2926]P77(a1)
% 179.72/179.57 [2927]P77(a99)
% 179.72/179.57 [2928]P119(a860)
% 179.72/179.57 [2929]P119(a1)
% 179.72/179.57 [2930]P119(a99)
% 179.72/179.57 [2931]P133(a1)
% 179.72/179.57 [2932]P109(a1)
% 179.72/179.57 [2933]P112(a860)
% 179.72/179.57 [2934]P112(a1)
% 179.72/179.57 [2935]P112(a99)
% 179.72/179.57 [2936]P135(a860)
% 179.72/179.57 [2937]P135(a1)
% 179.72/179.57 [2938]P67(a860)
% 179.72/179.57 [2939]P67(a1)
% 179.72/179.57 [2940]P67(a99)
% 179.72/179.57 [2941]P69(a860)
% 179.72/179.57 [2942]P69(a1)
% 179.72/179.57 [2943]P69(a99)
% 179.72/179.57 [2944]P70(a860)
% 179.72/179.57 [2945]P70(a1)
% 179.72/179.57 [2946]P70(a99)
% 179.72/179.57 [2947]P80(a860)
% 179.72/179.57 [2948]P80(a1)
% 179.72/179.57 [2949]P80(a99)
% 179.72/179.57 [2950]P81(a860)
% 179.72/179.57 [2951]P81(a1)
% 179.72/179.57 [2952]P81(a99)
% 179.72/179.57 [2953]P83(a860)
% 179.72/179.57 [2954]P83(a1)
% 179.72/179.57 [2955]P83(a99)
% 179.72/179.57 [2956]P113(a860)
% 179.72/179.57 [2957]P113(a1)
% 179.72/179.57 [2958]P113(a99)
% 179.72/179.57 [2959]P136(a860)
% 179.72/179.57 [2960]P136(a1)
% 179.72/179.57 [2961]P136(a99)
% 179.72/179.57 [2962]P122(a1)
% 179.72/179.57 [2963]P73(a860)
% 179.72/179.57 [2964]P73(a1)
% 179.72/179.57 [2965]P73(a99)
% 179.72/179.57 [2966]P88(a860)
% 179.72/179.57 [2967]P88(a1)
% 179.72/179.57 [2968]P88(a99)
% 179.72/179.57 [2969]P78(a860)
% 179.72/179.57 [2970]P78(a1)
% 179.72/179.57 [2971]P78(a99)
% 179.72/179.57 [2972]P72(a860)
% 179.72/179.57 [2973]P72(a1)
% 179.72/179.57 [2974]P72(a99)
% 179.72/179.57 [2975]P74(a1)
% 179.72/179.57 [2976]P123(a860)
% 179.72/179.57 [2977]P123(a1)
% 179.72/179.57 [2978]P123(a99)
% 179.72/179.57 [2979]P137(a1)
% 179.72/179.57 [2980]P124(a860)
% 179.72/179.57 [2981]P124(a1)
% 179.72/179.57 [2982]P124(a99)
% 179.72/179.57 [2983]P138(a860)
% 179.72/179.57 [2984]P138(a1)
% 179.72/179.57 [2985]P138(a99)
% 179.72/179.57 [2986]P120(a1)
% 179.72/179.57 [2987]P121(a1)
% 179.72/179.57 [2988]P84(a860)
% 179.72/179.57 [2989]P84(a1)
% 179.72/179.57 [2990]P84(a99)
% 179.72/179.57 [2991]P129(a860)
% 179.72/179.57 [2992]P129(a1)
% 179.72/179.57 [2993]P129(a99)
% 179.72/179.57 [2994]P131(a860)
% 179.72/179.57 [2995]P131(a1)
% 179.72/179.57 [2996]P131(a99)
% 179.72/179.57 [2997]P130(a860)
% 179.72/179.57 [2998]P130(a1)
% 179.72/179.57 [2999]P130(a99)
% 179.72/179.57 [3000]P125(a860)
% 179.72/179.57 [3001]P125(a1)
% 179.72/179.57 [3002]P125(a99)
% 179.72/179.57 [3003]P117(a860)
% 179.72/179.57 [3004]P117(a1)
% 179.72/179.57 [3005]P117(a99)
% 179.72/179.57 [3006]P126(a860)
% 179.72/179.57 [3007]P126(a1)
% 179.72/179.57 [3008]P126(a99)
% 179.72/179.57 [3009]P127(a1)
% 179.72/179.57 [3010]P128(a1)
% 179.72/179.57 [3011]P134(a1)
% 179.72/179.57 [3012]P89(a1)
% 179.72/179.57 [3013]P85(a1)
% 179.72/179.57 [3014]P139(a860)
% 179.72/179.57 [3015]P139(a1)
% 179.72/179.57 [3016]P139(a99)
% 179.72/179.57 [3017]P99(a860)
% 179.72/179.57 [3018]P99(a1)
% 179.72/179.57 [3019]P99(a99)
% 179.72/179.57 [3020]P140(a860)
% 179.72/179.57 [3021]P140(a1)
% 179.72/179.57 [3022]P140(a99)
% 179.72/179.57 [3023]P82(a1)
% 179.72/179.57 [3024]P132(a1)
% 179.72/179.57 [3025]P71(a1)
% 179.72/179.57 [3026]P6(a855)
% 179.72/179.57 [3027]P110(a860)
% 179.72/179.57 [3028]P110(a1)
% 179.72/179.57 [3029]P110(a99)
% 179.72/179.57 [3030]P57(a860)
% 179.72/179.57 [3031]P57(a1)
% 179.72/179.57 [3032]P57(a99)
% 179.72/179.57 [3033]P58(a1)
% 179.72/179.57 [3034]P90(a1)
% 179.72/179.57 [3035]P91(a860)
% 179.72/179.57 [3036]P91(a1)
% 179.72/179.57 [3037]P91(a99)
% 179.72/179.57 [3038]P141(a863)
% 179.72/179.57 [3039]P141(a1)
% 179.72/179.57 [3040]P92(a855)
% 179.72/179.57 [3041]P92(a856)
% 179.72/179.57 [3042]P92(a860)
% 179.72/179.57 [3043]P92(a858)
% 179.72/179.57 [3044]P92(a857)
% 179.72/179.57 [3045]P92(a863)
% 179.72/179.57 [3046]P92(a1)
% 179.72/179.57 [3047]P92(a319)
% 179.72/179.57 [3048]P92(a99)
% 179.72/179.57 [3049]P86(a860)
% 179.72/179.57 [3050]P86(a1)
% 179.72/179.57 [3051]P86(a99)
% 179.72/179.57 [3052]P111(a860)
% 179.72/179.57 [3053]P100(a855)
% 179.72/179.57 [3054]P100(a856)
% 179.72/179.57 [3055]P100(a860)
% 179.72/179.57 [3056]P100(a858)
% 179.72/179.57 [3057]P100(a857)
% 179.72/179.57 [3058]P100(a863)
% 179.72/179.57 [3059]P100(a319)
% 179.72/179.57 [3060]P100(a99)
% 179.72/179.57 [3061]P94(a855)
% 179.72/179.57 [3081]P38(a860,a242)
% 179.72/179.57 [3082]P38(a860,a313)
% 179.72/179.57 [4458]~E(a97,a81)
% 179.72/179.57 [4459]~P101(a241)
% 179.72/179.57 [2863]E(f2(a1),a81)
% 179.72/179.57 [2864]E(f100(a99),a3)
% 179.72/179.57 [2865]E(f22(a99),a23)
% 179.72/179.57 [3062]E(f188(a860),f2(a860))
% 179.72/179.57 [3063]E(f28(a24),f2(a860))
% 179.72/179.57 [3064]E(f101(a860),f235(a860))
% 179.72/179.57 [3065]E(f110(a860),f236(a860))
% 179.72/179.57 [3066]E(f102(a1),f32(a1))
% 179.72/179.57 [3067]E(f82(a241),f2(a860))
% 179.72/179.57 [3068]E(f82(a187),f2(a860))
% 179.72/179.57 [3069]P7(f76(a1))
% 179.72/179.57 [3070]P7(f2(a1))
% 179.72/179.57 [3129]P38(f866(a860,a860),a33)
% 179.72/179.57 [3480]E(f315(a860,a860,a242,a242),a33)
% 179.72/179.57 [4460]~E(f76(a1),f2(a1))
% 179.72/179.57 [3071]E(f111(f2(a860)),f2(a860))
% 179.72/179.57 [3072]E(f4(f2(a99)),f2(a860))
% 179.72/179.57 [3084]E(f323(f77(a1),a81),a81)
% 179.72/179.57 [3087]E(f323(a112,f2(a860)),f76(a860))
% 179.72/179.57 [3088]E(f323(a104,f76(a1)),f76(a860))
% 179.72/179.57 [3089]E(f323(a3,f76(a860)),f76(a99))
% 179.72/179.57 [3091]E(f323(a3,f2(a860)),f2(a99))
% 179.72/179.57 [3093]E(f323(f103(a1),a81),f2(a1))
% 179.72/179.57 [3094]E(f323(f103(a99),a81),f2(a99))
% 179.72/179.57 [3095]E(f323(a104,f2(a1)),f2(a860))
% 179.72/179.57 [3096]E(f323(f189(a855),a241),f2(a860))
% 179.72/179.57 [3097]E(f323(f189(a855),a187),f2(a860))
% 179.72/179.57 [3098]E(f323(f189(a857),a24),f2(a860))
% 179.72/179.57 [3099]E(f323(f103(a860),a81),f2(a860))
% 179.72/179.57 [3103]E(f323(f77(a1),f76(a1)),a97)
% 179.72/179.57 [3110]E(f323(f77(a1),f2(a1)),f2(a1))
% 179.72/179.57 [3112]E(f323(f189(a99),f2(a99)),f2(a860))
% 179.72/179.57 [3113]E(f323(f100(a1),f76(a860)),f76(a1))
% 179.72/179.57 [3114]E(f323(f100(a1),f2(a860)),f2(a1))
% 179.72/179.57 [3125]E(f323(a104,f76(a1)),f323(a112,f2(a860)))
% 179.72/179.57 [3127]E(f314(f866(a860,a860),a33),a34)
% 179.72/179.57 [3128]E(f316(f866(a860,a860),a33),a66)
% 179.72/179.57 [3149]E(f323(f244(a860),f2(a860)),f188(f867(a860,a855)))
% 179.72/179.57 [3150]E(f323(f245(a860),f2(a860)),f246(f867(a860,a855)))
% 179.72/179.57 [3159]P39(f188(f867(a1,a855)))
% 179.72/179.57 [3195]E(f323(f323(f22(a99),f2(a99)),f76(a99)),f2(a99))
% 179.72/179.57 [3273]P101(f323(f323(f238(a1),a97),f2(a1)))
% 179.72/179.57 [3298]P101(f323(f323(f237(a1),f2(a1)),f76(a1)))
% 179.72/179.57 [3300]P101(f323(f323(f238(a1),f2(a1)),f76(a1)))
% 179.72/179.57 [3510]E(f323(f323(f280(a860,a860,a860),a313),f299(a860,a313)),a242)
% 179.72/179.57 [3549]P41(a1,a860,a104,f323(f237(a1),f2(a1)))
% 179.72/179.57 [3553]E(f323(f323(f39(a860,f867(a860,a855)),f246(f867(a860,a855))),f244(a860)),f246(f867(a860,a855)))
% 179.72/179.57 [3554]E(f323(f323(f39(a860,f867(a860,a855)),f246(f867(a860,a855))),f245(a860)),f246(f867(a860,a855)))
% 179.72/179.57 [3555]E(f323(f323(f39(a860,f867(a860,a855)),f246(f867(a860,a855))),f292(a860)),f246(f867(a860,a855)))
% 179.72/179.57 [3556]E(f323(f323(f40(a860,f867(a860,a855)),f246(f867(a860,a855))),f295(a860)),f188(f867(a860,a855)))
% 179.72/179.57 [3572]P27(a860,a1,f100(a1),f246(f867(a860,a855)))
% 179.72/179.57 [3586]P41(a860,a1,f100(a1),f323(f16(a855,a860),a187))
% 179.72/179.57 [3720]E(f323(f71(a860,a99,a1,a3),a104),f103(a99))
% 179.72/179.57 [3949]P53(a99,a860,a19,a3,f246(f867(a860,a855)))
% 179.72/179.57 [3958]P53(a1,f867(f866(a860,a860),a855),a107,a87,a98)
% 179.72/179.57 [4224]E(f263(a1,a1,a1,a1,f32(a1),f77(a1)),a48)
% 179.72/179.57 [4483]~E(f323(f103(a1),a97),f323(f103(a1),a81))
% 179.72/179.57 [4484]~P101(f323(a193,f76(a1)))
% 179.72/179.57 [4485]~P101(f323(a193,f2(a1)))
% 179.72/179.57 [4526]~P101(f323(f323(f238(a1),a81),f2(a1)))
% 179.72/179.57 [3142]E(f323(f323(f22(a1),a97),a97),a81)
% 179.72/179.57 [3157]E(f323(f100(a1),f323(a112,f2(a860))),f76(a1))
% 179.72/179.57 [3224]E(f323(f35(a863),f246(f867(a863,a855))),f76(a860))
% 179.72/179.57 [3245]P101(f323(a193,f323(f103(a1),a97)))
% 179.72/179.57 [3247]P101(f323(f323(f237(a1),a97),a81))
% 179.72/179.57 [3249]P101(f323(f323(f238(a1),a97),a81))
% 179.72/179.57 [3309]E(f323(f323(f301(a860),f2(a860)),f188(f867(a860,a855))),f323(f292(a860),f2(a860)))
% 179.72/179.57 [3365]P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),a81)))
% 179.72/179.57 [3377]E(f323(f302(a860,a860,a112),f246(f867(a860,a855))),f323(f295(a860),f2(a860)))
% 179.72/179.57 [3417]P9(f866(a860,a860),f246(f867(f866(a860,a860),a855)),a108)
% 179.72/179.57 [3728]E(f323(f71(a860,a1,a99,f100(a1)),a19),a20)
% 179.72/179.57 [3790]P38(a860,f323(f243(f866(a860,a860)),f323(f262(a860,a860,a855),f238(a860))))
% 179.72/179.57 [4515]~P101(f323(a193,f323(f103(a1),a81)))
% 179.72/179.57 [4516]~P101(f323(f323(f237(a1),a81),a97))
% 179.72/179.57 [4517]~P101(f323(f323(f238(a1),a81),a81))
% 179.72/179.57 [4518]~P101(f323(f323(f238(a1),a81),a97))
% 179.72/179.57 [4519]~P101(f323(f323(f238(a1),a97),a97))
% 179.72/179.57 [4520]~P101(f323(f323(f89(a1),a81),a97))
% 179.72/179.57 [4521]~P101(f323(f323(f89(a1),a97),a81))
% 179.72/179.57 [4532]~P101(f323(f59(a860),f246(f867(a860,a855))))
% 179.72/179.57 [4533]~P101(f323(f59(a1),f246(f867(a1,a855))))
% 179.72/179.57 [4396]E(f323(f262(a1,a1,a855),f323(f323(f8(f867(a1,a855),f867(a1,a855),a1),f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f238(a1),f2(a1))))),f323(f323(f7(a1,a1,f867(a1,a855)),f323(f323(f8(f867(a1,f867(a1,a855)),f867(a1,f867(a1,a855)),a1),f7(a1,a1,a855)),f323(f323(f8(f867(a1,a1),f867(a1,f867(a1,a855)),a1),f323(f8(a1,f867(a1,a855),a1),a320)),a219))),f76(a1)))),a215)
% 179.72/179.57 [4565]~P26(a854,a868,f323(f323(f301(f859(a854)),f323(f323(f323(f90(a854),f323(f16(f867(a856,a855),a854),f323(f16(a855,a856),a241))),a869),a870)),f188(f867(f859(a854),a855))))
% 179.72/179.57 [3455]E(f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97),f323(f77(a1),a97))
% 179.72/179.57 [3493]E(f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97),f323(f323(f22(a1),a81),a97))
% 179.72/179.57 [3653]E(f323(f323(f58(f866(a860,a860)),f246(f867(f866(a860,a860),a855))),a108),a98)
% 179.72/179.57 [3682]E(f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f76(a1))
% 179.72/179.57 [3683]E(f323(f103(a99),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f76(a99))
% 179.72/179.57 [3684]E(f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f76(a860))
% 179.72/179.57 [3688]E(f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(a112,f2(a860)))
% 179.72/179.57 [4084]E(f323(f323(f110(f867(f866(f866(a860,a860),f866(a860,a860)),a855)),a33),f299(f866(a860,a860),f188(f867(f866(f866(a860,a860),f866(a860,a860)),a855)))),a68)
% 179.72/179.57 [4154]E(f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),f76(a860)),f2(a860))),f188(f867(f866(a860,a860),a855))))),f76(a1))
% 179.72/179.57 [4155]E(f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),f2(a860)),f2(a860))),f188(f867(f866(a860,a860),a855))))),f2(a1))
% 179.72/179.57 [4170]E(f323(f243(f866(a860,a860)),f323(f262(a860,a860,a855),f323(f323(f8(a860,f867(a860,a855),a860),f323(f7(a860,a860,a855),a320)),a112))),a313)
% 179.72/179.57 [4140]E(f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),f323(a112,f323(a112,f2(a860))))
% 179.72/179.57 [4143]E(f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),f323(f323(f78(a860),f76(a860)),f76(a860)))
% 179.72/179.57 [4144]E(f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),f323(f35(a855),f246(f867(a855,a855))))
% 179.72/179.57 [4210]P7(f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))
% 179.72/179.57 [4282]P29(f867(f866(a860,a860),a855),f323(f323(f258(f867(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),a855),f867(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),a855)),a34),a67))
% 179.72/179.57 [4283]P29(f867(f866(a860,a860),a855),f323(f323(f258(f867(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),a855),f867(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),a855)),a66),a69))
% 179.72/179.57 [4323]E(f323(f323(f110(f867(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),a855)),f316(f866(a860,a860),a68)),f323(f323(f301(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),f188(f867(f866(a860,a860),a855))),f188(f867(f866(a860,a860),a855)))),f188(f867(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),a855)))),a69)
% 179.72/179.57 [4324]E(f323(f323(f110(f867(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),a855)),f314(f866(a860,a860),a68)),f323(f323(f301(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),f188(f867(f866(a860,a860),a855))),f188(f867(f866(a860,a860),a855)))),f188(f867(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),a855)))),a67)
% 179.72/179.57 [4212]E(f323(a104,f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(a112,f323(a112,f2(a860))))
% 179.72/179.57 [4259]E(f323(f100(a1),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))
% 179.72/179.57 [4294]P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.57 [4295]E(f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97)),f323(a112,f323(a112,f323(a112,f2(a860)))))
% 179.72/179.57 [4338]P7(f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97)))
% 179.72/179.57 [4366]E(f323(f100(a1),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97))),f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97)))
% 179.72/179.57 [4381]P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97))))
% 179.72/179.57 [3083]P8(x30831,a320)
% 179.72/179.57 [3481]P27(a860,a860,a112,x34811)
% 179.72/179.57 [3073]P92(f859(x30731))
% 179.72/179.57 [3074]P92(f864(x30741))
% 179.72/179.57 [3075]P92(f861(x30751))
% 179.72/179.57 [3076]P92(f862(x30761))
% 179.72/179.57 [3077]P100(f859(x30771))
% 179.72/179.57 [3078]P100(f864(x30781))
% 179.72/179.57 [3079]P100(f861(x30791))
% 179.72/179.57 [3080]P100(f862(x30801))
% 179.72/179.57 [3100]P38(a1,f105(x31001))
% 179.72/179.57 [3101]P38(a1,f106(x31011))
% 179.72/179.57 [3146]P38(f867(x31461,a855),f298(x31461))
% 179.72/179.57 [3171]E(f247(x31711,x31711,a320),a320)
% 179.72/179.57 [3186]E(f42(a1,x31861,x31861),f2(a1))
% 179.72/179.57 [3242]P17(x32421,f867(x32421,a855),f301(x32421))
% 179.72/179.57 [4462]~E(f323(a112,x44621),x44621)
% 179.72/179.57 [4474]~E(f323(a112,x44741),f2(a860))
% 179.72/179.57 [3085]E(f323(f189(a860),x30851),x30851)
% 179.72/179.57 [3086]E(f323(f103(a1),x30861),x30861)
% 179.72/179.57 [3102]E(f323(a87,f324(x31021)),x31021)
% 179.72/179.57 [3115]E(f145(x31151,f113(x31151)),f113(x31151))
% 179.72/179.57 [3116]E(f114(x31161,f113(x31161)),f113(x31161))
% 179.72/179.57 [3122]E(f323(f161(x31221),f113(x31221)),f113(x31221))
% 179.72/179.57 [3123]E(f323(f165(x31231),f113(x31231)),f113(x31231))
% 179.72/179.57 [3124]E(f323(f162(x31241),f113(x31241)),f113(x31241))
% 179.72/179.57 [3130]E(f323(f103(a1),x31301),f323(f102(a1),x31301))
% 179.72/179.57 [3131]E(f323(a87,f323(a107,x31311)),x31311)
% 179.72/179.57 [3133]E(f323(a3,f323(a19,x31331)),x31331)
% 179.72/179.57 [3134]E(f323(a19,f323(a3,x31341)),x31341)
% 179.72/179.57 [3135]P7(f323(f100(a1),x31351))
% 179.72/179.57 [3140]E(f323(f189(f864(x31401)),f200(x31401)),f2(a860))
% 179.72/179.57 [3141]E(f323(f189(f861(x31411)),f113(x31411)),f2(a860))
% 179.72/179.57 [3155]E(f229(x31551,f200(x31551)),f188(f867(x31551,a855)))
% 179.72/179.57 [3162]E(f323(f323(f22(a860),x31621),f2(a860)),x31621)
% 179.72/179.57 [3163]E(f323(f323(f79(a860),x31631),f76(a860)),x31631)
% 179.72/179.57 [3164]E(f323(f323(f79(a1),x31641),f76(a1)),x31641)
% 179.72/179.57 [3165]E(f323(f323(f78(a860),x31651),f2(a860)),x31651)
% 179.72/179.57 [3166]E(f323(f323(f78(a1),x31661),f2(a1)),x31661)
% 179.72/179.57 [3167]E(f323(f323(f236(a860),x31671),f2(a860)),x31671)
% 179.72/179.57 [3168]E(f323(f323(f79(a860),x31681),f2(a860)),f2(a860))
% 179.72/179.57 [3169]E(f323(f323(f235(a860),x31691),f2(a860)),f2(a860))
% 179.72/179.57 [3170]E(f323(f323(f36(a1),x31701),f2(a1)),f2(a1))
% 179.72/179.57 [3177]E(f323(f166(x31771),f113(x31771)),f188(f867(x31771,a855)))
% 179.72/179.57 [3181]P101(f323(f130(x31811),f113(x31811)))
% 179.72/179.57 [3187]E(f323(f201(x31871,x31871),f5(x31871)),f32(f864(x31871)))
% 179.72/179.57 [3188]E(f323(f201(x31881,x31881),f32(x31881)),f32(f864(x31881)))
% 179.72/179.57 [3189]E(f323(f147(x31891,x31891),f5(x31891)),f32(f861(x31891)))
% 179.72/179.57 [3190]E(f323(f147(x31901,x31901),f32(x31901)),f32(f861(x31901)))
% 179.72/179.57 [3191]E(f42(a1,x31911,f2(a1)),x31911)
% 179.72/179.57 [3192]E(f323(f237(a860),f323(a112,x31921)),f323(f238(a860),x31921))
% 179.72/179.57 [3193]E(f323(f244(a860),f323(a112,x31931)),f323(f292(a860),x31931))
% 179.72/179.57 [3194]E(f323(f245(a860),f323(a112,x31941)),f323(f295(a860),x31941))
% 179.72/179.57 [3196]E(f42(a1,f2(a1),x31961),f2(a1))
% 179.72/179.57 [3208]E(f323(f323(f78(a860),x32081),f76(a860)),f323(a112,x32081))
% 179.72/179.57 [3218]E(f323(f293(a860,x32181),f2(a860)),f188(f867(a860,a855)))
% 179.72/179.57 [3230]E(f294(a860,f2(a860),x32301),f323(f292(a860),x32301))
% 179.72/179.57 [3276]E(f323(f323(f22(a860),f323(a112,x32761)),f76(a860)),x32761)
% 179.72/179.57 [3289]E(f44(f2(a1),x32891),f323(f323(f258(a1,a1),f2(a1)),f2(a1)))
% 179.72/179.57 [3339]P101(f323(f323(f238(a860),x33391),f323(a112,x33391)))
% 179.72/179.57 [3351]P101(f323(f323(f238(a860),f2(a860)),f323(a112,x33511)))
% 179.72/179.57 [3585]E(f91(x35851,x35851,f246(f867(x35851,a855)),f32(x35851)),f32(x35851))
% 179.72/179.57 [3640]E(f323(f323(f22(a99),f323(a3,f323(a112,f323(a19,x36401)))),f76(a99)),x36401)
% 179.72/179.57 [3712]P101(f323(f323(f237(a1),f323(f77(a1),f323(f100(a1),x37121))),f2(a1)))
% 179.72/179.57 [3864]P101(f323(f323(f238(a1),f323(f77(a1),f323(f100(a1),f323(a112,x38641)))),f2(a1)))
% 179.72/179.57 [4490]~E(f246(f867(x44901,a855)),f188(f867(x44901,a855)))
% 179.72/179.57 [4529]~P101(f323(f323(f238(a860),x45291),f2(a860)))
% 179.72/179.57 [4541]~P101(f323(f323(f238(a1),f323(f100(a1),x45411)),f2(a1)))
% 179.72/179.57 [3145]E(f173(x31451,f113(f861(x31451))),f113(f861(x31451)))
% 179.72/179.57 [3147]E(f323(f323(f79(a1),a81),x31471),a81)
% 179.72/179.57 [3148]E(f323(f323(f78(a1),a81),x31481),x31481)
% 179.72/179.57 [3151]E(f323(a104,f323(f100(a1),x31511)),x31511)
% 179.72/179.57 [3152]E(f323(f323(f22(a1),x31521),a81),x31521)
% 179.72/179.57 [3153]E(f323(f323(f78(a1),x31531),a81),x31531)
% 179.72/179.57 [3156]E(f323(f323(f22(a860),x31561),x31561),f2(a860))
% 179.72/179.57 [3160]E(f323(f77(a1),f323(f77(a1),x31601)),x31601)
% 179.72/179.57 [3161]E(f323(f35(a860),f323(f244(a860),x31611)),x31611)
% 179.72/179.57 [3172]E(f323(f323(f79(a860),f76(a860)),x31721),x31721)
% 179.72/179.57 [3173]E(f323(f323(f79(a1),f76(a1)),x31731),x31731)
% 179.72/179.57 [3174]E(f323(f323(f78(a860),f2(a860)),x31741),x31741)
% 179.72/179.57 [3175]E(f323(f323(f78(a1),f2(a1)),x31751),x31751)
% 179.72/179.57 [3176]E(f323(f323(f236(a860),f2(a860)),x31761),x31761)
% 179.72/179.57 [3182]E(f323(f323(f22(a860),f2(a860)),x31821),f2(a860))
% 179.72/179.57 [3183]E(f323(f323(f79(a860),f2(a860)),x31831),f2(a860))
% 179.72/179.57 [3184]E(f323(f323(f235(a860),f2(a860)),x31841),f2(a860))
% 179.72/179.57 [3185]E(f323(f323(f36(a1),f2(a1)),x31851),f2(a1))
% 179.72/179.57 [3202]E(f323(f293(a860,f2(a860)),x32021),f323(f244(a860),x32021))
% 179.72/179.57 [3203]E(f323(f323(f79(a1),a97),x32031),f323(f77(a1),x32031))
% 179.72/179.57 [3210]E(f323(a104,f323(f103(a1),x32101)),f323(f103(a860),x32101))
% 179.72/179.57 [3211]E(f323(a19,f323(f103(a99),x32111)),f323(f103(a860),x32111))
% 179.72/179.57 [3212]E(f323(f35(a860),f323(f292(a860),x32121)),f323(a112,x32121))
% 179.72/179.57 [3222]E(f323(f323(f78(a860),f76(a860)),x32221),f323(a112,x32221))
% 179.72/179.57 [3226]E(f323(f102(a1),f323(f100(a1),x32261)),f323(f100(a1),x32261))
% 179.72/179.57 [3227]E(f323(f73(a1),f323(f100(a1),x32271)),f323(f100(a1),x32271))
% 179.72/179.57 [3232]E(f323(f35(x32321),f188(f867(x32321,a855))),f2(a860))
% 179.72/179.57 [3234]E(f323(f323(f36(a860),x32341),f323(a112,f2(a860))),x32341)
% 179.72/179.57 [3243]E(f42(a860,x32431,f323(a112,f2(a860))),f2(a860))
% 179.72/179.57 [3244]E(f42(a1,x32441,f323(f103(a1),a97)),f2(a1))
% 179.72/179.57 [3260]E(f323(f323(f36(a1),x32601),f323(f103(a1),a97)),f323(f77(a1),x32601))
% 179.72/179.57 [3264]E(f132(a860,f323(f293(a860,x32641),f2(a860))),f113(a860))
% 179.72/179.57 [3265]E(f323(f323(f78(a1),x32651),f76(a1)),f323(f323(f22(a1),x32651),a97))
% 179.72/179.57 [3266]E(f323(f323(f22(a1),x32661),f76(a1)),f323(f323(f78(a1),x32661),a97))
% 179.72/179.57 [3270]P101(f323(f323(f237(a860),x32701),x32701))
% 179.72/179.57 [3271]P101(f323(f323(f237(a1),x32711),x32711))
% 179.72/179.57 [3272]P101(f323(f323(f89(a1),x32721),x32721))
% 179.72/179.57 [3277]E(f323(f77(a1),f323(f103(a1),x32771)),f323(f103(a1),f323(f77(a1),x32771)))
% 179.72/179.57 [3278]P101(f323(f59(a860),f323(f244(a860),x32781)))
% 179.72/179.57 [3279]P101(f323(f59(a860),f323(f292(a860),x32791)))
% 179.72/179.57 [3287]E(f154(x32871,f246(f867(x32871,a855))),f246(f867(f861(x32871),a855)))
% 179.72/179.57 [3292]P101(f323(f323(f237(a860),f2(a860)),x32921))
% 179.72/179.57 [3302]E(f323(f323(f78(a860),f111(x33021)),f323(a112,f2(a860))),f111(f323(a112,x33021)))
% 179.72/179.57 [3303]E(f323(f243(x33031),f323(f16(a855,x33031),a241)),f188(f867(x33031,a855)))
% 179.72/179.57 [3304]E(f323(f243(x33041),f323(f16(a855,x33041),a187)),f246(f867(x33041,a855)))
% 179.72/179.57 [3308]E(f323(f323(f301(a860),x33081),f323(f244(a860),x33081)),f323(f244(a860),f323(a112,x33081)))
% 179.72/179.57 [3320]E(f323(f323(f78(a1),f76(a1)),f323(f100(a1),x33201)),f323(f100(a1),f323(a112,x33201)))
% 179.72/179.57 [3322]E(f323(f323(f144(f861(x33221)),f113(x33221)),f113(f861(x33221))),f51(x33221,f113(x33221)))
% 179.72/179.57 [3342]E(f188(f867(f866(x33421,x33421),a855)),f255(x33421,f188(f867(x33421,a855))))
% 179.72/179.57 [3343]E(f323(f300(x33431),f246(f867(x33431,a855))),f246(f867(f867(x33431,a855),a855)))
% 179.72/179.57 [3344]E(f323(f77(f867(x33441,a855)),f188(f867(x33441,a855))),f246(f867(x33441,a855)))
% 179.72/179.57 [3345]E(f323(f77(f867(x33451,a855)),f246(f867(x33451,a855))),f188(f867(x33451,a855)))
% 179.72/179.57 [3347]P101(f323(f59(x33471),f188(f867(x33471,a855))))
% 179.72/179.57 [3349]E(f323(f293(a860,x33491),f323(a112,x33491)),f323(f323(f301(a860),x33491),f188(f867(a860,a855))))
% 179.72/179.57 [3350]E(f83(f866(a860,a860),f45(x33501,f2(a860))),f323(f323(f258(a860,a860),f2(a860)),x33501))
% 179.72/179.57 [3364]E(f323(f323(f301(a860),f323(a112,x33641)),f323(f292(a860),x33641)),f323(f292(a860),f323(a112,x33641)))
% 179.72/179.57 [3368]P38(x33681,f188(f867(f866(x33681,x33681),a855)))
% 179.72/179.57 [3371]P101(f323(f323(f237(a1),f2(a1)),f323(f100(a1),x33711)))
% 179.72/179.57 [3379]E(f323(f323(f78(a860),f323(f189(a860),x33791)),f323(a112,f2(a860))),f323(f189(a860),f323(a112,x33791)))
% 179.72/179.57 [3488]P39(f323(f302(a860,a1,f100(a1)),x34881))
% 179.72/179.57 [3526]P40(x35261,f188(f867(x35261,a855)),f188(f867(f866(x35261,x35261),a855)))
% 179.72/179.57 [3545]E(f323(f323(f258(a1,a1),f323(f103(a1),a97)),f323(f323(f22(a1),x35451),f76(a1))),f47(f323(f103(a1),a97),x35451))
% 179.72/179.57 [3598]P56(x35981,f323(f16(f867(x35981,a855),x35981),f323(f16(a855,x35981),a241)))
% 179.72/179.57 [3802]P101(f323(f323(f325(f867(f866(a860,a860),a855)),f324(x38021)),a98))
% 179.72/179.57 [3828]P101(f323(f323(f325(f867(f866(a860,a860),a855)),f323(a107,x38281)),a98))
% 179.72/179.57 [3968]P27(x39681,f867(x39681,a855),f323(f323(f7(x39681,f867(x39681,a855),f867(x39681,a855)),f301(x39681)),f188(f867(x39681,a855))),f246(f867(x39681,a855)))
% 179.72/179.57 [4487]~E(f323(f323(f78(a1),x44871),x44871),a97)
% 179.72/179.57 [4514]~E(f323(a3,f323(a112,f323(a19,x45141))),f2(a99))
% 179.72/179.57 [4522]~P101(f323(a193,f323(f100(a1),x45221)))
% 179.72/179.57 [4525]~P101(f323(f323(f238(a860),x45251),x45251))
% 179.72/179.57 [4534]~P101(f323(f323(f237(a860),f323(a112,x45341)),x45341))
% 179.72/179.57 [3294]E(f323(a104,f323(f77(a1),f323(f100(a1),x32941))),f2(a860))
% 179.72/179.57 [3297]E(f323(f323(f78(a1),f323(f77(a1),x32971)),x32971),f2(a1))
% 179.72/179.57 [3301]E(f323(f35(a1),f323(f293(a1,f2(a1)),x33011)),f323(a104,x33011))
% 179.72/179.57 [3313]E(f323(f323(f248(a860),f323(a112,f2(a860))),x33131),f323(a112,f2(a860)))
% 179.72/179.57 [3414]E(f323(f276(x34141),f188(f867(f866(x34141,x34141),a855))),f188(f867(x34141,a855)))
% 179.72/179.57 [3422]E(f37(f867(x34221,a855),f188(f867(f867(x34221,a855),a855))),f188(f867(x34221,a855)))
% 179.72/179.57 [3423]E(f37(f867(x34231,a855),f246(f867(f867(x34231,a855),a855))),f246(f867(x34231,a855)))
% 179.72/179.57 [3424]E(f38(f867(x34241,a855),f188(f867(f867(x34241,a855),a855))),f246(f867(x34241,a855)))
% 179.72/179.57 [3425]E(f38(f867(x34251,a855),f246(f867(f867(x34251,a855),a855))),f188(f867(x34251,a855)))
% 179.72/179.57 [3471]E(f323(f323(f301(f861(x34711)),f113(x34711)),f188(f867(f861(x34711),a855))),f155(x34711,f113(f867(x34711,a855))))
% 179.72/179.57 [3472]E(f323(f323(f301(f861(x34721)),f113(x34721)),f188(f867(f861(x34721),a855))),f154(x34721,f188(f867(x34721,a855))))
% 179.72/179.57 [3509]E(f323(f323(f78(a860),f4(x35091)),f323(a112,f2(a860))),f4(f323(a3,f323(a112,f323(a19,x35091)))))
% 179.72/179.57 [3537]E(f323(f35(a1),f323(f302(a860,a1,f100(a1)),x35371)),f323(f35(a860),x35371))
% 179.72/179.57 [3538]P101(f323(f323(f237(a860),x35381),f323(f323(f79(a860),x35381),x35381)))
% 179.72/179.57 [3576]E(f323(f302(a1,a860,a104),f294(a1,f2(a1),f323(f100(a1),x35761))),f323(f292(a860),x35761))
% 179.72/179.57 [3593]E(f323(f323(f36(a860),f323(a112,f2(a860))),f323(f103(a860),x35931)),f323(a104,f323(f323(f36(a1),f76(a1)),f323(f103(a1),x35931))))
% 179.72/179.57 [3595]E(f323(f166(a860),f132(a860,f323(f293(a860,f2(a860)),f323(a112,x35951)))),f323(f292(a860),x35951))
% 179.72/179.57 [3596]E(f323(f323(f78(a860),f323(f189(a99),x35961)),f323(a112,f2(a860))),f323(f189(a99),f323(a3,f323(a112,f323(a19,x35961)))))
% 179.72/179.57 [3613]E(f323(f302(a1,a860,a104),f323(f302(a860,a1,f100(a1)),x36131)),x36131)
% 179.72/179.57 [3646]E(f323(f323(f301(a860),f2(a860)),f323(f302(a860,a860,a112),f323(f244(a860),x36461))),f323(f244(a860),f323(a112,x36461)))
% 179.72/179.57 [3652]P51(x36521,x36521,f299(x36521,f188(f867(f866(x36521,x36521),a855))))
% 179.72/179.57 [3658]P101(f323(a193,f323(f77(a1),f323(f100(a1),f323(a112,x36581)))))
% 179.72/179.57 [3669]E(f323(f323(f22(f867(a860,a855)),f323(f245(a860),x36691)),f323(f323(f301(a860),x36691),f188(f867(a860,a855)))),f323(f245(a860),f323(a112,x36691)))
% 179.72/179.57 [3685]E(f323(f323(f78(a1),f323(f323(f22(a1),a81),x36851)),f323(f323(f22(a1),a81),x36851)),f323(f323(f22(a1),a81),f323(f323(f78(a1),x36851),x36851)))
% 179.72/179.57 [3701]E(f323(f323(f301(f867(x37011,a855)),f188(f867(x37011,a855))),f188(f867(f867(x37011,a855),a855))),f323(f300(x37011),f188(f867(x37011,a855))))
% 179.72/179.57 [3729]E(f323(f323(f22(f867(a860,a855)),f323(f295(a860),x37291)),f323(f323(f301(a860),f323(a112,x37291)),f188(f867(a860,a855)))),f323(f295(a860),f323(a112,x37291)))
% 179.72/179.57 [3738]E(f323(f323(f301(f864(x37381)),f200(x37381)),f323(f302(x37381,f864(x37381),f230(x37381)),f246(f867(x37381,a855)))),f246(f867(f864(x37381),a855)))
% 179.72/179.57 [3840]E(f323(f103(a860),f323(f323(f78(a1),x38401),x38401)),f323(f323(f84(a860,a860),f323(f103(a860),x38401)),f323(f323(f18(a860,a860,a860),f78(a860)),f5(a860))))
% 179.72/179.57 [4233]P17(x42331,f867(x42331,a855),f323(f323(f8(f867(x42331,a855),f867(f867(x42331,a855),f867(x42331,a855)),x42331),f323(f7(f867(x42331,a855),f867(x42331,a855),f867(x42331,a855)),f22(f867(x42331,a855)))),f323(f323(f7(x42331,f867(x42331,a855),f867(x42331,a855)),f301(x42331)),f188(f867(x42331,a855)))))
% 179.72/179.57 [4322]E(f323(f243(f866(a1,a1)),f323(f262(a1,a1,a855),f323(f323(f8(f867(a1,a855),f867(a1,a855),a1),f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),x43221)))),f238(a1)))),f105(x43221))
% 179.72/179.57 [4356]E(f323(f243(f866(a1,a1)),f323(f262(a1,a1,a855),f323(f323(f18(a1,f867(a1,a855),f867(a1,a855)),f323(f323(f8(f867(a855,a855),f867(f867(a1,a855),f867(a1,a855)),a1),f8(a855,a855,a1)),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),x43561)))),f238(a1)))),f106(x43561))
% 179.72/179.57 [4411]E(f323(f243(f866(f867(x44111,a855),f867(x44111,a855))),f323(f262(f867(x44111,a855),f867(x44111,a855),a855),f323(f323(f7(f867(x44111,a855),f867(f867(x44111,a855),a855),f867(f867(x44111,a855),a855)),f323(f323(f8(f867(f867(x44111,a855),f867(a855,a855)),f867(f867(f867(x44111,a855),a855),f867(f867(x44111,a855),a855)),f867(x44111,a855)),f18(f867(x44111,a855),a855,a855)),f323(f323(f8(f867(f867(x44111,a855),a855),f867(f867(x44111,a855),f867(a855,a855)),f867(x44111,a855)),f323(f8(a855,f867(a855,a855),f867(x44111,a855)),a321)),f238(f867(x44111,a855))))),f59(x44111)))),f298(x44111))
% 179.72/179.57 [4538]~P101(f323(f59(f861(x45381)),f246(f867(f861(x45381),a855))))
% 179.72/179.57 [4543]~P101(f323(f323(f89(a1),a97),f323(f323(f78(a1),x45431),x45431)))
% 179.72/179.57 [4553]~P101(f323(f323(f237(a1),f2(a1)),f323(f77(a1),f323(f100(a1),f323(a112,x45531)))))
% 179.72/179.57 [3449]E(f323(f323(f22(a1),f323(f323(f78(a1),x34491),a97)),a97),x34491)
% 179.72/179.57 [3465]E(f323(f166(a860),f132(a860,f323(f293(a860,f2(a860)),x34651))),f323(f244(a860),x34651))
% 179.72/179.57 [3708]E(f323(f323(f78(a1),f323(f323(f78(a1),f76(a1)),x37081)),x37081),f323(f323(f22(a1),f323(f323(f78(a1),x37081),x37081)),a97))
% 179.72/179.57 [3757]E(f323(f278(x37571,x37571),f299(x37571,f188(f867(f866(x37571,x37571),a855)))),f299(x37571,f188(f867(f866(x37571,x37571),a855))))
% 179.72/179.57 [3805]P101(f323(f323(f237(a860),x38051),f323(f323(f79(a860),x38051),f323(f323(f79(a860),x38051),x38051))))
% 179.72/179.57 [4088]P101(f323(f59(a860),f323(f243(a860),f323(f323(f7(a860,a860,a855),f237(a860)),x40881))))
% 179.72/179.57 [4089]P101(f323(f59(a860),f323(f243(a860),f323(f323(f7(a860,a860,a855),f238(a860)),x40891))))
% 179.72/179.57 [4376]E(f323(f243(f866(x43761,x43761)),f323(f323(f8(f867(x43761,a855),a855,f866(x43761,x43761)),f85(x43761)),f323(f323(f7(f866(x43761,x43761),f867(x43761,f866(x43761,x43761)),f867(x43761,a855)),f323(f323(f8(f867(f866(x43761,x43761),a855),f867(f867(x43761,f866(x43761,x43761)),f867(x43761,a855)),f866(x43761,x43761)),f8(f866(x43761,x43761),a855,x43761)),a320)),f323(f323(f18(x43761,x43761,f866(x43761,x43761)),f258(x43761,x43761)),f5(x43761))))),f299(x43761,f188(f867(f866(x43761,x43761),a855))))
% 179.72/179.57 [4540]~E(f323(f323(f22(a1),f323(f323(f78(a1),x45401),x45401)),a97),a81)
% 179.72/179.57 [4542]~E(f323(f323(f78(a1),f323(f323(f78(a1),f76(a1)),x45421)),x45421),f2(a1))
% 179.72/179.57 [4550]~P101(f323(f323(f89(a1),f323(f323(f78(a1),x45501),x45501)),a97))
% 179.72/179.57 [3853]E(f323(f323(f78(a1),f323(f323(f22(a1),a97),x38531)),f323(f323(f22(a1),a97),x38531)),f323(f323(f22(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x38531),x38531)),a97)))
% 179.72/179.57 [3977]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),a97),x39771)),f323(f323(f22(a1),a97),x39771))),a97),f323(f323(f22(a1),a97),f323(f323(f78(a1),x39771),x39771)))
% 179.72/179.57 [4012]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f78(a1),x40121),a97)),f323(f323(f78(a1),x40121),a97))),a97),f323(f323(f78(a1),f323(f323(f78(a1),x40121),x40121)),a97))
% 179.72/179.57 [4050]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),a97),x40501)),f323(f323(f22(a1),a97),x40501))),a97),f323(f323(f22(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x40501),x40501)),a97)))
% 179.72/179.57 [4150]E(f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x41501),f2(a860))),f188(f867(f866(a860,a860),a855))))),f323(f100(a1),x41501))
% 179.72/179.57 [4160]E(f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),f328(x41601)),f528(x41601))),f188(f867(f866(a860,a860),a855))))),x41601)
% 179.72/179.57 [4195]E(f323(f243(a1),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),f2(a1)))),x41951)),f323(f302(a860,a1,f100(a1)),f323(f243(a860),f323(f323(f8(a1,a855,a860),x41951),f100(a1)))))
% 179.72/179.57 [4241]P39(f323(f243(a1),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),f2(a1)))),x42411)))
% 179.72/179.57 [4262]P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),x42621),f188(f867(f866(a860,a860),a855)))),a69))
% 179.72/179.57 [4268]E(f323(f302(a1,a860,a104),f323(f243(a1),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),f2(a1)))),f323(f323(f8(a860,a855,a1),x42681),a104)))),f323(f243(a860),x42681))
% 179.72/179.57 [4425]E(f304(a860,f323(f323(f39(f866(a860,a860),f867(a860,a855)),f323(a107,x44251)),f323(f262(a860,a860,f867(a860,a855)),f323(f323(f7(a860,f867(a860,a855),f867(a860,f867(a860,a855))),f323(f323(f8(f867(a860,f867(f867(a860,a855),f867(a860,a855))),f867(f867(a860,a855),f867(a860,f867(a860,a855))),a860),f7(a860,f867(a860,a855),f867(a860,a855))),f323(f323(f8(f867(a860,a860),f867(a860,f867(f867(a860,a855),f867(a860,a855))),a860),f323(f8(a860,f867(f867(a860,a855),f867(a860,a855)),a860),f301(a860))),f22(a860)))),f188(f867(a860,a855)))))),f323(a104,x44251))
% 179.72/179.57 [4555]~P101(f323(f323(f89(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x45551),x45551)),a97)))
% 179.72/179.57 [3898]E(f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),x38981),x38981)),a97)),a97),f323(f323(f78(a1),x38981),x38981))
% 179.72/179.57 [3950]E(f323(f323(f22(a1),f323(f323(f22(a1),f323(f323(f78(a1),x39501),x39501)),a97)),a97),f323(f323(f78(a1),f323(f323(f22(a1),x39501),a97)),f323(f323(f22(a1),x39501),a97)))
% 179.72/179.57 [4168]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f78(a1),f323(f77(a1),x41681)),a97)),f323(f323(f78(a1),f323(f77(a1),x41681)),a97))),a97),f323(f77(a1),f323(f323(f22(a1),f323(f323(f78(a1),x41681),x41681)),a97)))
% 179.72/179.57 [4563]~P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x45631),x45631)),a97)),a81))
% 179.72/179.57 [4213]E(f323(f323(f78(a860),x42131),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(a112,f323(a112,x42131)))
% 179.72/179.57 [4214]E(f323(f323(f79(a860),x42141),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(f323(f78(a860),x42141),x42141))
% 179.72/179.57 [4215]E(f323(f323(f36(a860),f323(f323(f78(a860),x42151),x42151)),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x42151)
% 179.72/179.57 [4297]E(f42(a860,f323(a112,f323(a112,x42971)),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f42(a860,x42971,f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.57 [4442]E(f323(a87,f323(f323(f39(f866(a860,a860),f867(f866(a860,a860),a855)),f323(a107,x44421)),f323(f262(a860,a860,f867(f866(a860,a860),a855)),f323(f323(f8(f867(a860,f867(f866(a860,a860),a855)),f867(a860,f867(f866(a860,a860),a855)),a860),f323(f8(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855),a860),f277(f866(a860,a860),f866(a860,a860),a108))),f323(f323(f7(a860,f867(f866(a860,a860),a855),f867(a860,f867(f866(a860,a860),a855))),f323(f323(f8(f867(a860,f867(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f867(f867(f866(a860,a860),a855),f867(a860,f867(f866(a860,a860),a855))),a860),f7(a860,f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f8(f867(a860,f866(a860,a860)),f867(a860,f867(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),a860),f323(f8(f866(a860,a860),f867(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),a860),f301(f866(a860,a860)))),f323(f7(a860,a860,f866(a860,a860)),f258(a860,a860))))),f188(f867(f866(a860,a860),a855))))))),f323(f77(a1),x44421))
% 179.72/179.57 [4292]E(f323(f323(f78(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x42921),f323(a112,f323(a112,x42921)))
% 179.72/179.57 [4293]E(f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x42931),f323(f323(f78(a860),x42931),x42931))
% 179.72/179.57 [4328]E(f323(f323(f36(a860),f323(a112,f323(a112,x43281))),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(a112,f323(f323(f36(a860),x43281),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))
% 179.72/179.57 [4382]E(f323(f323(f78(a860),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97))),x43821),f323(a112,f323(a112,f323(a112,x43821))))
% 179.72/179.57 [4456]E(f323(f262(a1,a1,f866(a1,a1)),f323(f323(f18(a1,f867(a1,f866(a1,a1)),f867(a1,f866(a1,a1))),f323(f323(f8(f867(a1,f867(f866(a1,a1),f866(a1,a1))),f867(f867(a1,f866(a1,a1)),f867(a1,f866(a1,a1))),a1),f18(a1,f866(a1,a1),f866(a1,a1))),f323(f323(f8(f867(a1,f866(a1,a1)),f867(a1,f867(f866(a1,a1),f866(a1,a1))),a1),f323(f18(a1,f866(a1,a1),f867(f866(a1,a1),f866(a1,a1))),f323(f323(f8(a855,f867(f866(a1,a1),f867(f866(a1,a1),f866(a1,a1))),a1),f96(f866(a1,a1))),f323(f323(f8(a1,a855,a1),f323(f237(a1),f2(a1))),f323(f323(f7(a1,a1,a1),f22(a1)),x44561))))),f323(f323(f7(a1,f867(a1,a1),f867(a1,f866(a1,a1))),f323(f323(f8(f867(a1,f866(a1,a1)),f867(f867(a1,a1),f867(a1,f866(a1,a1))),a1),f8(a1,f866(a1,a1),a1)),f323(f323(f8(a1,f867(a1,f866(a1,a1)),a1),f258(a1,a1)),f323(f323(f7(a1,a1,a1),f323(f323(f8(a1,f867(a1,a1),a1),f78(a1)),f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))),f76(a1))))),f323(f323(f7(a1,a1,a1),f22(a1)),x44561))))),f323(f323(f8(a1,f867(a1,f866(a1,a1)),a1),f258(a1,a1)),f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))),f41(x44561))
% 179.72/179.57 [3118]P92(f865(x31181,x31182))
% 179.72/179.57 [3119]P92(f866(x31191,x31192))
% 179.72/179.57 [3120]P100(f865(x31201,x31202))
% 179.72/179.57 [3121]P100(f866(x31211,x31212))
% 179.72/179.57 [3138]P16(a1,f172(x31381,x31382))
% 179.72/179.57 [3139]P38(x31391,f146(x31391,x31392))
% 179.72/179.57 [3204]P32(x32041,x32042,f113(x32041))
% 179.72/179.57 [3238]P40(x32381,x32382,f255(x32381,x32382))
% 179.72/179.57 [3239]P51(x32391,x32391,f255(x32391,x32392))
% 179.72/179.57 [3512]P27(x35121,x35121,f5(x35121),x35122)
% 179.72/179.57 [3513]P27(x35131,x35131,f32(x35131),x35132)
% 179.72/179.57 [3521]P33(x35211,x35212,f113(x35211),f113(x35211))
% 179.72/179.57 [3522]P27(x35221,f864(x35221),f230(x35221),x35222)
% 179.72/179.57 [3531]P27(f861(x35311),f861(x35311),f162(x35311),x35312)
% 179.72/179.57 [3941]P28(x39411,x39411,f32(x39411),x39412,x39412)
% 179.72/179.57 [4466]~E(f30(x44661,x44662),a24)
% 179.72/179.57 [4467]~E(f29(x44671,x44672),a24)
% 179.72/179.57 [4468]~E(f25(x44681,x44682),a24)
% 179.72/179.57 [4497]~P34(x44971,x44972,f113(x44971))
% 179.72/179.57 [4498]~P36(x44981,x44982,f113(x44981))
% 179.72/179.57 [3104]E(f323(f243(x31041),x31042),x31042)
% 179.72/179.57 [3105]E(f323(f5(x31051),x31052),x31052)
% 179.72/179.57 [3107]E(f323(f32(x31071),x31072),x31072)
% 179.72/179.57 [3117]E(f323(f191(x31171),x31172),f115(x31171))
% 179.72/179.57 [3126]E(f28(f25(x31261,x31262)),f2(a860))
% 179.72/179.57 [3136]E(f83(x31361,f323(a320,x31362)),x31362)
% 179.72/179.57 [3137]E(f88(x31371,f323(a320,x31372)),x31372)
% 179.72/179.57 [3154]E(f323(f189(a857),f25(x31541,x31542)),f2(a860))
% 179.72/179.57 [3158]E(f323(f129(x31581,x31582),f113(x31581)),f113(x31581))
% 179.72/179.57 [3178]E(f145(x31781,f145(x31781,x31782)),f145(x31781,x31782))
% 179.72/179.57 [3179]E(f299(x31791,f299(x31791,x31792)),f299(x31791,x31792))
% 179.72/179.57 [3199]E(f323(f323(f121(x31991),x31992),f113(x31991)),x31992)
% 179.72/179.57 [3205]E(f167(x32051,x32052,f113(x32051)),x32052)
% 179.72/179.57 [3206]E(f167(x32061,f113(x32061),x32062),x32062)
% 179.72/179.57 [3207]E(f163(x32071,f2(a860),x32072),f113(x32071))
% 179.72/179.57 [3213]E(f323(f323(f169(x32131),x32132),f113(x32131)),f113(x32131))
% 179.72/179.57 [3214]E(f323(f323(f131(x32141),x32142),f113(x32141)),f113(x32141))
% 179.72/179.57 [3216]E(f231(x32161,x32162,f200(x32161)),f2(a860))
% 179.72/179.57 [3217]E(f148(x32171,x32172,f113(x32171)),f2(a860))
% 179.72/179.57 [3219]E(f164(x32191,x32192,f113(x32191)),f113(x32191))
% 179.72/179.57 [3220]E(f171(x32201,x32202,f113(x32201)),f113(x32201))
% 179.72/179.57 [3221]E(f170(x32211,f113(x32211),x32212),f113(x32211))
% 179.72/179.57 [3225]E(f323(f166(x32251),f145(x32251,x32252)),f323(f166(x32251),x32252))
% 179.72/179.57 [3228]E(f323(f254(x32281,x32281),f255(x32281,x32282)),x32282)
% 179.72/179.57 [3229]E(f323(f256(x32291,x32291),f255(x32291,x32292)),x32292)
% 179.72/179.57 [3237]E(f323(f278(x32371,x32371),f255(x32371,x32372)),f255(x32371,x32372))
% 179.72/179.57 [3252]E(f299(f861(x32521),f150(x32521,x32522)),f151(x32521,f299(x32521,x32522)))
% 179.72/179.57 [3254]P101(f323(f130(a1),f172(x32541,x32542)))
% 179.72/179.57 [3262]E(f323(f254(x32621,x32621),f299(x32621,x32622)),f246(f867(x32621,a855)))
% 179.72/179.57 [3263]E(f323(f256(x32631,x32631),f299(x32631,x32632)),f246(f867(x32631,a855)))
% 179.72/179.57 [3267]P101(f323(f130(x32671),f145(x32671,x32672)))
% 179.72/179.57 [3269]P101(f323(f153(x32691,x32692),f113(x32691)))
% 179.72/179.57 [3275]E(f323(f166(a1),f172(x32751,x32752)),f294(a1,x32751,x32752))
% 179.72/179.57 [3290]P52(x32901,f188(f867(x32901,a855)),x32902)
% 179.72/179.57 [3295]E(f323(f261(a1,a1),f43(x32951,x32952)),f42(a1,x32951,x32952))
% 179.72/179.57 [3296]E(f323(f293(a860,x32961),f323(a112,x32962)),f294(a860,x32961,x32962))
% 179.72/179.57 [3312]E(f323(f323(f144(x33121),x33122),f113(x33121)),f133(x33121,x33122,f113(x33121)))
% 179.72/179.57 [3324]E(f294(a860,f323(a112,x33241),x33242),f296(a860,x33241,x33242))
% 179.72/179.57 [3327]P40(x33271,f246(f867(x33271,a855)),f299(x33271,x33272))
% 179.72/179.57 [3391]E(f323(f323(f22(a860),x33911),f323(a112,x33912)),f323(f35(a860),f297(a860,x33912,x33911)))
% 179.72/179.57 [3450]E(f160(x34501,x34502,f113(x34501)),f323(f323(f258(f861(x34501),f861(x34501)),f113(x34501)),f113(x34501)))
% 179.72/179.57 [3469]E(f323(f262(x34691,x34692,f866(x34691,x34692)),f258(x34691,x34692)),f32(f866(x34691,x34692)))
% 179.72/179.57 [3473]P101(f323(f323(f325(f861(x34731)),f113(x34731)),f154(x34731,x34732)))
% 179.72/179.57 [3474]E(f323(f189(f861(x34741)),f114(x34741,x34742)),f323(f323(f22(a860),f323(f189(f861(x34741)),x34742)),f76(a860)))
% 179.72/179.57 [3482]P101(f323(f59(a860),f294(a860,x34821,x34822)))
% 179.72/179.57 [3483]P101(f323(f59(a860),f297(a860,x34831,x34832)))
% 179.72/179.57 [3484]P101(f323(f59(a860),f296(a860,x34841,x34842)))
% 179.72/179.57 [3485]P101(f323(f59(a1),f294(a1,x34851,x34852)))
% 179.72/179.57 [3486]P101(f323(f59(a1),f297(a1,x34861,x34862)))
% 179.72/179.57 [3487]P101(f323(f59(a1),f296(a1,x34871,x34872)))
% 179.72/179.57 [3592]E(f323(f302(a860,a860,a112),f294(a860,x35921,x35922)),f294(a860,f323(a112,x35921),f323(a112,x35922)))
% 179.72/179.57 [3610]E(f323(f323(f280(x36101,x36101,x36101),f299(x36101,x36102)),f299(x36101,x36102)),f299(x36101,x36102))
% 179.72/179.57 [3644]E(f323(f323(f258(a1,a1),f323(f323(f36(a1),x36441),x36442)),f42(a1,x36441,x36442)),f43(x36441,x36442))
% 179.72/179.57 [3645]E(f323(f323(f258(a99,a99),f323(f323(f36(a99),x36451),x36452)),f42(a99,x36451,x36452)),f21(x36451,x36452))
% 179.72/179.57 [3673]E(f323(f323(f258(a860,a860),f323(f323(f36(a860),x36731),x36732)),f42(a860,x36731,x36732)),f83(f866(a860,a860),f45(x36731,x36732)))
% 179.72/179.57 [3725]P101(f323(f323(f238(a860),f323(f323(f22(a860),x37251),x37252)),f323(a112,x37251)))
% 179.72/179.57 [3827]E(f323(f323(f78(a1),f323(f323(f79(a1),x38271),f323(f323(f36(a1),x38272),x38271))),f42(a1,x38272,x38271)),x38272)
% 179.72/179.57 [3831]E(f323(f323(f39(a860,f867(f866(f861(x38311),f861(x38311)),a855)),f246(f867(a860,a855))),f136(x38311,x38312)),f138(x38311,x38312))
% 179.72/179.57 [4063]P101(f323(f323(f325(f866(f861(x40631),f861(x40631))),f323(f323(f258(f861(x40631),f861(x40631)),f113(x40631)),f113(x40631))),f151(x40631,x40632)))
% 179.72/179.57 [4226]E(f263(x42261,x42261,x42262,x42262,f5(x42261),f5(x42262)),f32(f866(x42261,x42262)))
% 179.72/179.57 [4228]E(f263(x42281,x42281,x42282,x42282,f32(x42281),f32(x42282)),f32(f866(x42281,x42282)))
% 179.72/179.57 [4476]~E(f323(f230(x44761),x44762),f200(x44761))
% 179.72/179.57 [3197]E(f323(f234(x31971),f323(f230(x31971),x31972)),x31972)
% 179.72/179.57 [3198]E(f323(f162(x31981),f323(f162(x31981),x31982)),x31982)
% 179.72/179.57 [3200]E(f323(f323(f131(x32001),f2(a860)),x32002),x32002)
% 179.72/179.57 [3215]E(f323(f323(f169(x32151),f2(a860)),x32152),f113(x32151))
% 179.72/179.57 [3223]E(f323(f323(f121(x32231),f113(x32231)),x32232),x32232)
% 179.72/179.57 [3231]E(f323(f189(f864(x32311)),f323(f230(x32311),x32312)),f2(a860))
% 179.72/179.57 [3233]E(f37(f867(x32331,a855),f323(f300(x32331),x32332)),x32332)
% 179.72/179.57 [3235]E(f323(f166(x32351),f323(f161(x32351),x32352)),f323(f166(x32351),x32352))
% 179.72/179.57 [3236]E(f323(f166(x32361),f323(f162(x32361),x32362)),f323(f166(x32361),x32362))
% 179.72/179.57 [3241]E(f323(f323(f22(a99),x32411),x32412),f323(f323(a23,x32411),x32412))
% 179.72/179.57 [3256]E(f323(f323(f79(a860),x32561),x32562),f323(f323(f79(a860),x32562),x32561))
% 179.72/179.57 [3257]E(f323(f323(f79(a1),x32571),x32572),f323(f323(f79(a1),x32572),x32571))
% 179.72/179.57 [3258]E(f323(f323(f78(a860),x32581),x32582),f323(f323(f78(a860),x32582),x32581))
% 179.72/179.57 [3259]E(f323(f323(f78(a1),x32591),x32592),f323(f323(f78(a1),x32592),x32591))
% 179.72/179.57 [3282]E(f323(f323(f183(x32821,x32821),f2(a860)),x32822),f32(x32821))
% 179.72/179.57 [3283]E(f323(f189(f861(x32831)),f323(f161(x32831),x32832)),f323(f189(f861(x32831)),x32832))
% 179.72/179.57 [3284]E(f323(f189(f861(x32841)),f323(f162(x32841),x32842)),f323(f189(f861(x32841)),x32842))
% 179.72/179.57 [3285]E(f170(x32851,x32852,f188(f867(a860,a855))),f113(x32851))
% 179.72/179.57 [3286]E(f323(f323(f147(x32861,x32861),f5(x32861)),x32862),x32862)
% 179.72/179.57 [3288]E(f323(f257(a1,a1),f43(x32881,x32882)),f323(f323(f36(a1),x32881),x32882))
% 179.72/179.57 [3305]E(f323(f189(f861(x33051)),f145(x33051,x33052)),f323(f35(x33051),f323(f166(x33051),x33052)))
% 179.72/179.57 [3306]E(f28(f29(x33061,x33062)),f323(f323(f78(a860),f28(x33062)),f323(a112,f2(a860))))
% 179.72/179.57 [3307]E(f323(f276(x33071),f323(f278(x33071,x33071),x33072)),f323(f276(x33071),x33072))
% 179.72/179.57 [3311]P101(f323(f59(x33111),f323(f166(x33111),x33112)))
% 179.72/179.57 [3319]E(f323(f323(f78(a1),x33191),f323(f77(a1),x33192)),f323(f323(f22(a1),x33191),x33192))
% 179.72/179.57 [3326]P26(x33261,x33262,f188(f867(f859(x33261),a855)))
% 179.72/179.57 [3328]E(f323(f302(x33281,x33281,f5(x33281)),x33282),x33282)
% 179.72/179.57 [3329]E(f323(f302(x33291,x33291,f32(x33291)),x33292),x33292)
% 179.72/179.57 [3330]E(f323(f303(x33301,x33301,f5(x33301)),x33302),x33302)
% 179.72/179.57 [3331]E(f323(f303(x33311,x33311,f32(x33311)),x33312),x33312)
% 179.72/179.57 [3332]P101(f323(f246(f867(x33321,a855)),x33322))
% 179.72/179.57 [3334]E(f323(f35(a860),f323(f293(a860,x33341),x33342)),f323(f323(f22(a860),x33342),x33341))
% 179.72/179.57 [3335]E(f323(f293(a860,f323(a112,x33351)),x33352),f297(a860,x33351,x33352))
% 179.72/179.57 [3348]E(f323(f323(f301(x33481),x33482),f188(f867(x33481,a855))),f323(f243(x33481),f323(a320,x33482)))
% 179.72/179.57 [3352]E(f323(f323(f301(x33521),x33522),f188(f867(x33521,a855))),f229(x33521,f323(f230(x33521),x33522)))
% 179.72/179.57 [3355]E(f299(x33551,f323(f278(x33551,x33551),x33552)),f323(f278(x33551,x33551),f299(x33551,x33552)))
% 179.72/179.57 [3359]E(f323(f323(f78(a860),f323(a112,x33591)),x33592),f323(f323(f78(a860),x33591),f323(a112,x33592)))
% 179.72/179.57 [3360]E(f323(f323(f22(a860),f323(a112,x33601)),f323(a112,x33602)),f323(f323(f22(a860),x33601),x33602))
% 179.72/179.57 [3366]E(f52(x33661,f2(a860),x33662),f323(f323(f144(f861(x33661)),f113(x33661)),f113(f861(x33661))))
% 179.72/179.57 [3367]E(f323(f35(a860),f296(a860,x33671,x33672)),f323(f323(f22(a860),x33672),x33671))
% 179.72/179.57 [3376]P38(x33761,f323(f323(f279(a860,x33761),a242),x33762))
% 179.72/179.57 [3378]P16(a860,f132(a860,f323(f293(a860,x33781),x33782)))
% 179.72/179.57 [3380]P101(f323(f59(a860),f323(f293(a860,x33801),x33802)))
% 179.72/179.57 [3381]P101(f323(f59(a1),f323(f293(a1,x33811),x33812)))
% 179.72/179.57 [3384]E(f323(f278(f861(x33841),f861(x33841)),f150(x33841,x33842)),f150(x33841,f323(f278(x33841,x33841),x33842)))
% 179.72/179.57 [3385]E(f323(f189(a857),f29(x33851,x33852)),f323(f323(f78(a860),f323(f189(a857),x33852)),f323(a112,f2(a860))))
% 179.72/179.57 [3387]E(f323(f293(a1,x33871),f323(f323(f78(a1),x33872),f76(a1))),f294(a1,x33871,x33872))
% 179.72/179.57 [3390]E(f323(f323(f36(a1),f323(f77(a1),x33901)),f323(f77(a1),x33902)),f323(f323(f36(a1),x33901),x33902))
% 179.72/179.57 [3398]E(f177(x33981,x33982,f323(f16(f864(x33982),x33981),f200(x33982))),f188(f867(x33981,a855)))
% 179.72/179.57 [3399]E(f178(x33991,x33992,f323(f16(f864(x33992),x33991),f200(x33992))),f188(f867(x33992,a855)))
% 179.72/179.57 [3400]E(f323(f323(f183(f866(x34001,x34001),a855),f76(a860)),x34002),x34002)
% 179.72/179.57 [3402]E(f323(f323(f110(f867(x34021,a855)),x34022),f188(f867(x34021,a855))),x34022)
% 179.72/179.57 [3403]E(f323(f323(f22(f867(x34031,a855)),x34032),f188(f867(x34031,a855))),x34032)
% 179.72/179.57 [3404]E(f323(f323(f101(f867(x34041,a855)),x34042),f246(f867(x34041,a855))),x34042)
% 179.72/179.57 [3405]E(f323(f257(a860,a860),f83(f866(a860,a860),f45(x34051,x34052))),f323(f323(f36(a860),x34051),x34052))
% 179.72/179.57 [3412]E(f305(x34121,f323(a20,x34122),f323(f77(a1),f323(a20,x34122))),f323(f323(f308(a1),x34121),x34122))
% 179.72/179.57 [3413]E(f294(a1,f323(f323(f78(a1),x34131),f76(a1)),x34132),f296(a1,x34131,x34132))
% 179.72/179.57 [3418]E(f323(f261(a860,a860),f83(f866(a860,a860),f45(x34181,x34182))),f42(a860,x34181,x34182))
% 179.72/179.57 [3426]E(f306(x34261,f323(a20,x34262),f323(f77(a1),f323(a20,x34262))),f307(a1,x34261,x34262))
% 179.72/179.57 [3429]P101(f323(f323(f325(x34291),x34292),f246(f867(x34291,a855))))
% 179.72/179.57 [3434]E(f323(f323(f22(a860),f323(a112,x34341)),x34342),f323(f35(a860),f294(a860,x34342,x34341)))
% 179.72/179.57 [3461]E(f323(f323(f110(f867(x34611,a855)),x34612),f246(f867(x34611,a855))),f246(f867(x34611,a855)))
% 179.72/179.57 [3462]E(f323(f323(f22(f867(x34621,a855)),x34622),f246(f867(x34621,a855))),f188(f867(x34621,a855)))
% 179.72/179.57 [3463]E(f323(f323(f101(f867(x34631,a855)),x34632),f188(f867(x34631,a855))),f188(f867(x34631,a855)))
% 179.72/179.57 [3477]E(f42(a1,f323(f77(a1),x34771),f323(f77(a1),x34772)),f323(f77(a1),f42(a1,x34771,x34772)))
% 179.72/179.57 [3478]E(f42(a1,f323(f100(a1),x34781),f323(f100(a1),x34782)),f323(f100(a1),f42(a860,x34781,x34782)))
% 179.72/179.57 [3489]E(f323(f189(f861(x34891)),f323(f165(x34891),x34892)),f323(f323(f22(a860),f323(f189(f861(x34891)),x34892)),f76(a860)))
% 179.72/179.57 [3514]E(f323(f323(f36(a1),f42(a1,x35141,x35142)),x35142),f2(a1))
% 179.72/179.57 [3524]E(f323(a3,f42(a860,f323(a19,x35241),f323(a19,x35242))),f42(a99,x35241,x35242))
% 179.72/179.57 [3558]E(f323(a3,f323(f323(f22(a860),f323(a19,x35581)),f323(a19,x35582))),f323(f323(f22(a99),x35581),x35582))
% 179.72/179.57 [3559]E(f323(a3,f323(f323(f79(a860),f323(a19,x35591)),f323(a19,x35592))),f323(f323(f79(a99),x35591),x35592))
% 179.72/179.57 [3560]E(f323(a3,f323(f323(f78(a860),f323(a19,x35601)),f323(a19,x35602))),f323(f323(f78(a99),x35601),x35602))
% 179.72/179.57 [3561]E(f323(a3,f323(f323(f36(a860),f323(a19,x35611)),f323(a19,x35612))),f323(f323(f36(a99),x35611),x35612))
% 179.72/179.57 [3570]E(f323(f302(a860,a860,a112),f323(f293(a860,x35701),x35702)),f323(f293(a860,f323(a112,x35701)),f323(a112,x35702)))
% 179.72/179.57 [3597]P101(f323(f45(x35971,x35972),f83(f866(a860,a860),f45(x35971,x35972))))
% 179.72/179.57 [3616]E(f323(f323(f78(a860),f323(f323(f78(a860),f28(x36161)),f28(x36162))),f323(a112,f2(a860))),f28(f30(x36161,x36162)))
% 179.72/179.57 [3617]E(f42(a860,f323(a112,f42(a860,x36171,x36172)),x36172),f42(a860,f323(a112,x36171),x36172))
% 179.72/179.57 [3631]E(f323(f323(f39(f867(x36311,a855),f867(x36311,a855)),x36312),f5(f867(x36311,a855))),f37(f867(x36311,a855),x36312))
% 179.72/179.57 [3632]E(f323(f323(f40(f867(x36321,a855),f867(x36321,a855)),x36322),f5(f867(x36321,a855))),f38(f867(x36321,a855),x36322))
% 179.72/179.57 [3633]E(f323(f302(f861(x36331),f867(x36331,a855),f166(x36331)),f323(f166(f861(x36331)),f51(x36331,x36332))),f323(f300(x36331),f323(f166(x36331),x36332)))
% 179.72/179.57 [3637]P101(f323(f323(f325(f867(x36371,a855)),x36372),f323(f300(x36371),x36372)))
% 179.72/179.57 [3643]E(f42(a1,f323(f77(a1),f42(a1,x36431,x36432)),x36432),f42(a1,f323(f77(a1),x36431),x36432))
% 179.72/179.57 [3654]P101(f323(f323(f237(f867(x36541,a855)),x36542),f246(f867(x36541,a855))))
% 179.72/179.57 [3656]E(f323(f323(f280(x36561,x36561,x36561),f299(x36561,x36562)),f299(x36561,f299(x36561,x36562))),f299(x36561,x36562))
% 179.72/179.57 [3657]E(f323(f323(f110(f867(x36571,a855)),f323(f256(x36571,x36571),x36572)),f323(f254(x36571,x36571),x36572)),f323(f276(x36571),x36572))
% 179.72/179.57 [3678]E(f310(x36781,x36782,f246(f867(x36781,a855)),f246(f867(x36782,a855))),f246(f867(f865(x36781,x36782),a855)))
% 179.72/179.57 [3730]P101(f323(f323(f237(a860),f42(a860,x37301,x37302)),x37301))
% 179.72/179.57 [3755]P101(f323(f323(f237(a1),f323(f77(a1),f323(f100(a1),x37551))),f323(f100(a1),x37552)))
% 179.72/179.57 [3781]P101(f323(f323(f325(f867(x37811,a855)),f188(f867(x37811,a855))),f323(f300(x37811),x37812)))
% 179.72/179.57 [3786]E(f299(x37861,f323(f323(f280(x37861,x37861,x37861),x37862),f299(x37861,x37862))),f299(x37861,x37862))
% 179.72/179.57 [3789]E(f323(f323(f280(x37891,x37891,x37891),f299(x37891,x37892)),x37892),f323(f323(f280(x37891,x37891,x37891),x37892),f299(x37891,x37892)))
% 179.72/179.57 [3791]E(f323(a104,f323(f323(f78(a1),f323(f323(f22(a1),x37911),x37912)),f76(a1))),f323(f35(a1),f294(a1,x37912,x37911)))
% 179.72/179.57 [3806]E(f323(f254(x38061,x38061),f323(f323(f280(x38061,x38061,x38061),x38062),f299(x38061,x38062))),f323(f254(x38061,x38061),x38062))
% 179.72/179.57 [3807]E(f323(f256(x38071,x38071),f323(f323(f280(x38071,x38071,x38071),x38072),f299(x38071,x38072))),f323(f256(x38071,x38071),x38072))
% 179.72/179.57 [3823]E(f323(f323(f78(a860),f323(f323(f78(a860),f323(f189(a857),x38231)),f323(f189(a857),x38232))),f323(a112,f2(a860))),f323(f189(a857),f30(x38231,x38232)))
% 179.72/179.57 [3826]E(f323(f135(f861(x38261),f861(x38261),f121(x38261),f113(x38261)),f163(f861(x38261),x38262,f113(x38261))),f113(x38261))
% 179.72/179.57 [3835]P27(a860,a860,f323(f323(f7(a860,a860,a860),f78(a860)),x38351),x38352)
% 179.72/179.57 [3837]P16(a860,f323(f162(a860),f323(f323(f147(f861(x38371),a860),f189(f861(x38371))),f173(x38371,x38372))))
% 179.72/179.57 [3884]P101(f323(f323(f238(a1),f323(f77(a1),f323(f100(a1),f323(a112,x38841)))),f323(f100(a1),x38842)))
% 179.72/179.57 [3930]E(f323(f135(f861(x39301),x39301,f323(f7(x39301,f861(x39301),f861(x39301)),f144(x39301)),f113(x39301)),x39302),f323(f162(x39301),x39302))
% 179.72/179.57 [3984]P101(f323(f323(f237(f867(f866(f861(x39841),f861(x39841)),a855)),f151(x39841,x39842)),f299(f861(x39841),f150(x39841,x39842))))
% 179.72/179.57 [4016]P101(f323(f45(x40161,x40162),f323(f323(f258(a860,a860),f323(f323(f36(a860),x40161),x40162)),f42(a860,x40161,x40162))))
% 179.72/179.57 [4027]P101(f323(f323(f237(f867(f866(f861(x40271),f861(x40271)),a855)),f150(x40271,f299(x40271,x40272))),f299(f861(x40271),f150(x40271,x40272))))
% 179.72/179.57 [4252]E(f323(f323(f264(f866(a99,a99),a99,f866(a99,a99),f866(x42521,f866(a99,a99))),f268(f323(f159(a99),f323(f323(f147(f866(a99,x42521),a99),f257(a99,x42521)),x42522)))),f323(f323(f8(x42521,f867(f866(a99,a99),f866(x42521,f866(a99,a99))),a99),f258(x42521,f866(a99,a99))),f269(x42521,x42522))),f267(x42521,x42522))
% 179.72/179.57 [4364]E(f323(f232(a860,f866(x43641,f862(x43641)),f2(a860),f323(f262(x43641,f862(x43641),a860),f323(f16(f867(f862(x43641),a860),x43641),f323(f323(f7(f862(x43641),a860,a860),f323(f323(f8(a860,f867(a860,a860),f862(x43641)),f78(a860)),f189(f862(x43641)))),f76(a860))))),f323(f128(x43641),x43642)),f323(f189(f862(x43641)),x43642))
% 179.72/179.57 [4441]E(f323(f262(f867(f866(x44411,x44411),a855),f867(f866(x44411,x44411),a855),f867(f867(x44412,x44411),f866(f867(f866(x44412,x44412),a855),f867(f866(x44412,x44412),a855)))),f323(f323(f7(f867(f866(x44411,x44411),a855),f867(f867(f866(x44411,x44411),a855),f867(f867(x44412,x44411),f867(f866(x44412,x44412),a855))),f867(f867(f866(x44411,x44411),a855),f867(f867(x44412,x44411),f866(f867(f866(x44412,x44412),a855),f867(f866(x44412,x44412),a855))))),f323(f323(f8(f867(f867(f867(x44412,x44411),f867(f866(x44412,x44412),a855)),f867(f867(x44412,x44411),f866(f867(f866(x44412,x44412),a855),f867(f866(x44412,x44412),a855)))),f867(f867(f867(f866(x44411,x44411),a855),f867(f867(x44412,x44411),f867(f866(x44412,x44412),a855))),f867(f867(f866(x44411,x44411),a855),f867(f867(x44412,x44411),f866(f867(f866(x44412,x44412),a855),f867(f866(x44412,x44412),a855))))),f867(f866(x44411,x44411),a855)),f8(f867(f867(x44412,x44411),f867(f866(x44412,x44412),a855)),f867(f867(x44412,x44411),f866(f867(f866(x44412,x44412),a855),f867(f866(x44412,x44412),a855))),f867(f866(x44411,x44411),a855))),f323(f323(f8(f867(f867(x44412,x44411),f867(f867(f866(x44412,x44412),a855),f866(f867(f866(x44412,x44412),a855),f867(f866(x44412,x44412),a855)))),f867(f867(f867(x44412,x44411),f867(f866(x44412,x44412),a855)),f867(f867(x44412,x44411),f866(f867(f866(x44412,x44412),a855),f867(f866(x44412,x44412),a855)))),f867(f866(x44411,x44411),a855)),f18(f867(x44412,x44411),f867(f866(x44412,x44412),a855),f866(f867(f866(x44412,x44412),a855),f867(f866(x44412,x44412),a855)))),f323(f323(f8(f867(f867(x44412,x44411),f867(f866(x44412,x44412),a855)),f867(f867(x44412,x44411),f867(f867(f866(x44412,x44412),a855),f866(f867(f866(x44412,x44412),a855),f867(f866(x44412,x44412),a855)))),f867(f866(x44411,x44411),a855)),f323(f8(f867(f866(x44412,x44412),a855),f867(f867(f866(x44412,x44412),a855),f866(f867(f866(x44412,x44412),a855),f867(f866(x44412,x44412),a855))),f867(x44412,x44411)),f258(f867(f866(x44412,x44412),a855),f867(f866(x44412,x44412),a855)))),f279(x44411,x44412))))),f279(x44411,x44412))),f72(x44411,x44412))
% 179.72/179.57 [4523]~E(f323(f300(x45231),x45232),f188(f867(f867(x45231,a855),a855)))
% 179.72/179.57 [4537]~P101(f323(f323(f325(x45371),x45372),f188(f867(x45371,a855))))
% 179.72/179.57 [4547]~P101(f323(f323(f238(f867(x45471,a855)),x45472),f188(f867(x45471,a855))))
% 179.72/179.57 [3337]E(f323(f323(f22(a860),x33371),f323(f323(f78(a860),x33371),x33372)),f2(a860))
% 179.72/179.57 [3340]E(f323(f323(f110(f867(x33401,a855)),x33402),x33402),x33402)
% 179.72/179.57 [3341]E(f323(f323(f101(f867(x33411,a855)),x33412),x33412),x33412)
% 179.72/179.57 [3369]E(f323(f323(f22(f867(x33691,a855)),x33692),x33692),f188(f867(x33691,a855)))
% 179.72/179.57 [3372]E(f323(f136(x33721,x33722),f2(a860)),f188(f867(f866(f861(x33721),f861(x33721)),a855)))
% 179.72/179.57 [3373]E(f323(f323(f78(a860),x33731),f323(a112,x33732)),f323(a112,f323(f323(f78(a860),x33731),x33732)))
% 179.72/179.57 [3386]E(f194(f323(f100(a1),x33861),f323(f100(a1),x33862)),f323(f100(a1),f323(f323(f22(a860),x33861),x33862)))
% 179.72/179.57 [3389]E(f323(f323(f36(a1),f323(f77(a1),x33891)),x33892),f323(f323(f36(a1),x33891),f323(f77(a1),x33892)))
% 179.72/179.57 [3393]E(f323(f35(a1),f323(f293(a1,x33931),x33932)),f323(a104,f323(f323(f22(a1),x33932),x33931)))
% 179.72/179.57 [3396]E(f323(f323(f78(a860),f323(a112,x33961)),x33962),f323(a112,f323(f323(f78(a860),x33961),x33962)))
% 179.72/179.57 [3401]E(f323(f77(f867(x34011,a855)),f323(f77(f867(x34011,a855)),x34012)),x34012)
% 179.72/179.57 [3415]E(f173(x34151,f323(f323(f144(f861(x34151)),f113(x34151)),x34152)),f173(x34151,x34152))
% 179.72/179.57 [3419]E(f323(f323(f78(a860),x34191),f323(f323(f79(a860),x34191),x34192)),f323(f323(f79(a860),x34191),f323(a112,x34192)))
% 179.72/179.57 [3427]E(f323(f323(a23,f323(a3,x34271)),f323(a3,x34272)),f323(a3,f323(f323(f22(a860),x34271),x34272)))
% 179.72/179.57 [3441]E(f323(f323(f79(a1),f323(f77(a1),x34411)),x34412),f323(f77(a1),f323(f323(f79(a1),x34411),x34412)))
% 179.72/179.57 [3443]E(f323(f323(f248(a1),f323(f100(a1),x34431)),x34432),f323(f100(a1),f323(f323(f248(a860),x34431),x34432)))
% 179.72/179.57 [3444]E(f323(f323(f79(a99),f323(a3,x34441)),f323(a3,x34442)),f323(a3,f323(f323(f79(a860),x34441),x34442)))
% 179.72/179.57 [3445]E(f323(f323(f78(a99),f323(a3,x34451)),f323(a3,x34452)),f323(a3,f323(f323(f78(a860),x34451),x34452)))
% 179.72/179.57 [3446]E(f323(f323(f235(a860),f323(a112,x34461)),f323(a112,x34462)),f323(a112,f323(f323(f235(a860),x34461),x34462)))
% 179.72/179.57 [3447]E(f323(f323(f236(a860),f323(a112,x34471)),f323(a112,x34472)),f323(a112,f323(f323(f236(a860),x34471),x34472)))
% 179.72/179.57 [3453]E(f323(f166(a860),f132(a860,f323(f293(a860,x34531),x34532))),f323(f293(a860,x34531),x34532))
% 179.72/179.57 [3454]E(f304(x34541,f323(f323(f301(x34541),x34542),f188(f867(x34541,a855)))),x34542)
% 179.72/179.57 [3459]E(f323(f254(x34591,x34592),f188(f867(f866(x34591,x34592),a855))),f188(f867(x34592,a855)))
% 179.72/179.57 [3460]E(f323(f256(x34601,x34602),f188(f867(f866(x34601,x34602),a855))),f188(f867(x34601,a855)))
% 179.72/179.57 [3464]E(f323(a104,f323(f323(f22(a1),x34641),x34642)),f323(f35(a1),f296(a1,x34642,x34641)))
% 179.72/179.57 [3468]E(f323(f323(f78(a860),x34681),f323(f323(f79(a860),x34682),x34681)),f323(f323(f79(a860),f323(a112,x34682)),x34681))
% 179.72/179.57 [3470]E(f323(f323(f58(x34701),f188(f867(x34701,a855))),x34702),f188(f867(f867(x34701,a855),a855)))
% 179.72/179.57 [3479]E(f323(f189(f861(a860)),f132(a860,f323(f293(a860,x34791),x34792))),f323(f323(f22(a860),x34792),x34791))
% 179.72/179.57 [3494]E(f323(f323(f110(f867(x34941,a855)),f188(f867(x34941,a855))),x34942),x34942)
% 179.72/179.57 [3495]E(f323(f323(f101(f867(x34951,a855)),f246(f867(x34951,a855))),x34952),x34952)
% 179.72/179.57 [3496]E(f323(f323(f78(a1),f323(f77(a1),x34961)),f323(f77(a1),x34962)),f323(f77(a1),f323(f323(f78(a1),x34961),x34962)))
% 179.72/179.57 [3501]E(f323(f323(f79(a1),f323(f100(a1),x35011)),f323(f100(a1),x35012)),f323(f100(a1),f323(f323(f79(a860),x35011),x35012)))
% 179.72/179.57 [3502]E(f323(f323(f79(a1),f323(f103(a1),x35021)),f323(f103(a1),x35022)),f323(f103(a1),f323(f323(f79(a1),x35021),x35022)))
% 179.72/179.57 [3504]E(f323(f323(f78(a1),f323(f100(a1),x35041)),f323(f100(a1),x35042)),f323(f100(a1),f323(f323(f78(a860),x35041),x35042)))
% 179.72/179.57 [3505]E(f323(f323(f78(a1),f323(f103(a1),x35051)),f323(f103(a1),x35052)),f323(f103(a1),f323(f323(f78(a1),x35051),x35052)))
% 179.72/179.57 [3506]E(f323(f323(f36(a1),f323(f100(a1),x35061)),f323(f100(a1),x35062)),f323(f100(a1),f323(f323(f36(a860),x35061),x35062)))
% 179.72/179.57 [3525]E(f323(f323(f6(x35251,a860),f323(f16(a860,x35251),f76(a860))),x35252),f323(f35(x35251),x35252))
% 179.72/179.57 [3532]E(f323(f77(a1),f42(a1,f323(f77(a1),x35321),x35322)),f42(a1,x35321,f323(f77(a1),x35322)))
% 179.72/179.57 [3534]E(f323(f166(a1),f172(x35341,f323(f323(f22(a1),x35342),f76(a1)))),f323(f293(a1,x35341),x35342))
% 179.72/179.57 [3539]P101(f323(f323(f237(a860),x35391),f323(f323(f78(a860),x35392),x35391)))
% 179.72/179.57 [3540]P101(f323(f323(f237(a860),x35401),f323(f323(f78(a860),x35401),x35402)))
% 179.72/179.57 [3542]E(f323(f323(f110(f867(x35421,a855)),f246(f867(x35421,a855))),x35422),f246(f867(x35421,a855)))
% 179.72/179.57 [3543]E(f323(f323(f22(f867(x35431,a855)),f188(f867(x35431,a855))),x35432),f188(f867(x35431,a855)))
% 179.72/179.57 [3544]E(f323(f323(f101(f867(x35441,a855)),f188(f867(x35441,a855))),x35442),f188(f867(x35441,a855)))
% 179.72/179.57 [3550]E(f323(f323(f258(a1,a1),x35501),f323(f77(a1),x35502)),f323(a48,f323(f323(f258(a1,a1),x35501),x35502)))
% 179.72/179.57 [3551]E(f323(f293(a1,f323(f323(f78(a1),x35511),f76(a1))),x35512),f297(a1,x35511,x35512))
% 179.72/179.57 [3562]E(f323(f323(f79(a860),x35621),f323(f323(f36(a860),x35622),x35621)),f323(f323(f22(a860),x35622),f42(a860,x35622,x35621)))
% 179.72/179.57 [3563]E(f323(f323(f79(a1),x35631),f323(f323(f36(a1),x35632),x35631)),f323(f323(f22(a1),x35632),f42(a1,x35632,x35631)))
% 179.72/179.57 [3567]E(f323(f166(a1),f172(f323(f323(f78(a1),x35671),f76(a1)),x35672)),f296(a1,x35671,x35672))
% 179.72/179.57 [3571]P101(f323(f323(f237(f867(x35711,a855)),x35712),x35712))
% 179.72/179.57 [3574]E(f323(f323(f110(f867(x35741,a855)),x35742),f323(f77(f867(x35741,a855)),x35742)),f246(f867(x35741,a855)))
% 179.72/179.57 [3575]E(f323(f323(f101(f867(x35751,a855)),x35752),f323(f77(f867(x35751,a855)),x35752)),f188(f867(x35751,a855)))
% 179.72/179.57 [3583]E(f323(f323(f22(a860),f323(f323(f22(a860),x35831),f76(a860))),x35832),f323(f323(f22(a860),x35831),f323(a112,x35832)))
% 179.72/179.57 [3589]E(f323(f323(f22(f867(x35891,a855)),f246(f867(x35891,a855))),x35892),f323(f77(f867(x35891,a855)),x35892))
% 179.72/179.57 [3590]E(f323(f323(f22(a1),f323(f103(a1),x35901)),f323(f103(a1),x35902)),f323(f103(a1),f323(f323(f78(a1),x35901),f323(f77(a1),x35902))))
% 179.72/179.57 [3602]E(f323(f166(a860),f132(a860,f323(f293(a860,x36021),f323(a112,x36022)))),f294(a860,x36021,x36022))
% 179.72/179.57 [3614]E(f323(f189(f861(f861(x36141))),f51(x36141,x36142)),f323(f323(f248(a860),f323(a112,f323(a112,f2(a860)))),f323(f189(f861(x36141)),x36142)))
% 179.72/179.57 [3635]E(f323(f323(f183(f866(x36351,x36351),a855),f2(a860)),x36352),f299(x36351,f188(f867(f866(x36351,x36351),a855))))
% 179.72/179.57 [3639]P101(f323(f130(a860),f132(a860,f323(f293(a860,x36391),x36392))))
% 179.72/179.57 [3655]E(f323(f302(a1,a860,a104),f294(a1,f323(f100(a1),x36551),f323(f100(a1),x36552))),f294(a860,x36551,x36552))
% 179.72/179.57 [3665]E(f185(a860,f2(a860),f5(a860),f323(f323(f22(a860),x36651),x36652)),f323(f323(f22(a860),x36651),f323(a112,x36652)))
% 179.72/179.57 [3666]E(f323(a104,f323(f323(f22(a1),x36661),f323(f323(f78(a1),x36662),f76(a1)))),f323(f35(a1),f297(a1,x36662,x36661)))
% 179.72/179.57 [3702]E(f323(f323(f147(a860,a860),a112),f132(a860,f323(f293(a860,x37021),x37022))),f132(a860,f323(f293(a860,f323(a112,x37021)),f323(a112,x37022))))
% 179.72/179.57 [3710]E(f323(f166(a1),f172(f323(f323(f78(a1),x37101),f76(a1)),f323(f323(f22(a1),x37102),f76(a1)))),f297(a1,x37101,x37102))
% 179.72/179.57 [3721]P101(f323(f323(f237(f867(x37211,a855)),f188(f867(x37211,a855))),x37212))
% 179.72/179.57 [3726]E(f83(x37261,f323(f323(f7(x37261,x37261,a855),a320),x37262)),x37262)
% 179.72/179.57 [3727]E(f88(x37271,f323(f323(f7(x37271,x37271,a855),a320),x37272)),x37272)
% 179.72/179.57 [3731]E(f323(f166(a860),f132(a860,f323(f293(a860,f323(a112,x37311)),f323(a112,x37312)))),f296(a860,x37311,x37312))
% 179.72/179.57 [3758]E(f323(f323(f260(x37581,x37582),f246(f867(x37581,a855))),f323(f16(f867(x37582,a855),x37581),f246(f867(x37582,a855)))),f246(f867(f866(x37581,x37582),a855)))
% 179.72/179.57 [3793]E(f323(f243(x37931),f323(f323(f8(a855,a855,x37931),a318),x37932)),f323(f77(f867(x37931,a855)),f323(f243(x37931),x37932)))
% 179.72/179.57 [3796]E(f323(f243(x37961),f323(f323(f7(x37961,x37961,a855),a320),x37962)),f323(f323(f301(x37961),x37962),f188(f867(x37961,a855))))
% 179.72/179.57 [3803]E(f323(f323(f78(a1),f323(f323(f22(a1),x38031),x38032)),f323(f323(f22(a1),x38031),x38032)),f323(f323(f22(a1),f323(f323(f78(a1),x38031),x38031)),f323(f323(f78(a1),x38032),x38032)))
% 179.72/179.57 [3804]E(f323(f323(f78(a1),f323(f323(f78(a1),x38041),x38041)),f323(f323(f78(a1),x38042),x38042)),f323(f323(f78(a1),f323(f323(f78(a1),x38041),x38042)),f323(f323(f78(a1),x38041),x38042)))
% 179.72/179.57 [3820]P101(f323(f323(f237(a860),f323(f35(x38201),f323(f166(x38201),x38202))),f323(f189(f861(x38201)),x38202)))
% 179.72/179.57 [3821]P101(f323(f323(f237(a860),f323(f189(f861(x38211)),f145(x38211,x38212))),f323(f189(f861(x38211)),x38212)))
% 179.72/179.57 [3832]E(f323(f243(x38321),f323(f323(f7(x38321,f867(x38321,a855),a855),f325(x38321)),x38322)),x38322)
% 179.72/179.57 [3848]E(f323(f323(f169(x38481),f323(f323(f22(a860),f323(f189(f861(x38481)),x38482)),f76(a860))),x38482),f114(x38481,x38482))
% 179.72/179.57 [3871]E(f185(a860,f2(a860),f323(f323(f8(a860,a860,a860),a112),f323(f235(a860),x38711)),x38712),f323(f323(f235(a860),f323(a112,x38711)),x38712))
% 179.72/179.57 [3875]E(f37(f867(x38751,a855),f323(f302(f867(f866(x38751,x38751),a855),f867(x38751,a855),f276(x38751)),x38752)),f323(f276(x38751),f37(f867(f866(x38751,x38751),a855),x38752)))
% 179.72/179.57 [3876]E(f185(a860,f323(a112,x38761),f323(f323(f8(a860,a860,a860),a112),f323(f236(a860),x38761)),x38762),f323(f323(f236(a860),f323(a112,x38761)),x38762))
% 179.72/179.57 [3878]E(f323(f323(f258(a1,a1),f323(f323(f36(a1),f323(f73(a1),x38781)),f323(f73(a1),x38782))),f42(a1,f323(f73(a1),x38781),f323(f73(a1),x38782))),f50(x38781,x38782))
% 179.72/179.57 [3901]P101(f323(f323(f237(f867(f867(x39011,a855),a855)),x39012),f323(f300(x39011),f37(f867(x39011,a855),x39012))))
% 179.72/179.57 [3935]E(f323(f323(f39(x39351,f867(x39351,a855)),x39352),f323(f323(f7(x39351,f867(x39351,a855),f867(x39351,a855)),f301(x39351)),f188(f867(x39351,a855)))),x39352)
% 179.72/179.57 [3936]E(f323(f323(f280(x39361,x39361,x39361),f323(f278(x39361,x39361),x39362)),f299(x39361,f323(f278(x39361,x39361),x39362))),f323(f278(x39361,x39361),f323(f323(f280(x39361,x39361,x39361),x39362),f299(x39361,x39362))))
% 179.72/179.57 [4007]E(f323(f166(x40071),f323(f135(f861(x40071),f861(x40071),f121(x40071),f113(x40071)),x40072)),f323(f323(f39(f861(x40071),f867(x40071,a855)),f323(f166(f861(x40071)),x40072)),f166(x40071)))
% 179.72/179.57 [4039]E(f323(f323(f110(f867(f866(x40391,x40391),a855)),f299(x40391,f188(f867(f866(x40391,x40391),a855)))),f323(f323(f280(x40391,x40391,x40391),f299(x40391,x40392)),x40392)),f299(x40391,x40392))
% 179.72/179.57 [4073]E(f323(f323(f175(x40731,x40731),x40732),x40732),f323(f323(f147(x40731,f866(x40731,x40731)),f323(f323(f18(x40731,x40731,f866(x40731,x40731)),f258(x40731,x40731)),f5(x40731))),x40732))
% 179.72/179.57 [4189]E(f323(f135(a860,f861(x41891),f323(f7(f861(x41891),a860,a860),f323(f323(f8(a860,f867(a860,a860),f861(x41891)),f236(a860)),f189(f861(x41891)))),f2(a860)),f323(f162(f861(x41891)),x41892)),f323(f189(f861(f861(x41891))),f173(x41891,x41892)))
% 179.72/179.57 [4267]E(f323(f323(f279(f866(a860,f861(x42671)),f861(x42671)),f315(a860,f861(x42671),a242,f138(x42671,x42672))),f323(f323(f18(f861(x42671),f861(x42671),f866(a860,f861(x42671))),f323(f323(f8(a860,f867(f861(x42671),f866(a860,f861(x42671))),f861(x42671)),f258(a860,f861(x42671))),f189(f861(x42671)))),f5(f861(x42671)))),f139(x42671,x42672))
% 179.72/179.57 [4398]E(f323(f243(x43981),f323(f323(f8(f867(f867(x43981,a855),a855),a855,x43981),f86(f867(x43981,a855))),f323(f323(f8(f867(f867(x43981,a855),a855),f867(f867(x43981,a855),a855),x43981),f323(f18(f867(x43981,a855),a855,a855),f323(f323(f8(a855,f867(a855,a855),f867(x43981,a855)),a326),f323(f323(f7(f867(x43981,a855),f867(f867(x43981,a855),a855),a855),f325(f867(x43981,a855))),x43982)))),f325(x43981)))),f38(f867(x43981,a855),x43982))
% 179.72/179.57 [4548]~P101(f323(f323(f238(a1),f323(f100(a1),x45481)),f323(f77(a1),f323(f100(a1),x45482))))
% 179.72/179.57 [4564]~P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x45641),x45641)),a97)),f323(f323(f78(a1),x45642),x45642)))
% 179.72/179.57 [3466]E(f323(f323(f22(a860),f323(f323(f78(a860),x34661),x34662)),x34662),x34661)
% 179.72/179.57 [3467]E(f323(f323(f22(a860),f323(f323(f78(a860),x34671),x34672)),x34671),x34672)
% 179.72/179.57 [3533]E(f323(f323(f78(a860),f323(f323(f22(a860),x35331),x35332)),x35332),f323(f323(f236(a860),x35331),x35332))
% 179.72/179.57 [3642]E(f323(f323(f79(a860),f323(f323(f36(a860),x36421),x36422)),x36422),f323(f323(f22(a860),x36421),f42(a860,x36421,x36422)))
% 179.72/179.57 [3670]E(f323(f166(a860),f132(a860,f323(f293(a860,f323(a112,x36701)),x36702))),f297(a860,x36701,x36702))
% 179.72/179.57 [3677]E(f323(f100(a1),f218(f323(a104,f323(f73(a1),x36771)),f323(a104,f323(f73(a1),x36772)))),f323(f323(a219,x36771),x36772))
% 179.72/179.57 [3679]E(f323(f323(f110(f867(x36791,a855)),f323(f77(f867(x36791,a855)),x36792)),x36792),f246(f867(x36791,a855)))
% 179.72/179.57 [3680]E(f323(f323(f101(f867(x36801,a855)),f323(f77(f867(x36801,a855)),x36802)),x36802),f188(f867(x36801,a855)))
% 179.72/179.57 [3698]P101(f323(f323(f237(a860),f323(f323(f22(a860),x36981),x36982)),x36981))
% 179.72/179.57 [3699]P101(f323(f323(f237(a860),f323(f323(f36(a860),x36991),x36992)),x36991))
% 179.72/179.57 [3723]P101(f323(f323(f238(a860),x37231),f323(a112,f323(f323(f78(a860),x37232),x37231))))
% 179.72/179.57 [3724]P101(f323(f323(f238(a860),x37241),f323(a112,f323(f323(f78(a860),x37241),x37242))))
% 179.72/179.57 [3742]E(f323(f323(f79(a860),f323(a104,f323(f73(a1),x37421))),f323(a104,f323(f73(a1),x37422))),f323(a104,f323(f73(a1),f323(f323(f79(a1),x37421),x37422))))
% 179.72/179.57 [3754]P101(f323(f323(f237(a1),f2(a1)),f323(f323(f248(a1),f323(f73(a1),x37541)),x37542)))
% 179.72/179.57 [3825]E(f323(f277(f861(x38251),f861(x38251),f151(x38251,x38252)),f323(f323(f301(f861(x38251)),f113(x38251)),f188(f867(f861(x38251),a855)))),f323(f323(f301(f861(x38251)),f113(x38251)),f188(f867(f861(x38251),a855))))
% 179.72/179.57 [3846]E(f323(f323(f110(f867(f866(x38461,x38461),a855)),f299(x38461,x38462)),f299(x38461,f188(f867(f866(x38461,x38461),a855)))),f299(x38461,x38462))
% 179.72/179.57 [3861]E(f323(f323(f36(a1),f323(f103(a1),f323(f323(f78(a1),x38611),x38611))),f323(f103(a1),f323(f323(f78(a1),x38612),x38612))),f323(f323(f36(a1),f323(f103(a1),x38611)),f323(f103(a1),x38612)))
% 179.72/179.57 [3925]E(f323(f323(f248(a1),x39251),f323(f103(a860),f323(f323(f78(a1),x39252),x39252))),f323(f323(f84(a1,a1),f323(f323(f248(a1),x39251),f323(f103(a860),x39252))),f323(f323(f18(a1,a1,a1),f79(a1)),f5(a1))))
% 179.72/179.57 [3931]E(f323(f243(f867(x39311,a855)),f323(f323(f7(f867(x39311,a855),f867(x39311,a855),a855),f237(f867(x39311,a855))),x39312)),f323(f300(x39311),x39312))
% 179.72/179.57 [3947]E(f323(f323(f147(a1,a860),a104),f323(f323(f121(a1),f323(f323(f147(a860,a1),f100(a1)),x39471)),f323(f323(f147(a860,a1),f100(a1)),x39472))),f323(f323(f121(a860),x39471),x39472))
% 179.72/179.57 [3983]E(f323(f302(a1,a1,f323(f323(f7(a1,a1,a1),f78(a1)),x39831)),f323(f293(a1,f2(a1)),f323(f323(f22(a1),x39832),x39831))),f323(f293(a1,x39831),x39832))
% 179.72/179.57 [3985]P42(x39851,f323(f323(f22(f867(f866(x39851,x39851),a855)),x39852),f299(x39851,f188(f867(f866(x39851,x39851),a855)))))
% 179.72/179.57 [4005]E(f323(f189(f861(x40051)),f323(f135(f861(x40051),f861(x40051),f121(x40051),f113(x40051)),x40052)),f323(f159(a860),f323(f323(f147(f861(x40051),a860),f189(f861(x40051))),x40052)))
% 179.72/179.57 [4010]P40(x40101,f246(f867(x40101,a855)),f323(f323(f110(f867(f866(x40101,x40101),a855)),x40102),f299(x40101,f188(f867(f866(x40101,x40101),a855)))))
% 179.72/179.57 [4053]E(f185(a860,f2(a860),f323(f323(f8(a860,a860,a860),a112),f323(f323(f7(a860,a860,a860),f235(a860)),x40531)),x40532),f323(f323(f235(a860),x40532),f323(a112,x40531)))
% 179.72/179.57 [4056]E(f185(a860,f323(a112,x40561),f323(f323(f8(a860,a860,a860),a112),f323(f323(f7(a860,a860,a860),f236(a860)),x40561)),x40562),f323(f323(f236(a860),x40562),f323(a112,x40561)))
% 179.72/179.57 [4059]E(f323(f302(x40591,f861(x40591),f323(f323(f7(x40591,f861(x40591),f861(x40591)),f144(x40591)),f113(x40591))),x40592),f168(x40591,x40592,f323(f323(f301(f861(x40591)),f113(x40591)),f188(f867(f861(x40591),a855)))))
% 179.72/179.57 [4060]E(f323(f323(f110(f867(f866(x40601,x40601),a855)),f323(f323(f280(x40601,x40601,x40601),x40602),f299(x40601,x40602))),f299(x40601,f188(f867(f866(x40601,x40601),a855)))),f299(x40601,x40602))
% 179.72/179.57 [4068]P101(f323(f323(f237(f867(f866(x40681,x40681),a855)),f255(x40681,x40682)),f323(f323(f260(x40681,x40681),x40682),f323(f16(f867(x40681,a855),x40681),x40682))))
% 179.72/179.57 [4071]E(f323(f302(a1,a860,a104),f323(f323(f110(f867(a1,a855)),f323(f302(a860,a1,f100(a1)),x40711)),f323(f302(a860,a1,f100(a1)),x40712))),f323(f323(f110(f867(a860,a855)),x40711),x40712))
% 179.72/179.57 [4072]E(f323(f302(a1,a860,a104),f323(f323(f101(f867(a1,a855)),f323(f302(a860,a1,f100(a1)),x40721)),f323(f302(a860,a1,f100(a1)),x40722))),f323(f323(f101(f867(a860,a855)),x40721),x40722))
% 179.72/179.57 [4076]E(f323(f243(x40761),f323(f323(f8(a855,a855,x40761),a318),f323(f323(f7(x40761,f867(x40761,a855),a855),f325(x40761)),x40762))),f323(f77(f867(x40761,a855)),x40762))
% 179.72/179.57 [4103]E(f323(f135(f861(x41031),f861(x41031),f121(x41031),f113(x41031)),f323(f323(f147(f861(x41031),f861(x41031)),f162(x41031)),f323(f162(f861(x41031)),x41032))),f323(f162(x41031),f323(f135(f861(x41031),f861(x41031),f121(x41031),f113(x41031)),x41032)))
% 179.72/179.57 [4131]E(f323(f323(f39(a860,f867(f866(x41311,x41311),a855)),f246(f867(a860,a855))),f323(f323(f7(a860,f867(f866(x41311,x41311),a855),f867(f866(x41311,x41311),a855)),f183(f866(x41311,x41311),a855)),x41312)),f299(x41311,x41312))
% 179.72/179.57 [4151]E(f83(x41511,f323(f323(f8(f867(x41511,a855),a855,x41511),f323(a320,x41512)),f323(f323(f7(x41511,f867(x41511,a855),f867(x41511,a855)),f301(x41511)),f188(f867(x41511,a855))))),f304(x41511,x41512))
% 179.72/179.57 [4159]E(f323(f189(f861(x41591)),f145(x41591,f323(f135(f861(x41591),f861(x41591),f121(x41591),f113(x41591)),x41592))),f323(f35(x41591),f323(f323(f39(f861(x41591),f867(x41591,a855)),f323(f166(f861(x41591)),x41592)),f166(x41591))))
% 179.72/179.57 [4175]E(f323(f323(f110(f867(f866(x41751,x41751),a855)),x41752),f323(f323(f280(x41751,x41751,x41751),f323(f323(f280(x41751,x41751,x41751),x41752),f299(x41751,x41752))),x41752)),f323(f323(f280(x41751,x41751,x41751),x41752),f299(x41751,x41752)))
% 179.72/179.57 [4199]P101(f323(f323(f237(f867(f866(x41991,x41991),a855)),f323(f323(f280(x41991,x41991,x41991),x41992),f299(x41991,x41992))),f323(f323(f260(x41991,x41991),f323(f276(x41991),x41992)),f323(f16(f867(x41991,a855),x41991),f323(f276(x41991),x41992)))))
% 179.72/179.57 [4242]E(f323(f243(f861(x42421)),f323(f323(f7(f861(x42421),f867(x42421,a855),a855),f323(f323(f8(f867(x42421,a855),f867(f867(x42421,a855),a855),f861(x42421)),f237(f867(x42421,a855))),f166(x42421))),x42422)),f154(x42421,x42422))
% 179.72/179.57 [4254]E(f323(f149(f861(x42541),x42541,f113(x42541),f323(f323(f8(f861(x42541),f867(f861(x42541),f861(x42541)),x42541),f323(f7(f861(x42541),f861(x42541),f861(x42541)),f121(x42541))),f323(f323(f7(x42541,f861(x42541),f861(x42541)),f144(x42541)),f113(x42541)))),x42542),f323(f161(x42541),x42542))
% 179.72/179.57 [4296]P27(f867(x42961,x42962),f867(f866(x42961,x42962),a855),f323(f323(f8(f867(f866(x42961,x42962),a855),f867(f866(x42961,x42962),a855),f867(x42961,x42962)),f243(f866(x42961,x42962))),f323(f323(f8(f867(x42961,f867(x42962,a855)),f867(f866(x42961,x42962),a855),f867(x42961,x42962)),f262(x42961,x42962,a855)),f323(f8(x42962,f867(x42962,a855),x42961),f323(f7(x42962,x42962,a855),a320)))),f246(f867(f867(x42961,x42962),a855)))
% 179.72/179.57 [4301]E(f42(a1,f323(f103(a1),f323(f323(f78(a1),x43011),x43011)),f323(f103(a1),f323(f323(f78(a1),x43012),x43012))),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f42(a1,f323(f103(a1),x43011),f323(f103(a1),x43012))))
% 179.72/179.57 [4345]E(f323(f323(f39(x43451,f867(f866(x43451,x43451),a855)),x43452),f323(f323(f7(x43451,f867(f866(x43451,x43451),a855),f867(f866(x43451,x43451),a855)),f323(f323(f8(f866(x43451,x43451),f867(f867(f866(x43451,x43451),a855),f867(f866(x43451,x43451),a855)),x43451),f301(f866(x43451,x43451))),f323(f323(f18(x43451,x43451,f866(x43451,x43451)),f258(x43451,x43451)),f5(x43451)))),f188(f867(f866(x43451,x43451),a855)))),f255(x43451,x43452))
% 179.72/179.57 [4353]E(f205(x43531,f323(f323(f258(a1,a1),f323(f77(a1),f323(f323(f71(f866(a1,a1),a1,x43531,f257(a1,a1)),f214(x43531)),x43532))),f323(f323(f71(f866(a1,a1),a1,x43531,f261(a1,a1)),f214(x43531)),x43532))),f222(x43531,x43532))
% 179.72/179.57 [4436]E(f323(f243(f867(x44361,a855)),f323(f323(f8(f867(f867(x44361,a855),a855),a855,f867(x44361,a855)),f85(f867(x44361,a855))),f323(f323(f7(f867(x44361,a855),f867(f867(x44361,a855),a855),f867(f867(x44361,a855),a855)),f323(f323(f8(f867(f867(x44361,a855),f867(a855,a855)),f867(f867(f867(x44361,a855),a855),f867(f867(x44361,a855),a855)),f867(x44361,a855)),f18(f867(x44361,a855),a855,a855)),f323(f323(f8(f867(f867(x44361,a855),a855),f867(f867(x44361,a855),f867(a855,a855)),f867(x44361,a855)),f323(f8(a855,f867(a855,a855),f867(x44361,a855)),a321)),f323(f323(f7(f867(x44361,a855),f867(f867(x44361,a855),f867(x44361,a855)),f867(f867(x44361,a855),a855)),f323(f323(f8(f867(f867(x44361,a855),a855),f867(f867(f867(x44361,a855),f867(x44361,a855)),f867(f867(x44361,a855),a855)),f867(x44361,a855)),f8(f867(x44361,a855),a855,f867(x44361,a855))),a320)),f77(f867(x44361,a855)))))),f323(f323(f8(f867(f867(x44361,a855),a855),a855,f867(x44361,a855)),f323(f325(f867(x44361,a855)),x44362)),f300(x44361))))),f323(f300(x44361),f323(f77(f867(x44361,a855)),x44362)))
% 179.72/179.57 [4545]~E(f323(f323(f78(a1),x45451),x45451),f323(f323(f22(a1),f323(f323(f78(a1),x45452),x45452)),a97))
% 179.72/179.57 [4551]~P101(f323(f323(f238(a860),f323(f323(f78(a860),x45511),x45512)),x45512))
% 179.72/179.57 [4552]~P101(f323(f323(f238(a860),f323(f323(f78(a860),x45521),x45522)),x45521))
% 179.72/179.57 [3759]E(f323(f323(f22(a860),x37591),f323(f323(f79(a860),f323(f323(f36(a860),x37591),x37592)),x37592)),f42(a860,x37591,x37592))
% 179.72/179.57 [3760]E(f323(f323(f22(a1),x37601),f323(f323(f79(a1),f323(f323(f36(a1),x37601),x37602)),x37602)),f42(a1,x37601,x37602))
% 179.72/179.57 [3794]E(f323(f323(f147(a860,x37941),f323(f158(x37941),x37942)),f132(a860,f323(f293(a860,f2(a860)),f323(f189(f861(x37941)),x37942)))),x37942)
% 179.72/179.57 [3857]E(f323(f277(x38571,x38571,f299(x38571,f188(f867(f866(x38571,x38571),a855)))),x38572),x38572)
% 179.72/179.57 [3988]E(f299(x39881,f323(f323(f110(f867(f866(x39881,x39881),a855)),x39882),f299(x39881,f188(f867(f866(x39881,x39881),a855))))),f299(x39881,x39882))
% 179.72/179.57 [3989]E(f299(x39891,f323(f323(f22(f867(f866(x39891,x39891),a855)),x39892),f299(x39891,f188(f867(f866(x39891,x39891),a855))))),f299(x39891,x39892))
% 179.72/179.57 [4042]E(f323(f323(f22(a1),f323(f323(f22(a1),f323(f323(f78(a1),x40421),x40421)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x40422),x40422)),a97)),f323(f323(f78(a1),f323(f323(f22(a1),x40421),x40422)),f323(f323(f22(a1),x40421),x40422)))
% 179.72/179.57 [4081]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f78(a1),x40811),x40812)),f323(f323(f78(a1),x40811),x40812))),a97),f323(f323(f78(a1),f323(f323(f78(a1),x40811),x40811)),f323(f323(f22(a1),f323(f323(f78(a1),x40812),x40812)),a97)))
% 179.72/179.57 [4107]E(f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),x41071),x41071)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x41072),x41072)),a97)),f323(f323(f78(a1),f323(f323(f78(a1),x41071),f323(f323(f22(a1),x41072),a97))),f323(f323(f78(a1),x41071),f323(f323(f22(a1),x41072),a97))))
% 179.72/179.57 [4117]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),x41171),x41172)),f323(f323(f22(a1),x41171),x41172))),a97),f323(f323(f22(a1),f323(f323(f22(a1),f323(f323(f78(a1),x41171),x41171)),a97)),f323(f323(f78(a1),x41172),x41172)))
% 179.72/179.57 [4118]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f78(a1),x41181),x41182)),f323(f323(f78(a1),x41181),x41182))),a97),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),x41181),x41181)),a97)),f323(f323(f78(a1),x41182),x41182)))
% 179.72/179.57 [4172]E(f323(f100(a1),f323(f323(f36(a860),f323(f323(f79(a860),f323(a104,f323(f73(a1),x41721))),f323(a104,f323(f73(a1),x41722)))),f218(f323(a104,f323(f73(a1),x41721)),f323(a104,f323(f73(a1),x41722))))),f220(x41721,x41722))
% 179.72/179.57 [4219]E(f323(f323(f264(f866(a99,a99),a99,f866(a99,a99),f866(x42191,f866(a99,a99))),f268(f323(a3,f323(f189(f861(x42191)),x42192)))),f323(f323(f8(x42191,f867(f866(a99,a99),f866(x42191,f866(a99,a99))),a99),f258(x42191,f866(a99,a99))),f323(f323(f8(a860,x42191,a99),f323(f158(x42191),x42192)),a19))),f274(x42191,x42192))
% 179.72/179.57 [4302]E(f323(f135(a860,f861(x43021),f323(f7(f861(x43021),a860,a860),f323(f323(f8(a860,f867(a860,a860),f861(x43021)),f236(a860)),f189(f861(x43021)))),f2(a860)),f323(f162(f861(x43021)),f173(x43021,x43022))),f323(f189(f861(f861(x43021))),f323(f129(f861(x43021),f323(f323(f8(a855,a855,f861(x43021)),a318),f323(f323(f7(f861(x43021),f861(x43021),a855),a320),f113(x43021)))),x43022)))
% 179.72/179.57 [4308]E(f323(f323(f39(a860,f867(x43081,a855)),f246(f867(a860,a855))),f323(f323(f7(a860,f867(a860,f867(x43081,a855)),f867(x43081,a855)),f323(f323(f8(f867(a860,a855),f867(f867(a860,f867(x43081,a855)),f867(x43081,a855)),a860),f39(a860,f867(x43081,a855))),f293(a860,f2(a860)))),x43082)),f323(f323(f39(a860,f867(x43081,a855)),f246(f867(a860,a855))),x43082))
% 179.72/179.57 [4329]P101(f323(f59(a860),f323(f243(a860),f323(f323(f18(a860,a855,a855),f323(f323(f8(a855,f867(a855,a855),a860),a321),x43291)),f323(f323(f7(a860,a860,a855),f238(a860)),x43292)))))
% 179.72/179.57 [4447]E(f323(f243(f866(f861(x44471),f861(x44471))),f323(f262(f861(x44471),f861(x44471),a855),f323(f323(f18(f861(x44471),f867(f861(x44471),a855),f867(f861(x44471),a855)),f323(f323(f8(f867(f861(x44471),f867(a855,a855)),f867(f867(f861(x44471),a855),f867(f861(x44471),a855)),f861(x44471)),f18(f861(x44471),a855,a855)),f323(f323(f8(f867(f861(x44471),a855),f867(f861(x44471),f867(a855,a855)),f861(x44471)),f323(f8(a855,f867(a855,a855),f861(x44471)),a322)),f323(f323(f7(f861(x44471),f867(f861(x44471),a860),f867(f861(x44471),a855)),f323(f323(f8(f867(a860,a855),f867(f867(f861(x44471),a860),f867(f861(x44471),a855)),f861(x44471)),f8(a860,a855,f861(x44471))),f323(f323(f8(a860,f867(a860,a855),f861(x44471)),f238(a860)),f189(f861(x44471))))),f189(f861(x44471)))))),f323(f323(f18(f861(x44471),f867(f861(x44471),a855),f867(f861(x44471),a855)),f323(f323(f8(f867(f861(x44471),f867(a855,a855)),f867(f867(f861(x44471),a855),f867(f861(x44471),a855)),f861(x44471)),f18(f861(x44471),a855,a855)),f323(f323(f8(f867(f861(x44471),a855),f867(f861(x44471),f867(a855,a855)),f861(x44471)),f323(f8(a855,f867(a855,a855),f861(x44471)),a321)),f323(f323(f7(f861(x44471),f867(f861(x44471),a860),f867(f861(x44471),a855)),f323(f323(f8(f867(a860,a855),f867(f867(f861(x44471),a860),f867(f861(x44471),a855)),f861(x44471)),f8(a860,a855,f861(x44471))),f323(f323(f8(a860,f867(a860,a855),f861(x44471)),a320),f189(f861(x44471))))),f189(f861(x44471)))))),f323(f323(f7(f861(x44471),f867(f866(f861(x44471),f861(x44471)),a855),f867(f861(x44471),a855)),f323(f323(f8(f867(f861(x44471),f867(f867(f866(f861(x44471),f861(x44471)),a855),a855)),f867(f867(f866(f861(x44471),f861(x44471)),a855),f867(f861(x44471),a855)),f861(x44471)),f7(f861(x44471),f867(f866(f861(x44471),f861(x44471)),a855),a855)),f323(f323(f8(f867(f861(x44471),f866(f861(x44471),f861(x44471))),f867(f861(x44471),f867(f867(f866(f861(x44471),f861(x44471)),a855),a855)),f861(x44471)),f323(f8(f866(f861(x44471),f861(x44471)),f867(f867(f866(f861(x44471),f861(x44471)),a855),a855),f861(x44471)),f325(f866(f861(x44471),f861(x44471))))),f258(f861(x44471),f861(x44471))))),f138(x44471,x44472)))))),f139(x44471,x44472))
% 179.72/179.57 [4557]~P101(f323(f323(f89(a1),f323(f323(f78(a1),x45571),x45571)),f323(f323(f22(a1),f323(f323(f78(a1),x45572),x45572)),a97)))
% 179.72/179.57 [4110]E(f323(f323(f78(a1),f323(f323(f78(a1),f323(f323(f79(a1),x41101),x41102)),f323(f323(f79(a1),x41101),x41102))),x41102),f323(f323(f79(a1),f323(f323(f22(a1),f323(f323(f78(a1),x41101),x41101)),a97)),x41102))
% 179.72/179.57 [4217]E(f323(a104,f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x42171),x42172)),f188(f867(f866(a860,a860),a855)))))),f323(f323(f22(a860),x42171),x42172))
% 179.72/179.57 [4222]E(f323(f323(f280(x42221,x42221,x42221),f323(f323(f110(f867(f866(x42221,x42221),a855)),x42222),f299(x42221,f188(f867(f866(x42221,x42221),a855))))),f299(x42221,f323(f323(f110(f867(f866(x42221,x42221),a855)),x42222),f299(x42221,f188(f867(f866(x42221,x42221),a855)))))),f299(x42221,x42222))
% 179.72/179.57 [4260]E(f267(x42601,f323(f129(f866(a99,x42601),f323(f262(a99,x42601,a855),f323(f323(f8(a855,f867(x42601,a855),a99),f16(a855,x42601)),f323(f238(a99),f2(a99))))),x42602)),f267(x42601,x42602))
% 179.72/179.57 [4261]E(f269(x42611,f323(f129(f866(a99,x42611),f323(f262(a99,x42611,a855),f323(f323(f8(a855,f867(x42611,a855),a99),f16(a855,x42611)),f323(f238(a99),f2(a99))))),x42612)),f269(x42611,x42612))
% 179.72/179.57 [4263]E(f323(f77(a1),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x42631),x42632)),f188(f867(f866(a860,a860),a855)))))),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x42632),x42631)),f188(f867(f866(a860,a860),a855))))))
% 179.72/179.57 [4320]E(f323(f323(f279(f861(a860),x43201),f138(a860,a242)),f323(f323(f7(x43201,f861(f867(x43201,a860)),f861(a860)),f323(f323(f8(f867(f867(x43201,a860),a860),f867(f861(f867(x43201,a860)),f861(a860)),x43201),f147(f867(x43201,a860),a860)),f323(f7(f867(x43201,a860),x43201,a860),f5(f867(x43201,a860))))),x43202)),f146(x43201,x43202))
% 179.72/179.57 [4342]E(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x43421),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f7(a1,a860,f867(a860,a860)),f323(f323(f8(a855,f867(a860,f867(a860,a860)),a1),f96(a860)),a193)),f2(a860))),f323(f323(f8(a860,a860,a1),a112),f323(f323(f8(a860,a860,a1),f323(f235(a860),x43422)),a104)))),f323(f323(f235(a860),f323(a112,x43422)),f323(f103(a860),x43421)))
% 179.72/179.57 [4343]E(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x43431),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f7(a1,a860,f867(a860,a860)),f323(f323(f8(a855,f867(a860,f867(a860,a860)),a1),f96(a860)),a193)),f323(a112,x43432))),f323(f323(f8(a860,a860,a1),a112),f323(f323(f8(a860,a860,a1),f323(f236(a860),x43432)),a104)))),f323(f323(f236(a860),f323(a112,x43432)),f323(f103(a860),x43431)))
% 179.72/179.57 [4363]E(f323(f135(f861(x43631),f861(x43631),f121(x43631),f113(x43631)),f323(f323(f147(f861(x43631),f861(x43631)),f149(f861(x43631),x43631,f113(x43631),f323(f323(f8(f861(x43631),f867(f861(x43631),f861(x43631)),x43631),f16(f861(x43631),f861(x43631))),f323(f323(f7(x43631,f861(x43631),f861(x43631)),f144(x43631)),f113(x43631))))),x43632)),f323(f323(f147(f861(x43631),x43631),f134(x43631)),f323(f129(f861(x43631),f323(f323(f8(a855,a855,f861(x43631)),a318),f323(f323(f7(f861(x43631),f861(x43631),a855),a320),f113(x43631)))),x43632)))
% 179.72/179.57 [4426]E(f323(f262(a1,a1,a855),f323(f323(f7(a1,f867(a1,a855),f867(a1,a855)),f323(f323(f8(f867(a1,f867(a855,a855)),f867(f867(a1,a855),f867(a1,a855)),a1),f18(a1,a855,a855)),f323(f323(f8(f867(a1,a855),f867(a1,f867(a855,a855)),a1),f323(f8(a855,f867(a855,a855),a1),a321)),f323(f323(f8(f867(a1,a1),f867(a1,a855),a1),f323(f8(a1,a855,a1),f323(a320,x44261))),f323(f323(f8(a1,f867(a1,a1),a1),f78(a1)),f323(f79(a1),x44262)))))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f323(f8(a855,a855,a1),f323(a326,f323(f323(f238(a1),f2(a1)),x44262))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),f2(a1)))),f323(f323(f7(a1,a1,a855),f238(a1)),x44262))))),f323(f323(f8(a855,a855,a1),f323(a326,f323(a318,f323(f323(f238(a1),f2(a1)),x44262)))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f238(a1),x44262))),f323(f323(f7(a1,a1,a855),f237(a1)),f2(a1))))))),f46(x44261,x44262))
% 179.72/179.57 [4428]E(f323(f243(x44281),f323(f323(f8(f867(a860,a855),a855,x44281),f85(a860)),f323(f323(f7(x44281,f867(a860,a855),f867(a860,a855)),f323(f323(f8(f867(a860,f867(a855,a855)),f867(f867(a860,a855),f867(a860,a855)),x44281),f18(a860,a855,a855)),f323(f323(f8(f867(a860,a855),f867(a860,f867(a855,a855)),x44281),f323(f8(a855,f867(a855,a855),a860),a321)),f323(f323(f7(x44281,f867(a860,x44281),f867(a860,a855)),f323(f323(f8(f867(x44281,a855),f867(f867(a860,x44281),f867(a860,a855)),x44281),f8(x44281,a855,a860)),a320)),f323(f158(x44281),x44282))))),f323(f323(f7(a860,a860,a855),f238(a860)),f323(f189(f861(x44281)),x44282))))),f323(f166(x44281),x44282))
% 179.72/179.57 [4232]E(f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),x42321),a97)),x42322)),f323(f323(f22(a1),f323(f323(f78(a1),x42321),a97)),x42322))),a97),f323(f323(f22(a1),f323(f323(f78(a1),x42321),x42321)),f323(f323(f22(a1),f323(f323(f78(a1),x42322),x42322)),a97)))
% 179.72/179.57 [4358]E(f323(f135(f861(f861(x43581)),f861(f861(x43581)),f121(f861(x43581)),f113(f861(x43581))),f323(f323(f147(f861(x43581),f861(f861(x43581))),f149(f861(f861(x43581)),x43581,f113(f861(x43581)),f323(f16(f867(f861(x43581),f861(f861(x43581))),x43581),f323(f323(f7(f861(x43581),f861(f861(x43581)),f861(f861(x43581))),f144(f861(x43581))),f113(f861(x43581)))))),x43582)),f323(f323(f147(f861(x43581),f861(x43581)),f165(x43581)),f323(f129(f861(x43581),f323(f323(f8(a855,a855,f861(x43581)),a318),f323(f323(f7(f861(x43581),f861(x43581),a855),a320),f113(x43581)))),x43582)))
% 179.72/179.57 [4369]E(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x43691),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f7(a1,a860,f867(a860,a860)),f323(f323(f8(a855,f867(a860,f867(a860,a860)),a1),f96(a860)),a193)),f2(a860))),f323(f323(f8(a860,a860,a1),a112),f323(f323(f7(a1,a860,a860),f323(f323(f8(a860,f867(a860,a860),a1),f235(a860)),a104)),x43692)))),f323(f323(f235(a860),f323(f103(a860),x43691)),f323(a112,x43692)))
% 179.72/179.57 [4370]E(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x43701),a97))),f323(f323(f18(a1,a860,a860),f323(f323(f7(a1,a860,f867(a860,a860)),f323(f323(f8(a855,f867(a860,f867(a860,a860)),a1),f96(a860)),a193)),f323(a112,x43702))),f323(f323(f8(a860,a860,a1),a112),f323(f323(f7(a1,a860,a860),f323(f323(f8(a860,f867(a860,a860),a1),f236(a860)),a104)),x43702)))),f323(f323(f236(a860),f323(f103(a860),x43701)),f323(a112,x43702)))
% 179.72/179.57 [4357]E(f323(f262(x43571,x43571,a855),f323(f323(f18(x43571,a855,f867(x43571,a855)),f323(f323(f8(f867(x43571,f867(a855,a855)),f867(a855,f867(x43571,a855)),x43571),f7(x43571,a855,a855)),f323(f323(f8(f867(x43571,a855),f867(x43571,f867(a855,a855)),x43571),f323(f8(a855,f867(a855,a855),x43571),a321)),a320))),x43572)),f255(x43571,x43572))
% 179.72/179.57 [4404]E(f323(f323(f36(a860),x44041),f323(f323(f78(a860),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97))),x44042)),f323(f323(f36(a860),x44041),f323(a112,f323(a112,f323(a112,x44042)))))
% 179.72/179.57 [4405]E(f42(a860,x44051,f323(f323(f78(a860),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97))),x44052)),f42(a860,x44051,f323(a112,f323(a112,f323(a112,x44052)))))
% 179.72/179.57 [4406]E(f42(a860,f323(f323(f78(a860),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97))),x44061),x44062),f42(a860,f323(a112,f323(a112,f323(a112,x44061))),x44062))
% 179.72/179.57 [4419]E(f120(f323(x44191,f323(f323(f79(a99),f323(f103(a99),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97))),x44192))),f323(f203(x44191),x44192))
% 179.72/179.57 [4420]E(f323(f323(f36(a860),f323(f323(f78(a860),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97))),x44201)),x44202),f323(f323(f36(a860),f323(a112,f323(a112,f323(a112,x44201)))),x44202))
% 179.72/179.57 [4493]~E(f27(x44931,x44932,x44933),a24)
% 179.72/179.57 [4494]~E(f26(x44941,x44942,x44943),a24)
% 179.72/179.57 [3180]E(f323(f192(x31801,x31802),x31803),f118(x31801,x31802))
% 179.72/179.57 [3201]E(f323(f202(x32011,x32012),x32013),f323(f122(x32011),x32012))
% 179.72/179.57 [3280]E(f323(f323(f201(x32801,x32802),x32803),f200(x32801)),f200(x32802))
% 179.72/179.57 [3281]E(f323(f323(f147(x32811,x32812),x32813),f113(x32811)),f113(x32812))
% 179.72/179.57 [3321]E(f323(f184(x33211,x33212,x33213),f2(a860)),x33212)
% 179.72/179.57 [3323]E(f323(f323(f175(x33231,x33232),x33233),f113(x33232)),f113(f866(x33231,x33232)))
% 179.72/179.57 [3338]E(f323(f189(f861(x33381)),f163(x33381,x33382,x33383)),x33382)
% 179.72/179.57 [3358]E(f83(x33581,f60(x33581,x33582,x33583)),f323(f61(x33581,x33582),x33583))
% 179.72/179.57 [3362]E(f247(x33621,x33622,f247(x33622,x33621,x33623)),x33623)
% 179.72/179.57 [3382]E(f323(f162(x33821),f163(x33821,x33822,x33823)),f163(x33821,x33822,x33823))
% 179.72/179.57 [3411]E(f133(x34111,x34112,f145(x34111,x34113)),f145(x34111,f133(x34111,x34112,x34113)))
% 179.72/179.57 [3430]E(f323(f257(f861(x34301),f861(x34301)),f160(x34301,x34302,x34303)),f323(f129(x34301,x34302),x34303))
% 179.72/179.57 [3475]E(f323(f323(f144(x34751),x34752),f163(x34751,x34753,x34752)),f163(x34751,f323(a112,x34753),x34752))
% 179.72/179.57 [3507]E(f185(x35071,x35072,x35073,f2(a860)),x35072)
% 179.72/179.57 [3508]E(f17(x35081,x35082,x35083,f2(a99)),x35082)
% 179.72/179.57 [3515]E(f156(x35151,x35152,x35153,f113(x35151)),f113(x35152))
% 179.72/179.57 [3516]E(f157(x35161,x35162,x35163,f113(x35161)),f113(x35162))
% 179.72/179.57 [3523]E(f323(f323(f158(x35231),f323(f323(f144(x35231),x35232),x35233)),f2(a860)),x35232)
% 179.72/179.57 [3552]E(f57(x35521,x35522,f113(x35521),x35523),f113(f866(x35521,x35522)))
% 179.72/179.57 [3573]P27(x35731,x35732,x35733,f188(f867(x35731,a855)))
% 179.72/179.57 [3732]E(f323(f71(x37321,x37322,x37321,x37323),f32(x37321)),x37323)
% 179.72/179.57 [3916]P101(f323(f323(f325(f866(x39161,x39161)),f323(f323(f258(x39161,x39161),x39162),x39162)),f299(x39161,x39163)))
% 179.72/179.57 [4558]~P101(f323(f323(f325(f866(f861(x45581),f861(x45581))),f323(f323(f258(f861(x45581),f861(x45581)),x45582),f113(x45581))),f138(x45581,x45583)))
% 179.72/179.57 [4559]~P101(f323(f323(f325(f866(f861(x45591),f861(x45591))),f323(f323(f258(f861(x45591),f861(x45591)),x45592),f113(x45591))),f140(x45591,x45593)))
% 179.72/179.57 [4560]~P101(f323(f323(f325(f866(f861(x45601),f861(x45601))),f323(f323(f258(f861(x45601),f861(x45601)),x45602),f113(x45601))),f150(x45601,x45603)))
% 179.72/179.57 [4561]~P101(f323(f323(f325(f866(f861(x45611),f861(x45611))),f323(f323(f258(f861(x45611),f861(x45611)),f113(x45611)),x45612)),f138(x45611,x45613)))
% 179.72/179.57 [4562]~P101(f323(f323(f325(f866(f861(x45621),f861(x45621))),f323(f323(f258(f861(x45621),f861(x45621)),f113(x45621)),x45622)),f150(x45621,x45623)))
% 179.72/179.57 [3255]E(f323(f323(f204(x32551),x32552),x32553),f205(x32551,f217(x32552,x32553)))
% 179.72/179.57 [3310]E(f323(f278(x33101,x33102),f323(f278(x33102,x33101),x33103)),x33103)
% 179.72/179.57 [3333]E(f323(f323(f175(x33331,x33332),f113(x33331)),x33333),f113(f866(x33331,x33332)))
% 179.72/179.57 [3336]E(f170(x33361,x33362,f323(f244(a860),x33363)),f323(f323(f169(x33361),x33363),x33362))
% 179.72/179.57 [3354]E(f145(x33541,f323(f129(x33541,x33542),x33543)),f323(f129(x33541,x33542),f145(x33541,x33543)))
% 179.72/179.57 [3356]E(f323(f254(x33561,x33562),f323(f278(x33562,x33561),x33563)),f323(f256(x33562,x33561),x33563))
% 179.72/179.57 [3357]E(f323(f256(x33571,x33572),f323(f278(x33572,x33571),x33573)),f323(f254(x33572,x33571),x33573))
% 179.72/179.57 [3374]E(f323(f129(x33741,x33742),f323(f162(x33741),x33743)),f323(f162(x33741),f323(f129(x33741,x33742),x33743)))
% 179.72/179.57 [3388]E(f323(f323(f131(x33881),x33882),f323(f165(x33881),x33883)),f323(f323(f131(x33881),f323(a112,x33882)),x33883))
% 179.72/179.57 [3406]E(f28(f26(x34061,x34062,x34063)),f323(f323(f78(a860),f28(x34063)),f323(a112,f2(a860))))
% 179.72/179.57 [3407]E(f323(f302(x34071,x34072,x34073),f188(f867(x34071,a855))),f188(f867(x34072,a855)))
% 179.72/179.57 [3408]E(f323(f303(x34081,x34082,x34083),f188(f867(x34082,a855))),f188(f867(x34081,a855)))
% 179.72/179.57 [3409]E(f323(f303(x34091,x34092,x34093),f246(f867(x34092,a855))),f246(f867(x34091,a855)))
% 179.72/179.57 [3410]E(f323(f277(x34101,x34102,x34103),f188(f867(x34101,a855))),f188(f867(x34102,a855)))
% 179.72/179.57 [3439]E(f323(f323(f301(x34391),x34392),f323(f166(x34391),x34393)),f323(f166(x34391),f133(x34391,x34392,x34393)))
% 179.72/179.57 [3451]E(f231(x34511,x34512,f323(f230(x34511),x34513)),f323(f323(f78(a860),f323(x34512,x34513)),f323(a112,f2(a860))))
% 179.72/179.57 [3527]E(f323(f189(a857),f26(x35271,x35272,x35273)),f323(f323(f78(a860),f323(f189(a857),x35273)),f323(a112,f2(a860))))
% 179.72/179.57 [3528]E(f323(f302(f866(x35281,x35282),x35282,f261(x35281,x35282)),x35283),f323(f254(x35281,x35282),x35283))
% 179.72/179.57 [3529]E(f323(f302(f866(x35291,x35292),x35291,f257(x35291,x35292)),x35293),f323(f256(x35291,x35292),x35293))
% 179.72/179.57 [3601]E(f323(f323(f258(x36011,x36012),f323(f257(x36011,x36012),x36013)),f323(f261(x36011,x36012),x36013)),x36013)
% 179.72/179.57 [3608]E(f323(f189(f862(x36081)),f123(x36081,x36082,x36083)),f323(f323(f78(a860),f323(f189(f862(x36081)),x36083)),f323(a112,f2(a860))))
% 179.72/179.57 [3609]E(f323(f323(f262(x36091,x36092,x36091),f16(x36091,x36092)),x36093),f323(f257(x36091,x36092),x36093))
% 179.72/179.57 [3629]E(f180(x36291,x36292,x36293,f323(f16(f864(x36292),x36291),f200(x36292))),x36293)
% 179.72/179.57 [3630]E(f180(x36301,x36302,f323(f16(f864(x36302),x36301),f200(x36302)),x36303),x36303)
% 179.72/179.57 [3686]E(f28(f27(x36861,x36862,x36863)),f323(f323(f78(a860),f323(f323(f78(a860),f28(x36862)),f28(x36863))),f323(a112,f2(a860))))
% 179.72/179.57 [3737]E(f323(f71(x37371,x37371,x37372,f32(x37371)),x37373),x37373)
% 179.72/179.57 [3745]E(f323(f323(f121(x37451),f163(x37451,x37452,x37453)),f323(f323(f144(x37451),x37453),f113(x37451))),f323(f323(f144(x37451),x37453),f163(x37451,x37452,x37453)))
% 179.72/179.57 [3849]E(f323(f189(a857),f27(x38491,x38492,x38493)),f323(f323(f78(a860),f323(f323(f78(a860),f323(f189(a857),x38492)),f323(f189(a857),x38493))),f323(a112,f2(a860))))
% 179.72/179.57 [3926]P101(f323(f323(f237(f867(x39261,a855)),f323(f166(x39261),f323(f129(x39261,x39262),x39263))),f323(f166(x39261),x39263)))
% 179.72/179.57 [3973]P101(f323(f323(f237(f867(x39731,a855)),f323(f166(x39731),f323(f323(f169(x39731),x39732),x39733))),f323(f166(x39731),x39733)))
% 179.72/179.57 [3974]P101(f323(f323(f237(f867(x39741,a855)),f323(f166(x39741),f323(f323(f131(x39741),x39742),x39743))),f323(f166(x39741),x39743)))
% 179.72/179.57 [3979]P101(f323(f323(f237(f867(x39791,a855)),f323(f166(x39791),f164(x39791,x39792,x39793))),f323(f166(x39791),x39793)))
% 179.72/179.57 [3980]P101(f323(f323(f237(f867(x39801,a855)),f323(f166(x39801),f170(x39801,x39802,x39803))),f323(f166(x39801),x39802)))
% 179.72/179.57 [4003]P27(f866(x40031,x40032),f866(x40032,x40031),f323(f262(x40031,x40032,f866(x40032,x40031)),f323(f7(x40032,x40031,f866(x40032,x40031)),f258(x40032,x40031))),x40033)
% 179.72/179.57 [4015]E(f323(f323(f323(f183(f861(x40151),f861(x40151)),f42(a860,x40152,f323(f189(f861(x40151)),x40153))),f161(x40151)),x40153),f323(f323(f323(f183(f861(x40151),f861(x40151)),x40152),f161(x40151)),x40153))
% 179.72/179.57 [4057]P101(f323(f323(f325(f866(f861(x40571),f861(x40571))),f323(f323(f258(f861(x40571),f861(x40571)),x40572),x40572)),f151(x40571,f299(x40571,x40573))))
% 179.72/179.57 [4202]E(f83(f866(x42021,x42022),f323(f323(f18(f866(x42021,x42022),x42022,a855),f323(f323(f8(x42021,f867(x42022,a855),f866(x42021,x42022)),x42023),f257(x42021,x42022))),f261(x42021,x42022))),f83(f866(x42021,x42022),f323(f262(x42021,x42022,a855),x42023)))
% 179.72/179.57 [4203]E(f88(f866(x42031,x42032),f323(f323(f18(f866(x42031,x42032),x42032,a855),f323(f323(f8(x42031,f867(x42032,a855),f866(x42031,x42032)),x42033),f257(x42031,x42032))),f261(x42031,x42032))),f88(f866(x42031,x42032),f323(f262(x42031,x42032,a855),x42033)))
% 179.72/179.57 [4239]E(f323(f323(f279(f866(a860,x42391),x42391),f315(a860,x42391,a242,x42392)),f323(f323(f18(x42391,x42391,f866(a860,x42391)),f323(f323(f8(a860,f867(x42391,f866(a860,x42391)),x42391),f258(a860,x42391)),x42393)),f5(x42391))),f317(x42391,x42393,x42392))
% 179.72/179.57 [4304]E(f323(f263(x43041,x43041,x43042,x43042,f5(x43041),f5(x43042)),x43043),x43043)
% 179.72/179.57 [4380]E(f323(f135(f861(f861(x43801)),f861(f861(x43801)),f121(f861(x43801)),f113(f861(x43801))),f323(f323(f147(f861(x43801),f861(f861(x43801))),f323(f323(f7(f861(x43801),f861(x43801),f861(f861(x43801))),f323(f323(f8(f867(x43801,f861(x43801)),f867(f861(x43801),f861(f861(x43801))),f861(x43801)),f147(x43801,f861(x43801))),f323(f7(x43801,f861(x43801),f861(x43801)),f144(x43801)))),x43802)),f52(x43801,x43803,x43802))),f52(x43801,f323(a112,x43803),x43802))
% 179.72/179.57 [4443]E(f323(f232(a860,f866(x44431,f862(x44431)),f2(a860),f323(f262(x44431,f862(x44431),a860),f323(f323(f7(x44431,a860,f867(f862(x44431),a860)),f323(f323(f8(f867(f862(x44431),f867(a860,a860)),f867(a860,f867(f862(x44431),a860)),x44431),f7(f862(x44431),a860,a860)),f323(f323(f8(f867(f862(x44431),a860),f867(f862(x44431),f867(a860,a860)),x44431),f323(f8(a860,f867(a860,a860),f862(x44431)),f78(a860))),f323(f323(f7(x44431,f867(f862(x44431),a860),f867(f862(x44431),a860)),f323(f323(f8(f867(a860,a860),f867(f867(f862(x44431),a860),f867(f862(x44431),a860)),x44431),f8(a860,a860,f862(x44431))),f323(f323(f8(a860,f867(a860,a860),x44431),f78(a860)),x44432))),f125(x44431,x44432))))),f76(a860)))),f323(f128(x44431),x44433)),f323(f125(x44431,x44432),x44433))
% 179.72/179.57 [4446]E(f323(f323(f84(a1,x44461),f220(f323(f323(f71(f866(a1,a1),a1,x44461,f261(a1,a1)),f214(x44461)),x44462),f323(f323(f71(f866(a1,a1),a1,x44461,f261(a1,a1)),f214(x44461)),x44463))),f323(f323(f18(a1,a1,x44461),f323(f323(f8(a1,f867(a1,x44461),a1),f204(x44461)),f323(f323(f18(a1,a1,a1),f323(f323(f8(a1,f867(a1,a1),a1),f78(a1)),f323(f323(f8(a1,a1,a1),f323(f79(a1),f323(f323(f71(f866(a1,a1),a1,x44461,f257(a1,a1)),f214(x44461)),x44462))),f323(f323(f7(a1,a1,a1),f36(a1)),f323(f323(f71(f866(a1,a1),a1,x44461,f261(a1,a1)),f214(x44461)),x44462))))),f323(f323(f8(a1,a1,a1),f323(f79(a1),f323(f323(f71(f866(a1,a1),a1,x44461,f257(a1,a1)),f214(x44461)),x44463))),f323(f323(f7(a1,a1,a1),f36(a1)),f323(f323(f71(f866(a1,a1),a1,x44461,f261(a1,a1)),f214(x44461)),x44463)))))),f5(a1))),f225(x44461,x44462,x44463))
% 179.72/179.57 [4489]~E(f323(f323(f144(x44891),x44892),x44893),x44893)
% 179.72/179.57 [4496]~E(f323(f323(f144(x44961),x44962),x44963),f113(x44961))
% 179.72/179.57 [4512]~E(f323(f323(f301(x45121),x45122),x45123),f188(f867(x45121,a855)))
% 179.72/179.57 [4535]~E(f323(f302(x45351,f867(x45351,a855),x45352),x45353),f323(f300(x45351),x45353))
% 179.72/179.57 [3315]E(f323(f323(f152(x33151,f113(x33151)),x33152),x33153),f113(x33151))
% 179.72/179.57 [3316]E(f323(f165(x33161),f323(f323(f144(x33161),x33162),x33163)),x33163)
% 179.72/179.57 [3317]E(f323(f134(x33171),f323(f323(f144(x33171),x33172),x33173)),x33172)
% 179.72/179.57 [3361]E(f323(f323(f131(x33611),f76(a860)),f323(f323(f144(x33611),x33612),x33613)),x33613)
% 179.72/179.57 [3395]E(f114(x33951,f323(f323(f131(x33951),x33952),x33953)),f323(f323(f131(x33951),x33952),f114(x33951,x33953)))
% 179.72/179.57 [3397]E(f323(f323(f152(x33971,x33972),x33973),f323(f323(f158(x33971),x33972),x33973)),x33972)
% 179.72/179.57 [3421]E(f323(f323(f301(x34211),x34212),f323(f323(f301(x34211),x34212),x34213)),f323(f323(f301(x34211),x34212),x34213))
% 179.72/179.57 [3432]E(f323(f323(f179(x34321,x34322),f113(f866(x34321,x34322))),x34323),f200(x34322))
% 179.72/179.57 [3435]E(f323(f323(f301(x34351),x34352),f323(f166(x34351),x34353)),f323(f166(x34351),f323(f323(f144(x34351),x34352),x34353)))
% 179.72/179.57 [3437]E(f323(f323(f131(x34371),x34372),f323(f165(x34371),x34373)),f323(f165(x34371),f323(f323(f131(x34371),x34372),x34373)))
% 179.72/179.57 [3448]E(f323(f323(f169(x34481),f76(a860)),f323(f323(f144(x34481),x34482),x34483)),f323(f323(f144(x34481),x34482),f113(x34481)))
% 179.72/179.57 [3492]E(f323(f61(x34921,x34922),f323(f323(f301(x34921),x34923),f188(f867(x34921,a855)))),x34923)
% 179.72/179.57 [3535]E(f323(f323(f78(a860),x35351),f323(f323(f78(a860),x35352),x35353)),f323(f323(f78(a860),x35352),f323(f323(f78(a860),x35351),x35353)))
% 179.72/179.57 [3536]E(f323(f323(f78(a1),x35361),f323(f323(f78(a1),x35362),x35363)),f323(f323(f78(a1),x35362),f323(f323(f78(a1),x35361),x35363)))
% 179.72/179.57 [3541]E(f323(f323(f260(x35411,x35412),f188(f867(x35411,a855))),x35413),f188(f867(f866(x35411,x35412),a855)))
% 179.72/179.57 [3565]E(f323(f323(f110(f867(x35651,a855)),x35652),x35653),f323(f323(f110(f867(x35651,a855)),x35653),x35652))
% 179.72/179.57 [3566]E(f323(f323(f101(f867(x35661,a855)),x35662),x35663),f323(f323(f101(f867(x35661,a855)),x35663),x35662))
% 179.72/179.57 [3568]E(f323(f323(f121(x35681),x35682),f323(f323(f144(x35681),x35683),f113(x35681))),f323(f161(x35681),f323(f323(f144(x35681),x35683),x35682)))
% 179.72/179.57 [3569]E(f323(f323(f121(x35691),f323(f162(x35691),x35692)),f323(f162(x35691),x35693)),f323(f162(x35691),f323(f323(f121(x35691),x35693),x35692)))
% 179.72/179.57 [3579]E(f323(f165(x35791),f323(f323(f169(x35791),f323(a112,x35792)),x35793)),f323(f323(f169(x35791),x35792),f323(f165(x35791),x35793)))
% 179.72/179.57 [3587]P101(f323(f323(f325(x35871),x35872),f323(f323(f301(x35871),x35872),x35873)))
% 179.72/179.57 [3591]E(f323(f323(f40(x35911,f867(x35912,a855)),f188(f867(x35911,a855))),x35913),f246(f867(x35912,a855)))
% 179.72/179.57 [3594]E(f323(f277(x35941,x35941,f255(x35941,x35942)),x35943),f323(f323(f101(f867(x35941,a855)),x35942),x35943))
% 179.72/179.57 [3607]E(f323(f189(f861(x36071)),f323(f323(f144(x36071),x36072),x36073)),f323(f323(f78(a860),f323(f189(f861(x36071)),x36073)),f323(a112,f2(a860))))
% 179.72/179.57 [3611]E(f137(x36111,f323(f323(f121(x36111),x36112),f323(f323(f144(x36111),x36113),f113(x36111)))),x36113)
% 179.72/179.57 [3612]E(f114(x36121,f323(f323(f121(x36121),x36122),f323(f323(f144(x36121),x36123),f113(x36121)))),x36122)
% 179.72/179.57 [3618]E(f323(f323(f121(x36181),f323(f323(f169(x36181),x36182),x36183)),f323(f323(f131(x36181),x36182),x36183)),x36183)
% 179.72/179.57 [3627]E(f323(f323(f22(a860),f323(f323(f78(a860),x36271),x36272)),f323(f323(f78(a860),x36273),x36272)),f323(f323(f22(a860),x36271),x36273))
% 179.72/179.57 [3628]E(f323(f323(f22(a860),f323(f323(f78(a860),x36281),x36282)),f323(f323(f78(a860),x36281),x36283)),f323(f323(f22(a860),x36282),x36283))
% 179.72/179.57 [3636]E(f323(f323(f121(x36361),f323(f162(x36361),x36362)),f323(f323(f144(x36361),x36363),f113(x36361))),f323(f162(x36361),f323(f323(f144(x36361),x36363),x36362)))
% 179.72/179.57 [3638]E(f323(f323(f78(a860),f323(f189(f861(x36381)),x36382)),f323(f189(f861(x36381)),x36383)),f323(f189(f861(x36381)),f323(f323(f121(x36381),x36382),x36383)))
% 179.72/179.57 [3641]E(f323(f323(f78(a860),f323(f189(f861(x36411)),x36412)),f323(f189(f861(x36411)),x36413)),f323(f189(f861(x36411)),f167(x36411,x36412,x36413)))
% 179.72/179.57 [3648]E(f323(f323(f110(f867(x36481,a855)),f323(f166(x36481),x36482)),f323(f166(x36481),x36483)),f323(f166(x36481),f323(f323(f121(x36481),x36482),x36483)))
% 179.72/179.57 [3649]E(f42(a860,f323(f323(f79(a860),x36491),x36492),f323(f323(f79(a860),x36491),x36493)),f323(f323(f79(a860),x36491),f42(a860,x36492,x36493)))
% 179.72/179.57 [3662]E(f323(f323(f169(x36621),f323(f323(f22(a860),x36622),f76(a860))),f323(f165(x36621),x36623)),f323(f165(x36621),f323(f323(f169(x36621),x36622),x36623)))
% 179.72/179.57 [3667]E(f323(f323(f101(f867(x36671,a855)),x36672),f323(f77(f867(x36671,a855)),x36673)),f323(f323(f22(f867(x36671,a855)),x36672),x36673))
% 179.72/179.57 [3668]E(f323(f323(f22(f867(x36681,a855)),x36682),f323(f77(f867(x36681,a855)),x36683)),f323(f323(f101(f867(x36681,a855)),x36682),x36683))
% 179.72/179.57 [3690]E(f323(f323(f260(x36901,x36902),x36903),f323(f16(f867(x36902,a855),x36901),f188(f867(x36902,a855)))),f188(f867(f866(x36901,x36902),a855)))
% 179.72/179.57 [3692]E(f323(f323(f22(a860),f323(f323(f79(a860),x36921),x36922)),f323(f323(f79(a860),x36921),x36923)),f323(f323(f79(a860),x36921),f323(f323(f22(a860),x36922),x36923)))
% 179.72/179.57 [3693]E(f323(f323(f78(a860),f323(f323(f79(a860),x36931),x36932)),f323(f323(f79(a860),x36931),x36933)),f323(f323(f79(a860),x36931),f323(f323(f78(a860),x36932),x36933)))
% 179.72/179.57 [3694]E(f323(f323(f22(a1),f323(f323(f79(a1),x36941),x36942)),f323(f323(f79(a1),x36941),x36943)),f323(f323(f79(a1),x36941),f323(f323(f22(a1),x36942),x36943)))
% 179.72/179.57 [3695]E(f323(f323(f78(a1),f323(f323(f79(a1),x36951),x36952)),f323(f323(f79(a1),x36951),x36953)),f323(f323(f79(a1),x36951),f323(f323(f78(a1),x36952),x36953)))
% 179.72/179.57 [3696]E(f323(f323(f79(a1),f323(f323(f248(a1),x36961),x36962)),f323(f323(f248(a1),x36961),x36963)),f323(f323(f248(a1),x36961),f323(f323(f78(a860),x36962),x36963)))
% 179.72/179.57 [3711]E(f323(f323(f39(x37111,f867(x37112,a855)),x37113),f323(f16(f867(x37112,a855),x37111),f188(f867(x37112,a855)))),f188(f867(x37112,a855)))
% 179.72/179.57 [3713]E(f42(a860,f323(f323(f79(a860),x37131),x37132),f323(f323(f79(a860),x37133),x37132)),f323(f323(f79(a860),f42(a860,x37131,x37133)),x37132))
% 179.72/179.57 [3717]E(f42(a1,f323(f323(f22(a1),x37171),f42(a1,x37172,x37173)),x37173),f42(a1,f323(f323(f22(a1),x37171),x37172),x37173))
% 179.72/179.57 [3718]E(f42(a1,f323(f323(f79(a1),x37181),f42(a1,x37182,x37183)),x37183),f42(a1,f323(f323(f79(a1),x37181),x37182),x37183))
% 179.72/179.57 [3719]P101(f323(f323(f237(f867(x37191,a855)),x37192),f323(f323(f301(x37191),x37193),x37192)))
% 179.72/179.57 [3722]E(f323(f302(f866(x37221,x37222),x37221,f257(x37221,x37222)),f323(f166(f866(x37221,x37222)),x37223)),f177(x37221,x37222,f323(f179(x37221,x37222),x37223)))
% 179.72/179.57 [3773]P101(f323(f59(x37731),f177(x37731,x37732,f323(f179(x37731,x37732),x37733))))
% 179.72/179.57 [3798]E(f323(f323(f40(f867(x37981,a855),f867(x37981,a855)),x37982),f323(f110(f867(x37981,a855)),x37983)),f323(f323(f110(f867(x37981,a855)),x37983),f38(f867(x37981,a855),x37982)))
% 179.72/179.57 [3799]E(f323(f323(f39(f867(x37991,a855),f867(x37991,a855)),x37992),f323(f101(f867(x37991,a855)),x37993)),f323(f323(f101(f867(x37991,a855)),x37993),f37(f867(x37991,a855),x37992)))
% 179.72/179.57 [3810]E(f323(f166(x38101),f323(f323(f323(f183(f861(x38101),f861(x38101)),x38102),f161(x38101)),x38103)),f323(f166(x38101),x38103))
% 179.72/179.57 [3814]E(f323(f323(f169(x38141),f323(f189(f861(x38141)),f171(x38141,x38142,x38143))),x38143),f171(x38141,x38142,x38143))
% 179.72/179.57 [3815]E(f177(x38151,x38152,f323(f323(f8(x38152,f864(x38152),x38151),f230(x38152)),x38153)),f246(f867(x38151,a855)))
% 179.72/179.57 [3819]E(f323(f189(f861(x38191)),f323(f323(f323(f183(f861(x38191),f861(x38191)),x38192),f161(x38191)),x38193)),f323(f189(f861(x38191)),x38193))
% 179.72/179.57 [3822]E(f323(f323(f262(x38221,x38222,x38222),f323(f16(f867(x38222,x38222),x38221),f5(x38222))),x38223),f323(f261(x38221,x38222),x38223))
% 179.72/179.57 [3829]E(f42(a1,f323(f323(f22(a1),f42(a1,x38291,x38292)),x38293),x38292),f42(a1,f323(f323(f22(a1),x38291),x38293),x38292))
% 179.72/179.57 [3830]E(f42(a1,f323(f323(f248(a1),f42(a1,x38301,x38302)),x38303),x38302),f42(a1,f323(f323(f248(a1),x38301),x38303),x38302))
% 179.72/179.57 [3833]E(f323(f323(f39(f867(f866(x38331,x38332),a855),f867(x38332,a855)),x38333),f254(x38331,x38332)),f323(f254(x38331,x38332),f37(f867(f866(x38331,x38332),a855),x38333)))
% 179.72/179.57 [3834]E(f323(f323(f39(f867(f866(x38341,x38342),a855),f867(x38341,a855)),x38343),f256(x38341,x38342)),f323(f256(x38341,x38342),f37(f867(f866(x38341,x38342),a855),x38343)))
% 179.72/179.57 [3862]E(f323(f71(x38621,x38621,x38621,x38622),f323(f323(f183(x38621,x38621),x38623),x38622)),f323(f323(f183(x38621,x38621),f323(a112,x38623)),x38622))
% 179.72/179.57 [3872]E(f232(f864(x38721),x38722,f200(x38721),f323(f323(f8(x38721,f864(x38721),x38722),f230(x38721)),x38723)),f323(f201(x38722,x38721),x38723))
% 179.72/179.57 [3879]E(f323(f323(f131(x38791),f323(f323(f22(a860),f323(f189(f861(x38791)),x38792)),x38793)),f323(f162(x38791),x38792)),f323(f162(x38791),f323(f323(f169(x38791),x38793),x38792)))
% 179.72/179.57 [3880]E(f323(f323(f169(x38801),f323(f323(f22(a860),f323(f189(f861(x38801)),x38802)),x38803)),f323(f162(x38801),x38802)),f323(f162(x38801),f323(f323(f131(x38801),x38803),x38802)))
% 179.72/179.57 [3883]E(f323(f323(f78(a860),f323(f159(a860),f323(f323(f147(x38831,a860),x38832),x38833))),f323(f189(f861(x38831)),x38833)),f148(x38831,x38832,x38833))
% 179.72/179.57 [3902]E(f323(f161(x39021),f323(f323(f323(f183(f861(x39021),f861(x39021)),x39022),f161(x39021)),x39023)),f323(f323(f323(f183(f861(x39021),f861(x39021)),f323(a112,x39022)),f161(x39021)),x39023))
% 179.72/179.57 [3917]P101(f323(f323(f237(a860),f323(f189(f861(x39171)),f323(f129(x39171,x39172),x39173))),f323(f189(f861(x39171)),x39173)))
% 179.72/179.57 [3934]E(f323(f323(f110(f867(f867(x39341,a855),a855)),f323(f300(x39341),x39342)),f323(f302(f867(x39341,a855),f867(x39341,a855),f323(f301(x39341),x39343)),f323(f300(x39341),x39342))),f323(f300(x39341),f323(f323(f301(x39341),x39343),x39342)))
% 179.72/179.57 [3954]P26(x39541,x39542,f323(f323(f301(f859(x39541)),f323(f323(f323(f90(x39541),x39543),a24),x39543)),f188(f867(f859(x39541),a855))))
% 179.72/179.57 [3970]P101(f323(f323(f237(a860),f323(f189(f861(x39701)),f171(x39701,x39702,x39703))),f323(f189(f861(x39701)),x39703)))
% 179.72/179.57 [3978]E(f323(f256(x39781,x39782),f323(f243(f866(x39781,x39782)),f323(f262(x39781,x39782,a855),x39783))),f323(f243(x39781),f323(f323(f8(f867(x39782,a855),a855,x39781),f85(x39782)),x39783)))
% 179.72/179.57 [3990]E(f323(f302(a860,a860,f323(f323(f7(a860,a860,a860),f78(a860)),x39901)),f294(a860,x39902,x39903)),f294(a860,f323(f323(f78(a860),x39902),x39901),f323(f323(f78(a860),x39903),x39901)))
% 179.72/179.57 [3993]P101(f323(f59(f864(x39931)),f323(f302(x39932,f864(x39931),f323(f179(x39932,x39931),x39933)),f246(f867(x39932,a855)))))
% 179.72/179.57 [4006]E(f323(f302(a860,a860,f323(f323(f7(a860,a860,a860),f78(a860)),x40061)),f323(f293(a860,x40062),x40063)),f323(f293(a860,f323(f323(f78(a860),x40062),x40061)),f323(f323(f78(a860),x40063),x40061)))
% 179.72/179.57 [4024]E(f323(f323(f175(x40241,x40242),f323(f323(f147(f866(x40241,x40242),x40241),f257(x40241,x40242)),x40243)),f323(f323(f147(f866(x40241,x40242),x40242),f261(x40241,x40242)),x40243)),x40243)
% 179.72/179.57 [4029]E(f323(f323(f78(a860),f323(f323(f79(a860),x40291),f42(a860,f323(f323(f36(a860),x40292),x40291),x40293))),f42(a860,x40292,x40291)),f42(a860,x40292,f323(f323(f79(a860),x40291),x40293)))
% 179.72/179.57 [4043]E(f323(f323(f121(x40431),x40432),f323(f135(f861(x40431),f861(x40431),f121(x40431),f113(x40431)),x40433)),f323(f135(f861(x40431),f861(x40431),f121(x40431),x40432),x40433))
% 179.72/179.57 [4061]P101(f323(f323(f325(f866(x40611,x40611)),f323(f323(f258(x40611,x40611),x40612),x40612)),f323(f323(f183(f866(x40611,x40611),a855),f2(a860)),x40613)))
% 179.72/179.57 [4067]E(f323(f243(x40671),f323(f323(f8(f867(x40672,a855),a855,x40671),f85(x40672)),f323(f7(x40672,x40671,a855),x40673))),f323(f254(x40672,x40671),f323(f243(f866(x40672,x40671)),f323(f262(x40672,x40671,a855),x40673))))
% 179.72/179.57 [4085]E(f323(f323(f110(f867(x40851,a855)),f323(f323(f39(a860,f867(x40851,a855)),f294(a860,f76(a860),x40852)),x40853)),f323(x40853,f2(a860))),f323(f323(f39(a860,f867(x40851,a855)),f323(f292(a860),x40852)),x40853))
% 179.72/179.57 [4100]E(f323(f135(f861(x41001),f861(x41001),f121(x41001),f113(x41001)),f323(f323(f147(f861(x41001),f861(x41001)),f129(x41001,x41002)),x41003)),f323(f129(x41001,x41002),f323(f135(f861(x41001),f861(x41001),f121(x41001),f113(x41001)),x41003)))
% 179.72/179.57 [4105]E(f323(f261(f861(x41051),f861(x41051)),f160(x41051,x41052,x41053)),f323(f129(x41051,f323(f71(a855,a855,x41051,a318),x41052)),x41053))
% 179.72/179.57 [4153]E(f323(f323(f78(a1),f323(f323(f78(a1),f323(f323(f79(a1),x41531),f323(f323(f36(a1),x41532),x41531))),f42(a1,x41532,x41531))),x41533),f323(f323(f78(a1),x41532),x41533))
% 179.72/179.57 [4191]E(f323(f323(f78(a1),f323(f323(f78(a1),f323(f323(f79(a1),f323(f323(f36(a1),x41911),x41912)),x41912)),f42(a1,x41911,x41912))),x41913),f323(f323(f78(a1),x41911),x41913))
% 179.72/179.57 [4220]E(f83(f866(x42201,x42202),f323(f262(x42201,x42202,a855),f323(f323(f8(f867(x42202,f866(x42201,x42202)),f867(x42202,a855),x42201),f323(f8(f866(x42201,x42202),a855,x42202),x42203)),f258(x42201,x42202)))),f83(f866(x42201,x42202),x42203))
% 179.72/179.57 [4221]E(f88(f866(x42211,x42212),f323(f262(x42211,x42212,a855),f323(f323(f8(f867(x42212,f866(x42211,x42212)),f867(x42212,a855),x42211),f323(f8(f866(x42211,x42212),a855,x42212),x42213)),f258(x42211,x42212)))),f88(f866(x42211,x42212),x42213))
% 179.72/179.57 [4249]P101(f323(f323(f237(f867(x42491,a855)),f37(f867(x42491,a855),f323(f323(f101(f867(f867(x42491,a855),a855)),x42492),x42493))),f323(f323(f101(f867(x42491,a855)),f37(f867(x42491,a855),x42492)),f37(f867(x42491,a855),x42493))))
% 179.72/179.57 [4250]E(f323(f162(x42501),f323(f323(f323(f183(f861(x42501),f861(x42501)),f323(f323(f22(a860),f323(f189(f861(x42501)),x42502)),f42(a860,x42503,f323(f189(f861(x42501)),x42502)))),f161(x42501)),x42502)),f323(f323(f323(f183(f861(x42501),f861(x42501)),x42503),f161(x42501)),f323(f162(x42501),x42502)))
% 179.72/179.57 [4264]E(f323(f243(x42641),f323(f323(f8(a855,a855,x42641),a318),f323(f323(f7(x42641,f864(x42642),a855),f323(f323(f8(f864(x42642),f867(f864(x42642),a855),x42641),a320),x42643)),f200(x42642)))),f177(x42641,x42642,x42643))
% 179.72/179.57 [4289]P101(f323(f323(f237(a860),f323(f189(f861(x42891)),f323(f323(f131(x42891),f323(f189(f861(x42891)),f171(x42891,x42892,x42893))),x42893))),f323(f189(f861(x42891)),x42893)))
% 179.72/179.57 [4331]E(f323(f243(x43311),f323(f323(f8(f867(x43312,a855),a855,x43311),f85(x43312)),f323(f323(f8(f864(x43311),f867(x43312,a855),x43311),f323(f7(x43312,f864(x43311),a855),f323(f323(f8(f864(x43311),f867(f864(x43311),a855),x43312),a320),x43313))),f230(x43311)))),f178(x43312,x43311,x43313))
% 179.72/179.57 [4549]~P101(f323(f60(x45491,x45492,f188(f867(x45491,a855))),x45493))
% 179.72/179.57 [4556]~P101(f323(f323(f325(f866(x45561,x45561)),f323(f323(f258(x45561,x45561),x45562),x45563)),f146(x45561,f113(f867(x45561,a860)))))
% 179.72/179.57 [3580]E(f323(f189(f861(x35801)),f323(f323(f169(x35801),x35802),x35803)),f323(f323(f235(a860),f323(f189(f861(x35801)),x35803)),x35802))
% 179.72/179.57 [3581]E(f323(f189(f861(x35811)),f323(f323(f131(x35811),x35812),x35813)),f323(f323(f22(a860),f323(f189(f861(x35811)),x35813)),x35812))
% 179.72/179.57 [3606]E(f323(f189(f861(f861(x36061))),f52(x36061,x36062,x36063)),f323(f323(f248(a860),f323(f189(f861(x36061)),x36063)),x36062))
% 179.72/179.57 [3620]E(f323(f323(f36(a860),f323(f323(f36(a860),x36201),x36202)),x36203),f323(f323(f36(a860),x36201),f323(f323(f79(a860),x36202),x36203)))
% 179.72/179.57 [3621]E(f323(f323(f22(a860),f323(f323(f22(a860),x36211),x36212)),x36213),f323(f323(f22(a860),x36211),f323(f323(f78(a860),x36212),x36213)))
% 179.72/179.57 [3622]E(f323(f323(f79(a860),f323(f323(f79(a860),x36221),x36222)),x36223),f323(f323(f79(a860),x36221),f323(f323(f79(a860),x36222),x36223)))
% 179.72/179.57 [3623]E(f323(f323(f79(a1),f323(f323(f79(a1),x36231),x36232)),x36233),f323(f323(f79(a1),x36231),f323(f323(f79(a1),x36232),x36233)))
% 179.72/179.57 [3624]E(f323(f323(f78(a860),f323(f323(f78(a860),x36241),x36242)),x36243),f323(f323(f78(a860),x36241),f323(f323(f78(a860),x36242),x36243)))
% 179.72/179.57 [3625]E(f323(f323(f78(a1),f323(f323(f78(a1),x36251),x36252)),x36253),f323(f323(f78(a1),x36251),f323(f323(f78(a1),x36252),x36253)))
% 179.72/179.57 [3626]E(f323(f323(f248(a1),f323(f323(f248(a1),x36261),x36262)),x36263),f323(f323(f248(a1),x36261),f323(f323(f79(a860),x36262),x36263)))
% 179.72/179.57 [3647]E(f155(x36471,f323(f323(f144(f867(x36471,a855)),x36472),x36473)),f168(x36471,x36472,f155(x36471,x36473)))
% 179.72/179.57 [3691]E(f323(f323(f22(a860),f323(f323(f22(a860),x36911),x36912)),x36913),f323(f323(f22(a860),f323(f323(f22(a860),x36911),x36913)),x36912))
% 179.72/179.57 [3697]E(f323(f230(f866(x36971,f862(x36971))),f323(f323(f258(x36971,f862(x36971)),x36972),x36973)),f323(f128(x36971),f123(x36971,x36972,x36973)))
% 179.72/179.57 [3700]E(f323(f323(f101(f867(x37001,a855)),x37002),f323(f323(f22(f867(x37001,a855)),x37003),x37002)),f188(f867(x37001,a855)))
% 179.72/179.57 [3704]E(f323(f323(f147(a860,x37041),f323(f16(x37041,a860),x37042)),f132(a860,f323(f293(a860,f2(a860)),x37043))),f163(x37041,x37043,x37042))
% 179.72/179.57 [3743]E(f37(f867(x37431,a855),f323(f323(f301(f867(x37431,a855)),x37432),x37433)),f323(f323(f110(f867(x37431,a855)),x37432),f37(f867(x37431,a855),x37433)))
% 179.72/179.57 [3744]E(f38(f867(x37441,a855),f323(f323(f301(f867(x37441,a855)),x37442),x37443)),f323(f323(f101(f867(x37441,a855)),x37442),f38(f867(x37441,a855),x37443)))
% 179.72/179.57 [3746]E(f163(x37461,f323(f189(f861(x37461)),f323(f129(x37461,f323(a320,x37462)),x37463)),x37462),f323(f129(x37461,f323(a320,x37462)),x37463))
% 179.72/179.57 [3748]E(f323(f323(f22(a860),f323(f323(f79(a860),x37481),x37482)),f323(f323(f79(a860),x37483),x37482)),f323(f323(f79(a860),f323(f323(f22(a860),x37481),x37483)),x37482))
% 179.72/179.57 [3749]E(f323(f323(f78(a860),f323(f323(f79(a860),x37491),x37492)),f323(f323(f79(a860),x37493),x37492)),f323(f323(f79(a860),f323(f323(f78(a860),x37491),x37493)),x37492))
% 179.72/179.57 [3750]E(f323(f323(f22(a1),f323(f323(f79(a1),x37501),x37502)),f323(f323(f79(a1),x37503),x37502)),f323(f323(f79(a1),f323(f323(f22(a1),x37501),x37503)),x37502))
% 179.72/179.57 [3751]E(f323(f323(f78(a1),f323(f323(f79(a1),x37511),x37512)),f323(f323(f79(a1),x37513),x37512)),f323(f323(f79(a1),f323(f323(f78(a1),x37511),x37513)),x37512))
% 179.72/179.57 [3753]E(f323(f323(f235(a860),f323(f323(f22(a860),x37531),x37532)),f323(f323(f22(a860),x37533),x37532)),f323(f323(f22(a860),f323(f323(f235(a860),x37531),x37533)),x37532))
% 179.72/179.57 [3776]E(f323(f323(f101(f867(f861(x37761),a855)),f153(x37761,x37762)),f153(x37761,x37763)),f153(x37761,f323(f323(f101(f867(x37761,a855)),x37762),x37763)))
% 179.72/179.57 [3778]E(f323(f323(f110(f867(x37781,a855)),x37782),f323(f323(f110(f867(x37781,a855)),x37782),x37783)),f323(f323(f110(f867(x37781,a855)),x37782),x37783))
% 179.72/179.57 [3779]E(f323(f323(f110(f867(x37791,a855)),x37792),f323(f323(f22(f867(x37791,a855)),x37793),x37792)),f323(f323(f110(f867(x37791,a855)),x37792),x37793))
% 179.72/179.57 [3780]E(f323(f323(f101(f867(x37801,a855)),x37802),f323(f323(f101(f867(x37801,a855)),x37802),x37803)),f323(f323(f101(f867(x37801,a855)),x37802),x37803))
% 179.72/179.57 [3792]E(f323(f323(f280(x37921,x37922,x37922),x37923),f299(x37922,f188(f867(f866(x37922,x37922),a855)))),x37923)
% 179.72/179.57 [3795]E(f323(f323(f110(f867(x37951,a855)),f323(f323(f301(x37951),x37952),f188(f867(x37951,a855)))),x37953),f323(f323(f301(x37951),x37952),x37953))
% 179.72/179.57 [3813]E(f323(f323(f22(a860),f323(f323(f22(a860),f323(a112,x38131)),x38132)),f323(a112,x38133)),f323(f323(f22(a860),f323(f323(f22(a860),x38131),x38132)),x38133))
% 179.72/179.57 [3843]E(f323(f323(f101(f867(f867(x38431,a855),a855)),f323(f300(x38431),x38432)),f323(f300(x38431),x38433)),f323(f300(x38431),f323(f323(f101(f867(x38431,a855)),x38432),x38433)))
% 179.72/179.57 [3847]E(f323(f323(f110(f867(x38471,a855)),f323(f77(f867(x38471,a855)),x38472)),x38473),f323(f77(f867(x38471,a855)),f323(f323(f22(f867(x38471,a855)),x38472),x38473)))
% 179.72/179.57 [3859]E(f323(f323(f301(x38591),x38592),f323(f323(f22(f867(x38591,a855)),x38593),f323(f323(f301(x38591),x38592),f188(f867(x38591,a855))))),f323(f323(f301(x38591),x38592),x38593))
% 179.72/179.57 [3869]P101(f323(f323(f237(f867(x38691,a855)),x38692),f323(f323(f110(f867(x38691,a855)),x38693),x38692)))
% 179.72/179.57 [3870]P101(f323(f323(f237(f867(x38701,a855)),x38702),f323(f323(f110(f867(x38701,a855)),x38702),x38703)))
% 179.72/179.57 [3873]E(f323(f323(f101(f867(x38731,a855)),f323(f77(f867(x38731,a855)),x38732)),f323(f77(f867(x38731,a855)),x38733)),f323(f77(f867(x38731,a855)),f323(f323(f110(f867(x38731,a855)),x38732),x38733)))
% 179.72/179.57 [3874]E(f323(f323(f110(f867(x38741,a855)),f323(f77(f867(x38741,a855)),x38742)),f323(f77(f867(x38741,a855)),x38743)),f323(f77(f867(x38741,a855)),f323(f323(f101(f867(x38741,a855)),x38742),x38743)))
% 179.72/179.57 [3888]P101(f323(f323(f237(f867(x38881,a855)),f323(f166(x38881),x38882)),f323(f166(x38881),f323(f323(f144(x38881),x38883),x38882))))
% 179.72/179.57 [3899]E(f323(f323(f110(f867(x38991,a855)),f323(f323(f22(f867(x38991,a855)),x38992),x38993)),f323(f323(f101(f867(x38991,a855)),x38992),x38993)),x38992)
% 179.72/179.57 [3956]E(f323(f323(f6(x39561,a1),f323(f323(f8(a860,a1,x39561),f100(a1)),x39562)),x39563),f323(f100(a1),f323(f323(f6(x39561,a860),x39562),x39563)))
% 179.72/179.57 [3957]E(f323(f323(f9(x39571,a1),f323(f323(f8(a860,a1,x39571),f100(a1)),x39572)),x39573),f323(f100(a1),f323(f323(f9(x39571,a860),x39572),x39573)))
% 179.72/179.57 [4008]E(f323(f323(f121(x40081),f171(x40081,x40082,x40083)),f323(f323(f131(x40081),f323(f189(f861(x40081)),f171(x40081,x40082,x40083))),x40083)),x40083)
% 179.72/179.57 [4013]E(f323(f77(f867(f866(x40131,x40132),a855)),f323(f323(f260(x40131,x40132),x40133),f323(f16(f867(x40132,a855),x40131),f246(f867(x40132,a855))))),f323(f323(f260(x40131,x40132),f323(f77(f867(x40131,a855)),x40133)),f323(f16(f867(x40132,a855),x40131),f246(f867(x40132,a855)))))
% 179.72/179.57 [4014]E(f323(f77(f867(f866(x40141,x40142),a855)),f323(f323(f260(x40141,x40142),f246(f867(x40141,a855))),f323(f16(f867(x40142,a855),x40141),x40143))),f323(f323(f260(x40141,x40142),f246(f867(x40141,a855))),f323(f16(f867(x40142,a855),x40141),f323(f77(f867(x40142,a855)),x40143))))
% 179.72/179.57 [4062]E(f323(f323(f39(f867(x40621,a855),f867(x40621,a855)),x40622),f323(f323(f7(f867(x40621,a855),f867(x40621,a855),f867(x40621,a855)),f101(f867(x40621,a855))),x40623)),f323(f323(f101(f867(x40621,a855)),f37(f867(x40621,a855),x40622)),x40623))
% 179.72/179.57 [4069]E(f323(f135(f861(x40691),f861(x40691),f121(x40691),f113(x40691)),f323(f323(f144(f861(x40691)),x40692),x40693)),f323(f323(f121(x40691),x40692),f323(f135(f861(x40691),f861(x40691),f121(x40691),f113(x40691)),x40693)))
% 179.72/179.57 [4091]E(f323(f323(f301(f867(x40911,a855)),f323(f277(x40911,x40911,x40912),f323(f323(f301(x40911),x40913),f188(f867(x40911,a855))))),f188(f867(f867(x40911,a855),a855))),f323(f323(f58(x40911),f323(f323(f301(x40911),x40913),f188(f867(x40911,a855)))),x40912))
% 179.72/179.57 [4101]E(f323(f323(f78(a860),f323(f323(f79(a860),x41011),f323(f323(f36(a860),x41012),x41013))),f323(f323(f36(a860),f323(f323(f79(a860),x41011),f42(a860,x41012,x41013))),x41013)),f323(f323(f36(a860),f323(f323(f79(a860),x41011),x41012)),x41013))
% 179.72/179.57 [4102]E(f323(f323(f78(a1),f323(f323(f79(a1),x41021),f323(f323(f36(a1),x41022),x41023))),f323(f323(f36(a1),f323(f323(f79(a1),x41021),f42(a1,x41022,x41023))),x41023)),f323(f323(f36(a1),f323(f323(f79(a1),x41021),x41022)),x41023))
% 179.72/179.57 [4138]E(f323(f323(f22(f867(x41381,a855)),f323(f166(x41381),x41382)),f323(f323(f301(x41381),x41383),f188(f867(x41381,a855)))),f323(f166(x41381),f323(f129(x41381,f323(f323(f8(a855,a855,x41381),a318),f323(a320,x41383))),x41382)))
% 179.72/179.57 [4188]E(f323(f323(f121(x41881),f323(f135(f861(x41881),f861(x41881),f121(x41881),f113(x41881)),x41882)),f323(f135(f861(x41881),f861(x41881),f121(x41881),f113(x41881)),x41883)),f323(f135(f861(x41881),f861(x41881),f121(x41881),f113(x41881)),f323(f323(f121(f861(x41881)),x41882),x41883)))
% 179.72/179.57 [4193]E(f323(f323(f258(f861(x41931),f861(x41931)),f323(f129(x41931,x41932),x41933)),f323(f129(x41931,f323(f71(a855,a855,x41931,a318),x41932)),x41933)),f160(x41931,x41932,x41933))
% 179.72/179.57 [4196]E(f323(f323(f78(a860),f323(f323(f78(a860),f323(f323(f36(a860),x41961),x41962)),f323(f323(f36(a860),x41963),x41962))),f323(f323(f36(a860),f323(f323(f78(a860),f42(a860,x41961,x41962)),f42(a860,x41963,x41962))),x41962)),f323(f323(f36(a860),f323(f323(f78(a860),x41961),x41963)),x41962))
% 179.72/179.57 [4197]E(f323(f323(f78(a1),f323(f323(f78(a1),f323(f323(f36(a1),x41971),x41972)),f323(f323(f36(a1),x41973),x41972))),f323(f323(f36(a1),f323(f323(f78(a1),f42(a1,x41971,x41972)),f42(a1,x41973,x41972))),x41972)),f323(f323(f36(a1),f323(f323(f78(a1),x41971),x41973)),x41972))
% 179.72/179.57 [4253]E(f323(f323(f101(f867(f861(x42531),a855)),f323(f323(f7(f861(x42531),f867(f861(x42531),a855),a855),f325(f861(x42531))),f154(x42531,x42532))),f323(f323(f7(f861(x42531),f867(f861(x42531),a855),a855),f325(f861(x42531))),f154(x42531,x42533))),f153(x42531,f323(f323(f101(f867(x42531,a855)),f323(f323(f7(x42531,f867(x42531,a855),a855),f325(x42531)),x42532)),f323(f323(f7(x42531,f867(x42531,a855),a855),f325(x42531)),x42533))))
% 179.72/179.57 [4266]E(f323(f243(x42661),f323(f323(f18(x42661,a855,a855),f323(f323(f8(a855,f867(a855,a855),x42661),a322),f323(f323(f7(x42661,x42661,a855),a320),x42662))),f323(f323(f7(x42661,f867(x42661,a855),a855),f325(x42661)),x42663))),f323(f323(f301(x42661),x42662),x42663))
% 179.72/179.57 [4286]E(f323(f323(f84(f861(f861(x42861)),f861(f861(x42861))),f51(x42861,x42862)),f323(f323(f18(f861(f861(x42861)),f861(f861(x42861)),f861(f861(x42861))),f323(f323(f8(f861(f861(x42861)),f867(f861(f861(x42861)),f861(f861(x42861))),f861(f861(x42861))),f121(f861(x42861))),f323(f147(f861(x42861),f861(x42861)),f323(f144(x42861),x42863)))),f5(f861(f861(x42861))))),f51(x42861,f323(f323(f144(x42861),x42863),x42862)))
% 179.72/179.57 [4290]E(f323(f243(x42901),f323(f323(f18(x42901,a855,a855),f323(f323(f8(a855,f867(a855,a855),x42901),a322),f323(f323(f7(x42901,f867(x42901,a855),a855),f325(x42901)),x42902))),f323(f323(f7(x42901,f867(x42901,a855),a855),f325(x42901)),x42903))),f323(f323(f110(f867(x42901,a855)),x42902),x42903))
% 179.72/179.57 [4291]E(f323(f243(x42911),f323(f323(f18(x42911,a855,a855),f323(f323(f8(a855,f867(a855,a855),x42911),a321),f323(f323(f7(x42911,f867(x42911,a855),a855),f325(x42911)),x42912))),f323(f323(f7(x42911,f867(x42911,a855),a855),f325(x42911)),x42913))),f323(f323(f101(f867(x42911,a855)),x42912),x42913))
% 179.72/179.57 [4383]E(f323(f323(f39(x43831,f867(f867(x43831,a855),a855)),x43832),f323(f323(f7(x43831,f867(f867(x43831,a855),a855),f867(f867(x43831,a855),a855)),f323(f323(f8(f867(x43831,a855),f867(f867(f867(x43831,a855),a855),f867(f867(x43831,a855),a855)),x43831),f301(f867(x43831,a855))),f323(f323(f8(f867(x43831,a855),f867(x43831,a855),x43831),f277(x43831,x43831,x43833)),f323(f323(f7(x43831,f867(x43831,a855),f867(x43831,a855)),f301(x43831)),f188(f867(x43831,a855)))))),f188(f867(f867(x43831,a855),a855)))),f323(f323(f58(x43831),x43832),x43833))
% 179.72/179.57 [4385]E(f323(f323(f204(x43851),f323(f323(f79(a1),f323(f323(f71(f866(a1,a1),a1,x43851,f257(a1,a1)),f214(x43851)),x43852)),f323(f323(f71(f866(a1,a1),a1,x43851,f257(a1,a1)),f214(x43851)),x43853))),f323(f323(f79(a1),f323(f323(f71(f866(a1,a1),a1,x43851,f261(a1,a1)),f214(x43851)),x43852)),f323(f323(f71(f866(a1,a1),a1,x43851,f261(a1,a1)),f214(x43851)),x43853))),f223(x43851,x43852,x43853))
% 179.72/179.57 [4388]E(f323(f243(f861(x43881)),f323(f323(f18(f861(x43881),a855,a855),f323(f323(f8(a855,f867(a855,a855),f861(x43881)),a321),f323(f323(f7(f861(x43881),a860,a855),f323(f323(f8(a860,f867(a860,a855),f861(x43881)),a320),f189(f861(x43881)))),x43882))),f323(f323(f7(f861(x43881),f867(x43881,a855),a855),f323(f323(f8(f867(x43881,a855),f867(f867(x43881,a855),a855),f861(x43881)),f237(f867(x43881,a855))),f166(x43881))),f323(f166(x43881),x43883)))),f323(f166(f861(x43881)),f52(x43881,x43882,x43883)))
% 179.72/179.57 [3766]E(f42(a860,f323(f323(f78(a860),f323(f323(f79(a860),x37661),x37662)),x37663),x37662),f42(a860,x37663,x37662))
% 179.72/179.57 [3812]E(f132(a860,f323(f293(a860,f323(f323(f78(a860),x38121),x38122)),x38123)),f323(f323(f131(a860),x38122),f132(a860,f323(f293(a860,x38121),x38123))))
% 179.72/179.57 [3858]E(f323(f323(f78(a1),f323(f100(a1),x38581)),f323(f323(f78(a1),f323(f100(a1),x38582)),x38583)),f323(f323(f78(a1),f323(f100(a1),f323(f323(f78(a860),x38581),x38582))),x38583))
% 179.72/179.57 [3865]E(f323(f323(f110(f867(x38651,a855)),f323(f323(f22(f867(x38651,a855)),x38652),x38653)),x38653),f323(f323(f110(f867(x38651,a855)),x38652),x38653))
% 179.72/179.57 [3866]E(f323(f323(f22(f867(x38661,a855)),f323(f323(f22(f867(x38661,a855)),x38662),x38663)),x38663),f323(f323(f22(f867(x38661,a855)),x38662),x38663))
% 179.72/179.57 [3889]E(f323(f323(f280(x38891,x38891,x38892),f299(x38891,f188(f867(f866(x38891,x38891),a855)))),x38893),x38893)
% 179.72/179.57 [3896]E(f323(f323(f110(f867(x38961,a855)),f323(f276(x38961),x38962)),f323(f276(x38961),x38963)),f323(f276(x38961),f323(f323(f110(f867(f866(x38961,x38961),a855)),x38962),x38963)))
% 179.72/179.57 [3907]E(f267(x39071,f323(f323(f144(f866(a99,x39071)),f323(f323(f258(a99,x39071),f2(a99)),x39072)),x39073)),f267(x39071,x39073))
% 179.72/179.57 [3910]E(f323(f323(f110(f867(x39101,a855)),f37(f867(x39101,a855),x39102)),f37(f867(x39101,a855),x39103)),f37(f867(x39101,a855),f323(f323(f110(f867(f867(x39101,a855),a855)),x39102),x39103)))
% 179.72/179.57 [3911]E(f323(f323(f101(f867(x39111,a855)),f38(f867(x39111,a855),x39112)),f38(f867(x39111,a855),x39113)),f38(f867(x39111,a855),f323(f323(f110(f867(f867(x39111,a855),a855)),x39112),x39113)))
% 179.72/179.57 [3948]E(f323(f323(f280(x39481,x39481,x39481),f323(f323(f183(f866(x39481,x39481),a855),x39482),x39483)),x39483),f323(f323(f183(f866(x39481,x39481),a855),f323(a112,x39482)),x39483))
% 179.72/179.57 [3999]P101(f323(f323(f237(f867(x39991,a855)),f323(f323(f22(f867(x39991,a855)),x39992),x39993)),x39992))
% 179.72/179.57 [4000]P101(f323(f323(f237(f867(x40001,a855)),f323(f323(f101(f867(x40001,a855)),x40002),x40003)),x40003))
% 179.72/179.57 [4001]P101(f323(f323(f237(f867(x40011,a855)),f323(f323(f101(f867(x40011,a855)),x40012),x40013)),x40012))
% 179.72/179.57 [4026]E(f299(x40261,f323(f323(f110(f867(f866(x40261,x40261),a855)),f299(x40261,x40262)),f299(x40261,x40263))),f299(x40261,f323(f323(f110(f867(f866(x40261,x40261),a855)),x40262),x40263)))
% 179.72/179.57 [4030]E(f37(f867(x40301,a855),f323(f323(f301(f867(x40301,a855)),x40302),f323(f323(f301(f867(x40301,a855)),x40303),f188(f867(f867(x40301,a855),a855))))),f323(f323(f110(f867(x40301,a855)),x40302),x40303))
% 179.72/179.57 [4031]E(f38(f867(x40311,a855),f323(f323(f301(f867(x40311,a855)),x40312),f323(f323(f301(f867(x40311,a855)),x40313),f188(f867(f867(x40311,a855),a855))))),f323(f323(f101(f867(x40311,a855)),x40312),x40313))
% 179.72/179.57 [4037]E(f323(f323(f280(x40371,x40371,x40371),f323(f323(f183(f866(x40371,x40371),a855),x40372),x40373)),x40373),f323(f323(f280(x40371,x40371,x40371),x40373),f323(f323(f183(f866(x40371,x40371),a855),x40372),x40373)))
% 179.72/179.57 [4106]E(f323(f323(f110(f867(x41061,a855)),f323(f243(x41061),f323(f323(f7(x41061,x41061,a855),a320),x41062))),x41063),f323(f323(f301(x41061),x41062),x41063))
% 179.72/179.57 [4108]E(f323(a104,f323(f323(f6(x41081,a1),f323(f323(f8(a860,a1,x41081),f100(a1)),x41082)),x41083)),f323(f323(f6(x41081,a860),x41082),x41083))
% 179.72/179.57 [4109]E(f323(a104,f323(f323(f9(x41091,a1),f323(f323(f8(a860,a1,x41091),f100(a1)),x41092)),x41093)),f323(f323(f9(x41091,a860),x41092),x41093))
% 179.72/179.57 [4185]E(f323(f149(f861(x41851),x41851,f323(f165(x41851),x41852),f323(f16(f867(f861(x41851),f861(x41851)),x41851),f323(f323(f7(f861(x41851),f861(x41851),f861(x41851)),f121(x41851)),x41852))),x41853),f323(f165(x41851),f323(f323(f121(x41851),x41853),x41852)))
% 179.72/179.57 [4216]P101(f323(f323(f237(f867(f867(x42161,a855),a855)),f323(f323(f110(f867(f867(x42161,a855),a855)),f323(f300(x42161),x42162)),f323(f300(x42161),x42163))),f323(f300(x42161),f323(f323(f110(f867(x42161,a855)),x42162),x42163))))
% 179.72/179.57 [4309]E(f323(f243(x43091),f323(f323(f18(x43091,a855,a855),f323(f323(f8(a855,f867(a855,a855),x43091),a321),f323(f323(f7(x43091,f867(x43091,a855),a855),f325(x43091)),x43092))),f323(f323(f8(a855,a855,x43091),a318),f323(f323(f7(x43091,f867(x43091,a855),a855),f325(x43091)),x43093)))),f323(f323(f22(f867(x43091,a855)),x43092),x43093))
% 179.72/179.57 [4332]E(f323(f35(a860),f323(f243(a860),f323(f323(f18(a860,a855,a855),f323(f323(f8(a855,f867(a855,a855),a860),a321),f323(f323(f7(a860,a860,a855),f238(a860)),f323(f189(f861(x43321)),x43322)))),f323(f323(f8(x43321,a855,a860),x43323),f323(f158(x43321),x43322))))),f323(f189(f861(x43321)),f323(f129(x43321,x43323),x43322)))
% 179.72/179.57 [4334]E(f323(f189(f861(x43341)),f170(x43341,x43342,x43343)),f323(f35(a860),f323(f243(a860),f323(f323(f18(a860,a855,a855),f323(f323(f8(a855,f867(a855,a855),a860),a321),f323(f323(f7(a860,a860,a855),f238(a860)),f323(f189(f861(x43341)),x43342)))),f323(f323(f7(a860,f867(a860,a855),a855),f325(a860)),x43343)))))
% 179.72/179.57 [4431]E(f323(f323(f101(f867(f866(f861(x44311),f861(x44311)),a855)),f323(f302(f866(f866(x44311,f861(x44311)),f866(x44311,f861(x44311))),f866(f861(x44311),f861(x44311)),f263(f866(x44311,f861(x44311)),f861(x44311),f866(x44311,f861(x44311)),f861(x44311),f323(f262(x44311,f861(x44311),f861(x44311)),f144(x44311)),f323(f262(x44311,f861(x44311),f861(x44311)),f144(x44311)))),f315(x44311,f861(x44311),x44312,f323(f136(x44311,x44312),x44313)))),f323(f243(f866(f861(x44311),f861(x44311))),f323(f262(f861(x44311),f861(x44311),a855),f323(f323(f7(f861(x44311),f867(f861(x44311),a855),f867(f861(x44311),a855)),f323(f323(f8(f867(a855,a855),f867(f867(f861(x44311),a855),f867(f861(x44311),a855)),f861(x44311)),f8(a855,a855,f861(x44311))),f323(f323(f8(a855,f867(a855,a855),f861(x44311)),a321),f323(f323(f7(f861(x44311),a860,a855),f323(f323(f8(a860,f867(a860,a855),f861(x44311)),a320),f189(f861(x44311)))),f323(a112,x44313))))),f323(f323(f7(f861(x44311),a860,a855),f323(f323(f8(a860,f867(a860,a855),f861(x44311)),a320),f189(f861(x44311)))),f323(a112,x44313)))))),f323(f136(x44311,x44312),f323(a112,x44313)))
% 179.72/179.57 [3912]E(f42(a860,f323(a112,f323(f323(f78(a860),f323(f323(f79(a860),x39121),x39122)),x39123)),x39122),f42(a860,f323(a112,x39123),x39122))
% 179.72/179.57 [4173]E(f323(f243(x41731),f323(f323(f18(x41731,a855,a855),f323(f323(f8(a855,f867(a855,a855),x41731),a321),x41732)),x41733)),f323(f323(f101(f867(x41731,a855)),f323(f243(x41731),x41732)),f323(f243(x41731),x41733)))
% 179.72/179.57 [4174]E(f323(f243(x41741),f323(f323(f18(x41741,a855,a855),f323(f323(f8(a855,f867(a855,a855),x41741),a322),x41742)),x41743)),f323(f323(f110(f867(x41741,a855)),f323(f243(x41741),x41742)),f323(f243(x41741),x41743)))
% 179.72/179.57 [4176]E(f323(f323(f121(x41761),f323(f323(f131(x41761),f42(a860,x41762,f323(f189(f861(x41761)),x41763))),x41763)),f323(f323(f169(x41761),f42(a860,x41762,f323(f189(f861(x41761)),x41763))),x41763)),f323(f323(f323(f183(f861(x41761),f861(x41761)),x41762),f161(x41761)),x41763))
% 179.72/179.57 [4181]E(f323(f243(x41811),f323(f323(f18(x41811,a855,a855),f323(f323(f8(a855,f867(a855,a855),x41811),a326),x41812)),x41813)),f323(f323(f110(f867(x41811,a855)),f323(f77(f867(x41811,a855)),f323(f243(x41811),x41812))),f323(f243(x41811),x41813)))
% 179.72/179.57 [4198]E(f323(f323(f78(a860),f323(f189(f861(x41981)),f323(f129(x41981,x41982),x41983))),f323(f189(f861(x41981)),f323(f129(x41981,f323(f323(f8(a855,a855,x41981),a318),x41982)),x41983))),f323(f189(f861(x41981)),x41983))
% 179.72/179.57 [4223]P101(f323(f323(f237(f867(x42231,a855)),f323(f323(f110(f867(x42231,a855)),f38(f867(x42231,a855),x42232)),f38(f867(x42231,a855),x42233))),f38(f867(x42231,a855),f323(f323(f101(f867(f867(x42231,a855),a855)),x42232),x42233))))
% 179.72/179.57 [4237]E(f323(f166(x42371),f323(f129(x42371,f323(f323(f8(a855,a855,x42371),a318),f323(f323(f7(x42371,x42371,a855),a320),x42372))),x42373)),f323(f323(f22(f867(x42371,a855)),f323(f166(x42371),x42373)),f323(f323(f301(x42371),x42372),f188(f867(x42371,a855)))))
% 179.72/179.57 [4246]P101(f323(f323(f237(f867(f866(x42461,x42461),a855)),f323(f323(f110(f867(f866(x42461,x42461),a855)),f299(x42461,x42462)),f299(x42461,x42463))),f299(x42461,f323(f323(f110(f867(f866(x42461,x42461),a855)),x42462),x42463))))
% 179.72/179.57 [4271]E(f323(f323(f79(a860),f323(a112,f323(a112,f2(a860)))),f323(f323(f6(a860,a860),f323(f323(f8(a860,a860,a860),f323(f78(a860),x42711)),f323(f323(f7(a860,a860,a860),f79(a860)),x42712))),f323(f244(a860),x42713))),f323(f323(f79(a860),x42713),f323(f323(f78(a860),x42711),f323(f323(f78(a860),x42711),f323(f323(f79(a860),f323(f323(f22(a860),x42713),f76(a860))),x42712)))))
% 179.72/179.57 [4281]E(f323(f243(x42811),f323(f323(f18(x42811,a855,a855),f323(f323(f8(a855,f867(a855,a855),x42811),a321),f323(f323(f7(x42811,f867(x42811,a855),a855),f325(x42811)),f323(f166(x42811),x42812)))),x42813)),f323(f166(x42811),f323(f129(x42811,x42813),x42812)))
% 179.72/179.57 [4430]E(f323(f243(x44301),f323(f323(f8(f867(a860,a855),a855,x44301),f85(a860)),f323(f323(f7(x44301,f867(a860,a855),f867(a860,a855)),f323(f323(f8(f867(a860,f867(a855,a855)),f867(f867(a860,a855),f867(a860,a855)),x44301),f18(a860,a855,a855)),f323(f323(f8(f867(a860,a855),f867(a860,f867(a855,a855)),x44301),f323(f8(a855,f867(a855,a855),a860),a321)),f323(f323(f7(x44301,f867(a860,x44301),f867(a860,a855)),f323(f323(f8(f867(x44301,a855),f867(f867(a860,x44301),f867(a860,a855)),x44301),f8(x44301,a855,a860)),a320)),f323(f158(x44301),x44302))))),f323(f323(f18(a860,a855,a855),f323(f323(f8(a855,f867(a855,a855),a860),a321),f323(f323(f7(a860,a860,a855),f238(a860)),f323(f189(f861(x44301)),x44302)))),f323(f323(f7(a860,f867(a860,a855),a855),f325(a860)),x44303))))),f323(f166(x44301),f170(x44301,x44302,x44303)))
% 179.72/179.57 [4321]E(f323(f243(x43211),f323(f323(f18(x43211,a855,a855),f323(f323(f8(a855,f867(a855,a855),x43211),a326),f323(f323(f8(a855,a855,x43211),a318),f323(f323(f7(x43211,x43211,a855),a320),x43212)))),x43213)),f323(f323(f301(x43211),x43212),f323(f243(x43211),x43213)))
% 179.72/179.57 [4354]E(f323(f323(f147(f866(x43541,a860),x43541),f257(x43541,a860)),f323(f129(f866(x43541,a860),f323(f323(f7(f866(x43541,a860),f867(a860,a855),a855),f323(f323(f8(a860,f867(f867(a860,a855),a855),f866(x43541,a860)),f325(a860)),f261(x43541,a860))),x43542)),f323(f323(f175(x43541,a860),x43543),f132(a860,f323(f293(a860,f2(a860)),f323(f189(f861(x43541)),x43543)))))),f170(x43541,x43543,x43542))
% 179.72/179.57 [4384]E(f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(f323(f6(a860,a1),f323(f323(f8(a1,a1,a860),f323(f78(a1),x43841)),f323(f323(f7(a860,a1,a1),f323(f323(f8(a1,f867(a1,a1),a860),f79(a1)),f100(a1))),x43842))),f323(f244(a860),x43843))),f323(f323(f79(a1),f323(f100(a1),x43843)),f323(f323(f78(a1),x43841),f323(f323(f78(a1),x43841),f323(f323(f79(a1),f323(f100(a1),f323(f323(f22(a860),x43843),f76(a860)))),x43842)))))
% 179.72/179.57 [4424]E(f323(f243(f866(x44241,x44242)),f323(f262(x44241,x44242,a855),f323(f323(f7(x44241,f867(f866(x44242,x44241),a855),f867(x44242,a855)),f323(f323(f8(f867(x44242,f867(f867(f866(x44242,x44241),a855),a855)),f867(f867(f866(x44242,x44241),a855),f867(x44242,a855)),x44241),f7(x44242,f867(f866(x44242,x44241),a855),a855)),f323(f323(f8(f867(x44242,f866(x44242,x44241)),f867(x44242,f867(f867(f866(x44242,x44241),a855),a855)),x44241),f323(f8(f866(x44242,x44241),f867(f867(f866(x44242,x44241),a855),a855),x44242),f325(f866(x44242,x44241)))),f323(f7(x44242,x44241,f866(x44242,x44241)),f258(x44242,x44241))))),x44243))),f323(f278(x44242,x44241),x44243))
% 179.72/179.57 [4454]E(f323(f243(f861(x44541)),f323(f323(f8(f867(x44541,a855),a855,f861(x44541)),f85(x44541)),f323(f323(f8(f867(x44541,f867(f861(x44541),a855)),f867(x44541,a855),f861(x44541)),f323(f8(f867(f861(x44541),a855),a855,x44541),f85(f861(x44541)))),f323(f323(f7(f861(x44541),f867(x44541,f867(f861(x44541),a855)),f867(x44541,f867(f861(x44541),a855))),f323(f323(f8(f867(x44541,f867(f867(f861(x44541),a855),f867(f861(x44541),a855))),f867(f867(x44541,f867(f861(x44541),a855)),f867(x44541,f867(f861(x44541),a855))),f861(x44541)),f18(x44541,f867(f861(x44541),a855),f867(f861(x44541),a855))),f323(f323(f8(f867(x44541,f867(f861(x44541),f867(a855,a855))),f867(x44541,f867(f867(f861(x44541),a855),f867(f861(x44541),a855))),f861(x44541)),f323(f8(f867(f861(x44541),f867(a855,a855)),f867(f867(f861(x44541),a855),f867(f861(x44541),a855)),x44541),f18(f861(x44541),a855,a855))),f323(f323(f8(f867(x44541,f867(f861(x44541),a855)),f867(x44541,f867(f861(x44541),f867(a855,a855))),f861(x44541)),f323(f8(f867(f861(x44541),a855),f867(f861(x44541),f867(a855,a855)),x44541),f323(f8(a855,f867(a855,a855),f861(x44541)),a321))),f323(f323(f7(f861(x44541),f867(x44541,f867(f861(x44541),f861(x44541))),f867(x44541,f867(f861(x44541),a855))),f323(f323(f8(f867(f867(f861(x44541),f861(x44541)),f867(f861(x44541),a855)),f867(f867(x44541,f867(f861(x44541),f861(x44541))),f867(x44541,f867(f861(x44541),a855))),f861(x44541)),f8(f867(f861(x44541),f861(x44541)),f867(f861(x44541),a855),x44541)),f323(f323(f8(f867(f861(x44541),a855),f867(f867(f861(x44541),f861(x44541)),f867(f861(x44541),a855)),f861(x44541)),f8(f861(x44541),a855,f861(x44541))),a320))),f144(x44541)))))),f323(f323(f7(x44541,f867(f861(x44541),a855),f867(f861(x44541),a855)),f323(f323(f8(f867(a855,a855),f867(f867(f861(x44541),a855),f867(f861(x44541),a855)),x44541),f8(a855,a855,f861(x44541))),f323(f323(f8(a855,f867(a855,a855),x44541),a321),f323(f323(f7(x44541,f867(x44541,a855),a855),f325(x44541)),x44542)))),f323(f323(f7(f861(x44541),f867(f861(x44541),a855),a855),f325(f861(x44541))),x44543)))))),f168(x44541,x44542,x44543))
% 179.72/179.57 [4445]E(f323(f323(f84(a1,f866(a1,a1)),f323(f323(f22(a1),x44451),x44452)),f323(f323(f7(a1,f866(a1,a1),f866(a1,a1)),f323(f323(f18(a1,f866(a1,a1),f867(f866(a1,a1),f866(a1,a1))),f323(f323(f8(a855,f867(f866(a1,a1),f867(f866(a1,a1),f866(a1,a1))),a1),f96(f866(a1,a1))),f323(f237(a1),f2(a1)))),f323(f258(a1,a1),f323(f323(f78(a1),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x44453)),f76(a1))))),f323(f323(f258(a1,a1),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x44453)),x44451))),f323(f41(x44452),f323(f323(f258(a1,a1),x44453),x44451)))
% 179.72/179.57 [4478]~E(f29(x44781,x44782),f30(x44783,x44784))
% 179.72/179.57 [4481]~E(f25(x44811,x44812),f30(x44813,x44814))
% 179.72/179.57 [4482]~E(f25(x44821,x44822),f29(x44823,x44824))
% 179.72/179.57 [3458]E(f323(f323(f323(f70(x34581,x34582),x34583),x34584),f323(x34583,x34584)),x34583)
% 179.72/179.57 [3517]E(f323(f323(f249(x35171,x35172,x35173),x35174),f2(a860)),x35172)
% 179.72/179.57 [3557]E(f185(x35571,x35572,x35573,f323(a112,x35574)),f323(x35573,x35574))
% 179.72/179.57 [3599]E(f164(x35991,x35992,f164(x35991,x35993,x35994)),f164(x35991,x35993,f164(x35991,x35992,x35994)))
% 179.72/179.57 [3733]E(f323(f232(x37331,x37332,x37333,x37334),f200(x37332)),x37333)
% 179.72/179.57 [3734]E(f323(f149(x37341,x37342,x37343,x37344),f113(x37342)),x37343)
% 179.72/179.57 [3735]E(f323(f135(x37351,x37352,x37353,x37354),f113(x37352)),x37354)
% 179.72/179.57 [3842]E(f323(f323(f121(x38421),f163(x38421,x38422,x38423)),f163(x38421,x38424,x38423)),f323(f323(f121(x38421),f163(x38421,x38424,x38423)),f163(x38421,x38422,x38423)))
% 179.72/179.57 [3855]E(f323(f232(f864(x38551),x38552,f200(x38551),f323(f16(f864(x38551),x38552),f200(x38551))),f323(x38553,x38554)),f200(x38551))
% 179.72/179.57 [3900]E(f323(f323(f110(f867(x39001,a855)),f177(x39001,x39002,x39003)),f177(x39001,x39002,x39004)),f177(x39001,x39002,f180(x39001,x39002,x39004,x39003)))
% 179.72/179.57 [3932]E(f323(f323(f264(x39321,x39322,x39323,f866(x39322,x39323)),x39324),f258(x39322,x39323)),x39324)
% 179.72/179.57 [3942]E(f233(x39421,x39422,x39423,x39424,f200(x39422)),x39423)
% 179.72/179.57 [3943]E(f181(x39431,x39432,x39433,x39434,f113(x39432)),x39433)
% 179.72/179.57 [3944]E(f181(x39441,x39442,x39443,f113(x39441),x39444),x39443)
% 179.72/179.57 [4230]P43(x42301,x42302,x42303,x42304,f188(f867(x42301,a855)),x42304)
% 179.72/179.57 [3261]E(f323(f323(f16(x32611,x32612),x32613),x32614),x32613)
% 179.72/179.57 [3375]E(f323(f323(f201(x33751,x33752),x33753),f323(f230(x33751),x33754)),f323(f230(x33752),f323(x33753,x33754)))
% 179.72/179.57 [3547]E(f164(x35471,x35472,f323(f129(x35471,x35473),x35474)),f323(f129(x35471,x35473),f164(x35471,x35472,x35474)))
% 179.72/179.57 [3582]E(f323(f323(f62(x35821,x35822,x35823),x35824),f188(f867(x35821,a855))),x35824)
% 179.72/179.57 [3605]E(f323(f323(f158(x36051),f323(f323(f144(x36051),x36052),x36053)),f323(a112,x36054)),f323(f323(f158(x36051),x36053),x36054))
% 179.72/179.57 [3672]E(f323(f323(x36721,x36722),f323(f184(x36723,x36724,x36721),x36722)),f323(f184(x36723,x36724,x36721),f323(a112,x36722)))
% 179.72/179.57 [3771]E(f323(f323(f152(x37711,f323(f323(f144(x37711),x37712),x37713)),f2(a860)),x37714),f323(f323(f144(x37711),x37714),x37713))
% 179.72/179.57 [3782]E(f323(f323(f39(f867(x37821,a855),f867(x37822,a855)),x37823),f302(x37821,x37822,x37824)),f323(f302(x37821,x37822,x37824),f37(f867(x37821,a855),x37823)))
% 179.72/179.57 [3783]E(f323(f323(f39(f867(x37831,a855),f867(x37832,a855)),x37833),f303(x37832,x37831,x37834)),f323(f303(x37832,x37831,x37834),f37(f867(x37831,a855),x37833)))
% 179.72/179.57 [3882]E(f177(x38821,x38822,f182(x38821,x38822,x38823,x38824)),f323(f323(f101(f867(x38821,a855)),f177(x38821,x38822,x38823)),x38824))
% 179.72/179.57 [3886]E(f323(f125(x38861,x38862),f123(x38861,x38863,x38864)),f323(f323(f78(a860),f323(f323(f78(a860),f323(x38862,x38863)),f323(f125(x38861,x38862),x38864))),f323(a112,f2(a860))))
% 179.72/179.57 [3906]E(f323(f135(x39061,x39062,f323(f7(x39062,x39061,x39061),x39063),x39064),f323(f162(x39062),f113(x39062))),x39064)
% 179.72/179.57 [3955]E(f74(x39551,x39552,x39553,x39554,f188(f867(x39551,a855))),x39553)
% 179.72/179.57 [4002]E(f323(f323(f323(f323(f70(x40021,f864(x40022)),f323(f16(f864(x40022),x40021),f200(x40022))),x40023),f200(x40022)),x40024),f200(x40022))
% 179.72/179.57 [4156]E(f323(f262(x41561,x41562,x41563),f323(f323(f8(f867(x41562,f866(x41561,x41562)),f867(x41562,x41563),x41561),f323(f8(f866(x41561,x41562),x41563,x41562),x41564)),f258(x41561,x41562))),x41564)
% 179.72/179.57 [3456]E(f323(f261(x34561,x34562),f323(f323(f258(x34561,x34562),x34563),x34564)),x34564)
% 179.72/179.57 [3457]E(f323(f257(x34571,x34572),f323(f323(f258(x34571,x34572),x34573),x34574)),x34573)
% 179.72/179.57 [3490]E(f323(f189(f861(x34901)),f323(f323(f147(x34902,x34901),x34903),x34904)),f323(f189(f861(x34902)),x34904))
% 179.72/179.57 [3491]E(f323(f189(f861(x34911)),f323(f323(f152(x34911,x34912),x34913),x34914)),f323(f189(f861(x34911)),x34912))
% 179.72/179.57 [3511]E(f323(f323(f131(x35111),f323(a112,x35112)),f323(f323(f144(x35111),x35113),x35114)),f323(f323(f131(x35111),x35112),x35114))
% 179.72/179.57 [3577]E(f323(f323(f169(x35771),x35772),f163(x35771,x35773,x35774)),f163(x35771,f323(f323(f235(a860),x35772),x35773),x35774))
% 179.72/179.57 [3578]E(f323(f323(f131(x35781),x35782),f163(x35781,x35783,x35784)),f163(x35781,f323(f323(f22(a860),x35783),x35782),x35784))
% 179.72/179.57 [3584]E(f323(f323(f301(x35841),x35842),f323(f323(f301(x35841),x35843),x35844)),f323(f323(f301(x35841),x35843),f323(f323(f301(x35841),x35842),x35844)))
% 179.72/179.57 [3588]E(f323(f323(f147(x35881,x35882),x35883),f114(x35881,x35884)),f114(x35882,f323(f323(f147(x35881,x35882),x35883),x35884)))
% 179.72/179.57 [3603]E(f323(f162(x36031),f323(f323(f147(x36032,x36031),x36033),x36034)),f323(f323(f147(x36032,x36031),x36033),f323(f162(x36032),x36034)))
% 179.72/179.57 [3604]E(f323(f323(f147(x36041,x36042),x36043),f323(f165(x36041),x36044)),f323(f165(x36042),f323(f323(f147(x36041,x36042),x36043),x36044)))
% 179.72/179.57 [3615]E(f323(f323(f169(x36151),f323(a112,x36152)),f323(f323(f144(x36151),x36153),x36154)),f323(f323(f144(x36151),x36153),f323(f323(f169(x36151),x36152),x36154)))
% 179.72/179.57 [3619]E(f323(f166(x36191),f323(f323(f147(x36192,x36191),x36193),x36194)),f323(f302(x36192,x36191,x36193),f323(f166(x36192),x36194)))
% 179.72/179.57 [3634]E(f323(f323(f147(x36341,x36342),f323(f16(x36342,x36341),x36343)),x36344),f163(x36342,f323(f189(f861(x36341)),x36344),x36343))
% 179.72/179.57 [3671]E(f17(x36711,x36712,x36713,f323(a3,f323(a112,f323(a19,x36714)))),f323(x36713,x36714))
% 179.72/179.57 [3674]E(f323(f323(f121(x36741),f323(f129(x36741,x36742),x36743)),f323(f129(x36741,x36742),x36744)),f323(f129(x36741,x36742),f323(f323(f121(x36741),x36743),x36744)))
% 179.72/179.57 [3687]E(f145(x36871,f323(f323(f147(x36872,x36871),x36873),f145(x36872,x36874))),f145(x36871,f323(f323(f147(x36872,x36871),x36873),x36874)))
% 179.72/179.57 [3703]E(f323(f278(x37031,x37031),f323(f323(f279(x37032,x37031),x37033),x37034)),f323(f323(f279(x37032,x37031),f323(f278(x37032,x37032),x37033)),x37034))
% 179.72/179.57 [3714]E(f323(f323(f280(x37141,x37142,x37143),x37144),f188(f867(f866(x37142,x37143),a855))),f188(f867(f866(x37141,x37143),a855)))
% 179.72/179.57 [3715]E(f323(f323(f169(x37151),f323(f323(f22(a860),x37152),x37153)),f323(f323(f131(x37151),x37153),x37154)),f323(f323(f131(x37151),x37153),f323(f323(f169(x37151),x37152),x37154)))
% 179.72/179.57 [3736]E(f323(f323(f121(x37361),f163(x37361,x37362,x37363)),f163(x37361,x37364,x37363)),f163(x37361,f323(f323(f78(a860),x37362),x37364),x37363))
% 179.72/179.57 [3763]E(f37(f867(x37631,a855),f323(f302(x37632,f867(x37631,a855),x37633),x37634)),f323(f323(f39(x37632,f867(x37631,a855)),x37634),x37633))
% 179.72/179.57 [3764]E(f38(f867(x37641,a855),f323(f302(x37642,f867(x37641,a855),x37643),x37644)),f323(f323(f40(x37642,f867(x37641,a855)),x37644),x37643))
% 179.72/179.57 [3765]E(f323(f189(f861(f866(x37651,x37652))),f323(f323(f175(x37651,x37652),x37653),x37654)),f323(f323(f235(a860),f323(f189(f861(x37651)),x37653)),f323(f189(f861(x37652)),x37654)))
% 179.72/179.57 [3767]E(f323(f303(x37671,x37672,x37673),f323(f77(f867(x37672,a855)),x37674)),f323(f77(f867(x37671,a855)),f323(f303(x37671,x37672,x37673),x37674)))
% 179.72/179.57 [3797]E(f323(f182(x37971,x37972,x37973,f188(f867(x37971,a855))),x37974),f200(x37972))
% 179.72/179.57 [3818]E(f323(f303(x38181,x38182,x38183),f323(f243(x38182),x38184)),f323(f243(x38181),f323(f323(f8(x38182,a855,x38181),x38184),x38183)))
% 179.72/179.57 [3836]E(f323(f323(f158(x38361),f323(f323(f121(x38361),x38362),f323(f323(f144(x38361),x38363),x38364))),f323(f189(f861(x38361)),x38362)),x38363)
% 179.72/179.57 [3841]E(f323(f182(x38411,x38412,f323(f16(f864(x38412),x38411),f200(x38412)),x38413),x38414),f200(x38412))
% 179.72/179.57 [3863]E(f323(f302(x38631,x38632,x38633),f323(f303(x38631,x38632,x38633),x38634)),f323(f323(f101(f867(x38632,a855)),x38634),f323(f302(x38631,x38632,x38633),f246(f867(x38631,a855)))))
% 179.72/179.57 [3881]P101(f323(f323(f325(x38811),f323(x38812,x38813)),f323(f302(x38814,x38811,x38812),f246(f867(x38814,a855)))))
% 179.72/179.57 [3893]E(f323(f323(f121(x38931),f163(x38931,x38932,x38933)),f323(f323(f144(x38931),x38933),x38934)),f323(f323(f144(x38931),x38933),f323(f323(f121(x38931),f163(x38931,x38932,x38933)),x38934)))
% 179.72/179.57 [3895]E(f323(f323(f260(x38951,x38952),f323(f166(x38951),x38953)),f323(f16(f867(x38952,a855),x38951),f323(f166(x38952),x38954))),f323(f166(f866(x38951,x38952)),f57(x38951,x38952,x38953,x38954)))
% 179.72/179.57 [3909]E(f148(x39091,x39092,f323(f323(f144(x39091),x39093),x39094)),f323(f323(f78(a860),f323(f323(f78(a860),f323(x39092,x39093)),f148(x39091,x39092,x39094))),f323(a112,f2(a860))))
% 179.72/179.57 [3923]E(f185(f861(x39231),f323(f323(f144(x39231),x39232),x39233),f323(f323(f7(a860,f861(x39231),f861(x39231)),f131(x39231)),x39233),x39234),f323(f323(f131(x39231),x39234),f323(f323(f144(x39231),x39232),x39233)))
% 179.72/179.57 [3924]P27(x39241,f866(x39242,x39241),f327(x39243,x39244,x39242,x39241),f323(f323(f39(x39242,f867(x39241,a855)),x39244),x39243))
% 179.72/179.57 [3933]E(f323(f323(f22(f867(x39331,a855)),f323(f323(f22(f867(x39331,a855)),x39332),x39333)),f323(f323(f301(x39331),x39334),f188(f867(x39331,a855)))),f323(f323(f22(f867(x39331,a855)),x39332),f323(f323(f301(x39331),x39334),x39333)))
% 179.72/179.57 [3946]E(f323(f323(f183(f867(x39461,x39462),f867(x39461,x39462)),x39463),f71(x39462,x39462,x39461,x39464)),f71(x39462,x39462,x39461,f323(f323(f183(x39462,x39462),x39463),x39464)))
% 179.72/179.57 [4025]E(f323(f323(f323(f183(f861(x40251),f861(x40251)),x40252),f161(x40251)),f323(f323(f323(f183(f861(x40251),f861(x40251)),x40253),f161(x40251)),x40254)),f323(f323(f323(f183(f861(x40251),f861(x40251)),f323(f323(f78(a860),x40252),x40253)),f161(x40251)),x40254))
% 179.72/179.57 [4111]P101(f323(f323(f237(f867(x41111,a855)),f323(f166(x41111),f323(f323(f152(x41111,x41112),x41113),x41114))),f323(f323(f301(x41111),x41114),f323(f166(x41111),x41112))))
% 179.72/179.57 [4146]E(f323(f323(f39(f867(x41461,a855),f867(f866(x41461,x41462),a855)),x41463),f323(f323(f7(f867(x41461,a855),f867(x41461,f867(x41462,a855)),f867(f866(x41461,x41462),a855)),f260(x41461,x41462)),x41464)),f323(f323(f260(x41461,x41462),f37(f867(x41461,a855),x41463)),x41464))
% 179.72/179.57 [4184]E(f211(x41841,x41842,x41843,f323(f71(x41842,f867(a99,f867(a99,f867(f866(a99,a99),f867(a99,f862(x41842))))),x41841,f210(x41842)),x41844)),f212(x41841,x41842,x41844,x41843))
% 179.72/179.57 [4201]E(f207(x42011,x42012,x42013,f323(f71(x42012,f867(a99,f867(a99,f867(f866(a99,a99),f867(a99,f862(f864(x42012)))))),x42011,f206(x42012)),x42014)),f208(x42011,x42012,x42014,x42013))
% 179.72/179.57 [4206]P101(f323(f64(x42061,x42062,x42063,x42064,f188(f867(x42061,a855))),x42064))
% 179.72/179.57 [4248]E(f323(f323(f39(x42481,f867(x42482,a855)),x42483),f323(f323(f7(x42481,f867(x42482,a855),f867(x42482,a855)),f323(f323(f8(x42482,f867(f867(x42482,a855),f867(x42482,a855)),x42481),f301(x42482)),x42484)),f188(f867(x42482,a855)))),f323(f302(x42481,x42482,x42484),x42483))
% 179.72/179.57 [4255]P101(f323(f323(f237(f867(x42551,a855)),f323(f254(x42552,x42551),f323(f323(f101(f867(f866(x42552,x42551),a855)),x42553),x42554))),f323(f323(f101(f867(x42551,a855)),f323(f254(x42552,x42551),x42553)),f323(f254(x42552,x42551),x42554))))
% 179.72/179.57 [4256]P101(f323(f323(f237(f867(x42561,a855)),f323(f256(x42561,x42562),f323(f323(f101(f867(f866(x42561,x42562),a855)),x42563),x42564))),f323(f323(f101(f867(x42561,a855)),f323(f256(x42561,x42562),x42563)),f323(f256(x42561,x42562),x42564))))
% 179.72/179.57 [4318]P101(f323(f323(f237(f867(f866(x43181,x43182),a855)),f323(f302(x43182,f866(x43181,x43182),f327(x43183,x43184,x43181,x43182)),f323(f323(f39(x43181,f867(x43182,a855)),x43184),x43183))),f323(f323(f260(x43181,x43182),x43184),x43183)))
% 179.72/179.57 [4319]E(f323(f116(x43191,f866(x43191,x43192),x43193),f323(f323(f8(f867(x43192,f862(f866(x43191,x43192))),f862(f866(x43191,x43192)),x43191),f116(x43192,f866(x43191,x43192),x43194)),f323(f323(f8(f867(x43192,f866(x43191,x43192)),f867(x43192,f862(f866(x43191,x43192))),x43191),f323(f8(f866(x43191,x43192),f862(f866(x43191,x43192)),x43192),f122(f866(x43191,x43192)))),f258(x43191,x43192)))),f127(x43191,x43192,x43193,x43194))
% 179.72/179.57 [4360]E(f83(f866(x43601,x43602),f323(f262(x43601,x43602,a855),f323(f323(f7(x43601,f867(x43602,a855),f867(x43602,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x43602,a855),f867(x43602,a855)),x43601),f8(a855,a855,x43602)),f323(f323(f8(a855,f867(a855,a855),x43601),a321),f323(a320,x43603)))),f323(a320,x43604)))),f323(f323(f258(x43601,x43602),x43603),x43604))
% 179.72/179.57 [4361]E(f88(f866(x43611,x43612),f323(f262(x43611,x43612,a855),f323(f323(f7(x43611,f867(x43612,a855),f867(x43612,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x43612,a855),f867(x43612,a855)),x43611),f8(a855,a855,x43612)),f323(f323(f8(a855,f867(a855,a855),x43611),a321),f323(a320,x43613)))),f323(a320,x43614)))),f323(f323(f258(x43611,x43612),x43613),x43614))
% 179.72/179.57 [4434]E(f323(f323(f262(f861(x44341),f861(x44341),f866(f861(x44341),f861(x44341))),f323(f323(f18(f861(x44341),f867(f861(x44341),f866(f861(x44341),f861(x44341))),f867(f861(x44341),f866(f861(x44341),f861(x44341)))),f323(f323(f8(f867(f861(x44341),f867(f866(f861(x44341),f861(x44341)),f866(f861(x44341),f861(x44341)))),f867(f867(f861(x44341),f866(f861(x44341),f861(x44341))),f867(f861(x44341),f866(f861(x44341),f861(x44341)))),f861(x44341)),f18(f861(x44341),f866(f861(x44341),f861(x44341)),f866(f861(x44341),f861(x44341)))),f323(f323(f8(f867(f861(x44341),f866(f861(x44341),f861(x44341))),f867(f861(x44341),f867(f866(f861(x44341),f861(x44341)),f866(f861(x44341),f861(x44341)))),f861(x44341)),f323(f8(f866(f861(x44341),f861(x44341)),f867(f866(f861(x44341),f861(x44341)),f866(f861(x44341),f861(x44341))),f861(x44341)),f323(f96(f866(f861(x44341),f861(x44341))),f323(x44342,x44343)))),f323(f323(f8(f861(x44341),f867(f861(x44341),f866(f861(x44341),f861(x44341))),f861(x44341)),f258(f861(x44341),f861(x44341))),f323(f144(x44341),x44343))))),f323(f323(f7(f861(x44341),f867(f861(x44341),f861(x44341)),f867(f861(x44341),f866(f861(x44341),f861(x44341)))),f323(f323(f8(f867(f861(x44341),f866(f861(x44341),f861(x44341))),f867(f867(f861(x44341),f861(x44341)),f867(f861(x44341),f866(f861(x44341),f861(x44341)))),f861(x44341)),f8(f861(x44341),f866(f861(x44341),f861(x44341)),f861(x44341))),f258(f861(x44341),f861(x44341)))),f323(f144(x44341),x44343)))),f160(x44341,x44342,x44344)),f160(x44341,x44342,f323(f323(f144(x44341),x44343),x44344)))
% 179.72/179.57 [4440]E(f323(f135(f867(x44401,f864(x44402)),f866(x44401,x44402),f323(f7(f866(x44401,x44402),f867(x44401,f864(x44402)),f867(x44401,f864(x44402))),f323(f262(x44401,x44402,f867(f867(x44401,f864(x44402)),f867(x44401,f864(x44402)))),f323(f323(f7(x44401,f867(x44402,f864(x44402)),f867(x44402,f867(f867(x44401,f864(x44402)),f867(x44401,f864(x44402))))),f323(f323(f8(f867(f864(x44402),f867(f867(x44401,f864(x44402)),f867(x44401,f864(x44402)))),f867(f867(x44402,f864(x44402)),f867(x44402,f867(f867(x44401,f864(x44402)),f867(x44401,f864(x44402))))),x44401),f8(f864(x44402),f867(f867(x44401,f864(x44402)),f867(x44401,f864(x44402))),x44402)),f323(f323(f8(f867(f867(x44401,f864(x44402)),f867(f864(x44402),f867(x44401,f864(x44402)))),f867(f864(x44402),f867(f867(x44401,f864(x44402)),f867(x44401,f864(x44402)))),x44401),f7(f867(x44401,f864(x44402)),f864(x44402),f867(x44401,f864(x44402)))),f323(f7(f867(x44401,f864(x44402)),x44401,f867(f864(x44402),f867(x44401,f864(x44402)))),f70(x44401,f864(x44402)))))),f230(x44402)))),x44403),f323(f162(f866(x44401,x44402)),x44404)),f180(x44401,x44402,x44403,f323(f179(x44401,x44402),x44404)))
% 179.72/179.57 [3530]E(f323(f189(f859(x35301)),f323(f323(f323(f90(x35301),x35302),x35303),x35304)),f2(a860))
% 179.72/179.57 [3650]E(f323(f323(f169(x36501),x36502),f323(f323(f169(x36501),x36503),x36504)),f323(f323(f169(x36501),f323(f323(f235(a860),x36502),x36503)),x36504))
% 179.72/179.57 [3651]E(f323(f323(f131(x36511),x36512),f323(f323(f131(x36511),x36513),x36514)),f323(f323(f131(x36511),f323(f323(f78(a860),x36512),x36513)),x36514))
% 179.72/179.57 [3663]E(f323(f323(f121(x36631),f323(f323(f144(x36631),x36632),x36633)),x36634),f323(f323(f144(x36631),x36632),f323(f323(f121(x36631),x36633),x36634)))
% 179.72/179.57 [3664]E(f323(f323(f121(x36641),f323(f323(f121(x36641),x36642),x36643)),x36644),f323(f323(f121(x36641),x36642),f323(f323(f121(x36641),x36643),x36644)))
% 179.72/179.57 [3747]E(f323(f323(f158(x37471),f323(f323(f144(x37471),x37472),x37473)),x37474),f185(x37471,x37472,f323(f158(x37471),x37473),x37474))
% 179.72/179.57 [3756]E(f323(f323(f183(x37561,x37561),x37562),f323(f323(f183(x37561,x37561),x37563),x37564)),f323(f323(f183(x37561,x37561),f323(f323(f79(a860),x37563),x37562)),x37564))
% 179.72/179.57 [3785]E(f323(f323(f110(f867(x37851,a855)),x37852),f323(f323(f301(x37851),x37853),x37854)),f323(f323(f301(x37851),x37853),f323(f323(f110(f867(x37851,a855)),x37852),x37854)))
% 179.72/179.57 [3800]E(f323(f323(f323(f183(x38001,x38001),x38002),x38003),f323(x38003,x38004)),f323(x38003,f323(f323(f323(f183(x38001,x38001),x38002),x38003),x38004)))
% 179.72/179.57 [3808]E(f323(f323(f280(x38081,x38082,x38083),f188(f867(f866(x38081,x38082),a855))),x38084),f188(f867(f866(x38081,x38083),a855)))
% 179.72/179.57 [3824]E(f323(f323(f110(f867(x38241,a855)),f323(f323(f301(x38241),x38242),x38243)),x38244),f323(f323(f301(x38241),x38242),f323(f323(f110(f867(x38241,a855)),x38243),x38244)))
% 179.72/179.57 [3844]E(f180(x38441,x38442,f323(f179(x38441,x38442),x38443),f323(f179(x38441,x38442),x38444)),f323(f179(x38441,x38442),f323(f323(f121(f866(x38441,x38442)),x38444),x38443)))
% 179.72/179.57 [3845]E(f323(f35(f866(x38451,x38452)),f323(f323(f260(x38451,x38452),x38453),f323(f16(f867(x38452,a855),x38451),x38454))),f323(f323(f79(a860),f323(f35(x38451),x38453)),f323(f35(x38452),x38454)))
% 179.72/179.57 [3852]E(f323(f323(f101(f867(x38521,a855)),f323(f323(f301(x38521),x38522),x38523)),f323(f323(f301(x38521),x38522),x38524)),f323(f323(f301(x38521),x38522),f323(f323(f101(f867(x38521,a855)),x38523),x38524)))
% 179.72/179.57 [3867]E(f323(f323(f110(f867(x38671,a855)),x38672),f323(f323(f110(f867(x38671,a855)),x38673),x38674)),f323(f323(f110(f867(x38671,a855)),x38673),f323(f323(f110(f867(x38671,a855)),x38672),x38674)))
% 179.72/179.57 [3868]E(f323(f323(f101(f867(x38681,a855)),x38682),f323(f323(f101(f867(x38681,a855)),x38683),x38684)),f323(f323(f101(f867(x38681,a855)),x38683),f323(f323(f101(f867(x38681,a855)),x38682),x38684)))
% 179.72/179.57 [3877]E(f62(x38771,x38772,f323(f323(f8(x38772,f867(x38772,x38772),x38771),x38773),x38774)),f323(f63(x38772,x38771,x38773),x38774))
% 179.72/179.57 [3887]E(f173(x38871,f323(f323(f147(f861(x38872),f861(x38871)),f323(f147(x38872,x38871),x38873)),x38874)),f323(f323(f147(f861(x38872),f861(x38871)),f323(f147(x38872,x38871),x38873)),f173(x38872,x38874)))
% 179.72/179.57 [3905]E(f323(f135(f861(x39051),f861(x39051),f121(x39051),f113(x39051)),f323(f323(f147(x39052,f861(x39051)),x39053),x39054)),f157(x39052,x39051,x39053,x39054))
% 179.72/179.57 [3908]E(f182(x39081,x39082,x39083,f323(f77(f867(x39081,a855)),f323(f323(f301(x39081),x39084),f188(f867(x39081,a855))))),f323(f323(f323(f70(x39081,f864(x39082)),x39083),x39084),f200(x39082)))
% 179.72/179.57 [3951]E(f323(f323(f323(f70(x39511,f864(x39512)),f323(f179(x39511,x39512),x39513)),f323(f257(x39511,x39512),x39514)),f323(f230(x39512),f323(f261(x39511,x39512),x39514))),f323(f179(x39511,x39512),f323(f323(f144(f866(x39511,x39512)),x39514),x39513)))
% 179.72/179.57 [3969]E(f323(f71(x39691,x39691,x39691,f323(f323(f183(x39691,x39691),x39692),x39693)),f323(f323(f183(x39691,x39691),x39694),x39693)),f323(f323(f183(x39691,x39691),f323(f323(f78(a860),x39692),x39694)),x39693))
% 179.72/179.57 [3994]E(f323(f323(f101(f867(x39941,a855)),f323(f323(f110(f867(x39941,a855)),x39942),x39943)),f323(f323(f110(f867(x39941,a855)),x39942),x39944)),f323(f323(f110(f867(x39941,a855)),x39942),f323(f323(f101(f867(x39941,a855)),x39943),x39944)))
% 179.72/179.57 [3995]E(f323(f323(f101(f867(x39951,a855)),f323(f323(f22(f867(x39951,a855)),x39952),x39953)),f323(f323(f22(f867(x39951,a855)),x39952),x39954)),f323(f323(f22(f867(x39951,a855)),x39952),f323(f323(f110(f867(x39951,a855)),x39953),x39954)))
% 179.72/179.57 [3996]E(f323(f323(f110(f867(x39961,a855)),f323(f323(f22(f867(x39961,a855)),x39962),x39963)),f323(f323(f22(f867(x39961,a855)),x39962),x39964)),f323(f323(f22(f867(x39961,a855)),x39962),f323(f323(f101(f867(x39961,a855)),x39963),x39964)))
% 179.72/179.57 [3997]E(f323(f323(f110(f867(x39971,a855)),f323(f323(f101(f867(x39971,a855)),x39972),x39973)),f323(f323(f101(f867(x39971,a855)),x39972),x39974)),f323(f323(f101(f867(x39971,a855)),x39972),f323(f323(f110(f867(x39971,a855)),x39973),x39974)))
% 179.72/179.57 [3998]E(f323(f323(f22(f867(x39981,a855)),f323(f323(f101(f867(x39981,a855)),x39982),x39983)),f323(f323(f101(f867(x39981,a855)),x39982),x39984)),f323(f323(f101(f867(x39981,a855)),x39982),f323(f323(f22(f867(x39981,a855)),x39983),x39984)))
% 179.72/179.57 [4004]E(f323(f35(f866(x40041,x40042)),f323(f323(f260(x40041,x40042),f323(f323(f301(x40041),x40043),f188(f867(x40041,a855)))),f323(f16(f867(x40042,a855),x40041),x40044))),f323(f35(x40042),x40044))
% 179.72/179.57 [4040]E(f323(f323(f40(x40401,f867(x40402,a855)),x40403),f323(f323(f8(f867(x40402,a855),f867(x40402,a855),x40401),f77(f867(x40402,a855))),x40404)),f323(f77(f867(x40402,a855)),f323(f323(f39(x40401,f867(x40402,a855)),x40403),x40404)))
% 179.72/179.57 [4041]E(f323(f323(f39(x40411,f867(x40412,a855)),x40413),f323(f323(f8(f867(x40412,a855),f867(x40412,a855),x40411),f77(f867(x40412,a855))),x40414)),f323(f77(f867(x40412,a855)),f323(f323(f40(x40411,f867(x40412,a855)),x40413),x40414)))
% 179.72/179.57 [4055]E(f323(f323(f280(x40551,x40551,x40551),f323(f323(f183(f866(x40551,x40551),a855),x40552),x40553)),f323(f323(f183(f866(x40551,x40551),a855),x40554),x40553)),f323(f323(f183(f866(x40551,x40551),a855),f323(f323(f78(a860),x40552),x40554)),x40553))
% 179.72/179.57 [4086]E(f323(f323(f40(x40861,f867(f867(x40862,a855),a855)),x40863),f323(f323(f8(f867(x40862,a855),f867(f867(x40862,a855),a855),x40861),f300(x40862)),x40864)),f323(f300(x40862),f323(f323(f40(x40861,f867(x40862,a855)),x40863),x40864)))
% 179.72/179.57 [4115]E(f323(f323(f39(f867(x41151,a855),f867(x41152,a855)),x41153),f323(f323(f7(f867(x41151,a855),f867(x41151,f867(x41152,a855)),f867(x41152,a855)),f39(x41151,f867(x41152,a855))),x41154)),f323(f323(f39(x41151,f867(x41152,a855)),f37(f867(x41151,a855),x41153)),x41154))
% 179.72/179.57 [4116]E(f323(f323(f40(f867(x41161,a855),f867(x41162,a855)),x41163),f323(f323(f7(f867(x41161,a855),f867(x41161,f867(x41162,a855)),f867(x41162,a855)),f40(x41161,f867(x41162,a855))),x41164)),f323(f323(f40(x41161,f867(x41162,a855)),f37(f867(x41161,a855),x41163)),x41164))
% 179.72/179.57 [4121]E(f323(f323(f147(x41211,x41212),x41213),f323(f135(f861(x41211),f861(x41211),f121(x41211),f113(x41211)),x41214)),f323(f135(f861(x41212),f861(x41212),f121(x41212),f113(x41212)),f323(f323(f147(f861(x41211),f861(x41212)),f323(f147(x41211,x41212),x41213)),x41214)))
% 179.72/179.57 [4124]E(f185(f861(x41241),f113(x41241),f323(f323(f8(f861(x41241),f861(x41241),a860),f323(f144(x41241),x41242)),f323(f323(f7(a860,f861(x41241),f861(x41241)),f169(x41241)),x41243)),x41244),f323(f323(f169(x41241),x41244),f323(f323(f144(x41241),x41242),x41243)))
% 179.72/179.57 [4166]P101(f323(f323(f237(f867(x41661,a855)),f323(f302(x41662,x41661,x41663),f323(f303(x41662,x41661,x41663),x41664))),x41664))
% 179.72/179.57 [4169]E(f323(f302(f866(x41691,x41692),f866(x41692,x41691),f323(f262(x41691,x41692,f866(x41692,x41691)),f323(f7(x41692,x41691,f866(x41692,x41691)),f258(x41692,x41691)))),f323(f323(f260(x41691,x41692),x41693),f323(f16(f867(x41692,a855),x41691),x41694))),f323(f323(f260(x41692,x41691),x41694),f323(f16(f867(x41691,a855),x41692),x41693)))
% 179.72/179.57 [4178]E(f323(f323(f39(x41781,f867(x41782,a855)),x41783),f323(f323(f8(f867(x41781,a855),f867(x41782,a855),x41781),f303(x41782,x41781,x41784)),f323(f323(f7(x41781,f867(x41781,a855),f867(x41781,a855)),f301(x41781)),f188(f867(x41781,a855))))),f323(f303(x41782,x41781,x41784),x41783))
% 179.72/179.57 [4179]E(f323(f323(f39(x41791,f867(x41792,a855)),x41793),f323(f323(f8(f867(x41791,a855),f867(x41792,a855),x41791),f277(x41791,x41792,x41794)),f323(f323(f7(x41791,f867(x41791,a855),f867(x41791,a855)),f301(x41791)),f188(f867(x41791,a855))))),f323(f277(x41791,x41792,x41794),x41793))
% 179.72/179.57 [4270]E(f323(f323(f110(f867(x42701,a855)),f323(f323(f110(f867(x42701,a855)),f323(f323(f101(f867(x42701,a855)),x42702),x42703)),f323(f323(f101(f867(x42701,a855)),x42703),x42704))),f323(f323(f101(f867(x42701,a855)),x42704),x42702)),f323(f323(f101(f867(x42701,a855)),f323(f323(f101(f867(x42701,a855)),f323(f323(f110(f867(x42701,a855)),x42702),x42703)),f323(f323(f110(f867(x42701,a855)),x42703),x42704))),f323(f323(f110(f867(x42701,a855)),x42704),x42702)))
% 179.72/179.57 [4333]E(f323(f135(f861(x43331),f861(x43331),f121(x43331),f113(x43331)),f323(f323(f147(x43332,f861(x43331)),f323(f323(f7(x43332,f861(x43331),f861(x43331)),f323(f323(f8(x43331,f867(f861(x43331),f861(x43331)),x43332),f144(x43331)),x43333)),f113(x43331))),x43334)),f323(f323(f147(x43332,x43331),x43333),x43334))
% 179.72/179.57 [4344]E(f323(f323(f84(a1,x43441),f323(f103(a1),f323(f323(f78(a1),x43442),a97))),f323(f323(f18(a1,x43441,x43441),f323(f323(f7(a1,x43441,f867(x43441,x43441)),f323(f323(f8(a855,f867(x43441,f867(x43441,x43441)),a1),f96(x43441)),a193)),x43443)),f323(f323(f8(a860,x43441,a1),x43444),a104))),f185(x43441,x43443,x43444,f323(f103(a860),x43442)))
% 179.72/179.57 [4554]~P101(f323(f323(f188(f867(x45541,f867(x45542,a855))),x45543),x45544))
% 179.72/179.57 [3811]E(f323(f323(f158(x38111),f323(f323(f121(x38111),x38112),x38113)),f323(f323(f78(a860),f323(f189(f861(x38111)),x38112)),x38114)),f323(f323(f158(x38111),x38113),x38114))
% 179.72/179.57 [3817]E(f323(f323(f131(x38171),x38172),f323(f323(f169(x38171),f323(f323(f78(a860),x38173),x38172)),x38174)),f323(f323(f169(x38171),x38173),f323(f323(f131(x38171),x38172),x38174)))
% 179.72/179.57 [3921]E(f323(f323(f110(f867(x39211,a855)),f323(f254(x39212,x39211),x39213)),f323(f254(x39212,x39211),x39214)),f323(f254(x39212,x39211),f323(f323(f110(f867(f866(x39212,x39211),a855)),x39213),x39214)))
% 179.72/179.57 [3922]E(f323(f323(f110(f867(x39221,a855)),f323(f256(x39221,x39222),x39223)),f323(f256(x39221,x39222),x39224)),f323(f256(x39221,x39222),f323(f323(f110(f867(f866(x39221,x39222),a855)),x39223),x39224)))
% 179.72/179.57 [3927]E(f323(f323(f110(f867(x39271,a855)),f323(f323(f110(f867(x39271,a855)),x39272),x39273)),x39274),f323(f323(f110(f867(x39271,a855)),x39272),f323(f323(f110(f867(x39271,a855)),x39273),x39274)))
% 179.72/179.57 [3928]E(f323(f323(f22(f867(x39281,a855)),f323(f323(f101(f867(x39281,a855)),x39282),x39283)),x39284),f323(f323(f101(f867(x39281,a855)),x39282),f323(f323(f22(f867(x39281,a855)),x39283),x39284)))
% 179.72/179.57 [3929]E(f323(f323(f101(f867(x39291,a855)),f323(f323(f101(f867(x39291,a855)),x39292),x39293)),x39294),f323(f323(f101(f867(x39291,a855)),x39292),f323(f323(f101(f867(x39291,a855)),x39293),x39294)))
% 179.72/179.57 [3971]E(f323(f323(f110(f867(f866(x39711,x39712),a855)),f323(f278(x39712,x39711),x39713)),f323(f278(x39712,x39711),x39714)),f323(f278(x39712,x39711),f323(f323(f110(f867(f866(x39712,x39711),a855)),x39713),x39714)))
% 179.72/179.57 [3972]E(f323(f323(f101(f867(f866(x39721,x39722),a855)),f323(f278(x39722,x39721),x39723)),f323(f278(x39722,x39721),x39724)),f323(f278(x39722,x39721),f323(f323(f101(f867(f866(x39722,x39721),a855)),x39723),x39724)))
% 179.72/179.57 [3986]E(f323(f323(f110(f867(x39861,f867(x39862,a855))),f247(x39862,x39861,x39863)),f247(x39862,x39861,x39864)),f247(x39862,x39861,f323(f323(f110(f867(x39862,f867(x39861,a855))),x39863),x39864)))
% 179.72/179.57 [3987]E(f323(f323(f101(f867(x39871,f867(x39872,a855))),f247(x39872,x39871,x39873)),f247(x39872,x39871,x39874)),f247(x39872,x39871,f323(f323(f101(f867(x39872,f867(x39871,a855))),x39873),x39874)))
% 179.72/179.57 [4044]E(f323(f323(f101(f867(x40441,a855)),f323(f323(f110(f867(x40441,a855)),x40442),x40443)),f323(f323(f110(f867(x40441,a855)),x40444),x40443)),f323(f323(f110(f867(x40441,a855)),f323(f323(f101(f867(x40441,a855)),x40442),x40444)),x40443))
% 179.72/179.57 [4045]E(f323(f323(f110(f867(x40451,a855)),f323(f323(f22(f867(x40451,a855)),x40452),x40453)),f323(f323(f22(f867(x40451,a855)),x40454),x40453)),f323(f323(f22(f867(x40451,a855)),f323(f323(f110(f867(x40451,a855)),x40452),x40454)),x40453))
% 179.72/179.57 [4046]E(f323(f323(f110(f867(x40461,a855)),f323(f323(f101(f867(x40461,a855)),x40462),x40463)),f323(f323(f101(f867(x40461,a855)),x40464),x40463)),f323(f323(f101(f867(x40461,a855)),f323(f323(f110(f867(x40461,a855)),x40462),x40464)),x40463))
% 179.72/179.57 [4047]E(f323(f323(f22(f867(x40471,a855)),f323(f323(f101(f867(x40471,a855)),x40472),x40473)),f323(f323(f101(f867(x40471,a855)),x40474),x40473)),f323(f323(f101(f867(x40471,a855)),f323(f323(f22(f867(x40471,a855)),x40472),x40474)),x40473))
% 179.72/179.57 [4048]E(f323(f323(f22(f867(x40481,a855)),f323(f323(f101(f867(x40481,a855)),x40482),x40483)),f323(f323(f101(f867(x40481,a855)),x40484),x40483)),f323(f323(f22(f867(x40481,a855)),f323(f323(f101(f867(x40481,a855)),x40482),x40483)),x40484))
% 179.72/179.57 [4058]E(f323(f323(f22(f867(x40581,a855)),f323(f323(f22(f867(x40581,a855)),x40582),f323(f323(f301(x40581),x40583),f188(f867(x40581,a855))))),x40584),f323(f323(f22(f867(x40581,a855)),x40582),f323(f323(f301(x40581),x40583),x40584)))
% 179.72/179.57 [4112]E(f323(f323(f110(f867(x41121,a855)),f323(f323(f301(x41121),x41122),f323(f323(f301(x41121),x41123),f188(f867(x41121,a855))))),f323(f276(x41121),x41124)),f323(f276(x41121),f323(f323(f301(f866(x41121,x41121)),f323(f323(f258(x41121,x41121),x41122),x41123)),x41124)))
% 179.72/179.57 [4141]E(f323(f323(f39(a860,f867(x41411,a855)),f323(f292(a860),x41412)),f323(f323(f8(a860,f867(x41411,a855),a860),x41413),f323(f323(f7(a860,a860,a860),f78(a860)),x41414))),f323(f323(f39(a860,f867(x41411,a855)),f294(a860,x41414,f323(f323(f78(a860),x41412),x41414))),x41413))
% 179.72/179.57 [4142]E(f168(x41421,f323(f277(x41421,x41421,x41422),f323(f323(f301(x41421),x41423),f188(f867(x41421,a855)))),f323(f277(f861(x41421),f861(x41421),f151(x41421,x41422)),f323(f323(f301(f861(x41421)),x41424),f188(f867(f861(x41421),a855))))),f323(f277(f861(x41421),f861(x41421),f151(x41421,x41422)),f323(f323(f301(f861(x41421)),f323(f323(f144(x41421),x41423),x41424)),f188(f867(f861(x41421),a855)))))
% 179.72/179.57 [4204]E(f323(f179(x42041,x42042),f323(f323(f147(x42041,f866(x42041,x42042)),f323(f323(f18(x42041,x42042,f866(x42041,x42042)),f258(x42041,x42042)),x42043)),x42044)),f182(x42041,x42042,f323(f71(x42042,f864(x42042),x42041,f230(x42042)),x42043),f323(f166(x42041),x42044)))
% 179.72/179.57 [4209]E(f323(f243(x42091),f323(f323(f7(x42091,f867(x42092,a855),a855),f323(f323(f8(x42092,f867(f867(x42092,a855),a855),x42091),f325(x42092)),x42093)),x42094)),f323(f303(x42091,x42092,x42093),x42094))
% 179.72/179.57 [4303]E(f323(f243(x43031),f323(f323(f7(x43031,f867(f866(x43032,x43031),a855),a855),f323(f323(f8(f866(x43032,x43031),f867(f867(f866(x43032,x43031),a855),a855),x43031),f325(f866(x43032,x43031))),f323(f258(x43032,x43031),x43033))),x43034)),f323(f277(x43032,x43031,x43034),f323(f323(f301(x43032),x43033),f188(f867(x43032,a855)))))
% 179.72/179.57 [4317]E(f323(f323(f147(f866(x43171,a860),x43171),f257(x43171,a860)),f323(f129(f866(x43171,a860),f323(f323(f8(a860,a855,f866(x43171,a860)),x43172),f323(f323(f8(a860,a860,f866(x43171,a860)),a112),f261(x43171,a860)))),f323(f323(f175(x43171,a860),x43173),x43174))),f323(f323(f147(f866(x43171,a860),x43171),f257(x43171,a860)),f323(f129(f866(x43171,a860),f323(f323(f8(a860,a855,f866(x43171,a860)),x43172),f261(x43171,a860))),f323(f323(f175(x43171,a860),x43173),f323(f323(f147(a860,a860),a112),x43174)))))
% 179.72/179.57 [4325]P101(f323(f323(f237(f867(f867(x43251,a855),a855)),f323(f323(f39(x43252,f867(f867(x43251,a855),a855)),x43253),f323(f323(f8(f867(x43251,a855),f867(f867(x43251,a855),a855),x43252),f300(x43251)),x43254))),f323(f300(x43251),f323(f323(f39(x43252,f867(x43251,a855)),x43253),x43254))))
% 179.72/179.57 [4368]E(f323(f323(f84(a1,x43681),f323(f103(a1),f323(f323(f78(a1),x43682),a97))),f323(f323(f18(a1,x43681,x43681),f323(f323(f7(a1,x43681,f867(x43681,x43681)),f323(f323(f8(a855,f867(x43681,f867(x43681,x43681)),a1),f96(x43681)),a193)),x43683)),f323(f323(f18(a1,x43681,x43681),f323(f323(f8(a860,f867(x43681,x43681),a1),x43684),a104)),f323(f323(f8(a860,x43681,a1),f184(x43681,x43683,x43684)),a104)))),f323(f184(x43681,x43683,x43684),f323(f103(a860),x43682)))
% 179.72/179.57 [4371]E(f323(f323(f147(x43711,x43712),f323(f71(f864(x43712),x43712,x43711,f234(x43712)),x43713)),f323(f129(x43711,f323(f323(f8(a855,a855,x43711),a318),f323(f323(f7(x43711,f864(x43712),a855),f323(f323(f8(f864(x43712),f867(f864(x43712),a855),x43711),a320),x43713)),f200(x43712)))),x43714)),f156(x43711,x43712,x43713,x43714))
% 179.72/179.57 [4394]E(f323(f243(f866(x43941,x43942)),f323(f262(x43941,x43942,a855),f323(f323(f7(x43941,f867(x43942,a855),f867(x43942,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x43942,a855),f867(x43942,a855)),x43941),f8(a855,a855,x43942)),f323(f323(f8(a855,f867(a855,a855),x43941),a321),f323(f323(f7(x43941,f867(x43941,a855),a855),f325(x43941)),x43943)))),f323(f323(f7(x43942,f867(x43942,a855),a855),f325(x43942)),x43944)))),f224(x43941,x43942,x43943,x43944))
% 179.72/179.57 [4427]E(f323(f323(f39(x44271,f867(f866(x44271,x44272),a855)),x44273),f323(f323(f18(x44271,f867(x44272,f867(f866(x44271,x44272),a855)),f867(f866(x44271,x44272),a855)),f323(f323(f8(f867(x44272,a855),f867(f867(x44272,f867(f866(x44271,x44272),a855)),f867(f866(x44271,x44272),a855)),x44271),f39(x44272,f867(f866(x44271,x44272),a855))),x44274)),f323(f323(f7(x44271,f867(f866(x44271,x44272),a855),f867(x44272,f867(f866(x44271,x44272),a855))),f323(f323(f8(f867(x44272,f867(f867(f866(x44271,x44272),a855),f867(f866(x44271,x44272),a855))),f867(f867(f866(x44271,x44272),a855),f867(x44272,f867(f866(x44271,x44272),a855))),x44271),f7(x44272,f867(f866(x44271,x44272),a855),f867(f866(x44271,x44272),a855))),f323(f323(f8(f867(x44272,f866(x44271,x44272)),f867(x44272,f867(f867(f866(x44271,x44272),a855),f867(f866(x44271,x44272),a855))),x44271),f323(f8(f866(x44271,x44272),f867(f867(f866(x44271,x44272),a855),f867(f866(x44271,x44272),a855)),x44272),f301(f866(x44271,x44272)))),f258(x44271,x44272)))),f188(f867(f866(x44271,x44272),a855))))),f323(f323(f260(x44271,x44272),x44273),x44274))
% 179.72/179.57 [3981]E(f323(f323(f121(x39811),f323(f323(f169(x39811),x39812),x39813)),f323(f323(f169(x39811),f323(f323(f22(a860),x39812),f323(f189(f861(x39811)),x39813))),x39814)),f323(f323(f169(x39811),x39812),f323(f323(f121(x39811),x39813),x39814)))
% 179.72/179.57 [3982]E(f323(f323(f121(x39821),f323(f323(f131(x39821),x39822),x39823)),f323(f323(f131(x39821),f323(f323(f22(a860),x39822),f323(f189(f861(x39821)),x39823))),x39824)),f323(f323(f131(x39821),x39822),f323(f323(f121(x39821),x39823),x39824)))
% 179.72/179.57 [4034]E(f323(f323(f78(a860),f323(f323(f79(a860),x40341),x40342)),f323(f323(f78(a860),f323(f323(f79(a860),x40343),x40342)),x40344)),f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f78(a860),x40341),x40343)),x40342)),x40344))
% 179.72/179.57 [4182]E(f88(x41821,f323(f323(f7(x41821,x41822,a855),f323(f323(f8(x41822,f867(x41822,a855),x41821),a320),x41823)),x41824)),f323(f91(x41821,x41822,f246(f867(x41821,a855)),x41823),x41824))
% 179.72/179.57 [4234]P101(f323(f323(f237(f867(x42341,a855)),f323(f323(f22(f867(x42341,a855)),f323(f254(x42342,x42341),x42343)),f323(f254(x42342,x42341),x42344))),f323(f254(x42342,x42341),f323(f323(f22(f867(f866(x42342,x42341),a855)),x42343),x42344))))
% 179.72/179.57 [4235]P101(f323(f323(f237(f867(x42351,a855)),f323(f323(f22(f867(x42351,a855)),f323(f256(x42351,x42352),x42353)),f323(f256(x42351,x42352),x42354))),f323(f256(x42351,x42352),f323(f323(f22(f867(f866(x42351,x42352),a855)),x42353),x42354))))
% 179.72/179.57 [4346]E(f323(f323(f78(a1),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x43461),x43462)),f188(f867(f866(a860,a860),a855)))))),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x43463),x43464)),f188(f867(f866(a860,a860),a855)))))),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),f323(f323(f78(a860),x43461),x43463)),f323(f323(f78(a860),x43462),x43464))),f188(f867(f866(a860,a860),a855))))))
% 179.72/179.57 [4389]E(f323(f323(f79(a1),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x43891),x43892)),f188(f867(f866(a860,a860),a855)))))),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x43893),x43894)),f188(f867(f866(a860,a860),a855)))))),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),f323(f323(f78(a860),f323(f323(f79(a860),x43891),x43893)),f323(f323(f79(a860),x43892),x43894))),f323(f323(f78(a860),f323(f323(f79(a860),x43891),x43894)),f323(f323(f79(a860),x43892),x43893)))),f188(f867(f866(a860,a860),a855))))))
% 179.72/179.57 [4409]E(f323(f243(x44091),f323(f323(f8(f867(x44092,a855),a855,x44091),f86(x44092)),f323(f323(f8(f867(x44092,a855),f867(x44092,a855),x44091),f323(f18(x44092,a855,a855),f323(f323(f8(a855,f867(a855,a855),x44092),a326),f323(f323(f7(x44092,f867(x44092,a855),a855),f325(x44092)),x44093)))),f323(f323(f7(x44091,f867(x44092,f867(x44091,a855)),f867(x44092,a855)),f323(f323(f8(f867(f867(x44091,a855),a855),f867(f867(x44092,f867(x44091,a855)),f867(x44092,a855)),x44091),f8(f867(x44091,a855),a855,x44092)),f325(x44091))),x44094)))),f323(f323(f40(x44092,f867(x44091,a855)),x44093),x44094))
% 179.72/179.57 [4444]E(f323(f323(f280(x44441,x44441,x44441),f323(f323(f301(f866(x44441,x44441)),f323(f323(f258(x44441,x44441),x44442),x44443)),x44444)),f299(x44441,f323(f323(f301(f866(x44441,x44441)),f323(f323(f258(x44441,x44441),x44442),x44443)),x44444))),f323(f323(f110(f867(f866(x44441,x44441),a855)),f323(f323(f280(x44441,x44441,x44441),x44444),f299(x44441,x44444))),f323(f243(f866(x44441,x44441)),f323(f262(x44441,x44441,a855),f323(f323(f7(x44441,f867(x44441,a855),f867(x44441,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x44441,a855),f867(x44441,a855)),x44441),f8(a855,a855,x44441)),f323(f323(f8(a855,f867(a855,a855),x44441),a321),f323(f323(f7(x44441,f867(f866(x44441,x44441),a855),a855),f323(f323(f8(f866(x44441,x44441),f867(f867(f866(x44441,x44441),a855),a855),x44441),f325(f866(x44441,x44441))),f323(f323(f7(x44441,x44441,f866(x44441,x44441)),f258(x44441,x44441)),x44442))),f299(x44441,x44444))))),f323(f323(f7(x44441,f867(f866(x44441,x44441),a855),a855),f323(f323(f8(f866(x44441,x44441),f867(f867(f866(x44441,x44441),a855),a855),x44441),f325(f866(x44441,x44441))),f323(f258(x44441,x44441),x44443))),f299(x44441,x44444)))))))
% 179.72/179.57 [4236]E(f323(f129(x42361,f323(f323(f18(x42361,a855,a855),f323(f323(f8(a855,f867(a855,a855),x42361),a321),x42362)),x42363)),x42364),f323(f129(x42361,x42363),f323(f129(x42361,x42362),x42364)))
% 179.72/179.57 [4340]E(f323(f323(f121(x43401),f323(f323(f323(f96(f861(x43401)),f323(f323(f325(a860),f2(a860)),x43402)),f323(f323(f144(x43401),x43403),f113(x43401))),f113(x43401))),f170(x43401,x43404,f323(f243(a860),f323(f323(f7(a860,f867(a860,a855),a855),f323(f323(f8(a860,f867(f867(a860,a855),a855),a860),f325(a860)),a112)),x43402)))),f170(x43401,f323(f323(f144(x43401),x43403),x43404),x43402))
% 179.72/179.57 [4438]E(f323(f243(f866(x44381,x44382)),f323(f323(f8(f867(a860,a855),a855,f866(x44381,x44382)),f85(a860)),f323(f323(f7(f866(x44381,x44382),f867(a860,a855),f867(a860,a855)),f323(f323(f8(f867(a860,f867(a855,a855)),f867(f867(a860,a855),f867(a860,a855)),f866(x44381,x44382)),f18(a860,a855,a855)),f323(f323(f8(f867(a860,a855),f867(a860,f867(a855,a855)),f866(x44381,x44382)),f323(f8(a855,f867(a855,a855),a860),a321)),f323(f323(f7(f866(x44381,x44382),f867(a860,f866(x44381,x44382)),f867(a860,a855)),f323(f323(f8(f867(f866(x44381,x44382),a855),f867(f867(a860,f866(x44381,x44382)),f867(a860,a855)),f866(x44381,x44382)),f8(f866(x44381,x44382),a855,a860)),a320)),f323(f323(f18(a860,x44382,f866(x44381,x44382)),f323(f323(f8(x44381,f867(x44382,f866(x44381,x44382)),a860),f258(x44381,x44382)),f323(f158(x44381),x44383))),f323(f158(x44382),x44384)))))),f323(f323(f7(a860,a860,a855),f238(a860)),f323(f323(f235(a860),f323(f189(f861(x44381)),x44383)),f323(f189(f861(x44382)),x44384)))))),f323(f166(f866(x44381,x44382)),f323(f323(f175(x44381,x44382),x44383),x44384)))
% 179.72/179.57 [4359]E(f323(f243(f866(x43591,x43592)),f323(f262(x43591,x43592,a855),f323(f323(f7(x43591,f867(x43592,a855),f867(x43592,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x43592,a855),f867(x43592,a855)),x43591),f8(a855,a855,x43592)),f323(f323(f8(a855,f867(a855,a855),x43591),a321),x43593))),x43594))),f323(f323(f260(x43591,x43592),f323(f243(x43591),x43593)),f323(f16(f867(x43592,a855),x43591),f323(f243(x43592),x43594))))
% 179.72/179.57 [4362]E(f323(f243(f866(x43621,x43622)),f323(f262(x43621,x43622,a855),f323(f323(f18(x43621,f867(x43622,a855),f867(x43622,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x43622,a855),f867(x43622,a855)),x43621),f8(a855,a855,x43622)),f323(f323(f8(a855,f867(a855,a855),x43621),a321),x43623))),x43624))),f323(f323(f260(x43621,x43622),f323(f243(x43621),x43623)),f323(f323(f8(f867(x43622,a855),f867(x43622,a855),x43621),f243(x43622)),x43624)))
% 179.72/179.57 [4378]E(f323(f243(x43781),f323(f323(f8(f867(x43782,a855),a855,x43781),f86(x43782)),f323(f323(f8(f867(x43782,a855),f867(x43782,a855),x43781),f323(f18(x43782,a855,a855),f323(f323(f8(a855,f867(a855,a855),x43782),a326),f323(f323(f7(x43782,f867(x43782,a855),a855),f325(x43782)),x43783)))),x43784))),f323(f323(f40(x43782,f867(x43781,a855)),x43783),f323(f323(f8(f867(x43781,a855),f867(x43781,a855),x43782),f243(x43781)),f323(f7(x43781,x43782,a855),x43784))))
% 179.72/179.57 [4422]E(f323(f323(f147(f866(x44221,a860),x44221),f257(x44221,a860)),f323(f129(f866(x44221,a860),f323(f323(f7(f866(x44221,a860),f867(a860,a855),a855),f323(f323(f8(a860,f867(f867(a860,a855),a855),f866(x44221,a860)),f325(a860)),f261(x44221,a860))),x44222)),f323(f323(f175(x44221,a860),x44223),f132(a860,f323(f293(a860,x44224),f323(f323(f78(a860),x44224),f323(f189(f861(x44221)),x44223))))))),f323(f323(f147(f866(x44221,a860),x44221),f257(x44221,a860)),f323(f129(f866(x44221,a860),f323(f323(f7(f866(x44221,a860),f867(a860,a855),a855),f323(f323(f8(a860,f867(f867(a860,a855),a855),f866(x44221,a860)),f325(a860)),f323(f323(f7(f866(x44221,a860),a860,a860),f323(f323(f8(a860,f867(a860,a860),f866(x44221,a860)),f78(a860)),f261(x44221,a860))),x44224))),x44222)),f323(f323(f175(x44221,a860),x44223),f132(a860,f323(f293(a860,f2(a860)),f323(f189(f861(x44221)),x44223)))))))
% 179.72/179.57 [4423]E(f323(a112,f323(f323(f236(a860),f323(f189(f861(x44231)),x44232)),f323(f135(a860,f861(x44233),f323(f7(f861(x44233),a860,a860),f323(f323(f8(a860,f867(a860,a860),f861(x44233)),f236(a860)),f323(f323(f7(f861(x44233),a860,a860),f323(f323(f8(a860,f867(a860,a860),f861(x44233)),f22(a860)),f189(f861(x44233)))),f323(a112,f2(a860))))),f2(a860)),f323(f162(f861(x44233)),f323(f129(f861(x44233),f323(f323(f8(a855,a855,f861(x44233)),a318),f323(f323(f7(f861(x44233),f861(x44233),a855),a320),f113(x44233)))),x44234))))),f323(f323(f236(a860),f323(a112,f323(f189(f861(x44231)),x44232))),f323(f135(a860,f861(x44233),f323(f7(f861(x44233),a860,a860),f323(f323(f8(a860,f867(a860,a860),f861(x44233)),f236(a860)),f189(f861(x44233)))),f2(a860)),f323(f162(f861(x44233)),x44234))))
% 179.72/179.57 [4377]E(f323(f323(f121(x43771),f170(x43771,x43772,x43773)),f170(x43771,x43774,f323(f243(a860),f323(f323(f7(a860,f867(a860,a855),a855),f323(f323(f8(a860,f867(f867(a860,a855),a855),a860),f325(a860)),f323(f323(f7(a860,a860,a860),f78(a860)),f323(f189(f861(x43771)),x43772)))),x43773)))),f170(x43771,f323(f323(f121(x43771),x43772),x43774),x43773))
% 179.72/179.57 [4429]E(f323(f323(f144(f861(x44291)),f323(f323(f144(x44291),x44292),f323(f135(f861(x44291),f861(x44291),f121(x44291),f113(x44291)),f323(f323(f147(f861(x44291),f861(x44291)),f149(f861(x44291),x44291,f113(x44291),f323(f323(f8(f861(x44291),f867(f861(x44291),f861(x44291)),x44291),f16(f861(x44291),f861(x44291))),f323(f323(f7(x44291,f861(x44291),f861(x44291)),f144(x44291)),f113(x44291))))),x44293)))),f173(x44291,f323(f323(f144(f861(x44291)),x44294),f323(f135(f861(f861(x44291)),f861(f861(x44291)),f121(f861(x44291)),f113(f861(x44291))),f323(f323(f147(f861(x44291),f861(f861(x44291))),f149(f861(f861(x44291)),x44291,f113(f861(x44291)),f323(f16(f867(f861(x44291),f861(f861(x44291))),x44291),f323(f323(f7(f861(x44291),f861(f861(x44291)),f861(f861(x44291))),f144(f861(x44291))),f113(f861(x44291)))))),x44293))))),f173(x44291,f323(f323(f144(f861(x44291)),f323(f323(f144(x44291),x44292),x44294)),x44293)))
% 179.72/179.57 [4439]E(f323(f243(f866(x44391,x44391)),f323(f262(x44391,x44391,a855),f323(f323(f7(x44391,f867(f866(x44392,x44392),a855),f867(x44391,a855)),f323(f323(f8(f867(x44391,f867(f867(f866(x44392,x44392),a855),a855)),f867(f867(f866(x44392,x44392),a855),f867(x44391,a855)),x44391),f7(x44391,f867(f866(x44392,x44392),a855),a855)),f323(f323(f8(f867(x44391,f866(x44392,x44392)),f867(x44391,f867(f867(f866(x44392,x44392),a855),a855)),x44391),f323(f8(f866(x44392,x44392),f867(f867(f866(x44392,x44392),a855),a855),x44391),f325(f866(x44392,x44392)))),f323(f323(f7(x44391,f867(x44391,x44392),f867(x44391,f866(x44392,x44392))),f323(f323(f8(f867(x44392,f866(x44392,x44392)),f867(f867(x44391,x44392),f867(x44391,f866(x44392,x44392))),x44391),f8(x44392,f866(x44392,x44392),x44391)),f323(f323(f8(x44392,f867(x44392,f866(x44392,x44392)),x44391),f258(x44392,x44392)),x44393))),x44393)))),x44394))),f323(f323(f279(x44392,x44391),x44394),x44393))
% 179.72/179.57 [4499]~E(f30(x44991,x44992),f27(x44993,x44994,x44995))
% 179.72/179.57 [4500]~E(f30(x45001,x45002),f26(x45003,x45004,x45005))
% 179.72/179.57 [4501]~E(f29(x45011,x45012),f27(x45013,x45014,x45015))
% 179.72/179.57 [4502]~E(f29(x45021,x45022),f26(x45023,x45024,x45025))
% 179.72/179.57 [4503]~E(f25(x45031,x45032),f27(x45033,x45034,x45035))
% 179.72/179.57 [4504]~E(f25(x45041,x45042),f26(x45043,x45044,x45045))
% 179.72/179.57 [4505]~E(f27(x45051,x45052,x45053),f30(x45054,x45055))
% 179.72/179.57 [4506]~E(f27(x45061,x45062,x45063),f29(x45064,x45065))
% 179.72/179.57 [4507]~E(f27(x45071,x45072,x45073),f25(x45074,x45075))
% 179.72/179.57 [4508]~E(f26(x45081,x45082,x45083),f30(x45084,x45085))
% 179.72/179.57 [4509]~E(f26(x45091,x45092,x45093),f29(x45094,x45095))
% 179.72/179.57 [4510]~E(f26(x45101,x45102,x45103),f25(x45104,x45105))
% 179.72/179.57 [3548]E(f323(f323(f147(x35481,x35482),x35483),f163(x35481,x35484,x35485)),f163(x35482,x35484,f323(x35483,x35485)))
% 179.72/179.57 [3919]E(f323(f180(x39191,x39192,x39193,x39194),x39195),f323(f232(f864(x39192),x39192,f323(x39193,x39195),f230(x39192)),f323(x39194,x39195)))
% 179.72/179.57 [4009]E(f180(x40091,x40092,f180(x40091,x40092,x40093,x40094),x40095),f180(x40091,x40092,x40093,f180(x40091,x40092,x40094,x40095)))
% 179.72/179.57 [4183]E(f259(x41831,x41832,x41833,f247(x41832,x41831,x41834),f247(x41833,x41832,x41835)),f247(x41833,x41831,f259(x41833,x41832,x41831,x41835,x41834)))
% 179.72/179.57 [4190]E(f323(f323(f110(f867(x41901,a855)),f323(f166(x41901),f323(f323(f169(x41901),f323(f189(f861(x41902)),x41903)),x41904))),f177(x41901,x41902,x41905)),f177(x41901,x41902,f181(x41901,x41902,x41905,x41904,x41903)))
% 179.72/179.57 [3741]E(f323(f323(f262(x37411,x37412,x37413),x37414),x37415),f323(f323(x37414,f323(f257(x37411,x37412),x37415)),f323(f261(x37411,x37412),x37415)))
% 179.72/179.57 [3768]E(f323(f232(x37681,x37682,x37683,x37684),f323(f230(x37682),x37685)),f323(x37684,x37685))
% 179.72/179.57 [3777]E(f323(f323(f323(f63(x37771,x37772,x37773),x37774),x37775),f188(f867(x37772,a855))),x37775)
% 179.72/179.57 [3952]E(f233(x39521,x39522,x39523,x39524,f323(f230(x39522),x39525)),f323(x39524,x39525))
% 179.72/179.57 [4064]E(f323(f71(f864(x40641),f864(x40642),f864(x40643),f323(f201(x40641,x40642),x40644)),f323(f201(x40643,x40641),x40645)),f323(f201(x40643,x40642),f323(f71(x40641,x40642,x40643,x40644),x40645)))
% 179.72/179.57 [4066]E(f323(f71(f861(x40661),f861(x40662),f861(x40663),f323(f147(x40661,x40662),x40664)),f323(f147(x40663,x40661),x40665)),f323(f147(x40663,x40662),f323(f71(x40661,x40662,x40663,x40664),x40665)))
% 179.72/179.57 [4122]E(f323(f232(x41221,f866(x41222,f862(x41222)),x41223,f323(f262(x41222,f862(x41222),x41221),x41224)),f323(f128(x41222),x41225)),f126(x41221,x41222,x41223,x41224,x41225))
% 179.72/179.57 [4145]E(f83(x41451,f64(x41452,x41451,x41453,x41454,x41455)),f323(f323(f62(x41452,x41451,x41453),x41454),x41455))
% 179.72/179.57 [4180]E(f323(f323(f78(a860),f323(f323(f78(a860),f323(x41801,f323(f257(x41802,x41803),x41804))),f323(x41805,f323(f261(x41802,x41803),x41804)))),f323(a112,f2(a860))),f266(x41802,x41803,x41801,x41805,x41804))
% 179.72/179.57 [4373]E(f156(x43731,x43732,f323(f323(f7(x43731,f864(x43732),f864(x43732)),f323(f323(f18(x43731,f864(x43732),f867(f864(x43732),f864(x43732))),f323(f323(f8(a855,f867(f864(x43732),f867(f864(x43732),f864(x43732))),x43731),f96(f864(x43732))),x43733)),f323(f323(f8(x43732,f864(x43732),x43731),f230(x43732)),x43734))),f200(x43732)),x43735),f323(f323(f147(x43731,x43732),x43734),f323(f129(x43731,x43733),x43735)))
% 179.72/179.57 [4546]~E(f323(f323(f323(f70(x45461,f864(x45462)),x45463),x45464),f323(f230(x45462),x45465)),f323(f16(f864(x45462),x45461),f200(x45462)))
% 179.72/179.57 [3675]E(f323(f323(f169(x36751),x36752),f323(f323(f147(x36753,x36751),x36754),x36755)),f323(f323(f147(x36753,x36751),x36754),f323(f323(f169(x36753),x36752),x36755)))
% 179.72/179.57 [3676]E(f323(f323(f131(x36761),x36762),f323(f323(f147(x36763,x36761),x36764),x36765)),f323(f323(f147(x36763,x36761),x36764),f323(f323(f131(x36763),x36762),x36765)))
% 179.72/179.57 [3709]E(f323(f323(f147(x37091,x37092),x37093),f323(f323(f144(x37091),x37094),x37095)),f323(f323(f144(x37092),f323(x37093,x37094)),f323(f323(f147(x37091,x37092),x37093),x37095)))
% 179.72/179.57 [3772]E(f323(f302(x37721,x37722,x37723),f323(f323(f301(x37721),x37724),x37725)),f323(f323(f301(x37722),f323(x37723,x37724)),f323(f302(x37721,x37722,x37723),x37725)))
% 179.72/179.57 [3801]E(f167(x38011,f323(f323(f144(x38011),x38012),x38013),f323(f323(f144(x38011),x38014),x38015)),f323(f323(f144(x38011),x38012),f323(f323(f144(x38011),x38014),f167(x38011,x38013,x38015))))
% 179.72/179.57 [3838]E(f323(f323(f175(x38381,x38382),f323(f323(f169(x38381),x38383),x38384)),f323(f323(f169(x38382),x38383),x38385)),f323(f323(f169(f866(x38381,x38382)),x38383),f323(f323(f175(x38381,x38382),x38384),x38385)))
% 179.72/179.57 [3839]E(f323(f323(f175(x38391,x38392),f323(f323(f131(x38391),x38393),x38394)),f323(f323(f131(x38392),x38393),x38395)),f323(f323(f131(f866(x38391,x38392)),x38393),f323(f323(f175(x38391,x38392),x38394),x38395)))
% 179.72/179.57 [3851]E(f323(f323(f152(x38511,f323(f323(f144(x38511),x38512),x38513)),f323(a112,x38514)),x38515),f323(f323(f144(x38511),x38512),f323(f323(f152(x38511,x38513),x38514),x38515)))
% 179.72/179.57 [3854]E(f323(f232(f864(x38541),x38542,f200(x38541),x38543),f323(f323(f16(f864(x38542),x38544),f200(x38542)),x38545)),f200(x38541))
% 179.72/179.57 [3856]E(f323(f323(f121(x38561),f323(f323(f147(x38562,x38561),x38563),x38564)),f323(f323(f147(x38562,x38561),x38563),x38565)),f323(f323(f147(x38562,x38561),x38563),f323(f323(f121(x38562),x38564),x38565)))
% 179.72/179.57 [3860]E(f323(f323(x38601,x38602),f323(f323(f249(x38603,x38604,x38601),x38602),x38605)),f323(f323(f249(x38603,x38604,x38601),x38602),f323(a112,x38605)))
% 179.72/179.57 [3890]E(f157(x38901,x38902,x38903,f323(f323(f144(x38901),x38904),x38905)),f323(f323(f121(x38902),f323(x38903,x38904)),f157(x38901,x38902,x38903,x38905)))
% 179.72/179.57 [3903]E(f323(f323(f280(x39031,x39032,x39033),f323(f278(x39032,x39031),x39034)),f323(f278(x39033,x39032),x39035)),f323(f278(x39033,x39031),f323(f323(f280(x39033,x39032,x39031),x39035),x39034)))
% 179.72/179.57 [3937]E(f323(f323(f323(f183(f861(x39371),f861(x39371)),x39372),f161(x39371)),f323(f323(f147(x39373,x39371),x39374),x39375)),f323(f323(f147(x39373,x39371),x39374),f323(f323(f323(f183(f861(x39373),f861(x39373)),x39372),f161(x39373)),x39375)))
% 179.72/179.57 [3938]E(f323(f323(f264(x39381,x39382,x39381,x39383),f323(f258(x39382,x39381),x39384)),x39385),f323(x39385,x39384))
% 179.72/179.57 [3966]E(f148(x39661,x39662,f323(f323(f147(x39663,x39661),x39664),x39665)),f148(x39663,f323(f71(x39661,a860,x39663,x39662),x39664),x39665))
% 179.72/179.57 [4032]E(f323(f323(f71(f864(x40321),f864(x40322),x40323,f323(f201(x40321,x40322),x40324)),f323(f16(f864(x40321),x40323),f200(x40321))),x40325),f200(x40322))
% 179.72/179.57 [4033]E(f171(f866(x40331,x40332),f323(f71(x40332,a855,f866(x40331,x40332),x40333),f261(x40331,x40332)),f323(f323(f175(x40331,x40332),x40334),x40335)),f323(f323(f175(x40331,x40332),x40334),f171(x40332,x40333,x40335)))
% 179.72/179.57 [4038]E(f323(f302(x40381,x40382,f323(f323(f8(x40383,x40382,x40381),x40384),x40385)),f246(f867(x40381,a855))),f323(f302(x40383,x40382,x40384),f323(f302(x40381,x40383,x40385),f246(f867(x40381,a855)))))
% 179.72/179.57 [4051]E(f171(f866(x40511,x40512),f323(f71(x40511,a855,f866(x40511,x40512),x40513),f257(x40511,x40512)),f323(f323(f175(x40511,x40512),x40514),x40515)),f323(f323(f175(x40511,x40512),f171(x40511,x40513,x40514)),x40515))
% 179.72/179.57 [4070]E(f323(f323(f110(f867(x40701,a855)),f323(f303(x40701,x40702,x40703),f323(f323(f301(x40702),x40704),f188(f867(x40702,a855))))),f323(f303(x40701,x40702,x40703),x40705)),f323(f303(x40701,x40702,x40703),f323(f323(f301(x40702),x40704),x40705)))
% 179.72/179.57 [4129]E(f323(f323(f121(f866(x41291,x41292)),f323(f323(f147(x41292,f866(x41291,x41292)),f323(f258(x41291,x41292),x41293)),x41294)),f57(x41291,x41292,x41295,x41294)),f57(x41291,x41292,f323(f323(f144(x41291),x41293),x41295),x41294))
% 179.72/179.57 [4130]E(f323(f323(f147(x41301,x41302),x41303),f171(x41301,f323(f71(x41302,a855,x41301,x41304),x41303),x41305)),f171(x41302,x41304,f323(f323(f147(x41301,x41302),x41303),x41305)))
% 179.72/179.57 [4136]E(f323(f135(x41361,x41362,f323(f7(x41362,x41361,x41361),f323(f7(x41361,x41362,x41361),x41363)),x41364),f323(f162(x41362),f323(f162(x41362),x41365))),f323(f135(x41361,x41362,x41363,x41364),x41365))
% 179.72/179.57 [4137]E(f323(f323(f323(f70(x41371,f864(x41372)),f182(x41371,x41372,x41373,x41374)),x41375),f323(x41373,x41375)),f182(x41371,x41372,x41373,f323(f323(f301(x41371),x41375),x41374)))
% 179.72/179.57 [4207]E(f323(f232(f861(x42071),x42071,f156(x42072,x42071,x42073,x42074),f323(f323(f7(x42071,f861(x42071),f861(x42071)),f144(x42071)),f156(x42072,x42071,x42073,x42074))),f323(x42073,x42075)),f156(x42072,x42071,x42073,f323(f323(f144(x42072),x42075),x42074)))
% 179.72/179.57 [4244]P101(f323(f323(f237(f867(x42441,a855)),f323(f302(x42442,x42441,x42443),f323(f323(f101(f867(x42442,a855)),x42444),x42445))),f323(f323(f101(f867(x42441,a855)),f323(f302(x42442,x42441,x42443),x42444)),f323(f302(x42442,x42441,x42443),x42445))))
% 179.72/179.57 [4245]P101(f323(f323(f237(f867(x42451,a855)),f323(f277(x42452,x42451,x42453),f323(f323(f101(f867(x42452,a855)),x42454),x42455))),f323(f323(f101(f867(x42451,a855)),f323(f277(x42452,x42451,x42453),x42454)),f323(f277(x42452,x42451,x42453),x42455))))
% 179.72/179.57 [4347]E(f323(f261(x43471,x43472),f323(f263(x43473,x43471,x43472,x43472,x43474,f32(x43472)),x43475)),f323(f261(x43473,x43472),x43475))
% 179.72/179.57 [4348]E(f323(f257(x43481,x43482),f323(f263(x43481,x43481,x43483,x43482,f32(x43481),x43484),x43485)),f323(f257(x43481,x43483),x43485))
% 179.72/179.57 [4433]P26(x44331,x44332,f323(f323(f301(f859(x44331)),f323(f323(f323(f90(x44331),f323(f323(f7(x44331,f867(a856,a856),f867(a856,a855)),f323(f323(f8(f867(a856,a855),f867(f867(a856,a856),f867(a856,a855)),x44331),f8(a856,a855,a856)),x44333)),f323(f323(f18(a856,a860,a856),f323(f323(f7(a856,a858,f867(a860,a856)),a196),x44334)),x44335))),f25(x44334,x44335)),x44333)),f188(f867(f859(x44331),a855))))
% 179.72/179.57 [4435]E(f323(f135(f867(x44351,f864(x44352)),f866(x44351,x44352),f323(f323(f8(f867(x44351,f867(x44352,f867(x44351,f864(x44352)))),f867(f866(x44351,x44352),f867(x44351,f864(x44352))),f867(x44351,f864(x44352))),f262(x44351,x44352,f867(x44351,f864(x44352)))),f323(f323(f7(f867(x44351,f864(x44352)),f867(x44352,f864(x44352)),f867(x44351,f867(x44352,f867(x44351,f864(x44352))))),f323(f323(f8(f867(x44351,f867(f867(x44352,f864(x44352)),f867(x44352,f867(x44351,f864(x44352))))),f867(f867(x44352,f864(x44352)),f867(x44351,f867(x44352,f867(x44351,f864(x44352))))),f867(x44351,f864(x44352))),f7(x44351,f867(x44352,f864(x44352)),f867(x44352,f867(x44351,f864(x44352))))),f323(f323(f8(f867(x44351,f867(f864(x44352),f867(x44351,f864(x44352)))),f867(x44351,f867(f867(x44352,f864(x44352)),f867(x44352,f867(x44351,f864(x44352))))),f867(x44351,f864(x44352))),f323(f8(f867(f864(x44352),f867(x44351,f864(x44352))),f867(f867(x44352,f864(x44352)),f867(x44352,f867(x44351,f864(x44352)))),x44351),f8(f864(x44352),f867(x44351,f864(x44352)),x44352))),f70(x44351,f864(x44352))))),f230(x44352))),x44353),f323(f323(f175(x44351,x44352),x44354),x44355)),f181(x44351,x44352,x44353,x44354,x44355))
% 179.72/179.57 [4437]P26(x44371,x44372,f323(f323(f301(f859(x44371)),f323(f323(f323(f90(x44371),f323(f323(f7(x44371,f867(a856,a855),f867(a856,a855)),f323(f323(f8(f867(a856,f867(a855,a855)),f867(f867(a856,a855),f867(a856,a855)),x44371),f18(a856,a855,a855)),f323(f323(f8(f867(a856,a855),f867(a856,f867(a855,a855)),x44371),f323(f8(a855,f867(a855,a855),a856),a321)),x44373))),f323(f323(f8(a855,a855,a856),a318),x44374))),f29(x44374,x44375)),x44373)),f188(f867(f859(x44371),a855))))
% 179.72/179.57 [3518]E(f323(f323(f323(f323(f206(x35181),x35182),x35183),x35184),x35185),f192(x35181,x35182))
% 179.72/179.57 [3519]E(f323(f323(f323(f323(f210(x35191),x35192),x35193),x35194),x35195),f202(x35191,x35192))
% 179.72/179.57 [3564]E(f93(x35641,x35642,f323(f323(f323(f90(x35641),x35643),x35644),x35645)),f2(a860))
% 179.72/179.57 [3659]E(f323(f323(f323(f323(f70(x36591,x36592),x36593),x36594),x36595),x36594),x36595)
% 179.72/179.57 [3891]E(f323(f323(f39(x38911,f867(x38912,a855)),f323(f323(f301(x38911),x38913),x38914)),x38915),f323(f323(f110(f867(x38912,a855)),f323(x38915,x38913)),f323(f323(f39(x38911,f867(x38912,a855)),x38914),x38915)))
% 179.72/179.57 [3892]E(f323(f323(f40(x38921,f867(x38922,a855)),f323(f323(f301(x38921),x38923),x38924)),x38925),f323(f323(f101(f867(x38922,a855)),f323(x38925,x38923)),f323(f323(f40(x38921,f867(x38922,a855)),x38924),x38925)))
% 179.72/179.57 [3945]E(f323(f116(x39451,x39452,f323(x39453,x39454)),f323(f323(f7(x39451,a99,f862(x39452)),x39455),x39454)),f323(f198(x39451,x39452,x39453,x39455),x39454))
% 179.72/179.57 [3959]E(f323(f323(f110(f867(x39591,a855)),f323(f302(x39592,x39591,x39593),x39594)),f323(f302(x39592,x39591,x39593),x39595)),f323(f302(x39592,x39591,x39593),f323(f323(f110(f867(x39592,a855)),x39594),x39595)))
% 179.72/179.57 [3960]E(f323(f323(f110(f867(x39601,a855)),f323(f303(x39601,x39602,x39603),x39604)),f323(f303(x39601,x39602,x39603),x39605)),f323(f303(x39601,x39602,x39603),f323(f323(f110(f867(x39602,a855)),x39604),x39605)))
% 179.72/179.57 [3961]E(f323(f323(f22(f867(x39611,a855)),f323(f303(x39611,x39612,x39613),x39614)),f323(f303(x39611,x39612,x39613),x39615)),f323(f303(x39611,x39612,x39613),f323(f323(f22(f867(x39612,a855)),x39614),x39615)))
% 179.72/179.57 [3962]E(f323(f323(f101(f867(x39621,a855)),f323(f303(x39621,x39622,x39623),x39624)),f323(f303(x39621,x39622,x39623),x39625)),f323(f303(x39621,x39622,x39623),f323(f323(f101(f867(x39622,a855)),x39624),x39625)))
% 179.72/179.57 [3963]E(f323(f323(f110(f867(x39631,a855)),f323(f277(x39632,x39631,x39633),x39634)),f323(f277(x39632,x39631,x39633),x39635)),f323(f277(x39632,x39631,x39633),f323(f323(f110(f867(x39632,a855)),x39634),x39635)))
% 179.72/179.57 [3965]E(f182(x39651,x39652,f182(x39651,x39652,x39653,x39654),x39655),f182(x39651,x39652,x39653,f323(f323(f101(f867(x39651,a855)),x39654),x39655)))
% 179.72/179.57 [4028]E(f323(f323(f152(x40281,f323(f323(f121(x40281),x40282),f323(f323(f144(x40281),x40283),x40284))),f323(f189(f861(x40281)),x40282)),x40285),f323(f323(f121(x40281),x40282),f323(f323(f144(x40281),x40285),x40284)))
% 179.72/179.57 [4036]E(f323(f323(f40(x40361,f867(x40362,a855)),x40363),f323(f323(f8(f867(x40362,a855),f867(x40362,a855),x40361),f323(f301(x40362),x40364)),x40365)),f323(f323(f301(x40362),x40364),f323(f323(f40(x40361,f867(x40362,a855)),x40363),x40365)))
% 179.72/179.57 [4104]E(f182(x41041,x41042,f323(f323(f323(f70(x41041,f864(x41042)),x41043),x41044),f323(f230(x41042),x41045)),f323(f77(f867(x41041,a855)),f323(f323(f301(x41041),x41044),f188(f867(x41041,a855))))),f182(x41041,x41042,x41043,f323(f77(f867(x41041,a855)),f323(f323(f301(x41041),x41044),f188(f867(x41041,a855))))))
% 179.72/179.57 [4194]E(f323(f323(f147(x41941,x41942),x41943),f323(f129(x41941,f323(f71(x41942,a855,x41941,x41944),x41943)),x41945)),f323(f129(x41942,x41944),f323(f323(f147(x41941,x41942),x41943),x41945)))
% 179.72/179.57 [4200]E(f323(f189(f861(x42001)),f323(f129(x42001,x42002),f323(f323(f147(x42003,x42001),x42004),x42005))),f323(f189(f861(x42003)),f323(f129(x42003,f323(f71(x42001,a855,x42003,x42002),x42004)),x42005)))
% 179.72/179.57 [4339]E(f323(f323(f110(f867(x43391,a855)),f323(f323(f22(f867(x43391,a855)),f177(x43391,x43392,x43393)),f323(f243(x43391),f323(f323(f7(x43391,f867(x43391,a855),a855),f325(x43391)),f323(f323(f22(f867(x43391,a855)),x43394),f177(x43391,x43392,x43395)))))),f323(f243(x43391),f323(f323(f7(x43391,f867(x43391,a855),a855),f325(x43391)),f323(f323(f101(f867(x43391,a855)),x43394),f177(x43391,x43392,x43395))))),f177(x43391,x43392,f74(x43391,f864(x43392),x43393,x43395,x43394)))
% 179.72/179.57 [4414]E(f323(f149(f861(f866(x44141,x44142)),x44142,f113(f866(x44141,x44142)),f323(f323(f7(x44142,f867(f861(x44142),f861(f866(x44141,x44142))),f867(f861(x44142),f861(f866(x44141,x44142)))),f323(f323(f8(f867(f861(f866(x44141,x44142)),f861(f866(x44141,x44142))),f867(f867(f861(x44142),f861(f866(x44141,x44142))),f867(f861(x44142),f861(f866(x44141,x44142)))),x44142),f8(f861(f866(x44141,x44142)),f861(f866(x44141,x44142)),f861(x44142))),f323(f323(f8(f866(x44141,x44142),f867(f861(f866(x44141,x44142)),f861(f866(x44141,x44142))),x44142),f144(f866(x44141,x44142))),f323(f258(x44141,x44142),x44143)))),f323(f175(x44141,x44142),x44144))),x44145),f323(f323(f175(x44141,x44142),f323(f323(f144(x44141),x44143),x44144)),x44145))
% 179.72/179.57 [3885]E(f323(f323(f152(x38851,f323(f323(f152(x38851,x38852),x38853),x38854)),x38853),x38855),f323(f323(f152(x38851,x38852),x38853),x38855))
% 179.72/179.57 [3939]E(f323(f254(x39391,x39392),f323(f323(f301(f866(x39391,x39392)),f323(f323(f258(x39391,x39392),x39393),x39394)),x39395)),f323(f323(f301(x39392),x39394),f323(f254(x39391,x39392),x39395)))
% 179.72/179.57 [3940]E(f323(f256(x39401,x39402),f323(f323(f301(f866(x39401,x39402)),f323(f323(f258(x39401,x39402),x39403),x39404)),x39405)),f323(f323(f301(x39401),x39403),f323(f256(x39401,x39402),x39405)))
% 179.72/179.57 [3991]E(f119(x39911,x39912,f323(x39913,x39914),f323(f323(f7(x39911,a99,f862(f864(x39912))),x39915),x39914)),f323(f195(x39911,x39912,x39913,x39915),x39914))
% 179.72/179.57 [4021]E(f323(f323(f110(f867(f866(x40211,x40212),a855)),f323(f323(f260(x40211,x40212),x40213),x40214)),f323(f323(f260(x40211,x40212),x40215),x40214)),f323(f323(f260(x40211,x40212),f323(f323(f110(f867(x40211,a855)),x40213),x40215)),x40214))
% 179.72/179.57 [4022]E(f323(f323(f22(f867(f866(x40221,x40222),a855)),f323(f323(f260(x40221,x40222),x40223),x40224)),f323(f323(f260(x40221,x40222),x40225),x40224)),f323(f323(f260(x40221,x40222),f323(f323(f22(f867(x40221,a855)),x40223),x40225)),x40224))
% 179.72/179.57 [4023]E(f323(f323(f101(f867(f866(x40231,x40232),a855)),f323(f323(f260(x40231,x40232),x40233),x40234)),f323(f323(f260(x40231,x40232),x40235),x40234)),f323(f323(f260(x40231,x40232),f323(f323(f101(f867(x40231,a855)),x40233),x40235)),x40234))
% 179.72/179.57 [4082]E(f323(f323(f110(f867(x40821,a855)),f323(f323(f39(x40822,f867(x40821,a855)),x40823),x40824)),f323(f323(f39(x40822,f867(x40821,a855)),x40825),x40824)),f323(f323(f39(x40822,f867(x40821,a855)),f323(f323(f110(f867(x40822,a855)),x40823),x40825)),x40824))
% 179.72/179.57 [4083]E(f323(f323(f101(f867(x40831,a855)),f323(f323(f40(x40832,f867(x40831,a855)),x40833),x40834)),f323(f323(f40(x40832,f867(x40831,a855)),x40835),x40834)),f323(f323(f40(x40832,f867(x40831,a855)),f323(f323(f110(f867(x40832,a855)),x40833),x40835)),x40834))
% 179.72/179.58 [4097]E(f323(f323(f39(x40971,f867(x40972,a855)),x40973),f323(f323(f8(f867(x40972,a855),f867(x40972,a855),x40971),f323(f22(f867(x40972,a855)),x40974)),x40975)),f323(f323(f22(f867(x40972,a855)),x40974),f323(f323(f40(x40971,f867(x40972,a855)),x40973),x40975)))
% 179.72/179.58 [4098]E(f323(f323(f39(x40981,f867(x40982,a855)),x40983),f323(f323(f8(f867(x40982,a855),f867(x40982,a855),x40981),f323(f101(f867(x40982,a855)),x40984)),x40985)),f323(f323(f101(f867(x40982,a855)),x40984),f323(f323(f39(x40981,f867(x40982,a855)),x40983),x40985)))
% 179.72/179.58 [4099]E(f323(f323(f40(x40991,f867(x40992,a855)),x40993),f323(f323(f8(f867(x40992,a855),f867(x40992,a855),x40991),f323(f110(f867(x40992,a855)),x40994)),x40995)),f323(f323(f110(f867(x40992,a855)),x40994),f323(f323(f40(x40991,f867(x40992,a855)),x40993),x40995)))
% 179.72/179.58 [4135]E(f180(x41351,x41352,x41353,f323(f179(x41351,x41352),f323(f162(f866(x41351,x41352)),f323(f323(f175(x41351,x41352),x41354),x41355)))),f181(x41351,x41352,x41353,x41354,x41355))
% 179.72/179.58 [4157]E(f185(f861(x41571),f323(f323(f144(x41571),x41572),x41573),f323(f323(f8(f861(x41571),f861(x41571),a860),f323(f144(x41571),x41574)),f323(f323(f7(a860,x41571,f861(x41571)),f152(x41571,x41573)),x41572)),x41575),f323(f323(f152(x41571,f323(f323(f144(x41571),x41574),x41573)),x41575),x41572))
% 179.72/179.58 [4161]E(f323(f323(f39(x41611,f867(f866(x41612,x41613),a855)),x41614),f323(f323(f8(f867(f866(x41613,x41612),a855),f867(f866(x41612,x41613),a855),x41611),f278(x41613,x41612)),x41615)),f323(f278(x41613,x41612),f323(f323(f39(x41611,f867(f866(x41613,x41612),a855)),x41614),x41615)))
% 179.72/179.58 [4162]E(f323(f323(f40(x41621,f867(f866(x41622,x41623),a855)),x41624),f323(f323(f8(f867(f866(x41623,x41622),a855),f867(f866(x41622,x41623),a855),x41621),f278(x41623,x41622)),x41625)),f323(f278(x41623,x41622),f323(f323(f40(x41621,f867(f866(x41623,x41622),a855)),x41624),x41625)))
% 179.72/179.58 [4218]E(f177(x42181,x42182,f323(f323(f18(x42181,f864(x42183),f864(x42182)),f323(f323(f8(f867(x42183,x42182),f867(f864(x42183),f864(x42182)),x42181),f201(x42183,x42182)),x42184)),x42185)),f177(x42181,x42183,x42185))
% 179.72/179.58 [4269]P101(f323(f323(f237(f867(x42691,a855)),f323(f323(f22(f867(x42691,a855)),f323(f302(x42692,x42691,x42693),x42694)),f323(f302(x42692,x42691,x42693),x42695))),f323(f302(x42692,x42691,x42693),f323(f323(f22(f867(x42692,a855)),x42694),x42695))))
% 179.72/179.58 [4418]E(f323(f149(f861(f866(x44181,x44182)),x44181,f113(f866(x44181,x44182)),f323(f323(f7(x44181,f867(f861(x44181),f861(f866(x44181,x44182))),f867(f861(x44181),f861(f866(x44181,x44182)))),f323(f323(f8(f867(f861(f866(x44181,x44182)),f861(f866(x44181,x44182))),f867(f867(f861(x44181),f861(f866(x44181,x44182))),f867(f861(x44181),f861(f866(x44181,x44182)))),x44181),f8(f861(f866(x44181,x44182)),f861(f866(x44181,x44182)),f861(x44181))),f323(f323(f8(f866(x44181,x44182),f867(f861(f866(x44181,x44182)),f861(f866(x44181,x44182))),x44181),f144(f866(x44181,x44182))),f323(f323(f7(x44181,x44182,f866(x44181,x44182)),f258(x44181,x44182)),x44183)))),f323(f323(f7(f861(x44181),f861(x44182),f861(f866(x44181,x44182))),f175(x44181,x44182)),x44184))),x44185),f323(f323(f175(x44181,x44182),x44185),f323(f323(f144(x44182),x44183),x44184)))
% 179.72/179.58 [4123]E(f323(f323(f110(f867(x41231,a855)),f323(f277(x41232,x41231,x41233),x41234)),f323(f277(x41232,x41231,x41235),x41234)),f323(f277(x41232,x41231,f323(f323(f110(f867(f866(x41232,x41231),a855)),x41233),x41235)),x41234))
% 179.72/179.58 [4164]E(f323(f323(f121(f866(x41641,x41642)),f323(f323(f175(x41641,x41642),x41643),f323(f323(f169(x41642),f323(f189(f861(x41641)),x41643)),x41644))),f323(f323(f175(x41641,x41642),x41645),f323(f323(f131(x41642),f323(f189(f861(x41641)),x41643)),x41644))),f323(f323(f175(x41641,x41642),f323(f323(f121(x41641),x41643),x41645)),x41644))
% 179.72/179.58 [4272]E(f323(f323(f260(x42721,x42722),x42723),f323(f323(f18(x42721,f867(x42722,a855),f867(x42722,a855)),f323(f323(f8(f867(x42722,a855),f867(f867(x42722,a855),f867(x42722,a855)),x42721),f110(f867(x42722,a855))),x42724)),x42725)),f323(f323(f110(f867(f866(x42721,x42722),a855)),f323(f323(f260(x42721,x42722),x42723),x42724)),f323(f323(f260(x42721,x42722),x42723),x42725)))
% 179.72/179.58 [4273]E(f323(f323(f260(x42731,x42732),x42733),f323(f323(f18(x42731,f867(x42732,a855),f867(x42732,a855)),f323(f323(f8(f867(x42732,a855),f867(f867(x42732,a855),f867(x42732,a855)),x42731),f22(f867(x42732,a855))),x42734)),x42735)),f323(f323(f22(f867(f866(x42731,x42732),a855)),f323(f323(f260(x42731,x42732),x42733),x42734)),f323(f323(f260(x42731,x42732),x42733),x42735)))
% 179.72/179.58 [4274]E(f323(f323(f260(x42741,x42742),x42743),f323(f323(f18(x42741,f867(x42742,a855),f867(x42742,a855)),f323(f323(f8(f867(x42742,a855),f867(f867(x42742,a855),f867(x42742,a855)),x42741),f101(f867(x42742,a855))),x42744)),x42745)),f323(f323(f101(f867(f866(x42741,x42742),a855)),f323(f323(f260(x42741,x42742),x42743),x42744)),f323(f323(f260(x42741,x42742),x42743),x42745)))
% 179.72/179.58 [4278]E(f323(f323(f39(x42781,f867(x42782,a855)),x42783),f323(f323(f7(x42781,f867(x42782,a855),f867(x42782,a855)),f323(f323(f8(f867(x42782,a855),f867(f867(x42782,a855),f867(x42782,a855)),x42781),f22(f867(x42782,a855))),x42784)),x42785)),f323(f323(f22(f867(x42782,a855)),f323(f323(f39(x42781,f867(x42782,a855)),x42783),x42784)),x42785))
% 179.72/179.58 [4279]E(f323(f323(f39(x42791,f867(x42792,a855)),x42793),f323(f323(f7(x42791,f867(x42792,a855),f867(x42792,a855)),f323(f323(f8(f867(x42792,a855),f867(f867(x42792,a855),f867(x42792,a855)),x42791),f101(f867(x42792,a855))),x42794)),x42795)),f323(f323(f101(f867(x42792,a855)),f323(f323(f39(x42791,f867(x42792,a855)),x42793),x42794)),x42795))
% 179.72/179.58 [4280]E(f323(f323(f40(x42801,f867(x42802,a855)),x42803),f323(f323(f7(x42801,f867(x42802,a855),f867(x42802,a855)),f323(f323(f8(f867(x42802,a855),f867(f867(x42802,a855),f867(x42802,a855)),x42801),f110(f867(x42802,a855))),x42804)),x42805)),f323(f323(f110(f867(x42802,a855)),f323(f323(f40(x42801,f867(x42802,a855)),x42803),x42804)),x42805))
% 179.72/179.58 [4284]E(f323(f323(f39(x42841,f867(x42842,a855)),x42843),f323(f323(f18(x42841,f867(x42842,a855),f867(x42842,a855)),f323(f323(f8(f867(x42842,a855),f867(f867(x42842,a855),f867(x42842,a855)),x42841),f110(f867(x42842,a855))),x42844)),x42845)),f323(f323(f110(f867(x42842,a855)),f323(f323(f39(x42841,f867(x42842,a855)),x42843),x42844)),f323(f323(f39(x42841,f867(x42842,a855)),x42843),x42845)))
% 179.72/179.58 [4285]E(f323(f323(f40(x42851,f867(x42852,a855)),x42853),f323(f323(f18(x42851,f867(x42852,a855),f867(x42852,a855)),f323(f323(f8(f867(x42852,a855),f867(f867(x42852,a855),f867(x42852,a855)),x42851),f101(f867(x42852,a855))),x42854)),x42855)),f323(f323(f101(f867(x42852,a855)),f323(f323(f40(x42851,f867(x42852,a855)),x42853),x42854)),f323(f323(f40(x42851,f867(x42852,a855)),x42853),x42855)))
% 179.72/179.58 [4299]E(f323(f323(f39(x42991,f867(x42992,a855)),x42993),f323(f323(f18(x42991,f867(x42992,a855),f867(x42992,a855)),f323(f323(f8(f867(x42992,a855),f867(f867(x42992,a855),f867(x42992,a855)),x42991),f110(f867(x42992,a855))),x42994)),x42995)),f323(f323(f110(f867(x42992,a855)),f37(f867(x42992,a855),f323(f302(x42991,f867(x42992,a855),x42994),x42993))),f37(f867(x42992,a855),f323(f302(x42991,f867(x42992,a855),x42995),x42993))))
% 179.72/179.58 [4300]E(f323(f323(f40(x43001,f867(x43002,a855)),x43003),f323(f323(f18(x43001,f867(x43002,a855),f867(x43002,a855)),f323(f323(f8(f867(x43002,a855),f867(f867(x43002,a855),f867(x43002,a855)),x43001),f101(f867(x43002,a855))),x43004)),x43005)),f323(f323(f101(f867(x43002,a855)),f38(f867(x43002,a855),f323(f302(x43001,f867(x43002,a855),x43004),x43003))),f38(f867(x43002,a855),f323(f302(x43001,f867(x43002,a855),x43005),x43003))))
% 179.72/179.58 [4335]E(f323(f323(f131(x43351),f323(f189(f861(x43351)),f171(x43351,x43352,f323(f323(f147(x43353,x43351),x43354),x43355)))),f323(f323(f147(x43353,x43351),x43354),x43355)),f323(f323(f147(x43353,x43351),x43354),f323(f323(f131(x43353),f323(f189(f861(x43353)),f171(x43353,f323(f71(x43351,a855,x43353,x43352),x43354),x43355))),x43355)))
% 179.72/179.58 [4208]E(f323(f323(f121(f866(x42081,x42082)),f323(f323(f175(x42081,x42082),f323(f323(f169(x42081),f323(f189(f861(x42082)),x42083)),x42084)),x42083)),f323(f323(f175(x42081,x42082),f323(f323(f131(x42081),f323(f189(f861(x42082)),x42083)),x42084)),x42085)),f323(f323(f175(x42081,x42082),x42084),f323(f323(f121(x42082),x42083),x42085)))
% 179.72/179.58 [4326]E(f83(x43261,f323(f323(f18(x43261,a855,a855),f323(f323(f8(a855,f867(a855,a855),x43261),a321),f323(f323(f7(x43261,f867(x43261,a855),a855),f325(x43261)),x43262))),f323(f323(f7(x43261,x43263,a855),f323(f323(f8(x43263,f867(x43263,a855),x43261),a320),x43264)),x43265))),f323(f75(x43261,x43263,x43262,x43264),x43265))
% 179.72/179.58 [4327]E(f88(x43271,f323(f323(f18(x43271,a855,a855),f323(f323(f8(a855,f867(a855,a855),x43271),a321),f323(f323(f7(x43271,f867(x43271,a855),a855),f325(x43271)),x43272))),f323(f323(f7(x43271,x43273,a855),f323(f323(f8(x43273,f867(x43273,a855),x43271),a320),x43274)),x43275))),f323(f91(x43271,x43273,x43272,x43274),x43275))
% 179.72/179.58 [4379]E(f323(f323(f84(a1,x43791),f323(f103(a1),f323(f323(f78(a1),x43792),a97))),f323(f323(f18(a1,x43791,x43791),f323(f323(f7(a1,x43791,f867(x43791,x43791)),f323(f323(f8(a855,f867(x43791,f867(x43791,x43791)),a1),f96(x43791)),a193)),f185(x43791,x43793,x43794,x43795))),f323(f323(f8(a860,x43791,a1),x43794),f323(f323(f7(a1,a860,a860),f323(f323(f8(a860,f867(a860,a860),a1),f78(a860)),a104)),x43795)))),f185(x43791,x43793,x43794,f323(f323(f78(a860),f323(f103(a860),x43792)),x43795)))
% 179.72/179.58 [4415]E(f323(f179(x44151,x44152),f323(f323(f147(f866(x44151,x44153),f866(x44151,x44152)),f323(f262(x44151,x44153,f866(x44151,x44152)),f323(f323(f7(x44151,f867(x44153,x44152),f867(x44153,f866(x44151,x44152))),f323(f323(f8(f867(x44152,f866(x44151,x44152)),f867(f867(x44153,x44152),f867(x44153,f866(x44151,x44152))),x44151),f8(x44152,f866(x44151,x44152),x44153)),f258(x44151,x44152))),x44154))),x44155)),f323(f71(f864(x44153),f864(x44152),x44151,f323(f201(x44153,x44152),x44154)),f323(f179(x44151,x44153),x44155)))
% 179.72/179.58 [4372]E(f177(x43721,x43722,f323(f323(f18(x43721,f864(x43722),f864(x43722)),f323(f323(f18(x43721,f864(x43722),f867(f864(x43722),f864(x43722))),f323(f323(f8(a855,f867(f864(x43722),f867(f864(x43722),f864(x43722))),x43721),f96(f864(x43722))),x43723)),x43724)),x43725)),f323(f323(f110(f867(x43721,a855)),f323(f323(f101(f867(x43721,a855)),f177(x43721,x43722,x43724)),f323(f243(x43721),x43723))),f323(f323(f101(f867(x43721,a855)),f177(x43721,x43722,x43725)),f323(f243(x43721),f323(f323(f8(a855,a855,x43721),a318),x43723)))))
% 179.72/179.58 [4413]E(f323(f323(f84(a1,x44131),f323(f103(a1),f323(f323(f78(a1),x44132),a97))),f323(f323(f18(a1,x44131,x44131),f323(f323(f7(a1,x44131,f867(x44131,x44131)),f323(f323(f8(a855,f867(x44131,f867(x44131,x44131)),a1),f96(x44131)),a193)),f323(f184(x44131,x44133,x44134),x44135))),f323(f323(f18(a1,x44131,x44131),f323(f323(f8(a860,f867(x44131,x44131),a1),x44134),f323(f323(f7(a1,a860,a860),f323(f323(f8(a860,f867(a860,a860),a1),f78(a860)),a104)),x44135))),f323(f323(f8(a860,x44131,a1),f184(x44131,x44133,x44134)),f323(f323(f7(a1,a860,a860),f323(f323(f8(a860,f867(a860,a860),a1),f78(a860)),a104)),x44135))))),f323(f184(x44131,x44133,x44134),f323(f323(f78(a860),f323(f103(a860),x44132)),x44135)))
% 179.72/179.58 [4455]E(f323(f243(f866(x44551,x44552)),f323(f262(x44551,x44552,a855),f323(f323(f8(f867(x44552,f867(x44553,a855)),f867(x44552,a855),x44551),f323(f8(f867(x44553,a855),a855,x44552),f85(x44553))),f323(f323(f7(x44551,f867(x44552,f867(x44553,a855)),f867(x44552,f867(x44553,a855))),f323(f323(f8(f867(f867(x44553,a855),f867(x44553,a855)),f867(f867(x44552,f867(x44553,a855)),f867(x44552,f867(x44553,a855))),x44551),f8(f867(x44553,a855),f867(x44553,a855),x44552)),f323(f323(f8(f867(x44553,f867(a855,a855)),f867(f867(x44553,a855),f867(x44553,a855)),x44551),f18(x44553,a855,a855)),f323(f323(f8(f867(x44553,a855),f867(x44553,f867(a855,a855)),x44551),f323(f8(a855,f867(a855,a855),x44553),a321)),f323(f323(f7(x44551,f867(f866(x44551,x44553),a855),f867(x44553,a855)),f323(f323(f8(f867(x44553,f867(f867(f866(x44551,x44553),a855),a855)),f867(f867(f866(x44551,x44553),a855),f867(x44553,a855)),x44551),f7(x44553,f867(f866(x44551,x44553),a855),a855)),f323(f323(f8(f867(x44553,f866(x44551,x44553)),f867(x44553,f867(f867(f866(x44551,x44553),a855),a855)),x44551),f323(f8(f866(x44551,x44553),f867(f867(f866(x44551,x44553),a855),a855),x44553),f325(f866(x44551,x44553)))),f258(x44551,x44553)))),x44554))))),f323(f323(f7(x44552,f867(f866(x44553,x44552),a855),f867(x44553,a855)),f323(f323(f8(f867(x44553,f867(f867(f866(x44553,x44552),a855),a855)),f867(f867(f866(x44553,x44552),a855),f867(x44553,a855)),x44552),f7(x44553,f867(f866(x44553,x44552),a855),a855)),f323(f323(f8(f867(x44553,f866(x44553,x44552)),f867(x44553,f867(f867(f866(x44553,x44552),a855),a855)),x44552),f323(f8(f866(x44553,x44552),f867(f867(f866(x44553,x44552),a855),a855),x44553),f325(f866(x44553,x44552)))),f323(f7(x44553,x44552,f866(x44553,x44552)),f258(x44553,x44552))))),x44555))))),f323(f323(f280(x44551,x44553,x44552),x44554),x44555))
% 179.72/179.58 [4531]~E(f26(x45311,x45312,x45313),f27(x45314,x45315,x45316))
% 179.72/179.58 [3976]E(f126(x39761,x39762,x39763,x39764,f123(x39762,x39765,x39766)),f323(f323(x39764,x39765),x39766))
% 179.72/179.58 [4192]E(f181(x41921,x41922,f180(x41921,x41922,x41923,x41924),x41925,x41926),f180(x41921,x41922,x41923,f181(x41921,x41922,x41924,x41925,x41926)))
% 179.72/179.58 [4315]E(f323(f71(f866(x43151,x43152),x43152,f866(x43153,x43154),f261(x43151,x43152)),f263(x43153,x43151,x43154,x43152,x43155,x43156)),f323(f71(x43154,x43152,f866(x43153,x43154),x43156),f261(x43153,x43154)))
% 179.72/179.58 [4316]E(f323(f71(f866(x43161,x43162),x43161,f866(x43163,x43164),f257(x43161,x43162)),f263(x43163,x43161,x43164,x43162,x43165,x43166)),f323(f71(x43163,x43161,f866(x43163,x43164),x43165),f257(x43163,x43164)))
% 179.72/179.58 [3914]E(f323(f323(f71(x39141,x39142,x39143,x39144),x39145),x39146),f323(x39144,f323(x39145,x39146)))
% 179.72/179.58 [3707]E(f323(f323(f262(x37071,x37072,x37073),x37074),f323(f323(f258(x37071,x37072),x37075),x37076)),f323(f323(x37074,x37075),x37076))
% 179.72/179.58 [3769]E(f323(f323(f323(f8(x37691,x37692,x37693),x37694),x37695),x37696),f323(x37694,f323(x37695,x37696)))
% 179.72/179.58 [3770]E(f323(f323(f323(f7(x37701,x37702,x37703),x37704),x37705),x37706),f323(f323(x37704,x37706),x37705))
% 179.72/179.58 [3787]E(f323(f323(f323(f18(x37871,x37872,x37873),x37874),x37875),x37876),f323(f323(x37874,x37876),f323(x37875,x37876)))
% 179.72/179.58 [3809]E(f323(f149(x38091,x38092,x38093,x38094),f323(f323(f144(x38092),x38095),x38096)),f323(f323(x38094,x38095),x38096))
% 179.72/179.58 [3850]E(f163(f866(x38501,x38502),f323(f323(f235(a860),x38503),x38504),f323(f323(f258(x38501,x38502),x38505),x38506)),f323(f323(f175(x38501,x38502),f163(x38501,x38503,x38505)),f163(x38502,x38504,x38506)))
% 179.72/179.58 [3918]E(f323(f323(f144(f866(x39181,x39182)),f323(f323(f258(x39181,x39182),x39183),x39184)),f323(f323(f175(x39181,x39182),x39185),x39186)),f323(f323(f175(x39181,x39182),f323(f323(f144(x39181),x39183),x39185)),f323(f323(f144(x39182),x39184),x39186)))
% 179.72/179.58 [3920]E(f323(f323(f147(x39201,x39202),x39203),f323(f323(f152(x39201,x39204),x39205),x39206)),f323(f323(f152(x39202,f323(f323(f147(x39201,x39202),x39203),x39204)),x39205),f323(x39203,x39206)))
% 179.72/179.58 [3964]E(f323(f135(x39641,x39642,x39643,x39644),f323(f323(f144(x39642),x39645),x39646)),f323(f135(x39641,x39642,x39643,f323(f323(x39643,x39644),x39645)),x39646))
% 179.72/179.58 [3992]E(f265(x39921,x39922,x39923,x39924,f323(f323(f258(x39921,x39922),x39925),x39926)),f323(f323(x39924,x39925),x39926))
% 179.72/179.58 [4075]E(f323(f323(f39(x40751,f867(x40752,a855)),x40753),f323(f71(x40754,f867(x40752,a855),x40751,x40755),x40756)),f323(f323(f39(x40754,f867(x40752,a855)),f323(f302(x40751,x40754,x40756),x40753)),x40755))
% 179.72/179.58 [4126]E(f323(f323(f201(x41261,x41262),x41263),f323(f323(f201(x41264,x41261),x41265),x41266)),f323(f323(f201(x41264,x41262),f323(f71(x41261,x41262,x41264,x41263),x41265)),x41266))
% 179.72/179.58 [4128]E(f323(f323(f147(x41281,x41282),x41283),f323(f323(f147(x41284,x41281),x41285),x41286)),f323(f323(f147(x41284,x41282),f323(f71(x41281,x41282,x41284,x41283),x41285)),x41286))
% 179.72/179.58 [4133]E(f323(f302(x41331,x41332,f323(f71(x41333,x41332,x41331,x41334),x41335)),x41336),f323(f302(x41333,x41332,x41334),f323(f302(x41331,x41333,x41335),x41336)))
% 179.72/179.58 [4134]E(f323(f303(x41341,x41342,f323(f71(x41343,x41342,x41341,x41344),x41345)),x41346),f323(f303(x41341,x41343,x41345),f323(f303(x41343,x41342,x41344),x41346)))
% 179.72/179.58 [4163]E(f180(x41631,x41632,x41633,f323(f323(f323(f70(x41631,f864(x41632)),x41634),x41635),f323(f230(x41632),x41636))),f323(f323(f323(f70(x41631,f864(x41632)),f180(x41631,x41632,x41633,x41634)),x41635),f323(f230(x41632),x41636)))
% 179.72/179.58 [4165]E(f323(f135(x41651,x41652,x41653,f323(f135(x41651,x41652,x41653,x41654),x41655)),x41656),f323(f135(x41651,x41652,x41653,x41654),f323(f323(f121(x41652),x41655),x41656)))
% 179.72/179.58 [4305]E(f323(f263(x43051,x43051,x43052,x43053,f32(x43051),x43054),f323(f323(f258(x43051,x43052),x43055),x43056)),f323(f323(f258(x43051,x43053),x43055),f323(x43054,x43056)))
% 179.72/179.58 [4306]E(f323(f263(x43061,x43062,x43063,x43063,x43064,f32(x43063)),f323(f323(f258(x43061,x43063),x43065),x43066)),f323(f323(f258(x43062,x43063),f323(x43064,x43065)),x43066))
% 179.72/179.58 [4397]E(f323(f323(f147(f866(x43971,x43972),f866(x43971,x43973)),f323(f262(x43971,x43972,f866(x43971,x43973)),f323(f323(f7(x43971,f867(x43972,x43973),f867(x43972,f866(x43971,x43973))),f323(f323(f8(f867(x43973,f866(x43971,x43973)),f867(f867(x43972,x43973),f867(x43972,f866(x43971,x43973))),x43971),f8(x43973,f866(x43971,x43973),x43972)),f258(x43971,x43973))),x43974))),f323(f323(f175(x43971,x43972),x43975),x43976)),f323(f323(f175(x43971,x43973),x43975),f323(f323(f147(x43972,x43973),x43974),x43976)))
% 179.72/179.58 [3774]E(f94(x37741,x37742,x37743,f323(f323(f323(f90(x37741),x37744),x37745),x37746)),f323(f323(f323(x37743,x37744),x37745),x37746))
% 179.72/179.58 [3775]E(f95(x37751,x37752,x37753,f323(f323(f323(f90(x37751),x37754),x37755),x37756)),f323(f323(f323(x37753,x37754),x37755),x37756))
% 179.72/179.58 [3975]E(f323(f323(f71(x39751,x39752,x39753,f323(f16(x39752,x39751),x39754)),x39755),x39756),x39754)
% 179.72/179.58 [4011]E(f323(f302(x40111,x40112,x40113),f323(f302(x40114,x40111,x40115),x40116)),f323(f302(x40114,x40112,f323(f323(f8(x40111,x40112,x40114),x40113),x40115)),x40116))
% 179.72/179.58 [4017]E(f323(f323(f39(x40171,f867(x40172,a855)),f323(f302(x40173,x40171,x40174),x40175)),x40176),f323(f323(f39(x40173,f867(x40172,a855)),x40175),f323(f323(f8(x40171,f867(x40172,a855),x40173),x40176),x40174)))
% 179.72/179.58 [4018]E(f323(f323(f40(x40181,f867(x40182,a855)),f323(f302(x40183,x40181,x40184),x40185)),x40186),f323(f323(f40(x40183,f867(x40182,a855)),x40185),f323(f323(f8(x40181,f867(x40182,a855),x40183),x40186),x40184)))
% 179.72/179.58 [4019]E(f323(f323(f39(x40191,f867(x40192,a855)),x40193),f323(f323(f8(x40194,f867(x40192,a855),x40191),x40195),x40196)),f323(f323(f39(x40194,f867(x40192,a855)),f323(f302(x40191,x40194,x40196),x40193)),x40195))
% 179.72/179.58 [4020]E(f323(f323(f40(x40201,f867(x40202,a855)),x40203),f323(f323(f8(x40204,f867(x40202,a855),x40201),x40205),x40206)),f323(f323(f40(x40204,f867(x40202,a855)),f323(f302(x40201,x40204,x40206),x40203)),x40205))
% 179.72/179.58 [4077]E(f323(f323(f39(x40771,f867(x40772,a855)),x40773),f323(f323(f8(f867(x40774,a855),f867(x40772,a855),x40771),f302(x40774,x40772,x40775)),x40776)),f323(f302(x40774,x40772,x40775),f323(f323(f39(x40771,f867(x40774,a855)),x40773),x40776)))
% 179.72/179.58 [4078]E(f323(f323(f39(x40781,f867(x40782,a855)),x40783),f323(f323(f8(f867(x40784,a855),f867(x40782,a855),x40781),f303(x40782,x40784,x40785)),x40786)),f323(f303(x40782,x40784,x40785),f323(f323(f39(x40781,f867(x40784,a855)),x40783),x40786)))
% 179.72/179.58 [4079]E(f323(f323(f40(x40791,f867(x40792,a855)),x40793),f323(f323(f8(f867(x40794,a855),f867(x40792,a855),x40791),f303(x40792,x40794,x40795)),x40796)),f323(f303(x40792,x40794,x40795),f323(f323(f40(x40791,f867(x40794,a855)),x40793),x40796)))
% 179.72/179.58 [4080]E(f323(f323(f39(x40801,f867(x40802,a855)),x40803),f323(f323(f8(f867(x40804,a855),f867(x40802,a855),x40801),f277(x40804,x40802,x40805)),x40806)),f323(f277(x40804,x40802,x40805),f323(f323(f39(x40801,f867(x40804,a855)),x40803),x40806)))
% 179.72/179.58 [4171]E(f323(f135(x41711,x41712,f323(f7(x41712,x41711,x41711),x41713),x41714),f323(f162(x41712),f323(f323(f144(x41712),x41715),x41716))),f323(f323(x41713,x41715),f323(f135(x41711,x41712,f323(f7(x41712,x41711,x41711),x41713),x41714),f323(f162(x41712),x41716))))
% 179.72/179.58 [4231]E(f323(f323(f18(f866(x42311,x42312),x42312,x42313),f323(f323(f8(x42314,f867(x42312,x42313),f866(x42311,x42312)),x42315),f323(f323(f8(x42311,x42314,f866(x42311,x42312)),x42316),f257(x42311,x42312)))),f261(x42311,x42312)),f323(f262(x42311,x42312,x42313),f323(f323(f8(x42314,f867(x42312,x42313),x42311),x42315),x42316)))
% 179.72/179.58 [4238]E(f323(f135(x42381,x42382,f323(f7(x42382,x42381,x42381),x42383),f323(f135(x42381,x42382,f323(f7(x42382,x42381,x42381),x42383),x42384),f323(f162(x42382),x42385))),f323(f162(x42382),x42386)),f323(f135(x42381,x42382,f323(f7(x42382,x42381,x42381),x42383),x42384),f323(f162(x42382),f323(f323(f121(x42382),x42386),x42385))))
% 179.72/179.58 [4240]E(f323(f323(f147(f866(x42401,x42402),f866(x42403,x42402)),f323(f262(x42401,x42402,f866(x42403,x42402)),f323(f323(f8(x42403,f867(x42402,f866(x42403,x42402)),x42401),f258(x42403,x42402)),x42404))),f323(f323(f175(x42401,x42402),x42405),x42406)),f323(f323(f175(x42403,x42402),f323(f323(f147(x42401,x42403),x42404),x42405)),x42406))
% 179.72/179.58 [4288]P101(f323(f323(f237(f867(x42881,a855)),f323(f277(x42882,x42881,x42883),f323(f323(f40(x42884,f867(x42882,a855)),x42885),x42886))),f323(f323(f40(x42884,f867(x42881,a855)),x42885),f323(f323(f8(f867(x42882,a855),f867(x42881,a855),x42884),f277(x42882,x42881,x42883)),x42886))))
% 179.72/179.58 [4090]E(f323(f323(f175(x40901,x40902),f323(f323(f152(x40901,x40903),x40904),f323(f257(x40901,x40902),x40905))),f323(f323(f152(x40902,x40906),x40904),f323(f261(x40901,x40902),x40905))),f323(f323(f152(f866(x40901,x40902),f323(f323(f175(x40901,x40902),x40903),x40906)),x40904),x40905))
% 179.72/179.58 [4152]E(f323(f323(f110(f867(f866(x41521,x41522),a855)),f323(f323(f280(x41521,x41523,x41522),x41524),x41525)),f323(f323(f280(x41521,x41523,x41522),x41524),x41526)),f323(f323(f280(x41521,x41523,x41522),x41524),f323(f323(f110(f867(f866(x41523,x41522),a855)),x41525),x41526)))
% 179.72/179.58 [4251]E(f323(f323(f301(f866(x42511,x42512)),f323(f323(f258(x42511,x42512),x42513),x42514)),f323(f323(f110(f867(f866(x42511,x42512),a855)),f323(f323(f260(x42511,x42512),x42515),f323(f16(f867(x42512,a855),x42511),f323(f323(f301(x42512),x42514),x42516)))),f323(f323(f260(x42511,x42512),f323(f323(f301(x42511),x42513),x42515)),f323(f16(f867(x42512,a855),x42511),x42516)))),f323(f323(f260(x42511,x42512),f323(f323(f301(x42511),x42513),x42515)),f323(f16(f867(x42512,a855),x42511),f323(f323(f301(x42512),x42514),x42516))))
% 179.72/179.58 [4330]E(f323(f323(f101(f867(x43301,a855)),f323(f303(x43301,x43302,f323(f71(f866(x43302,x43303),x43302,x43301,f257(x43302,x43303)),x43304)),x43305)),f323(f303(x43301,x43303,f323(f71(f866(x43302,x43303),x43303,x43301,f261(x43302,x43303)),x43304)),x43306)),f323(f303(x43301,f866(x43302,x43303),x43304),f323(f323(f260(x43302,x43303),x43305),f323(f16(f867(x43303,a855),x43302),x43306))))
% 179.72/179.58 [4074]E(f323(f323(f323(f70(x40741,x40742),f323(f323(f323(f70(x40741,x40742),x40743),x40744),x40745)),x40744),x40746),f323(f323(f323(f70(x40741,x40742),x40743),x40744),x40746))
% 179.72/179.58 [4177]E(f323(f323(f110(f867(f866(x41771,x41772),a855)),f323(f323(f280(x41771,x41773,x41772),x41774),x41775)),f323(f323(f280(x41771,x41773,x41772),x41776),x41775)),f323(f323(f280(x41771,x41773,x41772),f323(f323(f110(f867(f866(x41771,x41773),a855)),x41774),x41776)),x41775))
% 179.72/179.58 [4313]E(f323(f323(f39(x43131,f867(x43132,a855)),x43133),f323(f323(f7(x43131,f867(x43134,f867(x43132,a855)),f867(x43132,a855)),f323(f323(f8(f867(x43134,a855),f867(f867(x43134,f867(x43132,a855)),f867(x43132,a855)),x43131),f39(x43134,f867(x43132,a855))),x43135)),x43136)),f323(f323(f39(x43134,f867(x43132,a855)),f323(f323(f39(x43131,f867(x43134,a855)),x43133),x43135)),x43136))
% 179.72/179.58 [4314]E(f323(f323(f40(x43141,f867(x43142,a855)),x43143),f323(f323(f7(x43141,f867(x43144,f867(x43142,a855)),f867(x43142,a855)),f323(f323(f8(f867(x43144,a855),f867(f867(x43144,f867(x43142,a855)),f867(x43142,a855)),x43141),f40(x43144,f867(x43142,a855))),x43145)),x43146)),f323(f323(f40(x43144,f867(x43142,a855)),f323(f323(f39(x43141,f867(x43144,a855)),x43143),x43145)),x43146))
% 179.72/179.58 [4367]E(f323(f262(x43671,x43672,f866(x43673,x43674)),f323(f323(f7(x43671,f867(x43672,x43674),f867(x43672,f866(x43673,x43674))),f323(f323(f8(f867(x43674,f866(x43673,x43674)),f867(f867(x43672,x43674),f867(x43672,f866(x43673,x43674))),x43671),f8(x43674,f866(x43673,x43674),x43672)),f323(f323(f8(x43673,f867(x43674,f866(x43673,x43674)),x43671),f258(x43673,x43674)),x43675))),x43676)),f263(x43671,x43673,x43672,x43674,x43675,x43676))
% 179.72/179.58 [4287]E(f323(f323(f323(f70(x42871,f864(x42872)),f182(x42871,x42872,x42873,f323(f323(f22(f867(x42871,a855)),x42874),f323(f323(f301(x42871),x42875),f188(f867(x42871,a855)))))),x42875),x42876),f323(f323(f323(f70(x42871,f864(x42872)),f182(x42871,x42872,x42873,x42874)),x42875),x42876))
% 179.72/179.58 [4392]E(f323(f302(x43921,x43922,f323(f323(f18(x43921,x43922,x43922),f323(f323(f18(x43921,x43922,f867(x43922,x43922)),f323(f323(f8(a855,f867(x43922,f867(x43922,x43922)),x43921),f96(x43922)),x43923)),x43924)),x43925)),x43926),f323(f323(f110(f867(x43922,a855)),f323(f302(x43921,x43922,x43924),f323(f323(f101(f867(x43921,a855)),x43926),f323(f243(x43921),x43923)))),f323(f302(x43921,x43922,x43925),f323(f323(f101(f867(x43921,a855)),x43926),f323(f243(x43921),f323(f323(f8(a855,a855,x43921),a318),x43923))))))
% 179.72/179.58 [4403]E(f323(f302(x44031,f866(x44032,x44033),f323(f323(f18(x44031,x44033,f866(x44032,x44033)),f323(f323(f8(x44032,f867(x44033,f866(x44032,x44033)),x44031),f258(x44032,x44033)),x44034)),x44035)),x44036),f323(f323(f260(x44032,x44033),f323(f302(x44031,x44032,x44034),x44036)),f323(f323(f8(f867(x44031,a855),f867(x44033,a855),x44032),f302(x44031,x44033,x44035)),f323(f323(f7(x44032,f867(x44031,a855),f867(x44031,a855)),f323(f323(f8(f867(x44031,a855),f867(f867(x44031,a855),f867(x44031,a855)),x44032),f101(f867(x44031,a855))),f323(f323(f8(f867(x44032,a855),f867(x44031,a855),x44032),f303(x44031,x44032,x44034)),f323(f323(f7(x44032,f867(x44032,a855),f867(x44032,a855)),f301(x44032)),f188(f867(x44032,a855)))))),x44036))))
% 179.72/179.58 [4349]E(f323(f261(x43491,x43492),f323(f263(x43493,x43491,x43494,x43492,x43495,x43496),x43497)),f323(x43496,f323(f261(x43493,x43494),x43497)))
% 179.72/179.58 [4350]E(f323(f257(x43501,x43502),f323(f263(x43503,x43501,x43504,x43502,x43505,x43506),x43507)),f323(x43505,f323(f257(x43503,x43504),x43507)))
% 179.72/179.58 [4052]E(f323(f323(f175(x40521,x40522),f323(f323(f152(x40521,x40523),x40524),x40525)),f323(f323(f152(x40522,x40526),x40524),x40527)),f323(f323(f152(f866(x40521,x40522),f323(f323(f175(x40521,x40522),x40523),x40526)),x40524),f323(f323(f258(x40521,x40522),x40525),x40527)))
% 179.72/179.58 [4120]E(f323(f323(f323(f264(x41201,x41202,x41203,x41204),x41205),x41206),x41207),f323(f323(f262(x41202,x41203,x41204),x41206),f323(x41205,x41207)))
% 179.72/179.58 [4132]E(f323(f323(f323(f264(x41321,x41322,x41323,x41324),x41325),x41326),x41327),f323(f323(x41326,f323(f257(x41322,x41323),f323(x41325,x41327))),f323(f261(x41322,x41323),f323(x41325,x41327))))
% 179.72/179.58 [4167]E(f181(x41671,x41672,f323(f323(f323(f70(x41671,f864(x41672)),x41673),x41674),f323(f230(x41672),x41675)),x41676,x41677),f181(x41671,x41672,x41673,f323(f323(f144(x41671),x41674),x41676),f323(f323(f144(x41672),x41675),x41677)))
% 179.72/179.58 [4186]E(f323(f71(x41861,x41862,x41863,x41864),f323(f71(x41865,x41861,x41863,x41866),x41867)),f323(f71(x41865,x41862,x41863,f323(f71(x41861,x41862,x41865,x41864),x41866)),x41867))
% 179.72/179.58 [4247]E(f323(f71(f864(x42471),f864(x42472),x42473,f323(f201(x42471,x42472),x42474)),f323(f323(f323(f70(x42473,f864(x42471)),x42475),x42476),f323(f230(x42471),x42477))),f323(f323(f323(f70(x42473,f864(x42472)),f323(f71(f864(x42471),f864(x42472),x42473,f323(f201(x42471,x42472),x42474)),x42475)),x42476),f323(f230(x42472),f323(x42474,x42477))))
% 179.72/179.58 [4374]E(f323(f263(x43741,x43742,x43743,x43743,x43744,f32(x43743)),f323(f263(x43741,x43741,x43745,x43743,f32(x43741),x43746),x43747)),f323(f323(f258(x43742,x43743),f323(x43744,f323(f257(x43741,x43745),x43747))),f323(x43746,f323(f261(x43741,x43745),x43747))))
% 179.72/179.58 [4375]E(f323(f263(x43751,x43751,x43752,x43753,f32(x43751),x43754),f323(f263(x43755,x43751,x43752,x43752,x43756,f32(x43752)),x43757)),f323(f323(f258(x43751,x43753),f323(x43756,f323(f257(x43755,x43752),x43757))),f323(x43754,f323(f261(x43755,x43752),x43757))))
% 179.72/179.58 [4390]E(f323(f263(x43901,x43902,x43903,x43903,x43904,f32(x43903)),f323(f263(x43905,x43901,x43903,x43903,x43906,f32(x43903)),x43907)),f323(f263(x43905,x43902,x43903,x43903,f323(f71(x43901,x43902,x43905,x43904),x43906),f32(x43903)),x43907))
% 179.72/179.58 [4391]E(f323(f263(x43911,x43911,x43912,x43913,f32(x43911),x43914),f323(f263(x43911,x43911,x43915,x43912,f32(x43911),x43916),x43917)),f323(f263(x43911,x43911,x43915,x43913,f32(x43911),f323(f71(x43912,x43913,x43915,x43914),x43916)),x43917))
% 179.72/179.58 [4400]E(f323(f263(x44001,x44002,x44003,x44003,x44004,f32(x44003)),f323(f263(x44001,x44001,x44005,x44003,f32(x44001),x44006),x44007)),f323(f263(x44002,x44002,x44005,x44003,f32(x44002),x44006),f323(f263(x44001,x44002,x44005,x44005,x44004,f32(x44005)),x44007)))
% 179.72/179.58 [4087]E(f323(f323(f280(x40871,x40872,x40873),f323(f323(f280(x40871,x40874,x40872),x40875),x40876)),x40877),f323(f323(f280(x40871,x40874,x40873),x40875),f323(f323(f280(x40874,x40872,x40873),x40876),x40877)))
% 179.72/179.58 [4158]E(f323(f323(f262(x41581,x41582,x41583),f323(f71(x41584,f867(x41582,x41583),x41581,x41585),x41586)),x41587),f323(f323(x41585,f323(x41586,f323(f257(x41581,x41582),x41587))),f323(f261(x41581,x41582),x41587)))
% 179.72/179.58 [4211]E(f323(f71(x42111,x42112,x42113,x42114),f323(f323(f323(f70(x42113,x42111),x42115),x42116),x42117)),f323(f323(f323(f70(x42113,x42112),f323(f71(x42111,x42112,x42113,x42114),x42115)),x42116),f323(x42114,x42117)))
% 179.72/179.58 [4243]E(f323(f135(x42431,x42432,f323(f7(x42432,x42431,x42431),x42433),x42434),f323(f162(x42432),f323(f323(f147(x42435,x42432),x42436),x42437))),f323(f135(x42431,x42435,f323(f7(x42435,x42431,x42431),f323(f71(x42432,f867(x42431,x42431),x42435,x42433),x42436)),x42434),f323(f162(x42435),x42437)))
% 179.72/179.58 [4187]E(f323(f323(f39(x41871,f867(f866(x41872,x41873),a855)),x41874),f323(f323(f8(f867(f866(x41875,x41873),a855),f867(f866(x41872,x41873),a855),x41871),f323(f280(x41872,x41875,x41873),x41876)),x41877)),f323(f323(f280(x41872,x41875,x41873),x41876),f323(f323(f39(x41871,f867(f866(x41875,x41873),a855)),x41874),x41877)))
% 179.72/179.58 [4336]E(f323(f323(f39(x43361,f867(f866(x43362,x43363),a855)),x43364),f323(f323(f7(x43361,f867(f866(x43365,x43363),a855),f867(f866(x43362,x43363),a855)),f323(f323(f8(f867(f866(x43362,x43365),a855),f867(f867(f866(x43365,x43363),a855),f867(f866(x43362,x43363),a855)),x43361),f280(x43362,x43365,x43363)),x43366)),x43367)),f323(f323(f280(x43362,x43365,x43363),f323(f323(f39(x43361,f867(f866(x43362,x43365),a855)),x43364),x43366)),x43367))
% 179.72/179.58 [4337]E(f323(f135(x43371,x43372,f323(f323(f7(x43371,f867(x43372,x43373),f867(x43372,x43371)),f323(f323(f8(f867(x43373,x43371),f867(f867(x43372,x43373),f867(x43372,x43371)),x43371),f8(x43373,x43371,x43372)),x43374)),x43375),x43376),x43377),f323(f135(x43371,x43373,x43374,x43376),f323(f323(f147(x43372,x43373),x43375),x43377)))
% 179.72/179.58 [4401]E(f323(f323(f40(x44011,f867(x44012,a855)),x44013),f323(f323(f8(f867(x44014,f867(x44012,a855)),f867(x44012,a855),x44011),f323(f40(x44014,f867(x44012,a855)),x44015)),f323(f323(f7(x44011,f867(x44014,f867(x44012,a855)),f867(x44014,f867(x44012,a855))),f323(f323(f8(f867(f867(x44012,a855),f867(x44012,a855)),f867(f867(x44014,f867(x44012,a855)),f867(x44014,f867(x44012,a855))),x44011),f8(f867(x44012,a855),f867(x44012,a855),x44014)),f323(f323(f8(f867(x44012,a855),f867(f867(x44012,a855),f867(x44012,a855)),x44011),f110(f867(x44012,a855))),x44016))),x44017))),f323(f323(f110(f867(x44012,a855)),f323(f323(f40(x44011,f867(x44012,a855)),x44013),x44016)),f323(f323(f40(x44014,f867(x44012,a855)),x44015),x44017)))
% 179.72/179.58 [4402]E(f323(f323(f39(x44021,f867(x44022,a855)),x44023),f323(f323(f8(f867(x44024,f867(x44022,a855)),f867(x44022,a855),x44021),f323(f39(x44024,f867(x44022,a855)),x44025)),f323(f323(f7(x44021,f867(x44024,f867(x44022,a855)),f867(x44024,f867(x44022,a855))),f323(f323(f8(f867(f867(x44022,a855),f867(x44022,a855)),f867(f867(x44024,f867(x44022,a855)),f867(x44024,f867(x44022,a855))),x44021),f8(f867(x44022,a855),f867(x44022,a855),x44024)),f323(f323(f8(f867(x44022,a855),f867(f867(x44022,a855),f867(x44022,a855)),x44021),f101(f867(x44022,a855))),x44026))),x44027))),f323(f323(f101(f867(x44022,a855)),f323(f323(f39(x44021,f867(x44022,a855)),x44023),x44026)),f323(f323(f39(x44024,f867(x44022,a855)),x44025),x44027)))
% 179.72/179.58 [4395]E(f198(x43951,x43952,f323(f323(f323(x43953,x43954),x43955),x43956),f323(f323(f7(x43951,f866(a99,a99),f867(a99,f862(x43952))),f323(f323(f7(x43951,a99,f867(f866(a99,a99),f867(a99,f862(x43952)))),f323(f323(f7(x43951,a99,f867(a99,f867(f866(a99,a99),f867(a99,f862(x43952))))),x43957),x43954)),x43955)),x43956)),f323(f323(f323(f211(x43951,x43952,x43953,x43957),x43954),x43955),x43956))
% 179.72/179.58 [4408]E(f199(x44081,x44082,f323(f323(f323(x44083,x44084),x44085),x44086),f323(f323(f7(x44081,f866(a99,a99),f867(a99,f862(x44082))),f323(f323(f7(x44081,a99,f867(f866(a99,a99),f867(a99,f862(x44082)))),f323(f323(f7(x44081,a99,f867(a99,f867(f866(a99,a99),f867(a99,f862(x44082))))),x44087),x44084)),x44085)),x44086)),f213(x44081,x44082,x44083,x44087,x44084,x44085,x44086))
% 179.72/179.58 [4399]E(f195(x43991,x43992,f323(f323(f323(x43993,x43994),x43995),x43996),f323(f323(f7(x43991,f866(a99,a99),f867(a99,f862(f864(x43992)))),f323(f323(f7(x43991,a99,f867(f866(a99,a99),f867(a99,f862(f864(x43992))))),f323(f323(f7(x43991,a99,f867(a99,f867(f866(a99,a99),f867(a99,f862(f864(x43992)))))),x43997),x43994)),x43995)),x43996)),f323(f323(f323(f207(x43991,x43992,x43993,x43997),x43994),x43995),x43996))
% 179.72/179.58 [4410]E(f197(x44101,x44102,f323(f323(f323(x44103,x44104),x44105),x44106),f323(f323(f7(x44101,f866(a99,a99),f867(a99,f862(f864(x44102)))),f323(f323(f7(x44101,a99,f867(f866(a99,a99),f867(a99,f862(f864(x44102))))),f323(f323(f7(x44101,a99,f867(a99,f867(f866(a99,a99),f867(a99,f862(f864(x44102)))))),x44107),x44104)),x44105)),x44106)),f209(x44101,x44102,x44103,x44107,x44104,x44105,x44106))
% 179.72/179.58 [4307]E(f323(f263(x43071,x43072,x43073,x43074,x43075,x43076),f323(f323(f258(x43071,x43073),x43077),x43078)),f323(f323(f258(x43072,x43074),f323(x43075,x43077)),f323(x43076,x43078)))
% 179.72/179.58 [4412]E(f323(f323(f147(f866(x44121,x44122),f866(x44123,x44124)),f323(f262(x44121,x44122,f866(x44123,x44124)),f323(f323(f7(x44121,f867(x44122,x44124),f867(x44122,f866(x44123,x44124))),f323(f323(f8(f867(x44124,f866(x44123,x44124)),f867(f867(x44122,x44124),f867(x44122,f866(x44123,x44124))),x44121),f8(x44124,f866(x44123,x44124),x44122)),f323(f323(f8(x44123,f867(x44124,f866(x44123,x44124)),x44121),f258(x44123,x44124)),x44125))),x44126))),f323(f323(f175(x44121,x44122),x44127),x44128)),f323(f323(f175(x44123,x44124),f323(f323(f147(x44121,x44123),x44125),x44127)),f323(f323(f147(x44122,x44124),x44126),x44128)))
% 179.72/179.58 [4416]E(f323(f323(f147(f866(x44161,x44162),x44163),f323(f262(x44161,x44162,x44163),f323(f323(f8(f867(x44162,f866(x44161,x44164)),f867(x44162,x44163),x44161),f323(f8(f866(x44161,x44164),x44163,x44162),x44165)),f323(f323(f7(x44161,f867(x44162,x44164),f867(x44162,f866(x44161,x44164))),f323(f323(f8(f867(x44164,f866(x44161,x44164)),f867(f867(x44162,x44164),f867(x44162,f866(x44161,x44164))),x44161),f8(x44164,f866(x44161,x44164),x44162)),f258(x44161,x44164))),x44166)))),f323(f323(f175(x44161,x44162),x44167),x44168)),f323(f323(f147(f866(x44161,x44164),x44163),x44165),f323(f323(f175(x44161,x44164),x44167),f323(f323(f147(x44162,x44164),x44166),x44168))))
% 179.72/179.58 [4341]E(f323(f323(f147(f866(x43411,x43412),x43413),f323(f262(x43411,x43412,x43413),f323(f323(f8(f867(x43412,f866(x43414,x43412)),f867(x43412,x43413),x43411),f323(f8(f866(x43414,x43412),x43413,x43412),x43415)),f323(f323(f8(x43414,f867(x43412,f866(x43414,x43412)),x43411),f258(x43414,x43412)),x43416)))),f323(f323(f175(x43411,x43412),x43417),x43418)),f323(f323(f147(f866(x43414,x43412),x43413),x43415),f323(f323(f175(x43414,x43412),f323(f323(f147(x43411,x43414),x43416),x43417)),x43418)))
% 179.72/179.58 [4298]E(f323(f323(f262(x42981,x42982,x42983),f323(f323(f8(f867(x42982,f866(x42984,x42985)),f867(x42982,x42983),x42981),f323(f8(f866(x42984,x42985),x42983,x42982),f323(f262(x42984,x42985,x42983),x42986))),x42987)),x42988),f323(f323(f262(x42984,x42985,x42983),x42986),f323(f323(f262(x42981,x42982,f866(x42984,x42985)),x42987),x42988)))
% 179.72/179.58 [4417]E(f323(f323(f39(f866(x44171,x44172),f867(f866(x44173,x44174),a855)),f323(f323(f260(x44171,x44172),x44175),f323(f16(f867(x44172,a855),x44171),x44176))),f323(f262(x44171,x44172,f867(f866(x44173,x44174),a855)),f323(f323(f7(x44171,f867(x44172,f867(x44173,f867(x44174,a855))),f867(x44172,f867(f866(x44173,x44174),a855))),f323(f323(f8(f867(f867(x44173,f867(x44174,a855)),f867(f866(x44173,x44174),a855)),f867(f867(x44172,f867(x44173,f867(x44174,a855))),f867(x44172,f867(f866(x44173,x44174),a855))),x44171),f8(f867(x44173,f867(x44174,a855)),f867(f866(x44173,x44174),a855),x44172)),f323(f323(f8(f867(x44173,a855),f867(f867(x44173,f867(x44174,a855)),f867(f866(x44173,x44174),a855)),x44171),f260(x44173,x44174)),x44177))),f323(f323(f8(f867(x44174,a855),f867(x44173,f867(x44174,a855)),x44172),f16(f867(x44174,a855),x44173)),x44178)))),f323(f323(f260(x44173,x44174),f323(f323(f39(x44171,f867(x44173,a855)),x44175),x44177)),f323(f16(f867(x44174,a855),x44173),f323(f323(f39(x44172,f867(x44174,a855)),x44176),x44178))))
% 179.72/179.58 [4448]E(f31(x44481,x44482,x44483,x44484,x44485,x44486,x44487,x44488,x44489,a24),x44482)
% 179.72/179.58 [4355]E(f323(f323(f264(x43551,x43552,x43553,x43554),f323(f323(f264(x43551,x43555,x43556,f866(x43552,x43553)),x43557),x43558)),x43559),f323(f323(f264(x43551,x43555,x43556,x43554),x43557),f323(f323(f7(x43555,f867(x43552,f867(x43553,x43554)),f867(x43556,x43554)),f323(f323(f8(f867(x43556,f866(x43552,x43553)),f867(f867(x43552,f867(x43553,x43554)),f867(x43556,x43554)),x43555),f264(x43556,x43552,x43553,x43554)),x43558)),x43559)))
% 179.72/179.58 [4387]E(f323(f71(f866(x43871,x43872),f866(x43873,x43874),f866(x43875,x43876),f263(x43871,x43873,x43872,x43874,x43877,x43878)),f263(x43875,x43871,x43876,x43872,x43879,x438710)),f263(x43875,x43873,x43876,x43874,f323(f71(x43871,x43873,x43875,x43877),x43879),f323(f71(x43872,x43874,x43876,x43878),x438710)))
% 179.72/179.58 [4449]E(f31(x44491,x44492,x44493,x44494,x44495,x44496,x44497,x44498,x44499,f30(x444910,x444911)),f323(f323(x44495,x444910),x444911))
% 179.72/179.58 [4450]E(f31(x44501,x44502,x44503,x44504,x44505,x44506,x44507,x44508,x44509,f29(x445010,x445011)),f323(f323(x44507,x445010),x445011))
% 179.72/179.58 [4451]E(f31(x44511,x44512,x44513,x44514,x44515,x44516,x44517,x44518,x44519,f25(x445110,x445111)),f323(f323(x44513,x445110),x445111))
% 179.72/179.58 [4393]E(f323(f263(x43931,x43932,x43933,x43934,x43935,x43936),f323(f263(x43937,x43931,x43938,x43933,x43939,x439310),x439311)),f323(f263(x43937,x43932,x43938,x43934,f323(f71(x43931,x43932,x43937,x43935),x43939),f323(f71(x43933,x43934,x43938,x43936),x439310)),x439311))
% 179.72/179.58 [4452]E(f31(x44521,x44522,x44523,x44524,x44525,x44526,x44527,x44528,x44529,f27(x445210,x445211,x445212)),f323(f323(f323(x44526,x445210),x445211),x445212))
% 179.72/179.58 [4453]E(f31(x44531,x44532,x44533,x44534,x44535,x44536,x44537,x44538,x44539,f26(x445310,x445311,x445312)),f323(f323(f323(x44534,x445310),x445311),x445312))
% 179.72/179.58 [4567]~P92(x45671)+E(f89(x45671),a320)
% 179.72/179.58 [4568]~P5(x45681)+P5(f864(x45681))
% 179.72/179.58 [4569]~P61(x45691)+P61(f864(x45691))
% 179.72/179.58 [4572]~P138(x45721)+~E(f76(x45721),f2(x45721))
% 179.72/179.58 [4574]~E(x45741,f2(a99))+E(f323(a20,x45741),f2(a1))
% 179.72/179.58 [4575]~E(x45751,f2(a1))+E(f80(a1,x45751),f2(a1))
% 179.72/179.58 [4581]~P140(x45811)+P30(x45811,f2(x45811))
% 179.72/179.58 [4583]~P103(x45831)+P16(x45831,f113(x45831))
% 179.72/179.58 [4592]P101(x45921)+P101(f323(a318,x45921))
% 179.72/179.58 [4635]~P140(x46351)+~P30(x46351,f76(x46351))
% 179.72/179.58 [4682]~P101(x46821)+~P101(f323(a318,x46821))
% 179.72/179.58 [4705]E(f323(a104,x47051),f2(a860))+~P101(f323(a193,x47051))
% 179.72/179.58 [4771]~P97(x47711)+P17(x47711,x47711,f110(x47711))
% 179.72/179.58 [4772]~P98(x47721)+P17(x47721,x47721,f101(x47721))
% 179.72/179.58 [4773]~P93(x47731)+P17(x47731,x47731,f79(x47731))
% 179.72/179.58 [4774]~P103(x47741)+P17(x47741,x47741,f235(x47741))
% 179.72/179.58 [4775]~P103(x47751)+P17(x47751,x47751,f236(x47751))
% 179.72/179.58 [4776]~P66(x47761)+P18(x47761,x47761,f79(x47761))
% 179.72/179.58 [4578]~E(x45781,f2(a860))+E(f323(f100(a1),x45781),f2(a1))
% 179.72/179.58 [4585]~P90(x45851)+E(f323(f103(x45851),a81),f2(x45851))
% 179.72/179.58 [4588]~E(f529(x45881),f2(a860))+E(f323(f159(a860),x45881),f2(a860))
% 179.72/179.58 [4589]~P104(x45891)+E(f239(x45891,f237(x45891)),f235(x45891))
% 179.72/179.58 [4590]~P104(x45901)+E(f240(x45901,f237(x45901)),f236(x45901))
% 179.72/179.58 [4591]~P85(x45911)+E(f80(x45911,f2(x45911)),f2(x45911))
% 179.72/179.58 [4600]~P140(x46001)+E(f323(f100(x46001),f76(a860)),f76(x46001))
% 179.72/179.58 [4601]~P140(x46011)+E(f323(f100(x46011),f2(a860)),f2(x46011))
% 179.72/179.58 [4602]~P134(x46021)+E(f323(f102(x46021),f76(a1)),f76(x46021))
% 179.72/179.58 [4603]~P134(x46031)+E(f323(f102(x46031),f2(a1)),f2(x46031))
% 179.72/179.58 [4604]E(x46041,f2(a860))+~E(f323(f100(a1),x46041),f2(a1))
% 179.72/179.58 [4629]~P87(x46291)+E(f323(f77(x46291),f188(x46291)),f246(x46291))
% 179.72/179.58 [4630]~P87(x46301)+E(f323(f77(x46301),f246(x46301)),f188(x46301))
% 179.72/179.58 [4631]~P59(x46311)+E(f323(f77(x46311),f2(x46311)),f2(x46311))
% 179.72/179.58 [4632]~P116(x46321)+E(f323(f73(x46321),f76(x46321)),f76(x46321))
% 179.72/179.58 [4633]~P82(x46331)+E(f323(f73(x46331),f2(x46331)),f2(x46331))
% 179.72/179.58 [4634]~P78(x46341)+E(f323(f159(x46341),f113(x46341)),f2(x46341))
% 179.72/179.58 [4654]~P37(x46541)+P39(f323(f166(a1),x46541))
% 179.72/179.58 [4687]~P90(x46871)+E(f323(f77(x46871),f76(x46871)),f323(f103(x46871),a97))
% 179.72/179.58 [4704]~P90(x47041)+P30(x47041,f323(f103(x47041),a81))
% 179.72/179.58 [4721]~P5(x47211)+E(f323(f166(x47211),f53(x47211)),f246(f867(x47211,a855)))
% 179.72/179.58 [4731]P37(x47311)+~P39(f323(f166(a1),x47311))
% 179.72/179.58 [4732]~P5(x47321)+P101(f323(f130(x47321),f53(x47321)))
% 179.72/179.58 [4777]E(f323(f100(a1),f323(a104,x47771)),x47771)+P101(f323(a193,x47771))
% 179.72/179.58 [4845]~P110(x48451)+E(f249(x48451,f76(x48451),f79(x48451)),f248(x48451))
% 179.72/179.58 [4875]~P90(x48751)+~P30(x48751,f323(f103(x48751),a97))
% 179.72/179.58 [5017]E(f323(f73(a1),x50171),x50171)+P101(f323(f323(f238(a1),x50171),f2(a1)))
% 179.72/179.58 [5035]~E(f323(a104,x50351),f2(a860))+P101(f323(f323(f237(a1),x50351),f2(a1)))
% 179.72/179.58 [5097]~P101(f323(a193,x50971))+P101(f323(f323(f238(a1),x50971),f2(a1)))
% 179.72/179.58 [5137]~P134(x51371)+P101(f323(f323(f325(x51371),f76(x51371)),f109(x51371)))
% 179.72/179.58 [5138]~P140(x51381)+P101(f323(f323(f325(x51381),f76(x51381)),f186(x51381)))
% 179.72/179.58 [5139]~P134(x51391)+P101(f323(f323(f325(x51391),f2(x51391)),f109(x51391)))
% 179.72/179.58 [5140]~P140(x51401)+P101(f323(f323(f325(x51401),f2(x51401)),f186(x51401)))
% 179.72/179.58 [5141]~P119(x51411)+P101(f323(f323(f237(x51411),f2(x51411)),f76(x51411)))
% 179.72/179.58 [5142]~P119(x51421)+P101(f323(f323(f238(x51421),f2(x51421)),f76(x51421)))
% 179.72/179.58 [5192]E(x51921,f2(a860))+~P101(f323(f323(f237(a860),x51921),f2(a860)))
% 179.72/179.58 [5234]E(f323(a104,x52341),f2(a860))+~P101(f323(f323(f237(a1),x52341),f2(a1)))
% 179.72/179.58 [5296]P101(f323(a193,x52961))+~P101(f323(f323(f238(a1),x52961),f2(a1)))
% 179.72/179.58 [5301]~P103(x53011)+P18(x53011,f861(x53011),f141(x53011,x53011,f5(x53011)))
% 179.72/179.58 [5318]P39(x53181)+~P101(f323(f323(f237(a1),f2(a1)),f362(x53181)))
% 179.72/179.58 [5324]E(f323(f73(a1),x53241),f323(f77(a1),x53241))+~P101(f323(f323(f238(a1),x53241),f2(a1)))
% 179.72/179.58 [5496]~P119(x54961)+~P101(f323(f323(f237(x54961),f76(x54961)),f2(x54961)))
% 179.72/179.58 [5497]~P119(x54971)+~P101(f323(f323(f238(x54971),f76(x54971)),f2(x54971)))
% 179.72/179.58 [5507]~E(x55071,f2(a860))+P101(f323(f323(f237(a1),f323(f100(a1),x55071)),f2(a1)))
% 179.72/179.58 [5508]~E(x55081,f2(a1))+P101(f323(f323(f238(a1),f323(f73(a1),x55081)),f76(a1)))
% 179.72/179.58 [5628]~P78(x56281)+E(f135(x56281,x56281,f78(x56281),f2(x56281)),f159(x56281))
% 179.72/179.58 [5798]~P99(x57981)+P27(a860,x57981,f100(x57981),f246(f867(a860,a855)))
% 179.72/179.58 [5987]E(x59871,f2(a860))+~P101(f323(f323(f237(a1),f323(f100(a1),x59871)),f2(a1)))
% 179.72/179.58 [5988]E(x59881,f2(a1))+~P101(f323(f323(f238(a1),f323(f73(a1),x59881)),f76(a1)))
% 179.72/179.58 [6774]~P101(f323(f323(f238(a1),x67741),f2(a1)))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x67741),x67741)),f2(a1)))
% 179.72/179.58 [7315]P101(f323(f323(f238(a1),x73151),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x73151),x73151)),f2(a1)))
% 179.72/179.58 [7870]E(x78701,f323(a3,f2(a860)))+P101(f323(f323(f238(a860),f323(f323(f22(a860),f323(a19,x78701)),f323(a112,f2(a860)))),f323(a19,x78701)))
% 179.72/179.58 [8634]~P101(f323(f323(f238(a1),x86341),f2(a1)))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86341),x86341)),a97)),f2(a1)))
% 179.72/179.58 [8731]~P101(f323(f323(f238(a1),x87311),f2(a1)))+P101(f323(f323(f238(a1),f323(f323(f78(a1),f323(f323(f78(a1),f76(a1)),x87311)),x87311)),f2(a1)))
% 179.72/179.58 [9051]P101(f323(f323(f238(a1),x90511),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90511),x90511)),a97)),f2(a1)))
% 179.72/179.58 [9111]P101(f323(f323(f238(a1),x91111),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),f323(f323(f78(a1),f76(a1)),x91111)),x91111)),f2(a1)))
% 179.72/179.58 [4675]~E(a81,x46751)+E(f323(f323(f78(a1),x46751),x46751),a81)
% 179.72/179.58 [4676]~E(x46761,a81)+E(f323(f323(f78(a1),x46761),x46761),a81)
% 179.72/179.58 [4690]E(x46901,f2(a1))+E(f323(f323(f36(a1),x46901),x46901),f76(a1))
% 179.72/179.58 [4822]E(x48221,a81)+~E(f323(f323(f78(a1),x48221),x48221),a81)
% 179.72/179.58 [4823]E(a81,x48231)+~E(f323(f323(f78(a1),x48231),x48231),a81)
% 179.72/179.58 [4835]~P103(x48351)+E(f132(x48351,f188(f867(x48351,a855))),f113(x48351))
% 179.72/179.58 [4836]~P6(x48361)+E(f37(x48361,f188(f867(x48361,a855))),f188(x48361))
% 179.72/179.58 [4837]~P6(x48371)+E(f37(x48371,f246(f867(x48371,a855))),f246(x48371))
% 179.72/179.58 [4838]~P6(x48381)+E(f38(x48381,f188(f867(x48381,a855))),f246(x48381))
% 179.72/179.58 [4839]~P6(x48391)+E(f38(x48391,f246(f867(x48391,a855))),f188(x48391))
% 179.72/179.58 [4975]E(x49751,f2(a860))+P101(f323(f323(f238(a860),f2(a860)),x49751))
% 179.72/179.58 [4994]~P7(x49941)+P101(f323(f323(f237(a1),f2(a1)),x49941))
% 179.72/179.58 [5026]~E(f323(f103(a860),x50261),f2(a860))+P101(f323(f323(f237(a1),x50261),a81))
% 179.72/179.58 [5031]P39(x50311)+P101(f323(f323(f325(a1),f362(x50311)),x50311))
% 179.72/179.58 [5032]E(x50321,f323(a3,f2(a860)))+P101(f323(f323(f237(a99),f76(a99)),x50321))
% 179.72/179.58 [5071]P101(f323(a193,x50711))+P101(f323(f323(f237(a1),f2(a1)),x50711))
% 179.72/179.58 [5119]E(f323(f100(a1),f323(a104,x51191)),f2(a1))+P101(f323(f323(f237(a1),f2(a1)),x51191))
% 179.72/179.58 [5178]E(f323(f100(a1),f323(f103(a860),x51781)),f323(f103(a1),x51781))+P101(f323(a193,f323(f103(a1),x51781)))
% 179.72/179.58 [5198]E(f323(f103(a860),x51981),f2(a860))+~P101(f323(a193,f323(f103(a1),x51981)))
% 179.72/179.58 [5199]E(f323(f103(a860),x51991),f2(a860))+~P101(f323(f323(f237(a1),x51991),a81))
% 179.72/179.58 [5231]P7(x52311)+~P101(f323(f323(f237(a1),f2(a1)),x52311))
% 179.72/179.58 [5304]E(f323(a112,f785(x53041)),x53041)+~P101(f323(f323(f238(a860),f2(a860)),x53041))
% 179.72/179.58 [5312]E(f323(a112,f323(f103(a860),x53121)),f76(a860))+~P101(f323(a193,f323(f103(a1),x53121)))
% 179.72/179.58 [5320]E(f323(f100(a1),f424(x53201)),x53201)+~P101(f323(f323(f238(a1),f2(a1)),x53201))
% 179.72/179.58 [5327]~E(x53271,f323(a3,f2(a860)))+~P101(f323(f323(f237(a99),f76(a99)),x53271))
% 179.72/179.58 [5334]E(f323(f100(a1),f323(f103(a860),x53341)),f2(a1))+~P101(f323(a193,f323(f103(a1),x53341)))
% 179.72/179.58 [5360]E(f323(f159(a860),x53601),f2(a860))+P101(f323(f323(f325(a860),f529(x53601)),f323(f166(a860),x53601)))
% 179.72/179.58 [5381]E(f323(f100(a1),f323(a104,x53811)),x53811)+~P101(f323(f323(f237(a1),f2(a1)),x53811))
% 179.72/179.58 [5390]~P101(f323(a193,x53901))+~P101(f323(f323(f237(a1),f2(a1)),x53901))
% 179.72/179.58 [5489]E(f323(f323(f78(a860),f76(a860)),f323(f103(a860),x54891)),f76(a860))+~P101(f323(f323(f238(a1),x54891),a81))
% 179.72/179.58 [5548]E(x55481,f2(a860))+~P101(f323(f323(f238(a860),x55481),f323(a112,f2(a860))))
% 179.72/179.58 [5587]E(f323(f323(f22(a860),f323(f103(a860),x55871)),f76(a860)),f2(a860))+~P101(f323(f323(f237(a1),x55871),a81))
% 179.72/179.58 [5588]E(f323(f323(f78(a860),f323(f103(a860),x55881)),f76(a860)),f76(a860))+~P101(f323(f323(f238(a1),x55881),a81))
% 179.72/179.58 [5598]~P39(x55981)+E(f323(f35(a860),f323(f302(a1,a860,a104),x55981)),f323(f35(a1),x55981))
% 179.72/179.58 [5629]~P103(x56291)+E(f239(x56291,f323(f7(x56291,x56291,a855),f237(x56291))),f236(x56291))
% 179.72/179.58 [5630]~P103(x56301)+E(f240(x56301,f323(f7(x56301,x56301,a855),f237(x56301))),f235(x56301))
% 179.72/179.58 [5640]E(f42(a860,f323(a112,f2(a860)),f323(f103(a860),x56401)),f323(a112,f2(a860)))+~P101(f323(a193,f323(f103(a1),x56401)))
% 179.72/179.58 [5649]~P101(f323(f323(f238(a1),f2(a1)),x56491))+P101(f323(f323(f237(a1),f76(a1)),x56491))
% 179.72/179.58 [5650]P101(f323(f323(f238(a1),f2(a1)),x56501))+~P101(f323(f323(f237(a1),f76(a1)),x56501))
% 179.72/179.58 [5661]E(f323(a112,f323(f323(f22(a860),x56611),f76(a860))),x56611)+~P101(f323(f323(f238(a860),f2(a860)),x56611))
% 179.72/179.58 [5717]P101(f323(f323(f238(a860),f2(a860)),f424(x57171)))+~P101(f323(f323(f238(a1),f2(a1)),x57171))
% 179.72/179.58 [5776]E(f42(a1,f323(f103(a1),a97),x57761),f323(f323(f22(a1),x57761),f76(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x57761))
% 179.72/179.58 [5810]~P101(f323(f323(f238(a1),a81),x58101))+P101(f323(f323(f238(a860),f2(a860)),f323(f103(a860),x58101)))
% 179.72/179.58 [5860]P101(f323(f323(f238(a860),f2(a860)),f323(a104,x58601)))+~P101(f323(f323(f238(a1),f2(a1)),x58601))
% 179.72/179.58 [5909]~P101(f323(f323(f238(a860),f2(a860)),x59091))+P101(f323(f323(f238(a1),f2(a1)),f323(f100(a1),x59091)))
% 179.72/179.58 [5944]~P101(f323(f323(f238(a860),f2(a860)),f323(a104,x59441)))+P101(f323(f323(f238(a1),f2(a1)),x59441))
% 179.72/179.58 [5958]~P39(x59581)+E(f323(f302(a860,a1,f100(a1)),f323(f302(a1,a860,a104),x59581)),x59581)
% 179.72/179.58 [5968]P101(f323(f323(f238(a1),a81),x59681))+~P101(f323(f323(f238(a860),f2(a860)),f323(f103(a860),x59681)))
% 179.72/179.58 [6016]~P5(x60161)+E(f323(f323(f144(f864(x60161)),f200(x60161)),f323(f323(f147(x60161,f864(x60161)),f230(x60161)),f53(x60161))),f53(f864(x60161)))
% 179.72/179.58 [6027]P101(f323(f323(f238(a860),f2(a860)),x60271))+~P101(f323(f323(f238(a1),f2(a1)),f323(f100(a1),x60271)))
% 179.72/179.58 [6136]E(f323(f302(a860,a1,f100(a1)),f323(f244(a860),f323(a104,x61361))),f323(f293(a1,f2(a1)),x61361))+~P101(f323(f323(f237(a1),f2(a1)),x61361))
% 179.72/179.58 [6151]~P119(x61511)+P101(f323(f323(f238(x61511),f2(x61511)),f323(f323(f78(x61511),f76(x61511)),f76(x61511))))
% 179.72/179.58 [6202]P101(f323(f323(f238(a860),f323(a112,f2(a860))),f323(a104,x62021)))+~P101(f323(f323(f238(a1),f76(a1)),x62021))
% 179.72/179.58 [6296]E(x62961,f2(a1))+P101(f323(f46(f2(a1),x62961),f323(f323(f258(a1,a1),f2(a1)),f2(a1))))
% 179.72/179.58 [6459]~P101(f323(f323(f238(a860),f323(a112,f2(a860))),f323(a104,x64591)))+P101(f323(f323(f238(a1),f76(a1)),x64591))
% 179.72/179.58 [6883]~P111(x68831)+P38(x68831,f323(f243(f866(x68831,x68831)),f323(f262(x68831,x68831,a855),f238(x68831))))
% 179.72/179.58 [5535]E(f323(f103(a860),f323(f323(f22(a1),x55351),a97)),f323(a112,f323(f103(a860),x55351)))+P101(f323(a193,f323(f103(a1),x55351)))
% 179.72/179.58 [5551]~P37(x55511)+E(f323(f323(f147(a860,a1),f100(a1)),f323(f323(f147(a1,a860),a104),x55511)),x55511)
% 179.72/179.58 [5667]E(f323(f77(a1),f323(f100(a1),f323(a112,f425(x56671)))),x56671)+~P101(f323(f323(f238(a1),x56671),f2(a1)))
% 179.72/179.58 [5677]E(f323(f323(f78(a860),f76(a860)),f323(f103(a860),x56771)),f323(f103(a860),f323(f323(f22(a1),x56771),a97)))+P101(f323(f323(f238(a1),x56771),a81))
% 179.72/179.58 [5719]E(f323(f323(f36(a1),f323(f103(a1),a97)),x57191),f323(f103(a1),a97))+~P101(f323(f323(f238(a1),f2(a1)),x57191))
% 179.72/179.58 [5806]E(f323(f323(f22(a860),f323(f103(a860),x58061)),f76(a860)),f323(f103(a860),f323(f323(f78(a1),x58061),a97)))+P101(f323(f323(f237(a1),x58061),a81))
% 179.72/179.58 [5807]E(f323(f323(f78(a860),f323(f103(a860),x58071)),f76(a860)),f323(f103(a860),f323(f323(f22(a1),x58071),a97)))+P101(f323(f323(f238(a1),x58071),a81))
% 179.72/179.58 [5848]E(f323(a104,f323(f323(f78(a1),f76(a1)),x58481)),f323(a112,f323(a104,x58481)))+~P101(f323(f323(f237(a1),f2(a1)),x58481))
% 179.72/179.58 [5882]E(f323(a112,f323(f323(f22(a860),x58821),f323(a112,f2(a860)))),x58821)+~P101(f323(f323(f238(a860),f2(a860)),x58821))
% 179.72/179.58 [6087]E(f42(a860,f323(a112,f2(a860)),f323(f103(a860),x60871)),f323(a104,f42(a1,f76(a1),f323(f103(a1),x60871))))+P101(f323(a193,f323(f103(a1),x60871)))
% 179.72/179.58 [6126]~P101(f323(f323(f237(a1),a81),x61261))+P101(f323(f323(f237(a1),a81),f323(f323(f78(a1),x61261),x61261)))
% 179.72/179.58 [6127]~P101(f323(f323(f238(a1),a97),x61271))+P101(f323(f323(f237(a1),a97),f323(f323(f78(a1),x61271),x61271)))
% 179.72/179.58 [6128]~P101(f323(f323(f238(a1),a81),x61281))+P101(f323(f323(f238(a1),a81),f323(f323(f78(a1),x61281),x61281)))
% 179.72/179.58 [6129]~P101(f323(f323(f238(a1),a97),x61291))+P101(f323(f323(f238(a1),a97),f323(f323(f78(a1),x61291),x61291)))
% 179.72/179.58 [6130]~P101(f323(f323(f89(a1),a81),x61301))+P101(f323(f323(f89(a1),a81),f323(f323(f78(a1),x61301),x61301)))
% 179.72/179.58 [6309]~P101(f323(f59(x63091),f246(f867(x63091,a855))))+P101(f323(f59(f864(x63091)),f246(f867(f864(x63091),a855))))
% 179.72/179.58 [6393]~P101(f323(f323(f237(a1),f2(a1)),x63931))+P101(f323(f323(f238(a1),f2(a1)),f323(f323(f78(a1),f76(a1)),x63931)))
% 179.72/179.58 [6400]E(f323(f257(a1,a1),f44(f76(a1),f323(f103(a1),x64001))),f323(f323(f36(a1),f76(a1)),f323(f103(a1),x64001)))+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x64001)))
% 179.72/179.58 [6420]E(f323(f261(a1,a1),f44(f76(a1),f323(f103(a1),x64201))),f42(a1,f76(a1),f323(f103(a1),x64201)))+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x64201)))
% 179.72/179.58 [6431]P101(f323(f59(x64311),f246(f867(x64311,a855))))+~P101(f323(f59(f864(x64311)),f246(f867(f864(x64311),a855))))
% 179.72/179.58 [6460]P101(f323(f323(f237(a1),a81),x64601))+~P101(f323(f323(f237(a1),a81),f323(f323(f78(a1),x64601),x64601)))
% 179.72/179.58 [6461]P101(f323(f323(f238(a1),a81),x64611))+~P101(f323(f323(f238(a1),a81),f323(f323(f78(a1),x64611),x64611)))
% 179.72/179.58 [6462]P101(f323(f323(f238(a1),a97),x64621))+~P101(f323(f323(f237(a1),a97),f323(f323(f78(a1),x64621),x64621)))
% 179.72/179.58 [6463]P101(f323(f323(f238(a1),a97),x64631))+~P101(f323(f323(f238(a1),a97),f323(f323(f78(a1),x64631),x64631)))
% 179.72/179.58 [6464]P101(f323(f323(f89(a1),a81),x64641))+~P101(f323(f323(f89(a1),a81),f323(f323(f78(a1),x64641),x64641)))
% 179.72/179.58 [6778]~P101(f323(f59(x67781),f246(f867(x67781,a855))))+P101(f323(f323(f238(a860),f2(a860)),f323(f35(x67781),f246(f867(x67781,a855)))))
% 179.72/179.58 [7357]P101(f323(f59(a860),x73571))+~P101(f323(f59(a1),f323(f302(a860,a1,f100(a1)),x73571)))
% 179.72/179.58 [5464]~E(a97,x54641)+E(f323(f323(f22(a1),f323(f323(f78(a1),x54641),x54641)),a97),a97)
% 179.72/179.58 [5465]~E(x54651,a97)+E(f323(f323(f22(a1),f323(f323(f78(a1),x54651),x54651)),a97),a97)
% 179.72/179.58 [5963]E(x59631,a97)+~E(f323(f323(f22(a1),f323(f323(f78(a1),x59631),x59631)),a97),a97)
% 179.72/179.58 [5964]E(a97,x59641)+~E(f323(f323(f22(a1),f323(f323(f78(a1),x59641),x59641)),a97),a97)
% 179.72/179.58 [6362]~E(f323(f103(a860),x63621),f2(a860))+P101(f323(a193,f323(f103(a1),f323(f323(f78(a1),x63621),a97))))
% 179.72/179.58 [6704]~P101(f323(a193,f323(f103(a1),x67041)))+P101(f323(a193,f323(f103(a1),f323(f323(f78(a1),x67041),x67041))))
% 179.72/179.58 [6705]~P101(f323(f323(f237(a1),x67051),a81))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x67051),x67051)),a81))
% 179.72/179.58 [6706]~P101(f323(f323(f237(a1),x67061),a97))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x67061),x67061)),a97))
% 179.72/179.58 [6707]~P101(f323(f323(f238(a1),x67071),a81))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x67071),x67071)),a81))
% 179.72/179.58 [6708]~P101(f323(f323(f237(a1),x67081),a97))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x67081),x67081)),a97))
% 179.72/179.58 [6709]~P101(f323(f323(f89(a1),x67091),a81))+P101(f323(f323(f89(a1),f323(f323(f78(a1),x67091),x67091)),a81))
% 179.72/179.58 [7028]E(f323(f103(a860),x70281),f2(a860))+~P101(f323(a193,f323(f103(a1),f323(f323(f78(a1),x70281),a97))))
% 179.72/179.58 [7267]~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x72671)))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),f323(f323(f78(a1),x72671),x72671))))
% 179.72/179.58 [7268]P101(f323(a193,f323(f103(a1),x72681)))+~P101(f323(a193,f323(f103(a1),f323(f323(f78(a1),x72681),x72681))))
% 179.72/179.58 [7269]P101(f323(f323(f237(a1),x72691),a81))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x72691),x72691)),a81))
% 179.72/179.58 [7270]P101(f323(f323(f237(a1),x72701),a97))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x72701),x72701)),a97))
% 179.72/179.58 [7271]P101(f323(f323(f237(a1),x72711),a97))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x72711),x72711)),a97))
% 179.72/179.58 [7272]P101(f323(f323(f238(a1),x72721),a81))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x72721),x72721)),a81))
% 179.72/179.58 [7273]P101(f323(f323(f89(a1),x72731),a81))+~P101(f323(f323(f89(a1),f323(f323(f78(a1),x72731),x72731)),a81))
% 179.72/179.58 [7637]E(f323(a107,f680(x76371)),x76371)+~P101(f323(f323(f325(f867(f866(a860,a860),a855)),x76371),a98))
% 179.72/179.58 [6282]~P90(x62821)+E(f323(f103(x62821),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f76(x62821))
% 179.72/179.58 [6756]~P101(f323(a193,f323(f103(a1),x67561)))+E(f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),x67561),x67561)),a97)),f2(a860))
% 179.72/179.58 [7813]~P101(f323(f323(f238(a1),f323(f103(a1),x78131)),f2(a1)))+E(f323(f257(a1,a1),f323(a48,f47(f323(f77(a1),f76(a1)),f323(f77(a1),f323(f103(a1),x78131))))),f323(f323(f36(a1),f76(a1)),f323(f103(a1),x78131)))
% 179.72/179.58 [7827]~P101(f323(f323(f238(a1),f323(f103(a1),x78271)),f2(a1)))+E(f323(f261(a1,a1),f323(a48,f47(f323(f77(a1),f76(a1)),f323(f77(a1),f323(f103(a1),x78271))))),f42(a1,f76(a1),f323(f103(a1),x78271)))
% 179.72/179.58 [7876]~P101(f323(f323(f237(a1),a81),x78761))+P101(f323(f323(f237(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x78761),x78761)),a97)))
% 179.72/179.58 [7877]~P101(f323(f323(f237(a1),a97),x78771))+P101(f323(f323(f237(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x78771),x78771)),a97)))
% 179.72/179.58 [7878]~P101(f323(f323(f237(a1),a81),x78781))+P101(f323(f323(f238(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x78781),x78781)),a97)))
% 179.72/179.58 [7879]~P101(f323(f323(f238(a1),a97),x78791))+P101(f323(f323(f238(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x78791),x78791)),a97)))
% 179.72/179.58 [7880]~P101(f323(f323(f89(a1),a97),x78801))+P101(f323(f323(f89(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x78801),x78801)),a97)))
% 179.72/179.58 [8178]~P90(x81781)+~P30(x81781,f323(f103(x81781),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))
% 179.72/179.58 [8362]P101(f323(f323(f237(a1),a81),x83621))+~P101(f323(f323(f237(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x83621),x83621)),a97)))
% 179.72/179.58 [8363]P101(f323(f323(f237(a1),a81),x83631))+~P101(f323(f323(f238(a1),a81),f323(f323(f22(a1),f323(f323(f78(a1),x83631),x83631)),a97)))
% 179.72/179.58 [8364]P101(f323(f323(f237(a1),a97),x83641))+~P101(f323(f323(f237(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x83641),x83641)),a97)))
% 179.72/179.58 [8365]P101(f323(f323(f238(a1),a97),x83651))+~P101(f323(f323(f238(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x83651),x83651)),a97)))
% 179.72/179.58 [8366]P101(f323(f323(f89(a1),a97),x83661))+~P101(f323(f323(f89(a1),a97),f323(f323(f22(a1),f323(f323(f78(a1),x83661),x83661)),a97)))
% 179.72/179.58 [8681]E(f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),x86811),x86811)),a97)),f323(f323(f84(a860,a860),f323(f103(a860),x86811)),f323(f323(f8(a860,a860,a860),a112),f323(f323(f18(a860,a860,a860),f78(a860)),f5(a860)))))+P101(f323(a193,f323(f103(a1),x86811)))
% 179.72/179.58 [9526]E(x95261,f188(f867(f866(a860,a860),a855)))+P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),x95261),f188(f867(f866(a860,a860),a855)))),a66))
% 179.72/179.58 [8607]~P101(f323(a193,f323(f103(a1),x86071)))+P101(f323(a193,f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86071),x86071)),a97))))
% 179.72/179.58 [8608]~P101(f323(f323(f238(a1),x86081),a81))+P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86081),x86081)),a97)),a81))
% 179.72/179.58 [8609]~P101(f323(f323(f237(a1),x86091),a97))+P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86091),x86091)),a97)),a97))
% 179.72/179.58 [8610]~P101(f323(f323(f238(a1),x86101),a81))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86101),x86101)),a97)),a81))
% 179.72/179.58 [8611]~P101(f323(f323(f238(a1),x86111),a97))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86111),x86111)),a97)),a97))
% 179.72/179.58 [8612]~P101(f323(f323(f89(a1),x86121),a97))+P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x86121),x86121)),a97)),a97))
% 179.72/179.58 [8722]~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x87221)))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x87221),x87221)),a97))))
% 179.72/179.58 [8883]~P90(x88831)+E(f323(f323(f78(x88831),f76(x88831)),f76(x88831)),f323(f103(x88831),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))
% 179.72/179.58 [9034]P101(f323(a193,f323(f103(a1),x90341)))+~P101(f323(a193,f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90341),x90341)),a97))))
% 179.72/179.58 [9035]P101(f323(f323(f237(a1),x90351),a97))+~P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90351),x90351)),a97)),a97))
% 179.72/179.58 [9036]P101(f323(f323(f238(a1),x90361),a81))+~P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90361),x90361)),a97)),a81))
% 179.72/179.58 [9037]P101(f323(f323(f238(a1),x90371),a81))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90371),x90371)),a97)),a81))
% 179.72/179.58 [9038]P101(f323(f323(f238(a1),x90381),a97))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90381),x90381)),a97)),a97))
% 179.72/179.58 [9039]P101(f323(f323(f89(a1),x90391),a97))+~P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90391),x90391)),a97)),a97))
% 179.72/179.58 [9573]~P101(f323(f59(f866(a860,a860)),x95731))+P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),f188(f867(f866(a860,a860),a855))),x95731)),a67))
% 179.72/179.58 [9357]~P140(x93571)+E(f323(f323(f248(x93571),f76(x93571)),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f76(x93571))
% 179.72/179.58 [9358]~P140(x93581)+E(f323(f323(f248(x93581),f2(x93581)),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f2(x93581))
% 179.72/179.58 [9803]~P101(f323(f323(f238(a860),f76(a860)),x98031))+P101(f323(f323(f238(a860),f2(a860)),f323(f323(f36(a860),x98031),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))
% 179.72/179.58 [9813]~P101(f323(f323(f238(a860),f2(a860)),x98131))+P101(f323(f323(f238(a860),f2(a860)),f323(f323(f36(a860),f323(f323(f78(a860),x98131),f76(a860))),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))
% 179.72/179.58 [9855]~E(f42(a860,x98551,f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f76(a860))+P101(f323(f323(f238(a860),f2(a860)),f42(a860,x98551,f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))
% 179.72/179.58 [9874]E(f42(a860,x98741,f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f76(a860))+~P101(f323(f323(f238(a860),f2(a860)),f42(a860,x98741,f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))
% 179.72/179.58 [4608]~P38(x46081,x46082)+P54(x46081,x46082)
% 179.72/179.58 [4609]~P44(x46091,x46092)+P54(x46091,x46092)
% 179.72/179.58 [4570]~E(x45701,x45702)+E(f270(x45701,x45702),f76(a99))
% 179.72/179.58 [4573]E(f218(x45731,x45732),x45731)+~E(x45732,f2(a860))
% 179.72/179.58 [4580]~E(x45802,f113(x45801))+E(f145(x45801,x45802),f113(x45801))
% 179.72/179.58 [4599]~E(f145(x45992,x45991),f113(x45992))+E(x45991,f113(x45992))
% 179.72/179.58 [4613]~P1(x46132)+P1(f867(x46131,x46132))
% 179.72/179.58 [4614]~P2(x46142)+P2(f867(x46141,x46142))
% 179.72/179.58 [4615]~P94(x46152)+P3(f867(x46151,x46152))
% 179.72/179.58 [4616]~P2(x46162)+P97(f867(x46161,x46162))
% 179.72/179.58 [4617]~P4(x46172)+P4(f867(x46171,x46172))
% 179.72/179.58 [4618]~P102(x46182)+P102(f867(x46181,x46182))
% 179.72/179.58 [4619]~P2(x46192)+P98(f867(x46191,x46192))
% 179.72/179.58 [4620]~P104(x46202)+P104(f867(x46201,x46202))
% 179.72/179.58 [4621]~P105(x46212)+P105(f867(x46211,x46212))
% 179.72/179.58 [4622]~P106(x46222)+P106(f867(x46221,x46222))
% 179.72/179.58 [4623]~P94(x46232)+P95(f867(x46231,x46232))
% 179.72/179.58 [4624]~P96(x46242)+P96(f867(x46241,x46242))
% 179.72/179.58 [4625]~P79(x46252)+P79(f867(x46251,x46252))
% 179.72/179.58 [4626]~P87(x46262)+P87(f867(x46261,x46262))
% 179.72/179.58 [4627]~P6(x46272)+P6(f867(x46271,x46272))
% 179.72/179.58 [4628]~P94(x46282)+P94(f867(x46281,x46282))
% 179.72/179.58 [4641]E(x46411,x46412)+~E(f323(a112,x46411),f323(a112,x46412))
% 179.72/179.58 [4642]E(x46421,x46422)+~E(f323(a107,x46421),f323(a107,x46422))
% 179.72/179.58 [4643]E(x46431,x46432)+~E(f323(a3,x46431),f323(a3,x46432))
% 179.72/179.58 [4645]E(x46451,x46452)+~E(f323(a19,x46451),f323(a19,x46452))
% 179.72/179.58 [4750]~P57(x47501)+E(f42(x47501,x47502,x47502),f2(x47501))
% 179.72/179.58 [4784]~P38(x47841,x47842)+P38(f861(x47841),f138(x47841,x47842))
% 179.72/179.58 [4785]~P38(x47851,x47852)+P38(f861(x47851),f139(x47851,x47852))
% 179.72/179.58 [4880]~P38(x48801,x48802)+P38(f867(x48801,a855),f316(x48801,x48802))
% 179.72/179.58 [4881]~P38(x48811,x48812)+P38(f867(x48811,a855),f314(x48811,x48812))
% 179.72/179.58 [5000]~P7(x50001)+P39(f294(a1,x50001,x50002))
% 179.72/179.58 [5100]~P38(x51001,x51002)+P56(x51001,f65(x51001,x51001,x51002))
% 179.72/179.58 [5592]~P75(x55921)+P27(x55921,x55921,f77(x55921),x55922)
% 179.72/179.58 [4594]~E(x45942,f113(x45941))+E(f323(f161(x45941),x45942),f113(x45941))
% 179.72/179.58 [4595]~E(x45952,f113(x45951))+E(f323(f162(x45951),x45952),f113(x45951))
% 179.72/179.58 [4649]E(x46491,f323(a104,x46492))+~E(f323(f100(a1),x46491),x46492)
% 179.72/179.58 [4652]E(x46521,f113(x46522))+~E(f323(f161(x46522),x46521),f113(x46522))
% 179.72/179.58 [4653]E(x46531,f113(x46532))+~E(f323(f162(x46532),x46531),f113(x46532))
% 179.72/179.58 [4672]~P90(x46721)+E(f323(f103(x46721),x46722),f323(f102(x46721),x46722))
% 179.72/179.58 [4679]~E(x46792,f200(x46791))+E(f229(x46791,x46792),f188(f867(x46791,a855)))
% 179.72/179.58 [4681]~P61(x46811)+P101(f323(f59(x46811),x46812))
% 179.72/179.58 [4688]E(x46881,f200(x46882))+E(f323(f230(x46882),f685(x46882,x46881)),x46881)
% 179.72/179.58 [4689]E(x46891,f200(x46892))+E(f323(f230(x46892),f769(x46892,x46891)),x46891)
% 179.72/179.58 [4691]~E(f543(x46912,x46911),f113(x46911))+E(f173(x46911,x46912),f113(f861(x46911)))
% 179.72/179.58 [4700]~E(x47002,f113(x47001))+E(f323(f166(x47001),x47002),f188(f867(x47001,a855)))
% 179.72/179.58 [4701]~E(x47012,f113(x47011))+E(f188(f867(x47011,a855)),f323(f166(x47011),x47012))
% 179.72/179.58 [4703]E(x47031,x47032)+~E(f323(f100(a1),x47031),f323(f100(a1),x47032))
% 179.72/179.58 [4706]E(f216(x47061,x47062),f2(a860))+P101(f323(f59(x47061),x47062))
% 179.72/179.58 [4726]~P116(x47261)+E(f80(x47261,f80(x47261,x47262)),f80(x47261,x47262))
% 179.72/179.58 [4739]~P77(x47391)+E(f323(f323(f248(x47391),x47392),f76(a860)),x47392)
% 179.72/179.58 [4740]~P112(x47401)+E(f323(f323(f248(x47401),x47402),f76(a860)),x47402)
% 179.72/179.58 [4744]E(x47441,x47442)+E(f270(x47441,x47442),f323(f323(f78(a99),x47442),f76(a99)))
% 179.72/179.58 [4747]E(f323(f35(x47471),x47472),f2(a860))+P101(f323(f59(x47471),x47472))
% 179.72/179.58 [4751]~E(f145(x47511,x47512),x47512)+P101(f323(f130(x47511),x47512))
% 179.72/179.58 [4754]~P3(x47541)+E(f323(f323(f110(x47541),x47542),f188(x47541)),x47542)
% 179.72/179.58 [4755]~P59(x47551)+E(f323(f323(f22(x47551),x47552),f2(x47551)),x47552)
% 179.72/179.58 [4756]~P95(x47561)+E(f323(f323(f101(x47561),x47562),f246(x47561)),x47562)
% 179.72/179.58 [4757]~P68(x47571)+E(f323(f323(f79(x47571),x47572),f76(x47571)),x47572)
% 179.72/179.58 [4758]~P77(x47581)+E(f323(f323(f79(x47581),x47582),f76(x47581)),x47582)
% 179.72/179.58 [4759]~P112(x47591)+E(f323(f323(f79(x47591),x47592),f76(x47591)),x47592)
% 179.72/179.58 [4760]~P112(x47601)+E(f323(f323(f78(x47601),x47602),f2(x47601)),x47602)
% 179.72/179.58 [4761]~P78(x47611)+E(f323(f323(f78(x47611),x47612),f2(x47611)),x47612)
% 179.72/179.58 [4762]~P72(x47621)+E(f323(f323(f78(x47621),x47622),f2(x47621)),x47622)
% 179.72/179.58 [4763]~P114(x47631)+E(f323(f323(f281(x47631),x47632),f76(x47631)),x47632)
% 179.72/179.58 [4764]~P57(x47641)+E(f323(f323(f36(x47641),x47642),f76(x47641)),x47642)
% 179.72/179.58 [4765]~P112(x47651)+E(f323(f323(f248(x47651),x47652),f2(a860)),f76(x47651))
% 179.72/179.58 [4766]~P110(x47661)+E(f323(f323(f248(x47661),x47662),f2(a860)),f76(x47661))
% 179.72/179.58 [4767]~E(x47672,f188(f867(x47671,a855)))+E(f323(f35(x47671),x47672),f2(a860))
% 179.72/179.58 [4778]~P57(x47781)+E(f42(x47781,x47782,f2(x47781)),x47782)
% 179.72/179.58 [4786]~P95(x47861)+E(f323(f323(f110(x47861),x47862),f246(x47861)),f246(x47861))
% 179.72/179.58 [4787]~P3(x47871)+E(f323(f323(f101(x47871),x47872),f188(x47871)),f188(x47871))
% 179.72/179.58 [4788]~P112(x47881)+E(f323(f323(f79(x47881),x47882),f2(x47881)),f2(x47881))
% 179.72/179.58 [4789]~P124(x47891)+E(f323(f323(f79(x47891),x47892),f2(x47891)),f2(x47891))
% 179.72/179.58 [4790]~P115(x47901)+E(f323(f323(f281(x47901),x47902),f2(x47901)),f2(x47901))
% 179.72/179.58 [4791]~P57(x47911)+E(f323(f323(f36(x47911),x47912),f2(x47911)),f2(x47911))
% 179.72/179.58 [4792]E(x47921,f200(x47922))+~E(f229(x47922,x47921),f188(f867(x47922,a855)))
% 179.72/179.58 [4794]~P57(x47941)+E(f42(x47941,x47942,f76(x47941)),f2(x47941))
% 179.72/179.58 [4795]~P57(x47951)+E(f42(x47951,f2(x47951),x47952),f2(x47951))
% 179.72/179.58 [4824]E(x48241,f2(a860))+E(f52(x48242,x48241,f113(x48242)),f113(f861(x48242)))
% 179.72/179.58 [4847]P38(x48471,x48472)+~E(f686(x48472,x48471),f188(f867(x48471,a855)))
% 179.72/179.58 [4848]E(x48481,f113(x48482))+~E(f323(f166(x48482),x48481),f188(f867(x48482,a855)))
% 179.72/179.58 [4849]E(x48491,f113(x48492))+~E(f188(f867(x48492,a855)),f323(f166(x48492),x48491))
% 179.72/179.58 [4852]~E(x48521,x48522)+P101(f323(f323(a320,x48521),x48522))
% 179.72/179.58 [4862]P101(x48621)+P101(f323(f323(a326,x48621),x48622))
% 179.72/179.58 [4863]E(x48631,f113(x48632))+E(f323(f323(f158(x48632),x48631),f2(a860)),f323(f134(x48632),x48631))
% 179.72/179.58 [4866]E(f145(x48661,x48662),x48662)+~P101(f323(f130(x48661),x48662))
% 179.72/179.58 [4871]~P101(x48712)+P101(f323(f323(a326,x48711),x48712))
% 179.72/179.58 [4872]~P101(x48722)+P101(f323(f323(a322,x48721),x48722))
% 179.72/179.58 [4873]~P101(x48731)+P101(f323(f323(a322,x48731),x48732))
% 179.72/179.58 [4883]~E(f530(x48832,x48831),f537(x48832,x48831))+P101(f323(f130(x48831),x48832))
% 179.72/179.58 [4890]E(f323(f243(x48901),x48902),f188(f867(x48901,a855)))+P101(f323(x48902,f329(x48902)))
% 179.72/179.58 [4891]E(f188(f867(x48911,a855)),f323(f243(x48911),x48912))+P101(f323(x48912,f330(x48912)))
% 179.72/179.58 [4957]~P116(x49571)+E(f323(f323(f79(x49571),x49572),f80(x49571,x49572)),f323(f73(x49571),x49572))
% 179.72/179.58 [4968]~E(x49681,f2(a1))+E(f43(x49681,x49682),f323(f323(f258(a1,a1),f2(a1)),f2(a1)))
% 179.72/179.58 [4999]~P54(x49991,x49992)+P54(x49991,f323(f278(x49991,x49991),x49992))
% 179.72/179.58 [5022]E(x50221,x50222)+~P101(f323(f323(a320,x50221),x50222))
% 179.72/179.58 [5033]P101(x50331)+~P101(f323(f323(a321,x50332),x50331))
% 179.72/179.58 [5034]P101(x50341)+~P101(f323(f323(a321,x50341),x50342))
% 179.72/179.58 [5039]~P106(x50391)+P101(f323(f323(f237(x50391),x50392),f246(x50391)))
% 179.72/179.58 [5043]E(x50431,x50432)+~E(f323(x50431,f423(x50432,x50431)),f323(x50432,f423(x50432,x50431)))
% 179.72/179.58 [5073]E(x50731,f2(a860))+E(f218(x50731,f42(a860,x50732,x50731)),f218(x50732,x50731))
% 179.72/179.58 [5078]~P103(x50781)+P16(x50781,f323(f323(f144(x50781),x50782),f113(x50781)))
% 179.72/179.58 [5080]E(x50801,f2(a1))+P101(f323(f46(x50802,x50801),f43(x50802,x50801)))
% 179.72/179.58 [5098]~E(x50981,x50982)+P101(f323(f323(f238(a860),x50981),f323(a112,x50982)))
% 179.72/179.58 [5108]~E(x51081,f2(a860))+P101(f323(f323(f238(a860),x51081),f323(a112,x51082)))
% 179.72/179.58 [5118]P101(f323(x51181,x51182))+P101(f323(f323(f237(a1),f2(a1)),f419(x51181)))
% 179.72/179.58 [5182]P54(x51821,x51822)+~P54(x51821,f323(f278(x51821,x51821),x51822))
% 179.72/179.58 [5185]~E(f42(a860,x51852,x51851),f2(a860))+E(f323(f323(f79(a860),x51851),f440(x51851,x51852)),x51852)
% 179.72/179.58 [5186]~E(f42(a1,x51862,x51861),f2(a1))+E(f323(f323(f79(a1),x51861),f441(x51861,x51862)),x51862)
% 179.72/179.58 [5210]~P101(f323(x52101,x52102))+P101(f323(f323(f237(a1),f2(a1)),f363(x52101)))
% 179.72/179.58 [5222]E(f323(f323(f22(a860),f323(a104,x52221)),f323(a104,x52222)),f323(a104,x52221))+~P101(f323(a193,x52222))
% 179.72/179.58 [5252]E(f271(x52521,x52522),f76(a99))+~P101(f323(f323(f237(a99),x52521),f76(a99)))
% 179.72/179.58 [5346]E(f323(f323(f158(x53461),x53462),f530(x53462,x53461)),f323(f323(f158(x53461),x53462),f537(x53462,x53461)))+P101(f323(f130(x53461),x53462))
% 179.72/179.58 [5391]~P101(f323(x53911,f88(x53912,x53911)))+P101(f323(x53911,f544(x53912,x53911)))
% 179.72/179.58 [5454]P56(x54541,x54542)+~P101(f323(f311(x54541,x54542),f672(x54542,x54541)))
% 179.72/179.58 [5599]~E(f323(a112,f42(a860,x55991,x55992)),x55992)+E(f42(a860,f323(a112,x55991),x55992),f2(a860))
% 179.72/179.58 [5656]P38(x56561,x56562)+P101(f323(f323(f325(x56561),f729(x56562,x56561)),f730(x56562,x56561)))
% 179.72/179.58 [5663]~P134(x56631)+P101(f323(f323(f325(x56631),f323(f100(x56631),x56632)),f109(x56631)))
% 179.72/179.58 [5664]~P140(x56641)+P101(f323(f323(f325(x56641),f323(f100(x56641),x56642)),f186(x56641)))
% 179.72/179.58 [5665]~P134(x56651)+P101(f323(f323(f325(x56651),f323(f102(x56651),x56652)),f109(x56651)))
% 179.72/179.58 [5666]~P90(x56661)+P101(f323(f323(f325(x56661),f323(f103(x56661),x56662)),f109(x56661)))
% 179.72/179.58 [5809]E(f323(a112,f42(a860,x58091,x58092)),x58092)+E(f42(a860,f323(a112,x58091),x58092),f323(a112,f42(a860,x58091,x58092)))
% 179.72/179.58 [6214]P38(x62141,x62142)+~P101(f323(f323(f325(x62141),f649(x62142,x62141)),f312(x62141,x62142)))
% 179.72/179.58 [6248]~P119(x62481)+~P101(f323(f323(f238(x62481),f323(f100(x62481),x62482)),f2(x62481)))
% 179.72/179.58 [6249]~P82(x62491)+~P101(f323(f323(f238(x62491),f323(f73(x62491),x62492)),f2(x62491)))
% 179.72/179.58 [6336]P101(f323(f323(f238(a1),x63361),f42(a1,x63362,x63361)))+~P101(f323(f323(f238(a1),x63361),f2(a1)))
% 179.72/179.58 [6433]E(f323(f323(f301(a860),f323(a112,x64331)),f294(a860,x64332,x64331)),f294(a860,x64332,f323(a112,x64331)))+~P101(f323(f323(f237(a860),x64332),f323(a112,x64331)))
% 179.72/179.58 [6521]~P103(x65211)+P16(x65211,f143(x65211,x65211,f5(x65211),x65212))
% 179.72/179.58 [6649]E(f323(f161(x66491),x66492),x66492)+~P101(f323(f323(f237(a860),f323(f189(f861(x66491)),x66492)),f76(a860)))
% 179.72/179.58 [6669]~P82(x66691)+P101(f323(f323(f237(x66691),f323(f77(x66691),f323(f73(x66691),x66692))),f2(x66691)))
% 179.72/179.58 [6701]~P38(x67011,x67012)+P38(x67011,f323(f323(f280(x67011,x67011,x67011),x67012),f299(x67011,x67012)))
% 179.72/179.58 [6921]~P101(f323(f323(f238(a1),x69212),f2(a1)))+P101(f323(f323(f237(a1),f42(a1,x69211,x69212)),f2(a1)))
% 179.72/179.58 [7312]~P140(x73121)+E(f190(x73121,f323(f323(f7(x73121,x73121,x73121),f78(x73121)),f76(x73121)),x73122,f2(x73121)),f323(f100(x73121),x73122))
% 179.72/179.58 [7340]~P121(x73401)+~P101(f323(f323(f238(x73401),f323(f323(f79(x73401),x73402),x73402)),f2(x73401)))
% 179.72/179.58 [9964]~P116(x99641)+~P101(f323(f323(f238(x99641),f323(f323(f248(x99641),x99642),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f2(x99641)))
% 179.72/179.58 [4650]~E(x46502,f113(x46501))+E(f323(f189(f861(x46501)),x46502),f2(a860))
% 179.72/179.58 [4692]~E(x46921,f2(a860))+E(f323(f323(f78(a860),x46921),x46922),x46922)
% 179.72/179.58 [4693]~E(x46932,f2(a860))+E(f323(f323(f79(a860),x46931),x46932),f2(a860))
% 179.72/179.58 [4695]~E(x46951,f2(a860))+E(f323(f323(f79(a860),x46951),x46952),f2(a860))
% 179.72/179.58 [4696]~E(x46962,f2(a860))+E(f323(f323(f248(a860),x46961),x46962),f76(a860))
% 179.72/179.58 [4697]~E(x46972,f2(a1))+E(f323(f323(f36(a1),x46971),x46972),f2(a1))
% 179.72/179.58 [4707]E(x47071,f113(x47072))+~E(f323(f189(f861(x47072)),x47071),f2(a860))
% 179.72/179.58 [4708]~P2(x47081)+E(f323(f323(f110(x47081),x47082),x47082),x47082)
% 179.72/179.58 [4710]~P97(x47101)+E(f323(f323(f110(x47101),x47102),x47102),x47102)
% 179.72/179.58 [4711]~P2(x47111)+E(f323(f323(f101(x47111),x47112),x47112),x47112)
% 179.72/179.58 [4713]~P98(x47131)+E(f323(f323(f101(x47131),x47132),x47132),x47132)
% 179.72/179.58 [4715]~P93(x47151)+E(f323(f323(f79(x47151),x47152),x47152),x47152)
% 179.72/179.58 [4717]~P103(x47171)+E(f323(f323(f235(x47171),x47172),x47172),x47172)
% 179.72/179.58 [4719]~P103(x47191)+E(f323(f323(f236(x47191),x47192),x47192),x47192)
% 179.72/179.58 [4738]~P59(x47381)+E(f323(f323(f22(x47381),x47382),x47382),f2(x47381))
% 179.72/179.58 [4752]~P87(x47521)+E(f323(f77(x47521),f323(f77(x47521),x47522)),x47522)
% 179.72/179.58 [4753]~P59(x47531)+E(f323(f77(x47531),f323(f77(x47531),x47532)),x47532)
% 179.72/179.58 [4770]~E(x47702,f2(a860))+E(f323(f323(f248(a860),x47701),x47702),f323(a112,f2(a860)))
% 179.72/179.58 [4803]~P3(x48031)+E(f323(f323(f110(x48031),f188(x48031)),x48032),x48032)
% 179.72/179.58 [4804]~P95(x48041)+E(f323(f323(f101(x48041),f246(x48041)),x48042),x48042)
% 179.72/179.58 [4805]~P68(x48051)+E(f323(f323(f79(x48051),f76(x48051)),x48052),x48052)
% 179.72/179.58 [4806]~P77(x48061)+E(f323(f323(f79(x48061),f76(x48061)),x48062),x48062)
% 179.72/179.58 [4807]~P112(x48071)+E(f323(f323(f79(x48071),f76(x48071)),x48072),x48072)
% 179.72/179.58 [4808]~P112(x48081)+E(f323(f323(f78(x48081),f2(x48081)),x48082),x48082)
% 179.72/179.58 [4809]~P78(x48091)+E(f323(f323(f78(x48091),f2(x48091)),x48092),x48092)
% 179.72/179.58 [4810]~P72(x48101)+E(f323(f323(f78(x48101),f2(x48101)),x48102),x48102)
% 179.72/179.58 [4828]~P95(x48281)+E(f323(f323(f110(x48281),f246(x48281)),x48282),f246(x48281))
% 179.72/179.58 [4829]~P3(x48291)+E(f323(f323(f101(x48291),f188(x48291)),x48292),f188(x48291))
% 179.72/179.58 [4830]~P112(x48301)+E(f323(f323(f79(x48301),f2(x48301)),x48302),f2(x48301))
% 179.72/179.58 [4831]~P124(x48311)+E(f323(f323(f79(x48311),f2(x48311)),x48312),f2(x48311))
% 179.72/179.58 [4832]~P77(x48321)+E(f323(f323(f248(x48321),f76(x48321)),x48322),f76(x48321))
% 179.72/179.58 [4833]~P114(x48331)+E(f323(f323(f281(x48331),f2(x48331)),x48332),f2(x48331))
% 179.72/179.58 [4834]~P57(x48341)+E(f323(f323(f36(x48341),f2(x48341)),x48342),f2(x48341))
% 179.72/179.58 [4842]E(x48421,f113(x48422))+E(f137(x48422,f323(f162(x48422),x48421)),f323(f134(x48422),x48421))
% 179.72/179.58 [4843]E(x48431,f113(x48432))+E(f323(f134(x48432),f323(f162(x48432),x48431)),f137(x48432,x48431))
% 179.72/179.58 [4844]E(x48441,f2(a860))+~E(f323(f323(f78(a860),x48442),x48441),x48442)
% 179.72/179.58 [4850]~P134(x48501)+E(f323(f102(x48501),f323(f100(a1),x48502)),f323(f100(x48501),x48502))
% 179.72/179.58 [4851]~P90(x48511)+E(f323(f102(x48511),f323(f103(a1),x48512)),f323(f103(x48511),x48512))
% 179.72/179.58 [4858]E(x48581,f76(a860))+~E(f323(f323(f79(a860),x48582),x48581),f76(a860))
% 179.72/179.58 [4859]E(x48591,f76(a860))+~E(f323(f323(f79(a860),x48591),x48592),f76(a860))
% 179.72/179.58 [4860]E(x48601,f2(a860))+~E(f323(f323(f78(a860),x48602),x48601),f2(a860))
% 179.72/179.58 [4861]E(x48611,f2(a860))+~E(f323(f323(f78(a860),x48611),x48612),f2(a860))
% 179.72/179.58 [4876]~P82(x48761)+E(f323(f73(x48761),f323(f77(x48761),x48762)),f323(f73(x48761),x48762))
% 179.72/179.58 [4877]~P116(x48771)+E(f323(f73(x48771),f323(f100(x48771),x48772)),f323(f100(x48771),x48772))
% 179.72/179.58 [4878]~P82(x48781)+E(f323(f73(x48781),f323(f73(x48781),x48782)),f323(f73(x48781),x48782))
% 179.72/179.58 [4879]~P72(x48791)+E(f323(f159(x48791),f323(f162(x48791),x48792)),f323(f159(x48791),x48792))
% 179.72/179.58 [4884]~E(x48841,f323(a112,f2(a860)))+E(f323(f323(f248(a860),x48841),x48842),f323(a112,f2(a860)))
% 179.72/179.58 [4893]~P59(x48931)+E(f323(f323(f22(x48931),f2(x48931)),x48932),f323(f77(x48931),x48932))
% 179.72/179.58 [4894]~E(x48942,f2(a860))+E(f132(a860,f323(f293(a860,x48941),x48942)),f113(a860))
% 179.72/179.58 [4903]~P90(x49031)+E(f323(f323(f78(x49031),x49032),f323(f103(x49031),a81)),x49032)
% 179.72/179.58 [4904]E(x49041,f2(a1))+E(f44(f323(f73(a1),x49042),f323(f73(a1),x49041)),f50(x49042,x49041))
% 179.72/179.58 [4920]~E(x49201,x49202)+P101(f323(f323(f237(a860),x49201),x49202))
% 179.72/179.58 [4927]~E(x49271,f2(a99))+E(f323(f323(f78(a860),f323(a19,x49271)),x49272),x49272)
% 179.72/179.58 [4928]~E(f323(f103(a1),x49282),f323(f100(a1),x49281))+E(x49281,f323(a104,f323(f103(a1),x49282)))
% 179.72/179.58 [4937]~P7(x49371)+P7(f323(f323(f248(a1),x49371),x49372))
% 179.72/179.58 [4938]~P87(x49381)+E(f323(f323(f110(x49381),x49382),f323(f77(x49381),x49382)),f246(x49381))
% 179.72/179.58 [4939]~P87(x49391)+E(f323(f323(f101(x49391),x49392),f323(f77(x49391),x49392)),f188(x49391))
% 179.72/179.58 [4940]~P59(x49401)+E(f323(f323(f78(x49401),x49402),f323(f77(x49401),x49402)),f2(x49401))
% 179.72/179.58 [4965]E(x49651,f2(a860))+~E(f323(f77(a1),f323(f100(a1),x49652)),f323(f100(a1),x49651))
% 179.72/179.58 [4966]E(x49661,f2(a860))+~E(f323(f77(a1),f323(f100(a1),x49661)),f323(f100(a1),x49662))
% 179.72/179.58 [4976]E(f194(x49761,x49762),f2(a1))+P101(f323(f323(f237(a1),x49762),x49761))
% 179.72/179.58 [4977]E(f172(x49771,x49772),f113(a1))+P101(f323(f323(f237(a1),x49771),x49772))
% 179.72/179.58 [4990]E(x49901,f323(a112,f2(a860)))+~E(f323(f323(f79(a860),x49902),x49901),f323(a112,f2(a860)))
% 179.72/179.58 [4991]E(x49911,f323(a112,f2(a860)))+~E(f323(f323(f79(a860),x49911),x49912),f323(a112,f2(a860)))
% 179.72/179.58 [4992]~P102(x49921)+P101(f323(f323(f237(x49921),x49922),x49922))
% 179.72/179.58 [4993]~P92(x49931)+P101(f323(f323(f89(x49931),x49932),x49932))
% 179.72/179.58 [4996]~P90(x49961)+E(f323(f323(f79(x49961),x49962),f323(f103(x49961),a97)),f323(f77(x49961),x49962))
% 179.72/179.58 [5014]~P134(x50141)+E(f323(f77(x50141),f323(f102(x50141),x50142)),f323(f102(x50141),f323(f77(a1),x50142)))
% 179.72/179.58 [5015]~P90(x50151)+E(f323(f77(x50151),f323(f103(x50151),x50152)),f323(f103(x50151),f323(f77(a1),x50152)))
% 179.72/179.58 [5044]~E(x50441,f323(a112,x50442))+P101(f323(f323(f238(a860),f2(a860)),x50441))
% 179.72/179.58 [5061]~P103(x50611)+E(f323(f77(f867(x50611,a855)),f323(f244(x50611),x50612)),f323(f245(x50611),x50612))
% 179.72/179.58 [5062]~P103(x50621)+E(f323(f77(f867(x50621,a855)),f323(f295(x50621),x50622)),f323(f292(x50621),x50622))
% 179.72/179.58 [5063]~P103(x50631)+E(f323(f77(f867(x50631,a855)),f323(f245(x50631),x50632)),f323(f244(x50631),x50632))
% 179.72/179.58 [5064]~P103(x50641)+E(f323(f77(f867(x50641,a855)),f323(f292(x50641),x50642)),f323(f295(x50641),x50642))
% 179.72/179.58 [5072]~E(f323(f100(a1),x50722),x50721)+P101(f323(f323(f237(a1),f2(a1)),x50721))
% 179.72/179.58 [5079]~E(x50792,f2(a1))+E(f50(x50791,x50792),f323(f323(f258(a1,a1),f2(a1)),f323(f73(a1),x50791)))
% 179.72/179.58 [5081]~P1(x50811)+P101(f323(f323(f237(x50811),f188(x50811)),x50812))
% 179.72/179.58 [5113]E(x51131,x51132)+~E(f323(f323(f78(a1),x51131),x51131),f323(f323(f78(a1),x51132),x51132))
% 179.72/179.58 [5117]~P101(f323(x51171,x51172))+P101(f323(x51171,f323(a104,f363(x51171))))
% 179.72/179.58 [5143]~P116(x51431)+E(f323(f323(f79(x51431),f80(x51431,x51432)),f323(f73(x51431),x51432)),x51432)
% 179.72/179.58 [5150]~E(x51502,f2(a860))+E(f83(f866(a860,a860),f45(x51501,x51502)),f323(f323(f258(a860,a860),f2(a860)),x51501))
% 179.72/179.58 [5155]~E(x51551,x51552)+~P101(f323(f323(f238(a860),x51551),x51552))
% 179.72/179.58 [5156]~E(x51561,x51562)+~P101(f323(f323(f238(a1),x51561),x51562))
% 179.72/179.58 [5159]~P140(x51591)+E(f323(f323(f78(x51591),f76(x51591)),f323(f100(x51591),x51592)),f323(f100(x51591),f323(a112,x51592)))
% 179.72/179.58 [5163]~E(x51631,f2(a860))+~P101(f323(f323(f238(a860),x51632),x51631))
% 179.72/179.58 [5179]E(f145(x51791,x51792),x51792)+~E(f323(f189(f861(x51791)),f145(x51791,x51792)),f323(f189(f861(x51791)),x51792))
% 179.72/179.58 [5180]E(f323(f35(x51801),f323(f166(x51801),x51802)),f323(f189(f861(x51801)),x51802))+~P101(f323(f130(x51801),x51802))
% 179.72/179.58 [5190]~P101(f323(x51901,f364(x51901)))+P101(f323(x51901,f323(f100(a1),x51902)))
% 179.72/179.58 [5201]E(f172(x52011,x52012),f113(a1))+~P101(f323(f323(f238(a1),x52012),x52011))
% 179.72/179.58 [5202]E(f271(x52021,x52022),f76(a99))+~P101(f323(f323(f238(a99),x52022),x52021))
% 179.72/179.58 [5203]~P105(x52031)+E(f294(x52031,x52032,x52032),f323(f323(f301(x52031),x52032),f188(f867(x52031,a855))))
% 179.72/179.58 [5225]~E(f323(f323(f22(a860),x52251),x52252),f2(a860))+P101(f323(f323(f237(a860),x52251),x52252))
% 179.72/179.58 [5226]~E(f323(f323(f22(a1),x52261),x52262),f2(a1))+P101(f323(f323(f89(a1),x52261),x52262))
% 179.72/179.58 [5249]~E(x52492,f2(a860))+E(f52(x52491,x52492,f113(x52491)),f323(f323(f144(f861(x52491)),f113(x52491)),f113(f861(x52491))))
% 179.72/179.58 [5253]~P102(x52531)+~P101(f323(f323(f238(x52531),x52532),x52532))
% 179.72/179.58 [5256]~E(f42(a1,x52561,x52562),f2(a1))+E(f42(a1,x52561,f323(f77(a1),x52562)),f2(a1))
% 179.72/179.58 [5258]~E(f42(a1,x52581,x52582),f2(a1))+E(f42(a1,f323(f77(a1),x52581),x52582),f2(a1))
% 179.72/179.58 [5266]E(f323(f293(a860,x52661),f323(a112,x52662)),f188(f867(a860,a855)))+P101(f323(f323(f237(a860),x52661),x52662))
% 179.72/179.58 [5287]E(f132(a860,f323(f293(a860,x52871),x52872)),f113(a860))+P101(f323(f323(f238(a860),x52871),x52872))
% 179.72/179.58 [5292]~E(f323(f35(x52921),f323(f166(x52921),x52922)),f323(f189(f861(x52921)),x52922))+P101(f323(f130(x52921),x52922))
% 179.72/179.58 [5297]~P101(f323(f130(x52971),x52972))+P101(f323(f130(x52971),f323(f161(x52971),x52972)))
% 179.72/179.58 [5298]~P101(f323(f130(x52981),x52982))+P101(f323(f130(x52981),f323(f165(x52981),x52982)))
% 179.72/179.58 [5299]~P101(f323(f130(x52991),x52992))+P101(f323(f130(x52991),f323(f162(x52991),x52992)))
% 179.72/179.58 [5306]P101(f323(x53061,x53062))+~P101(f323(x53061,f323(a104,f419(x53061))))
% 179.72/179.58 [5307]P101(f323(f323(f237(a860),x53072),x53071))+P101(f323(f323(f237(a860),x53071),x53072))
% 179.72/179.58 [5308]P101(f323(f323(f237(a1),x53082),x53081))+P101(f323(f323(f237(a1),x53081),x53082))
% 179.72/179.58 [5310]~P82(x53101)+P101(f323(f323(f237(x53101),x53102),f323(f73(x53101),x53102)))
% 179.72/179.58 [5313]P101(f323(x53131,f380(x53131)))+~P101(f323(x53131,f323(f100(a1),x53132)))
% 179.72/179.58 [5338]E(f323(f323(f22(a860),x53381),x53382),f2(a860))+~P101(f323(f323(f237(a860),x53381),x53382))
% 179.72/179.58 [5339]E(f323(f323(f22(a1),x53391),x53392),f2(a1))+~P101(f323(f323(f89(a1),x53391),x53392))
% 179.72/179.58 [5340]E(f323(f323(f36(a860),x53401),x53402),f2(a860))+~P101(f323(f323(f238(a860),x53401),x53402))
% 179.72/179.58 [5358]E(f42(a860,x53581,x53582),x53581)+~P101(f323(f323(f238(a860),x53581),x53582))
% 179.72/179.58 [5367]E(f42(a1,x53671,f323(f77(a1),x53672)),f282(x53671,x53672))+P101(f323(f323(f237(a1),f2(a1)),x53672))
% 179.72/179.58 [5379]E(f323(f323(f22(a1),x53791),x53792),f194(x53791,x53792))+~P101(f323(f323(f237(a1),x53792),x53791))
% 179.72/179.58 [5398]P101(f323(f323(f237(a1),f2(a1)),f364(x53981)))+P101(f323(x53981,f323(f100(a1),x53982)))
% 179.72/179.58 [5410]~P5(x54101)+P101(f323(f323(f325(x54101),x54102),f323(f166(x54101),f53(x54101))))
% 179.72/179.58 [5412]~P119(x54121)+P101(f323(f323(f237(x54121),f2(x54121)),f323(f100(x54121),x54122)))
% 179.72/179.58 [5413]~P82(x54131)+P101(f323(f323(f237(x54131),f2(x54131)),f323(f73(x54131),x54132)))
% 179.72/179.58 [5440]E(f323(f323(f78(a860),x54401),f786(x54402,x54401)),x54402)+~P101(f323(f323(f237(a860),x54401),x54402))
% 179.72/179.58 [5452]~E(f323(f103(a1),x54521),f323(f100(a1),x54522))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x54521)))
% 179.72/179.58 [5455]E(f294(a1,x54551,x54552),f188(f867(a1,a855)))+~P101(f323(f323(f238(a1),x54552),x54551))
% 179.72/179.58 [5458]~P116(x54581)+E(f323(f323(f79(x54581),f323(f73(x54581),x54582)),f323(f73(x54581),x54582)),f323(f323(f79(x54581),x54582),x54582))
% 179.72/179.58 [5463]E(f132(a860,f323(f293(a860,x54631),f323(a112,x54632))),f113(a860))+P101(f323(f323(f237(a860),x54631),x54632))
% 179.72/179.58 [5467]E(f323(f323(f36(a1),x54671),x54672),f283(x54671,x54672))+~P101(f323(f323(f237(a1),f2(a1)),x54672))
% 179.72/179.58 [5487]P101(f323(f130(x54871),x54872))+~P101(f323(f130(x54871),f323(f161(x54871),x54872)))
% 179.72/179.58 [5488]P101(f323(f130(x54881),x54882))+~P101(f323(f130(x54881),f323(f162(x54881),x54882)))
% 179.72/179.58 [5509]P101(f323(f59(a860),x55091))+P101(f323(f323(f325(a860),f787(x55091,x55092)),x55091))
% 179.72/179.58 [5510]P101(f323(f59(a860),x55101))+P101(f323(f323(f325(a860),f810(x55101,x55102)),x55101))
% 179.72/179.58 [5512]P101(f323(f323(f238(a860),x55122),f323(a112,x55121)))+P101(f323(f323(f238(a860),x55121),x55122))
% 179.72/179.58 [5513]E(f42(a1,x55131,x55132),f282(x55131,x55132))+~P101(f323(f323(f237(a1),f2(a1)),x55132))
% 179.72/179.58 [5516]E(f132(a860,f323(f293(a860,x55161),x55162)),f113(a860))+~P101(f323(f323(f237(a860),x55162),x55161))
% 179.72/179.58 [5517]~P75(x55171)+E(f323(f302(x55171,x55171,f77(x55171)),f323(f244(x55171),x55172)),f323(f295(x55171),f323(f77(x55171),x55172)))
% 179.72/179.58 [5518]~P75(x55181)+E(f323(f302(x55181,x55181,f77(x55181)),f323(f295(x55181),x55182)),f323(f244(x55181),f323(f77(x55181),x55182)))
% 179.72/179.58 [5519]~P75(x55191)+E(f323(f302(x55191,x55191,f77(x55191)),f323(f245(x55191),x55192)),f323(f292(x55191),f323(f77(x55191),x55192)))
% 179.72/179.58 [5520]~P75(x55201)+E(f323(f302(x55201,x55201,f77(x55201)),f323(f292(x55201),x55202)),f323(f245(x55201),f323(f77(x55201),x55202)))
% 179.72/179.58 [5531]E(x55311,f188(f867(x55312,a855)))+P101(f323(f323(f325(x55312),f430(x55311,x55312)),x55311))
% 179.72/179.58 [5532]E(x55321,f188(f867(x55322,a855)))+P101(f323(f323(f325(x55322),f442(x55321,x55322)),x55321))
% 179.72/179.58 [5543]~P101(f323(f323(f238(a860),x55431),x55432))+P101(f323(f323(f237(a860),x55431),x55432))
% 179.72/179.58 [5544]~P101(f323(f323(f238(a1),x55441),x55442))+P101(f323(f323(f237(a1),x55441),x55442))
% 179.72/179.58 [5560]E(f44(x55601,x55602),f323(f323(f258(a1,a1),f2(a1)),x55601))+~P101(f323(f323(f238(a1),x55601),x55602))
% 179.72/179.58 [5562]E(f217(f323(f77(a1),x55621),f323(f77(a1),x55622)),f217(x55621,x55622))+~P101(f323(f323(f238(a1),x55622),f2(a1)))
% 179.72/179.58 [5573]E(x55731,x55732)+~E(f323(a3,f323(a112,f323(a19,x55731))),f323(a3,f323(a112,f323(a19,x55732))))
% 179.72/179.58 [5578]E(f44(x55781,x55782),f323(f323(f258(a1,a1),f2(a1)),x55781))+~P101(f323(f323(f237(a1),x55782),f2(a1)))
% 179.72/179.58 [5605]E(f42(a860,f323(f103(a860),x56051),f323(f103(a860),x56052)),f2(a860))+~P101(f323(a193,f323(f103(a1),x56051)))
% 179.72/179.58 [5620]P101(f323(f323(f237(a1),f2(a1)),f380(x56201)))+~P101(f323(x56201,f323(f100(a1),x56202)))
% 179.72/179.58 [5654]P39(f294(a1,x56541,x56542))+~P101(f323(f323(f237(a1),f2(a1)),x56541))
% 179.72/179.58 [5659]~P101(f323(f59(x56591),x56592))+P101(f323(f59(f867(x56591,a855)),f323(f300(x56591),x56592)))
% 179.72/179.58 [5672]E(f323(f323(f78(a1),x56721),f323(f100(a1),f366(x56722,x56721))),x56722)+~P101(f323(f323(f237(a1),x56721),x56722))
% 179.72/179.58 [5680]P101(f323(f323(f237(a860),x56801),x56802))+P101(f323(f323(f237(a860),f323(a112,x56802)),x56801))
% 179.72/179.58 [5723]E(f323(f323(f36(a860),f323(f103(a860),x57231)),f323(f103(a860),x57232)),f2(a860))+~P101(f323(a193,f323(f103(a1),x57231)))
% 179.72/179.58 [5724]E(f323(f323(f79(a860),f323(f103(a860),x57241)),f323(f103(a860),x57242)),f2(a860))+~P101(f323(f323(f238(a1),x57241),a81))
% 179.72/179.58 [5726]P101(f323(f323(f237(a860),x57261),f323(a112,x57262)))+~P101(f323(f323(f237(a860),x57261),x57262))
% 179.72/179.58 [5728]P101(f323(f323(f238(a860),x57281),f323(a112,x57282)))+~P101(f323(f323(f237(a860),x57281),x57282))
% 179.72/179.58 [5730]P101(f323(f323(f238(a860),x57301),f323(a112,x57302)))+~P101(f323(f323(f238(a860),x57301),x57302))
% 179.72/179.58 [5733]~E(x57331,x57332)+P101(f323(f323(f238(a1),x57331),f323(f323(f78(a1),x57332),f76(a1))))
% 179.72/179.58 [5736]E(f42(a1,x57361,x57362),f2(a1))+E(f323(f323(f22(a1),x57362),f42(a1,x57361,x57362)),f42(a1,f323(f77(a1),x57361),x57362))
% 179.72/179.58 [5745]E(x57451,f113(x57452))+P101(f323(f323(f325(x57452),f137(x57452,x57451)),f323(f166(x57452),x57451)))
% 179.72/179.58 [5757]E(f83(f866(a860,a860),f45(x57571,x57572)),f323(f323(f258(a860,a860),f2(a860)),x57571))+~P101(f323(f323(f238(a860),x57571),x57572))
% 179.72/179.58 [5790]E(f323(f323(f22(a860),f323(f103(a860),x57901)),f323(f103(a860),x57902)),f323(f103(a860),x57901))+~P101(f323(f323(f238(a1),x57902),a81))
% 179.72/179.58 [5791]E(f323(f323(f78(a860),f323(f103(a860),x57911)),f323(f103(a860),x57912)),f323(f103(a860),x57912))+~P101(f323(f323(f238(a1),x57911),a81))
% 179.72/179.58 [5796]E(f323(a112,f323(f323(f78(a860),x57961),f812(x57962,x57961))),x57962)+~P101(f323(f323(f238(a860),x57961),x57962))
% 179.72/179.58 [5819]P101(f323(x58191,x58192))+~P101(f323(x58191,f323(a87,f682(x58192,x58191))))
% 179.72/179.58 [5827]~P101(f323(f323(f238(a860),x58271),f323(a112,x58272)))+P101(f323(f323(f237(a860),x58271),x58272))
% 179.72/179.58 [5873]E(f323(f323(f301(a860),x58731),f323(f293(a860,x58732),x58731)),f323(f293(a860,x58732),f323(a112,x58731)))+~P101(f323(f323(f237(a860),x58732),x58731))
% 179.72/179.58 [5875]E(x58751,f113(x58752))+E(f323(f323(f121(x58752),f114(x58752,x58751)),f323(f323(f144(x58752),f137(x58752,x58751)),f113(x58752))),x58751)
% 179.72/179.58 [5889]P101(f323(f59(x58891),x58892))+~P101(f323(f323(f238(a860),f2(a860)),f323(f35(x58891),x58892)))
% 179.72/179.58 [5891]~E(x58911,f188(f867(x58912,a855)))+~P101(f323(f323(f238(a860),f2(a860)),f323(f35(x58912),x58911)))
% 179.72/179.58 [5903]~P101(f323(f323(f238(a860),x59031),x59032))+P101(f323(f323(f237(a860),f323(a112,x59031)),x59032))
% 179.72/179.58 [5910]~P103(x59101)+E(f143(x59101,x59101,f5(x59101),f145(x59101,x59102)),f132(x59101,f323(f166(x59101),x59102)))
% 179.72/179.58 [5913]E(x59131,f113(x59132))+P101(f323(f323(f325(x59132),f323(f134(x59132),x59131)),f323(f166(x59132),x59131)))
% 179.72/179.58 [5919]~P119(x59191)+P101(f323(f323(f238(x59191),x59192),f323(f323(f78(x59191),x59192),f76(x59191))))
% 179.72/179.58 [5921]~P82(x59211)+P101(f323(f323(f237(x59211),f323(f77(x59211),x59212)),f323(f73(x59211),x59212)))
% 179.72/179.58 [5951]P101(f323(f59(a860),x59511))+~P101(f323(f323(f237(a860),f787(x59511,x59512)),x59512))
% 179.72/179.58 [5952]P101(f323(f59(a860),x59521))+~P101(f323(f323(f238(a860),f810(x59521,x59522)),x59522))
% 179.72/179.58 [5955]~P101(f323(f59(f866(x59551,x59551)),x59552))+P101(f323(f59(x59551),f323(f276(x59551),x59552)))
% 179.72/179.58 [6008]~P101(f323(f323(f238(a860),x60082),f323(a112,x60081)))+~P101(f323(f323(f238(a860),x60081),x60082))
% 179.72/179.58 [6009]~P105(x60091)+E(f323(f323(f101(f867(x60091,a855)),f323(f292(x60091),x60092)),f323(f245(x60091),x60092)),f323(f323(f301(x60091),x60092),f188(f867(x60091,a855))))
% 179.72/179.58 [6022]P101(f323(f59(x60221),x60222))+~P101(f323(f59(f867(x60221,a855)),f323(f300(x60221),x60222)))
% 179.72/179.58 [6046]P101(f323(f323(f237(a860),f323(a112,x60461)),f323(a112,x60462)))+~P101(f323(f323(f237(a860),x60461),x60462))
% 179.72/179.58 [6047]P101(f323(f323(f237(a860),f323(a19,x60471)),f323(a19,x60472)))+~P101(f323(f323(f237(a99),x60471),x60472))
% 179.72/179.58 [6048]P101(f323(f323(f237(a99),f323(a3,x60481)),f323(a3,x60482)))+~P101(f323(f323(f237(a860),x60481),x60482))
% 179.72/179.58 [6050]P101(f323(f323(f238(a860),f323(a112,x60501)),f323(a112,x60502)))+~P101(f323(f323(f238(a860),x60501),x60502))
% 179.72/179.58 [6051]P101(f323(f323(f238(a860),f323(a19,x60511)),f323(a19,x60512)))+~P101(f323(f323(f238(a99),x60511),x60512))
% 179.72/179.58 [6052]P101(f323(f323(f238(a99),f323(a3,x60521)),f323(a3,x60522)))+~P101(f323(f323(f238(a860),x60521),x60522))
% 179.72/179.58 [6055]E(x60551,x60552)+~E(f323(f302(a860,a1,f100(a1)),x60551),f323(f302(a860,a1,f100(a1)),x60552))
% 179.72/179.58 [6071]P101(f323(f323(f237(a860),x60711),x60712))+~P101(f323(f323(f237(a860),f323(a112,x60711)),x60712))
% 179.72/179.58 [6074]P101(f323(f323(f238(a860),x60741),x60742))+~P101(f323(f323(f237(a860),f323(a112,x60741)),x60742))
% 179.72/179.58 [6075]P101(f323(f323(f238(a860),x60751),x60752))+~P101(f323(f323(f238(a860),f323(a112,x60751)),x60752))
% 179.72/179.58 [6090]E(f42(a1,x60901,x60902),f2(a1))+E(f323(f323(f22(a1),f42(a1,x60901,x60902)),x60902),f42(a1,x60901,f323(f77(a1),x60902)))
% 179.72/179.58 [6154]E(f323(f35(f867(x61541,a855)),f323(f300(x61541),x61542)),f323(f323(f248(a860),f323(a112,f323(a112,f2(a860)))),f323(f35(x61541),x61542)))+~P101(f323(f59(x61541),x61542))
% 179.72/179.58 [6157]E(x61571,f113(x61572))+E(f323(f323(f158(x61572),x61571),f323(f323(f22(a860),f323(f189(f861(x61572)),x61571)),f76(a860))),f137(x61572,x61571))
% 179.72/179.58 [6182]E(x61821,f113(x61822))+E(f323(f323(f121(x61822),f323(f165(x61822),x61821)),f323(f323(f144(x61822),f323(f134(x61822),x61821)),f113(x61822))),f323(f161(x61822),x61821))
% 179.72/179.58 [6211]~P101(f323(f59(x62111),f37(f867(x62111,a855),x62112)))+P101(f323(f59(f867(x62111,a855)),x62112))
% 179.72/179.58 [6233]P101(f323(f323(f237(a860),f323(f103(a860),x62331)),f323(f103(a860),x62332)))+~P101(f323(f323(f237(a1),x62331),a81))
% 179.72/179.58 [6250]~P101(f323(f323(f238(a1),x62501),x62502))+P101(f323(f323(f237(a1),x62501),f323(f323(f22(a1),x62502),f76(a1))))
% 179.72/179.58 [6251]~P101(f323(f323(f237(a1),x62511),x62512))+P101(f323(f323(f238(a1),x62511),f323(f323(f78(a1),x62512),f76(a1))))
% 179.72/179.58 [6252]~P101(f323(f323(f238(a1),x62521),x62522))+P101(f323(f323(f238(a1),x62521),f323(f323(f78(a1),x62522),f76(a1))))
% 179.72/179.58 [6254]~P101(f323(f323(f237(a1),x62541),x62542))+P101(f323(f323(f237(a860),f323(f103(a860),x62541)),f323(f103(a860),x62542)))
% 179.72/179.58 [6256]~P101(f323(f323(f237(a860),x62561),x62562))+P101(f323(f323(f237(a1),f323(f100(a1),x62561)),f323(f100(a1),x62562)))
% 179.72/179.58 [6257]~P101(f323(f323(f237(a1),x62571),x62572))+P101(f323(f323(f237(a1),f323(f103(a1),x62571)),f323(f103(a1),x62572)))
% 179.72/179.58 [6259]~P101(f323(f323(f238(a860),x62591),x62592))+P101(f323(f323(f238(a1),f323(f100(a1),x62591)),f323(f100(a1),x62592)))
% 179.72/179.58 [6260]~P101(f323(f323(f238(a1),x62601),x62602))+P101(f323(f323(f238(a1),f323(f103(a1),x62601)),f323(f103(a1),x62602)))
% 179.72/179.58 [6261]~P101(f323(f323(f89(a1),x62611),x62612))+P101(f323(f323(f89(a1),f323(f103(a1),x62611)),f323(f103(a1),x62612)))
% 179.72/179.58 [6279]~P101(f323(f323(f237(a860),x62791),x62792))+~P101(f323(f323(f237(a860),f323(a112,x62792)),x62791))
% 179.72/179.58 [6321]~P101(f323(f323(f237(a860),f323(a112,x63211)),f323(a112,x63212)))+P101(f323(f323(f237(a860),x63211),x63212))
% 179.72/179.58 [6322]~P101(f323(f323(f237(a99),f323(a3,x63221)),f323(a3,x63222)))+P101(f323(f323(f237(a860),x63221),x63222))
% 179.72/179.58 [6323]~P101(f323(f323(f237(a860),f323(a19,x63231)),f323(a19,x63232)))+P101(f323(f323(f237(a99),x63231),x63232))
% 179.72/179.58 [6325]~P101(f323(f323(f238(a860),f323(a112,x63251)),f323(a112,x63252)))+P101(f323(f323(f238(a860),x63251),x63252))
% 179.72/179.58 [6326]~P101(f323(f323(f238(a99),f323(a3,x63261)),f323(a3,x63262)))+P101(f323(f323(f238(a860),x63261),x63262))
% 179.72/179.58 [6327]~P101(f323(f323(f238(a860),f323(a104,x63271)),f323(a104,x63272)))+P101(f323(f323(f238(a1),x63271),x63272))
% 179.72/179.58 [6328]~P101(f323(f323(f238(a860),f323(a19,x63281)),f323(a19,x63282)))+P101(f323(f323(f238(a99),x63281),x63282))
% 179.72/179.58 [6368]~P101(f323(f323(f238(a860),f323(a104,x63682)),f323(a104,x63681)))+P101(f323(f323(f238(a1),f2(a1)),x63681))
% 179.72/179.58 [6399]P101(f323(f323(f237(a1),f2(a1)),f42(a1,x63991,x63992)))+~P101(f323(f323(f238(a1),f2(a1)),x63992))
% 179.72/179.58 [6556]P38(x65561,x65562)+~E(f323(f323(f280(x65561,x65561,x65561),x65562),x65562),f188(f867(f866(x65561,x65561),a855)))
% 179.72/179.58 [6568]~P38(x65681,x65682)+P38(x65681,f323(f323(f280(x65681,x65681,x65681),x65682),x65682))
% 179.72/179.58 [6579]P101(f323(f323(f237(a1),x65791),x65792))+~P101(f323(f323(f238(a1),x65791),f323(f323(f78(a1),x65792),f76(a1))))
% 179.72/179.58 [6580]P101(f323(f323(f238(a1),x65801),x65802))+~P101(f323(f323(f237(a1),x65801),f323(f323(f22(a1),x65802),f76(a1))))
% 179.72/179.58 [6583]P101(f323(f323(f237(a860),x65831),x65832))+~P101(f323(f323(f237(a1),f323(f100(a1),x65831)),f323(f100(a1),x65832)))
% 179.72/179.58 [6584]P101(f323(f323(f237(a1),x65841),x65842))+~P101(f323(f323(f237(a1),f323(f103(a1),x65841)),f323(f103(a1),x65842)))
% 179.72/179.58 [6586]P101(f323(f323(f238(a860),x65861),x65862))+~P101(f323(f323(f238(a1),f323(f100(a1),x65861)),f323(f100(a1),x65862)))
% 179.72/179.58 [6587]P101(f323(f323(f238(a1),x65871),x65872))+~P101(f323(f323(f238(a860),f323(f103(a860),x65871)),f323(f103(a860),x65872)))
% 179.72/179.58 [6588]P101(f323(f323(f238(a1),x65881),x65882))+~P101(f323(f323(f238(a1),f323(f103(a1),x65881)),f323(f103(a1),x65882)))
% 179.72/179.58 [6589]P101(f323(f323(f89(a1),x65891),x65892))+~P101(f323(f323(f89(a1),f323(f103(a1),x65891)),f323(f103(a1),x65892)))
% 179.72/179.58 [6682]~E(f579(x66822,x66821),f113(x66821))+E(f323(f135(f861(x66821),f861(x66821),f121(x66821),f113(x66821)),x66822),f113(x66821))
% 179.72/179.58 [6683]~E(f580(x66832,x66831),f113(x66831))+E(f323(f135(f861(x66831),f861(x66831),f121(x66831),f113(x66831)),x66832),f113(x66831))
% 179.72/179.58 [6689]~P6(x66891)+E(f323(f135(x66891,x66891,f110(x66891),f188(x66891)),x66892),f37(x66891,f323(f166(x66891),x66892)))
% 179.72/179.58 [6690]~P6(x66901)+E(f323(f135(x66901,x66901,f101(x66901),f246(x66901)),x66902),f38(x66901,f323(f166(x66901),x66902)))
% 179.72/179.58 [6702]E(x67021,f2(a99))+E(f323(f323(f78(a860),f323(a19,f323(f323(f22(a99),x67021),f76(a99)))),f323(a112,x67022)),f323(f323(f78(a860),f323(a19,x67021)),x67022))
% 179.72/179.58 [6752]P101(f323(f323(f238(a1),f323(f323(f22(a1),x67521),x67522)),f2(a1)))+~P101(f323(f323(f238(a1),x67521),x67522))
% 179.72/179.58 [6780]~P103(x67801)+E(f323(f323(f110(f867(x67801,a855)),f323(f323(f301(x67801),x67802),f188(f867(x67801,a855)))),f323(f295(x67801),x67802)),f323(f245(x67801),x67802))
% 179.72/179.58 [6854]~P56(x68541,x68542)+P38(x68541,f323(f243(f866(x68541,x68541)),f323(f262(x68541,x68541,a855),x68542)))
% 179.72/179.58 [6855]~P56(x68551,x68552)+P54(x68551,f323(f243(f866(x68551,x68551)),f323(f262(x68551,x68551,a855),x68552)))
% 179.72/179.58 [6856]E(x68561,f188(f867(x68562,a855)))+~P101(f323(f323(f237(f867(x68562,a855)),x68561),f188(f867(x68562,a855))))
% 179.72/179.58 [6937]~P101(f323(f323(f238(a860),f2(a860)),x69372))+P101(f323(f323(f237(a860),f42(a860,x69371,x69372)),x69372))
% 179.72/179.58 [6938]~P101(f323(f323(f237(a1),f2(a1)),x69381))+P101(f323(f323(f237(a1),f42(a1,x69381,x69382)),x69381))
% 179.72/179.58 [6939]~P101(f323(f323(f238(a860),f2(a860)),x69392))+P101(f323(f323(f238(a860),f42(a860,x69391,x69392)),x69392))
% 179.72/179.58 [6941]~P101(f323(f323(f238(a1),f2(a1)),x69412))+P101(f323(f323(f238(a1),f42(a1,x69411,x69412)),x69412))
% 179.72/179.58 [7017]~P105(x70171)+E(f323(f323(f22(f867(x70171,a855)),f323(f323(f301(x70171),x70172),f188(f867(x70171,a855)))),f323(f244(x70171),x70172)),f323(f323(f301(x70171),x70172),f188(f867(x70171,a855))))
% 179.72/179.58 [7090]~P49(x70901,x70902)+P40(x70901,f246(f867(x70901,a855)),f323(f243(f866(x70901,x70901)),f323(f262(x70901,x70901,a855),x70902)))
% 179.72/179.58 [7091]P101(f323(x70911,x70912))+P101(f323(f323(f325(f867(f866(a860,a860),a855)),f682(x70912,x70911)),a98))
% 179.72/179.58 [7136]E(f323(f323(f121(a860),f132(a860,f323(f293(a860,x71361),x71362))),f323(f323(f144(a860),x71362),f113(a860))),f132(a860,f323(f293(a860,x71361),f323(a112,x71362))))+~P101(f323(f323(f237(a860),x71361),x71362))
% 179.72/179.58 [7277]E(x72771,f2(a860))+~E(f323(f135(a860,a860,f78(a860),x72771),x72772),f2(a860))
% 179.72/179.58 [7302]~P101(f323(f323(f238(a1),f323(f323(f22(a1),x73021),x73022)),f2(a1)))+P101(f323(f323(f238(a1),x73021),x73022))
% 179.72/179.58 [7331]P38(x73311,x73312)+~P38(x73311,f323(f323(f280(x73311,x73311,x73311),x73312),x73312))
% 179.72/179.58 [7360]~P101(f323(f323(f237(a860),f323(a112,x73601)),x73602))+P101(f185(a855,a241,f323(f237(a860),x73601),x73602))
% 179.72/179.58 [7516]P27(a860,a860,f323(f323(f7(a860,a860,a860),f22(a860)),x75161),x75162)+P101(f323(f323(f325(a860),f354(x75161,x75162)),x75162))
% 179.72/179.58 [7572]E(f323(f323(f323(f63(a860,x75721,f78(a860)),f323(f16(a860,x75721),f76(a860))),f2(a860)),x75722),f323(f35(x75721),x75722))+~P101(f323(f59(x75721),x75722))
% 179.72/179.58 [7614]P27(a860,a860,f323(f323(f7(a860,a860,a860),f22(a860)),x76141),x76142)+~P101(f323(f323(f237(a860),x76141),f354(x76141,x76142)))
% 179.72/179.58 [7672]P38(x76721,x76722)+P101(f323(f323(f237(f867(x76721,a855)),f686(x76722,x76721)),f323(f277(x76721,x76721,x76722),f686(x76722,x76721))))
% 179.72/179.58 [7677]P56(x76771,x76772)+~P38(x76771,f323(f243(f866(x76771,x76771)),f323(f262(x76771,x76771,a855),x76772)))
% 179.72/179.58 [7745]P101(f323(f323(f237(a860),f323(a112,x77451)),x77452))+~P101(f185(a855,a241,f323(f237(a860),x77451),x77452))
% 179.72/179.58 [7800]P101(f323(f323(f325(f866(a860,a860)),f323(f323(f258(a860,a860),x78001),x78002)),f299(a860,a313)))+~P101(f323(f323(f237(a860),x78001),x78002))
% 179.72/179.58 [7901]P49(x79011,x79012)+~P40(x79011,f246(f867(x79011,a855)),f323(f243(f866(x79011,x79011)),f323(f262(x79011,x79011,a855),x79012)))
% 179.72/179.58 [7955]~P101(f323(f130(x79551),x79552))+P101(f323(f130(f867(x79551,a855)),f323(f323(f147(f861(x79551),f867(x79551,a855)),f166(x79551)),f51(x79551,x79552))))
% 179.72/179.58 [8154]~P38(x81541,f323(f278(x81541,x81541),x81542))+P38(x81541,f323(f278(x81541,x81541),f323(f323(f280(x81541,x81541,x81541),x81542),f299(x81541,x81542))))
% 179.72/179.58 [8252]P28(x82521,a860,f462(x82522,x82521),x82522,f323(f293(a860,f2(a860)),f323(f35(x82521),x82522)))+~P101(f323(f59(x82521),x82522))
% 179.72/179.58 [8253]P28(a860,x82531,f463(x82532,x82531),f323(f293(a860,f2(a860)),f323(f35(x82531),x82532)),x82532)+~P101(f323(f59(x82531),x82532))
% 179.72/179.58 [8270]P28(a860,x82701,f455(x82702,x82701),f294(a860,f76(a860),f323(f35(x82701),x82702)),x82702)+~P101(f323(f59(x82701),x82702))
% 179.72/179.58 [8279]P101(f323(f59(f866(x82791,x82791)),f323(f323(f280(x82791,x82791,x82791),x82792),f299(x82791,x82792))))+~P101(f323(f59(f866(x82791,x82791)),x82792))
% 179.72/179.58 [8310]E(x83101,f2(a1))+P101(f323(f46(x83102,x83101),f323(f323(f258(a1,a1),f323(f323(f36(a1),x83102),x83101)),f42(a1,x83102,x83101))))
% 179.72/179.58 [8324]~P101(f323(f323(f325(f866(a860,a860)),f323(f323(f258(a860,a860),x83241),x83242)),f299(a860,a313)))+P101(f323(f323(f237(a860),x83241),x83242))
% 179.72/179.58 [8339]~P78(x83391)+E(f323(f135(x83391,x83391,f323(f7(x83391,x83391,x83391),f78(x83391)),f2(x83391)),f323(f162(x83391),x83392)),f323(f135(x83391,x83391,f78(x83391),f2(x83391)),x83392))
% 179.72/179.58 [8506]~P103(x85061)+E(f323(f135(f861(x85061),x85061,f323(f7(x85061,f861(x85061),f861(x85061)),f141(x85061,x85061,f5(x85061))),f113(x85061)),x85062),f143(x85061,x85061,f5(x85061),x85062))
% 179.72/179.58 [8619]~P54(x86191,f323(f243(f866(x86191,x86191)),f323(f262(x86191,x86191,a855),x86192)))+P54(x86191,f323(f243(f866(x86191,x86191)),f323(f262(x86191,x86191,a855),f247(x86191,x86191,x86192))))
% 179.72/179.58 [8633]P101(f323(f323(f325(f866(a860,a860)),f323(f323(f258(a860,a860),x86331),x86332)),f323(f323(f280(a860,a860,a860),a313),f299(a860,a313))))+~P101(f323(f323(f238(a860),x86331),x86332))
% 179.72/179.58 [8679]~P101(f323(f59(f866(x86791,x86791)),f323(f323(f280(x86791,x86791,x86791),x86792),f299(x86791,x86792))))+P101(f323(f59(f866(x86791,x86791)),x86792))
% 179.72/179.58 [8738]~P54(x87381,f323(f243(f866(x87381,x87381)),f323(f262(x87381,x87381,a855),f247(x87381,x87381,x87382))))+P54(x87381,f323(f243(f866(x87381,x87381)),f323(f262(x87381,x87381,a855),x87382)))
% 179.72/179.58 [8933]P54(x89331,x89332)+P101(f323(f323(f325(f866(x89331,x89331)),f323(f323(f258(x89331,x89331),f721(x89332,x89331)),f721(x89332,x89331))),f323(f323(f280(x89331,x89331,x89331),x89332),f299(x89331,x89332))))
% 179.72/179.58 [8934]P54(x89341,x89342)+P101(f323(f323(f325(f866(x89341,x89341)),f323(f323(f258(x89341,x89341),f735(x89342,x89341)),f735(x89342,x89341))),f323(f323(f280(x89341,x89341,x89341),x89342),f299(x89341,x89342))))
% 179.72/179.58 [9054]~P101(f323(f323(f325(f866(a860,a860)),f323(f323(f258(a860,a860),x90541),x90542)),f323(f323(f280(a860,a860,a860),a313),f299(a860,a313))))+P101(f323(f323(f238(a860),x90541),x90542))
% 179.72/179.58 [5057]~P90(x50571)+E(f323(f323(f78(x50571),f323(f103(x50571),a81)),x50572),x50572)
% 179.72/179.58 [5086]~P87(x50861)+E(f323(f323(f110(x50861),f323(f77(x50861),x50862)),x50862),f246(x50861))
% 179.72/179.58 [5087]~P87(x50871)+E(f323(f323(f101(x50871),f323(f77(x50871),x50872)),x50872),f188(x50871))
% 179.72/179.58 [5088]~P59(x50881)+E(f323(f323(f78(x50881),f323(f77(x50881),x50882)),x50882),f2(x50881))
% 179.72/179.58 [5089]~P60(x50891)+E(f323(f323(f78(x50891),f323(f77(x50891),x50892)),x50892),f2(x50891))
% 179.72/179.58 [5121]~P90(x51211)+E(f323(f323(f79(x51211),f323(f103(x51211),a97)),x51212),f323(f77(x51211),x51212))
% 179.72/179.58 [5280]~P109(x52801)+E(f323(f323(f79(x52801),f323(f77(x52801),f76(x52801))),x52802),f323(f77(x52801),x52802))
% 179.72/179.58 [5323]E(f323(f73(a1),x53231),f76(a1))+~E(f323(f73(a1),f323(f323(f79(a1),x53231),x53232)),f76(a1))
% 179.72/179.58 [5415]~P90(x54151)+E(f323(f323(f78(x54151),f76(x54151)),f323(f103(x54151),x54152)),f323(f103(x54151),f323(f323(f22(a1),x54152),a97)))
% 179.72/179.58 [5468]~P2(x54681)+E(f11(x54681,f323(f323(f301(x54681),x54682),f188(f867(x54681,a855)))),x54682)
% 179.72/179.58 [5469]~P2(x54691)+E(f10(x54691,f323(f323(f301(x54691),x54692),f188(f867(x54691,a855)))),x54692)
% 179.72/179.58 [5470]~P103(x54701)+E(f14(x54701,f323(f323(f301(x54701),x54702),f188(f867(x54701,a855)))),x54702)
% 179.72/179.58 [5471]~P103(x54711)+E(f15(x54711,f323(f323(f301(x54711),x54712),f188(f867(x54711,a855)))),x54712)
% 179.72/179.58 [5472]~P6(x54721)+E(f37(x54721,f323(f323(f301(x54721),x54722),f188(f867(x54721,a855)))),x54722)
% 179.72/179.58 [5473]~P6(x54731)+E(f38(x54731,f323(f323(f301(x54731),x54732),f188(f867(x54731,a855)))),x54732)
% 179.72/179.58 [5495]E(f323(f323(f78(a860),x54951),f323(f323(f22(a860),x54952),x54951)),x54952)+P101(f323(f323(f238(a860),x54952),x54951))
% 179.72/179.58 [5526]E(x55261,f113(x55262))+P101(f323(f323(f238(a860),f2(a860)),f323(f189(f861(x55262)),x55261)))
% 179.72/179.58 [5651]~P103(x56511)+E(f12(x56511,f235(x56511),f323(f323(f301(x56511),x56512),f188(f867(x56511,a855)))),x56512)
% 179.72/179.58 [5652]~P103(x56521)+E(f13(x56521,f236(x56521),f323(f323(f301(x56521),x56522),f188(f867(x56521,a855)))),x56522)
% 179.72/179.58 [5713]E(f323(f323(f22(a860),x57131),f323(f323(f22(a860),x57131),x57132)),x57132)+~P101(f323(f323(f237(a860),x57132),x57131))
% 179.72/179.58 [5714]E(f323(f323(f78(a860),x57141),f323(f323(f22(a860),x57142),x57141)),x57142)+~P101(f323(f323(f237(a860),x57141),x57142))
% 179.72/179.58 [5735]E(f42(a860,f323(f323(f22(a860),x57351),x57352),x57352),f42(a860,x57351,x57352))+P101(f323(f323(f238(a860),x57351),x57352))
% 179.72/179.58 [5746]E(f323(f77(a1),f323(f323(f36(a1),x57461),f323(f77(a1),x57462))),f283(x57461,x57462))+P101(f323(f323(f237(a1),f2(a1)),x57462))
% 179.72/179.58 [5748]~E(x57482,f2(a860))+P101(f323(f323(f238(a860),f2(a860)),f323(f323(f248(a860),x57481),x57482)))
% 179.72/179.58 [5799]~P90(x57991)+E(f323(f323(f78(x57991),f323(f77(x57991),f76(x57991))),f323(f103(x57991),x57992)),f323(f103(x57991),f323(f323(f78(a1),x57992),a97)))
% 179.72/179.58 [5800]E(f323(f323(f248(a860),f323(f103(a860),x58001)),x58002),f323(f323(f248(a860),f2(a860)),x58002))+~P101(f323(a193,f323(f103(a1),x58001)))
% 179.72/179.58 [5895]E(f323(f134(a860),f132(a860,f323(f293(a860,x58951),x58952))),x58951)+~P101(f323(f323(f238(a860),x58951),x58952))
% 179.72/179.58 [5914]E(f323(f323(f79(a860),f323(f103(a860),x59141)),f323(f103(a860),x59142)),f323(f103(a860),f323(f323(f79(a1),x59141),x59142)))+P101(f323(f323(f238(a1),x59141),a81))
% 179.72/179.58 [5920]~P121(x59201)+P101(f323(f323(f237(x59201),f2(x59201)),f323(f323(f79(x59201),x59202),x59202)))
% 179.72/179.58 [5932]E(f323(f323(f22(a860),f323(a112,x59321)),x59322),f323(a112,f323(f323(f22(a860),x59321),x59322)))+~P101(f323(f323(f237(a860),x59322),x59321))
% 179.72/179.58 [5935]E(f42(a860,f323(f323(f22(a860),x59351),x59352),x59352),f42(a860,x59351,x59352))+~P101(f323(f323(f237(a860),x59352),x59351))
% 179.72/179.58 [5983]E(f323(f323(f248(a860),f323(a104,x59831)),x59832),f323(a104,f323(f323(f248(a1),x59831),x59832)))+~P101(f323(f323(f237(a1),f2(a1)),x59831))
% 179.72/179.58 [5999]P101(f323(f130(x59991),x59992))+P101(f323(f323(f238(a860),f530(x59992,x59991)),f323(f189(f861(x59991)),x59992)))
% 179.72/179.58 [6000]P101(f323(f130(x60001),x60002))+P101(f323(f323(f238(a860),f537(x60002,x60001)),f323(f189(f861(x60001)),x60002)))
% 179.72/179.58 [6015]~E(x60151,f113(x60152))+~P101(f323(f323(f238(a860),f2(a860)),f323(f189(f861(x60152)),x60151)))
% 179.72/179.58 [6029]E(f137(a860,f132(a860,f323(f293(a860,x60291),x60292))),f323(f323(f22(a860),x60292),f76(a860)))+~P101(f323(f323(f238(a860),x60291),x60292))
% 179.72/179.58 [6032]E(f323(f323(f78(a1),x60321),f323(f100(a1),f323(a112,f367(x60322,x60321)))),x60322)+~P101(f323(f323(f238(a1),x60321),x60322))
% 179.72/179.58 [6039]E(x60391,f2(a860))+E(f323(f323(f79(a860),x60392),f323(f323(f248(a860),x60392),f323(f323(f22(a860),x60391),f76(a860)))),f323(f323(f248(a860),x60392),x60391))
% 179.72/179.58 [6065]E(f323(f323(f79(a860),f323(a104,x60651)),f323(a104,x60652)),f323(a104,f323(f323(f79(a1),x60651),x60652)))+~P101(f323(f323(f237(a1),f2(a1)),x60651))
% 179.72/179.58 [6066]E(f323(f323(f36(a860),f323(a104,x60661)),f323(a104,x60662)),f323(a104,f323(f323(f36(a1),x60661),x60662)))+~P101(f323(f323(f237(a1),f2(a1)),x60661))
% 179.72/179.58 [6080]~P112(x60801)+E(f323(f323(f78(x60801),x60802),x60802),f323(f323(f79(x60801),f323(f323(f78(x60801),f76(x60801)),f76(x60801))),x60802))
% 179.72/179.58 [6097]E(f323(f323(f22(a1),f323(f100(a1),x60971)),f323(f100(a1),x60972)),f323(f100(a1),f323(f323(f22(a860),x60971),x60972)))+~P101(f323(f323(f237(a860),x60972),x60971))
% 179.72/179.58 [6099]E(f323(f323(f258(a1,a1),f323(f103(a1),a97)),f323(f323(f78(a1),x60991),x60992)),f47(x60991,x60992))+~P101(f323(f323(f237(a1),x60992),f2(a1)))
% 179.72/179.58 [6133]E(f173(x61331,x61332),f113(f861(x61331)))+P101(f323(f323(f325(f861(x61331)),f543(x61332,x61331)),f323(f166(f861(x61331)),x61332)))
% 179.72/179.58 [6217]E(f323(f323(f144(a1),x62171),f172(f323(f323(f78(a1),x62171),f76(a1)),x62172)),f172(x62171,x62172))+~P101(f323(f323(f237(a1),x62171),x62172))
% 179.72/179.58 [6253]~P101(f323(f323(f238(a860),x62532),x62531))+P101(f323(f323(f238(a860),f2(a860)),f323(f323(f22(a860),x62531),x62532)))
% 179.72/179.58 [6284]~P101(f323(f323(f238(a860),x62841),f323(a104,x62842)))+P101(f323(f323(f238(a1),f323(f100(a1),x62841)),x62842))
% 179.72/179.58 [6313]~P103(x63131)+E(f323(f323(f110(f867(x63131,a855)),f323(f244(x63131),x63132)),f323(f323(f301(x63131),x63132),f188(f867(x63131,a855)))),f323(f292(x63131),x63132))
% 179.72/179.58 [6314]~P101(f323(f323(f237(a1),f2(a1)),x63141))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f248(a1),x63141),x63142)))
% 179.72/179.58 [6317]~P101(f323(f323(f238(a860),f2(a860)),x63171))+P101(f323(f323(f238(a860),f2(a860)),f323(f323(f248(a860),x63171),x63172)))
% 179.72/179.58 [6344]~E(f323(x63441,f2(a860)),f2(a860))+E(f323(f323(f6(a860,a860),x63441),f294(a860,f323(a112,f2(a860)),x63442)),f323(f323(f6(a860,a860),x63441),f294(a860,f2(a860),x63442)))
% 179.72/179.58 [6407]~P90(x64071)+E(f323(f323(f79(x64071),f323(f323(f78(x64071),f76(x64071)),f76(x64071))),f323(f103(x64071),x64072)),f323(f103(x64071),f323(f323(f78(a1),x64072),x64072)))
% 179.72/179.58 [6422]E(f323(f323(f301(a1),x64221),f294(a1,f323(f323(f78(a1),x64221),f76(a1)),x64222)),f294(a1,x64221,x64222))+P101(f323(f323(f238(a1),x64222),x64221))
% 179.72/179.58 [6423]P101(f323(f323(f238(a860),x64231),f323(a104,x64232)))+~P101(f323(f323(f238(a1),f323(f100(a1),x64231)),x64232))
% 179.72/179.58 [6524]E(f323(a104,f323(f323(f36(a1),f323(f103(a1),x65241)),f323(f103(a1),x65242))),f323(f323(f36(a860),f323(f103(a860),x65241)),f323(f103(a860),x65242)))+P101(f323(a193,f323(f103(a1),x65241)))
% 179.72/179.58 [6581]P101(f323(f323(f238(a860),x65811),x65812))+~P101(f323(f323(f238(a860),f2(a860)),f323(f323(f22(a860),x65812),x65811)))
% 179.72/179.58 [6625]P101(f323(f323(f238(a860),f2(a860)),x66251))+~P101(f323(f323(f238(a860),f2(a860)),f323(f323(f79(a860),x66252),x66251)))
% 179.72/179.58 [6626]P101(f323(f323(f238(a860),f2(a860)),x66261))+~P101(f323(f323(f238(a860),f2(a860)),f323(f323(f79(a860),x66261),x66262)))
% 179.72/179.58 [6643]~P101(f323(f323(f237(a1),x66431),f2(a1)))+E(f323(f323(f79(a860),f323(a104,f323(f77(a1),x66431))),f323(a104,f323(f77(a1),x66432))),f323(a104,f323(f323(f79(a1),x66431),x66432)))
% 179.72/179.58 [6700]~E(x67002,f188(f867(x67001,a855)))+P101(f323(f323(f237(f867(x67001,a855)),x67002),f323(f77(f867(x67001,a855)),x67002)))
% 179.72/179.58 [6763]~P90(x67631)+E(f323(f323(f78(x67631),f323(f323(f78(x67631),f2(x67631)),f323(f103(x67631),x67632))),f323(f103(x67631),x67632)),f323(f103(x67631),f323(f323(f78(a1),x67632),x67632)))
% 179.72/179.58 [6820]~P101(f323(f323(f238(a1),x68201),x68202))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x68201),f76(a1))),x68202))
% 179.72/179.58 [6884]E(x68841,f2(a860))+~P101(f323(f323(f237(a1),f323(f100(a1),x68842)),f323(f77(a1),f323(f100(a1),x68841))))
% 179.72/179.58 [6885]E(x68851,f2(a860))+~P101(f323(f323(f237(a1),f323(f100(a1),x68851)),f323(f77(a1),f323(f100(a1),x68852))))
% 179.72/179.58 [6988]E(f323(f323(f258(a1,a1),f323(f103(a1),a97)),f323(f323(f78(a1),x69881),x69882)),f47(x69881,x69882))+~P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),x69881),x69882)))
% 179.72/179.58 [7030]~P29(x70301,x70302)+P38(x70301,f323(f257(f867(f866(x70301,x70301),a855),f867(f866(x70301,x70301),a855)),x70302))
% 179.72/179.58 [7048]~P101(f323(f323(f237(a860),f323(a112,f2(a860))),x70481))+P101(f323(f323(f237(a860),f323(a112,f2(a860))),f323(f323(f248(a860),x70481),x70482)))
% 179.72/179.58 [7218]~P101(f323(f323(f237(a1),x72181),x72182))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x72181),x72181)),f323(f323(f78(a1),x72182),x72182)))
% 179.72/179.58 [7223]~P101(f323(f323(f238(a1),x72231),x72232))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x72231),x72231)),f323(f323(f78(a1),x72232),x72232)))
% 179.72/179.58 [7224]~P101(f323(f323(f89(a1),x72241),x72242))+P101(f323(f323(f89(a1),f323(f323(f78(a1),x72241),x72241)),f323(f323(f78(a1),x72242),x72242)))
% 179.72/179.58 [7279]~P101(f323(f323(f238(a860),f2(a860)),x72791))+P101(f323(f323(f238(a860),f323(f323(f22(a860),x72791),f323(a112,x72792))),x72791))
% 179.72/179.58 [7313]P101(f323(f323(f237(a860),f323(a112,f2(a860))),x73131))+~P101(f323(f323(f237(a860),f323(a112,f2(a860))),f323(f323(f79(a860),x73132),x73131)))
% 179.72/179.58 [7314]P101(f323(f323(f237(a860),f323(a112,f2(a860))),x73141))+~P101(f323(f323(f237(a860),f323(a112,f2(a860))),f323(f323(f79(a860),x73141),x73142)))
% 179.72/179.58 [7318]P101(f323(f323(f237(a860),f323(f323(f158(a860),x73181),x73182)),f323(f159(a860),x73181)))+~P101(f323(f323(f238(a860),x73182),f323(f189(f861(a860)),x73181)))
% 179.72/179.58 [7359]P101(f323(f323(f238(a1),x73591),x73592))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x73591),f76(a1))),x73592))
% 179.72/179.58 [7403]P101(f323(f59(x74031),f246(f867(x74031,a855))))+~P101(f323(f59(f867(x74032,x74031)),f246(f867(f867(x74032,x74031),a855))))
% 179.72/179.58 [7404]P101(f323(f59(x74041),f246(f867(x74041,a855))))+~P101(f323(f59(f865(x74042,x74041)),f246(f867(f865(x74042,x74041),a855))))
% 179.72/179.58 [7405]P101(f323(f59(x74051),f246(f867(x74051,a855))))+~P101(f323(f59(f865(x74051,x74052)),f246(f867(f865(x74051,x74052),a855))))
% 179.72/179.58 [7446]E(x74461,f188(f867(x74462,a855)))+~P101(f323(f323(f237(f867(x74462,a855)),x74461),f323(f77(f867(x74462,a855)),x74461)))
% 179.72/179.58 [7582]E(f323(f135(f861(x75821),f861(x75821),f121(x75821),f113(x75821)),x75822),f113(x75821))+P101(f323(f323(f325(f861(x75821)),f579(x75822,x75821)),f323(f166(f861(x75821)),x75822)))
% 179.72/179.58 [7583]E(f323(f135(f861(x75831),f861(x75831),f121(x75831),f113(x75831)),x75832),f113(x75831))+P101(f323(f323(f325(f861(x75831)),f580(x75832,x75831)),f323(f166(f861(x75831)),x75832)))
% 179.72/179.58 [7819]P101(f323(f323(f237(a1),x78191),x78192))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x78191),x78191)),f323(f323(f78(a1),x78192),x78192)))
% 179.72/179.58 [7824]P101(f323(f323(f238(a1),x78241),x78242))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x78241),x78241)),f323(f323(f78(a1),x78242),x78242)))
% 179.72/179.58 [7825]P101(f323(f323(f89(a1),x78251),x78252))+~P101(f323(f323(f89(a1),f323(f323(f78(a1),x78251),x78251)),f323(f323(f78(a1),x78252),x78252)))
% 179.72/179.58 [7921]~P112(x79211)+E(f323(f323(f79(x79211),f323(f323(f78(x79211),f76(x79211)),f76(x79211))),f323(f323(f6(a860,x79211),f100(x79211)),f294(a860,f76(a860),x79212))),f323(f323(f79(x79211),f323(f100(x79211),x79212)),f323(f323(f78(x79211),f323(f100(x79211),x79212)),f76(x79211))))
% 179.72/179.58 [7969]P101(f323(f323(f325(a860),x79691),x79692))+~P101(f323(f323(f325(a1),f323(f100(a1),x79691)),f323(f302(a860,a1,f100(a1)),x79692)))
% 179.72/179.58 [8126]~P101(f323(f59(x81261),x81262))+E(f323(f302(a860,x81261,f825(x81262,x81261)),f323(f243(a860),f323(f323(f7(a860,a860,a855),f238(a860)),f826(x81262,x81261)))),x81262)
% 179.72/179.58 [8410]P42(x84101,x84102)+P101(f323(f323(f325(f866(x84101,x84101)),f323(f323(f258(x84101,x84101),f511(x84102,x84101)),f511(x84102,x84101))),x84102))
% 179.72/179.58 [8550]~P90(x85501)+E(f323(f323(f22(x85501),f76(x85501)),f323(f103(x85501),x85502)),f323(f103(x85501),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f77(a1),x85502))))
% 179.72/179.58 [8676]~P101(f323(f323(f238(f867(a860,a855)),x86761),x86762))+P101(f323(f323(f238(f867(a1,a855)),f323(f302(a860,a1,f100(a1)),x86761)),f323(f302(a860,a1,f100(a1)),x86762)))
% 179.72/179.58 [8710]~P101(f323(f323(f238(a1),x87101),x87102))+P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x87101),x87101)),a97)),f323(f323(f78(a1),x87102),x87102)))
% 179.72/179.58 [8712]~P101(f323(f323(f238(a1),x87121),x87122))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x87121),x87121)),a97)),f323(f323(f78(a1),x87122),x87122)))
% 179.72/179.58 [8786]~P101(f323(f323(f325(a860),x87861),f323(f166(a860),x87862)))+P101(f323(f323(f237(a860),x87861),f323(f135(a860,a860,f78(a860),f2(a860)),x87862)))
% 179.72/179.58 [8878]P46(x88781,x88782)+~P101(f323(f323(f325(f866(x88781,x88781)),f323(f323(f258(x88781,x88781),f505(x88782,x88781)),f505(x88782,x88781))),x88782))
% 179.72/179.58 [9015]~P101(f323(f323(f237(f867(a1,a855)),f323(f302(a860,a1,f100(a1)),x90151)),f323(f302(a860,a1,f100(a1)),x90152)))+P101(f323(f323(f237(f867(a860,a855)),x90151),x90152))
% 179.72/179.58 [9016]~P101(f323(f323(f238(f867(a1,a855)),f323(f302(a860,a1,f100(a1)),x90161)),f323(f302(a860,a1,f100(a1)),x90162)))+P101(f323(f323(f238(f867(a860,a855)),x90161),x90162))
% 179.72/179.58 [9100]P101(f323(f323(f238(a1),x91001),x91002))+~P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x91001),x91001)),a97)),f323(f323(f78(a1),x91002),x91002)))
% 179.72/179.58 [9102]P101(f323(f323(f238(a1),x91021),x91022))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x91021),x91021)),a97)),f323(f323(f78(a1),x91022),x91022)))
% 179.72/179.58 [10004]~P101(f323(f59(x100041),x100042))+E(f323(f189(f861(x100041)),f88(f861(x100041),f323(f323(f18(f861(x100041),a855,a855),f323(f323(f8(a855,f867(a855,a855),f861(x100041)),a321),f323(f323(f7(f861(x100041),f867(x100041,a855),a855),f323(f323(f8(f867(x100041,a855),f867(f867(x100041,a855),a855),f861(x100041)),a320),f166(x100041))),x100042))),f130(x100041)))),f216(x100041,x100042))
% 179.72/179.58 [6028]E(f323(f323(f78(a860),f323(f323(f22(a860),x60281),x60282)),x60282),x60281)+~P101(f323(f323(f237(a860),x60282),x60281))
% 179.72/179.58 [6093]E(f323(f323(f36(a860),f323(f323(f79(a860),x60931),x60932)),x60932),x60931)+~P101(f323(f323(f238(a860),f2(a860)),x60932))
% 179.72/179.58 [6094]E(f323(f323(f36(a860),f323(f323(f79(a860),x60941),x60942)),x60941),x60942)+~P101(f323(f323(f238(a860),f2(a860)),x60941))
% 179.72/179.58 [6098]~P72(x60981)+E(f323(f323(f6(a860,x60981),f323(f158(x60981),x60982)),f323(f293(a860,f2(a860)),f323(f189(f861(x60981)),x60982))),f323(f159(x60981),x60982))
% 179.72/179.58 [6209]E(f42(a860,f323(a112,f323(f323(f79(a860),x62091),x62092)),x62091),f76(a860))+~P101(f323(f323(f238(a860),f76(a860)),x62091))
% 179.72/179.58 [6215]E(f323(a112,f323(f323(f78(a860),f323(f103(a860),x62151)),x62152)),f323(f323(f78(a860),f76(a860)),x62152))+~P101(f323(a193,f323(f103(a1),x62151)))
% 179.72/179.58 [6242]E(f323(a104,f323(f323(f248(a1),f323(f103(a1),x62421)),x62422)),f323(f323(f248(a860),f323(f103(a860),x62421)),x62422))+P101(f323(a193,f323(f103(a1),x62421)))
% 179.72/179.58 [6476]E(f323(f323(f22(a860),x64761),f323(f103(a860),f323(f323(f78(a1),x64762),a97))),f323(f323(f22(a860),f323(a112,x64761)),f323(f103(a860),x64762)))+~P101(f323(f323(f238(a1),a81),x64762))
% 179.72/179.58 [6555]E(x65551,f2(a860))+E(f323(a112,f323(f323(f78(a860),f323(f323(f22(a860),x65551),f76(a860))),x65552)),f323(f323(f78(a860),x65551),x65552))
% 179.72/179.58 [6595]E(x65951,f2(a1))+P101(f323(f323(f238(a1),f2(a1)),f323(f323(f248(a1),f323(f73(a1),x65951)),x65952)))
% 179.72/179.58 [6610]~E(x66102,f2(a860))+P101(f323(f323(f238(a1),f2(a1)),f323(f323(f248(a1),f323(f73(a1),x66101)),x66102)))
% 179.72/179.58 [6647]E(x66471,f2(a860))+E(f323(f323(f78(a860),x66472),f323(f323(f79(a860),f323(f323(f22(a860),x66471),f76(a860))),x66472)),f323(f323(f79(a860),x66471),x66472))
% 179.72/179.58 [6694]~P101(f323(f323(f237(a1),x66941),x66942))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x66941),a97)),x66942))
% 179.72/179.58 [6823]E(f323(f323(f144(a860),x68231),f132(a860,f323(f293(a860,f323(a112,x68231)),x68232))),f132(a860,f323(f293(a860,x68231),x68232)))+~P101(f323(f323(f238(a860),x68231),x68232))
% 179.72/179.58 [7021]E(x70211,x70212)+~E(f323(f323(f22(a1),f323(f323(f78(a1),x70211),x70211)),a97),f323(f323(f22(a1),f323(f323(f78(a1),x70212),x70212)),a97))
% 179.72/179.58 [7024]E(x70241,f113(x70242))+E(f267(x70242,f323(f323(f147(x70242,f866(a99,x70242)),f323(f258(a99,x70242),f76(a99))),x70241)),f274(x70242,x70241))
% 179.72/179.58 [7248]P101(f323(f323(f237(a1),x72481),x72482))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x72481),a97)),x72482))
% 179.72/179.58 [7725]~P101(f323(f323(f238(a860),x77251),x77252))+P101(f323(f323(f325(f866(a860,a860)),f323(f323(f258(a860,a860),x77251),x77252)),a242))
% 179.72/179.58 [7946]~P101(f323(f323(f238(a99),f2(a99)),x79461))+P101(f323(f323(f238(a99),f323(f257(a99,f866(a99,a99)),f323(f268(x79461),x79462))),x79461))
% 179.72/179.58 [8256]~P82(x82561)+P101(f323(f323(f237(x82561),f323(f73(x82561),f323(f159(x82561),x82562))),f323(f159(x82561),f323(f323(f147(x82561,x82561),f73(x82561)),x82562))))
% 179.72/179.58 [8281]P101(f323(f323(f238(a860),x82811),x82812))+~P101(f323(f323(f325(f866(a860,a860)),f323(f323(f258(a860,a860),x82811),x82812)),a242))
% 179.72/179.58 [8430]E(f323(f323(f258(x84301,x84301),f733(x84302,x84301)),f733(x84302,x84301)),x84302)+~P101(f323(f323(f325(f866(x84301,x84301)),x84302),f299(x84301,f188(f867(f866(x84301,x84301),a855)))))
% 179.72/179.58 [8472]E(f323(f293(a860,x84721),f323(f323(f78(a860),x84721),f323(f35(a860),x84722))),x84722)+~P101(f323(f323(f237(f867(a860,a855)),x84722),f323(f293(a860,x84721),f323(f323(f78(a860),x84721),f323(f35(a860),x84722)))))
% 179.72/179.58 [8824]E(f323(f323(f36(a1),f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x88241),x88241)),a97))),f323(f103(a1),f323(f323(f78(a1),x88242),x88242))),f323(f323(f36(a1),f323(f103(a1),x88241)),f323(f103(a1),x88242)))+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x88242)))
% 179.72/179.58 [8944]E(f171(f861(x89441),f323(f323(f8(a855,a855,f861(x89441)),a318),f323(f323(f7(f861(x89441),f861(x89441),a855),a320),f113(x89441))),x89442),f173(x89441,f173(x89441,x89442)))+~P16(a860,f323(f162(a860),f323(f323(f147(f861(x89441),a860),f189(f861(x89441))),x89442)))
% 179.72/179.58 [8947]E(f323(f323(f36(a1),f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x89471),x89471)),a97))),f323(f103(a1),f323(f323(f78(a1),x89472),x89472))),f323(f323(f36(a1),f323(f323(f78(a1),f323(f103(a1),x89471)),f76(a1))),f323(f103(a1),x89472)))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x89472)))
% 179.72/179.58 [9783]P101(f323(a193,x97832))+E(f323(f323(f84(a1,a860),f323(f323(f22(a1),x97831),x97832)),f323(f323(f18(a1,a860,a860),f323(f323(f7(a1,a860,f867(a860,a860)),f323(f323(f8(a855,f867(a860,f867(a860,a860)),a1),f96(a860)),a193)),f2(a860))),a104)),f323(f323(f22(a860),f323(a104,x97831)),f323(a104,x97832)))
% 179.72/179.58 [9792]E(f323(f323(f84(a1,a860),f323(f103(a1),f323(f323(f78(a1),x97921),f323(f77(a1),x97922)))),f323(f323(f18(a1,a860,a860),f323(f323(f7(a1,a860,f867(a860,a860)),f323(f323(f8(a855,f867(a860,f867(a860,a860)),a1),f96(a860)),a193)),f2(a860))),a104)),f323(f323(f22(a860),f323(f103(a860),x97921)),f323(f103(a860),x97922)))+P101(f323(f323(f238(a1),x97922),a81))
% 179.72/179.58 [9793]~P29(x97931,x97932)+P101(f323(f323(f237(f867(f866(x97931,x97931),a855)),f323(f323(f280(x97931,x97931,x97931),f323(f257(f867(f866(x97931,x97931),a855),f867(f866(x97931,x97931),a855)),x97932)),f323(f261(f867(f866(x97931,x97931),a855),f867(f866(x97931,x97931),a855)),x97932))),f323(f257(f867(f866(x97931,x97931),a855),f867(f866(x97931,x97931),a855)),x97932)))
% 179.72/179.58 [9856]~E(f323(f35(a860),f323(f243(a860),f323(f323(f18(a860,a855,a855),f323(f323(f8(a855,f867(a855,a855),a860),a321),f323(f323(f7(a860,f867(a860,a855),a855),f325(a860)),x98561))),f323(f323(f7(a860,a860,a855),f238(a860)),f323(a112,x98562))))),f2(a860))+~P101(f323(f323(f325(a860),f2(a860)),x98561))
% 179.72/179.58 [9912]E(f42(a1,f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x99121),x99121)),a97)),f323(f103(a1),f323(f323(f78(a1),x99122),x99122))),f323(f323(f78(a1),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f42(a1,f323(f103(a1),x99121),f323(f103(a1),x99122)))),f76(a1)))+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x99122)))
% 179.72/179.58 [9921]E(f42(a1,f323(f103(a1),f323(f323(f22(a1),f323(f323(f78(a1),x99211),x99211)),a97)),f323(f103(a1),f323(f323(f78(a1),x99212),x99212))),f323(f323(f22(a1),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f42(a1,f323(f323(f78(a1),f323(f103(a1),x99211)),f76(a1)),f323(f103(a1),x99212)))),f76(a1)))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x99212)))
% 179.72/179.58 [9973]~P6(x99731)+E(f37(x99731,f323(f243(x99731),f323(f323(f8(f867(x99731,a855),a855,x99731),f86(x99731)),f323(f323(f8(f867(x99731,a855),f867(x99731,a855),x99731),f323(f18(x99731,a855,a855),f323(f323(f8(a855,f867(a855,a855),x99731),a326),f323(f323(f7(x99731,f867(x99731,a855),a855),f325(x99731)),x99732)))),f237(x99731))))),f38(x99731,x99732))
% 179.72/179.58 [9997]~P38(x99971,x99972)+P56(x99971,f323(f323(f7(x99971,f867(f866(x99971,x99971),a855),f867(x99971,a855)),f323(f323(f8(f867(x99971,f867(f867(f866(x99971,x99971),a855),a855)),f867(f867(f866(x99971,x99971),a855),f867(x99971,a855)),x99971),f7(x99971,f867(f866(x99971,x99971),a855),a855)),f323(f323(f8(f867(x99971,f866(x99971,x99971)),f867(x99971,f867(f867(f866(x99971,x99971),a855),a855)),x99971),f323(f8(f866(x99971,x99971),f867(f867(f866(x99971,x99971),a855),a855),x99971),f325(f866(x99971,x99971)))),f258(x99971,x99971)))),x99972))
% 179.72/179.58 [9998]~P9(x99981,f246(f867(x99981,a855)),x99982)+P8(x99981,f323(f323(f7(x99981,f867(f866(x99981,x99981),a855),f867(x99981,a855)),f323(f323(f8(f867(x99981,f867(f867(f866(x99981,x99981),a855),a855)),f867(f867(f866(x99981,x99981),a855),f867(x99981,a855)),x99981),f7(x99981,f867(f866(x99981,x99981),a855),a855)),f323(f323(f8(f867(x99981,f866(x99981,x99981)),f867(x99981,f867(f867(f866(x99981,x99981),a855),a855)),x99981),f323(f8(f866(x99981,x99981),f867(f867(f866(x99981,x99981),a855),a855),x99981),f325(f866(x99981,x99981)))),f258(x99981,x99981)))),x99982))
% 179.72/179.58 [10035]P38(x100351,x100352)+~P56(x100351,f323(f323(f7(x100351,f867(f866(x100351,x100351),a855),f867(x100351,a855)),f323(f323(f8(f867(x100351,f867(f867(f866(x100351,x100351),a855),a855)),f867(f867(f866(x100351,x100351),a855),f867(x100351,a855)),x100351),f7(x100351,f867(f866(x100351,x100351),a855),a855)),f323(f323(f8(f867(x100351,f866(x100351,x100351)),f867(x100351,f867(f867(f866(x100351,x100351),a855),a855)),x100351),f323(f8(f866(x100351,x100351),f867(f867(f866(x100351,x100351),a855),a855),x100351),f325(f866(x100351,x100351)))),f258(x100351,x100351)))),x100352))
% 179.72/179.58 [10036]P9(x100361,f246(f867(x100361,a855)),x100362)+~P8(x100361,f323(f323(f7(x100361,f867(f866(x100361,x100361),a855),f867(x100361,a855)),f323(f323(f8(f867(x100361,f867(f867(f866(x100361,x100361),a855),a855)),f867(f867(f866(x100361,x100361),a855),f867(x100361,a855)),x100361),f7(x100361,f867(f866(x100361,x100361),a855),a855)),f323(f323(f8(f867(x100361,f866(x100361,x100361)),f867(x100361,f867(f867(f866(x100361,x100361),a855),a855)),x100361),f323(f8(f866(x100361,x100361),f867(f867(f866(x100361,x100361),a855),a855),x100361),f325(f866(x100361,x100361)))),f258(x100361,x100361)))),x100362))
% 179.72/179.58 [7199]E(f323(f323(f78(a860),f323(f103(a860),f323(f323(f22(a1),x71991),a97))),x71992),f323(a112,f323(f323(f78(a860),f323(f103(a860),x71991)),x71992)))+P101(f323(a193,f323(f103(a1),x71991)))
% 179.72/179.58 [7641]~P90(x76411)+E(f323(f323(f78(x76411),f323(f323(f78(x76411),f76(x76411)),f323(f103(x76411),x76412))),f323(f103(x76411),x76412)),f323(f103(x76411),f323(f323(f22(a1),f323(f323(f78(a1),x76412),x76412)),a97)))
% 179.72/179.58 [8283]~P101(f323(f323(f237(a1),x82831),x82832))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x82831),x82831)),f323(f323(f22(a1),f323(f323(f78(a1),x82832),x82832)),a97)))
% 179.72/179.58 [8285]~P101(f323(f323(f237(a1),x82851),x82852))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x82851),x82851)),f323(f323(f22(a1),f323(f323(f78(a1),x82852),x82852)),a97)))
% 179.72/179.58 [8714]P101(f323(f323(f237(a1),x87141),x87142))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x87141),x87141)),f323(f323(f22(a1),f323(f323(f78(a1),x87142),x87142)),a97)))
% 179.72/179.58 [8716]P101(f323(f323(f237(a1),x87161),x87162))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),x87161),x87161)),f323(f323(f22(a1),f323(f323(f78(a1),x87162),x87162)),a97)))
% 179.72/179.58 [9003]~P101(f323(f323(f237(a1),x90031),x90032))+P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90031),x90031)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x90032),x90032)),a97)))
% 179.72/179.58 [9005]~P101(f323(f323(f238(a1),x90051),x90052))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90051),x90051)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x90052),x90052)),a97)))
% 179.72/179.58 [9006]~P101(f323(f323(f89(a1),x90061),x90062))+P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x90061),x90061)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x90062),x90062)),a97)))
% 179.72/179.58 [9269]P101(f323(f323(f237(a1),x92691),x92692))+~P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),x92691),x92691)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x92692),x92692)),a97)))
% 179.72/179.58 [9271]P101(f323(f323(f238(a1),x92711),x92712))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),x92711),x92711)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x92712),x92712)),a97)))
% 179.72/179.58 [9272]P101(f323(f323(f89(a1),x92721),x92722))+~P101(f323(f323(f89(a1),f323(f323(f22(a1),f323(f323(f78(a1),x92721),x92721)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),x92722),x92722)),a97)))
% 179.72/179.58 [9305]~P101(f323(f59(x93051),x93052))+P101(f323(f59(f867(x93051,a855)),f323(f243(f867(x93051,a855)),f323(f323(f7(f867(x93051,a855),f867(x93051,a855),a855),f237(f867(x93051,a855))),x93052))))
% 179.72/179.58 [9352]~E(f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),x93521),f188(f867(f866(a860,a860),a855)))),f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),x93522),f188(f867(f866(a860,a860),a855)))))+P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),x93521),x93522)),a108))
% 179.72/179.58 [9437]E(f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),x94371),f188(f867(f866(a860,a860),a855)))),f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),x94372),f188(f867(f866(a860,a860),a855)))))+~P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),x94371),x94372)),a108))
% 179.72/179.58 [9473]P101(f323(f323(f237(a1),f2(a1)),f768(x94731,x94732)))+E(f323(f243(a1),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),f2(a1)))),x94731)),f323(f243(a1),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),f2(a1)))),x94732)))
% 179.72/179.58 [9983]~P6(x99831)+E(f38(x99831,f323(f243(x99831),f323(f323(f8(f867(x99831,a855),a855,x99831),f86(x99831)),f323(f323(f8(f867(x99831,a855),f867(x99831,a855),x99831),f323(f18(x99831,a855,a855),f323(f323(f8(a855,f867(a855,a855),x99831),a326),f323(f323(f7(x99831,f867(x99831,a855),a855),f325(x99831)),x99832)))),f323(f7(x99831,x99831,a855),f237(x99831)))))),f37(x99831,x99832))
% 179.72/179.58 [10003]P101(f323(f323(f325(a860),f2(a860)),x100031))+E(f323(f35(a860),f323(f243(a860),f323(f323(f18(a860,a855,a855),f323(f323(f8(a855,f867(a855,a855),a860),a321),f323(f323(f7(a860,f867(a860,a855),a855),f323(f323(f8(a860,f867(f867(a860,a855),a855),a860),f325(a860)),a112)),x100031))),f323(f323(f7(a860,a860,a855),f238(a860)),x100032)))),f323(f35(a860),f323(f243(a860),f323(f323(f18(a860,a855,a855),f323(f323(f8(a855,f867(a855,a855),a860),a321),f323(f323(f7(a860,f867(a860,a855),a855),f325(a860)),x100031))),f323(f323(f7(a860,a860,a855),f238(a860)),f323(a112,x100032))))))
% 179.72/179.58 [7510]~P90(x75101)+E(f323(f323(f79(x75101),x75102),f323(f103(x75101),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),x75102)
% 179.72/179.58 [7770]~P90(x77701)+E(f323(f323(f78(x77701),f323(f103(x77701),x77702)),f76(x77701)),f323(f103(x77701),f323(f323(f78(a1),x77702),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))
% 179.72/179.58 [7919]P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x79192)))+E(f323(f323(f248(a1),x79191),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),x79192),x79192)),a97))),f76(a1))
% 179.72/179.58 [9330]~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x93302)))+E(f323(f323(f248(a1),x93301),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),x93302),x93302)),a97))),f323(f323(f84(a1,a1),f323(f323(f248(a1),x93301),f323(f103(a860),x93302))),f323(f323(f18(a1,a1,a1),f323(f323(f8(a1,f867(a1,a1),a1),f79(a1)),f323(f79(a1),x93301))),f5(a1))))
% 179.72/179.58 [9697]~P101(f323(f323(f237(a860),f796(x96972,x96971)),f323(x96971,f796(x96972,x96971))))+P101(f323(f59(a860),f323(f243(a860),f323(f323(f7(a860,a860,a855),f323(f323(f8(a860,f867(a860,a855),a860),f237(a860)),x96971)),x96972))))
% 179.72/179.58 [9846]~P101(f323(f323(f237(a860),f323(f103(a860),x98461)),f323(a112,x98462)))+P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x98461),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f7(a1,a860,a855),f323(f323(f8(a860,f867(a860,a855),a1),f237(a860)),a104)),x98462))))
% 179.72/179.58 [9847]~P101(f323(f323(f238(a860),f323(f103(a860),x98471)),f323(a112,x98472)))+P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x98471),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f7(a1,a860,a855),f323(f323(f8(a860,f867(a860,a855),a1),f238(a860)),a104)),x98472))))
% 179.72/179.58 [9896]P101(f323(f323(f237(a860),f323(f103(a860),x98961)),f323(a112,x98962)))+~P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x98961),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f7(a1,a860,a855),f323(f323(f8(a860,f867(a860,a855),a1),f237(a860)),a104)),x98962))))
% 179.72/179.58 [9897]P101(f323(f323(f238(a860),f323(f103(a860),x98971)),f323(a112,x98972)))+~P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x98971),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f7(a1,a860,a855),f323(f323(f8(a860,f867(a860,a855),a1),f238(a860)),a104)),x98972))))
% 179.72/179.58 [9927]~P101(f323(f323(f237(a860),f323(a112,x99272)),f323(f103(a860),x99271)))+P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x99271),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f8(a860,a855,a1),f323(f237(a860),x99272)),a104)))))
% 179.72/179.58 [9928]~P101(f323(f323(f238(a860),f323(a112,x99282)),f323(f103(a860),x99281)))+P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x99281),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f8(a860,a855,a1),f323(f238(a860),x99282)),a104)))))
% 179.72/179.58 [9971]P101(f323(f323(f237(a860),f323(a112,x99711)),f323(f103(a860),x99712)))+~P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x99712),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f8(a860,a855,a1),f323(f237(a860),x99711)),a104)))))
% 179.72/179.58 [9972]P101(f323(f323(f238(a860),f323(a112,x99721)),f323(f103(a860),x99722)))+~P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x99722),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f8(a860,a855,a1),f323(f238(a860),x99721)),a104)))))
% 179.72/179.58 [10042]~P101(f323(f323(f325(a860),f2(a860)),x100421))+E(f323(a112,f323(f35(a860),f323(f243(a860),f323(f323(f18(a860,a855,a855),f323(f323(f8(a855,f867(a855,a855),a860),a321),f323(f323(f7(a860,f867(a860,a855),a855),f323(f323(f8(a860,f867(f867(a860,a855),a855),a860),f325(a860)),a112)),x100421))),f323(f323(f7(a860,a860,a855),f238(a860)),x100422))))),f323(f35(a860),f323(f243(a860),f323(f323(f18(a860,a855,a855),f323(f323(f8(a855,f867(a855,a855),a860),a321),f323(f323(f7(a860,f867(a860,a855),a855),f325(a860)),x100421))),f323(f323(f7(a860,a860,a855),f238(a860)),f323(a112,x100422))))))
% 179.72/179.58 [8455]~P90(x84551)+E(f323(f323(f79(x84551),f323(f103(x84551),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),x84552),x84552)
% 179.72/179.58 [8515]~P90(x85151)+E(f323(f323(f78(x85151),f76(x85151)),f323(f103(x85151),x85152)),f323(f103(x85151),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),x85152)))
% 179.72/179.58 [8578]~P90(x85781)+E(f323(f323(f22(x85781),f323(f103(x85781),x85782)),f76(x85781)),f323(f103(x85781),f323(f323(f78(a1),x85782),f323(f77(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.58 [8734]~P101(f323(f323(f238(a860),f323(f103(a860),a81)),x87342))+E(f323(f323(f22(a860),x87341),f323(f323(f22(a860),x87342),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(f323(f22(a860),f323(a112,x87341)),x87342))
% 179.72/179.58 [9368]~P112(x93681)+E(f323(f323(f79(x93681),x93682),x93682),f323(f323(f248(x93681),x93682),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.58 [9369]~P77(x93691)+E(f323(f323(f248(x93691),x93692),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(f323(f79(x93691),x93692),x93692))
% 179.72/179.58 [9371]~P90(x93711)+E(f323(f323(f79(x93711),x93712),f323(f103(x93711),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(f323(f78(x93711),x93712),x93712))
% 179.72/179.58 [9614]~P134(x96141)+E(f323(f323(f248(x96141),f323(f77(x96141),x96142)),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(f323(f248(x96141),x96142),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.58 [9615]~P116(x96151)+E(f323(f323(f248(x96151),f323(f73(x96151),x96152)),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(f323(f248(x96151),x96152),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.58 [9611]~P90(x96111)+E(f323(f323(f79(x96111),f323(f103(x96111),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x96112),f323(f323(f78(x96111),x96112),x96112))
% 179.72/179.58 [9737]~P116(x97371)+E(f323(f73(x97371),f323(f323(f248(x97371),x97372),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x97371),x97372),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.58 [9800]~P116(x98001)+P101(f323(f323(f237(x98001),f2(x98001)),f323(f323(f248(x98001),x98002),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))
% 179.72/179.58 [9962]~E(f323(a112,x99622),f323(f103(a860),x99621))+P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x99621),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f7(a1,a860,a855),f323(f323(f8(a860,f867(a860,a855),a1),a320),a104)),x99622)))))
% 179.72/179.58 [9963]~E(f323(f103(a860),x99631),f323(a112,x99632))+P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x99631),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f7(a1,a860,a855),f323(f323(f8(a860,f867(a860,a855),a1),a320),a104)),x99632)))))
% 179.72/179.58 [10006]E(f323(a112,x100061),f323(f103(a860),x100062))+~P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x100062),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f7(a1,a860,a855),f323(f323(f8(a860,f867(a860,a855),a1),a320),a104)),x100061)))))
% 179.72/179.58 [10007]E(f323(f103(a860),x100071),f323(a112,x100072))+~P101(f323(f323(f84(a1,a855),f323(f103(a1),f323(f323(f78(a1),x100071),a97))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a326),f323(f323(f8(a855,a855,a1),a318),a193))),f323(f323(f7(a1,a860,a855),f323(f323(f8(a860,f867(a860,a855),a1),a320),a104)),x100072)))))
% 179.72/179.58 [9798]~P90(x97981)+E(f323(f323(f248(x97981),f323(f103(x97981),a97)),f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x97982)),f76(x97981))
% 179.72/179.58 [9799]~P134(x97991)+E(f323(f323(f248(x97991),f323(f77(x97991),f76(x97991))),f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x97992)),f76(x97991))
% 179.72/179.58 [9802]~P77(x98021)+E(f323(f323(f248(x98021),x98022),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),a97))),f323(f323(f79(x98021),f323(f323(f79(x98021),x98022),x98022)),x98022))
% 179.72/179.58 [9986]~P101(f323(f323(f237(a1),f2(a1)),x99862))+E(f42(a1,f323(f323(f78(a1),f76(a1)),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x99861)),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x99862)),f323(f323(f78(a1),f76(a1)),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f42(a1,x99861,x99862))))
% 179.72/179.58 [10009]~P101(f323(f323(f237(a1),f2(a1)),x100092))+E(f323(f323(f36(a1),f323(f323(f78(a1),f76(a1)),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x100091))),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x100092)),f323(f323(f36(a1),x100091),x100092))
% 179.72/179.58 [10011]~P101(f323(f323(f237(a1),x100112),f2(a1)))+E(f323(f323(f36(a1),f323(f323(f78(a1),f76(a1)),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x100111))),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x100112)),f323(f323(f36(a1),f323(f323(f78(a1),x100111),f76(a1))),x100112))
% 179.72/179.58 [10012]~P101(f323(f323(f237(a1),x100122),f2(a1)))+E(f42(a1,f323(f323(f78(a1),f76(a1)),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x100121)),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x100122)),f323(f323(f22(a1),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f42(a1,f323(f323(f78(a1),x100121),f76(a1)),x100122))),f76(a1)))
% 179.72/179.58 [9887]~P90(x98871)+E(f323(f323(f248(x98871),f323(f103(x98871),a97)),f323(a112,f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98872))),f323(f103(x98871),a97))
% 179.72/179.58 [9889]~P134(x98891)+E(f323(f323(f248(x98891),f323(f77(x98891),f76(x98891))),f323(a112,f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98892))),f323(f77(x98891),f76(x98891)))
% 179.72/179.58 [5094]~P26(x50941,x50942,x50943)+P31(x50941,x50942,x50943)
% 179.72/179.58 [7984]~E(x79842,x79843)+P35(x79841,x79841,a320,x79842,x79843)
% 179.72/179.58 [8529]E(x85291,x85292)+~P35(x85293,x85293,a320,x85291,x85292)
% 179.72/179.58 [4742]E(f163(x47421,x47422,x47423),f113(x47421))+~E(x47422,f2(a860))
% 179.72/179.58 [4906]~E(f163(x49062,x49061,x49063),f113(x49062))+E(x49061,f2(a860))
% 179.72/179.58 [5099]~P38(x50991,x50993)+P38(x50991,f317(x50991,x50992,x50993))
% 179.72/179.58 [5347]~P9(x53471,x53472,x53473)+P9(f861(x53471),f154(x53471,x53472),f151(x53471,x53473))
% 179.72/179.58 [5348]~P40(x53481,x53482,x53483)+P40(f861(x53481),f154(x53481,x53482),f151(x53481,x53483))
% 179.72/179.58 [5460]P51(x54601,x54602,x54603)+~E(f700(x54603,x54602,x54601),f701(x54603,x54602,x54601))
% 179.72/179.58 [5461]P52(x54611,x54612,x54613)+~E(f727(x54613,x54612,x54611),f728(x54613,x54612,x54611))
% 179.72/179.58 [7990]~E(x79902,x79903)+P28(x79901,x79901,f32(x79901),x79902,x79903)
% 179.72/179.58 [8537]E(x85371,x85372)+~P28(x85373,x85373,f32(x85373),x85371,x85372)
% 179.72/179.58 [4647]~E(x46471,f200(x46472))+~E(x46471,f323(f230(x46472),x46473))
% 179.72/179.58 [4698]~E(f323(f162(x46982),x46981),x46983)+E(x46981,f323(f162(x46982),x46983))
% 179.72/179.58 [4699]~E(x46992,f323(f162(x46991),x46993))+E(f323(f162(x46991),x46992),x46993)
% 179.72/179.58 [4748]E(x47481,x47482)+~E(f323(f230(x47483),x47481),f323(f230(x47483),x47482))
% 179.72/179.58 [4749]E(x47491,x47492)+~E(f323(f162(x47493),x47491),f323(f162(x47493),x47492))
% 179.72/179.58 [4953]~P8(x49533,x49531)+P101(f323(f323(x49531,x49532),x49532))
% 179.72/179.58 [4954]~P49(x49543,x49541)+P101(f323(f323(x49541,x49542),x49542))
% 179.72/179.58 [4956]~P56(x49561,x49562)+P101(f323(f311(x49561,x49562),x49563))
% 179.72/179.58 [5018]~P38(x50181,x50182)+P38(f861(x50181),f323(f136(x50181,x50182),x50183))
% 179.72/179.58 [5023]~P101(f323(x50232,x50233))+~E(f323(f243(x50231),x50232),f188(f867(x50231,a855)))
% 179.72/179.58 [5024]~P101(f323(x50242,x50243))+~E(f188(f867(x50241,a855)),f323(f243(x50241),x50242))
% 179.72/179.58 [5036]E(x50361,f2(a860))+E(f137(x50362,f163(x50362,x50361,x50363)),x50363)
% 179.72/179.58 [5054]~P101(f323(x50541,x50543))+P101(f323(x50541,f88(x50542,x50541)))
% 179.72/179.58 [5066]E(x50661,f2(a860))+E(f323(f134(x50662),f163(x50662,x50661,x50663)),x50663)
% 179.72/179.58 [5171]~E(x51712,x51713)+P101(f323(f323(f325(x51711),x51712),f323(a320,x51713)))
% 179.72/179.58 [5183]~E(x51832,f2(a860))+E(f323(f166(x51831),f163(x51831,x51832,x51833)),f188(f867(x51831,a855)))
% 179.72/179.58 [5227]E(f323(f162(x52271),x52272),f323(f323(f144(x52271),x52273),f113(x52271)))+~E(x52272,f323(f323(f144(x52271),x52273),f113(x52271)))
% 179.72/179.58 [5228]~E(x52283,f323(f323(f144(x52281),x52282),f113(x52281)))+E(f323(f323(f144(x52281),x52282),f113(x52281)),f323(f162(x52281),x52283))
% 179.72/179.58 [5254]~E(x52543,f323(f16(f864(x52542),x52541),f200(x52542)))+E(f177(x52541,x52542,x52543),f188(f867(x52541,a855)))
% 179.72/179.58 [5275]~P34(x52751,x52752,x52753)+P34(x52751,x52752,f323(f162(x52751),x52753))
% 179.72/179.58 [5276]~P32(x52761,x52762,x52763)+P32(x52761,x52762,f323(f162(x52761),x52763))
% 179.72/179.58 [5279]E(f323(f35(x52791),f781(x52792,x52793,x52791)),x52792)+~E(f323(f35(x52791),x52793),f323(a112,x52792))
% 179.72/179.58 [5285]~P38(x52851,x52853)+P101(f323(f323(f325(x52851),x52852),f312(x52851,x52853)))
% 179.72/179.58 [5289]~E(f323(f162(x52892),x52891),f323(f323(f144(x52892),x52893),f113(x52892)))+E(x52891,f323(f323(f144(x52892),x52893),f113(x52892)))
% 179.72/179.58 [5290]~E(f323(f323(f144(x52902),x52903),f113(x52902)),f323(f162(x52902),x52901))+E(x52901,f323(f323(f144(x52902),x52903),f113(x52902)))
% 179.72/179.58 [5305]E(x53051,f323(f16(f864(x53052),x53053),f200(x53052)))+~E(f177(x53053,x53052,x53051),f188(f867(x53053,a855)))
% 179.72/179.58 [5311]E(f83(f866(a860,a860),f45(x53111,x53112)),x53113)+~P101(f323(f45(x53111,x53112),x53113))
% 179.72/179.58 [5319]~E(x53193,f323(f230(x53191),x53192))+P101(f323(f323(f325(x53191),x53192),f229(x53191,x53193)))
% 179.72/179.58 [5351]P34(x53511,x53512,x53513)+~P34(x53511,x53512,f323(f162(x53511),x53513))
% 179.72/179.58 [5352]P32(x53521,x53522,x53523)+~P32(x53521,x53522,f323(f162(x53521),x53523))
% 179.72/179.58 [5414]~E(x54142,f113(x54141))+P101(f323(f323(f325(f861(x54141)),x54142),f154(x54141,x54143)))
% 179.72/179.58 [5421]~P40(x54211,x54212,x54213)+P40(x54211,x54212,f323(f278(x54211,x54211),x54213))
% 179.72/179.58 [5422]~P52(x54221,x54222,x54223)+P52(x54221,x54222,f323(f278(x54221,x54221),x54223))
% 179.72/179.58 [5441]~P57(x54411)+E(f42(x54411,f42(x54411,x54412,x54413),x54413),f42(x54411,x54412,x54413))
% 179.72/179.58 [5537]E(x55371,x55372)+~P101(f323(f323(f325(x55373),x55371),f323(a320,x55372)))
% 179.72/179.58 [5583]~P140(x55831)+E(f190(x55831,x55832,f2(a860),x55833),x55833)
% 179.72/179.58 [5603]P40(x56031,x56032,x56033)+~P40(x56031,x56032,f323(f278(x56031,x56031),x56033))
% 179.72/179.58 [5604]P52(x56041,x56042,x56043)+~P52(x56041,x56042,f323(f278(x56041,x56041),x56043))
% 179.72/179.58 [5608]~P103(x56082)+E(f143(x56081,x56082,x56083,f113(x56081)),f113(x56081))
% 179.72/179.58 [5621]E(f164(x56211,x56212,f145(x56211,x56213)),f145(x56211,f164(x56211,x56212,x56213)))+~P101(f323(f130(x56211),x56213))
% 179.72/179.58 [5627]E(x56271,f323(f230(x56272),x56273))+~P101(f323(f323(f325(x56272),x56273),f229(x56272,x56271)))
% 179.72/179.58 [5722]E(f323(f129(x57221,x57222),x57223),f113(x57221))+P101(f323(x57222,f561(x57223,x57222,x57221)))
% 179.72/179.58 [5865]~P101(f323(f130(x58651),x58653))+P101(f323(f130(x58651),f164(x58651,x58652,x58653)))
% 179.72/179.58 [5866]~P101(f323(f130(x58661),x58662))+P101(f323(f130(x58661),f170(x58661,x58662,x58663)))
% 179.72/179.58 [5867]~P101(f323(f130(x58671),x58673))+P101(f323(f130(x58671),f171(x58671,x58672,x58673)))
% 179.72/179.58 [5868]~P101(f323(f130(x58681),x58683))+P101(f323(f130(x58681),f133(x58681,x58682,x58683)))
% 179.72/179.58 [5869]~P142(x58691,x58692,x58693)+P101(f323(x58691,f42(a1,x58692,x58693)))
% 179.72/179.58 [5886]~P34(x58863,x58861,x58862)+P101(f323(x58861,f702(x58862,x58861,x58863)))
% 179.72/179.58 [5887]~P36(x58873,x58871,x58872)+P101(f323(x58871,f789(x58872,x58871,x58873)))
% 179.72/179.58 [5908]E(f323(f129(x59081,x59082),x59083),f171(x59081,x59082,x59083))+P101(f323(x59082,f612(x59083,x59082,x59081)))
% 179.72/179.58 [5947]~P101(f323(f130(x59471),x59473))+P101(f323(f130(f861(x59471)),f52(x59471,x59472,x59473)))
% 179.72/179.58 [5978]~P105(x59781)+E(f323(f323(f101(f867(x59781,a855)),f323(f244(x59781),x59782)),f294(x59781,x59782,x59783)),f188(f867(x59781,a855)))
% 179.72/179.58 [5979]~P105(x59791)+E(f323(f323(f101(f867(x59791,a855)),f323(f292(x59791),x59792)),f297(x59791,x59792,x59793)),f188(f867(x59791,a855)))
% 179.72/179.58 [5980]~P105(x59801)+E(f323(f323(f101(f867(x59801,a855)),f323(f292(x59801),x59802)),f296(x59801,x59802,x59803)),f188(f867(x59801,a855)))
% 179.72/179.58 [6205]E(f323(f129(x62051,x62052),x62053),x62053)+~P101(f323(x62052,f553(x62053,x62052,x62051)))
% 179.72/179.58 [6207]E(f323(f323(f301(x62071),f849(x62072,x62073,x62071)),f781(x62072,x62073,x62071)),x62073)+~E(f323(f35(x62071),x62073),f323(a112,x62072))
% 179.72/179.58 [6222]P142(x62221,x62222,x62223)+~P101(f323(x62221,f42(a1,x62222,x62223)))
% 179.72/179.58 [6269]P32(x62691,x62692,x62693)+~P101(f323(x62692,f770(x62692,x62693,x62691)))
% 179.72/179.58 [6270]P32(x62701,x62702,x62703)+~P101(f323(x62702,f779(x62703,x62702,x62701)))
% 179.72/179.58 [6271]P32(x62711,x62712,x62713)+~P101(f323(x62712,f780(x62713,x62712,x62711)))
% 179.72/179.58 [6273]E(f171(x62731,x62732,x62733),x62733)+~P101(f323(x62732,f602(x62733,x62732,x62731)))
% 179.72/179.58 [6351]~P101(f323(x63512,f562(x63513,x63512,x63511)))+P101(f323(f251(x63511,x63512),x63513))
% 179.72/179.58 [6352]~P101(f323(x63522,f638(x63523,x63522,x63521)))+P101(f323(f153(x63521,x63522),x63523))
% 179.72/179.58 [6596]~P101(f323(f311(x65961,x65962),f495(x65963,x65962,x65961)))+P101(f323(f311(x65961,x65962),x65963))
% 179.72/179.58 [6597]~P101(f323(f311(x65971,x65972),f510(x65973,x65972,x65971)))+P101(f323(f311(x65971,x65972),x65973))
% 179.72/179.58 [7200]~P57(x72001)+E(f323(f323(f78(x72001),f323(f323(f79(x72001),x72002),f323(f323(f36(x72001),x72003),x72002))),f42(x72001,x72003,x72002)),x72003)
% 179.72/179.58 [7664]E(f323(f323(f258(x76641,x76641),f525(x76642,x76643,x76641)),f525(x76642,x76643,x76641)),x76643)+~P101(f323(f323(f325(f866(x76641,x76641)),x76643),f255(x76641,x76642)))
% 179.72/179.58 [7778]~P101(f323(f323(f325(x77781),f650(x77783,x77782,x77781)),f312(x77781,x77783)))+P101(f323(f323(f325(x77781),x77782),f312(x77781,x77783)))
% 179.72/179.58 [7779]~P101(f323(f323(f325(x77791),f704(x77793,x77792,x77791)),f312(x77791,x77793)))+P101(f323(f323(f325(x77791),x77792),f312(x77791,x77793)))
% 179.72/179.58 [7780]~P101(f323(f323(f325(x77801),f713(x77803,x77802,x77801)),f312(x77801,x77803)))+P101(f323(f323(f325(x77801),x77802),f312(x77801,x77803)))
% 179.72/179.58 [7965]~P57(x79651)+E(f323(f323(f78(x79651),f323(f323(f79(x79651),f323(f323(f36(x79651),x79652),x79653)),x79653)),f42(x79651,x79652,x79653)),x79652)
% 179.72/179.58 [8011]~E(f323(f35(x80111),x80112),f323(a112,x80113))+~P101(f323(f323(f325(x80111),f849(x80113,x80112,x80111)),f781(x80113,x80112,x80111)))
% 179.72/179.58 [8635]P101(f323(f323(f237(f867(f866(x86351,x86351),a855)),f299(x86351,x86352)),f299(x86351,x86353)))+~P101(f323(f323(f237(f867(f866(x86351,x86351),a855)),x86352),f299(x86351,x86353)))
% 179.72/179.58 [8914]E(x89141,f113(x89142))+~P101(f323(f323(f325(f866(f861(x89142),f861(x89142))),f323(f323(f258(f861(x89142),f861(x89142)),x89141),f113(x89142))),f151(x89142,x89143)))
% 179.72/179.58 [8938]E(x89381,f113(x89382))+~P101(f323(f323(f325(f866(f861(x89382),f861(x89382))),f323(f323(f258(f861(x89382),f861(x89382)),f113(x89382)),x89381)),f151(x89382,x89383)))
% 179.72/179.58 [9065]E(f323(f323(f144(x90651),f621(x90652,x90653,x90651)),f622(x90652,x90653,x90651)),x90653)+~P101(f323(f323(f325(f866(f861(x90651),f861(x90651))),f323(f323(f258(f861(x90651),f861(x90651)),f113(x90651)),x90653)),f140(x90651,x90652)))
% 179.72/179.58 [9298]~P121(x92981)+~P101(f323(f323(f238(x92981),f323(f323(f78(x92981),f323(f323(f79(x92981),x92982),x92982)),f323(f323(f79(x92981),x92983),x92983))),f2(x92981)))
% 179.72/179.58 [9347]P101(f323(f59(x93471),x93472))+~P101(f323(f323(f325(f866(f867(x93471,a855),f867(x93471,a855))),f323(f323(f258(f867(x93471,a855),f867(x93471,a855)),x93473),x93472)),f298(x93471)))
% 179.72/179.58 [9637]~P47(x96371,x96372,x96373)+P101(f323(f323(f237(a1),f323(f323(f71(f866(a1,a1),a1,x96371,f257(a1,a1)),f214(x96371)),f225(x96371,x96372,f222(x96371,x96373)))),f2(a1)))
% 179.72/179.58 [9638]~P48(x96381,x96382,x96383)+P101(f323(f323(f238(a1),f323(f323(f71(f866(a1,a1),a1,x96381,f257(a1,a1)),f214(x96381)),f225(x96381,x96382,f222(x96381,x96383)))),f2(a1)))
% 179.72/179.58 [9766]P48(x97661,x97662,x97663)+~P101(f323(f323(f238(a1),f323(f323(f71(f866(a1,a1),a1,x97661,f257(a1,a1)),f214(x97661)),f225(x97661,x97662,f222(x97661,x97663)))),f2(a1)))
% 179.72/179.58 [9767]P47(x97671,x97672,x97673)+~P101(f323(f323(f237(a1),f323(f323(f71(f866(a1,a1),a1,x97671,f257(a1,a1)),f214(x97671)),f225(x97671,x97672,f222(x97671,x97673)))),f2(a1)))
% 179.72/179.58 [10087]~P116(x100871)+~P101(f323(f323(f238(x100871),f323(f323(f78(x100871),f323(f323(f248(x100871),x100872),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x100871),x100873),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))),f2(x100871)))
% 179.72/179.58 [4729]~E(x47293,f113(x47291))+E(f323(f323(f121(x47291),x47292),x47293),x47292)
% 179.72/179.58 [4730]~E(x47302,f113(x47301))+E(f323(f323(f121(x47301),x47302),x47303),x47303)
% 179.72/179.58 [4737]~E(x47372,f2(a860))+E(f323(f323(f169(x47371),x47372),x47373),f113(x47371))
% 179.72/179.58 [4743]~E(x47433,f113(x47431))+E(f323(f323(f169(x47431),x47432),x47433),f113(x47431))
% 179.72/179.58 [4783]~E(x47831,x47833)+E(x47831,f323(f323(f121(x47832),f113(x47832)),x47833))
% 179.72/179.58 [4869]~P1(x48692)+E(f323(f188(f867(x48691,x48692)),x48693),f188(x48692))
% 179.72/179.58 [4870]~P106(x48702)+E(f323(f246(f867(x48701,x48702)),x48703),f246(x48702))
% 179.72/179.58 [4888]E(x48881,f113(x48882))+~E(f323(f323(f121(x48882),x48883),x48881),x48883)
% 179.72/179.58 [4889]E(x48891,f113(x48892))+~E(f323(f323(f121(x48892),x48891),x48893),x48893)
% 179.72/179.58 [4897]E(x48971,f113(x48972))+~E(f323(f323(f121(x48972),x48973),x48971),f113(x48972))
% 179.72/179.58 [4898]E(x48981,f113(x48982))+~E(f323(f323(f121(x48982),x48981),x48983),f113(x48982))
% 179.72/179.58 [4923]~E(x49232,f2(a860))+E(f323(f323(f79(a860),x49231),x49232),f323(f323(f79(a860),x49233),x49232))
% 179.72/179.58 [4925]~E(x49251,f2(a860))+E(f323(f323(f79(a860),x49251),x49252),f323(f323(f79(a860),x49251),x49253))
% 179.72/179.58 [4978]~P2(x49781)+E(f323(f323(f110(x49781),x49782),x49783),f323(f323(f110(x49781),x49783),x49782))
% 179.72/179.58 [4980]~P97(x49801)+E(f323(f323(f110(x49801),x49802),x49803),f323(f323(f110(x49801),x49803),x49802))
% 179.72/179.58 [4981]~P2(x49811)+E(f323(f323(f101(x49811),x49812),x49813),f323(f323(f101(x49811),x49813),x49812))
% 179.72/179.58 [4983]~P98(x49831)+E(f323(f323(f101(x49831),x49832),x49833),f323(f323(f101(x49831),x49833),x49832))
% 179.72/179.58 [4984]~P112(x49841)+E(f323(f323(f79(x49841),x49842),x49843),f323(f323(f79(x49841),x49843),x49842))
% 179.72/179.58 [4985]~P112(x49851)+E(f323(f323(f78(x49851),x49852),x49853),f323(f323(f78(x49851),x49853),x49852))
% 179.72/179.58 [4987]~P103(x49871)+E(f323(f323(f235(x49871),x49872),x49873),f323(f323(f235(x49871),x49873),x49872))
% 179.72/179.58 [4989]~P103(x49891)+E(f323(f323(f236(x49891),x49892),x49893),f323(f323(f236(x49891),x49893),x49892))
% 179.72/179.58 [5049]E(f42(a860,x50491,x50492),f2(a860))+~E(x50491,f323(f323(f79(a860),x50492),x50493))
% 179.72/179.58 [5050]E(f42(a1,x50501,x50502),f2(a1))+~E(x50501,f323(f323(f79(a1),x50502),x50503))
% 179.72/179.58 [5111]E(x51111,x51112)+~E(f323(f323(f78(a860),x51113),x51111),f323(f323(f78(a860),x51113),x51112))
% 179.72/179.58 [5112]E(x51121,x51122)+~E(f323(f323(f78(a860),x51121),x51123),f323(f323(f78(a860),x51122),x51123))
% 179.72/179.58 [5122]~P87(x51221)+E(f323(f323(f101(x51221),x51222),f323(f77(x51221),x51223)),f323(f323(f22(x51221),x51222),x51223))
% 179.72/179.58 [5123]~P59(x51231)+E(f323(f323(f78(x51231),x51232),f323(f77(x51231),x51233)),f323(f323(f22(x51231),x51232),x51233))
% 179.72/179.58 [5124]~P60(x51241)+E(f323(f323(f78(x51241),x51242),f323(f77(x51241),x51243)),f323(f323(f22(x51241),x51242),x51243))
% 179.72/179.58 [5125]~P109(x51251)+E(f323(f323(f78(x51251),x51252),f323(f77(x51251),x51253)),f323(f323(f22(x51251),x51252),x51253))
% 179.72/179.58 [5126]~P59(x51261)+E(f323(f323(f22(x51261),x51262),f323(f77(x51261),x51263)),f323(f323(f78(x51261),x51262),x51263))
% 179.72/179.58 [5164]~P101(f323(x51643,x51642))+P101(f323(f323(f325(x51641),x51642),x51643))
% 179.72/179.58 [5166]~P72(x51662)+E(f323(f323(f6(x51661,x51662),x51663),f188(f867(x51661,a855))),f2(x51662))
% 179.72/179.58 [5168]~P68(x51682)+E(f323(f323(f9(x51681,x51682),x51683),f188(f867(x51681,a855))),f76(x51682))
% 179.72/179.58 [5215]~E(x52152,f323(f323(f78(a860),x52151),x52153))+P101(f323(f323(f237(a860),x52151),x52152))
% 179.72/179.58 [5218]~E(x52182,f188(f867(x52181,a855)))+E(f323(f323(f58(x52181),x52182),x52183),f188(f867(f867(x52181,a855),a855)))
% 179.72/179.58 [5219]~E(x52192,f188(f867(x52191,a855)))+E(f188(f867(f867(x52191,a855),a855)),f323(f323(f58(x52191),x52192),x52193))
% 179.72/179.58 [5294]~E(f323(f254(x52942,x52943),x52941),f188(f867(x52943,a855)))+E(x52941,f188(f867(f866(x52942,x52943),a855)))
% 179.72/179.58 [5295]~E(f323(f256(x52952,x52953),x52951),f188(f867(x52952,a855)))+E(x52951,f188(f867(f866(x52952,x52953),a855)))
% 179.72/179.58 [5325]E(f323(f254(x53251,x53252),x53253),f188(f867(x53252,a855)))+~E(x53253,f188(f867(f866(x53251,x53252),a855)))
% 179.72/179.58 [5326]E(f323(f256(x53261,x53262),x53263),f188(f867(x53261,a855)))+~E(x53263,f188(f867(f866(x53261,x53262),a855)))
% 179.72/179.58 [5329]E(f273(x53291,x53292,x53293),f323(f323(f22(a99),x53292),x53293))+P101(f323(f323(f238(a99),x53292),x53293))
% 179.72/179.58 [5345]P101(f323(x53451,x53452))+~P101(f323(f323(f325(x53453),x53452),x53451))
% 179.72/179.58 [5384]E(x53841,x53842)+~E(f323(f77(f867(x53843,a855)),x53841),f323(f77(f867(x53843,a855)),x53842))
% 179.72/179.58 [5389]E(f305(x53891,x53892,x53893),f200(f861(a319)))+~P101(f323(f323(f238(a1),x53892),x53893))
% 179.72/179.58 [5394]~E(x53941,f188(f867(x53942,a855)))+~P101(f323(f323(f325(x53942),x53943),x53941))
% 179.72/179.58 [5423]~E(x54232,f323(f323(f78(a1),x54231),f323(f100(a1),x54233)))+P101(f323(f323(f237(a1),x54231),x54232))
% 179.72/179.58 [5439]E(f323(f323(f301(x54391),x54392),x54393),x54393)+~P101(f323(f323(f325(x54391),x54392),x54393))
% 179.72/179.58 [5450]E(x54501,f188(f867(x54502,a855)))+~E(f323(f323(f58(x54502),x54501),x54503),f188(f867(f867(x54502,a855),a855)))
% 179.72/179.58 [5451]E(x54511,f188(f867(x54512,a855)))+~E(f188(f867(f867(x54512,a855),a855)),f323(f323(f58(x54512),x54511),x54513))
% 179.72/179.58 [5457]~P107(x54571)+E(f323(f323(f79(x54571),f323(f77(x54571),x54572)),f323(f77(x54571),x54573)),f323(f323(f79(x54571),x54572),x54573))
% 179.72/179.58 [5459]~P62(x54591)+E(f323(f323(f281(x54591),f323(f77(x54591),x54592)),f323(f77(x54591),x54593)),f323(f323(f281(x54591),x54592),x54593))
% 179.72/179.58 [5491]~P101(f323(x54913,x54912))+P101(f323(f323(f325(x54911),x54912),f323(f243(x54911),x54913)))
% 179.72/179.58 [5511]E(x55111,f2(a860))+E(f323(f166(x55112),f163(x55112,x55111,x55113)),f323(f323(f301(x55112),x55113),f188(f867(x55112,a855))))
% 179.72/179.58 [5530]E(f164(x55301,x55302,x55303),x55303)+P101(f323(f323(f325(x55301),x55302),f323(f166(x55301),x55303)))
% 179.72/179.58 [5612]~P101(f323(f130(x56121),x56123))+P101(f323(f130(x56121),f323(f129(x56121,x56122),x56123)))
% 179.72/179.58 [5657]~P57(x56571)+E(f323(f323(f36(x56571),f42(x56571,x56572,x56573)),x56573),f2(x56571))
% 179.72/179.58 [5676]E(f170(x56761,f323(f323(f144(x56761),x56762),f113(x56761)),x56763),f113(x56761))+P101(f323(f323(f325(a860),f2(a860)),x56763))
% 179.72/179.58 [5682]E(x56821,f2(a860))+E(f323(f165(x56822),f163(x56822,x56821,x56823)),f163(x56822,f323(f323(f22(a860),x56821),f76(a860)),x56823))
% 179.72/179.58 [5732]E(f323(f323(f144(x57321),x57322),x57323),f133(x57321,x57322,x57323))+P101(f323(f323(f325(x57321),x57322),f323(f166(x57321),x57323)))
% 179.72/179.58 [5741]E(x57411,x57412)+~E(f323(f323(f79(a860),f323(a112,x57413)),x57411),f323(f323(f79(a860),f323(a112,x57413)),x57412))
% 179.72/179.58 [5742]~E(x57422,f323(f323(f78(a1),x57421),f323(f100(a1),f323(a112,x57423))))+P101(f323(f323(f238(a1),x57421),x57422))
% 179.72/179.58 [5847]~E(x58473,f113(x58471))+E(f323(f323(f323(f183(f861(x58471),f861(x58471)),x58472),f161(x58471)),x58473),f113(x58471))
% 179.72/179.58 [5851]P101(f323(x58511,x58512))+~P101(f323(f323(f325(x58513),x58512),f323(f243(x58513),x58511)))
% 179.72/179.58 [5881]E(x58811,x58812)+~E(f323(f323(f301(x58813),x58811),f188(f867(x58813,a855))),f323(f323(f301(x58813),x58812),f188(f867(x58813,a855))))
% 179.72/179.58 [5892]~P105(x58921)+E(f323(f323(f101(f867(x58921,a855)),f323(f244(x58921),x58922)),f323(f293(x58921,x58922),x58923)),f188(f867(x58921,a855)))
% 179.72/179.58 [5934]E(f133(x59341,x59342,x59343),x59343)+~P101(f323(f323(f325(x59341),x59342),f323(f166(x59341),x59343)))
% 179.72/179.58 [5954]~P75(x59541)+E(f323(f302(x59541,x59541,f77(x59541)),f323(f293(x59541,x59542),x59543)),f296(x59541,f323(f77(x59541),x59543),f323(f77(x59541),x59542)))
% 179.72/179.58 [5962]E(f323(f189(f861(x59621)),f164(x59621,x59622,x59623)),f323(f189(f861(x59621)),x59623))+P101(f323(f323(f325(x59621),x59622),f323(f166(x59621),x59623)))
% 179.72/179.58 [6014]~P105(x60141)+E(f323(f323(f101(f867(x60141,a855)),f323(f293(x60141,x60142),x60143)),f323(f245(x60141),x60143)),f188(f867(x60141,a855)))
% 179.72/179.58 [6037]~P75(x60371)+E(f323(f302(x60371,x60371,f77(x60371)),f294(x60371,x60372,x60373)),f294(x60371,f323(f77(x60371),x60373),f323(f77(x60371),x60372)))
% 179.72/179.58 [6038]~P75(x60381)+E(f323(f302(x60381,x60381,f77(x60381)),f297(x60381,x60382,x60383)),f297(x60381,f323(f77(x60381),x60383),f323(f77(x60381),x60382)))
% 179.72/179.58 [6095]E(f170(x60951,f323(f323(f144(x60951),x60952),f113(x60951)),x60953),f323(f323(f144(x60951),x60952),f113(x60951)))+~P101(f323(f323(f325(a860),f2(a860)),x60953))
% 179.72/179.58 [6102]~P75(x61021)+E(f323(f302(x61021,x61021,f77(x61021)),f296(x61021,x61022,x61023)),f323(f293(x61021,f323(f77(x61021),x61023)),f323(f77(x61021),x61022)))
% 179.72/179.58 [6122]~P58(x61221)+E(f42(x61221,f323(f77(x61221),f42(x61221,x61222,x61223)),x61223),f42(x61221,f323(f77(x61221),x61222),x61223))
% 179.72/179.58 [6220]~P101(f323(f59(f866(x62202,x62201)),x62203))+P101(f323(f59(x62201),f323(f254(x62202,x62201),x62203)))
% 179.72/179.58 [6221]~P101(f323(f59(f866(x62211,x62212)),x62213))+P101(f323(f59(x62211),f323(f256(x62211,x62212),x62213)))
% 179.72/179.58 [6226]~P105(x62261)+E(f323(f323(f101(f867(x62261,a855)),f294(x62261,x62262,x62263)),f323(f295(x62261),x62263)),f188(f867(x62261,a855)))
% 179.72/179.58 [6227]~P105(x62271)+E(f323(f323(f101(f867(x62271,a855)),f297(x62271,x62272,x62273)),f323(f245(x62271),x62273)),f188(f867(x62271,a855)))
% 179.72/179.58 [6228]~P105(x62281)+E(f323(f323(f101(f867(x62281,a855)),f296(x62281,x62282,x62283)),f323(f295(x62281),x62283)),f188(f867(x62281,a855)))
% 179.72/179.58 [6294]E(f323(f323(f158(x62941),x62942),f541(x62942,x62943,x62941)),x62943)+~P101(f323(f323(f325(x62941),x62943),f323(f166(x62941),x62942)))
% 179.72/179.58 [6432]E(x64321,f113(x64322))+~E(f323(f323(f323(f183(f861(x64322),f861(x64322)),x64323),f161(x64322)),x64321),f113(x64322))
% 179.72/179.58 [6534]~P101(f323(f59(f866(x65342,x65341)),x65343))+P101(f323(f59(f866(x65341,x65342)),f323(f278(x65342,x65341),x65343)))
% 179.72/179.58 [6684]P52(x66841,x66842,x66843)+P101(f323(f323(f325(x66841),f728(x66843,x66842,x66841)),x66842))
% 179.72/179.58 [6685]P52(x66851,x66852,x66853)+P101(f323(f323(f325(x66851),f727(x66853,x66852,x66851)),x66852))
% 179.72/179.58 [6696]P101(f323(f311(x66961,x66962),x66963))+P101(f323(f323(x66962,f495(x66963,x66962,x66961)),x66963))
% 179.72/179.58 [6697]P101(f323(f311(x66971,x66972),x66973))+P101(f323(f323(x66972,f510(x66973,x66972,x66971)),x66973))
% 179.72/179.58 [6728]E(f323(f189(f861(x67281)),f164(x67281,x67282,x67283)),f323(f323(f22(a860),f323(f189(f861(x67281)),x67283)),f76(a860)))+~P101(f323(f323(f325(x67281),x67282),f323(f166(x67281),x67283)))
% 179.72/179.58 [6768]P101(f323(f251(x67681,x67682),x67683))+P101(f323(f323(f325(x67681),f562(x67683,x67682,x67681)),x67683))
% 179.72/179.58 [6779]~P101(f323(f59(f866(x67792,x67791)),f323(f278(x67791,x67792),x67793)))+P101(f323(f59(f866(x67791,x67792)),x67793))
% 179.72/179.58 [6835]~P101(f323(f323(f325(x68351),x68352),f323(f166(x68351),f114(x68351,x68353))))+P101(f323(f323(f325(x68351),x68352),f323(f166(x68351),x68353)))
% 179.72/179.58 [6867]E(f323(f129(x68671,x68672),x68673),x68673)+P101(f323(f323(f325(x68671),f553(x68673,x68672,x68671)),f323(f166(x68671),x68673)))
% 179.72/179.58 [6882]E(f323(f129(x68821,x68822),x68823),f113(x68821))+P101(f323(f323(f325(x68821),f561(x68823,x68822,x68821)),f323(f166(x68821),x68823)))
% 179.72/179.58 [6905]P32(x69051,x69052,x69053)+P101(f323(f323(f325(x69051),f779(x69053,x69052,x69051)),f323(f166(x69051),x69053)))
% 179.72/179.58 [6906]P32(x69061,x69062,x69063)+P101(f323(f323(f325(x69061),f780(x69063,x69062,x69061)),f323(f166(x69061),x69063)))
% 179.72/179.58 [6907]P32(x69071,x69072,x69073)+P101(f323(f323(f325(x69071),f770(x69072,x69073,x69071)),f323(f166(x69071),x69073)))
% 179.72/179.58 [6910]E(f171(x69101,x69102,x69103),x69103)+P101(f323(f323(f325(x69101),f602(x69103,x69102,x69101)),f323(f166(x69101),x69103)))
% 179.72/179.58 [6989]P101(f323(f153(x69891,x69892),x69893))+P101(f323(f323(f325(x69891),f638(x69893,x69892,x69891)),f323(f166(x69891),x69893)))
% 179.72/179.58 [6998]~P34(x69981,x69983,x69982)+P101(f323(f323(f325(x69981),f702(x69982,x69983,x69981)),f323(f166(x69981),x69982)))
% 179.72/179.58 [6999]~P36(x69991,x69993,x69992)+P101(f323(f323(f325(x69991),f789(x69992,x69993,x69991)),f323(f166(x69991),x69992)))
% 179.72/179.58 [7034]P101(f323(f323(f325(x70341),x70342),f766(x70343,x70342,x70341)))+~P101(f323(f323(f325(x70341),x70342),f37(f867(x70341,a855),x70343)))
% 179.72/179.58 [7035]~P72(x70351)+E(f323(f323(f78(x70351),f323(f323(f6(a860,x70351),x70352),f323(f244(a860),x70353))),f323(x70352,x70353)),f323(f323(f6(a860,x70351),x70352),f323(f244(a860),f323(a112,x70353))))
% 179.72/179.58 [7124]~P34(x71242,x71241,x71243)+P101(f323(x71241,f323(f323(f158(x71242),x71243),f717(x71243,x71241,x71242))))
% 179.72/179.58 [7137]~P101(f323(f323(f325(x71371),x71372),f718(x71372,x71373,x71371)))+P101(f323(f323(f325(x71371),x71372),f38(f867(x71371,a855),x71373)))
% 179.72/179.58 [7167]~P72(x71671)+E(f323(f323(f78(x71671),f323(f323(f6(a860,x71671),x71672),f323(f292(a860),x71673))),f323(x71672,f323(a112,x71673))),f323(f323(f6(a860,x71671),x71672),f323(f292(a860),f323(a112,x71673))))
% 179.72/179.58 [7300]P101(f323(f323(f325(f861(x73001)),x73002),f154(x73001,x73003)))+P101(f323(f323(f325(x73001),f613(x73003,x73002,x73001)),f323(f166(x73001),x73002)))
% 179.72/179.58 [7316]~P101(f323(f323(f325(f861(x73161)),x73162),f154(x73161,f312(x73161,x73163))))+P101(f323(f323(f325(f861(x73161)),x73162),f312(f861(x73161),f150(x73161,x73163))))
% 179.72/179.58 [7341]~P101(f323(f323(f325(f861(x73411)),x73412),f312(f861(x73411),f150(x73411,x73413))))+P101(f323(f323(f325(f861(x73411)),x73412),f154(x73411,f312(x73411,x73413))))
% 179.72/179.58 [7377]E(f323(f323(f323(f183(f861(x73771),f861(x73771)),x73772),f161(x73771)),x73773),x73773)+~P101(f323(f323(f237(a860),f323(f189(f861(x73771)),x73773)),f76(a860)))
% 179.72/179.58 [7412]E(f323(f323(f121(x74121),f732(x74122,x74123,x74121)),f323(f323(f144(x74121),x74123),f754(x74122,x74123,x74121))),x74122)+~P101(f323(f323(f325(x74121),x74123),f323(f166(x74121),x74122)))
% 179.72/179.58 [7413]E(f323(f323(f121(x74131),f755(x74132,x74133,x74131)),f323(f323(f144(x74131),x74133),f756(x74132,x74133,x74131))),x74132)+~P101(f323(f323(f325(x74131),x74133),f323(f166(x74131),x74132)))
% 179.72/179.58 [7414]E(f323(f323(f121(x74141),f757(x74142,x74143,x74141)),f323(f323(f144(x74141),x74143),f758(x74142,x74143,x74141))),x74142)+~P101(f323(f323(f325(x74141),x74143),f323(f166(x74141),x74142)))
% 179.72/179.58 [7437]~P27(x74371,x74372,x74373,f246(f867(x74371,a855)))+P27(f861(x74371),f861(x74372),f323(f147(x74371,x74372),x74373),f246(f867(f861(x74371),a855)))
% 179.72/179.58 [7585]E(x75851,f323(f323(f78(a860),f323(f323(f79(a860),f323(f257(a860,a860),x75852)),x75853)),f323(f261(a860,a860),x75852)))+~P101(f323(f45(x75851,x75853),x75852))
% 179.72/179.58 [7593]P27(x75931,x75932,x75933,f246(f867(x75931,a855)))+~P27(f861(x75931),f861(x75932),f323(f147(x75931,x75932),x75933),f246(f867(f861(x75931),a855)))
% 179.72/179.58 [7636]P101(f323(f323(f325(f867(x76361,a855)),f718(x76362,x76363,x76361)),x76363))+P101(f323(f323(f325(x76361),x76362),f38(f867(x76361,a855),x76363)))
% 179.72/179.58 [7728]P101(f323(f323(f325(f861(x77281)),x77282),f154(x77281,x77283)))+~P101(f323(f323(f325(x77281),f613(x77283,x77282,x77281)),x77283))
% 179.72/179.58 [7829]P32(x78291,x78292,x78293)+~P101(f323(x78292,f323(f323(f158(x78291),x78293),f771(x78293,x78292,x78291))))
% 179.72/179.58 [7853]E(x78531,x78532)+~E(f323(f323(f7(x78533,f867(x78533,a855),a855),f325(x78533)),x78531),f323(f323(f7(x78533,f867(x78533,a855),a855),f325(x78533)),x78532))
% 179.72/179.58 [7861]~P101(f323(f323(f325(f866(x78611,x78611)),x78613),f255(x78611,x78612)))+P101(f323(f323(f325(x78611),f525(x78612,x78613,x78611)),x78612))
% 179.72/179.58 [7863]~P101(f323(f323(f325(x78631),x78633),f37(f867(x78631,a855),x78632)))+P101(f323(f323(f325(f867(x78631,a855)),f766(x78632,x78633,x78631)),x78632))
% 179.72/179.58 [7985]P27(x79851,x79852,f91(x79852,x79851,f246(f867(x79852,a855)),x79853),f246(f867(x79851,a855)))+~E(f323(f302(x79852,x79851,x79853),f246(f867(x79852,a855))),f246(f867(x79851,a855)))
% 179.72/179.58 [8037]~P101(f323(f323(f325(x80371),x80372),f323(f166(x80371),f755(x80373,x80372,x80371))))+~P101(f323(f323(f325(x80371),x80372),f323(f166(x80371),x80373)))
% 179.72/179.58 [8038]~P101(f323(f323(f325(x80381),x80382),f323(f166(x80381),f758(x80383,x80382,x80381))))+~P101(f323(f323(f325(x80381),x80382),f323(f166(x80381),x80383)))
% 179.72/179.58 [8125]E(f323(f232(f864(f861(a319)),f861(a319),f305(x81251,x81252,f323(f323(f78(a1),x81253),f76(a1))),f230(f861(a319))),f323(x81251,x81253)),f305(x81251,x81252,x81253))+P101(f323(f323(f238(a1),x81252),x81253))
% 179.72/179.58 [8227]E(x82271,f113(x82272))+P101(f323(f323(f325(x82272),f323(f257(x82272,f866(a99,a99)),f323(f274(x82272,x82271),x82273))),f323(f166(x82272),x82271)))
% 179.72/179.58 [8329]~P67(x83291)+E(f323(f135(x83291,x83291,f323(f7(x83291,x83291,x83291),f78(x83291)),x83292),f323(f162(x83291),x83293)),f323(f135(x83291,x83291,f78(x83291),x83292),x83293))
% 179.72/179.58 [8516]~P27(x85162,x85161,x85163,f246(f867(x85162,a855)))+E(f323(f302(x85161,x85162,f91(x85162,x85161,f246(f867(x85162,a855)),x85163)),f246(f867(x85161,a855))),f246(f867(x85162,a855)))
% 179.72/179.58 [8830]~P103(x88301)+E(f323(f166(x88301),f142(x88301,x88301,f5(x88301),x88302,x88303)),f323(f323(f301(x88301),x88302),f323(f166(x88301),x88303)))
% 179.72/179.58 [8840]~E(f323(x88403,f323(f91(x88401,x88402,f246(f867(x88401,a855)),x88403),f691(x88403,x88402,x88401))),f691(x88403,x88402,x88401))+E(f323(f302(x88401,x88402,x88403),f246(f867(x88401,a855))),f246(f867(x88402,a855)))
% 179.72/179.58 [8842]P101(f323(f323(f238(a860),f2(a860)),f736(x88421,x88422,x88423)))+~P101(f323(f323(f325(f866(x88423,x88423)),x88422),f323(f323(f280(x88423,x88423,x88423),x88421),f299(x88423,x88421))))
% 179.72/179.58 [9122]~P54(x91221,x91222)+~P101(f323(f323(f325(f866(x91221,x91221)),f323(f323(f258(x91221,x91221),x91223),x91223)),f323(f323(f280(x91221,x91221,x91221),x91222),f299(x91221,x91222))))
% 179.72/179.58 [9252]~E(f323(f323(f101(f867(f866(x92521,x92521),a855)),f323(f278(x92521,x92521),x92522)),f299(x92521,x92522)),f188(f867(f866(x92521,x92521),a855)))+~P101(f323(f323(f325(f866(x92521,x92521)),f323(f323(f258(x92521,x92521),x92523),x92523)),f323(f323(f280(x92521,x92521,x92521),x92522),f299(x92521,x92522))))
% 179.72/179.58 [9431]~P101(f323(f59(x94311),x94312))+P101(f323(f323(f237(a860),f323(f35(x94311),f323(f323(f22(f867(x94311,a855)),x94312),f323(f323(f301(x94311),x94313),f188(f867(x94311,a855)))))),f323(f35(x94311),x94312)))
% 179.72/179.58 [5038]~E(x50383,f113(x50381))+E(f137(x50381,f323(f323(f144(x50381),x50382),x50383)),x50382)
% 179.72/179.58 [5046]~E(x50463,f113(x50461))+E(f114(x50461,f323(f323(f144(x50461),x50462),x50463)),f113(x50461))
% 179.72/179.58 [5075]E(x50751,f113(x50752))+E(f137(x50752,f323(f323(f144(x50752),x50753),x50751)),f137(x50752,x50751))
% 179.72/179.58 [5077]E(x50771,f113(x50772))+E(f137(x50772,f323(f323(f121(x50772),x50773),x50771)),f137(x50772,x50771))
% 179.72/179.58 [5083]~E(x50833,f113(x50831))+E(f137(x50831,f323(f323(f121(x50831),x50832),x50833)),f137(x50831,x50832))
% 179.72/179.58 [5084]~E(x50843,f113(x50841))+E(f114(x50841,f323(f323(f121(x50841),x50842),x50843)),f114(x50841,x50842))
% 179.72/179.58 [5116]E(x51161,f113(x51162))+E(f323(f134(x51162),f323(f323(f121(x51162),x51161),x51163)),f323(f134(x51162),x51161))
% 179.72/179.58 [5144]~E(x51442,f113(x51441))+E(f323(f134(x51441),f323(f323(f121(x51441),x51442),x51443)),f323(f134(x51441),x51443))
% 179.72/179.58 [5193]~P2(x51931)+E(f323(f323(f110(x51931),x51932),f323(f323(f101(x51931),x51932),x51933)),x51932)
% 179.72/179.58 [5194]~P2(x51941)+E(f323(f323(f101(x51941),x51942),f323(f323(f110(x51941),x51942),x51943)),x51942)
% 179.72/179.58 [5195]~P103(x51951)+E(f323(f323(f235(x51951),x51952),f323(f323(f236(x51951),x51952),x51953)),x51952)
% 179.72/179.58 [5196]~P103(x51961)+E(f323(f323(f236(x51961),x51962),f323(f323(f235(x51961),x51962),x51963)),x51962)
% 179.72/179.58 [5213]~P57(x52131)+E(f42(x52131,f323(f323(f79(x52131),x52132),x52133),x52133),f2(x52131))
% 179.72/179.58 [5214]~P57(x52141)+E(f42(x52141,f323(f323(f79(x52141),x52142),x52143),x52142),f2(x52141))
% 179.72/179.58 [5288]~P60(x52881)+E(f323(f77(x52881),f323(f323(f22(x52881),x52882),x52883)),f323(f323(f22(x52881),x52883),x52882))
% 179.72/179.58 [5349]E(x53491,f113(x53492))+E(f114(x53492,f323(f323(f144(x53492),x53493),x53491)),f323(f323(f144(x53492),x53493),f114(x53492,x53491)))
% 179.72/179.58 [5350]E(x53501,f113(x53502))+E(f114(x53502,f323(f323(f121(x53502),x53503),x53501)),f323(f323(f121(x53502),x53503),f114(x53502,x53501)))
% 179.72/179.58 [5353]~P6(x53531)+E(f37(x53531,f323(f323(f301(x53531),x53532),x53533)),f323(f323(f110(x53531),x53532),f37(x53531,x53533)))
% 179.72/179.58 [5354]~P6(x53541)+E(f38(x53541,f323(f323(f301(x53541),x53542),x53543)),f323(f323(f101(x53541),x53542),f38(x53541,x53543)))
% 179.72/179.58 [5399]~P2(x53991)+E(f323(f323(f110(x53991),x53992),f323(f323(f110(x53991),x53992),x53993)),f323(f323(f110(x53991),x53992),x53993))
% 179.72/179.58 [5401]~P97(x54011)+E(f323(f323(f110(x54011),x54012),f323(f323(f110(x54011),x54012),x54013)),f323(f323(f110(x54011),x54012),x54013))
% 179.72/179.58 [5402]~P2(x54021)+E(f323(f323(f101(x54021),x54022),f323(f323(f101(x54021),x54022),x54023)),f323(f323(f101(x54021),x54022),x54023))
% 179.72/179.58 [5404]~P98(x54041)+E(f323(f323(f101(x54041),x54042),f323(f323(f101(x54041),x54042),x54043)),f323(f323(f101(x54041),x54042),x54043))
% 179.72/179.58 [5405]~P93(x54051)+E(f323(f323(f79(x54051),x54052),f323(f323(f79(x54051),x54052),x54053)),f323(f323(f79(x54051),x54052),x54053))
% 179.72/179.58 [5407]~P103(x54071)+E(f323(f323(f235(x54071),x54072),f323(f323(f235(x54071),x54072),x54073)),f323(f323(f235(x54071),x54072),x54073))
% 179.72/179.58 [5409]~P103(x54091)+E(f323(f323(f236(x54091),x54092),f323(f323(f236(x54091),x54092),x54093)),f323(f323(f236(x54091),x54092),x54093))
% 179.72/179.58 [5417]~P57(x54171)+E(f42(x54171,f323(f323(f78(x54171),x54172),x54173),x54173),f42(x54171,x54172,x54173))
% 179.72/179.58 [5418]~P57(x54181)+E(f42(x54181,f323(f323(f78(x54181),x54182),x54183),x54182),f42(x54181,x54183,x54182))
% 179.72/179.58 [5424]~P107(x54241)+E(f323(f323(f79(x54241),x54242),f323(f77(x54241),x54243)),f323(f77(x54241),f323(f323(f79(x54241),x54242),x54243)))
% 179.72/179.58 [5425]~P62(x54251)+E(f323(f323(f281(x54251),x54252),f323(f77(x54251),x54253)),f323(f77(x54251),f323(f323(f281(x54251),x54252),x54253)))
% 179.72/179.58 [5426]~P78(x54261)+E(f323(f323(f78(x54261),x54262),f323(f159(x54261),x54263)),f323(f159(x54261),f323(f323(f144(x54261),x54262),x54263)))
% 179.72/179.58 [5456]~P107(x54561)+E(f323(f323(f79(x54561),f323(f77(x54561),x54562)),x54563),f323(f323(f79(x54561),x54562),f323(f77(x54561),x54563)))
% 179.72/179.58 [5462]~P9(x54621,x54622,x54623)+E(f37(f867(x54621,a855),f323(f323(f58(x54621),x54622),x54623)),x54622)
% 179.72/179.58 [5522]~P110(x55221)+E(f323(f323(f79(x55221),x55222),f323(f323(f248(x55221),x55222),x55223)),f323(f323(f248(x55221),x55222),f323(a112,x55223)))
% 179.72/179.58 [5523]~P112(x55231)+E(f323(f323(f79(x55231),x55232),f323(f323(f248(x55231),x55232),x55233)),f323(f323(f248(x55231),x55232),f323(a112,x55233)))
% 179.72/179.58 [5533]~P59(x55331)+E(f323(f323(f78(x55331),f323(f77(x55331),x55332)),f323(f323(f78(x55331),x55332),x55333)),x55333)
% 179.72/179.58 [5556]~P140(x55561)+E(f323(f323(f248(x55561),f323(f100(x55561),x55562)),x55563),f323(f100(x55561),f323(f323(f248(a860),x55562),x55563)))
% 179.72/179.58 [5557]~P134(x55571)+E(f323(f323(f248(x55571),f323(f102(x55571),x55572)),x55573),f323(f102(x55571),f323(f323(f248(a1),x55572),x55573)))
% 179.72/179.58 [5563]~P82(x55631)+E(f323(f73(x55631),f323(f323(f22(x55631),x55632),x55633)),f323(f73(x55631),f323(f323(f22(x55631),x55633),x55632)))
% 179.72/179.58 [5565]~P116(x55651)+E(f323(f323(f79(x55651),f80(x55651,x55652)),f80(x55651,x55653)),f80(x55651,f323(f323(f79(x55651),x55652),x55653)))
% 179.72/179.58 [5569]E(x55691,f113(x55692))+E(f323(f323(f121(x55692),f323(f165(x55692),x55691)),x55693),f323(f165(x55692),f323(f323(f121(x55692),x55691),x55693)))
% 179.72/179.58 [5574]~E(x55742,f323(a112,f323(f323(f78(a860),x55741),x55743)))+P101(f323(f323(f238(a860),x55741),x55742))
% 179.72/179.58 [5575]~P107(x55751)+E(f323(f323(f79(x55751),f323(f77(x55751),x55752)),x55753),f323(f77(x55751),f323(f323(f79(x55751),x55752),x55753)))
% 179.72/179.58 [5576]~P114(x55761)+E(f323(f323(f281(x55761),f323(f77(x55761),x55762)),x55763),f323(f77(x55761),f323(f323(f281(x55761),x55762),x55763)))
% 179.72/179.58 [5577]~P116(x55771)+E(f323(f323(f248(x55771),f323(f73(x55771),x55772)),x55773),f323(f73(x55771),f323(f323(f248(x55771),x55772),x55773)))
% 179.72/179.58 [5675]E(f538(x56751,x56752,x56753),f545(x56751,x56752,x56753))+E(f323(f323(f101(f867(x56753,a855)),x56752),x56751),f188(f867(x56753,a855)))
% 179.72/179.58 [5690]~P72(x56902)+E(f323(f323(f6(x56901,x56902),f323(f16(x56902,x56901),f2(x56902))),x56903),f2(x56902))
% 179.72/179.58 [5691]~P68(x56912)+E(f323(f323(f9(x56911,x56912),f323(f16(x56912,x56911),f76(x56912))),x56913),f76(x56912))
% 179.72/179.58 [5693]~P140(x56931)+E(f323(f323(f79(x56931),f323(f100(x56931),x56932)),f323(f100(x56931),x56933)),f323(f100(x56931),f323(f323(f79(a860),x56932),x56933)))
% 179.72/179.58 [5694]~P140(x56941)+E(f323(f323(f78(x56941),f323(f100(x56941),x56942)),f323(f100(x56941),x56943)),f323(f100(x56941),f323(f323(f78(a860),x56942),x56943)))
% 179.72/179.58 [5695]~P134(x56951)+E(f323(f323(f22(x56951),f323(f102(x56951),x56952)),f323(f102(x56951),x56953)),f323(f102(x56951),f323(f323(f22(a1),x56952),x56953)))
% 179.72/179.58 [5696]~P134(x56961)+E(f323(f323(f79(x56961),f323(f102(x56961),x56962)),f323(f102(x56961),x56963)),f323(f102(x56961),f323(f323(f79(a1),x56962),x56963)))
% 179.72/179.58 [5697]~P134(x56971)+E(f323(f323(f78(x56971),f323(f102(x56971),x56972)),f323(f102(x56971),x56973)),f323(f102(x56971),f323(f323(f78(a1),x56972),x56973)))
% 179.72/179.58 [5698]~P90(x56981)+E(f323(f323(f22(x56981),f323(f103(x56981),x56982)),f323(f103(x56981),x56983)),f323(f103(x56981),f323(f323(f22(a1),x56982),x56983)))
% 179.72/179.58 [5701]~P90(x57011)+E(f323(f323(f79(x57011),f323(f103(x57011),x57012)),f323(f103(x57011),x57013)),f323(f103(x57011),f323(f323(f79(a1),x57012),x57013)))
% 179.72/179.58 [5702]~P90(x57021)+E(f323(f323(f78(x57021),f323(f103(x57021),x57022)),f323(f103(x57021),x57023)),f323(f103(x57021),f323(f323(f78(a1),x57022),x57023)))
% 179.72/179.58 [5749]~E(x57493,x57492)+P101(f323(f323(f237(f867(x57491,a855)),x57492),x57493))
% 179.72/179.58 [5755]~E(x57552,x57553)+P101(f323(f323(f237(f867(x57551,a855)),x57552),x57553))
% 179.72/179.58 [5760]~P87(x57601)+E(f323(f323(f101(x57601),f323(f77(x57601),x57602)),f323(f77(x57601),x57603)),f323(f77(x57601),f323(f323(f110(x57601),x57602),x57603)))
% 179.72/179.58 [5761]~P87(x57611)+E(f323(f323(f110(x57611),f323(f77(x57611),x57612)),f323(f77(x57611),x57613)),f323(f77(x57611),f323(f323(f101(x57611),x57612),x57613)))
% 179.72/179.58 [5762]~P59(x57621)+E(f323(f323(f78(x57621),f323(f77(x57621),x57622)),f323(f77(x57621),x57623)),f323(f77(x57621),f323(f323(f78(x57621),x57623),x57622)))
% 179.72/179.58 [5763]~P60(x57631)+E(f323(f323(f78(x57631),f323(f77(x57631),x57632)),f323(f77(x57631),x57633)),f323(f77(x57631),f323(f323(f78(x57631),x57632),x57633)))
% 179.72/179.58 [5764]~P74(x57641)+E(f323(f323(f236(x57641),f323(f77(x57641),x57642)),f323(f77(x57641),x57643)),f323(f77(x57641),f323(f323(f235(x57641),x57642),x57643)))
% 179.72/179.58 [5765]~P74(x57651)+E(f323(f323(f235(x57651),f323(f77(x57651),x57652)),f323(f77(x57651),x57653)),f323(f77(x57651),f323(f323(f236(x57651),x57652),x57653)))
% 179.72/179.58 [5766]~P116(x57661)+E(f323(f323(f79(x57661),f323(f73(x57661),x57662)),f323(f73(x57661),x57663)),f323(f73(x57661),f323(f323(f79(x57661),x57662),x57663)))
% 179.72/179.58 [5767]~P64(x57671)+E(f323(f323(f281(x57671),f323(f73(x57671),x57672)),f323(f73(x57671),x57673)),f323(f73(x57671),f323(f323(f281(x57671),x57672),x57673)))
% 179.72/179.58 [5768]~P78(x57681)+E(f323(f323(f78(x57681),f323(f159(x57681),x57682)),f323(f159(x57681),x57683)),f323(f159(x57681),f323(f323(f121(x57681),x57682),x57683)))
% 179.72/179.58 [5769]E(x57691,f188(f867(x57692,a855)))+~E(f323(f323(f110(f867(x57692,a855)),x57693),x57691),f188(f867(x57692,a855)))
% 179.72/179.58 [5770]E(x57701,f188(f867(x57702,a855)))+~E(f323(f323(f110(f867(x57702,a855)),x57701),x57703),f188(f867(x57702,a855)))
% 179.72/179.58 [5771]~P143(x57711,x57712,x57713)+P101(f323(x57711,f323(f323(f36(a1),x57712),x57713)))
% 179.72/179.58 [5821]~P101(f323(f59(x58211),x58213))+P101(f323(f59(x58211),f323(f323(f301(x58211),x58212),x58213)))
% 179.72/179.58 [5822]~P101(f323(f130(x58221),x58223))+P101(f323(f130(x58221),f323(f323(f169(x58221),x58222),x58223)))
% 179.72/179.58 [5823]~P101(f323(f130(x58231),x58233))+P101(f323(f130(x58231),f323(f323(f131(x58231),x58232),x58233)))
% 179.72/179.58 [5852]~P2(x58521)+P101(f323(f323(f237(x58521),x58522),f323(f323(f110(x58521),x58523),x58522)))
% 179.72/179.58 [5853]~P97(x58531)+P101(f323(f323(f237(x58531),x58532),f323(f323(f110(x58531),x58533),x58532)))
% 179.72/179.58 [5854]~P2(x58541)+P101(f323(f323(f237(x58541),x58542),f323(f323(f110(x58541),x58542),x58543)))
% 179.72/179.58 [5855]~P97(x58551)+P101(f323(f323(f237(x58551),x58552),f323(f323(f110(x58551),x58552),x58553)))
% 179.72/179.58 [5856]~P103(x58561)+P101(f323(f323(f237(x58561),x58562),f323(f323(f236(x58561),x58563),x58562)))
% 179.72/179.58 [5857]~P103(x58571)+P101(f323(f323(f237(x58571),x58572),f323(f323(f236(x58571),x58572),x58573)))
% 179.72/179.58 [5871]~E(x58711,f2(a860))+E(f323(f323(f36(a860),f323(f323(f79(a860),x58711),x58712)),f323(f323(f79(a860),x58711),x58713)),f2(a860))
% 179.72/179.58 [5949]~P90(x59491)+E(f323(f323(f22(x59491),f323(f103(x59491),x59492)),f323(f103(x59491),x59493)),f323(f103(x59491),f323(f323(f78(a1),x59492),f323(f77(a1),x59493))))
% 179.72/179.58 [6001]E(x60011,f2(a860))+E(f323(f323(f36(a860),f323(f323(f79(a860),x60011),x60012)),f323(f323(f79(a860),x60011),x60013)),f323(f323(f36(a860),x60012),x60013))
% 179.72/179.58 [6035]E(f145(x60351,f323(f323(f144(x60351),x60352),x60353)),f323(f323(f144(x60351),x60352),f145(x60351,x60353)))+P101(f323(f323(f325(x60351),x60352),f323(f166(x60351),x60353)))
% 179.72/179.58 [6069]P143(x60691,x60692,x60693)+~P101(f323(x60691,f323(f323(f36(a1),x60692),x60693)))
% 179.72/179.58 [6138]E(x61381,f113(x61382))+E(f323(f323(f144(x61382),f323(f134(x61382),x61381)),f323(f323(f169(x61382),x61383),f323(f165(x61382),x61381))),f323(f323(f169(x61382),f323(a112,x61383)),x61381))
% 179.72/179.58 [6144]E(f323(f323(f22(f867(x61441,a855)),x61442),x61443),x61442)+~E(f323(f323(f101(f867(x61441,a855)),x61442),x61443),f188(f867(x61441,a855)))
% 179.72/179.58 [6158]E(f145(x61581,f323(f323(f144(x61581),x61582),x61583)),f145(x61581,x61583))+~P101(f323(f323(f325(x61581),x61582),f323(f166(x61581),x61583)))
% 179.72/179.58 [6190]~P101(f323(f323(f237(a860),x61901),x61903))+P101(f323(f323(f237(a860),x61901),f323(f323(f78(a860),x61902),x61903)))
% 179.72/179.58 [6192]~P101(f323(f323(f237(a860),x61921),x61922))+P101(f323(f323(f237(a860),x61921),f323(f323(f78(a860),x61922),x61923)))
% 179.72/179.58 [6194]~P101(f323(f323(f238(a860),x61941),x61943))+P101(f323(f323(f238(a860),x61941),f323(f323(f78(a860),x61942),x61943)))
% 179.72/179.58 [6196]~P101(f323(f323(f238(a860),x61961),x61962))+P101(f323(f323(f238(a860),x61961),f323(f323(f78(a860),x61962),x61963)))
% 179.72/179.58 [6234]P101(f323(f59(x62341),x62342))+~P101(f323(f59(x62341),f323(f323(f301(x62341),x62343),x62342)))
% 179.72/179.58 [6235]P101(f323(f130(x62351),x62352))+~P101(f323(f130(x62351),f323(f323(f144(x62351),x62353),x62352)))
% 179.72/179.58 [6236]P101(f323(f130(x62361),x62362))+~P101(f323(f130(x62361),f323(f323(f121(x62361),x62363),x62362)))
% 179.72/179.58 [6237]P101(f323(f130(x62371),x62372))+~P101(f323(f130(x62371),f323(f323(f121(x62371),x62372),x62373)))
% 179.72/179.58 [6283]~P112(x62831)+E(f323(f323(f78(x62831),x62832),f323(f323(f79(x62831),x62833),x62832)),f323(f323(f79(x62831),f323(f323(f78(x62831),x62833),f76(x62831))),x62832))
% 179.72/179.58 [6329]~E(x63291,x63292)+~P101(f323(f323(f238(f867(x63293,a855)),x63291),x63292))
% 179.72/179.58 [6374]P101(f323(f323(f325(x63741),x63742),x63743))+P101(f323(f323(f325(x63741),x63742),f323(f77(f867(x63741,a855)),x63743)))
% 179.72/179.58 [6380]E(f137(x63801,f323(f323(f131(x63801),x63802),x63803)),f137(x63801,x63803))+~P101(f323(f323(f238(a860),x63802),f323(f189(f861(x63801)),x63803)))
% 179.72/179.58 [6381]E(f323(f323(f169(x63811),x63812),f114(x63811,x63813)),f323(f323(f169(x63811),x63812),x63813))+~P101(f323(f323(f238(a860),x63812),f323(f189(f861(x63811)),x63813)))
% 179.72/179.58 [6434]E(f323(f323(f323(f183(f861(x64341),f861(x64341)),x64342),f161(x64341)),x64343),x64343)+~E(f42(a860,x64342,f323(f189(f861(x64341)),x64343)),f2(a860))
% 179.72/179.58 [6441]~P9(x64411,x64413,x64412)+E(f323(f323(f280(x64411,x64411,x64411),f323(f278(x64411,x64411),x64412)),x64412),x64412)
% 179.72/179.58 [6483]~E(f323(f323(f110(f867(x64831,a855)),x64832),x64833),x64833)+P101(f323(f323(f237(f867(x64831,a855)),x64832),x64833))
% 179.72/179.58 [6488]~P51(x64881,x64881,x64883)+P51(x64881,x64881,f323(f323(f183(f866(x64881,x64881),a855),x64882),x64883))
% 179.72/179.58 [6491]~P101(f323(f323(f325(x64911),x64913),f323(f166(x64911),x64912)))+P101(f323(f323(f238(a860),f2(a860)),f323(f189(f861(x64911)),x64912)))
% 179.72/179.58 [6517]~P82(x65171)+E(f323(f73(x65171),f323(f323(f78(x65171),f323(f73(x65171),x65172)),f323(f73(x65171),x65173))),f323(f323(f78(x65171),f323(f73(x65171),x65172)),f323(f73(x65171),x65173)))
% 179.72/179.58 [6527]E(f323(f323(f36(a860),f323(f323(f79(a860),x65271),x65272)),f323(f323(f79(a860),x65271),x65273)),f323(f323(f36(a860),x65272),x65273))+~P101(f323(f323(f238(a860),f2(a860)),x65271))
% 179.72/179.58 [6663]~P101(f323(f59(x66631),x66633))+E(f323(f323(f62(x66631,f867(x66631,a855),f301(x66631)),x66632),x66633),f323(f323(f110(f867(x66631,a855)),x66633),x66632))
% 179.72/179.58 [6721]E(f323(f323(f110(f867(x67211,a855)),x67212),x67213),x67212)+~P101(f323(f323(f237(f867(x67211,a855)),x67213),x67212))
% 179.72/179.58 [6723]E(f323(f323(f110(f867(x67231,a855)),x67232),x67233),x67233)+~P101(f323(f323(f237(f867(x67231,a855)),x67232),x67233))
% 179.72/179.58 [6724]E(f323(f323(f101(f867(x67241,a855)),x67242),x67243),x67243)+~P101(f323(f323(f237(f867(x67241,a855)),x67243),x67242))
% 179.72/179.58 [6725]E(f323(f323(f101(f867(x67251,a855)),x67252),x67253),x67252)+~P101(f323(f323(f237(f867(x67251,a855)),x67252),x67253))
% 179.72/179.58 [6777]~P101(f323(f130(x67771),x67772))+E(f323(f323(f22(f867(x67771,a855)),f323(f166(x67771),x67772)),f323(f323(f301(x67771),x67773),f188(f867(x67771,a855)))),f323(f166(x67771),f164(x67771,x67773,x67772)))
% 179.72/179.58 [6830]P38(x68301,x68302)+~P38(x68301,f323(f323(f183(f866(x68301,x68301),a855),x68303),x68302))
% 179.72/179.58 [6893]P101(f323(f46(x68931,x68932),f323(a48,x68933)))+~P101(f323(f46(f323(f77(a1),x68931),f323(f77(a1),x68932)),x68933))
% 179.72/179.58 [6898]E(f323(f323(f22(f867(x68981,a855)),f323(f323(f301(x68981),x68982),x68983)),f323(f323(f301(x68981),x68982),f188(f867(x68981,a855)))),x68983)+P101(f323(f323(f325(x68981),x68982),x68983))
% 179.72/179.58 [6919]E(f323(f323(f101(f867(x69191,a855)),f323(f166(x69191),x69192)),f323(f166(x69191),x69193)),f188(f867(x69191,a855)))+~P101(f323(f130(x69191),f323(f323(f121(x69191),x69192),x69193)))
% 179.72/179.58 [6935]~P101(f323(f323(f325(x69351),x69352),f323(f166(x69351),x69353)))+~P101(f323(f130(x69351),f323(f323(f144(x69351),x69352),x69353)))
% 179.72/179.58 [7005]P32(x70051,x70052,x70053)+P101(f323(f323(f238(a860),f771(x70053,x70052,x70051)),f323(f189(f861(x70051)),x70053)))
% 179.72/179.58 [7015]E(f323(f323(f101(f867(x70151,a855)),x70152),x70153),f188(f867(x70151,a855)))+P101(f323(f323(f325(x70151),f538(x70153,x70152,x70151)),x70152))
% 179.72/179.58 [7016]E(f323(f323(f101(f867(x70161,a855)),x70162),x70163),f188(f867(x70161,a855)))+P101(f323(f323(f325(x70161),f545(x70163,x70162,x70161)),x70163))
% 179.72/179.58 [7020]E(f114(x70201,f323(f323(f169(x70201),x70202),x70203)),f323(f323(f169(x70201),f323(f323(f22(a860),x70202),f76(a860))),x70203))+~P101(f323(f323(f237(a860),x70202),f323(f189(f861(x70201)),x70203)))
% 179.72/179.58 [7079]~P34(x70793,x70792,x70791)+P101(f323(f323(f238(a860),f717(x70791,x70792,x70793)),f323(f189(f861(x70793)),x70791)))
% 179.72/179.58 [7097]P101(f323(f323(f238(a860),f2(a860)),x70971))+P101(f323(f323(f237(a860),f323(f323(f79(a860),x70972),x70971)),f323(f323(f79(a860),x70973),x70971)))
% 179.72/179.58 [7098]P101(f323(f323(f238(a860),f2(a860)),x70981))+P101(f323(f323(f237(a860),f323(f323(f79(a860),x70981),x70982)),f323(f323(f79(a860),x70981),x70983)))
% 179.72/179.58 [7101]~P101(f323(f323(f325(x71011),x71012),x71013))+~P101(f323(f323(f325(x71011),x71012),f323(f77(f867(x71011,a855)),x71013)))
% 179.72/179.58 [7108]~P101(f323(f323(f238(f867(x71081,a855)),x71082),x71083))+P101(f323(f323(f237(f867(x71081,a855)),x71082),x71083))
% 179.72/179.58 [7207]~P101(f323(f323(f237(a860),x72073),x72072))+P101(f323(f323(f237(a860),f323(f323(f22(a860),x72071),x72072)),f323(f323(f22(a860),x72071),x72073)))
% 179.72/179.58 [7208]~P101(f323(f323(f237(a860),x72081),x72083))+P101(f323(f323(f237(a860),f323(f323(f22(a860),x72081),x72082)),f323(f323(f22(a860),x72083),x72082)))
% 179.72/179.58 [7210]~P101(f323(f323(f237(a860),x72102),x72103))+P101(f323(f323(f237(a860),f323(f323(f79(a860),x72101),x72102)),f323(f323(f79(a860),x72101),x72103)))
% 179.72/179.58 [7212]~P101(f323(f323(f237(a860),x72121),x72123))+P101(f323(f323(f237(a860),f323(f323(f79(a860),x72121),x72122)),f323(f323(f79(a860),x72123),x72122)))
% 179.72/179.58 [7213]~P101(f323(f323(f237(a860),x72132),x72133))+P101(f323(f323(f237(a860),f323(f323(f78(a860),x72131),x72132)),f323(f323(f78(a860),x72131),x72133)))
% 179.72/179.58 [7214]~P101(f323(f323(f237(a860),x72141),x72143))+P101(f323(f323(f237(a860),f323(f323(f78(a860),x72141),x72142)),f323(f323(f78(a860),x72143),x72142)))
% 179.72/179.58 [7215]~P101(f323(f323(f237(a860),x72151),x72153))+P101(f323(f323(f237(a860),f323(f323(f36(a860),x72151),x72152)),f323(f323(f36(a860),x72153),x72152)))
% 179.72/179.58 [7216]~P101(f323(f323(f237(a1),x72162),x72163))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x72161),x72162)),f323(f323(f78(a1),x72161),x72163)))
% 179.72/179.58 [7219]~P101(f323(f323(f238(a860),x72192),x72193))+P101(f323(f323(f238(a860),f323(f323(f78(a860),x72191),x72192)),f323(f323(f78(a860),x72191),x72193)))
% 179.72/179.58 [7220]~P101(f323(f323(f238(a860),x72201),x72203))+P101(f323(f323(f238(a860),f323(f323(f78(a860),x72201),x72202)),f323(f323(f78(a860),x72203),x72202)))
% 179.72/179.58 [7221]~P101(f323(f323(f238(a1),x72211),x72213))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x72211),x72212)),f323(f323(f78(a1),x72213),x72212)))
% 179.72/179.58 [7299]E(x72991,x72992)+~P101(f323(f323(f325(x72993),x72991),f323(f323(f301(x72993),x72992),f188(f867(x72993,a855)))))
% 179.72/179.58 [7301]~E(f323(f323(f101(f867(x73011,a855)),x73012),x73013),f188(f867(x73011,a855)))+P101(f323(f323(f237(f867(x73011,a855)),x73012),f323(f77(f867(x73011,a855)),x73013)))
% 179.72/179.58 [7308]P101(f323(f323(f325(f867(x73081,a855)),x73082),f323(f300(x73081),x73083)))+~P101(f323(f323(f237(f867(x73081,a855)),x73082),x73083))
% 179.72/179.58 [7361]E(f323(f323(f144(x73611),f323(f323(f158(x73611),x73612),x73613)),f323(f323(f131(x73611),f323(a112,x73613)),x73612)),f323(f323(f131(x73611),x73613),x73612))+~P101(f323(f323(f238(a860),x73613),f323(f189(f861(x73611)),x73612)))
% 179.72/179.58 [7388]P101(f323(f323(f325(f866(x73881,x73881)),x73882),f299(x73881,x73883)))+~P101(f323(f323(f325(f866(x73881,x73881)),x73882),x73883))
% 179.72/179.58 [7398]~P101(f323(f323(f325(f867(x73981,a855)),x73982),f323(f300(x73981),x73983)))+P101(f323(f323(f237(f867(x73981,a855)),x73982),x73983))
% 179.72/179.58 [7443]P101(f323(f323(f237(f867(x74431,a855)),x74432),f37(f867(x74431,a855),x74433)))+~P101(f323(f323(f325(f867(x74431,a855)),x74432),x74433))
% 179.72/179.58 [7468]~P134(x74681)+E(f323(f323(f79(x74681),f323(f323(f248(x74681),f323(f77(x74681),f76(x74681))),x74682)),f323(f323(f248(x74681),x74683),x74682)),f323(f323(f248(x74681),f323(f77(x74681),x74683)),x74682))
% 179.72/179.58 [7489]E(f323(f323(f158(x74891),x74892),f323(f323(f22(a860),f323(f189(f861(x74891)),x74892)),f323(a112,x74893))),f323(f323(f158(x74891),f323(f162(x74891),x74892)),x74893))+~P101(f323(f323(f238(a860),x74893),f323(f189(f861(x74891)),x74892)))
% 179.72/179.58 [7506]~E(f323(f323(f101(f867(x75061,a855)),f549(x75063,x75062,x75061)),x75063),f188(f867(x75061,a855)))+E(f323(f323(f101(f867(x75061,a855)),f37(f867(x75061,a855),x75062)),x75063),f188(f867(x75061,a855)))
% 179.72/179.58 [7567]~P101(f323(f323(f325(x75673),x75672),f323(f166(x75673),x75671)))+P101(f323(f323(f238(a860),f541(x75671,x75672,x75673)),f323(f189(f861(x75673)),x75671)))
% 179.72/179.58 [7575]P101(f323(f323(f325(x75751),f323(f323(f158(x75751),x75752),x75753)),f323(f166(x75751),x75752)))+~P101(f323(f323(f238(a860),x75753),f323(f189(f861(x75751)),x75752)))
% 179.72/179.58 [7675]~P101(f323(x76752,f603(x76753,x76752,x76751)))+E(f323(f323(f131(x76751),f323(f189(f861(x76751)),f171(x76751,x76752,x76753))),x76753),f113(x76751))
% 179.72/179.58 [7686]P101(f323(f323(f237(f867(f861(x76861),a855)),f154(x76861,x76862)),f154(x76861,x76863)))+~P101(f323(f323(f237(f867(x76861,a855)),x76862),x76863))
% 179.72/179.58 [7687]P101(f323(f323(f237(f867(f861(x76871),a855)),f153(x76871,x76872)),f153(x76871,x76873)))+~P101(f323(f323(f237(f867(x76871,a855)),x76872),x76873))
% 179.72/179.58 [7714]E(f323(f323(f101(f867(x77141,a855)),f37(f867(x77141,a855),x77142)),x77143),f188(f867(x77141,a855)))+P101(f323(f323(f325(f867(x77141,a855)),f549(x77143,x77142,x77141)),x77142))
% 179.72/179.58 [7717]~P101(f323(f323(f325(f867(x77171,a855)),x77173),x77172))+P101(f323(f323(f237(f867(x77171,a855)),f38(f867(x77171,a855),x77172)),x77173))
% 179.72/179.58 [7719]E(f323(f323(f101(f867(x77191,a855)),x77192),x77193),f188(f867(x77191,a855)))+~P101(f323(f323(f237(f867(x77191,a855)),x77192),f323(f77(f867(x77191,a855)),x77193)))
% 179.72/179.58 [7765]E(f323(f323(f22(a860),f323(f323(f78(a860),f323(f159(a860),x77651)),x77652)),f323(f323(f158(a860),x77651),x77653)),f323(f159(a860),f323(f323(f152(a860,x77651),x77653),x77652)))+~P101(f323(f323(f238(a860),x77653),f323(f189(f861(a860)),x77651)))
% 179.72/179.58 [7817]P101(f323(f323(f237(a860),x78171),x78172))+~P101(f323(f323(f237(a860),f323(f323(f78(a860),x78173),x78171)),f323(f323(f78(a860),x78173),x78172)))
% 179.72/179.58 [7820]P101(f323(f323(f238(a860),x78201),x78202))+~P101(f323(f323(f238(a860),f323(f323(f78(a860),x78203),x78201)),f323(f323(f78(a860),x78203),x78202)))
% 179.72/179.58 [7821]P101(f323(f323(f238(a860),x78211),x78212))+~P101(f323(f323(f238(a860),f323(f323(f79(a860),x78213),x78211)),f323(f323(f79(a860),x78213),x78212)))
% 179.72/179.58 [7822]P101(f323(f323(f238(a860),x78221),x78222))+~P101(f323(f323(f238(a860),f323(f323(f79(a860),x78221),x78223)),f323(f323(f79(a860),x78222),x78223)))
% 179.72/179.58 [7851]P101(f323(f323(f238(a860),f2(a860)),x78511))+~P101(f323(f323(f238(a860),f323(f323(f79(a860),x78512),x78511)),f323(f323(f79(a860),x78513),x78511)))
% 179.72/179.58 [7852]P101(f323(f323(f238(a860),f2(a860)),x78521))+~P101(f323(f323(f238(a860),f323(f323(f79(a860),x78521),x78522)),f323(f323(f79(a860),x78521),x78523)))
% 179.72/179.58 [7928]E(f250(x79281,x79282,x79283),x79282)+~P101(f323(f323(f237(f867(x79281,a855)),x79283),f323(f323(f301(x79281),x79282),f188(f867(x79281,a855)))))
% 179.72/179.58 [7978]~P101(f323(f130(x79781),x79783))+E(f323(f129(x79781,f323(f323(f8(a855,a855,x79781),a318),f323(a320,x79782))),x79783),f164(x79781,x79782,x79783))
% 179.72/179.58 [8003]E(f323(f323(f131(x80031),f323(f189(f861(x80031)),f171(x80031,x80032,x80033))),x80033),f113(x80031))+P101(f323(f323(f325(x80031),f603(x80033,x80032,x80031)),f323(f166(x80031),x80033)))
% 179.72/179.58 [8007]E(f323(f323(f121(x80071),f323(f323(f169(x80071),x80072),x80073)),f323(f323(f144(x80071),f323(f323(f158(x80071),x80073),x80072)),f113(x80071))),f323(f323(f169(x80071),f323(a112,x80072)),x80073))+~P101(f323(f323(f238(a860),x80072),f323(f189(f861(x80071)),x80073)))
% 179.72/179.58 [8066]E(f323(f129(x80661,f323(f323(f8(a855,a855,x80661),a318),f323(a320,x80662))),x80663),x80663)+P101(f323(f323(f325(x80661),x80662),f323(f166(x80661),x80663)))
% 179.72/179.58 [8073]P101(f323(f323(f237(f867(f867(x80731,a855),a855)),f251(x80731,x80732)),f251(x80731,x80733)))+~P101(f323(f323(f237(f867(x80731,a855)),x80732),x80733))
% 179.72/179.58 [8116]~P101(f323(f130(x81161),x81163))+P101(f323(f130(x81161),f323(f323(f323(f183(f861(x81161),f861(x81161)),x81162),f161(x81161)),x81163)))
% 179.72/179.58 [8122]~P101(f323(f323(f238(a860),x81222),x81223))+P101(f323(f323(f238(a860),f323(f323(f79(a860),f323(a112,x81221)),x81222)),f323(f323(f79(a860),f323(a112,x81221)),x81223)))
% 179.72/179.58 [8143]P101(f323(f323(f237(f867(f867(x81431,a855),a855)),f323(f300(x81431),x81432)),f323(f300(x81431),x81433)))+~P101(f323(f323(f237(f867(x81431,a855)),x81432),x81433))
% 179.72/179.58 [8212]~E(f323(f302(x82121,x82122,x82123),f246(f867(x82121,a855))),f246(f867(x82122,a855)))+E(f323(f71(x82121,x82122,x82122,x82123),f91(x82121,x82122,f246(f867(x82121,a855)),x82123)),f32(x82122))
% 179.72/179.58 [8309]~P101(f323(f323(f237(f867(x83091,a855)),x83093),x83092))+P101(f323(f323(f237(f867(x83091,a855)),f323(f77(f867(x83091,a855)),x83092)),f323(f77(f867(x83091,a855)),x83093)))
% 179.72/179.58 [8342]E(f323(f302(a860,a860,f323(f323(f7(a860,a860,a860),f22(a860)),x83421)),f323(f293(a860,x83422),x83423)),f323(f293(a860,f323(f323(f22(a860),x83422),x83421)),f323(f323(f22(a860),x83423),x83421)))+~P101(f323(f323(f238(a860),x83421),x83423))
% 179.72/179.58 [8370]~P78(x83701)+E(f323(f323(f78(x83701),x83702),f323(f135(x83701,x83701,f78(x83701),f2(x83701)),x83703)),f323(f135(x83701,x83701,f78(x83701),x83702),x83703))
% 179.72/179.58 [8442]~P82(x84421)+P101(f323(f323(f237(x84421),f323(f73(x84421),f323(f323(f22(x84421),x84422),x84423))),f323(f323(f78(x84421),f323(f73(x84421),x84422)),f323(f73(x84421),x84423))))
% 179.72/179.58 [8443]~P82(x84431)+P101(f323(f323(f237(x84431),f323(f73(x84431),f323(f323(f78(x84431),x84432),x84433))),f323(f323(f78(x84431),f323(f73(x84431),x84432)),f323(f73(x84431),x84433))))
% 179.72/179.58 [8453]E(f323(f323(f78(a1),f323(f323(f79(a1),x84531),f42(a1,f323(f323(f36(a1),x84532),x84531),x84533))),f42(a1,x84532,x84531)),f42(a1,x84532,f323(f323(f79(a1),x84531),x84533)))+~P101(f323(f323(f238(a1),f2(a1)),x84533))
% 179.72/179.58 [8459]E(f323(f323(f121(x84591),f323(f323(f169(x84591),x84592),x84593)),f323(f323(f144(x84591),f323(f134(x84591),f323(f323(f131(x84591),x84592),x84593))),f113(x84591))),f323(f323(f169(x84591),f323(a112,x84592)),x84593))+~P101(f323(f323(f238(a860),x84592),f323(f189(f861(x84591)),x84593)))
% 179.72/179.58 [8479]E(f323(f269(x84791,f323(f323(f147(x84791,f866(a99,x84791)),f323(f258(a99,x84791),f76(a99))),x84792)),f323(a3,x84793)),f323(f323(f158(x84791),x84792),x84793))+~P101(f323(f323(f238(a860),x84793),f323(f189(f861(x84791)),x84792)))
% 179.72/179.58 [8547]P101(f323(f323(f325(f866(x85471,x85471)),x85472),f323(f323(f280(x85471,x85471,x85471),x85473),f299(x85471,x85473))))+~P101(f323(f323(f325(f866(x85471,x85471)),x85472),x85473))
% 179.72/179.58 [8558]E(f323(f302(x85581,x85582,x85583),f246(f867(x85581,a855))),f246(f867(x85582,a855)))+~E(f323(f71(x85581,x85582,x85582,x85583),f91(x85581,x85582,f246(f867(x85581,a855)),x85583)),f32(x85582))
% 179.72/179.58 [8568]P101(f323(f323(f237(a860),x85681),x85682))+~P101(f323(f323(f237(a860),f323(f323(f79(a860),f323(a112,x85683)),x85681)),f323(f323(f79(a860),f323(a112,x85683)),x85682)))
% 179.72/179.58 [8583]P101(f323(f323(f237(f867(x85831,a855)),x85832),x85833))+~P101(f323(f323(f237(f867(x85831,a855)),f323(f77(f867(x85831,a855)),x85833)),f323(f77(f867(x85831,a855)),x85832)))
% 179.72/179.58 [8606]P101(f323(f130(x86061),x86062))+~P101(f323(f130(x86061),f323(f323(f323(f183(f861(x86061),f861(x86061)),x86063),f161(x86061)),x86062)))
% 179.72/179.58 [8671]E(f323(f302(f866(x86711,x86712),x86712,f261(x86711,x86712)),f323(f166(f866(x86711,x86712)),x86713)),f178(x86711,x86712,f323(f179(x86711,x86712),x86713)))+~P101(f323(f130(x86711),f323(f323(f147(f866(x86711,x86712),x86711),f257(x86711,x86712)),x86713)))
% 179.72/179.58 [8680]E(f323(f277(x86801,x86801,f299(x86801,x86802)),x86803),x86803)+~P101(f323(f323(f237(f867(x86801,a855)),f323(f277(x86801,x86801,x86802),x86803)),x86803))
% 179.72/179.58 [8728]~P103(x87281)+P16(x87281,f323(f129(x87281,f323(f323(f7(x87281,x87281,a855),a320),f323(x87282,x87283))),x87283))
% 179.72/179.58 [8736]~P101(f323(f323(f237(a860),x87361),x87362))+P101(f323(f323(f237(a860),x87361),f323(f135(a860,a860,f78(a860),x87362),x87363)))
% 179.72/179.58 [8815]~P101(f323(f323(f325(f866(x88151,x88151)),x88152),f299(x88151,x88153)))+P101(f323(f323(f325(f866(x88151,x88151)),x88152),f323(f323(f183(f866(x88151,x88151),a855),f734(x88153,x88152,x88151)),x88153)))
% 179.72/179.58 [8903]~P78(x89031)+E(f323(f323(f78(x89031),x89032),f323(f135(x89031,x89031,f323(f7(x89031,x89031,x89031),f78(x89031)),f2(x89031)),f323(f162(x89031),x89033))),f323(f135(x89031,x89031,f78(x89031),x89032),x89033))
% 179.72/179.58 [9019]~P28(x90192,x90191,x90193,f246(f867(x90192,a855)),f246(f867(x90191,a855)))+E(f91(x90191,x90192,f246(f867(x90191,a855)),f91(x90192,x90191,f246(f867(x90192,a855)),x90193)),x90193)
% 179.72/179.58 [9173]P51(x91731,x91732,x91733)+P101(f323(f323(f325(f866(x91731,x91732)),f323(f323(f258(x91731,x91732),f724(x91733,x91732,x91731)),f701(x91733,x91732,x91731))),x91733))
% 179.72/179.58 [9174]P51(x91741,x91742,x91743)+P101(f323(f323(f325(f866(x91741,x91742)),f323(f323(f258(x91741,x91742),f724(x91743,x91742,x91741)),f700(x91743,x91742,x91741))),x91743))
% 179.72/179.58 [9239]~P101(f323(f323(f325(f866(x92391,x92391)),x92392),f323(f323(f280(x92391,x92391,x92391),x92393),f299(x92391,x92393))))+P101(f323(f323(f325(f866(x92391,x92391)),x92392),f323(f323(f183(f866(x92391,x92391),a855),f736(x92393,x92392,x92391)),x92393)))
% 179.72/179.58 [9240]~P101(f323(x92401,f323(f323(f158(x92402),x92403),f323(f189(f861(x92402)),f171(x92402,x92401,x92403)))))+~P101(f323(f323(f238(a860),f323(f189(f861(x92402)),f171(x92402,x92401,x92403))),f323(f189(f861(x92402)),x92403)))
% 179.72/179.58 [9328]~P101(f323(f323(f237(f867(x93281,a855)),x93282),x93283))+P101(f323(f323(f237(f867(x93281,a855)),f323(f323(f7(x93281,f867(x93281,a855),a855),f325(x93281)),x93282)),f323(f323(f7(x93281,f867(x93281,a855),a855),f325(x93281)),x93283)))
% 179.72/179.58 [9381]~P101(f323(f323(f325(f866(f867(x93811,a855),f867(x93811,a855))),f323(f323(f258(f867(x93811,a855),f867(x93811,a855)),x93812),x93813)),f298(x93811)))+P101(f323(f323(f238(f867(x93811,a855)),x93812),x93813))
% 179.72/179.58 [9404]P52(x94041,x94042,x94043)+~P101(f323(f323(f325(f866(x94041,x94041)),f323(f323(f258(x94041,x94041),f728(x94043,x94042,x94041)),f727(x94043,x94042,x94041))),x94043))
% 179.72/179.58 [9405]P52(x94051,x94052,x94053)+~P101(f323(f323(f325(f866(x94051,x94051)),f323(f323(f258(x94051,x94051),f727(x94053,x94052,x94051)),f728(x94053,x94052,x94051))),x94053))
% 179.72/179.58 [9444]~P101(f323(f323(f325(f866(f861(x94441),f861(x94441))),f323(f323(f258(f861(x94441),f861(x94441)),x94442),x94442)),f140(x94441,x94443)))+P101(f323(f323(f325(f866(x94441,x94441)),f323(f323(f258(x94441,x94441),f625(x94442,x94443,x94441)),f625(x94442,x94443,x94441))),x94443))
% 179.72/179.58 [9494]P101(f323(f323(f237(f867(x94941,a855)),x94942),x94943))+~P101(f323(f323(f237(f867(x94941,a855)),f323(f323(f7(x94941,f867(x94941,a855),a855),f325(x94941)),x94942)),f323(f323(f7(x94941,f867(x94941,a855),a855),f325(x94941)),x94943)))
% 179.72/179.58 [9577]E(f323(f323(f22(a860),f323(f323(f6(a860,a860),x95771),f323(f244(a860),x95772))),f323(f323(f6(a860,a860),x95773),f323(f244(a860),x95772))),f323(f323(f6(a860,a860),f323(f323(f18(a860,a860,a860),f323(f323(f8(a860,f867(a860,a860),a860),f22(a860)),x95771)),x95773)),f323(f244(a860),x95772)))+~P101(f323(f323(f237(a860),f323(x95773,f368(x95772,x95771,x95773))),f323(x95771,f368(x95772,x95771,x95773))))
% 179.72/179.58 [9881]E(f323(f243(f866(x98811,x98812)),f323(f262(x98811,x98812,a855),f323(f323(f7(x98811,f867(x98812,f864(x98812)),f867(x98812,a855)),f323(f323(f8(f867(f864(x98812),a855),f867(f867(x98812,f864(x98812)),f867(x98812,a855)),x98811),f8(f864(x98812),a855,x98812)),f323(f323(f8(f864(x98812),f867(f864(x98812),a855),x98811),a320),f323(f179(x98811,x98812),x98813)))),f230(x98812)))),f323(f166(f866(x98811,x98812)),x98813))+~P101(f323(f130(x98811),f323(f323(f147(f866(x98811,x98812),x98811),f257(x98811,x98812)),x98813)))
% 179.72/179.58 [5609]~P59(x56091)+E(f323(f323(f22(x56091),f323(f323(f78(x56091),x56092),x56093)),x56093),x56092)
% 179.72/179.58 [5610]~P59(x56101)+E(f323(f323(f78(x56101),f323(f323(f22(x56101),x56102),x56103)),x56103),x56102)
% 179.72/179.58 [5829]~P59(x58291)+E(f323(f323(f78(x58291),x58292),f323(f323(f78(x58291),f323(f77(x58291),x58292)),x58293)),x58293)
% 179.72/179.58 [5911]~P77(x59111)+E(f323(f323(f79(x59111),f323(f323(f248(x59111),x59112),x59113)),x59112),f323(f323(f248(x59111),x59112),f323(a112,x59113)))
% 179.72/179.58 [5912]~P112(x59121)+E(f323(f323(f79(x59121),f323(f323(f248(x59121),x59122),x59123)),x59122),f323(f323(f248(x59121),x59122),f323(a112,x59123)))
% 179.72/179.58 [6119]~P116(x61191)+E(f323(f73(x61191),f323(f323(f248(x61191),f323(f77(x61191),x61192)),x61193)),f323(f73(x61191),f323(f323(f248(x61191),x61192),x61193)))
% 179.72/179.58 [6170]~P77(x61701)+E(f323(f323(f79(x61701),f323(f323(f248(x61701),x61702),x61703)),x61702),f323(f323(f79(x61701),x61702),f323(f323(f248(x61701),x61702),x61703)))
% 179.72/179.58 [6225]E(f323(f323(f22(a99),f323(f323(f78(a99),x62251),x62252)),x62253),f273(x62251,x62252,x62253))+~P101(f323(f323(f238(a99),x62252),x62253))
% 179.72/179.58 [6246]~E(f323(f323(f131(x62461),x62463),x62462),f113(x62461))+P101(f323(f323(f237(a860),f323(f189(f861(x62461)),x62462)),x62463))
% 179.72/179.58 [6379]E(f323(f323(f79(a860),f323(f103(a860),x63791)),f323(f323(f79(a860),f323(f103(a860),x63792)),x63793)),f2(a860))+~P101(f323(f323(f238(a1),x63791),a81))
% 179.72/179.58 [6394]~P62(x63941)+E(f323(f323(f248(x63941),f323(f323(f281(x63941),f76(x63941)),x63942)),x63943),f323(f323(f281(x63941),f76(x63941)),f323(f323(f248(x63941),x63942),x63943)))
% 179.72/179.58 [6470]E(f323(f323(f22(a860),f323(f323(f78(a860),x64701),x64702)),x64703),f323(f323(f22(a860),x64701),f323(f323(f22(a860),x64703),x64702)))+~P101(f323(f323(f237(a860),x64702),x64703))
% 179.72/179.58 [6472]E(f323(f323(f22(a860),f323(f323(f78(a860),x64721),x64722)),x64723),f323(f323(f78(a860),x64721),f323(f323(f22(a860),x64722),x64723)))+~P101(f323(f323(f237(a860),x64723),x64722))
% 179.72/179.58 [6508]~P2(x65081)+P101(f323(f323(f237(x65081),f323(f323(f101(x65081),x65082),x65083)),x65083))
% 179.72/179.58 [6509]~P98(x65091)+P101(f323(f323(f237(x65091),f323(f323(f101(x65091),x65092),x65093)),x65093))
% 179.72/179.58 [6510]~P2(x65101)+P101(f323(f323(f237(x65101),f323(f323(f101(x65101),x65102),x65103)),x65102))
% 179.72/179.58 [6511]~P98(x65111)+P101(f323(f323(f237(x65111),f323(f323(f101(x65111),x65112),x65113)),x65112))
% 179.72/179.58 [6512]~P103(x65121)+P101(f323(f323(f237(x65121),f323(f323(f235(x65121),x65122),x65123)),x65123))
% 179.72/179.58 [6513]~P103(x65131)+P101(f323(f323(f237(x65131),f323(f323(f235(x65131),x65132),x65133)),x65132))
% 179.72/179.58 [6526]E(f323(f323(f36(a1),f323(f323(f36(a1),x65261),x65262)),x65263),f323(f323(f36(a1),x65261),f323(f323(f79(a1),x65262),x65263)))+~P101(f323(f323(f238(a1),f2(a1)),x65263))
% 179.72/179.58 [6577]~P112(x65771)+E(f323(f323(f78(x65771),f323(f323(f79(x65771),x65772),x65773)),x65773),f323(f323(f79(x65771),f323(f323(f78(x65771),x65772),f76(x65771))),x65773))
% 179.72/179.58 [6578]~P90(x65781)+E(f323(f323(f79(x65781),f323(f77(x65781),f323(f103(x65781),x65782))),x65783),f323(f323(f79(x65781),f323(f103(x65781),f323(f77(a1),x65782))),x65783))
% 179.72/179.58 [6650]~P78(x66501)+E(f323(f159(x66501),f323(f323(f147(x66502,x66501),f323(f16(x66501,x66502),f2(x66501))),x66503)),f2(x66501))
% 179.72/179.58 [6666]E(f323(f323(f78(a860),f323(f103(a860),x66661)),f323(f323(f78(a860),f323(f103(a860),x66662)),x66663)),f323(f323(f78(a860),f323(f103(a860),x66662)),x66663))+~P101(f323(a193,f323(f103(a1),x66661)))
% 179.72/179.58 [6680]~P6(x66801)+E(f37(x66801,f323(f323(f301(x66801),x66802),f323(f323(f301(x66801),x66803),f188(f867(x66801,a855))))),f323(f323(f110(x66801),x66802),x66803))
% 179.72/179.58 [6681]~P6(x66811)+E(f38(x66811,f323(f323(f301(x66811),x66812),f323(f323(f301(x66811),x66813),f188(f867(x66811,a855))))),f323(f323(f101(x66811),x66812),x66813))
% 179.72/179.58 [6703]E(f323(f323(f169(x67031),x67032),x67033),x67033)+~P101(f323(f323(f237(a860),f323(f189(f861(x67031)),x67033)),x67032))
% 179.72/179.58 [6716]E(f323(f323(f131(x67161),x67162),x67163),f113(x67161))+~P101(f323(f323(f237(a860),f323(f189(f861(x67161)),x67163)),x67162))
% 179.72/179.58 [6727]E(f323(f323(f78(a860),f323(f323(f22(a860),x67271),x67272)),x67273),f323(f323(f22(a860),f323(f323(f78(a860),x67271),x67273)),x67272))+~P101(f323(f323(f237(a860),x67272),x67271))
% 179.72/179.58 [6741]~P101(f323(f323(f238(a860),x67411),x67413))+P101(f323(f323(f238(a860),f323(f323(f22(a860),x67411),x67412)),x67413))
% 179.72/179.58 [6769]~P103(x67691)+E(f164(x67691,x67692,f323(f323(f141(x67691,x67691,f5(x67691)),x67692),x67693)),x67693)
% 179.72/179.58 [6857]E(f323(f323(f22(a860),f323(f323(f78(a860),x68571),x68572)),f323(a112,x68573)),f323(f323(f22(a860),x68571),f323(a112,f323(f323(f22(a860),x68573),x68572))))+~P101(f323(f323(f237(a860),x68572),x68573))
% 179.72/179.58 [6858]~P116(x68581)+P101(f323(f323(f237(x68581),f2(x68581)),f323(f323(f248(x68581),f323(f73(x68581),x68582)),x68583)))
% 179.72/179.58 [6903]P26(x69031,x69032,x69033)+~P101(f323(f323(f237(f867(f859(x69031),a855)),x69033),x69032))
% 179.72/179.58 [6946]~P101(f323(f59(x69461),x69462))+P101(f323(f59(x69461),f323(f323(f22(f867(x69461,a855)),x69462),x69463)))
% 179.72/179.58 [6947]~P101(f323(f59(x69471),x69473))+P101(f323(f59(x69471),f323(f323(f101(f867(x69471,a855)),x69472),x69473)))
% 179.72/179.58 [6948]~P101(f323(f59(x69481),x69482))+P101(f323(f59(x69481),f323(f323(f101(f867(x69481,a855)),x69482),x69483)))
% 179.72/179.58 [7087]~P38(x70871,x70873)+P38(x70871,f323(f323(f101(f867(f866(x70871,x70871),a855)),x70872),x70873))
% 179.72/179.58 [7088]~P38(x70881,x70882)+P38(x70881,f323(f323(f101(f867(f866(x70881,x70881),a855)),x70882),x70883))
% 179.72/179.58 [7203]~P2(x72031)+E(f11(x72031,f323(f166(x72031),f323(f323(f144(x72031),x72032),x72033))),f323(f135(x72031,x72031,f101(x72031),x72032),x72033))
% 179.72/179.58 [7204]~P2(x72041)+E(f10(x72041,f323(f166(x72041),f323(f323(f144(x72041),x72042),x72043))),f323(f135(x72041,x72041,f110(x72041),x72042),x72043))
% 179.72/179.58 [7205]~P103(x72051)+E(f14(x72051,f323(f166(x72051),f323(f323(f144(x72051),x72052),x72053))),f323(f135(x72051,x72051,f236(x72051),x72052),x72053))
% 179.72/179.58 [7206]~P103(x72061)+E(f15(x72061,f323(f166(x72061),f323(f323(f144(x72061),x72062),x72063))),f323(f135(x72061,x72061,f235(x72061),x72062),x72063))
% 179.72/179.58 [7266]~P101(f323(f59(x72661),x72662))+P101(f323(f323(f237(a860),f323(f35(x72661),x72662)),f323(f35(x72661),f323(f323(f301(x72661),x72663),x72662))))
% 179.72/179.58 [7274]E(f323(f323(f110(f867(a860,a855)),f323(f293(a860,x72741),x72742)),f323(f293(a860,x72742),f323(f323(f78(a860),x72742),x72743))),f323(f293(a860,x72741),f323(f323(f78(a860),x72742),x72743)))+~P101(f323(f323(f237(a860),x72741),x72742))
% 179.72/179.58 [7284]P101(f323(f323(f237(a860),x72841),x72842))+~P101(f323(f323(f237(a860),f323(f323(f78(a860),x72843),x72841)),x72842))
% 179.72/179.58 [7285]P101(f323(f323(f237(a860),x72851),x72852))+~P101(f323(f323(f237(a860),f323(f323(f78(a860),x72851),x72853)),x72852))
% 179.72/179.58 [7286]P101(f323(f323(f238(a860),x72861),x72862))+~P101(f323(f323(f238(a860),f323(f323(f78(a860),x72861),x72863)),x72862))
% 179.72/179.58 [7325]~P103(x73251)+E(f12(x73251,f235(x73251),f323(f166(x73251),f323(f323(f144(x73251),x73252),x73253))),f323(f135(x73251,x73251,f235(x73251),x73252),x73253))
% 179.72/179.58 [7326]~P103(x73261)+E(f13(x73261,f236(x73261),f323(f166(x73261),f323(f323(f144(x73261),x73262),x73263))),f323(f135(x73261,x73261,f236(x73261),x73262),x73263))
% 179.72/179.58 [7330]~E(x73302,f188(f867(f866(x73301,x73301),a855)))+P101(f323(f323(f237(f867(f866(x73301,x73301),a855)),x73302),x73303))
% 179.72/179.58 [7438]E(f323(f323(f110(f867(x74381,a855)),x74382),f323(f323(f22(f867(x74381,a855)),x74383),x74382)),x74383)+~P101(f323(f323(f237(f867(x74381,a855)),x74382),x74383))
% 179.72/179.58 [7439]~P101(f323(f323(f237(a860),x74391),f323(f323(f78(a860),x74393),x74392)))+P101(f323(f323(f237(a860),f323(f323(f22(a860),x74391),x74392)),x74393))
% 179.72/179.58 [7440]~P101(f323(f323(f238(a860),x74401),f323(f323(f22(a860),x74403),x74402)))+P101(f323(f323(f238(a860),f323(f323(f78(a860),x74401),x74402)),x74403))
% 179.72/179.58 [7496]E(x74961,f113(x74962))+E(f323(f134(x74962),f323(f323(f323(f183(f861(x74962),f861(x74962)),x74963),f161(x74962)),x74961)),f323(f323(f158(x74962),x74961),f42(a860,x74963,f323(f189(f861(x74962)),x74961))))
% 179.72/179.58 [7505]E(f323(f323(f301(x75051),x75052),f323(f323(f22(f867(x75051,a855)),x75053),f323(f323(f301(x75051),x75052),f188(f867(x75051,a855))))),x75053)+~P101(f323(f323(f325(x75051),x75052),x75053))
% 179.72/179.58 [7666]P101(f323(f323(f237(a860),x76661),f323(f323(f78(a860),x76662),x76663)))+~P101(f323(f323(f237(a860),f323(f323(f22(a860),x76661),x76663)),x76662))
% 179.72/179.58 [7667]P101(f323(f323(f238(a860),x76671),f323(f323(f22(a860),x76672),x76673)))+~P101(f323(f323(f238(a860),f323(f323(f78(a860),x76671),x76673)),x76672))
% 179.72/179.58 [7690]P101(f323(f59(x76901),x76902))+~P101(f323(f59(x76901),f323(f323(f110(f867(x76901,a855)),x76903),x76902)))
% 179.72/179.58 [7691]P101(f323(f59(x76911),x76912))+~P101(f323(f59(x76911),f323(f323(f110(f867(x76911,a855)),x76912),x76913)))
% 179.72/179.58 [7764]~P46(x77641,x77643)+P101(f323(f323(f325(f866(x77641,x77641)),f323(f323(f258(x77641,x77641),x77642),x77642)),x77643))
% 179.72/179.58 [7902]E(f323(f323(f158(a860),f132(a860,f323(f293(a860,x79021),x79022))),x79023),f323(f323(f78(a860),x79021),x79023))+~P101(f323(f323(f238(a860),f323(f323(f78(a860),x79021),x79023)),x79022))
% 179.72/179.58 [7967]E(f323(f323(f169(a860),x79671),f132(a860,f323(f293(a860,x79672),x79673))),f132(a860,f323(f293(a860,x79672),f323(f323(f78(a860),x79672),x79671))))+~P101(f323(f323(f237(a860),f323(f323(f78(a860),x79672),x79671)),x79673))
% 179.72/179.58 [8021]~P90(x80211)+E(f323(f323(f248(x80211),x80212),f323(f103(a860),f323(f323(f78(a1),x80213),x80213))),f323(f323(f84(x80211,x80211),f323(f323(f248(x80211),x80212),f323(f103(a860),x80213))),f323(f323(f18(x80211,x80211,x80211),f79(x80211)),f5(x80211))))
% 179.72/179.58 [8289]E(f323(f323(f121(x82891),f323(f323(f169(x82891),x82892),x82893)),f323(f323(f144(x82891),f323(f323(f158(x82891),x82893),x82892)),f323(f323(f131(x82891),f323(a112,x82892)),x82893))),x82893)+~P101(f323(f323(f238(a860),x82892),f323(f189(f861(x82891)),x82893)))
% 179.72/179.58 [8296]P101(f323(f323(f237(f867(x82961,a855)),f311(x82961,x82962)),f311(x82961,x82963)))+~P101(f323(f323(f237(f867(x82961,f867(x82961,a855))),x82963),x82962))
% 179.72/179.58 [8298]~P52(x82981,x82982,x82983)+P52(x82981,x82982,f323(f323(f22(f867(f866(x82981,x82981),a855)),x82983),f299(x82981,f188(f867(f866(x82981,x82981),a855)))))
% 179.72/179.58 [8317]P101(f323(f323(f237(f867(x83171,a855)),f312(x83171,x83172)),f312(x83171,x83173)))+~P101(f323(f323(f237(f867(f866(x83171,x83171),a855)),x83173),x83172))
% 179.72/179.58 [8323]~P101(f323(f323(f238(f867(x83231,a855)),x83233),x83232))+P101(f323(f323(f325(x83231),f661(x83232,x83233,x83231)),f323(f323(f22(f867(x83231,a855)),x83232),x83233)))
% 179.72/179.58 [8325]~P121(x83251)+P101(f323(f323(f237(x83251),f2(x83251)),f323(f323(f78(x83251),f323(f323(f79(x83251),x83252),x83252)),f323(f323(f79(x83251),x83253),x83253))))
% 179.72/179.58 [8358]P101(f323(f323(f237(f867(x83581,a855)),f323(f276(x83581),x83582)),f323(f276(x83581),x83583)))+~P101(f323(f323(f237(f867(f866(x83581,x83581),a855)),x83582),x83583))
% 179.72/179.58 [8388]~P42(x83881,x83882)+~P101(f323(f323(f325(f866(x83881,x83881)),f323(f323(f258(x83881,x83881),x83883),x83883)),x83882))
% 179.72/179.58 [8390]~P38(x83901,x83902)+~P101(f323(f323(f325(f866(x83901,x83901)),f323(f323(f258(x83901,x83901),x83903),x83903)),x83902))
% 179.72/179.58 [8444]P101(f323(f323(f237(f867(x84441,a855)),f37(f867(x84441,a855),x84442)),f37(f867(x84441,a855),x84443)))+~P101(f323(f323(f237(f867(f867(x84441,a855),a855)),x84442),x84443))
% 179.72/179.58 [8445]P101(f323(f323(f237(f867(x84451,a855)),f38(f867(x84451,a855),x84452)),f38(f867(x84451,a855),x84453)))+~P101(f323(f323(f237(f867(f867(x84451,a855),a855)),x84453),x84452))
% 179.72/179.58 [8498]~P9(x84981,x84983,x84982)+P101(f323(f323(f237(f867(f866(x84981,x84981),a855)),x84982),f323(f323(f260(x84981,x84981),x84983),f323(f16(f867(x84981,a855),x84981),x84983))))
% 179.72/179.58 [8499]~P40(x84991,x84993,x84992)+P101(f323(f323(f237(f867(f866(x84991,x84991),a855)),x84992),f323(f323(f260(x84991,x84991),x84993),f323(f16(f867(x84991,a855),x84991),x84993))))
% 179.72/179.58 [8548]~P82(x85481)+P101(f323(f323(f237(x85481),f323(f323(f22(x85481),f323(f73(x85481),x85482)),f323(f73(x85481),x85483))),f323(f73(x85481),f323(f323(f22(x85481),x85483),x85482))))
% 179.72/179.58 [8549]~P82(x85491)+P101(f323(f323(f237(x85491),f323(f323(f22(x85491),f323(f73(x85491),x85492)),f323(f73(x85491),x85493))),f323(f73(x85491),f323(f323(f22(x85491),x85492),x85493))))
% 179.72/179.58 [8581]P101(f323(f323(f237(f867(f866(x85811,x85811),a855)),f299(x85811,x85812)),f299(x85811,x85813)))+~P101(f323(f323(f237(f867(f866(x85811,x85811),a855)),x85812),x85813))
% 179.72/179.58 [8693]~P27(x86932,x86931,x86933,f246(f867(x86932,a855)))+E(f323(f71(x86931,x86932,x86932,f91(x86932,x86931,f246(f867(x86932,a855)),x86933)),x86933),f32(x86932))
% 179.72/179.58 [8754]P52(x87541,x87542,x87543)+~P52(x87541,x87542,f323(f323(f22(f867(f866(x87541,x87541),a855)),x87543),f299(x87541,f188(f867(f866(x87541,x87541),a855)))))
% 179.72/179.58 [8774]P101(f323(f323(f237(f867(f866(f861(x87741),f861(x87741)),a855)),f151(x87741,x87742)),f151(x87741,x87743)))+~P101(f323(f323(f237(f867(f866(x87741,x87741),a855)),x87742),x87743))
% 179.72/179.58 [8775]P101(f323(f323(f237(f867(f866(f861(x87751),f861(x87751)),a855)),f150(x87751,x87752)),f150(x87751,x87753)))+~P101(f323(f323(f237(f867(f866(x87751,x87751),a855)),x87752),x87753))
% 179.72/179.58 [8794]~P40(x87941,x87943,x87942)+P101(f323(f323(f237(f867(f866(x87941,x87941),a855)),x87942),f323(f323(f280(x87941,x87941,x87941),f323(f278(x87941,x87941),x87942)),x87942)))
% 179.72/179.58 [8843]~P101(f323(f130(x88431),x88432))+E(f323(f129(x88431,f323(f323(f7(x88431,f867(x88431,a855),a855),f325(x88431)),f323(f166(x88431),f170(x88431,x88432,x88433)))),x88432),f170(x88431,x88432,x88433))
% 179.72/179.58 [8901]E(x89011,x89012)+~P101(f323(f323(f325(f866(x89013,x89013)),f323(f323(f258(x89013,x89013),x89011),x89012)),f299(x89013,f188(f867(f866(x89013,x89013),a855)))))
% 179.72/179.58 [8981]P101(f323(f323(f325(x89811),x89812),f312(x89811,x89813)))+P101(f323(f323(f325(f866(x89811,x89811)),f323(f323(f258(x89811,x89811),f650(x89813,x89812,x89811)),x89812)),x89813))
% 179.72/179.58 [8982]P101(f323(f323(f325(x89821),x89822),f312(x89821,x89823)))+P101(f323(f323(f325(f866(x89821,x89821)),f323(f323(f258(x89821,x89821),f704(x89823,x89822,x89821)),x89822)),x89823))
% 179.72/179.58 [8983]P101(f323(f323(f325(x89831),x89832),f312(x89831,x89833)))+P101(f323(f323(f325(f866(x89831,x89831)),f323(f323(f258(x89831,x89831),f713(x89833,x89832,x89831)),x89832)),x89833))
% 179.72/179.58 [9020]P27(x90201,x90202,x90203,f246(f867(x90201,a855)))+~E(f323(f71(x90202,x90201,x90201,f91(x90201,x90202,f246(f867(x90201,a855)),x90203)),x90203),f32(x90201))
% 179.72/179.58 [9074]~P101(f323(f323(f325(f861(x90741)),x90743),f154(x90741,x90742)))+P101(f323(f153(x90741,f323(f323(f7(x90741,f867(x90741,a855),a855),f325(x90741)),x90742)),x90743))
% 179.72/179.58 [9095]P101(f323(x90953,x90952))+E(f323(f243(x90951),f323(f323(f18(x90951,a855,a855),f323(f323(f8(a855,f867(a855,a855),x90951),a321),f323(a320,x90952))),x90953)),f188(f867(x90951,a855)))
% 179.72/179.58 [9113]~P82(x91131)+P101(f323(f323(f237(x91131),f323(f73(x91131),f323(f323(f22(x91131),f323(f73(x91131),x91132)),f323(f73(x91131),x91133)))),f323(f73(x91131),f323(f323(f22(x91131),x91132),x91133))))
% 179.72/179.58 [9127]~P101(f323(x91273,x91272))+E(f323(f243(x91271),f323(f323(f18(x91271,a855,a855),f323(f323(f8(a855,f867(a855,a855),x91271),a321),f323(a320,x91272))),x91273)),f323(f323(f301(x91271),x91272),f188(f867(x91271,a855))))
% 179.72/179.58 [9135]~P101(f323(f323(f325(f867(x91351,a855)),x91353),f323(f300(x91351),x91352)))+P101(f323(f251(x91351,f323(f323(f7(x91351,f867(x91351,a855),a855),f325(x91351)),x91352)),x91353))
% 179.72/179.58 [9172]P38(x91721,x91722)+P101(f323(f323(f325(f866(x91721,x91721)),f323(f323(f258(x91721,x91721),f323(f663(x91722,x91721),f323(a112,x91723))),f323(f663(x91722,x91721),x91723))),x91722))
% 179.72/179.58 [9307]P101(f323(f323(f325(f861(x93071)),x93072),f154(x93071,x93073)))+~P101(f323(f153(x93071,f323(f323(f7(x93071,f867(x93071,a855),a855),f325(x93071)),x93073)),x93072))
% 179.72/179.58 [9320]P101(f323(f323(f325(f867(x93201,a855)),x93202),f323(f300(x93201),x93203)))+~P101(f323(f251(x93201,f323(f323(f7(x93201,f867(x93201,a855),a855),f325(x93201)),x93203)),x93202))
% 179.72/179.58 [9376]P101(f323(f323(f325(x93761),f323(f269(x93761,x93762),x93763)),f323(f166(x93761),f323(f323(f147(f866(a99,x93761),x93761),f261(a99,x93761)),x93762))))+~P101(f323(f323(f238(a99),x93763),f323(f159(a99),f323(f323(f147(f866(a99,x93761),a99),f257(a99,x93761)),x93762))))
% 179.72/179.58 [9424]P101(f323(f323(f237(f867(f866(f861(x94241),f861(x94241)),a855)),f151(x94241,x94242)),f323(f323(f260(f861(x94241),f861(x94241)),f154(x94241,x94243)),f323(f16(f867(f861(x94241),a855),f861(x94241)),f154(x94241,x94243)))))+~P101(f323(f323(f237(f867(f866(x94241,x94241),a855)),x94242),f323(f323(f260(x94241,x94241),x94243),f323(f16(f867(x94241,a855),x94241),x94243))))
% 179.72/179.58 [9447]P101(f323(f323(f325(x94471),f323(f257(x94471,f866(a99,a99)),f323(f267(x94471,x94472),x94473))),f323(f166(x94471),f323(f323(f147(f866(a99,x94471),x94471),f261(a99,x94471)),x94472))))+~P101(f323(f323(f238(a99),f2(a99)),f323(f159(a99),f323(f323(f147(f866(a99,x94471),a99),f257(a99,x94471)),x94472))))
% 179.72/179.58 [9463]~P101(f323(f323(f237(f867(f866(x94631,x94631),a855)),x94632),f323(f323(f260(x94631,x94631),x94633),f323(f16(f867(x94631,a855),x94631),x94633))))+P101(f323(f323(f237(f867(f866(x94631,x94631),a855)),f323(f323(f280(x94631,x94631,x94631),x94632),f299(x94631,x94632))),f323(f323(f260(x94631,x94631),x94633),f323(f16(f867(x94631,a855),x94631),x94633))))
% 179.72/179.58 [9769]~P38(x97691,x97692)+~P101(f323(f323(f325(f866(x97691,x97691)),f323(f323(f258(x97691,x97691),f323(x97693,f323(a112,f666(x97692,x97691,x97693)))),f323(x97693,f666(x97692,x97691,x97693)))),x97692))
% 179.72/179.58 [9770]~P38(x97701,x97702)+~P101(f323(f323(f325(f866(x97701,x97701)),f323(f323(f258(x97701,x97701),f323(x97703,f323(a112,f720(x97703,x97702,x97701)))),f323(x97703,f720(x97703,x97702,x97701)))),x97702))
% 179.72/179.58 [10020]P101(f323(f323(f237(f867(f866(f867(x100201,a855),f867(x100201,a855)),a855)),f323(f323(f280(f867(x100201,a855),f867(x100201,a855),f867(x100201,a855)),f316(x100201,x100202)),f323(f323(f110(f867(f866(f867(x100201,a855),f867(x100201,a855)),a855)),f316(x100201,x100203)),f323(f323(f301(f866(f867(x100201,a855),f867(x100201,a855))),f323(f323(f258(f867(x100201,a855),f867(x100201,a855)),f188(f867(x100201,a855))),f188(f867(x100201,a855)))),f188(f867(f866(f867(x100201,a855),f867(x100201,a855)),a855)))))),f316(x100201,x100202)))+~P101(f323(f323(f237(f867(f866(x100201,x100201),a855)),f323(f323(f280(x100201,x100201,x100201),x100202),x100203)),x100202))
% 179.72/179.58 [10021]P101(f323(f323(f237(f867(f866(f867(x100211,a855),f867(x100211,a855)),a855)),f323(f323(f280(f867(x100211,a855),f867(x100211,a855),f867(x100211,a855)),f314(x100211,x100212)),f323(f323(f110(f867(f866(f867(x100211,a855),f867(x100211,a855)),a855)),f314(x100211,x100213)),f323(f323(f301(f866(f867(x100211,a855),f867(x100211,a855))),f323(f323(f258(f867(x100211,a855),f867(x100211,a855)),f188(f867(x100211,a855))),f188(f867(x100211,a855)))),f188(f867(f866(f867(x100211,a855),f867(x100211,a855)),a855)))))),f314(x100211,x100212)))+~P101(f323(f323(f237(f867(f866(x100211,x100211),a855)),f323(f323(f280(x100211,x100211,x100211),x100212),x100213)),x100212))
% 179.72/179.58 [7202]~P101(f323(f323(f237(a860),x72022),x72021))+E(f323(f323(f22(a860),f323(a112,f323(f323(f22(a860),x72021),x72022))),x72023),f323(f323(f22(a860),f323(a112,x72021)),f323(f323(f78(a860),x72022),x72023)))
% 179.72/179.58 [7241]~P57(x72411)+E(f323(f323(f78(x72411),f42(x72411,x72412,x72413)),f323(f323(f79(x72411),f323(f323(f36(x72411),x72412),x72413)),x72413)),x72412)
% 179.72/179.58 [7444]E(f323(f323(f79(a860),f323(f103(a860),x74441)),f323(f323(f79(a860),f323(f103(a860),x74442)),x74443)),f323(f323(f79(a860),f323(f103(a860),f323(f323(f79(a1),x74441),x74442))),x74443))+P101(f323(f323(f238(a1),x74441),a81))
% 179.72/179.58 [7911]~P101(f323(f323(f237(a860),x79113),x79112))+P101(f323(f323(f237(a860),x79111),f323(f323(f22(a860),f323(f323(f78(a860),x79112),x79111)),x79113)))
% 179.72/179.58 [8106]~P101(f323(f323(f237(a860),x81061),x81062))+E(f323(f323(f121(a860),f132(a860,f323(f293(a860,x81061),x81062))),f132(a860,f323(f293(a860,x81062),f323(f323(f78(a860),x81062),x81063)))),f132(a860,f323(f293(a860,x81061),f323(f323(f78(a860),x81062),x81063))))
% 179.72/179.58 [8367]~P101(f323(f59(x83671),x83672))+E(f323(a112,f323(f35(x83671),f323(f323(f22(f867(x83671,a855)),x83672),f323(f323(f301(x83671),x83673),f188(f867(x83671,a855)))))),f323(f35(x83671),f323(f323(f301(x83671),x83673),x83672)))
% 179.72/179.58 [8407]~P101(f323(f59(x84071),x84072))+E(f323(f323(f78(a860),f76(a860)),f323(f35(x84071),f323(f323(f22(f867(x84071,a855)),x84072),f323(f323(f301(x84071),x84073),f188(f867(x84071,a855)))))),f323(f35(x84071),f323(f323(f301(x84071),x84073),x84072)))
% 179.72/179.58 [8590]E(f323(f323(f22(a860),f323(f35(x85901),x85902)),f323(f35(x85901),f323(f323(f101(f867(x85901,a855)),x85902),x85903))),f323(f35(x85901),f323(f323(f22(f867(x85901,a855)),x85902),x85903)))+~P101(f323(f59(x85901),f323(f323(f101(f867(x85901,a855)),x85902),x85903)))
% 179.72/179.58 [8838]~P7(f323(x88382,f427(x88382,x88383,x88381)))+E(f323(f100(a1),f323(f323(f6(x88381,a860),f323(f323(f8(a1,a860,x88381),a104),x88382)),x88383)),f323(f323(f6(x88381,a1),x88382),x88383))
% 179.72/179.58 [8839]~P7(f323(x88392,f472(x88392,x88393,x88391)))+E(f323(f100(a1),f323(f323(f9(x88391,a860),f323(f323(f8(a1,a860,x88391),a104),x88392)),x88393)),f323(f323(f9(x88391,a1),x88392),x88393))
% 179.72/179.58 [8886]~P101(f323(f59(x88861),x88863))+P101(f323(f323(f237(a860),f323(f323(f22(a860),f323(f35(x88861),x88862)),f323(f35(x88861),x88863))),f323(f35(x88861),f323(f323(f22(f867(x88861,a855)),x88862),x88863))))
% 179.72/179.58 [8909]P101(f323(f323(f325(x89091),f427(x89092,x89093,x89091)),x89093))+E(f323(f100(a1),f323(f323(f6(x89091,a860),f323(f323(f8(a1,a860,x89091),a104),x89092)),x89093)),f323(f323(f6(x89091,a1),x89092),x89093))
% 179.72/179.58 [8910]P101(f323(f323(f325(x89101),f472(x89102,x89103,x89101)),x89103))+E(f323(f100(a1),f323(f323(f9(x89101,a860),f323(f323(f8(a1,a860,x89101),a104),x89102)),x89103)),f323(f323(f9(x89101,a1),x89102),x89103))
% 179.72/179.58 [8973]E(f83(x89731,f323(f323(f7(x89731,f867(x89731,a855),a855),f325(x89731)),f323(f323(f22(f867(x89731,a855)),x89732),f323(f323(f301(x89731),x89733),f188(f867(x89731,a855)))))),f250(x89731,x89733,x89732))+P101(f323(f323(f237(f867(x89731,a855)),x89732),f323(f323(f301(x89731),x89733),f188(f867(x89731,a855)))))
% 179.72/179.58 [9321]E(f323(f323(f147(f861(x93211),x93211),f323(f323(f7(f861(x93211),a860,x93211),f158(x93211)),x93212)),f323(f129(f861(x93211),f323(f323(f8(a860,a855,f861(x93211)),f323(f238(a860),x93212)),f189(f861(x93211)))),x93213)),f323(f323(f158(f861(x93211)),f173(x93211,x93213)),x93212))+~P101(f323(f323(f238(a860),x93212),f323(f189(f861(f861(x93211))),f173(x93211,x93213))))
% 179.72/179.58 [9394]E(f323(f129(x93941,x93942),x93943),f171(x93941,x93942,x93943))+P101(f323(f323(f325(x93941),f612(x93943,x93942,x93941)),f323(f166(x93941),f323(f323(f131(x93941),f323(f189(f861(x93941)),f171(x93941,x93942,x93943))),x93943))))
% 179.72/179.58 [9535]E(f323(f323(f131(x95351),f323(f189(f861(x95351)),f171(x95351,x95352,x95353))),x95353),f113(x95351))+~P101(f323(x95352,f323(f134(x95351),f323(f323(f131(x95351),f323(f189(f861(x95351)),f171(x95351,x95352,x95353))),x95353))))
% 179.72/179.58 [9629]~P101(f323(f323(f325(f866(x96291,x96291)),x96292),f299(x96291,x96293)))+P101(f323(f323(f325(f866(x96291,x96291)),x96292),f323(f323(f39(a860,f867(f866(x96291,x96291),a855)),f246(f867(a860,a855))),f323(f323(f7(a860,f867(f866(x96291,x96291),a855),f867(f866(x96291,x96291),a855)),f183(f866(x96291,x96291),a855)),x96293))))
% 179.72/179.58 [9687]~P101(f323(f323(f237(f867(x96871,a855)),f323(f323(f39(a860,f867(x96871,a855)),f323(f293(a860,f2(a860)),f457(x96873,x96872,x96871))),x96872)),x96873))+P101(f323(f323(f237(f867(x96871,a855)),f323(f323(f39(a860,f867(x96871,a855)),f246(f867(a860,a855))),x96872)),x96873))
% 179.72/179.58 [9745]~P101(f323(f323(f238(a1),f2(a1)),x97453))+P101(f323(f323(f238(a1),x97451),f323(f323(f78(a1),x97452),f323(f323(f79(a1),f323(f323(f78(a1),f323(f73(a1),f323(f323(f22(a1),x97452),x97451))),f76(a1))),x97453))))
% 179.72/179.58 [9756]~P38(x97561,f323(f323(f110(f867(f866(x97561,x97561),a855)),x97562),x97563))+P38(x97561,f323(f323(f110(f867(f866(x97561,x97561),a855)),f323(f323(f110(f867(f866(x97561,x97561),a855)),f323(f323(f280(x97561,x97561,x97561),x97562),x97562)),f323(f323(f280(x97561,x97561,x97561),x97563),x97562))),x97563))
% 179.72/179.58 [9837]P38(x98371,f323(f323(f110(f867(f866(x98371,x98371),a855)),x98372),x98373))+~P38(x98371,f323(f323(f110(f867(f866(x98371,x98371),a855)),f323(f323(f110(f867(f866(x98371,x98371),a855)),f323(f323(f280(x98371,x98371,x98371),x98372),x98372)),f323(f323(f280(x98371,x98371,x98371),x98373),x98372))),x98373))
% 179.72/179.58 [9397]~P134(x93971)+E(f323(f102(x93971),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x93972),x93973)),f188(f867(f866(a860,a860),a855)))))),f323(f323(f22(x93971),f323(f100(x93971),x93972)),f323(f100(x93971),x93973)))
% 179.72/179.58 [9481]P101(f323(x94813,x94812))+E(f323(f243(x94811),f323(f323(f18(x94811,a855,a855),f323(f323(f8(a855,f867(a855,a855),x94811),a321),f323(f323(f7(x94811,x94811,a855),a320),x94812))),x94813)),f188(f867(x94811,a855)))
% 179.72/179.58 [9483]~P101(f323(x94833,x94832))+E(f323(f243(x94831),f323(f323(f18(x94831,a855,a855),f323(f323(f8(a855,f867(a855,a855),x94831),a321),f323(f323(f7(x94831,x94831,a855),a320),x94832))),x94833)),f323(f323(f301(x94831),x94832),f188(f867(x94831,a855))))
% 179.72/179.58 [9723]E(x97231,x97232)+P101(f323(f323(f247(x97233,x97233,f323(f323(f8(f867(x97233,a855),f867(x97233,a855),x97233),f323(f8(a855,a855,x97233),a318)),a320)),x97231),x97232))
% 179.72/179.58 [9815]~E(x98151,x98152)+~P101(f323(f323(f247(x98153,x98153,f323(f323(f8(f867(x98153,a855),f867(x98153,a855),x98153),f323(f8(a855,a855,x98153),a318)),a320)),x98151),x98152))
% 179.72/179.58 [9829]~P101(f323(f59(x98291),x98293))+E(f323(f323(f62(x98291,f867(x98291,a855),f323(f323(f8(f867(x98291,a855),f867(f867(x98291,a855),f867(x98291,a855)),x98291),f323(f7(f867(x98291,a855),f867(x98291,a855),f867(x98291,a855)),f22(f867(x98291,a855)))),f323(f323(f7(x98291,f867(x98291,a855),f867(x98291,a855)),f301(x98291)),f188(f867(x98291,a855))))),x98292),x98293),f323(f323(f22(f867(x98291,a855)),x98292),x98293))
% 179.72/179.58 [9861]~P101(f323(f323(f238(a1),f2(a1)),x98613))+P101(f323(f323(f238(a1),f323(f323(f22(a1),x98611),f323(f323(f79(a1),f323(f323(f78(a1),f323(f73(a1),f323(f323(f22(a1),x98611),x98612))),f76(a1))),x98613))),x98612))
% 179.72/179.58 [10083]~P101(f323(f323(f325(x100831),x100833),f312(x100831,x100832)))+P101(f323(f311(x100831,f323(f323(f7(x100831,f867(f866(x100831,x100831),a855),f867(x100831,a855)),f323(f323(f8(f867(x100831,f867(f867(f866(x100831,x100831),a855),a855)),f867(f867(f866(x100831,x100831),a855),f867(x100831,a855)),x100831),f7(x100831,f867(f866(x100831,x100831),a855),a855)),f323(f323(f8(f867(x100831,f866(x100831,x100831)),f867(x100831,f867(f867(f866(x100831,x100831),a855),a855)),x100831),f323(f8(f866(x100831,x100831),f867(f867(f866(x100831,x100831),a855),a855),x100831),f325(f866(x100831,x100831)))),f258(x100831,x100831)))),x100832)),x100833))
% 179.72/179.58 [10096]P101(f323(f323(f325(x100961),x100962),f312(x100961,x100963)))+~P101(f323(f311(x100961,f323(f323(f7(x100961,f867(f866(x100961,x100961),a855),f867(x100961,a855)),f323(f323(f8(f867(x100961,f867(f867(f866(x100961,x100961),a855),a855)),f867(f867(f866(x100961,x100961),a855),f867(x100961,a855)),x100961),f7(x100961,f867(f866(x100961,x100961),a855),a855)),f323(f323(f8(f867(x100961,f866(x100961,x100961)),f867(x100961,f867(f867(f866(x100961,x100961),a855),a855)),x100961),f323(f8(f866(x100961,x100961),f867(f867(f866(x100961,x100961),a855),a855),x100961),f325(f866(x100961,x100961)))),f258(x100961,x100961)))),x100963)),x100962))
% 179.72/179.58 [9685]~P101(f323(f59(x96851),f323(f243(x96851),x96853)))+P101(f323(f59(x96851),f323(f243(x96851),f323(f323(f18(x96851,a855,a855),f323(f323(f8(a855,f867(a855,a855),x96851),a321),x96852)),x96853))))
% 179.72/179.58 [9686]~P101(f323(f59(x96861),f323(f243(x96861),x96862)))+P101(f323(f59(x96861),f323(f243(x96861),f323(f323(f18(x96861,a855,a855),f323(f323(f8(a855,f867(a855,a855),x96861),a321),x96862)),x96863))))
% 179.72/179.58 [9790]P101(f323(f59(x97901),f323(f243(x97901),x97902)))+~P101(f323(f59(x97901),f323(f243(x97901),f323(f323(f18(x97901,a855,a855),f323(f323(f8(a855,f867(a855,a855),x97901),a322),x97903)),x97902))))
% 179.72/179.58 [9791]P101(f323(f59(x97911),f323(f243(x97911),x97912)))+~P101(f323(f59(x97911),f323(f243(x97911),f323(f323(f18(x97911,a855,a855),f323(f323(f8(a855,f867(a855,a855),x97911),a322),x97912)),x97913))))
% 179.72/179.58 [10068]~P101(f323(f59(x100681),x100682))+P101(f323(f59(f861(x100681)),f323(f243(f861(x100681)),f323(f323(f18(f861(x100681),a855,a855),f323(f323(f8(a855,f867(a855,a855),f861(x100681)),a321),f323(f323(f7(f861(x100681),f867(x100681,a855),a855),f323(f323(f8(f867(x100681,a855),f867(f867(x100681,a855),a855),f861(x100681)),f237(f867(x100681,a855))),f166(x100681))),x100682))),f323(f323(f7(f861(x100681),a860,a855),f323(f323(f8(a860,f867(a860,a855),f861(x100681)),a320),f189(f861(x100681)))),x100683)))))
% 179.72/179.58 [10069]~P101(f323(f59(x100691),x100692))+P101(f323(f59(f861(x100691)),f323(f243(f861(x100691)),f323(f323(f18(f861(x100691),a855,a855),f323(f323(f8(a855,f867(a855,a855),f861(x100691)),a321),f323(f323(f7(f861(x100691),f867(x100691,a855),a855),f323(f323(f8(f867(x100691,a855),f867(f867(x100691,a855),a855),f861(x100691)),f237(f867(x100691,a855))),f166(x100691))),x100692))),f323(f323(f7(f861(x100691),a860,a855),f323(f323(f8(a860,f867(a860,a855),f861(x100691)),f237(a860)),f189(f861(x100691)))),x100693)))))
% 179.72/179.58 [9804]~P112(x98041)+E(f323(f323(f248(x98041),x98042),f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98043)),f323(f323(f79(x98041),f323(f323(f248(x98041),x98042),x98043)),f323(f323(f248(x98041),x98042),x98043)))
% 179.72/179.58 [9842]~P77(x98421)+E(f323(f323(f248(x98421),f323(f323(f248(x98421),x98422),x98423)),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(f323(f248(x98421),x98422),f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98423)))
% 179.72/179.58 [9888]~P134(x98881)+E(f323(f323(f248(x98881),f323(f77(x98881),x98882)),f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98883)),f323(f323(f248(x98881),x98882),f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98883)))
% 179.72/179.58 [10027]~P116(x100271)+P101(f323(f323(f237(x100271),f2(x100271)),f323(f323(f78(x100271),f323(f323(f248(x100271),x100272),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x100271),x100273),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))))
% 179.72/179.58 [9898]~P112(x98981)+E(f323(f323(f248(x98981),x98982),f323(a112,f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98983))),f323(f323(f79(x98981),x98982),f323(f323(f79(x98981),f323(f323(f248(x98981),x98982),x98983)),f323(f323(f248(x98981),x98982),x98983))))
% 179.72/179.58 [9947]~P77(x99471)+E(f323(f323(f79(x99471),x99472),f323(f323(f248(x99471),f323(f323(f248(x99471),x99472),x99473)),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x99471),x99472),f323(a112,f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x99473))))
% 179.72/179.58 [9985]~P116(x99851)+P101(f323(f323(f237(x99851),f2(x99851)),f323(f323(f248(x99851),x99852),f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x99853))))
% 179.72/179.58 [10049]~P90(x100491)+E(f323(f323(f22(x100491),f323(f323(f78(x100491),f323(f323(f248(x100491),x100492),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x100491),x100493),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))),f323(f323(f79(x100491),f323(f323(f79(x100491),f323(f103(x100491),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x100492)),x100493)),f323(f323(f248(x100491),f323(f323(f22(x100491),x100492),x100493)),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.58 [10050]~P90(x100501)+E(f323(f323(f78(x100501),f323(f323(f78(x100501),f323(f323(f248(x100501),x100502),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x100501),x100503),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))),f323(f323(f79(x100501),f323(f323(f79(x100501),f323(f103(x100501),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x100502)),x100503)),f323(f323(f248(x100501),f323(f323(f78(x100501),x100502),x100503)),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.58 [4666]E(x46661,x46662)+~E(f30(x46663,x46661),f30(x46664,x46662))
% 179.72/179.58 [4667]E(x46671,x46672)+~E(f30(x46671,x46673),f30(x46672,x46674))
% 179.72/179.58 [4668]E(x46681,x46682)+~E(f29(x46683,x46681),f29(x46684,x46682))
% 179.72/179.58 [4669]E(x46691,x46692)+~E(f29(x46691,x46693),f29(x46692,x46694))
% 179.72/179.58 [4670]E(x46701,x46702)+~E(f25(x46703,x46701),f25(x46704,x46702))
% 179.72/179.58 [4671]E(x46711,x46712)+~E(f25(x46711,x46713),f25(x46712,x46714))
% 179.72/179.58 [7708]P27(x77081,x77082,x77083,x77084)+~E(f498(x77084,x77083,x77082,x77081),f504(x77084,x77083,x77082,x77081))
% 179.72/179.58 [8001]P35(x80011,x80012,x80013,x80014,f113(x80012))+~E(x80014,f113(x80011))
% 179.72/179.58 [8002]P35(x80021,x80022,x80023,f113(x80021),x80024)+~E(x80024,f113(x80022))
% 179.72/179.58 [8211]~P27(x82111,f864(x82112),x82114,f177(x82111,x82112,x82114))+P27(x82111,f864(x82112),f180(x82111,x82112,x82113,x82114),f177(x82111,x82112,x82114))
% 179.72/179.58 [8421]~P27(x84211,f864(x84212),f180(x84211,x84212,x84214,x84213),f177(x84211,x84212,x84213))+P27(x84211,f864(x84212),x84213,f177(x84211,x84212,x84213))
% 179.72/179.58 [8538]~P35(x85382,x85383,x85384,x85381,f113(x85383))+E(x85381,f113(x85382))
% 179.72/179.58 [8539]~P35(x85393,x85392,x85394,f113(x85393),x85391)+E(x85391,f113(x85392))
% 179.72/179.58 [5042]~P19(x50423,x50421,x50424)+E(f323(f323(x50421,x50422),x50422),x50422)
% 179.72/179.58 [5286]P101(f323(x52862,x52864))+E(f323(f129(x52861,x52862),f163(x52861,x52863,x52864)),f113(x52861))
% 179.72/179.58 [5322]~E(x53224,f188(f867(x53221,a855)))+E(f323(f302(x53221,x53222,x53223),x53224),f188(f867(x53222,a855)))
% 179.72/179.58 [5561]~P101(f323(x55612,x55614))+E(f323(f129(x55611,x55612),f163(x55611,x55613,x55614)),f163(x55611,x55613,x55614))
% 179.72/179.58 [5590]~E(f323(f302(x55902,x55903,x55904),x55901),f188(f867(x55903,a855)))+E(x55901,f188(f867(x55902,a855)))
% 179.72/179.58 [5872]~P103(x58722)+E(f323(f323(f141(x58721,x58722,x58723),x58724),f113(x58721)),f323(f323(f144(x58721),x58724),f113(x58721)))
% 179.72/179.58 [5907]E(f323(x59071,x59072),f200(x59073))+P101(f323(f323(f325(x59074),x59072),f177(x59074,x59073,x59071)))
% 179.72/179.58 [6219]~E(x62191,f188(f867(x62192,a855)))+~P101(f323(f60(x62192,x62193,x62191),x62194))
% 179.72/179.58 [6240]~P55(x62401,x62403,x62404,x62402)+P101(f323(f59(x62401),x62402))
% 179.72/179.58 [6241]~P55(x62411,x62413,x62412,x62414)+P101(f323(f59(x62411),x62412))
% 179.72/179.58 [6247]~P55(x62472,x62473,x62474,x62471)+~E(x62471,f188(f867(x62472,a855)))
% 179.72/179.58 [6278]~P105(x62781)+E(f323(f323(f101(f867(x62781,a855)),f323(f293(x62781,x62782),x62783)),f294(x62781,x62783,x62784)),f188(f867(x62781,a855)))
% 179.72/179.58 [6305]~P101(f323(f323(x63053,x63054),x63052))+P101(f323(f323(f325(x63051),x63052),f284(x63051,x63053,x63054)))
% 179.72/179.58 [6306]~P101(f323(f323(x63063,x63064),x63062))+P101(f323(f323(f325(x63061),x63062),f285(x63061,x63063,x63064)))
% 179.72/179.58 [6307]~P101(f323(f323(x63073,x63072),x63074))+P101(f323(f323(f325(x63071),x63072),f289(x63071,x63073,x63074)))
% 179.72/179.58 [6308]~P101(f323(f323(x63083,x63082),x63084))+P101(f323(f323(f325(x63081),x63082),f286(x63081,x63083,x63084)))
% 179.72/179.58 [6370]~P50(x63704,x63701,x63702,x63703)+P101(f323(f323(x63701,x63702),x63703))
% 179.72/179.58 [6445]~P105(x64451)+E(f323(f323(f101(f867(x64451,a855)),f294(x64451,x64452,x64453)),f297(x64451,x64453,x64454)),f188(f867(x64451,a855)))
% 179.72/179.58 [6446]~P105(x64461)+E(f323(f323(f101(f867(x64461,a855)),f294(x64461,x64462,x64463)),f296(x64461,x64463,x64464)),f188(f867(x64461,a855)))
% 179.72/179.58 [6447]~P105(x64471)+E(f323(f323(f101(f867(x64471,a855)),f297(x64471,x64472,x64473)),f294(x64471,x64473,x64474)),f188(f867(x64471,a855)))
% 179.72/179.58 [6448]~P105(x64481)+E(f323(f323(f101(f867(x64481,a855)),f296(x64481,x64482,x64483)),f297(x64481,x64483,x64484)),f188(f867(x64481,a855)))
% 179.72/179.58 [6449]~P105(x64491)+E(f323(f323(f101(f867(x64491,a855)),f296(x64491,x64492,x64493)),f296(x64491,x64493,x64494)),f188(f867(x64491,a855)))
% 179.72/179.58 [6486]P101(f323(f323(x64861,x64862),f673(x64862,x64861)))+~P101(f323(f252(x64863,x64864,x64861),x64862))
% 179.72/179.58 [6490]~P50(x64901,x64902,x64903,x64904)+~P101(f323(f323(x64902,x64904),x64903))
% 179.72/179.58 [6535]~E(f323(x65351,x65352),f200(x65353))+~P101(f323(f323(f325(x65354),x65352),f177(x65354,x65353,x65351)))
% 179.72/179.58 [6564]~P103(x65642)+E(f323(f166(x65641),f143(x65641,x65642,x65643,x65644)),f323(f166(x65641),x65644))
% 179.72/179.58 [6615]~P140(x66151)+E(f190(x66151,x66152,f323(a112,x66153),x66154),f190(x66151,x66152,x66153,f323(x66152,x66154)))
% 179.72/179.58 [6675]~P101(f323(f323(f325(x66754),x66753),f284(x66754,x66751,x66752)))+P101(f323(f323(x66751,x66752),x66753))
% 179.72/179.58 [6676]~P101(f323(f323(f325(x66764),x66763),f285(x66764,x66761,x66762)))+P101(f323(f323(x66761,x66762),x66763))
% 179.72/179.58 [6677]~P101(f323(f323(f325(x66774),x66772),f289(x66774,x66771,x66773)))+P101(f323(f323(x66771,x66772),x66773))
% 179.72/179.58 [6678]~P101(f323(f323(f325(x66784),x66782),f286(x66784,x66781,x66783)))+P101(f323(f323(x66781,x66782),x66783))
% 179.72/179.58 [6754]E(f323(f35(f865(x67541,x67542)),f310(x67541,x67542,x67543,x67544)),f2(a860))+P101(f323(f59(x67542),x67544))
% 179.72/179.58 [6755]E(f323(f35(f865(x67551,x67552)),f310(x67551,x67552,x67553,x67554)),f2(a860))+P101(f323(f59(x67551),x67553))
% 179.72/179.58 [6955]~P17(x69554,x69551,x69552)+E(f323(f71(x69551,x69551,x69551,f323(x69552,x69553)),f323(x69552,x69553)),f323(x69552,x69553))
% 179.72/179.58 [7830]~E(x78302,x78303)+P101(f323(f323(f325(f866(x78301,x78301)),f323(f323(f258(x78301,x78301),x78302),x78303)),f299(x78301,x78304)))
% 179.72/179.58 [7859]~P27(x78591,x78592,x78593,f246(f867(x78591,a855)))+E(f323(f75(x78591,x78592,f246(f867(x78591,a855)),x78593),f323(x78593,x78594)),x78594)
% 179.72/179.58 [7860]~P27(x78601,x78602,x78603,f246(f867(x78601,a855)))+E(f323(f91(x78601,x78602,f246(f867(x78601,a855)),x78603),f323(x78603,x78604)),x78604)
% 179.72/179.58 [7950]~P101(f323(f323(f325(f861(x79501)),f323(f323(f144(x79501),x79504),x79502)),f154(x79501,x79503)))+P101(f323(f323(f325(f861(x79501)),x79502),f154(x79501,x79503)))
% 179.72/179.58 [7951]~P101(f323(f323(f325(f861(x79511)),f323(f323(f121(x79511),x79514),x79512)),f154(x79511,x79513)))+P101(f323(f323(f325(f861(x79511)),x79512),f154(x79511,x79513)))
% 179.72/179.58 [7952]~P101(f323(f323(f325(f861(x79521)),f323(f323(f121(x79521),x79522),x79524)),f154(x79521,x79523)))+P101(f323(f323(f325(f861(x79521)),x79522),f154(x79521,x79523)))
% 179.72/179.58 [7963]~P103(x79631)+P16(x79631,f323(f323(f147(x79632,x79631),x79633),f143(x79632,x79631,x79633,x79634)))
% 179.72/179.58 [8060]P27(x80604,x80603,x80601,x80602)+E(f323(x80601,f498(x80602,x80601,x80603,x80604)),f323(x80601,f504(x80602,x80601,x80603,x80604)))
% 179.72/179.58 [8072]E(f180(x80721,x80722,x80723,x80724),f180(x80721,x80722,x80724,x80723))+~E(f323(f323(f101(f867(x80721,a855)),f177(x80721,x80722,x80723)),f177(x80721,x80722,x80724)),f188(f867(x80721,a855)))
% 179.72/179.58 [8174]~P27(x81742,x81741,x81744,x81743)+P27(x81741,x81742,f75(x81742,x81741,x81743,x81744),f323(f302(x81742,x81741,x81744),x81743))
% 179.72/179.58 [8315]P38(f866(x83152,x83154),f275(x83152,x83154,x83151,x83153))+P101(f323(x83151,f660(x83152,x83153,x83154,x83151)))
% 179.72/179.58 [8428]E(x84281,x84282)+~P101(f323(f323(f325(f866(x84283,x84283)),f323(f323(f258(x84283,x84283),x84281),x84282)),f255(x84283,x84284)))
% 179.72/179.58 [8490]~P101(f323(f59(f865(x84903,x84901)),f310(x84903,x84901,x84904,x84902)))+P101(f323(f59(x84901),x84902))
% 179.72/179.58 [8491]~P101(f323(f59(f865(x84911,x84913)),f310(x84911,x84913,x84912,x84914)))+P101(f323(f59(x84911),x84912))
% 179.72/179.58 [8500]~P27(x85001,x85002,x85003,x85004)+P28(x85001,x85002,x85003,x85004,f323(f302(x85001,x85002,x85003),x85004))
% 179.72/179.58 [8591]~P28(x85912,x85913,x85914,x85911,f188(f867(x85913,a855)))+E(x85911,f188(f867(x85912,a855)))
% 179.72/179.58 [8592]~P28(x85923,x85922,x85924,f188(f867(x85923,a855)),x85921)+E(x85921,f188(f867(x85922,a855)))
% 179.72/179.58 [8685]P38(f866(x86851,x86852),f275(x86851,x86852,x86853,x86854))+~P38(x86852,f323(x86854,f660(x86851,x86854,x86852,x86853)))
% 179.72/179.58 [9244]E(f323(f323(f152(x92441,x92442),f584(x92443,x92444,x92442,x92441)),f585(x92443,x92444,x92442,x92441)),x92444)+~P101(f323(f323(f325(f866(f861(x92441),f861(x92441))),f323(f323(f258(f861(x92441),f861(x92441)),x92442),x92444)),f150(x92441,x92443)))
% 179.72/179.58 [9249]~P101(f323(f323(f325(f866(f861(x92491),f861(x92491))),f323(f323(f258(f861(x92491),f861(x92491)),x92492),x92493)),f138(x92491,x92494)))+P101(f323(f323(f325(f866(f861(x92491),f861(x92491))),f323(f323(f258(f861(x92491),f861(x92491)),x92492),x92493)),f140(x92491,x92494)))
% 179.72/179.58 [9355]P101(f323(f59(x93551),x93552))+~P101(f323(f323(f325(f866(f867(x93551,a855),f867(x93551,a855))),f323(f323(f258(f867(x93551,a855),f867(x93551,a855)),x93553),x93552)),f314(x93551,x93554)))
% 179.72/179.58 [9356]P101(f323(f59(x93561),x93562))+~P101(f323(f323(f325(f866(f867(x93561,a855),f867(x93561,a855))),f323(f323(f258(f867(x93561,a855),f867(x93561,a855)),x93562),x93563)),f314(x93561,x93564)))
% 179.72/179.58 [9359]~E(x93591,f188(f867(x93592,a855)))+~P101(f323(f323(f325(f866(f867(x93592,a855),f867(x93592,a855))),f323(f323(f258(f867(x93592,a855),f867(x93592,a855)),x93593),x93591)),f314(x93592,x93594)))
% 179.72/179.58 [9996]P14(x99961,x99962,x99963,x99964)+~P101(f323(f323(f262(x99961,x99961,a855),f323(f323(f7(x99961,f867(x99961,x99962),f867(x99961,a855)),f323(f323(f8(f867(x99962,a855),f867(f867(x99961,x99962),f867(x99961,a855)),x99961),f8(x99962,a855,x99961)),f323(f323(f8(x99962,f867(x99962,a855),x99961),a320),x99964))),x99964)),f583(x99964,x99963,x99962,x99961)))
% 179.72/179.58 [4944]~E(x49444,f200(x49441))+E(f323(f323(f201(x49441,x49442),x49443),x49444),f200(x49442))
% 179.72/179.58 [4945]~E(x49454,f113(x49451))+E(f323(f323(f147(x49451,x49452),x49453),x49454),f113(x49452))
% 179.72/179.58 [4946]~E(x49462,f113(x49461))+E(f323(f323(f152(x49461,x49462),x49463),x49464),f113(x49461))
% 179.72/179.58 [5173]E(x51731,f200(x51732))+~E(f323(f323(f201(x51732,x51733),x51734),x51731),f200(x51733))
% 179.72/179.58 [5174]E(x51741,f113(x51742))+~E(f323(f323(f147(x51742,x51743),x51744),x51741),f113(x51743))
% 179.72/179.58 [5175]E(x51751,f113(x51752))+~E(f323(f323(f152(x51752,x51751),x51753),x51754),f113(x51752))
% 179.72/179.58 [5205]E(x52051,x52052)+~E(f323(f323(f121(x52053),x52054),x52051),f323(f323(f121(x52053),x52054),x52052))
% 179.72/179.58 [5206]E(x52061,x52062)+~E(f323(f323(f121(x52063),x52061),x52064),f323(f323(f121(x52063),x52062),x52064))
% 179.72/179.58 [5359]P101(f323(x53593,x53592))+E(f164(x53591,x53592,f323(f129(x53591,x53593),x53594)),f323(f129(x53591,x53593),x53594))
% 179.72/179.58 [5362]~P101(f323(x53622,x53623))+P34(x53621,x53622,f323(f323(f144(x53621),x53623),x53624))
% 179.72/179.58 [5371]E(x53711,x53712)+~E(f132(a860,f323(f293(a860,x53711),x53713)),f323(f323(f144(a860),x53712),x53714))
% 179.72/179.58 [5419]~P29(x54192,x54193)+P29(x54191,f323(f323(f72(x54192,x54191),x54193),x54194))
% 179.72/179.58 [5420]~P38(x54202,x54203)+P38(x54201,f323(f323(f279(x54202,x54201),x54203),x54204))
% 179.72/179.58 [5545]~P34(x55451,x55452,x55454)+P34(x55451,x55452,f323(f323(f144(x55451),x55453),x55454))
% 179.72/179.58 [5546]~P34(x55461,x55462,x55464)+P34(x55461,x55462,f323(f323(f121(x55461),x55463),x55464))
% 179.72/179.58 [5547]~P34(x55471,x55472,x55473)+P34(x55471,x55472,f323(f323(f121(x55471),x55473),x55474))
% 179.72/179.58 [5633]~E(x56331,f113(x56332))+~E(f323(f323(f121(x56332),x56333),f323(f323(f144(x56332),x56334),f113(x56332))),x56331)
% 179.72/179.58 [5658]~P32(x56583,x56581,f323(f323(f144(x56583),x56582),x56584))+P101(f323(x56581,x56582))
% 179.72/179.58 [5668]E(f137(x56681,x56682),x56683)+~E(f323(f323(f121(x56681),x56684),f323(f323(f144(x56681),x56683),f113(x56681))),x56682)
% 179.72/179.58 [5669]E(f114(x56691,x56692),x56693)+~E(f323(f323(f121(x56691),x56693),f323(f323(f144(x56691),x56694),f113(x56691))),x56692)
% 179.72/179.58 [5777]~E(f132(a860,f323(f293(a860,x57771),x57772)),f323(f323(f144(a860),x57773),x57774))+P101(f323(f323(f238(a860),x57771),x57772))
% 179.72/179.58 [5785]P32(x57851,x57852,x57853)+~P32(x57851,x57852,f323(f323(f144(x57851),x57854),x57853))
% 179.72/179.58 [5786]P32(x57861,x57862,x57863)+~P32(x57861,x57862,f323(f323(f121(x57861),x57864),x57863))
% 179.72/179.58 [5787]P32(x57871,x57872,x57873)+~P32(x57871,x57872,f323(f323(f121(x57871),x57873),x57874))
% 179.72/179.58 [5969]E(x59691,f323(f323(f121(x59692),f323(f162(x59692),x59693)),f323(f323(f144(x59692),x59694),f113(x59692))))+~E(f323(f162(x59692),x59691),f323(f323(f144(x59692),x59694),x59693))
% 179.72/179.58 [6140]~P105(x61401)+E(f323(f323(f101(f867(x61401,a855)),f323(f293(x61401,x61402),x61403)),f323(f293(x61401,x61403),x61404)),f188(f867(x61401,a855)))
% 179.72/179.58 [6150]E(f323(f323(f158(x61501),f163(x61501,x61502,x61503)),x61504),x61503)+~P101(f323(f323(f238(a860),x61504),x61502))
% 179.72/179.58 [6177]~P72(x61771)+E(f323(f159(x61771),f323(f323(f147(a1,x61771),x61772),f172(x61773,x61774))),f323(f323(f6(a1,x61771),x61772),f323(f166(a1),f172(x61773,x61774))))
% 179.72/179.58 [6178]~P72(x61781)+E(f323(f323(f6(a1,x61781),x61782),f323(f166(a1),f172(x61783,x61784))),f323(f159(x61781),f323(f323(f147(a1,x61781),x61782),f172(x61783,x61784))))
% 179.72/179.58 [6318]~E(x63182,f323(f323(f121(x63181),f323(f162(x63181),x63184)),f323(f323(f144(x63181),x63183),f113(x63181))))+E(f323(f162(x63181),x63182),f323(f323(f144(x63181),x63183),x63184))
% 179.72/179.58 [6333]~P21(x63332,x63333,x63334,x63331)+E(f323(x63331,f188(f867(x63332,a855))),f32(x63333))
% 179.72/179.58 [6359]~P105(x63591)+E(f323(f323(f101(f867(x63591,a855)),f297(x63591,x63592,x63593)),f323(f293(x63591,x63593),x63594)),f188(f867(x63591,a855)))
% 179.72/179.58 [6565]E(x65651,f188(f867(x65652,a855)))+~E(f310(x65653,x65652,x65654,x65651),f188(f867(f865(x65653,x65652),a855)))
% 179.72/179.58 [6566]E(x65661,f188(f867(x65662,a855)))+~E(f310(x65662,x65663,x65661,x65664),f188(f867(f865(x65662,x65663),a855)))
% 179.72/179.58 [6634]~P103(x66342)+E(f323(f189(f861(x66341)),f143(x66341,x66342,x66343,x66344)),f323(f189(f861(x66341)),x66344))
% 179.72/179.58 [6646]~P101(f323(f253(x66463,x66464,x66461),x66462))+P101(f323(f323(x66461,f674(x66462,x66461)),x66462))
% 179.72/179.58 [6686]~P101(f323(f59(x66862),x66864))+P101(f323(f59(x66861),f323(f302(x66862,x66861,x66863),x66864)))
% 179.72/179.58 [6915]~P27(x69152,x69151,x69153,x69154)+E(f323(f35(x69151),f323(f302(x69152,x69151,x69153),x69154)),f323(f35(x69152),x69154))
% 179.72/179.58 [6934]E(f323(f302(x69341,x69342,x69343),f323(f303(x69341,x69342,x69343),x69344)),x69344)+~E(f323(f302(x69341,x69342,x69343),f246(f867(x69341,a855))),f246(f867(x69342,a855)))
% 179.72/179.58 [7339]~P27(x73391,x73392,x73393,f246(f867(x73391,a855)))+E(f323(f303(x73391,x73392,x73393),f323(f302(x73391,x73392,x73393),x73394)),x73394)
% 179.72/179.58 [7624]E(x76241,x76242)+~P101(f323(f323(f325(x76243),x76241),f323(f166(x76243),f163(x76243,x76244,x76242))))
% 179.72/179.58 [7633]~E(x76331,f2(a860))+~P101(f323(f323(f325(x76332),x76333),f323(f166(x76332),f163(x76332,x76331,x76334))))
% 179.72/179.58 [7669]P101(f323(x76691,x76692))+~P101(f323(f323(f325(x76693),x76692),f323(f166(x76693),f171(x76693,x76691,x76694))))
% 179.72/179.58 [7775]~P101(f323(f323(f325(f861(x77751)),f323(f323(f144(x77751),x77752),x77754)),f154(x77751,x77753)))+P101(f323(f323(f325(x77751),x77752),x77753))
% 179.72/179.58 [7907]~P101(f323(f323(f325(x79071),x79072),f323(f166(x79071),f164(x79071,x79074,x79073))))+P101(f323(f323(f325(x79071),x79072),f323(f166(x79071),x79073)))
% 179.72/179.58 [7909]~P101(f323(f323(f325(x79091),x79092),f323(f166(x79091),f170(x79091,x79093,x79094))))+P101(f323(f323(f325(x79091),x79092),f323(f166(x79091),x79093)))
% 179.72/179.58 [7910]~P101(f323(f323(f325(x79101),x79102),f323(f166(x79101),f171(x79101,x79104,x79103))))+P101(f323(f323(f325(x79101),x79102),f323(f166(x79101),x79103)))
% 179.72/179.58 [7920]E(f323(f189(f861(x79201)),x79202),x79203)+~P101(f323(f323(f325(f861(x79201)),x79202),f323(f166(f861(x79201)),f52(x79201,x79203,x79204))))
% 179.72/179.58 [8012]P101(f323(x80123,x80122))+E(f323(f129(x80121,f323(f323(f8(a855,a855,x80121),a318),f323(a320,x80122))),f323(f129(x80121,x80123),x80124)),f323(f129(x80121,x80123),x80124))
% 179.72/179.58 [8123]E(f323(f323(f158(x81231),f171(x81231,x81232,x81233)),x81234),f323(f323(f158(x81231),x81233),x81234))+~P101(f323(f323(f238(a860),x81234),f323(f189(f861(x81231)),f171(x81231,x81232,x81233))))
% 179.72/179.58 [8209]~P72(x82091)+E(f323(f323(f6(a860,x82091),f323(f323(f8(a860,x82091,a860),x82092),a112)),f323(f293(a860,x82093),x82094)),f323(f323(f6(a860,x82091),x82092),f323(f293(a860,f323(a112,x82093)),f323(a112,x82094))))
% 179.72/179.58 [8220]~P72(x82201)+E(f323(f323(f6(a860,x82201),f323(f323(f8(a860,x82201,a860),x82202),a112)),f294(a860,x82203,x82204)),f323(f323(f6(a860,x82201),x82202),f294(a860,f323(a112,x82203),f323(a112,x82204))))
% 179.72/179.58 [8351]~P27(x83511,x83513,x83514,f246(f867(x83511,a855)))+P27(x83511,f867(x83512,x83513),f323(f323(f8(x83513,f867(x83512,x83513),x83511),f16(x83513,x83512)),x83514),f246(f867(x83511,a855)))
% 179.72/179.58 [8433]~P27(x84332,x84331,x84334,x84333)+E(f323(f302(x84331,x84332,f75(x84332,x84331,x84333,x84334)),f323(f302(x84332,x84331,x84334),x84333)),x84333)
% 179.72/179.58 [8492]~P101(f323(f323(f325(f866(x84921,x84921)),f323(f323(f258(x84921,x84921),x84922),x84924)),f255(x84921,x84923)))+P101(f323(f323(f325(x84921),x84922),x84923))
% 179.72/179.58 [8586]E(f323(f323(f323(f70(x85861,f864(x85862)),f323(f16(f864(x85862),x85861),f200(x85862))),x85863),f323(f230(x85862),f759(x85863,x85864,x85862,x85861))),x85864)+~E(f177(x85861,x85862,x85864),f323(f323(f301(x85861),x85863),f188(f867(x85861,a855))))
% 179.72/179.58 [8616]~P27(x86162,x86161,x86163,f246(f867(x86162,a855)))+E(f323(f302(x86161,x86162,f91(x86162,x86161,f246(f867(x86162,a855)),x86163)),f323(f302(x86162,x86161,x86163),x86164)),x86164)
% 179.72/179.58 [8691]~P28(x86911,x86912,x86913,x86914,f246(f867(x86912,a855)))+E(f323(f302(x86911,x86912,x86913),f246(f867(x86911,a855))),f246(f867(x86912,a855)))
% 179.72/179.58 [8724]~E(f323(f323(f6(x87241,a860),x87244),x87243),f323(a112,x87242))+P101(f323(f323(f325(x87241),f464(x87242,x87243,x87244,x87241)),x87243))
% 179.72/179.58 [8746]~E(f323(f323(f6(x87464,a860),x87461),x87463),f323(a112,x87462))+P101(f323(f323(f238(a860),f2(a860)),f323(x87461,f464(x87462,x87463,x87461,x87464))))
% 179.72/179.58 [8757]~P101(f323(f59(x87572),x87574))+P101(f323(f323(f237(a860),f323(f35(x87571),f323(f302(x87572,x87571,x87573),x87574))),f323(f35(x87572),x87574)))
% 179.72/179.58 [8758]E(f323(f323(f258(x87581,x87582),f772(x87583,x87584,x87582,x87581)),f773(x87583,x87584,x87582,x87581)),x87584)+~P101(f323(f323(f325(f866(x87581,x87582)),x87584),f323(f278(x87582,x87581),x87583)))
% 179.72/179.58 [8766]P27(x87661,x87662,x87663,x87664)+P101(f323(f323(f325(x87661),f498(x87664,x87663,x87662,x87661)),x87664))
% 179.72/179.58 [8767]P27(x87671,x87672,x87673,x87674)+P101(f323(f323(f325(x87671),f504(x87674,x87673,x87672,x87671)),x87674))
% 179.72/179.58 [8829]P14(x88291,x88292,x88293,x88294)+P101(f323(f323(f325(f866(x88291,x88291)),f583(x88294,x88293,x88292,x88291)),x88293))
% 179.72/179.58 [8890]P101(f323(x88901,x88902))+~P101(f323(x88901,f323(f323(f258(x88903,x88904),f506(x88904,x88903,x88901)),f507(x88904,x88903,x88901))))
% 179.72/179.58 [8906]E(f323(f189(f861(x89061)),x89062),f323(f189(f861(x89061)),x89063))+~P101(f323(f323(f325(f866(f861(x89061),f861(x89061))),f323(f323(f258(f861(x89061),f861(x89061)),x89062),x89063)),f151(x89061,x89064)))
% 179.72/179.58 [8907]E(f323(f189(f861(x89071)),x89072),f323(f189(f861(x89071)),x89073))+~P101(f323(f323(f325(f866(f861(x89071),f861(x89071))),f323(f323(f258(f861(x89071),f861(x89071)),x89072),x89073)),f138(x89071,x89074)))
% 179.72/179.58 [8908]E(f323(f189(f861(x89081)),x89082),f323(f189(f861(x89081)),x89083))+~P101(f323(f323(f325(f866(f861(x89081),f861(x89081))),f323(f323(f258(f861(x89081),f861(x89081)),x89082),x89083)),f150(x89081,x89084)))
% 179.72/179.58 [8977]P101(f323(f323(f237(a860),f148(x89771,x89772,x89773)),f148(x89771,x89774,x89773)))+P101(f323(f323(f325(x89771),f631(x89774,x89772,x89773,x89771)),f323(f166(x89771),x89773)))
% 179.72/179.58 [8980]E(f323(f189(f861(x89801)),x89802),f323(f189(f861(x89801)),x89803))+~P101(f323(f323(f325(f866(f861(x89801),f861(x89801))),f323(f323(f258(f861(x89801),f861(x89801)),x89802),x89803)),f299(f861(x89801),f150(x89801,x89804))))
% 179.72/179.58 [9216]~P27(x92161,x92162,x92163,x92164)+~P101(f323(f323(f238(a860),f323(f35(x92162),f323(f302(x92161,x92162,x92163),x92164))),f323(f35(x92161),x92164)))
% 179.72/179.58 [9260]~P101(f323(f323(f325(f866(f861(x92601),f861(x92601))),f323(f323(f258(f861(x92601),f861(x92601)),x92602),x92603)),f150(x92601,x92604)))+P101(f323(f323(f325(f866(f861(x92601),f861(x92601))),f323(f323(f258(f861(x92601),f861(x92601)),x92602),x92603)),f151(x92601,f299(x92601,x92604))))
% 179.72/179.58 [9264]~P101(f323(f323(f325(f866(f861(x92641),f861(x92641))),f323(f323(f258(f861(x92641),f861(x92641)),x92642),x92643)),f151(x92641,x92644)))+P101(f323(f323(f325(f866(f861(x92641),f861(x92641))),f323(f323(f258(f861(x92641),f861(x92641)),x92642),x92643)),f299(f861(x92641),f150(x92641,x92644))))
% 179.72/179.58 [9281]P101(f323(f323(f325(f866(x92811,x92811)),f323(f323(f258(x92811,x92811),x92812),x92813)),f299(x92811,x92814)))+~P101(f323(f323(f325(f866(x92811,x92811)),f323(f323(f258(x92811,x92811),x92812),x92813)),f323(f323(f280(x92811,x92811,x92811),x92814),f299(x92811,x92814))))
% 179.72/179.58 [9464]E(f323(f323(f121(x94641),f589(x94642,x94643,x94644,x94641)),f323(f323(f144(x94641),f590(x94642,x94643,x94644,x94641)),f592(x94642,x94643,x94644,x94641))),x94644)+~P101(f323(f323(f325(f866(f861(x94641),f861(x94641))),f323(f323(f258(f861(x94641),f861(x94641)),x94644),x94643)),f150(x94641,x94642)))
% 179.72/179.58 [9465]E(f323(f323(f121(x94651),f589(x94652,x94653,x94654,x94651)),f323(f323(f144(x94651),f591(x94652,x94653,x94654,x94651)),f592(x94652,x94653,x94654,x94651))),x94653)+~P101(f323(f323(f325(f866(f861(x94651),f861(x94651))),f323(f323(f258(f861(x94651),f861(x94651)),x94654),x94653)),f150(x94651,x94652)))
% 179.72/179.58 [9542]P101(f323(f323(f325(f866(x95421,x95421)),f323(f323(f258(x95421,x95421),x95422),f743(x95423,x95424,x95422,x95421))),f299(x95421,x95423)))+~P101(f323(f323(f325(f866(x95421,x95421)),f323(f323(f258(x95421,x95421),x95422),x95424)),f323(f323(f280(x95421,x95421,x95421),x95423),f299(x95421,x95423))))
% 179.72/179.58 [9612]P101(f323(f323(f237(a860),f148(x96121,x96122,x96123)),f148(x96121,x96124,x96123)))+~P101(f323(f323(f238(a860),f323(x96122,f631(x96124,x96122,x96123,x96121))),f323(x96124,f631(x96124,x96122,x96123,x96121))))
% 179.72/179.58 [9681]P101(f323(f323(f325(f866(x96811,x96811)),f323(f323(f258(x96811,x96811),f742(x96812,x96813,x96814,x96811)),x96813)),f299(x96811,x96812)))+~P101(f323(f323(f325(f866(x96811,x96811)),f323(f323(f258(x96811,x96811),x96814),x96813)),f323(f323(f280(x96811,x96811,x96811),x96812),f299(x96811,x96812))))
% 179.72/179.58 [5189]~E(x51892,x51893)+E(f164(x51891,x51892,f323(f323(f144(x51891),x51893),x51894)),x51894)
% 179.72/179.58 [5314]P101(f323(x53142,x53143))+E(f171(x53141,x53142,f323(f323(f144(x53141),x53143),x53144)),f113(x53141))
% 179.72/179.58 [5383]~P79(x53832)+E(f323(f323(f77(f867(x53831,x53832)),x53833),x53834),f323(f77(x53832),f323(x53833,x53834)))
% 179.72/179.58 [5395]~E(x53952,f2(a860))+E(f323(f323(f131(x53951),x53952),f323(f323(f144(x53951),x53953),x53954)),f323(f323(f144(x53951),x53953),x53954))
% 179.72/179.58 [5396]P101(f323(x53962,x53963))+E(f323(f129(x53961,x53962),f323(f323(f144(x53961),x53963),x53964)),f323(f129(x53961,x53962),x53964))
% 179.72/179.58 [5528]~E(x55282,x55284)+P101(f323(f323(f323(f301(x55281),x55282),x55283),x55284))
% 179.72/179.58 [5536]E(x55361,f113(x55362))+E(f137(x55363,f323(f323(f147(x55362,x55363),x55364),x55361)),f323(x55364,f137(x55362,x55361)))
% 179.72/179.58 [5550]~E(x55501,f61(x55502,x55504))+E(f323(x55501,f323(f323(f301(x55502),x55503),f188(f867(x55502,a855)))),x55503)
% 179.72/179.58 [5585]E(x55851,f113(x55852))+E(f323(f134(x55853),f323(f323(f147(x55852,x55853),x55854),x55851)),f323(x55854,f323(f134(x55852),x55851)))
% 179.72/179.58 [5688]~P101(f323(x56883,x56884))+P101(f323(f323(f323(f301(x56881),x56882),x56883),x56884))
% 179.72/179.58 [5802]~P20(x58022,x58024,x58021)+E(f323(x58021,f323(f323(f301(x58022),x58023),f188(f867(x58022,a855)))),x58023)
% 179.72/179.58 [5826]~E(x58262,x58263)+P101(f323(f323(f325(x58261),x58262),f323(f323(f301(x58261),x58263),x58264)))
% 179.72/179.58 [5830]~P2(x58301)+E(f323(f323(f110(x58301),x58302),f323(f323(f110(x58301),x58303),x58304)),f323(f323(f110(x58301),x58303),f323(f323(f110(x58301),x58302),x58304)))
% 179.72/179.58 [5832]~P97(x58321)+E(f323(f323(f110(x58321),x58322),f323(f323(f110(x58321),x58323),x58324)),f323(f323(f110(x58321),x58323),f323(f323(f110(x58321),x58322),x58324)))
% 179.72/179.58 [5833]~P2(x58331)+E(f323(f323(f101(x58331),x58332),f323(f323(f101(x58331),x58333),x58334)),f323(f323(f101(x58331),x58333),f323(f323(f101(x58331),x58332),x58334)))
% 179.72/179.58 [5835]~P98(x58351)+E(f323(f323(f101(x58351),x58352),f323(f323(f101(x58351),x58353),x58354)),f323(f323(f101(x58351),x58353),f323(f323(f101(x58351),x58352),x58354)))
% 179.72/179.58 [5836]~P112(x58361)+E(f323(f323(f79(x58361),x58362),f323(f323(f79(x58361),x58363),x58364)),f323(f323(f79(x58361),x58363),f323(f323(f79(x58361),x58362),x58364)))
% 179.72/179.58 [5837]~P112(x58371)+E(f323(f323(f78(x58371),x58372),f323(f323(f78(x58371),x58373),x58374)),f323(f323(f78(x58371),x58373),f323(f323(f78(x58371),x58372),x58374)))
% 179.72/179.58 [5839]~P103(x58391)+E(f323(f323(f235(x58391),x58392),f323(f323(f235(x58391),x58393),x58394)),f323(f323(f235(x58391),x58393),f323(f323(f235(x58391),x58392),x58394)))
% 179.72/179.58 [5841]~P103(x58411)+E(f323(f323(f236(x58411),x58412),f323(f323(f236(x58411),x58413),x58414)),f323(f323(f236(x58411),x58413),f323(f323(f236(x58411),x58412),x58414)))
% 179.72/179.58 [5846]E(x58461,x58462)+E(f164(x58463,x58461,f323(f323(f144(x58463),x58462),x58464)),f323(f323(f144(x58463),x58462),f164(x58463,x58461,x58464)))
% 179.72/179.58 [5859]~P101(f323(x58592,x58593))+E(f323(f129(x58591,x58592),f323(f323(f144(x58591),x58593),x58594)),f323(f323(f144(x58591),x58593),f323(f129(x58591,x58592),x58594)))
% 179.72/179.58 [5989]~P101(f323(x59892,x59893))+E(f171(x59891,x59892,f323(f323(f144(x59891),x59893),x59894)),f323(f323(f144(x59891),x59893),f171(x59891,x59892,x59894)))
% 179.72/179.58 [6040]P26(x60401,x60402,x60403)+~P26(x60401,x60402,f323(f323(f301(f859(x60401)),x60404),x60403))
% 179.72/179.58 [6053]E(x60531,f188(f867(x60532,a855)))+E(f323(f323(f39(x60532,f867(x60533,a855)),x60531),f323(f16(f867(x60533,a855),x60532),x60534)),x60534)
% 179.72/179.58 [6054]E(x60541,f188(f867(x60542,a855)))+E(f323(f323(f40(x60542,f867(x60543,a855)),x60541),f323(f16(f867(x60543,a855),x60542),x60544)),x60544)
% 179.72/179.58 [6063]~E(x60634,f188(f867(x60632,a855)))+E(f323(f323(f260(x60631,x60632),x60633),f323(f16(f867(x60632,a855),x60631),x60634)),f188(f867(f866(x60631,x60632),a855)))
% 179.72/179.58 [6064]~E(x60643,f188(f867(x60641,a855)))+E(f323(f323(f260(x60641,x60642),x60643),f323(f16(f867(x60642,a855),x60641),x60644)),f188(f867(f866(x60641,x60642),a855)))
% 179.72/179.58 [6110]E(x61101,f2(a860))+E(f323(f323(f131(x61102),x61101),f323(f323(f144(x61102),x61103),x61104)),f323(f323(f131(x61102),f323(f323(f22(a860),x61101),f76(a860))),x61104))
% 179.72/179.58 [6134]E(x61341,f188(f867(x61342,a855)))+E(f323(f302(x61342,x61343,f323(f16(x61343,x61342),x61344)),x61341),f323(f323(f301(x61343),x61344),f188(f867(x61343,a855))))
% 179.72/179.58 [6137]E(f323(f303(x61371,x61372,f323(f16(x61372,x61371),x61373)),x61374),f188(f867(x61371,a855)))+P101(f323(f323(f325(x61372),x61373),x61374))
% 179.72/179.58 [6203]~E(x62033,f188(f867(x62031,a855)))+E(f323(f323(f39(x62031,f867(x62032,a855)),x62033),f323(f16(f867(x62032,a855),x62031),x62034)),f188(f867(x62032,a855)))
% 179.72/179.58 [6204]~E(x62043,f188(f867(x62041,a855)))+E(f323(f323(f40(x62041,f867(x62042,a855)),x62043),f323(f16(f867(x62042,a855),x62041),x62044)),f246(f867(x62042,a855)))
% 179.72/179.58 [6206]~P57(x62061)+E(f42(x62061,f323(f323(f79(x62061),x62062),x62063),f323(f323(f79(x62061),x62062),x62064)),f323(f323(f79(x62061),x62062),f42(x62061,x62063,x62064)))
% 179.72/179.58 [6369]E(f323(f303(x63691,x63692,f323(f16(x63692,x63691),x63693)),x63694),f246(f867(x63691,a855)))+~P101(f323(f323(f325(x63692),x63693),x63694))
% 179.72/179.58 [6392]~P101(f323(f323(f325(x63921),x63922),x63924))+P101(f323(f323(f325(x63921),x63922),f323(f323(f301(x63921),x63923),x63924)))
% 179.72/179.58 [6397]P101(f323(x63971,x63972))+~P101(f323(f153(x63973,x63971),f323(f323(f144(x63973),x63972),x63974)))
% 179.72/179.58 [6406]~E(x64063,f323(f323(f22(a860),f323(f189(f861(x64061)),x64062)),f76(a860)))+E(f114(x64061,f323(f323(f152(x64061,x64062),x64063),x64064)),f114(x64061,x64062))
% 179.72/179.58 [6424]~P103(x64241)+E(f323(f323(f101(f867(x64241,a855)),f323(f292(x64241),x64242)),f294(x64241,x64243,x64244)),f294(x64241,x64243,f323(f323(f235(x64241),x64242),x64244)))
% 179.72/179.58 [6425]~P103(x64251)+E(f323(f323(f101(f867(x64251,a855)),f323(f245(x64251),x64252)),f294(x64251,x64253,x64254)),f294(x64251,f323(f323(f236(x64251),x64252),x64253),x64254))
% 179.72/179.58 [6440]E(f323(f323(f101(f867(x64401,a855)),x64402),f323(f323(f301(x64401),x64403),x64404)),f323(f323(f101(f867(x64401,a855)),x64402),x64404))+P101(f323(f323(f325(x64401),x64403),x64402))
% 179.72/179.58 [6452]E(f164(x64521,x64522,f323(f323(f121(x64521),x64523),x64524)),f323(f323(f121(x64521),x64523),f164(x64521,x64522,x64524)))+P101(f323(f323(f325(x64521),x64522),f323(f166(x64521),x64523)))
% 179.72/179.58 [6456]~P77(x64561)+E(f323(f323(f79(x64561),f323(f323(f248(x64561),x64562),x64563)),f323(f323(f248(x64561),x64562),x64564)),f323(f323(f248(x64561),x64562),f323(f323(f78(a860),x64563),x64564)))
% 179.72/179.58 [6457]~P112(x64571)+E(f323(f323(f79(x64571),f323(f323(f248(x64571),x64572),x64573)),f323(f323(f248(x64571),x64572),x64574)),f323(f323(f248(x64571),x64572),f323(f323(f78(a860),x64573),x64574)))
% 179.72/179.58 [6494]~P96(x64941)+E(f323(f323(f101(x64941),f323(f323(f110(x64941),x64942),x64943)),f323(f323(f110(x64941),x64942),x64944)),f323(f323(f110(x64941),x64942),f323(f323(f101(x64941),x64943),x64944)))
% 179.72/179.58 [6495]~P96(x64951)+E(f323(f323(f110(x64951),f323(f323(f101(x64951),x64952),x64953)),f323(f323(f101(x64951),x64952),x64954)),f323(f323(f101(x64951),x64952),f323(f323(f110(x64951),x64953),x64954)))
% 179.72/179.58 [6496]~P112(x64961)+E(f323(f323(f78(x64961),f323(f323(f79(x64961),x64962),x64963)),f323(f323(f79(x64961),x64962),x64964)),f323(f323(f79(x64961),x64962),f323(f323(f78(x64961),x64963),x64964)))
% 179.72/179.58 [6497]~P103(x64971)+E(f323(f323(f236(x64971),f323(f323(f235(x64971),x64972),x64973)),f323(f323(f235(x64971),x64972),x64974)),f323(f323(f235(x64971),x64972),f323(f323(f236(x64971),x64973),x64974)))
% 179.72/179.58 [6498]~P103(x64981)+E(f323(f323(f235(x64981),f323(f323(f236(x64981),x64982),x64983)),f323(f323(f236(x64981),x64982),x64984)),f323(f323(f236(x64981),x64982),f323(f323(f235(x64981),x64983),x64984)))
% 179.72/179.58 [6529]~P57(x65291)+E(f42(x65291,f323(f323(f79(x65291),x65292),x65293),f323(f323(f79(x65291),x65294),x65293)),f323(f323(f79(x65291),f42(x65291,x65292,x65294)),x65293))
% 179.72/179.58 [6532]~E(f323(f189(f861(x65321)),x65323),f323(f189(f861(x65322)),x65324))+E(f323(f323(f147(f866(x65321,x65322),x65322),f261(x65321,x65322)),f323(f323(f175(x65321,x65322),x65323),x65324)),x65324)
% 179.72/179.58 [6533]~E(f323(f189(f861(x65331)),x65333),f323(f189(f861(x65332)),x65334))+E(f323(f323(f147(f866(x65331,x65332),x65331),f257(x65331,x65332)),f323(f323(f175(x65331,x65332),x65333),x65334)),x65333)
% 179.72/179.58 [6539]P101(f323(f153(x65391,x65392),x65393))+~P101(f323(f153(x65391,x65392),f323(f323(f144(x65391),x65394),x65393)))
% 179.72/179.58 [6540]P101(f323(f153(x65401,x65402),x65403))+~P101(f323(f153(x65401,x65402),f323(f323(f121(x65401),x65404),x65403)))
% 179.72/179.58 [6541]P101(f323(f153(x65411,x65412),x65413))+~P101(f323(f153(x65411,x65412),f323(f323(f121(x65411),x65413),x65414)))
% 179.72/179.58 [6546]~P58(x65461)+E(f42(x65461,f323(f323(f22(x65461),x65462),f42(x65461,x65463,x65464)),x65464),f42(x65461,f323(f323(f22(x65461),x65462),x65463),x65464))
% 179.72/179.58 [6547]~P57(x65471)+E(f42(x65471,f323(f323(f79(x65471),x65472),f42(x65471,x65473,x65474)),x65474),f42(x65471,f323(f323(f79(x65471),x65472),x65473),x65474))
% 179.72/179.58 [6549]~P57(x65491)+E(f42(x65491,f323(f323(f78(x65491),x65492),f42(x65491,x65493,x65494)),x65494),f42(x65491,f323(f323(f78(x65491),x65492),x65493),x65494))
% 179.72/179.58 [6628]~P103(x66281)+E(f323(f323(f101(f867(x66281,a855)),f294(x66281,x66282,x66283)),f323(f292(x66281),x66284)),f294(x66281,x66282,f323(f323(f235(x66281),x66283),x66284)))
% 179.72/179.58 [6629]~P103(x66291)+E(f323(f323(f101(f867(x66291,a855)),f294(x66291,x66292,x66293)),f323(f245(x66291),x66294)),f294(x66291,f323(f323(f236(x66291),x66292),x66294),x66293))
% 179.72/179.58 [6632]~E(f323(f189(f861(x66321)),x66323),f323(f189(f861(x66322)),x66324))+E(f323(f323(f175(x66321,x66322),f323(f162(x66321),x66323)),f323(f162(x66322),x66324)),f323(f162(f866(x66321,x66322)),f323(f323(f175(x66321,x66322),x66323),x66324)))
% 179.72/179.58 [6642]E(x66421,f323(f323(f22(a860),f323(f189(f861(x66422)),x66423)),f76(a860)))+E(f114(x66422,f323(f323(f152(x66422,x66423),x66421),x66424)),f323(f323(f152(x66422,f114(x66422,x66423)),x66421),x66424))
% 179.72/179.58 [6657]~P101(f323(f130(x66572),x66574))+P101(f323(f130(f866(x66571,x66572)),f323(f323(f175(x66571,x66572),x66573),x66574)))
% 179.72/179.58 [6658]~P101(f323(f130(x66581),x66583))+P101(f323(f130(f866(x66581,x66582)),f323(f323(f175(x66581,x66582),x66583),x66584)))
% 179.72/179.58 [6918]E(f323(f323(f36(a860),x69181),x69182),x69183)+~P101(f323(f45(x69181,x69182),f323(f323(f258(a860,a860),x69183),x69184)))
% 179.72/179.58 [6942]E(f42(a860,x69421,x69422),x69423)+~P101(f323(f45(x69421,x69422),f323(f323(f258(a860,a860),x69424),x69423)))
% 179.72/179.58 [6945]P101(f323(f130(x69451),x69452))+~P101(f323(f130(x69453),f323(f323(f147(x69451,x69453),x69454),x69452)))
% 179.72/179.58 [6953]~P26(x69531,x69532,f323(f323(f301(f859(x69531)),x69533),x69534))+P26(x69531,x69532,f323(f323(f301(f859(x69531)),x69533),f188(f867(f859(x69531),a855))))
% 179.72/179.58 [7029]E(f164(x70291,x70292,f323(f323(f121(x70291),x70293),x70294)),f323(f323(f121(x70291),f164(x70291,x70292,x70293)),x70294))+~P101(f323(f323(f325(x70291),x70292),f323(f166(x70291),x70293)))
% 179.72/179.58 [7119]~P58(x71191)+E(f42(x71191,f323(f323(f22(x71191),f42(x71191,x71192,x71193)),x71194),x71193),f42(x71191,f323(f323(f22(x71191),x71192),x71194),x71193))
% 179.72/179.58 [7122]~P57(x71221)+E(f42(x71221,f323(f323(f79(x71221),f42(x71221,x71222,x71223)),x71224),x71223),f42(x71221,f323(f323(f79(x71221),x71222),x71224),x71223))
% 179.72/179.58 [7123]~P57(x71231)+E(f42(x71231,f323(f323(f78(x71231),f42(x71231,x71232,x71233)),x71234),x71233),f42(x71231,f323(f323(f78(x71231),x71232),x71234),x71233))
% 179.72/179.58 [7310]~E(x73101,f323(f323(f144(x73102),x73103),x73104))+~P101(f323(f323(f237(a860),f323(f189(f861(x73102)),x73101)),f323(f189(f861(x73102)),x73104)))
% 179.72/179.58 [7385]~E(f323(f179(x73851,x73852),x73853),f323(f179(x73851,x73852),x73854))+E(f323(f302(f866(x73851,x73852),x73851,f257(x73851,x73852)),f323(f166(f866(x73851,x73852)),x73853)),f323(f302(f866(x73851,x73852),x73851,f257(x73851,x73852)),f323(f166(f866(x73851,x73852)),x73854)))
% 179.72/179.58 [7517]P27(x75171,x75172,x75173,f323(f166(x75171),x75174))+~P101(f323(f130(x75172),f323(f323(f147(x75171,x75172),x75173),x75174)))
% 179.72/179.58 [7591]~P101(f323(f323(f237(f867(x75911,a855)),x75912),x75914))+P101(f323(f323(f237(f867(x75911,a855)),x75912),f323(f323(f301(x75911),x75913),x75914)))
% 179.72/179.58 [7625]~P58(x76251)+E(f42(x76251,f323(f323(f22(x76251),f42(x76251,x76252,x76253)),f42(x76251,x76254,x76253)),x76253),f42(x76251,f323(f323(f22(x76251),x76252),x76254),x76253))
% 179.72/179.58 [7626]~P57(x76261)+E(f42(x76261,f323(f323(f79(x76261),f42(x76261,x76262,x76263)),f42(x76261,x76264,x76263)),x76263),f42(x76261,f323(f323(f79(x76261),x76262),x76264),x76263))
% 179.72/179.58 [7627]~P57(x76271)+E(f42(x76271,f323(f323(f78(x76271),f42(x76271,x76272,x76273)),f42(x76271,x76274,x76273)),x76273),f42(x76271,f323(f323(f78(x76271),x76272),x76274),x76273))
% 179.72/179.58 [7732]~E(f323(x77324,f443(x77324,x77323,x77321,x77322)),f188(f867(x77322,a855)))+E(f323(f323(f39(x77321,f867(x77322,a855)),x77323),x77324),f188(f867(x77322,a855)))
% 179.72/179.58 [7733]~E(f323(x77334,f629(x77334,x77333,x77331,x77332)),f246(f867(x77332,a855)))+E(f323(f323(f40(x77331,f867(x77332,a855)),x77333),x77334),f246(f867(x77332,a855)))
% 179.72/179.58 [7734]~E(f323(x77344,f451(x77344,x77343,x77342,x77341)),f188(f867(x77342,a855)))+E(f323(f323(f39(x77341,f867(x77342,a855)),x77343),x77344),f188(f867(x77342,a855)))
% 179.72/179.58 [7735]~E(f323(x77354,f633(x77354,x77353,x77352,x77351)),f246(f867(x77352,a855)))+E(f323(f323(f40(x77351,f867(x77352,a855)),x77353),x77354),f246(f867(x77352,a855)))
% 179.72/179.58 [8124]P101(f323(x81241,x81242))+~P101(f323(f323(f325(x81243),x81242),f323(f323(f101(f867(x81243,a855)),x81244),f323(f243(x81243),x81241))))
% 179.72/179.58 [8162]~P101(f323(f323(f237(f867(x81621,a855)),x81623),x81624))+P101(f323(f323(f237(f867(x81621,a855)),f323(f323(f301(x81621),x81622),x81623)),f323(f323(f301(x81621),x81622),x81624)))
% 179.72/179.58 [8173]E(f323(x81731,f628(x81731,x81732,x81733)),x81733)+~P101(f323(f323(f325(x81734),x81733),f323(f302(x81732,x81734,x81731),f246(f867(x81732,a855)))))
% 179.72/179.58 [8343]P101(f323(x83432,x83433))+E(f323(f323(f131(x83431),f323(f189(f861(x83431)),f171(x83431,x83432,f323(f323(f144(x83431),x83433),x83434)))),f323(f323(f144(x83431),x83433),x83434)),f323(f323(f144(x83431),x83433),x83434))
% 179.72/179.58 [8447]~P101(f323(f323(f238(a860),f323(x84474,x84472)),f323(x84474,x84473)))+P101(f323(f323(f325(f866(x84471,x84471)),f323(f323(f258(x84471,x84471),x84472),x84473)),f323(f323(f279(a860,x84471),a242),x84474)))
% 179.72/179.58 [8541]~P101(f323(x85412,f698(x85414,x85412,x85413,x85411)))+E(f171(x85411,x85412,f323(f323(f121(x85411),x85413),x85414)),f323(f323(f121(x85411),x85413),f171(x85411,x85412,x85414)))
% 179.72/179.58 [8620]P27(f861(x86201),f861(x86202),f323(f147(x86201,x86202),x86203),x86204)+~P27(x86201,x86202,x86203,f37(f867(x86201,a855),f323(f302(f861(x86201),f867(x86201,a855),f166(x86201)),x86204)))
% 179.72/179.58 [8695]~P101(f323(x86952,x86953))+E(f323(f323(f131(x86951),f323(f189(f861(x86951)),f171(x86951,x86952,f323(f323(f144(x86951),x86953),x86954)))),f323(f323(f144(x86951),x86953),x86954)),f323(f323(f131(x86951),f323(f189(f861(x86951)),f171(x86951,x86952,x86954))),x86954))
% 179.72/179.58 [8737]~E(x87372,x87373)+E(f323(f129(x87371,f323(f323(f8(a855,a855,x87371),a318),f323(a320,x87372))),f323(f323(f144(x87371),x87373),x87374)),f323(f129(x87371,f323(f323(f8(a855,a855,x87371),a318),f323(a320,x87372))),x87374))
% 179.72/179.58 [8747]E(f323(f323(f39(x87471,f867(x87472,a855)),x87473),x87474),f188(f867(x87472,a855)))+P101(f323(f323(f325(x87471),f443(x87474,x87473,x87471,x87472)),x87473))
% 179.72/179.58 [8748]E(f323(f323(f40(x87481,f867(x87482,a855)),x87483),x87484),f246(f867(x87482,a855)))+P101(f323(f323(f325(x87481),f629(x87484,x87483,x87481,x87482)),x87483))
% 179.72/179.58 [8749]E(f323(f323(f39(x87491,f867(x87492,a855)),x87493),x87494),f188(f867(x87492,a855)))+P101(f323(f323(f325(x87491),f451(x87494,x87493,x87492,x87491)),x87493))
% 179.72/179.58 [8750]E(f323(f323(f40(x87501,f867(x87502,a855)),x87503),x87504),f246(f867(x87502,a855)))+P101(f323(f323(f325(x87501),f633(x87504,x87503,x87502,x87501)),x87503))
% 179.72/179.58 [8788]P101(f323(f323(f238(a860),f323(x87881,x87882)),f323(x87881,x87883)))+~P101(f323(f323(f325(f866(x87884,x87884)),f323(f323(f258(x87884,x87884),x87882),x87883)),f323(f323(f279(a860,x87884),a242),x87881)))
% 179.72/179.58 [8809]E(f171(x88091,x88092,f323(f323(f121(x88091),x88093),x88094)),f323(f323(f121(x88091),x88093),f171(x88091,x88092,x88094)))+P101(f323(f323(f325(x88091),f698(x88094,x88092,x88093,x88091)),f323(f166(x88091),x88093)))
% 179.72/179.58 [8864]~P28(x88641,x88642,x88643,f246(f867(x88641,a855)),f246(f867(x88642,a855)))+E(f323(f302(x88641,x88642,x88643),f323(f77(f867(x88641,a855)),x88644)),f323(f77(f867(x88642,a855)),f323(f302(x88641,x88642,x88643),x88644)))
% 179.72/179.58 [8966]P101(f323(f323(f325(x89661),f493(x89662,x89663,x89664,x89661)),x89663))+~P101(f323(f323(f325(f867(x89661,a855)),x89664),f323(f323(f58(x89661),x89663),x89662)))
% 179.72/179.58 [8969]E(x89691,x89692)+~P101(f323(f323(f325(f866(x89693,x89693)),f323(f323(f258(x89693,x89693),x89691),x89692)),f323(f323(f183(f866(x89693,x89693),a855),f2(a860)),x89694)))
% 179.72/179.58 [9053]E(f323(f277(x90531,x90531,x90532),f323(f323(f301(x90531),f493(x90532,x90533,x90534,x90531)),f188(f867(x90531,a855)))),x90534)+~P101(f323(f323(f325(f867(x90531,a855)),x90534),f323(f323(f58(x90531),x90533),x90532)))
% 179.72/179.58 [9058]~P101(f323(f323(f325(f866(x90581,x90581)),f323(f323(f258(x90581,x90581),x90583),x90582)),f299(x90581,x90584)))+P101(f323(f323(f325(f866(x90581,x90581)),f323(f323(f258(x90581,x90581),x90582),x90583)),f299(x90581,f323(f278(x90581,x90581),x90584))))
% 179.72/179.58 [9070]~P57(x90701)+E(f323(f323(f78(x90701),f323(f323(f78(x90701),f323(f323(f79(x90701),x90702),f323(f323(f36(x90701),x90703),x90702))),f42(x90701,x90703,x90702))),x90704),f323(f323(f78(x90701),x90703),x90704))
% 179.72/179.58 [9080]~P101(f323(f323(f325(x90801),x90803),x90804))+P101(f323(f323(f325(f867(x90801,a855)),f323(f277(x90801,x90801,x90802),f323(f323(f301(x90801),x90803),f188(f867(x90801,a855))))),f323(f323(f58(x90801),x90804),x90802)))
% 179.72/179.58 [9091]P101(f323(f323(f325(f866(x90911,x90911)),f323(f323(f258(x90911,x90911),x90912),x90913)),f299(x90911,x90914)))+~P101(f323(f323(f325(f866(x90911,x90911)),f323(f323(f258(x90911,x90911),x90913),x90912)),f299(x90911,f323(f278(x90911,x90911),x90914))))
% 179.72/179.58 [9179]E(f323(f323(f152(x91791,f323(f162(x91791),x91792)),f323(f323(f22(a860),f323(f323(f22(a860),f323(f189(f861(x91791)),x91792)),x91793)),f76(a860))),x91794),f323(f162(x91791),f323(f323(f152(x91791,x91792),x91793),x91794)))+~P101(f323(f323(f238(a860),x91793),f323(f189(f861(x91791)),x91792)))
% 179.72/179.58 [9182]~P101(f323(x91822,f692(x91824,x91822,x91823,x91821)))+E(f323(f323(f131(x91821),f323(f189(f861(x91821)),f171(x91821,x91822,f323(f323(f121(x91821),x91823),x91824)))),f323(f323(f121(x91821),x91823),x91824)),f323(f323(f131(x91821),f323(f189(f861(x91821)),f171(x91821,x91822,x91824))),x91824))
% 179.72/179.58 [9224]~P27(x92242,x92241,x92243,f246(f867(x92242,a855)))+P101(f323(f323(f237(f867(x92241,a855)),f323(f302(x92242,x92241,x92243),f323(f77(f867(x92242,a855)),x92244))),f323(f77(f867(x92241,a855)),f323(f302(x92242,x92241,x92243),x92244))))
% 179.72/179.58 [9235]~P6(x92351)+E(f323(f135(x92351,x92352,f323(f7(x92352,x92351,x92351),f323(f323(f8(x92351,f867(x92351,x92351),x92352),f110(x92351)),x92353)),f188(x92351)),x92354),f323(f323(f39(x92352,x92351),f323(f166(x92352),x92354)),x92353))
% 179.72/179.58 [9236]~P6(x92361)+E(f323(f135(x92361,x92362,f323(f7(x92362,x92361,x92361),f323(f323(f8(x92361,f867(x92361,x92361),x92362),f101(x92361)),x92363)),f246(x92361)),x92364),f323(f323(f40(x92362,x92361),f323(f166(x92362),x92364)),x92363))
% 179.72/179.58 [9246]E(f323(f323(f131(x92461),f323(f189(f861(x92461)),f171(x92461,x92462,f323(f323(f121(x92461),x92463),x92464)))),f323(f323(f121(x92461),x92463),x92464)),f323(f323(f131(x92461),f323(f189(f861(x92461)),f171(x92461,x92462,x92464))),x92464))+P101(f323(f323(f325(x92461),f692(x92464,x92462,x92463,x92461)),f323(f166(x92461),x92463)))
% 179.72/179.58 [9315]~P101(f323(f323(f325(f866(f861(x93154),f861(x93154))),f323(f323(f258(f861(x93154),f861(x93154)),x93153),x93152)),f150(x93154,x93151)))+P101(f323(f323(f238(a860),f584(x93151,x93152,x93153,x93154)),f323(f189(f861(x93154)),x93153)))
% 179.72/179.58 [9316]~P57(x93161)+E(f323(f323(f78(x93161),f323(f323(f78(x93161),f323(f323(f79(x93161),f323(f323(f36(x93161),x93162),x93163)),x93163)),f42(x93161,x93162,x93163))),x93164),f323(f323(f78(x93161),x93162),x93164))
% 179.72/179.58 [9343]~P101(f323(f323(f325(f866(f861(x93431),f861(x93431))),f323(f323(f258(f861(x93431),f861(x93431)),x93432),x93433)),f323(f278(f861(x93431),f861(x93431)),f150(x93431,x93434))))+P101(f323(f323(f325(f866(f861(x93431),f861(x93431))),f323(f323(f258(f861(x93431),f861(x93431)),x93432),x93433)),f150(x93431,f323(f278(x93431,x93431),x93434))))
% 179.72/179.58 [9344]P101(f323(f323(f325(f866(f861(x93441),f861(x93441))),f323(f323(f258(f861(x93441),f861(x93441)),x93442),x93443)),f323(f278(f861(x93441),f861(x93441)),f150(x93441,x93444))))+~P101(f323(f323(f325(f866(f861(x93441),f861(x93441))),f323(f323(f258(f861(x93441),f861(x93441)),x93442),x93443)),f150(x93441,f323(f278(x93441,x93441),x93444))))
% 179.72/179.58 [9379]~P101(f323(f323(f325(x93791),x93793),f323(f256(x93791,x93792),x93794)))+P101(f323(f323(f325(f866(x93791,x93792)),f323(f323(f258(x93791,x93792),x93793),f677(x93794,x93792,x93793,x93791))),x93794))
% 179.72/179.58 [9380]~P101(f323(f323(f325(x93801),x93803),f323(f256(x93801,x93802),x93804)))+P101(f323(f323(f325(f866(x93801,x93802)),f323(f323(f258(x93801,x93802),x93803),f679(x93804,x93802,x93803,x93801))),x93804))
% 179.72/179.58 [9489]~P101(f323(f59(f864(x94891)),f323(f302(x94892,f864(x94891),x94893),f246(f867(x94892,a855)))))+P101(f323(f59(f864(x94891)),f323(f302(x94892,f864(x94891),f180(x94892,x94891,x94893,f323(f179(x94892,x94891),x94894))),f246(f867(x94892,a855)))))
% 179.72/179.58 [9537]~P101(f323(f323(f325(f866(x95371,x95371)),f323(f323(f258(x95371,x95371),x95372),x95374)),f323(f323(f280(x95371,x95371,x95371),x95373),f299(x95371,x95373))))+P101(f323(f323(f325(f866(x95371,x95371)),f323(f323(f258(x95371,x95371),x95372),f742(x95373,x95374,x95372,x95371))),x95373))
% 179.72/179.58 [9708]~P101(f323(f323(f325(f866(x97082,x97081)),x97084),f323(f278(x97081,x97082),x97083)))+P101(f323(f323(f325(f866(x97081,x97082)),f323(f323(f258(x97081,x97082),f773(x97083,x97084,x97081,x97082)),f772(x97083,x97084,x97081,x97082))),x97083))
% 179.72/179.58 [9736]~P101(f323(f323(f325(f866(f861(x97361),f861(x97361))),f323(f323(f258(f861(x97361),f861(x97361)),x97364),x97363)),f150(x97361,x97362)))+P101(f323(f323(f325(f866(x97361,x97361)),f323(f323(f258(x97361,x97361),f590(x97362,x97363,x97364,x97361)),f591(x97362,x97363,x97364,x97361))),x97362))
% 179.72/179.58 [9831]~P101(f323(f323(f325(f866(f861(x98311),f861(x98311))),f323(f323(f258(f861(x98311),f861(x98311)),x98312),x98314)),f150(x98311,x98313)))+P101(f323(f323(f325(f866(x98311,x98311)),f323(f323(f258(x98311,x98311),f323(f323(f158(x98311),x98312),f584(x98313,x98314,x98312,x98311))),f585(x98313,x98314,x98312,x98311))),x98313))
% 179.72/179.58 [9853]~P101(f323(f59(x98532),x98534))+E(f323(f323(f323(f63(f867(x98531,a855),x98532,f110(f867(x98531,a855))),f323(f323(f7(x98532,f867(x98531,a855),f867(x98531,a855)),f323(f323(f8(x98531,f867(f867(x98531,a855),f867(x98531,a855)),x98532),f301(x98531)),x98533)),f188(f867(x98531,a855)))),f188(f867(x98531,a855))),x98534),f323(f302(x98532,x98531,x98533),x98534))
% 179.72/179.58 [9948]~P27(x99481,x99482,x99483,f246(f867(x99481,a855)))+P101(f323(f323(f237(f867(x99481,a855)),f323(f303(x99481,x99482,x99483),f323(f323(f301(x99482),x99484),f188(f867(x99482,a855))))),f323(f323(f301(x99481),f83(x99481,f323(f323(f7(x99481,x99482,a855),f323(f323(f8(x99482,f867(x99482,a855),x99481),a320),x99483)),x99484))),f188(f867(x99481,a855)))))
% 179.72/179.58 [5594]~E(f323(f323(f121(x55941),x55942),x55944),x55943)+E(f323(f323(f169(x55941),f323(f189(f861(x55941)),x55942)),x55943),x55942)
% 179.72/179.58 [5595]~E(f323(f323(f121(x55952),x55953),x55951),x55954)+E(x55951,f323(f323(f131(x55952),f323(f189(f861(x55952)),x55953)),x55954))
% 179.72/179.58 [5606]~E(x56064,f2(a860))+E(f323(f323(f158(x56061),f323(f323(f144(x56061),x56062),x56063)),x56064),x56062)
% 179.72/179.58 [6123]~P112(x61231)+E(f323(f323(f248(x61231),f323(f323(f248(x61231),x61232),x61233)),x61234),f323(f323(f248(x61231),x61232),f323(f323(f79(a860),x61233),x61234)))
% 179.72/179.58 [6124]~P77(x61241)+E(f323(f323(f248(x61241),f323(f323(f248(x61241),x61242),x61243)),x61244),f323(f323(f248(x61241),x61242),f323(f323(f79(a860),x61243),x61244)))
% 179.72/179.58 [6135]E(x61351,f2(a860))+E(f323(f323(f158(x61352),f323(f323(f144(x61352),x61353),x61354)),x61351),f323(f323(f158(x61352),x61354),f323(f323(f22(a860),x61351),f76(a860))))
% 179.72/179.58 [6160]~P114(x61601)+E(f323(f323(f281(x61601),f323(f323(f79(x61601),x61602),x61603)),x61604),f323(f323(f79(x61601),x61602),f323(f323(f281(x61601),x61603),x61604)))
% 179.72/179.58 [6162]~P2(x61621)+E(f323(f323(f110(x61621),f323(f323(f110(x61621),x61622),x61623)),x61624),f323(f323(f110(x61621),x61622),f323(f323(f110(x61621),x61623),x61624)))
% 179.72/179.58 [6164]~P97(x61641)+E(f323(f323(f110(x61641),f323(f323(f110(x61641),x61642),x61643)),x61644),f323(f323(f110(x61641),x61642),f323(f323(f110(x61641),x61643),x61644)))
% 179.72/179.58 [6165]~P2(x61651)+E(f323(f323(f101(x61651),f323(f323(f101(x61651),x61652),x61653)),x61654),f323(f323(f101(x61651),x61652),f323(f323(f101(x61651),x61653),x61654)))
% 179.72/179.58 [6167]~P98(x61671)+E(f323(f323(f101(x61671),f323(f323(f101(x61671),x61672),x61673)),x61674),f323(f323(f101(x61671),x61672),f323(f323(f101(x61671),x61673),x61674)))
% 179.72/179.58 [6168]~P66(x61681)+E(f323(f323(f79(x61681),f323(f323(f79(x61681),x61682),x61683)),x61684),f323(f323(f79(x61681),x61682),f323(f323(f79(x61681),x61683),x61684)))
% 179.72/179.58 [6169]~P112(x61691)+E(f323(f323(f79(x61691),f323(f323(f79(x61691),x61692),x61693)),x61694),f323(f323(f79(x61691),x61692),f323(f323(f79(x61691),x61693),x61694)))
% 179.72/179.58 [6171]~P112(x61711)+E(f323(f323(f78(x61711),f323(f323(f78(x61711),x61712),x61713)),x61714),f323(f323(f78(x61711),x61712),f323(f323(f78(x61711),x61713),x61714)))
% 179.72/179.58 [6172]~P67(x61721)+E(f323(f323(f78(x61721),f323(f323(f78(x61721),x61722),x61723)),x61724),f323(f323(f78(x61721),x61722),f323(f323(f78(x61721),x61723),x61724)))
% 179.72/179.58 [6174]~P103(x61741)+E(f323(f323(f235(x61741),f323(f323(f235(x61741),x61742),x61743)),x61744),f323(f323(f235(x61741),x61742),f323(f323(f235(x61741),x61743),x61744)))
% 179.72/179.58 [6176]~P103(x61761)+E(f323(f323(f236(x61761),f323(f323(f236(x61761),x61762),x61763)),x61764),f323(f323(f236(x61761),x61762),f323(f323(f236(x61761),x61763),x61764)))
% 179.72/179.58 [6187]~P57(x61871)+E(f42(x61871,f323(f323(f78(x61871),x61872),f323(f323(f79(x61871),x61873),x61874)),x61874),f42(x61871,x61872,x61874))
% 179.72/179.58 [6188]~P57(x61881)+E(f42(x61881,f323(f323(f78(x61881),x61882),f323(f323(f79(x61881),x61883),x61884)),x61883),f42(x61881,x61882,x61883))
% 179.72/179.58 [6319]E(f323(f323(f158(x63191),f323(f323(f169(x63191),x63192),x63193)),x63194),f323(f323(f158(x63191),x63193),x63194))+~P101(f323(f323(f238(a860),x63194),x63192))
% 179.72/179.58 [6492]~P112(x64921)+E(f323(f323(f79(x64921),f323(f323(f79(x64921),x64922),x64923)),x64924),f323(f323(f79(x64921),f323(f323(f79(x64921),x64922),x64924)),x64923))
% 179.72/179.58 [6493]~P112(x64931)+E(f323(f323(f78(x64931),f323(f323(f78(x64931),x64932),x64933)),x64934),f323(f323(f78(x64931),f323(f323(f78(x64931),x64932),x64934)),x64933))
% 179.72/179.58 [6552]~P140(x65522)+E(f323(f323(f6(x65521,x65522),f323(f16(x65522,x65521),x65523)),x65524),f323(f323(f79(x65522),f323(f100(x65522),f323(f35(x65521),x65524))),x65523))
% 179.72/179.58 [6719]E(f323(f323(f101(f867(x67191,a855)),f323(f323(f301(x67191),x67192),x67193)),x67194),f323(f323(f101(f867(x67191,a855)),x67193),x67194))+P101(f323(f323(f325(x67191),x67192),x67194))
% 179.72/179.58 [6789]~P96(x67891)+E(f323(f323(f101(x67891),f323(f323(f110(x67891),x67892),x67893)),f323(f323(f110(x67891),x67894),x67893)),f323(f323(f110(x67891),f323(f323(f101(x67891),x67892),x67894)),x67893))
% 179.72/179.58 [6790]~P75(x67901)+E(f323(f323(f235(x67901),f323(f323(f22(x67901),x67902),x67903)),f323(f323(f22(x67901),x67904),x67903)),f323(f323(f22(x67901),f323(f323(f235(x67901),x67902),x67904)),x67903))
% 179.72/179.58 [6791]~P75(x67911)+E(f323(f323(f236(x67911),f323(f323(f22(x67911),x67912),x67913)),f323(f323(f22(x67911),x67914),x67913)),f323(f323(f22(x67911),f323(f323(f236(x67911),x67912),x67914)),x67913))
% 179.72/179.58 [6792]~P96(x67921)+E(f323(f323(f110(x67921),f323(f323(f101(x67921),x67922),x67923)),f323(f323(f101(x67921),x67924),x67923)),f323(f323(f101(x67921),f323(f323(f110(x67921),x67922),x67924)),x67923))
% 179.72/179.58 [6794]~P113(x67941)+E(f323(f323(f78(x67941),f323(f323(f79(x67941),x67942),x67943)),f323(f323(f79(x67941),x67944),x67943)),f323(f323(f79(x67941),f323(f323(f78(x67941),x67942),x67944)),x67943))
% 179.72/179.58 [6795]~P80(x67951)+E(f323(f323(f235(x67951),f323(f323(f78(x67951),x67952),x67953)),f323(f323(f78(x67951),x67954),x67953)),f323(f323(f78(x67951),f323(f323(f235(x67951),x67952),x67954)),x67953))
% 179.72/179.58 [6796]~P80(x67961)+E(f323(f323(f236(x67961),f323(f323(f78(x67961),x67962),x67963)),f323(f323(f78(x67961),x67964),x67963)),f323(f323(f78(x67961),f323(f323(f236(x67961),x67962),x67964)),x67963))
% 179.72/179.58 [6797]~P103(x67971)+E(f323(f323(f236(x67971),f323(f323(f235(x67971),x67972),x67973)),f323(f323(f235(x67971),x67974),x67973)),f323(f323(f235(x67971),f323(f323(f236(x67971),x67972),x67974)),x67973))
% 179.72/179.58 [6798]~P103(x67981)+E(f323(f323(f235(x67981),f323(f323(f236(x67981),x67982),x67983)),f323(f323(f236(x67981),x67984),x67983)),f323(f323(f236(x67981),f323(f323(f235(x67981),x67982),x67984)),x67983))
% 179.72/179.58 [6799]~P68(x67991)+E(f323(f323(f79(x67991),f323(f323(f248(x67991),x67992),x67993)),f323(f323(f248(x67991),x67994),x67993)),f323(f323(f248(x67991),f323(f323(f79(x67991),x67992),x67994)),x67993))
% 179.72/179.58 [6800]~P112(x68001)+E(f323(f323(f79(x68001),f323(f323(f248(x68001),x68002),x68003)),f323(f323(f248(x68001),x68004),x68003)),f323(f323(f248(x68001),f323(f323(f79(x68001),x68002),x68004)),x68003))
% 179.72/179.58 [6801]~P62(x68011)+E(f323(f323(f281(x68011),f323(f323(f248(x68011),x68012),x68013)),f323(f323(f248(x68011),x68014),x68013)),f323(f323(f248(x68011),f323(f323(f281(x68011),x68012),x68014)),x68013))
% 179.72/179.58 [6802]~P114(x68021)+E(f323(f323(f22(x68021),f323(f323(f281(x68021),x68022),x68023)),f323(f323(f281(x68021),x68024),x68023)),f323(f323(f281(x68021),f323(f323(f22(x68021),x68022),x68024)),x68023))
% 179.72/179.58 [6803]~P114(x68031)+E(f323(f323(f78(x68031),f323(f323(f281(x68031),x68032),x68033)),f323(f323(f281(x68031),x68034),x68033)),f323(f323(f281(x68031),f323(f323(f78(x68031),x68032),x68034)),x68033))
% 179.72/179.58 [6804]~P112(x68041)+E(f323(f323(f78(x68041),f323(f323(f79(x68041),x68042),x68043)),f323(f323(f79(x68041),x68044),x68043)),f323(f323(f79(x68041),f323(f323(f78(x68041),x68042),x68044)),x68043))
% 179.72/179.58 [6836]E(f323(f323(f152(x68361,x68362),x68363),x68364),x68362)+~P101(f323(f323(f237(a860),f323(f189(f861(x68361)),x68362)),x68363))
% 179.72/179.58 [6860]~P101(f323(x68603,x68604))+P101(f323(f323(f323(f110(f867(x68601,a855)),x68602),x68603),x68604))
% 179.72/179.58 [6862]~P101(f323(x68622,x68624))+P101(f323(f323(f323(f110(f867(x68621,a855)),x68622),x68623),x68624))
% 179.72/179.58 [6881]E(f323(f323(f158(x68811),f323(f323(f121(x68811),x68812),x68813)),x68814),f323(f323(f158(x68811),x68812),x68814))+~P101(f323(f323(f238(a860),x68814),f323(f189(f861(x68811)),x68812)))
% 179.72/179.58 [6891]E(f323(f323(f22(f867(x68911,a855)),f323(f323(f301(x68911),x68912),x68913)),x68914),f323(f323(f22(f867(x68911,a855)),x68913),x68914))+~P101(f323(f323(f325(x68911),x68912),x68914))
% 179.72/179.58 [6932]~E(f132(a860,f323(f293(a860,x69321),x69322)),f323(f323(f144(a860),x69324),x69323))+E(f132(a860,f323(f293(a860,f323(f323(f78(a860),x69321),f76(a860))),x69322)),x69323)
% 179.72/179.58 [7003]E(x70031,f2(a860))+E(f323(f323(f144(x70032),x70033),f323(f323(f169(x70032),f323(f323(f22(a860),x70031),f76(a860))),x70034)),f323(f323(f169(x70032),x70031),f323(f323(f144(x70032),x70033),x70034)))
% 179.72/179.58 [7103]E(f323(f323(f158(x71031),x71032),f323(f323(f22(a860),x71033),f323(f189(f861(x71031)),x71034))),f323(f323(f158(x71031),f323(f323(f121(x71031),x71034),x71032)),x71033))+P101(f323(f323(f238(a860),x71033),f323(f189(f861(x71031)),x71034)))
% 179.72/179.58 [7133]E(f323(f323(f101(f867(x71331,a855)),x71332),f323(f323(f301(x71331),x71333),x71334)),f323(f323(f301(x71331),x71333),f323(f323(f101(f867(x71331,a855)),x71332),x71334)))+~P101(f323(f323(f325(x71331),x71333),x71332))
% 179.72/179.58 [7168]E(f323(f323(f158(x71681),f323(f323(f152(x71681,x71682),x71683),x71684)),x71683),x71684)+~P101(f323(f323(f238(a860),x71683),f323(f189(f861(x71681)),x71682)))
% 179.72/179.58 [7189]E(x71891,f188(f867(x71892,a855)))+E(f323(f302(f866(x71893,x71892),x71893,f257(x71893,x71892)),f323(f323(f260(x71893,x71892),x71894),f323(f16(f867(x71892,a855),x71893),x71891))),x71894)
% 179.72/179.58 [7190]E(x71901,f188(f867(x71902,a855)))+E(f323(f302(f866(x71902,x71903),x71903,f261(x71902,x71903)),f323(f323(f260(x71902,x71903),x71901),f323(f16(f867(x71903,a855),x71902),x71904))),x71904)
% 179.72/179.58 [7257]E(f323(f323(f22(f867(x72571,a855)),f323(f323(f301(x72571),x72572),x72573)),x72574),f323(f323(f301(x72571),x72572),f323(f323(f22(f867(x72571,a855)),x72573),x72574)))+P101(f323(f323(f325(x72571),x72572),x72574))
% 179.72/179.58 [7294]~E(x72944,f188(f867(x72942,a855)))+E(f323(f302(f866(x72941,x72942),x72941,f257(x72941,x72942)),f323(f323(f260(x72941,x72942),x72943),f323(f16(f867(x72942,a855),x72941),x72944))),f188(f867(x72941,a855)))
% 179.72/179.58 [7295]~E(x72953,f188(f867(x72951,a855)))+E(f323(f302(f866(x72951,x72952),x72952,f261(x72951,x72952)),f323(f323(f260(x72951,x72952),x72953),f323(f16(f867(x72952,a855),x72951),x72954))),f188(f867(x72952,a855)))
% 179.72/179.58 [7350]~P101(f323(f323(f325(x73501),x73502),x73504))+P101(f323(f323(f325(x73501),x73502),f323(f323(f110(f867(x73501,a855)),x73503),x73504)))
% 179.72/179.58 [7353]~P101(f323(f323(f325(x73531),x73532),x73533))+P101(f323(f323(f325(x73531),x73532),f323(f323(f110(f867(x73531,a855)),x73533),x73534)))
% 179.72/179.58 [7372]E(f323(f323(f101(f867(x73721,a855)),f323(f323(f301(x73721),x73722),x73723)),x73724),f323(f323(f301(x73721),x73722),f323(f323(f101(f867(x73721,a855)),x73723),x73724)))+~P101(f323(f323(f325(x73721),x73722),x73724))
% 179.72/179.58 [7648]P101(f323(x76481,x76482))+~P101(f323(f323(f323(f101(f867(x76483,a855)),x76484),x76481),x76482))
% 179.72/179.58 [7649]P101(f323(x76491,x76492))+~P101(f323(f323(f323(f101(f867(x76493,a855)),x76491),x76494),x76492))
% 179.72/179.58 [7652]E(f323(f323(f6(x76521,a860),x76522),f323(f323(f22(f867(x76521,a855)),x76523),f323(f323(f301(x76521),x76524),f188(f867(x76521,a855))))),f323(f323(f6(x76521,a860),x76522),x76523))+P101(f323(f323(f325(x76521),x76524),x76523))
% 179.72/179.58 [7657]~P72(x76571)+E(f323(f159(x76571),f323(f323(f147(a860,x76571),x76572),f132(a860,f323(f293(a860,x76573),x76574)))),f323(f323(f6(a860,x76571),x76572),f323(f166(a860),f132(a860,f323(f293(a860,x76573),x76574)))))
% 179.72/179.58 [7658]~P72(x76581)+E(f323(f323(f6(a860,x76581),x76582),f323(f166(a860),f132(a860,f323(f293(a860,x76583),x76584)))),f323(f159(x76581),f323(f323(f147(a860,x76581),x76582),f132(a860,f323(f293(a860,x76583),x76584)))))
% 179.72/179.58 [7768]~E(x77683,x77684)+P101(f323(f60(x77681,x77682,f323(f323(f301(x77681),x77683),f188(f867(x77681,a855)))),x77684))
% 179.72/179.58 [7868]P101(f323(f323(f325(x78681),x78682),f323(f166(x78681),x78683)))+~P101(f323(f323(f325(x78681),x78682),f323(f166(x78681),f323(f323(f169(x78681),x78684),x78683))))
% 179.72/179.58 [7869]P101(f323(f323(f325(x78691),x78692),f323(f166(x78691),x78693)))+~P101(f323(f323(f325(x78691),x78692),f323(f166(x78691),f323(f323(f131(x78691),x78694),x78693))))
% 179.72/179.58 [7940]P101(f323(f323(f325(x79401),x79402),x79403))+~P101(f323(f323(f325(x79401),x79402),f323(f323(f22(f867(x79401,a855)),x79403),x79404)))
% 179.72/179.58 [7942]P101(f323(f323(f325(x79421),x79422),x79423))+~P101(f323(f323(f325(x79421),x79422),f323(f323(f101(f867(x79421,a855)),x79424),x79423)))
% 179.72/179.58 [7945]P101(f323(f323(f325(x79451),x79452),x79453))+~P101(f323(f323(f325(x79451),x79452),f323(f323(f101(f867(x79451,a855)),x79453),x79454)))
% 179.72/179.58 [7960]E(f323(f323(f121(x79601),f323(f323(f169(x79601),x79602),x79603)),f323(f323(f144(x79601),x79604),f323(f323(f131(x79601),f323(a112,x79602)),x79603))),f323(f323(f152(x79601,x79603),x79602),x79604))+~P101(f323(f323(f238(a860),x79602),f323(f189(f861(x79601)),x79603)))
% 179.72/179.58 [7983]P101(f323(f323(f325(x79831),x79832),x79833))+~P101(f323(f323(f237(f867(x79831,a855)),f323(f323(f301(x79831),x79832),x79834)),x79833))
% 179.72/179.58 [8017]~P101(f323(f323(f325(x80171),x80172),x80173))+~P101(f323(f323(f325(x80171),x80172),f323(f323(f22(f867(x80171,a855)),x80174),x80173)))
% 179.72/179.58 [8048]~P101(f323(f323(f238(a860),x80484),f323(f189(f861(x80481)),x80483)))+P101(f323(f323(f325(x80481),x80482),f323(f166(x80481),f323(f323(f152(x80481,x80483),x80484),x80482))))
% 179.72/179.58 [8101]E(f323(f323(f158(x81011),f323(f323(f131(x81011),x81012),x81013)),x81014),f323(f323(f158(x81011),x81013),f323(f323(f78(a860),x81012),x81014)))+~P101(f323(f323(f237(a860),f323(f323(f78(a860),x81012),x81014)),f323(f189(f861(x81011)),x81013)))
% 179.72/179.58 [8111]~P140(x81112)+E(f323(f323(f6(x81111,x81112),f323(f323(f8(a860,x81112,x81111),f100(x81112)),x81113)),x81114),f323(f100(x81112),f323(f323(f6(x81111,a860),x81113),x81114)))
% 179.72/179.58 [8112]~P134(x81122)+E(f323(f323(f6(x81121,x81122),f323(f323(f8(a1,x81122,x81121),f102(x81122)),x81123)),x81124),f323(f102(x81122),f323(f323(f6(x81121,a1),x81123),x81124)))
% 179.72/179.58 [8164]~P65(x81642)+E(f323(f323(f9(x81641,x81642),f323(f323(f8(x81642,x81642,x81641),f73(x81642)),x81643)),x81644),f323(f73(x81642),f323(f323(f9(x81641,x81642),x81643),x81644)))
% 179.72/179.58 [8165]~P60(x81652)+E(f323(f323(f6(x81651,x81652),f323(f323(f8(x81652,x81652,x81651),f77(x81652)),x81653)),x81654),f323(f77(x81652),f323(f323(f6(x81651,x81652),x81653),x81654)))
% 179.72/179.58 [8167]E(f323(f323(f6(x81671,a860),x81672),f323(f323(f22(f867(x81671,a855)),x81673),f323(f323(f301(x81671),x81674),f188(f867(x81671,a855))))),f323(f323(f22(a860),f323(f323(f6(x81671,a860),x81672),x81673)),f323(x81672,x81674)))+~P101(f323(f323(f325(x81671),x81674),x81673))
% 179.72/179.58 [8188]P101(f323(f323(f237(f867(x81881,a855)),x81882),x81883))+~P101(f323(f323(f237(f867(x81881,a855)),f323(f323(f301(x81881),x81884),x81882)),x81883))
% 179.72/179.58 [8313]~E(f323(f302(x83132,x83133,x83131),f246(f867(x83132,a855))),f246(f867(x83133,a855)))+E(f323(x83131,f323(f91(x83132,x83133,f246(f867(x83132,a855)),x83131),x83134)),x83134)
% 179.72/179.58 [8397]E(f323(f323(f179(x83971,x83972),x83973),x83974),f200(x83972))+P101(f323(f323(f325(x83971),x83974),f323(f302(f866(x83971,x83972),x83971,f257(x83971,x83972)),f323(f166(f866(x83971,x83972)),x83973))))
% 179.72/179.58 [8398]P38(x83981,x83982)+~P38(x83981,f323(f323(f301(f866(x83981,x83981)),f323(f323(f258(x83981,x83981),x83983),x83984)),x83982))
% 179.72/179.58 [8399]P54(x83991,x83992)+~P54(x83991,f323(f323(f301(f866(x83991,x83991)),f323(f323(f258(x83991,x83991),x83993),x83994)),x83992))
% 179.72/179.58 [8404]~P103(x84041)+E(f323(f323(f141(x84041,x84041,f5(x84041)),x84042),f323(f323(f141(x84041,x84041,f5(x84041)),x84043),x84044)),f323(f323(f141(x84041,x84041,f5(x84041)),x84043),f323(f323(f141(x84041,x84041,f5(x84041)),x84042),x84044)))
% 179.72/179.58 [8414]E(x84141,x84142)+~P101(f323(f60(x84143,x84144,f323(f323(f301(x84143),x84141),f188(f867(x84143,a855)))),x84142))
% 179.72/179.58 [8424]E(f323(f323(f121(x84241),f323(f323(f169(x84241),x84242),x84243)),f323(f323(f169(x84241),x84244),f323(f323(f131(x84241),x84242),x84243))),f323(f323(f169(x84241),f323(f323(f78(a860),x84242),x84244)),x84243))+~P101(f323(f323(f237(a860),f323(f323(f78(a860),x84242),x84244)),f323(f189(f861(x84241)),x84243)))
% 179.72/179.58 [8462]P101(f323(f59(x84621),x84622))+~E(x84622,f323(f302(a860,x84621,x84623),f323(f243(a860),f323(f323(f7(a860,a860,a855),f238(a860)),x84624))))
% 179.72/179.58 [8482]~P86(x84821)+E(f323(f135(x84821,x84821,f78(x84821),f323(f323(f78(x84821),x84822),x84823)),x84824),f323(f323(f78(x84821),x84822),f323(f135(x84821,x84821,f78(x84821),x84823),x84824)))
% 179.72/179.58 [8517]P101(f323(f323(f237(f867(x85171,a855)),f323(f256(x85171,x85172),x85173)),f323(f256(x85171,x85172),x85174)))+~P101(f323(f323(f237(f867(f866(x85171,x85172),a855)),x85173),x85174))
% 179.72/179.58 [8530]~P101(f323(f323(f237(a860),x85302),x85304))+P101(f323(f323(f237(f867(x85301,a855)),f323(f166(x85301),f323(f323(f169(x85301),x85302),x85303))),f323(f166(x85301),f323(f323(f169(x85301),x85304),x85303))))
% 179.72/179.58 [8531]~P101(f323(f323(f237(a860),x85314),x85312))+P101(f323(f323(f237(f867(x85311,a855)),f323(f166(x85311),f323(f323(f131(x85311),x85312),x85313))),f323(f166(x85311),f323(f323(f131(x85311),x85314),x85313))))
% 179.72/179.58 [8588]~P101(f323(f59(x85881),f323(f323(f22(f867(x85881,a855)),x85882),x85884)))+P101(f323(f59(x85881),f323(f323(f22(f867(x85881,a855)),x85882),f323(f323(f301(x85881),x85883),x85884))))
% 179.72/179.58 [8631]P101(f323(f323(f325(f866(x86311,x86311)),x86312),f299(x86311,x86313)))+~P101(f323(f323(f325(f866(x86311,x86311)),x86312),f323(f323(f183(f866(x86311,x86311),a855),x86314),x86313)))
% 179.72/179.58 [8717]~P101(f323(f59(x87171),f323(f323(f22(f867(x87171,a855)),x87172),f323(f323(f301(x87171),x87174),x87173))))+P101(f323(f59(x87171),f323(f323(f22(f867(x87171,a855)),x87172),x87173)))
% 179.72/179.58 [8867]~E(f323(f323(f179(x88671,x88672),x88673),x88674),f200(x88672))+~P101(f323(f323(f325(x88671),x88674),f323(f302(f866(x88671,x88672),x88671,f257(x88671,x88672)),f323(f166(f866(x88671,x88672)),x88673))))
% 179.72/179.58 [8927]~P2(x89271)+P101(f323(f323(f237(x89271),f323(f323(f110(x89271),x89272),f323(f323(f101(x89271),x89273),x89274))),f323(f323(f101(x89271),f323(f323(f110(x89271),x89272),x89273)),f323(f323(f110(x89271),x89272),x89274))))
% 179.72/179.58 [8928]~P103(x89281)+P101(f323(f323(f237(x89281),f323(f323(f236(x89281),x89282),f323(f323(f235(x89281),x89283),x89284))),f323(f323(f235(x89281),f323(f323(f236(x89281),x89282),x89283)),f323(f323(f236(x89281),x89282),x89284))))
% 179.72/179.58 [9076]E(x90761,x90762)+~P101(f323(f323(f325(f866(x90763,x90763)),f323(f323(f258(x90763,x90763),x90761),x90762)),f323(f166(f866(x90763,x90763)),f323(f323(f175(x90763,x90763),x90764),x90764))))
% 179.72/179.58 [9106]~P101(f323(f323(f325(f866(x91061,x91061)),f323(f323(f258(x91061,x91061),x91063),x91062)),f299(x91061,x91064)))+~P38(x91061,f323(f323(f301(f866(x91061,x91061)),f323(f323(f258(x91061,x91061),x91062),x91063)),x91064))
% 179.72/179.58 [9107]~P101(f323(f323(f325(f866(x91071,x91071)),f323(f323(f258(x91071,x91071),x91073),x91072)),f299(x91071,x91074)))+~P54(x91071,f323(f323(f301(f866(x91071,x91071)),f323(f323(f258(x91071,x91071),x91072),x91073)),x91074))
% 179.72/179.58 [9112]E(x91121,x91122)+E(f323(f129(x91123,f323(f323(f8(a855,a855,x91123),a318),f323(a320,x91121))),f323(f323(f144(x91123),x91122),x91124)),f323(f323(f144(x91123),x91122),f323(f129(x91123,f323(f323(f8(a855,a855,x91123),a318),f323(a320,x91121))),x91124)))
% 179.72/179.58 [9142]~P28(x91422,x91421,x91423,f246(f867(x91422,a855)),f246(f867(x91421,a855)))+E(f323(f302(x91421,x91422,f91(x91422,x91421,f246(f867(x91422,a855)),x91423)),x91424),f323(f303(x91422,x91421,x91423),x91424))
% 179.72/179.58 [9161]~P2(x91611)+P101(f323(f323(f237(x91611),f323(f323(f110(x91611),f323(f323(f101(x91611),x91612),x91613)),f323(f323(f101(x91611),x91612),x91614))),f323(f323(f101(x91611),x91612),f323(f323(f110(x91611),x91613),x91614))))
% 179.72/179.58 [9162]~P103(x91621)+P101(f323(f323(f237(x91621),f323(f323(f236(x91621),f323(f323(f235(x91621),x91622),x91623)),f323(f323(f235(x91621),x91622),x91624))),f323(f323(f235(x91621),x91622),f323(f323(f236(x91621),x91623),x91624))))
% 179.72/179.58 [9218]~P28(x92182,x92181,x92184,f246(f867(x92182,a855)),f246(f867(x92181,a855)))+E(f323(f243(x92181),f323(f323(f8(x92182,a855,x92181),x92183),f91(x92182,x92181,f246(f867(x92182,a855)),x92184))),f323(f302(x92182,x92181,x92184),f323(f243(x92182),x92183)))
% 179.72/179.58 [9231]~E(f323(f302(x92312,x92311,x92313),f246(f867(x92312,a855))),f246(f867(x92311,a855)))+P101(f323(f323(f237(f867(x92311,a855)),f323(f77(f867(x92311,a855)),f323(f302(x92312,x92311,x92313),x92314))),f323(f302(x92312,x92311,x92313),f323(f77(f867(x92312,a855)),x92314))))
% 179.72/179.58 [9552]P101(f323(f323(f325(f866(x95521,x95521)),f323(f323(f258(x95521,x95521),x95522),x95523)),f323(f278(x95521,x95521),f323(f323(f280(x95521,x95521,x95521),x95524),f299(x95521,x95524)))))+~P101(f323(f323(f325(f866(x95521,x95521)),f323(f323(f258(x95521,x95521),x95522),x95523)),f323(f323(f280(x95521,x95521,x95521),f323(f278(x95521,x95521),x95524)),f299(x95521,f323(f278(x95521,x95521),x95524)))))
% 179.72/179.58 [9553]~P101(f323(f323(f325(f866(x95531,x95531)),f323(f323(f258(x95531,x95531),x95532),x95533)),f323(f278(x95531,x95531),f323(f323(f280(x95531,x95531,x95531),x95534),f299(x95531,x95534)))))+P101(f323(f323(f325(f866(x95531,x95531)),f323(f323(f258(x95531,x95531),x95532),x95533)),f323(f323(f280(x95531,x95531,x95531),f323(f278(x95531,x95531),x95534)),f299(x95531,f323(f278(x95531,x95531),x95534)))))
% 179.72/179.58 [9574]~P101(f323(f323(f325(x95742),x95744),f323(f254(x95741,x95742),x95743)))+P101(f323(f323(f325(f866(x95741,x95742)),f323(f323(f258(x95741,x95742),f675(x95743,x95741,x95744,x95742)),x95744)),x95743))
% 179.72/179.58 [9575]~P101(f323(f323(f325(x95752),x95754),f323(f254(x95751,x95752),x95753)))+P101(f323(f323(f325(f866(x95751,x95752)),f323(f323(f258(x95751,x95752),f676(x95753,x95751,x95754,x95752)),x95754)),x95753))
% 179.72/179.58 [9600]~P101(f323(f323(f325(x96001),x96004),f323(f323(f110(f867(x96001,a855)),x96002),x96003)))+P101(f323(f323(f323(f110(f867(x96001,a855)),f323(f323(f7(x96001,f867(x96001,a855),a855),f325(x96001)),x96002)),f323(f323(f7(x96001,f867(x96001,a855),a855),f325(x96001)),x96003)),x96004))
% 179.72/179.58 [9601]~P101(f323(f323(f325(x96011),x96014),f323(f323(f101(f867(x96011,a855)),x96012),x96013)))+P101(f323(f323(f323(f101(f867(x96011,a855)),f323(f323(f7(x96011,f867(x96011,a855),a855),f325(x96011)),x96012)),f323(f323(f7(x96011,f867(x96011,a855),a855),f325(x96011)),x96013)),x96014))
% 179.72/179.58 [9679]~P101(f323(f323(f325(f866(x96791,x96791)),f323(f323(f258(x96791,x96791),x96794),x96793)),f323(f323(f280(x96791,x96791,x96791),x96792),f299(x96791,x96792))))+P101(f323(f323(f325(f866(x96791,x96791)),f323(f323(f258(x96791,x96791),f743(x96792,x96793,x96794,x96791)),x96793)),x96792))
% 179.72/179.58 [9724]P101(f323(f323(f325(x97241),x97242),f323(f323(f110(f867(x97241,a855)),x97243),x97244)))+~P101(f323(f323(f323(f110(f867(x97241,a855)),f323(f323(f7(x97241,f867(x97241,a855),a855),f325(x97241)),x97243)),f323(f323(f7(x97241,f867(x97241,a855),a855),f325(x97241)),x97244)),x97242))
% 179.72/179.58 [9725]P101(f323(f323(f325(x97251),x97252),f323(f323(f101(f867(x97251,a855)),x97253),x97254)))+~P101(f323(f323(f323(f101(f867(x97251,a855)),f323(f323(f7(x97251,f867(x97251,a855),a855),f325(x97251)),x97253)),f323(f323(f7(x97251,f867(x97251,a855),a855),f325(x97251)),x97254)),x97252))
% 179.72/179.58 [10001]P33(x100011,f323(f323(f7(x100011,f867(f866(x100011,x100011),a855),f867(x100011,a855)),f323(f323(f8(f867(x100011,f867(f867(f866(x100011,x100011),a855),a855)),f867(f867(f866(x100011,x100011),a855),f867(x100011,a855)),x100011),f7(x100011,f867(f866(x100011,x100011),a855),a855)),f323(f323(f8(f867(x100011,f866(x100011,x100011)),f867(x100011,f867(f867(f866(x100011,x100011),a855),a855)),x100011),f323(f8(f866(x100011,x100011),f867(f867(f866(x100011,x100011),a855),a855),x100011),f325(f866(x100011,x100011)))),f258(x100011,x100011)))),x100012),x100013,x100014)+~P101(f323(f323(f325(f866(f861(x100011),f861(x100011))),f323(f323(f258(f861(x100011),f861(x100011)),x100013),x100014)),f151(x100011,x100012)))
% 179.72/179.58 [10005]P55(x100051,f323(f323(f7(x100051,f867(f866(x100051,x100051),a855),f867(x100051,a855)),f323(f323(f8(f867(x100051,f867(f867(f866(x100051,x100051),a855),a855)),f867(f867(f866(x100051,x100051),a855),f867(x100051,a855)),x100051),f7(x100051,f867(f866(x100051,x100051),a855),a855)),f323(f323(f8(f867(x100051,f866(x100051,x100051)),f867(x100051,f867(f867(f866(x100051,x100051),a855),a855)),x100051),f323(f8(f866(x100051,x100051),f867(f867(f866(x100051,x100051),a855),a855),x100051),f325(f866(x100051,x100051)))),f258(x100051,x100051)))),x100052),x100053,x100054)+~P101(f323(f323(f325(f866(f867(x100051,a855),f867(x100051,a855))),f323(f323(f258(f867(x100051,a855),f867(x100051,a855)),x100053),x100054)),f314(x100051,x100052)))
% 179.72/179.58 [10034]E(x100341,x100342)+~E(f323(f323(f7(x100343,f867(f866(x100343,x100344),a855),f867(x100344,a855)),f323(f323(f8(f867(x100344,f867(f867(f866(x100343,x100344),a855),a855)),f867(f867(f866(x100343,x100344),a855),f867(x100344,a855)),x100343),f7(x100344,f867(f866(x100343,x100344),a855),a855)),f323(f323(f8(f867(x100344,f866(x100343,x100344)),f867(x100344,f867(f867(f866(x100343,x100344),a855),a855)),x100343),f323(f8(f866(x100343,x100344),f867(f867(f866(x100343,x100344),a855),a855),x100344),f325(f866(x100343,x100344)))),f258(x100343,x100344)))),x100341),f323(f323(f7(x100343,f867(f866(x100343,x100344),a855),f867(x100344,a855)),f323(f323(f8(f867(x100344,f867(f867(f866(x100343,x100344),a855),a855)),f867(f867(f866(x100343,x100344),a855),f867(x100344,a855)),x100343),f7(x100344,f867(f866(x100343,x100344),a855),a855)),f323(f323(f8(f867(x100344,f866(x100343,x100344)),f867(x100344,f867(f867(f866(x100343,x100344),a855),a855)),x100343),f323(f8(f866(x100343,x100344),f867(f867(f866(x100343,x100344),a855),a855),x100344),f325(f866(x100343,x100344)))),f258(x100343,x100344)))),x100342))
% 179.72/179.58 [10037]~P33(x100371,f323(f323(f7(x100371,f867(f866(x100371,x100371),a855),f867(x100371,a855)),f323(f323(f8(f867(x100371,f867(f867(f866(x100371,x100371),a855),a855)),f867(f867(f866(x100371,x100371),a855),f867(x100371,a855)),x100371),f7(x100371,f867(f866(x100371,x100371),a855),a855)),f323(f323(f8(f867(x100371,f866(x100371,x100371)),f867(x100371,f867(f867(f866(x100371,x100371),a855),a855)),x100371),f323(f8(f866(x100371,x100371),f867(f867(f866(x100371,x100371),a855),a855),x100371),f325(f866(x100371,x100371)))),f258(x100371,x100371)))),x100374),x100372,x100373)+P101(f323(f323(f325(f866(f861(x100371),f861(x100371))),f323(f323(f258(f861(x100371),f861(x100371)),x100372),x100373)),f151(x100371,x100374)))
% 179.72/179.58 [10038]~P55(x100381,f323(f323(f7(x100381,f867(f866(x100381,x100381),a855),f867(x100381,a855)),f323(f323(f8(f867(x100381,f867(f867(f866(x100381,x100381),a855),a855)),f867(f867(f866(x100381,x100381),a855),f867(x100381,a855)),x100381),f7(x100381,f867(f866(x100381,x100381),a855),a855)),f323(f323(f8(f867(x100381,f866(x100381,x100381)),f867(x100381,f867(f867(f866(x100381,x100381),a855),a855)),x100381),f323(f8(f866(x100381,x100381),f867(f867(f866(x100381,x100381),a855),a855),x100381),f325(f866(x100381,x100381)))),f258(x100381,x100381)))),x100384),x100382,x100383)+P101(f323(f323(f325(f866(f867(x100381,a855),f867(x100381,a855))),f323(f323(f258(f867(x100381,a855),f867(x100381,a855)),x100382),x100383)),f314(x100381,x100384)))
% 179.72/179.58 [7423]~P90(x74231)+E(f323(f323(f79(x74231),f323(f103(x74231),x74232)),f323(f323(f79(x74231),f323(f103(x74231),x74233)),x74234)),f323(f323(f79(x74231),f323(f103(x74231),f323(f323(f79(a1),x74232),x74233))),x74234))
% 179.72/179.58 [7424]~P90(x74241)+E(f323(f323(f78(x74241),f323(f103(x74241),x74242)),f323(f323(f22(x74241),f323(f103(x74241),x74243)),x74244)),f323(f323(f22(x74241),f323(f103(x74241),f323(f323(f78(a1),x74242),x74243))),x74244))
% 179.72/179.58 [7425]~P90(x74251)+E(f323(f323(f78(x74251),f323(f103(x74251),x74252)),f323(f323(f78(x74251),f323(f103(x74251),x74253)),x74254)),f323(f323(f78(x74251),f323(f103(x74251),f323(f323(f78(a1),x74252),x74253))),x74254))
% 179.72/179.58 [7469]~P140(x74691)+E(f323(f159(x74691),f323(f323(f147(x74692,x74691),f323(f16(x74691,x74692),x74693)),x74694)),f323(f323(f79(x74691),f323(f100(x74691),f323(f189(f861(x74692)),x74694))),x74693))
% 179.72/179.58 [7704]E(f323(f269(x77041,f323(f323(f144(f866(a99,x77041)),x77042),x77043)),x77044),f323(f261(a99,x77041),x77042))+~P101(f323(f323(f238(a99),x77044),f323(f257(a99,x77041),x77042)))
% 179.72/179.58 [7746]~P90(x77461)+E(f323(f323(f78(x77461),f323(f103(x77461),x77462)),f323(f323(f22(x77461),x77463),f323(f103(x77461),x77464))),f323(f323(f78(x77461),f323(f103(x77461),f323(f323(f78(a1),x77462),f323(f77(a1),x77464)))),x77463))
% 179.72/179.58 [7881]E(f323(f269(x78811,x78812),f323(f323(f22(a99),x78813),f323(f257(a99,x78811),x78814))),f323(f269(x78811,f323(f323(f144(f866(a99,x78811)),x78814),x78812)),x78813))+P101(f323(f323(f238(a99),x78813),f323(f257(a99,x78811),x78814)))
% 179.72/179.58 [8319]~P101(f323(f323(f325(x83191),x83192),f323(f166(x83191),f114(x83191,x83194))))+P101(f323(f323(f325(x83191),x83192),f323(f166(x83191),f114(x83191,f323(f323(f121(x83191),x83193),x83194)))))
% 179.72/179.58 [8320]~P101(f323(f323(f325(x83201),x83202),f323(f166(x83201),f114(x83201,x83203))))+P101(f323(f323(f325(x83201),x83202),f323(f166(x83201),f114(x83201,f323(f323(f121(x83201),x83203),x83204)))))
% 179.72/179.58 [8338]E(f323(f323(f110(f867(x83381,a855)),f323(f323(f101(f867(x83381,a855)),x83382),x83383)),x83384),f323(f323(f101(f867(x83381,a855)),x83382),f323(f323(f110(f867(x83381,a855)),x83383),x83384)))+~P101(f323(f323(f237(f867(x83381,a855)),x83384),x83382))
% 179.72/179.58 [8645]~E(f323(f323(f110(f867(x86451,a855)),f323(f323(f101(f867(x86451,a855)),x86453),x86454)),x86452),f323(f323(f101(f867(x86451,a855)),x86453),f323(f323(f110(f867(x86451,a855)),x86454),x86452)))+P101(f323(f323(f237(f867(x86451,a855)),x86452),x86453))
% 179.72/179.58 [8932]~P101(f323(f323(f237(f867(x89321,a855)),x89322),f323(f323(f110(f867(x89321,a855)),x89323),x89324)))+P101(f323(f323(f237(f867(x89321,a855)),f323(f323(f22(f867(x89321,a855)),x89322),x89323)),x89324))
% 179.72/179.58 [9050]~E(f323(f302(x90501,x90502,x90503),f246(f867(x90501,a855))),f246(f867(x90502,a855)))+E(f323(f302(x90501,x90502,x90503),f323(f302(x90502,x90501,f91(x90501,x90502,f246(f867(x90501,a855)),x90503)),x90504)),x90504)
% 179.72/179.58 [9055]P101(f323(f323(f237(f867(x90551,a855)),x90552),f323(f323(f110(f867(x90551,a855)),x90553),x90554)))+~P101(f323(f323(f237(f867(x90551,a855)),f323(f323(f22(f867(x90551,a855)),x90552),x90553)),x90554))
% 179.72/179.58 [9138]~P82(x91381)+E(f323(f73(x91381),f323(f323(f6(x91382,x91381),f323(f323(f8(x91381,x91381,x91382),f73(x91381)),x91383)),x91384)),f323(f323(f6(x91382,x91381),f323(f323(f8(x91381,x91381,x91382),f73(x91381)),x91383)),x91384))
% 179.72/179.58 [9306]~P82(x93061)+P101(f323(f323(f237(x93061),f2(x93061)),f323(f323(f6(x93062,x93061),f323(f323(f8(x93061,x93061,x93062),f73(x93061)),x93063)),x93064)))
% 179.72/179.58 [9310]~P60(x93101)+E(f323(f159(x93101),f323(f323(f147(x93102,x93101),f323(f71(x93101,x93101,x93102,f77(x93101)),x93103)),x93104)),f323(f77(x93101),f323(f159(x93101),f323(f323(f147(x93102,x93101),x93103),x93104))))
% 179.72/179.58 [9446]~P82(x94461)+P101(f323(f323(f237(x94461),f323(f73(x94461),f323(f323(f6(x94462,x94461),x94463),x94464))),f323(f323(f6(x94462,x94461),f323(f323(f8(x94461,x94461,x94462),f73(x94461)),x94463)),x94464)))
% 179.72/179.58 [9475]~E(f323(f323(f78(a860),x94751),x94754),f323(f323(f78(a860),x94753),x94752))+P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),f323(f323(f258(a860,a860),x94751),x94752)),f323(f323(f258(a860,a860),x94753),x94754))),a108))
% 179.72/179.58 [9476]~P101(f323(f323(f238(a860),x94761),x94763))+P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),f323(f323(f258(a860,a860),x94761),x94762)),f323(f323(f258(a860,a860),x94763),x94764))),a33))
% 179.72/179.58 [9477]~P101(f323(f323(f238(a860),x94771),x94773))+P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),f323(f323(f258(a860,a860),x94771),x94772)),f323(f323(f258(a860,a860),x94773),x94774))),a68))
% 179.72/179.58 [9625]E(f323(f323(f78(a860),x96251),x96252),f323(f323(f78(a860),x96253),x96254))+~P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),f323(f323(f258(a860,a860),x96251),x96254)),f323(f323(f258(a860,a860),x96253),x96252))),a108))
% 179.72/179.58 [9653]E(f323(f323(f158(x96531),f323(f323(f131(x96531),f323(f189(f861(x96531)),f171(x96531,x96532,x96533))),x96533)),x96534),f323(f323(f158(x96531),x96533),f323(f323(f78(a860),x96534),f323(f189(f861(x96531)),f171(x96531,x96532,x96533)))))+~P101(f323(f323(f238(a860),x96534),f323(f189(f861(x96531)),f323(f323(f131(x96531),f323(f189(f861(x96531)),f171(x96531,x96532,x96533))),x96533))))
% 179.72/179.58 [9670]~P101(f323(f323(f325(x96702),x96704),f323(f323(f39(x96701,f867(x96702,a855)),f246(f867(x96701,a855))),x96703)))+P101(f323(f323(f323(f39(x96701,f867(x96702,a855)),f246(f867(x96701,a855))),f323(f323(f8(f867(x96702,a855),f867(x96702,a855),x96701),f323(f7(x96702,f867(x96702,a855),a855),f325(x96702))),x96703)),x96704))
% 179.72/179.58 [9671]~P101(f323(f323(f325(x96712),x96714),f323(f323(f40(x96711,f867(x96712,a855)),f246(f867(x96711,a855))),x96713)))+P101(f323(f323(f323(f40(x96711,f867(x96712,a855)),f246(f867(x96711,a855))),f323(f323(f8(f867(x96712,a855),f867(x96712,a855),x96711),f323(f7(x96712,f867(x96712,a855),a855),f325(x96712))),x96713)),x96714))
% 179.72/179.58 [9752]~P101(f323(f46(x97521,x97522),f323(f323(f258(a1,a1),x97524),x97523)))+P101(f323(f46(f323(f77(a1),x97521),x97522),f323(f323(f258(a1,a1),f323(f323(f323(f96(a1),f323(f323(a320,x97523),f2(a1))),f323(f77(a1),x97524)),f323(f323(f22(a1),f323(f77(a1),x97524)),f76(a1)))),f323(f323(f323(f96(a1),f323(f323(a320,x97523),f2(a1))),f2(a1)),f323(f323(f22(a1),x97522),x97523)))))
% 179.72/179.58 [9761]P101(f323(f323(f325(x97611),x97612),f323(f323(f39(x97613,f867(x97611,a855)),f246(f867(x97613,a855))),x97614)))+~P101(f323(f323(f323(f39(x97613,f867(x97611,a855)),f246(f867(x97613,a855))),f323(f323(f8(f867(x97611,a855),f867(x97611,a855),x97613),f323(f7(x97611,f867(x97611,a855),a855),f325(x97611))),x97614)),x97612))
% 179.72/179.58 [9762]P101(f323(f323(f325(x97621),x97622),f323(f323(f40(x97623,f867(x97621,a855)),f246(f867(x97623,a855))),x97624)))+~P101(f323(f323(f323(f40(x97623,f867(x97621,a855)),f246(f867(x97623,a855))),f323(f323(f8(f867(x97621,a855),f867(x97621,a855),x97623),f323(f7(x97621,f867(x97621,a855),a855),f325(x97621))),x97624)),x97622))
% 179.72/179.58 [9774]E(f323(f323(f39(a860,f867(x97741,a855)),f246(f867(a860,a855))),x97742),f323(f323(f39(a860,f867(x97741,a855)),f246(f867(a860,a855))),x97743))+~E(f323(f323(f39(a860,f867(x97741,a855)),f323(f293(a860,f2(a860)),f458(x97742,x97744,x97743,x97741))),x97743),f323(f323(f39(a860,f867(x97741,a855)),f323(f293(a860,f2(a860)),f323(f323(f78(a860),f458(x97742,x97744,x97743,x97741)),x97744))),x97742))
% 179.72/179.58 [10094]~P101(f323(f323(f237(f867(f866(x100941,x100942),a855)),x100943),x100944))+P101(f323(f323(f237(f867(x100941,f867(x100942,a855))),f323(f323(f7(x100941,f867(f866(x100941,x100942),a855),f867(x100942,a855)),f323(f323(f8(f867(x100942,f867(f867(f866(x100941,x100942),a855),a855)),f867(f867(f866(x100941,x100942),a855),f867(x100942,a855)),x100941),f7(x100942,f867(f866(x100941,x100942),a855),a855)),f323(f323(f8(f867(x100942,f866(x100941,x100942)),f867(x100942,f867(f867(f866(x100941,x100942),a855),a855)),x100941),f323(f8(f866(x100941,x100942),f867(f867(f866(x100941,x100942),a855),a855),x100942),f325(f866(x100941,x100942)))),f258(x100941,x100942)))),x100943)),f323(f323(f7(x100941,f867(f866(x100941,x100942),a855),f867(x100942,a855)),f323(f323(f8(f867(x100942,f867(f867(f866(x100941,x100942),a855),a855)),f867(f867(f866(x100941,x100942),a855),f867(x100942,a855)),x100941),f7(x100942,f867(f866(x100941,x100942),a855),a855)),f323(f323(f8(f867(x100942,f866(x100941,x100942)),f867(x100942,f867(f867(f866(x100941,x100942),a855),a855)),x100941),f323(f8(f866(x100941,x100942),f867(f867(f866(x100941,x100942),a855),a855),x100942),f325(f866(x100941,x100942)))),f258(x100941,x100942)))),x100944)))
% 179.72/179.58 [10111]P101(f323(f323(f237(f867(f866(x101111,x101112),a855)),x101113),x101114))+~P101(f323(f323(f237(f867(x101111,f867(x101112,a855))),f323(f323(f7(x101111,f867(f866(x101111,x101112),a855),f867(x101112,a855)),f323(f323(f8(f867(x101112,f867(f867(f866(x101111,x101112),a855),a855)),f867(f867(f866(x101111,x101112),a855),f867(x101112,a855)),x101111),f7(x101112,f867(f866(x101111,x101112),a855),a855)),f323(f323(f8(f867(x101112,f866(x101111,x101112)),f867(x101112,f867(f867(f866(x101111,x101112),a855),a855)),x101111),f323(f8(f866(x101111,x101112),f867(f867(f866(x101111,x101112),a855),a855),x101112),f325(f866(x101111,x101112)))),f258(x101111,x101112)))),x101113)),f323(f323(f7(x101111,f867(f866(x101111,x101112),a855),f867(x101112,a855)),f323(f323(f8(f867(x101112,f867(f867(f866(x101111,x101112),a855),a855)),f867(f867(f866(x101111,x101112),a855),f867(x101112,a855)),x101111),f7(x101112,f867(f866(x101111,x101112),a855),a855)),f323(f323(f8(f867(x101112,f866(x101111,x101112)),f867(x101112,f867(f867(f866(x101111,x101112),a855),a855)),x101111),f323(f8(f866(x101111,x101112),f867(f867(f866(x101111,x101112),a855),a855),x101112),f325(f866(x101111,x101112)))),f258(x101111,x101112)))),x101114)))
% 179.72/179.58 [9185]~P101(f323(f323(f325(f866(x91851,x91851)),x91852),f299(x91851,x91854)))+P101(f323(f323(f325(f866(x91851,x91851)),x91852),f299(x91851,f323(f323(f110(f867(f866(x91851,x91851),a855)),x91853),x91854))))
% 179.72/179.58 [9186]~P101(f323(f323(f325(f866(x91861,x91861)),x91862),f299(x91861,x91863)))+P101(f323(f323(f325(f866(x91861,x91861)),x91862),f299(x91861,f323(f323(f110(f867(f866(x91861,x91861),a855)),x91863),x91864))))
% 179.72/179.58 [9543]~E(f323(f166(x95431),x95434),f177(x95431,x95432,x95433))+E(f323(f179(x95431,x95432),f323(f323(f147(x95431,f866(x95431,x95432)),f323(f323(f18(x95431,x95432,f866(x95431,x95432)),f258(x95431,x95432)),f323(f323(f8(f864(x95432),x95432,x95431),f234(x95432)),x95433))),x95434)),x95433)
% 179.72/179.58 [9867]~P101(f323(f323(f237(a860),f323(f323(f78(a860),x98671),x98674)),f323(f323(f78(a860),x98673),x98672)))+P101(f323(f323(f237(a1),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x98671),x98672)),f188(f867(f866(a860,a860),a855)))))),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x98673),x98674)),f188(f867(f866(a860,a860),a855)))))))
% 179.72/179.58 [9868]~P101(f323(f323(f238(a860),f323(f323(f78(a860),x98681),x98684)),f323(f323(f78(a860),x98683),x98682)))+P101(f323(f323(f238(a1),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x98681),x98682)),f188(f867(f866(a860,a860),a855)))))),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x98683),x98684)),f188(f867(f866(a860,a860),a855)))))))
% 179.72/179.58 [9945]P101(f323(f323(f237(a860),f323(f323(f78(a860),x99451),x99452)),f323(f323(f78(a860),x99453),x99454)))+~P101(f323(f323(f237(a1),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x99451),x99454)),f188(f867(f866(a860,a860),a855)))))),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x99453),x99452)),f188(f867(f866(a860,a860),a855)))))))
% 179.72/179.58 [9946]P101(f323(f323(f238(a860),f323(f323(f78(a860),x99461),x99462)),f323(f323(f78(a860),x99463),x99464)))+~P101(f323(f323(f238(a1),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x99461),x99464)),f188(f867(f866(a860,a860),a855)))))),f323(a87,f323(f277(f866(a860,a860),f866(a860,a860),a108),f323(f323(f301(f866(a860,a860)),f323(f323(f258(a860,a860),x99463),x99462)),f188(f867(f866(a860,a860),a855)))))))
% 179.72/179.58 [9987]P101(f323(f323(f237(f867(x99871,a855)),f323(f323(f39(a860,f867(x99871,a855)),f246(f867(a860,a855))),x99872)),f323(f323(f39(a860,f867(x99871,a855)),f246(f867(a860,a855))),x99873)))+~P101(f323(f323(f237(f867(x99871,a855)),f323(f323(f39(a860,f867(x99871,a855)),f323(f293(a860,f2(a860)),f459(x99873,x99874,x99872,x99871))),x99872)),f323(f323(f39(a860,f867(x99871,a855)),f323(f293(a860,f2(a860)),f323(f323(f78(a860),f459(x99873,x99874,x99872,x99871)),x99874))),x99873)))
% 179.72/179.58 [10084]~P101(f323(f323(f325(x100842),x100844),f323(f254(x100841,x100842),x100843)))+P101(f323(f253(x100841,x100842,f323(f323(f7(x100841,f867(f866(x100841,x100842),a855),f867(x100842,a855)),f323(f323(f8(f867(x100842,f867(f867(f866(x100841,x100842),a855),a855)),f867(f867(f866(x100841,x100842),a855),f867(x100842,a855)),x100841),f7(x100842,f867(f866(x100841,x100842),a855),a855)),f323(f323(f8(f867(x100842,f866(x100841,x100842)),f867(x100842,f867(f867(f866(x100841,x100842),a855),a855)),x100841),f323(f8(f866(x100841,x100842),f867(f867(f866(x100841,x100842),a855),a855),x100842),f325(f866(x100841,x100842)))),f258(x100841,x100842)))),x100843)),x100844))
% 179.72/179.58 [10085]~P101(f323(f323(f325(x100851),x100854),f323(f256(x100851,x100852),x100853)))+P101(f323(f252(x100851,x100852,f323(f323(f7(x100851,f867(f866(x100851,x100852),a855),f867(x100852,a855)),f323(f323(f8(f867(x100852,f867(f867(f866(x100851,x100852),a855),a855)),f867(f867(f866(x100851,x100852),a855),f867(x100852,a855)),x100851),f7(x100852,f867(f866(x100851,x100852),a855),a855)),f323(f323(f8(f867(x100852,f866(x100851,x100852)),f867(x100852,f867(f867(f866(x100851,x100852),a855),a855)),x100851),f323(f8(f866(x100851,x100852),f867(f867(f866(x100851,x100852),a855),a855),x100852),f325(f866(x100851,x100852)))),f258(x100851,x100852)))),x100853)),x100854))
% 179.72/179.58 [10097]P101(f323(f323(f325(x100971),x100972),f323(f254(x100973,x100971),x100974)))+~P101(f323(f253(x100973,x100971,f323(f323(f7(x100973,f867(f866(x100973,x100971),a855),f867(x100971,a855)),f323(f323(f8(f867(x100971,f867(f867(f866(x100973,x100971),a855),a855)),f867(f867(f866(x100973,x100971),a855),f867(x100971,a855)),x100973),f7(x100971,f867(f866(x100973,x100971),a855),a855)),f323(f323(f8(f867(x100971,f866(x100973,x100971)),f867(x100971,f867(f867(f866(x100973,x100971),a855),a855)),x100973),f323(f8(f866(x100973,x100971),f867(f867(f866(x100973,x100971),a855),a855),x100971),f325(f866(x100973,x100971)))),f258(x100973,x100971)))),x100974)),x100972))
% 179.72/179.58 [10098]P101(f323(f323(f325(x100981),x100982),f323(f256(x100981,x100983),x100984)))+~P101(f323(f252(x100981,x100983,f323(f323(f7(x100981,f867(f866(x100981,x100983),a855),f867(x100983,a855)),f323(f323(f8(f867(x100983,f867(f867(f866(x100981,x100983),a855),a855)),f867(f867(f866(x100981,x100983),a855),f867(x100983,a855)),x100981),f7(x100983,f867(f866(x100981,x100983),a855),a855)),f323(f323(f8(f867(x100983,f866(x100981,x100983)),f867(x100983,f867(f867(f866(x100981,x100983),a855),a855)),x100981),f323(f8(f866(x100981,x100983),f867(f867(f866(x100981,x100983),a855),a855),x100983),f325(f866(x100981,x100983)))),f258(x100981,x100983)))),x100984)),x100982))
% 179.72/179.58 [9785]P101(f323(f153(x97851,x97852),x97853))+~P101(f323(f153(x97851,f323(f323(f18(x97851,a855,a855),f323(f323(f8(a855,f867(a855,a855),x97851),a321),x97854)),x97852)),x97853))
% 179.72/179.58 [9786]P101(f323(f153(x97861,x97862),x97863))+~P101(f323(f153(x97861,f323(f323(f18(x97861,a855,a855),f323(f323(f8(a855,f867(a855,a855),x97861),a321),x97862)),x97864)),x97863))
% 179.72/179.58 [9869]~P112(x98691)+E(f323(f323(f79(x98691),f323(f323(f78(x98691),f76(x98691)),f76(x98691))),f323(f323(f6(a860,x98691),f323(f323(f8(x98691,x98691,a860),f323(f78(x98691),x98692)),f323(f323(f7(a860,x98691,x98691),f323(f323(f8(x98691,f867(x98691,x98691),a860),f79(x98691)),f100(x98691))),x98693))),f323(f244(a860),x98694))),f323(f323(f79(x98691),f323(f100(x98691),x98694)),f323(f323(f78(x98691),x98692),f323(f323(f78(x98691),x98692),f323(f323(f79(x98691),f323(f100(x98691),f323(f323(f22(a860),x98694),f76(a860)))),x98693)))))
% 179.72/179.58 [10008]P101(f323(x100081,f668(x100082,x100083,x100084,x100081)))+P38(x100082,f323(f243(f866(x100082,x100082)),f323(f262(x100082,x100082,a855),f323(f323(f8(f867(x100082,a855),f867(x100082,a855),x100082),f323(f18(x100082,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100082),a321),x100081))),f323(f323(f7(x100082,f867(x100082,x100082),f867(x100082,a855)),f323(f323(f8(f867(x100082,a855),f867(f867(x100082,x100082),f867(x100082,a855)),x100082),f8(x100082,a855,x100082)),a320)),x100083)))))
% 179.72/179.58 [10022]~P101(f323(f323(f238(a860),f323(x100224,f323(x100223,f668(x100221,x100223,x100224,x100222)))),f323(x100224,f668(x100221,x100223,x100224,x100222))))+P38(x100221,f323(f243(f866(x100221,x100221)),f323(f262(x100221,x100221,a855),f323(f323(f8(f867(x100221,a855),f867(x100221,a855),x100221),f323(f18(x100221,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100221),a321),x100222))),f323(f323(f7(x100221,f867(x100221,x100221),f867(x100221,a855)),f323(f323(f8(f867(x100221,a855),f867(f867(x100221,x100221),f867(x100221,a855)),x100221),f8(x100221,a855,x100221)),a320)),x100223)))))
% 179.72/179.58 [10123]~P101(f323(f323(f325(f866(x101231,x101231)),f323(f323(f258(x101231,x101231),x101233),x101234)),f323(f323(f110(f867(f866(x101231,x101231),a855)),x101232),f299(x101231,f188(f867(f866(x101231,x101231),a855))))))+P101(f323(f323(f323(f323(f110(f867(x101231,f867(x101231,a855))),f323(f323(f7(x101231,f867(f866(x101231,x101231),a855),f867(x101231,a855)),f323(f323(f8(f867(x101231,f867(f867(f866(x101231,x101231),a855),a855)),f867(f867(f866(x101231,x101231),a855),f867(x101231,a855)),x101231),f7(x101231,f867(f866(x101231,x101231),a855),a855)),f323(f323(f8(f867(x101231,f866(x101231,x101231)),f867(x101231,f867(f867(f866(x101231,x101231),a855),a855)),x101231),f323(f8(f866(x101231,x101231),f867(f867(f866(x101231,x101231),a855),a855),x101231),f325(f866(x101231,x101231)))),f258(x101231,x101231)))),x101232)),a320),x101233),x101234))
% 179.72/179.58 [10131]P101(f323(f323(f325(f866(x101311,x101311)),f323(f323(f258(x101311,x101311),x101312),x101313)),f323(f323(f110(f867(f866(x101311,x101311),a855)),x101314),f299(x101311,f188(f867(f866(x101311,x101311),a855))))))+~P101(f323(f323(f323(f323(f110(f867(x101311,f867(x101311,a855))),f323(f323(f7(x101311,f867(f866(x101311,x101311),a855),f867(x101311,a855)),f323(f323(f8(f867(x101311,f867(f867(f866(x101311,x101311),a855),a855)),f867(f867(f866(x101311,x101311),a855),f867(x101311,a855)),x101311),f7(x101311,f867(f866(x101311,x101311),a855),a855)),f323(f323(f8(f867(x101311,f866(x101311,x101311)),f867(x101311,f867(f867(f866(x101311,x101311),a855),a855)),x101311),f323(f8(f866(x101311,x101311),f867(f867(f866(x101311,x101311),a855),a855),x101311),f325(f866(x101311,x101311)))),f258(x101311,x101311)))),x101314)),a320),x101312),x101313))
% 179.72/179.58 [10081]E(f323(f323(f144(f861(x100811)),f323(f323(f144(x100811),x100812),f323(f135(f861(x100811),f861(x100811),f121(x100811),f113(x100811)),f323(f323(f147(f861(x100811),f861(x100811)),f149(f861(x100811),x100811,f113(x100811),f323(f323(f8(f861(x100811),f867(f861(x100811),f861(x100811)),x100811),f16(f861(x100811),f861(x100811))),f323(f323(f7(x100811,f861(x100811),f861(x100811)),f144(x100811)),f113(x100811))))),x100813)))),f173(x100811,f323(f323(f144(f861(x100811)),x100814),f323(f135(f861(f861(x100811)),f861(f861(x100811)),f121(f861(x100811)),f113(f861(x100811))),f323(f323(f147(f861(x100811),f861(f861(x100811))),f149(f861(f861(x100811)),x100811,f113(f861(x100811)),f323(f16(f867(f861(x100811),f861(f861(x100811))),x100811),f323(f323(f7(f861(x100811),f861(f861(x100811)),f861(f861(x100811))),f144(f861(x100811))),f113(f861(x100811)))))),x100813))))),f173(x100811,f323(f323(f144(f861(x100811)),f323(f323(f144(x100811),x100812),x100814)),x100813)))+~P101(f323(f311(f861(f861(x100811)),f174(x100811)),f323(f323(f144(f861(x100811)),f323(f323(f144(x100811),x100812),x100814)),x100813)))
% 179.72/179.58 [10122]~P101(f323(f59(x101222),f323(f243(x101222),x101224)))+P101(f323(f59(x101221),f323(f243(x101221),f323(f323(f8(f867(x101222,a855),a855,x101221),f85(x101222)),f323(f323(f7(x101221,f867(x101222,a855),f867(x101222,a855)),f323(f323(f8(f867(x101222,f867(a855,a855)),f867(f867(x101222,a855),f867(x101222,a855)),x101221),f18(x101222,a855,a855)),f323(f323(f8(f867(x101222,a855),f867(x101222,f867(a855,a855)),x101221),f323(f8(a855,f867(a855,a855),x101222),a321)),f323(f323(f7(x101221,f867(x101222,x101221),f867(x101222,a855)),f323(f323(f8(f867(x101221,a855),f867(f867(x101222,x101221),f867(x101222,a855)),x101221),f8(x101221,a855,x101222)),a320)),x101223)))),x101224)))))
% 179.72/179.58 [8683]P27(x86831,x86832,x86833,x86834)+~P28(x86831,x86832,x86833,x86834,x86835)
% 179.72/179.58 [5241]E(x52411,x52412)+~E(f123(x52413,x52414,x52411),f123(x52413,x52415,x52412))
% 179.72/179.58 [5242]E(x52421,x52422)+~E(f123(x52423,x52421,x52424),f123(x52423,x52422,x52425))
% 179.72/179.58 [5243]E(x52431,x52432)+~E(f163(x52433,x52431,x52434),f163(x52433,x52432,x52435))
% 179.72/179.58 [9159]~P28(x91592,x91591,x91594,x91593,x91595)+P28(x91591,x91592,f75(x91592,x91591,x91593,x91594),x91595,x91593)
% 179.72/179.58 [9160]~P28(x91602,x91601,x91604,x91603,x91605)+P28(x91601,x91602,f91(x91602,x91601,x91603,x91604),x91605,x91603)
% 179.72/179.58 [5619]E(f323(f323(f301(x56191),x56192),f177(x56191,x56193,x56194)),f177(x56191,x56193,x56194))+~E(f323(x56194,x56192),f323(f230(x56193),x56195))
% 179.72/179.58 [6019]P101(f323(f253(x60191,x60192,x60193),x60194))+~P101(f323(f323(x60193,x60195),x60194))
% 179.72/179.58 [6021]P101(f323(f252(x60211,x60212,x60213),x60214))+~P101(f323(f323(x60213,x60214),x60215))
% 179.72/179.58 [6024]~E(f323(x60244,x60242),f323(f230(x60243),x60245))+P101(f323(f323(f325(x60241),x60242),f177(x60241,x60243,x60244)))
% 179.72/179.58 [6025]~E(f323(x60254,x60255),f323(f230(x60251),x60252))+P101(f323(f323(f325(x60251),x60252),f178(x60253,x60251,x60254)))
% 179.72/179.58 [6481]~E(x64815,f2(a99))+E(f323(f197(x64811,x64812,x64813,x64814),x64815),f124(x64812))
% 179.72/179.58 [6482]~E(x64825,f2(a99))+E(f323(f199(x64821,x64822,x64823,x64824),x64825),f115(x64822))
% 179.72/179.58 [6617]~E(x66173,f2(a99))+E(f323(f272(x66171,x66172,x66173,x66174),x66175),f323(f258(x66171,x66172),x66175))
% 179.72/179.58 [6688]~E(f323(x66884,x66885),f200(x66882))+E(f323(f232(f864(x66881),x66882,f200(x66881),x66883),f323(x66884,x66885)),f200(x66881))
% 179.72/179.58 [7305]E(f323(x73051,x73052),f200(x73053))+~E(f323(f180(x73054,x73053,x73055,x73051),x73052),f200(x73053))
% 179.72/179.58 [7306]E(f323(x73061,x73062),f200(x73063))+~E(f323(f180(x73064,x73063,x73061,x73065),x73062),f200(x73063))
% 179.72/179.58 [7342]E(f323(f180(x73421,x73422,x73423,x73424),x73425),f323(x73423,x73425))+P101(f323(f323(f325(x73421),x73425),f177(x73421,x73422,x73424)))
% 179.72/179.58 [7343]E(f323(f180(x73431,x73432,x73433,x73434),x73435),f323(x73434,x73435))+P101(f323(f323(f325(x73431),x73435),f177(x73431,x73432,x73433)))
% 179.72/179.58 [7662]~P22(x76624,x76621,x76622,x76625)+E(f323(f71(x76621,x76621,x76621,f323(x76622,x76623)),f323(x76622,x76623)),f323(x76622,x76623))
% 179.72/179.58 [7706]E(f323(f180(x77061,x77062,x77063,x77064),x77065),f323(x77064,x77065))+~P101(f323(f323(f325(x77061),x77065),f177(x77061,x77062,x77064)))
% 179.72/179.58 [8049]~P18(x80495,x80491,x80492)+E(f323(f71(x80491,x80491,x80491,f323(x80492,x80493)),f323(x80492,x80494)),f323(f71(x80491,x80491,x80491,f323(x80492,x80494)),f323(x80492,x80493)))
% 179.72/179.58 [8380]P101(f323(f323(f325(f866(x83801,x83801)),f323(f323(f258(x83801,x83801),x83802),x83803)),f317(x83801,x83804,x83805)))+~P101(f323(f323(f238(a860),f323(x83804,x83802)),f323(x83804,x83803)))
% 179.72/179.58 [8468]~P101(f323(f323(f325(x84684),x84683),f290(x84684,x84681,x84682,x84685)))+P101(f323(f323(x84681,x84682),x84683))
% 179.72/179.58 [8469]~P101(f323(f323(f325(x84694),x84693),f287(x84694,x84691,x84692,x84695)))+P101(f323(f323(x84691,x84692),x84693))
% 179.72/179.58 [8470]~P101(f323(f323(f325(x84704),x84702),f290(x84704,x84701,x84705,x84703)))+P101(f323(f323(x84701,x84702),x84703))
% 179.72/179.58 [8471]~P101(f323(f323(f325(x84714),x84712),f287(x84714,x84711,x84715,x84713)))+P101(f323(f323(x84711,x84712),x84713))
% 179.72/179.58 [8552]~P28(x85521,x85523,x85525,x85522,x85524)+E(f323(f35(x85521),x85522),f323(f35(x85523),x85524))
% 179.72/179.58 [8600]~P28(x86001,x86002,x86003,x86004,x86005)+E(f323(f302(x86001,x86002,x86003),x86004),x86005)
% 179.72/179.58 [8621]~P53(x86212,x86211,x86215,x86213,x86214)+E(f323(f302(x86211,x86212,x86213),x86214),f246(f867(x86212,a855)))
% 179.72/179.58 [9066]~P35(x90661,x90662,x90663,x90664,x90665)+P35(x90661,x90662,x90663,f323(f162(x90661),x90664),f323(f162(x90662),x90665))
% 179.72/179.58 [9068]~P35(x90681,x90682,x90683,f323(f162(x90681),x90684),x90685)+P35(x90681,x90682,x90683,x90684,f323(f162(x90682),x90685))
% 179.72/179.58 [9069]~P35(x90691,x90692,x90693,x90694,f323(f162(x90692),x90695))+P35(x90691,x90692,x90693,f323(f162(x90691),x90694),x90695)
% 179.72/179.58 [9075]P35(x90751,x90752,x90753,x90754,x90755)+~P35(x90751,x90752,x90753,f323(f162(x90751),x90754),f323(f162(x90752),x90755))
% 179.72/179.58 [9466]P101(f323(f323(f325(f866(f861(x94661),f861(x94661))),f323(f323(f258(f861(x94661),f861(x94661)),f323(f323(f144(x94661),x94662),x94663)),f323(f323(f144(x94661),x94662),x94664))),f150(x94661,x94665)))+~P101(f323(f323(f325(f866(f861(x94661),f861(x94661))),f323(f323(f258(f861(x94661),f861(x94661)),x94663),x94664)),f150(x94661,x94665)))
% 179.72/179.58 [9467]P101(f323(f323(f325(f866(f861(x94671),f861(x94671))),f323(f323(f258(f861(x94671),f861(x94671)),f323(f323(f121(x94671),x94672),x94673)),f323(f323(f121(x94671),x94672),x94674))),f140(x94671,x94675)))+~P101(f323(f323(f325(f866(f861(x94671),f861(x94671))),f323(f323(f258(f861(x94671),f861(x94671)),x94673),x94674)),f140(x94671,x94675)))
% 179.72/179.58 [9660]E(f323(f323(f144(x96601),f574(x96602,x96603,x96604,x96605,x96601)),f576(x96602,x96603,x96604,x96605,x96601)),x96605)+~P101(f323(f323(f325(f866(f861(x96601),f861(x96601))),f323(f323(f258(f861(x96601),f861(x96601)),x96605),f323(f323(f144(x96601),x96604),x96603))),f151(x96601,x96602)))
% 179.72/179.58 [9682]E(f323(f323(f144(x96821),f577(x96822,x96823,x96824,x96825,x96821)),f578(x96822,x96823,x96824,x96825,x96821)),x96823)+~P101(f323(f323(f325(f866(f861(x96821),f861(x96821))),f323(f323(f258(f861(x96821),f861(x96821)),f323(f323(f144(x96821),x96825),x96824)),x96823)),f151(x96821,x96822)))
% 179.72/179.58 [9843]~P101(f323(f323(f325(f866(f861(x98431),f861(x98431))),f323(f323(f258(f861(x98431),f861(x98431)),f323(f323(f144(x98431),x98435),x98432)),x98434)),f151(x98431,x98433)))+P101(f323(f323(f325(f866(f861(x98431),f861(x98431))),f323(f323(f258(f861(x98431),f861(x98431)),x98432),f578(x98433,x98434,x98432,x98435,x98431))),f151(x98431,x98433)))
% 179.72/179.58 [9913]~P101(f323(f323(f325(f866(f861(x99131),f861(x99131))),f323(f323(f258(f861(x99131),f861(x99131)),x99135),f323(f323(f144(x99131),x99134),x99133))),f151(x99131,x99132)))+P101(f323(f323(f325(f866(f861(x99131),f861(x99131))),f323(f323(f258(f861(x99131),f861(x99131)),f576(x99132,x99133,x99134,x99135,x99131)),x99133)),f151(x99131,x99132)))
% 179.72/179.58 [10076]P101(f323(f323(f325(f866(x100761,x100761)),f323(f323(f258(x100761,x100761),f323(x100762,f323(f323(f78(a860),x100763),x100764))),f323(x100762,x100763))),f299(x100761,x100765)))+~P101(f323(f323(f325(f866(x100761,x100761)),f323(f323(f258(x100761,x100761),f323(x100762,f323(a112,f725(x100764,x100763,x100765,x100762,x100761)))),f323(x100762,f725(x100764,x100763,x100765,x100762,x100761)))),f299(x100761,x100765)))
% 179.72/179.58 [5207]E(x52071,x52072)+~E(f323(f323(f144(x52073),x52074),x52071),f323(f323(f144(x52073),x52075),x52072))
% 179.72/179.58 [5208]E(x52081,x52082)+~E(f323(f323(f144(x52083),x52081),x52084),f323(f323(f144(x52083),x52082),x52085))
% 179.72/179.58 [5259]P101(f323(x52591,x52592))+~E(f323(f129(x52593,x52591),x52594),f323(f323(f144(x52593),x52592),x52595))
% 179.72/179.58 [5260]P101(f323(x52601,x52602))+~E(f323(f323(f144(x52603),x52602),x52604),f323(f129(x52603,x52601),x52605))
% 179.72/179.58 [5416]~E(f323(f323(f131(x54161),x54163),x54162),f323(f323(f144(x54161),x54164),x54165))+E(f323(f323(f158(x54161),x54162),x54163),x54164)
% 179.72/179.58 [5549]~P17(x55494,x55495,x55491)+E(f323(f323(x55491,x55492),f323(f323(x55491,x55492),x55493)),f323(f323(x55491,x55492),x55493))
% 179.72/179.58 [6077]~E(x60774,f2(a99))+E(f323(f323(f117(x60771,x60772,x60773),x60774),x60775),f323(f323(f258(f861(x60772),x60771),f113(x60772)),x60775))
% 179.72/179.58 [6143]~P103(x61432)+~E(f323(f323(f141(x61431,x61432,x61433),x61434),x61435),f113(x61431))
% 179.72/179.58 [6519]E(x65191,x65192)+~E(f323(f323(f121(x65193),x65194),f323(f323(f144(x65193),x65191),f113(x65193))),f323(f323(f121(x65193),x65195),f323(f323(f144(x65193),x65192),f113(x65193))))
% 179.72/179.58 [6520]E(x65201,x65202)+~E(f323(f323(f121(x65203),x65201),f323(f323(f144(x65203),x65204),f113(x65203))),f323(f323(f121(x65203),x65202),f323(f323(f144(x65203),x65205),f113(x65203))))
% 179.72/179.58 [6772]E(f323(f182(x67721,x67722,x67723,x67724),x67725),f200(x67722))+P101(f323(f323(f325(x67721),x67725),x67724))
% 179.72/179.58 [6834]E(f323(f323(f301(x68341),f323(x68342,x68343)),f323(f302(x68344,x68341,x68342),x68345)),f323(f302(x68344,x68341,x68342),x68345))+~P101(f323(f323(f325(x68344),x68343),x68345))
% 179.72/179.58 [6840]~P101(f323(x68404,f323(x68403,x68405)))+P101(f323(f323(f303(x68401,x68402,x68403),x68404),x68405))
% 179.72/179.58 [6843]~P101(f323(f323(x68433,x68435),x68434))+P101(f323(f323(f247(x68431,x68432,x68433),x68434),x68435))
% 179.72/179.58 [6936]~E(f323(f302(x69361,x69362,x69363),x69364),x69365)+E(f323(f302(f867(x69361,a855),f867(x69362,a855),f302(x69361,x69362,x69363)),f323(f300(x69361),x69364)),f323(f300(x69362),x69365))
% 179.72/179.58 [6966]E(f323(f182(x69661,x69662,x69663,x69664),x69665),f323(x69663,x69665))+~P101(f323(f323(f325(x69661),x69665),x69664))
% 179.72/179.58 [7265]P27(x72651,x72652,x72653,x72654)+~P27(x72651,x72652,x72653,f323(f323(f301(x72651),x72655),x72654))
% 179.72/179.58 [7332]P101(f323(x73321,x73322))+~P101(f323(f323(f92(x73323,x73324,x73321),x73325),x73322))
% 179.72/179.58 [7376]~P101(f323(f323(f325(x73764),x73763),x73765))+P101(f323(f323(f325(x73761),f323(x73762,x73763)),f323(f302(x73764,x73761,x73762),x73765)))
% 179.72/179.58 [7399]~P103(x73992)+E(f143(x73991,x73992,x73993,f323(f129(x73991,x73994),x73995)),f323(f129(x73991,x73994),f143(x73991,x73992,x73993,x73995)))
% 179.72/179.58 [7431]P101(f323(x74311,f323(x74312,x74313)))+~P101(f323(f323(f303(x74314,x74315,x74312),x74311),x74313))
% 179.72/179.58 [7434]P101(f323(f323(x74341,x74342),x74343))+~P101(f323(f323(f247(x74344,x74345,x74341),x74343),x74342))
% 179.72/179.58 [7435]P101(f323(f323(x74351,x74352),x74353))+~P101(f323(f323(f92(x74354,x74351,x74355),x74352),x74353))
% 179.72/179.58 [7498]~P101(f323(f323(f325(x74983),f323(x74984,x74982)),x74985))+P101(f323(f323(f325(x74981),x74982),f323(f303(x74981,x74983,x74984),x74985)))
% 179.72/179.58 [7896]~P101(f323(f323(f325(x78965),x78963),f323(f303(x78965,x78961,x78962),x78964)))+P101(f323(f323(f325(x78961),f323(x78962,x78963)),x78964))
% 179.72/179.58 [8113]~E(x81133,f323(f323(f323(f70(x81131,f864(x81132)),f323(f16(f864(x81132),x81131),f200(x81132))),x81134),f323(f230(x81132),x81135)))+E(f177(x81131,x81132,x81133),f323(f323(f301(x81131),x81134),f188(f867(x81131,a855))))
% 179.72/179.58 [8193]~P18(x81932,x81931,x81933)+E(f323(f135(x81931,x81932,f323(f7(x81932,x81931,x81931),x81933),x81934),f145(x81932,x81935)),f323(f323(f62(x81932,x81931,x81933),x81934),f323(f166(x81932),x81935)))
% 179.72/179.58 [8213]E(f323(x82131,f461(x82132,x82131,x82133,x82134)),x82134)+~P101(f323(f323(f325(x82135),x82134),f323(f302(x82133,x82135,x82131),x82132)))
% 179.72/179.58 [8214]E(f323(x82141,f471(x82142,x82141,x82143,x82144)),x82144)+~P101(f323(f323(f325(x82145),x82144),f323(f302(x82143,x82145,x82141),x82142)))
% 179.72/179.58 [8514]~E(x85142,f323(f323(f144(x85141),x85144),x85145))+P101(f323(f323(f325(f866(f861(x85141),f861(x85141))),f323(f323(f258(f861(x85141),f861(x85141)),f113(x85141)),x85142)),f140(x85141,x85143)))
% 179.72/179.58 [8561]E(f323(x85611,f323(f91(x85612,x85613,x85614,x85611),x85615)),x85615)+~P101(f323(f323(f325(x85613),x85615),f323(f302(x85612,x85613,x85611),x85614)))
% 179.72/179.58 [8564]P27(x85641,x85642,f91(x85642,x85641,x85643,x85644),x85645)+~P101(f323(f323(f237(f867(x85641,a855)),x85645),f323(f302(x85642,x85641,x85644),x85643)))
% 179.72/179.58 [8572]~P35(x85721,x85723,x85725,x85722,x85724)+E(f323(f189(f861(x85721)),x85722),f323(f189(f861(x85723)),x85724))
% 179.72/179.58 [8582]P101(f323(f323(f237(f867(x85821,a855)),f323(f323(f40(x85822,f867(x85821,a855)),x85823),x85824)),f323(x85824,x85825)))+~P101(f323(f323(f325(x85822),x85825),x85823))
% 179.72/179.58 [8637]~P53(x86371,x86372,x86373,x86375,x86374)+E(f323(f302(x86371,x86372,x86373),f246(f867(x86371,a855))),x86374)
% 179.72/179.58 [8853]E(f323(f323(f323(f70(x88531,f864(x88532)),f182(x88531,x88532,x88533,x88534)),x88535),f200(x88532)),f182(x88531,x88532,x88533,x88534))+P101(f323(f323(f325(x88531),x88535),x88534))
% 179.72/179.58 [8858]E(f323(f129(x88581,x88582),f705(x88583,x88584,x88585,x88582,x88581)),x88583)+~E(f323(f129(x88581,x88582),x88585),f323(f323(f144(x88581),x88584),x88583))
% 179.72/179.58 [8859]E(f323(f129(x88591,x88592),f706(x88593,x88592,x88594,x88595,x88591)),x88594)+~E(f323(f323(f144(x88591),x88595),x88594),f323(f129(x88591,x88592),x88593))
% 179.72/179.58 [8860]E(f323(x88601,f834(x88602,x88603,x88601,x88604,x88605)),x88602)+~E(f323(f323(f201(x88605,x88604),x88601),x88603),f323(f230(x88604),x88602))
% 179.72/179.58 [8863]E(f323(f230(x88631),f834(x88632,x88633,x88634,x88635,x88631)),x88633)+~E(f323(f323(f201(x88631,x88635),x88634),x88633),f323(f230(x88635),x88632))
% 179.72/179.58 [8953]E(f323(f189(f861(x89531)),x89532),x89533)+~P101(f323(f323(f325(f866(f861(x89531),f861(x89531))),f323(f323(f258(f861(x89531),f861(x89531)),x89534),x89532)),f323(f136(x89531,x89535),x89533)))
% 179.72/179.58 [8954]E(f323(f189(f861(x89541)),x89542),x89543)+~P101(f323(f323(f325(f866(f861(x89541),f861(x89541))),f323(f323(f258(f861(x89541),f861(x89541)),x89542),x89544)),f323(f136(x89541,x89545),x89543)))
% 179.72/179.58 [9024]P101(f323(f323(f325(x90241),f461(x90242,x90243,x90241,x90244)),x90242))+~P101(f323(f323(f325(x90245),x90244),f323(f302(x90241,x90245,x90243),x90242)))
% 179.72/179.58 [9025]P101(f323(f323(f325(x90251),f471(x90252,x90253,x90251,x90254)),x90252))+~P101(f323(f323(f325(x90255),x90254),f323(f302(x90251,x90255,x90253),x90252)))
% 179.72/179.58 [9183]E(f323(f302(x91831,x91832,x91833),f564(x91834,x91833,x91831,x91835,x91832)),x91835)+~P101(f323(f323(f237(f867(x91832,a855)),x91835),f323(f302(x91831,x91832,x91833),x91834)))
% 179.72/179.58 [9436]E(f323(x94361,f806(x94362,x94361,x94363,x94364,x94365)),f323(f230(x94365),x94364))+~P101(f323(f323(f325(x94365),x94364),f178(x94363,x94365,f182(x94363,x94365,x94361,x94362))))
% 179.72/179.58 [9482]P101(f323(f323(f325(f866(f861(x94821),f861(x94821))),f323(f323(f258(f861(x94821),f861(x94821)),f323(f323(f144(x94821),x94822),x94823)),f323(f323(f144(x94821),x94822),x94824))),f299(f861(x94821),f150(x94821,x94825))))+~P101(f323(f323(f325(f866(f861(x94821),f861(x94821))),f323(f323(f258(f861(x94821),f861(x94821)),x94823),x94824)),f299(f861(x94821),f150(x94821,x94825))))
% 179.72/179.58 [9514]~E(f323(x95143,f534(x95145,x95144,x95143,x95142,x95141)),f323(x95145,f534(x95145,x95144,x95143,x95142,x95141)))+E(f323(f323(f147(x95141,x95142),x95143),x95144),f323(f323(f147(x95141,x95142),x95145),x95144))
% 179.72/179.58 [9591]~E(f323(f129(x95911,x95915),x95914),f323(f323(f144(x95911),x95913),x95912))+E(f323(f323(f121(x95911),f708(x95912,x95913,x95914,x95915,x95911)),f323(f323(f144(x95911),x95913),f705(x95912,x95913,x95914,x95915,x95911))),x95914)
% 179.72/179.58 [9592]~E(f323(f323(f144(x95921),x95925),x95924),f323(f129(x95921,x95923),x95922))+E(f323(f323(f121(x95921),f707(x95922,x95923,x95924,x95925,x95921)),f323(f323(f144(x95921),x95925),f706(x95922,x95923,x95924,x95925,x95921))),x95922)
% 179.72/179.58 [9596]E(f323(f323(f147(x95961,x95962),x95963),x95964),f323(f323(f147(x95961,x95962),x95965),x95964))+P101(f323(f323(f325(x95961),f534(x95963,x95964,x95965,x95962,x95961)),f323(f166(x95961),x95964)))
% 179.72/179.58 [9626]~P101(f323(f323(f325(x96265),x96264),f323(f277(x96261,x96265,x96263),x96262)))+P101(f323(f323(f325(x96261),f500(x96262,x96263,x96261,x96264,x96265)),x96262))
% 179.72/179.58 [9627]~P101(f323(f323(f325(x96275),x96274),f323(f277(x96271,x96275,x96273),x96272)))+P101(f323(f323(f325(x96271),f526(x96272,x96273,x96271,x96274,x96275)),x96272))
% 179.72/179.58 [9654]~P101(f323(f323(f237(f867(x96545,a855)),x96544),f323(f302(x96541,x96545,x96543),x96542)))+P101(f323(f323(f237(f867(x96541,a855)),f564(x96542,x96543,x96541,x96544,x96545)),x96542))
% 179.72/179.58 [9705]~P101(f323(f323(f325(x97055),x97054),f178(x97051,x97055,f182(x97051,x97055,x97053,x97052))))+P101(f323(f323(f325(x97051),f806(x97052,x97053,x97051,x97054,x97055)),x97052))
% 179.72/179.58 [10100]E(x101001,f2(a99))+E(f323(f232(f866(f861(x101002),x101003),f866(x101002,x101003),f323(f323(f258(f861(x101002),x101003),f113(x101002)),x101004),f323(f262(x101002,x101003,f866(f861(x101002),x101003)),f323(f323(f7(x101002,f867(x101003,f866(f861(x101002),x101003)),f867(x101003,f866(f861(x101002),x101003))),f323(f323(f8(f867(f866(f861(x101002),x101003),f866(f861(x101002),x101003)),f867(f867(x101003,f866(f861(x101002),x101003)),f867(x101003,f866(f861(x101002),x101003))),x101002),f8(f866(f861(x101002),x101003),f866(f861(x101002),x101003),x101003)),f323(f323(f8(f867(f861(x101002),f867(x101003,f866(f861(x101002),x101003))),f867(f866(f861(x101002),x101003),f866(f861(x101002),x101003)),x101002),f262(f861(x101002),x101003,f866(f861(x101002),x101003))),f323(f323(f8(f867(f861(x101002),f861(x101002)),f867(f861(x101002),f867(x101003,f866(f861(x101002),x101003))),x101002),f323(f8(f861(x101002),f867(x101003,f866(f861(x101002),x101003)),f861(x101002)),f258(f861(x101002),x101003))),f144(x101002))))),f323(f117(x101003,x101002,x101005),f323(f323(f22(a99),x101001),f76(a99)))))),f323(x101005,x101004)),f323(f323(f117(x101003,x101002,x101005),x101001),x101004))
% 179.72/179.58 [5429]~E(f323(x54293,x54294),x54295)+E(f323(f323(f323(f70(x54291,x54292),x54293),x54294),x54295),x54293)
% 179.72/179.58 [5870]E(f323(x58701,x58702),x58703)+~E(f323(f323(f323(f70(x58704,x58705),x58701),x58702),x58703),x58701)
% 179.72/179.58 [5959]E(x59591,x59592)+~E(f323(f261(x59593,x59594),f323(f323(f258(x59593,x59594),x59595),x59591)),x59592)
% 179.72/179.58 [5960]E(x59601,x59602)+~E(f323(f257(x59603,x59604),f323(f323(f258(x59603,x59604),x59601),x59605)),x59602)
% 179.72/179.58 [6218]~E(x62183,f323(f323(f121(x62181),x62184),f323(f323(f144(x62181),x62182),x62185)))+P101(f323(f323(f325(x62181),x62182),f323(f166(x62181),x62183)))
% 179.72/179.58 [6604]E(f323(f302(x66041,x66042,f323(f16(x66042,x66041),x66043)),x66044),f323(f323(f301(x66042),x66043),f188(f867(x66042,a855))))+~P101(f323(f323(f325(x66041),x66045),x66044))
% 179.72/179.58 [6674]E(f323(f323(f110(f867(x66741,a855)),f323(f166(x66741),x66742)),f323(f166(x66741),x66743)),f323(f166(x66741),x66744))+~E(f160(x66741,x66745,x66744),f323(f323(f258(f861(x66741),f861(x66741)),x66742),x66743))
% 179.72/179.58 [6776]~P103(x67762)+E(f323(f189(f861(x67761)),f323(f323(f141(x67761,x67762,x67763),x67764),x67765)),f323(a112,f323(f189(f861(x67761)),x67765)))
% 179.72/179.58 [6788]~P103(x67882)+E(f323(f166(x67881),f323(f323(f141(x67881,x67882,x67883),x67884),x67885)),f323(f323(f301(x67881),x67884),f323(f166(x67881),x67885)))
% 179.72/179.58 [7057]~P112(x70571)+E(f323(f323(f79(x70571),f323(f323(f79(x70571),x70572),x70573)),f323(f323(f79(x70571),x70574),x70575)),f323(f323(f79(x70571),f323(f323(f79(x70571),x70572),x70574)),f323(f323(f79(x70571),x70573),x70575)))
% 179.72/179.58 [7058]~P112(x70581)+E(f323(f323(f78(x70581),f323(f323(f78(x70581),x70582),x70583)),f323(f323(f78(x70581),x70584),x70585)),f323(f323(f78(x70581),f323(f323(f78(x70581),x70582),x70584)),f323(f323(f78(x70581),x70583),x70585)))
% 179.72/179.58 [7059]~P62(x70591)+E(f323(f323(f281(x70591),f323(f323(f79(x70591),x70592),x70593)),f323(f323(f79(x70591),x70594),x70595)),f323(f323(f79(x70591),f323(f323(f281(x70591),x70592),x70594)),f323(f323(f281(x70591),x70593),x70595)))
% 179.72/179.58 [7073]~P103(x70731)+E(f294(x70731,f323(f323(f236(x70731),x70732),x70733),f323(f323(f235(x70731),x70734),x70735)),f323(f323(f101(f867(x70731,a855)),f294(x70731,x70732,x70734)),f294(x70731,x70733,x70735)))
% 179.72/179.58 [7074]~P103(x70741)+E(f297(x70741,f323(f323(f236(x70741),x70742),x70743),f323(f323(f235(x70741),x70744),x70745)),f323(f323(f101(f867(x70741,a855)),f297(x70741,x70742,x70744)),f297(x70741,x70743,x70745)))
% 179.72/179.58 [7075]~P103(x70751)+E(f296(x70751,f323(f323(f236(x70751),x70752),x70753),f323(f323(f235(x70751),x70754),x70755)),f323(f323(f101(f867(x70751,a855)),f296(x70751,x70752,x70754)),f296(x70751,x70753,x70755)))
% 179.72/179.58 [7076]~P103(x70761)+E(f323(f323(f101(f867(x70761,a855)),f323(f293(x70761,x70762),x70763)),f323(f293(x70761,x70764),x70765)),f323(f293(x70761,f323(f323(f236(x70761),x70762),x70764)),f323(f323(f235(x70761),x70763),x70765)))
% 179.72/179.58 [7191]~P101(f323(x71911,f499(x71913,x71912,x71911)))+P101(f323(x71911,f323(f323(f258(x71912,x71913),x71914),x71915)))
% 179.72/179.58 [7278]~E(f323(x72783,x72784),f200(x72782))+E(f178(x72781,x72782,f323(f323(f323(f70(x72781,f864(x72782)),x72783),x72784),f323(f230(x72782),x72785))),f323(f323(f301(x72782),x72785),f178(x72781,x72782,x72783)))
% 179.72/179.58 [7297]~E(x72972,f323(x72974,x72975))+P101(f323(f323(f325(x72971),x72972),f323(f302(x72973,x72971,x72974),f246(f867(x72973,a855)))))
% 179.72/179.58 [7354]~E(f323(x73543,x73544),f200(x73542))+E(f323(f323(f22(f867(x73541,a855)),f177(x73541,x73542,x73543)),f323(f323(f301(x73541),x73544),x73545)),f323(f323(f22(f867(x73541,a855)),f177(x73541,x73542,x73543)),x73545))
% 179.72/179.58 [7373]~P17(x73733,x73732,x73734)+P17(x73731,x73732,f323(f323(f8(x73733,f867(x73732,x73732),x73731),x73734),x73735))
% 179.72/179.58 [7374]~P18(x73743,x73742,x73744)+P18(x73741,x73742,f323(f323(f8(x73743,f867(x73742,x73742),x73741),x73744),x73745))
% 179.72/179.58 [7514]~P27(x75141,x75142,x75143,x75144)+P27(x75141,x75142,x75143,f323(f323(f22(f867(x75141,a855)),x75144),x75145))
% 179.72/179.58 [7671]~P101(f323(f323(x76713,x76714),x76715))+P101(f323(f323(f262(x76711,x76712,a855),x76713),f323(f323(f258(x76711,x76712),x76714),x76715)))
% 179.72/179.58 [7781]~P101(f323(x77812,x77814))+~E(f323(f323(f131(x77811),f323(f189(f861(x77811)),f171(x77811,x77812,x77813))),x77813),f323(f323(f144(x77811),x77814),x77815))
% 179.72/179.58 [7801]P27(x78011,x78012,x78013,x78014)+~P27(x78011,x78012,x78013,f323(f323(f110(f867(x78011,a855)),x78015),x78014))
% 179.72/179.58 [7802]P27(x78021,x78022,x78023,x78024)+~P27(x78021,x78022,x78023,f323(f323(f110(f867(x78021,a855)),x78024),x78025))
% 179.72/179.58 [7850]~P103(x78502)+E(f323(f323(f141(x78501,x78502,x78503),x78504),f143(x78501,x78502,x78503,x78505)),f143(x78501,x78502,x78503,f323(f323(f144(x78501),x78504),x78505)))
% 179.72/179.58 [8168]~P17(x81682,x81681,x81683)+E(f323(f135(x81681,x81682,f323(f7(x81682,x81681,x81681),x81683),x81684),x81685),f323(f323(f62(x81682,x81681,x81683),x81684),f323(f166(x81682),x81685)))
% 179.72/179.58 [8198]~E(f323(f323(f131(x81981),f323(f189(f861(x81981)),f171(x81981,x81982,x81983))),x81983),f323(f323(f144(x81981),x81984),x81985))+E(f323(f323(f121(x81981),f171(x81981,x81982,x81983)),f323(f323(f144(x81981),x81984),x81985)),x81983)
% 179.72/179.58 [8224]P101(f323(f323(x82241,x82242),x82243))+~P101(f323(f323(f262(x82244,x82245,a855),x82241),f323(f323(f258(x82244,x82245),x82242),x82243)))
% 179.72/179.58 [8288]~E(f323(f323(f179(x82881,x82882),x82885),x82883),f323(f230(x82882),x82884))+P101(f323(f323(f325(f866(x82881,x82882)),f323(f323(f258(x82881,x82882),x82883),x82884)),f323(f166(f866(x82881,x82882)),x82885)))
% 179.72/179.58 [8700]P101(f323(f323(f237(f867(x87001,a855)),f323(f302(x87002,x87001,x87003),x87004)),f323(f302(x87002,x87001,x87003),x87005)))+~P101(f323(f323(f237(f867(x87002,a855)),x87004),x87005))
% 179.72/179.58 [8701]P101(f323(f323(f237(f867(x87011,a855)),f323(f303(x87011,x87012,x87013),x87014)),f323(f303(x87011,x87012,x87013),x87015)))+~P101(f323(f323(f237(f867(x87012,a855)),x87014),x87015))
% 179.72/179.58 [8781]E(x87811,f2(a99))+E(f323(f323(f264(x87812,x87813,x87812,f866(x87813,x87812)),f323(x87814,x87815)),f272(x87813,x87812,f323(f323(f22(a99),x87811),f76(a99)),x87814)),f323(f272(x87813,x87812,x87811,x87814),x87815))
% 179.72/179.58 [9292]E(f323(f230(x92921),f533(x92922,x92923,x92924,x92921,x92925)),f323(f323(f179(x92925,x92921),x92922),x92924))+~P101(f323(f323(f325(f866(x92925,x92921)),f323(f323(f258(x92925,x92921),x92924),x92923)),f323(f166(f866(x92925,x92921)),x92922)))
% 179.72/179.58 [9338]~P101(f323(f323(f325(x93382),x93385),f323(f302(x93381,x93382,x93384),x93383)))+P101(f323(f323(f325(x93381),f323(f91(x93381,x93382,x93383,x93384),x93385)),x93383))
% 179.72/179.58 [9426]~P101(f323(f59(x94263),f323(f302(x94262,x94263,x94265),f246(f867(x94262,a855)))))+P101(f323(f59(x94261),f323(f302(x94262,x94261,f323(f323(f8(x94263,x94261,x94262),x94264),x94265)),f246(f867(x94262,a855)))))
% 179.72/179.58 [9450]P101(f323(f323(f237(f867(f867(x94501,a855),a855)),f323(f302(f867(x94502,a855),f867(x94501,a855),f302(x94502,x94501,x94503)),f323(f300(x94502),x94504))),f323(f300(x94501),x94505)))+~P101(f323(f323(f237(f867(x94501,a855)),f323(f302(x94502,x94501,x94503),x94504)),x94505))
% 179.72/179.58 [9461]~P101(f323(f59(f864(x94611)),f323(f302(x94612,f864(x94611),x94613),f246(f867(x94612,a855)))))+P101(f323(f59(f864(x94611)),f323(f302(x94612,f864(x94611),f323(f323(f323(f70(x94612,f864(x94611)),x94613),x94614),f323(f230(x94611),x94615))),f246(f867(x94612,a855)))))
% 179.72/179.58 [9522]E(x95221,x95222)+~P101(f323(f64(x95223,x95224,x95225,x95221,f188(f867(x95223,a855))),x95222))
% 179.72/179.58 [9538]E(f323(f323(f258(x95381,x95382),f655(x95383,x95384,x95385,x95382,x95381)),f658(x95383,x95384,x95385,x95382,x95381)),x95385)+~P101(f323(f323(f325(f866(x95381,x95382)),x95385),f323(f323(f260(x95381,x95382),x95384),x95383)))
% 179.72/179.58 [9631]P101(f323(f323(f325(x96311),f655(x96312,x96313,x96314,x96315,x96311)),x96313))+~P101(f323(f323(f325(f866(x96311,x96315)),x96314),f323(f323(f260(x96311,x96315),x96313),x96312)))
% 179.72/179.58 [9741]P26(x97415,x97414,f323(f323(f301(f859(x97415)),f323(f323(f323(f90(x97415),x97411),x97413),x97412)),f188(f867(f859(x97415),a855))))+P101(f323(f323(x97411,f552(x97412,x97413,x97414,x97415,x97411)),f664(x97412,x97413,x97414,x97415,x97411)))
% 179.72/179.58 [9794]P101(f323(f323(f325(x97941),f658(x97942,x97943,x97944,x97941,x97945)),f323(x97942,f655(x97942,x97943,x97944,x97941,x97945))))+~P101(f323(f323(f325(f866(x97945,x97941)),x97944),f323(f323(f260(x97945,x97941),x97943),x97942)))
% 179.72/179.58 [9819]P101(f323(f323(f325(f866(x98191,x98191)),f323(f323(f258(x98191,x98191),x98192),f748(x98193,x98194,x98195,x98192,x98191))),x98193))+~P101(f323(f323(f325(f866(x98191,x98191)),f323(f323(f258(x98191,x98191),x98192),x98195)),f323(f323(f183(f866(x98191,x98191),a855),f323(a112,x98194)),x98193)))
% 179.72/179.58 [9820]P101(f323(f323(f325(f866(x98201,x98201)),f323(f323(f258(x98201,x98201),x98202),f749(x98203,x98204,x98205,x98202,x98201))),x98203))+~P101(f323(f323(f325(f866(x98201,x98201)),f323(f323(f258(x98201,x98201),x98202),x98205)),f323(f323(f183(f866(x98201,x98201),a855),f323(a112,x98204)),x98203)))
% 179.72/179.58 [9838]~P101(f323(f323(f325(f866(f861(x98381),f861(x98381))),f323(f323(f258(f861(x98381),f861(x98381)),f323(f323(f144(x98381),x98382),x98385)),x98384)),f151(x98381,x98383)))+P101(f323(f323(f325(f866(x98381,x98381)),f323(f323(f258(x98381,x98381),x98382),f577(x98383,x98384,x98385,x98382,x98381))),x98383))
% 179.72/179.58 [9840]~P26(x98401,x98402,f323(f323(f301(f859(x98401)),f323(f323(f323(f90(x98401),f92(x98401,x98403,x98404)),x98405),x98403)),f188(f867(f859(x98401),a855))))+P26(x98401,x98402,f323(f323(f301(f859(x98401)),f323(f323(f323(f90(x98401),x98403),f29(x98404,x98405)),f92(x98401,x98403,f323(f71(a855,a855,a856,a318),x98404)))),f188(f867(f859(x98401),a855))))
% 179.72/179.58 [9841]~P31(x98411,x98412,f323(f323(f301(f859(x98411)),f323(f323(f323(f90(x98411),f92(x98411,x98413,x98414)),x98415),x98413)),f188(f867(f859(x98411),a855))))+P31(x98411,x98412,f323(f323(f301(f859(x98411)),f323(f323(f323(f90(x98411),x98413),f29(x98414,x98415)),f92(x98411,x98413,f323(f71(a855,a855,a856,a318),x98414)))),f188(f867(f859(x98411),a855))))
% 179.72/179.58 [10101]P26(x101011,x101012,f323(f323(f301(f859(x101011)),f323(f323(f323(f90(x101011),x101013),x101014),x101015)),f188(f867(f859(x101011),a855))))+~P26(x101011,x101012,f323(f323(f301(f859(x101011)),f323(f323(f323(f90(x101011),f323(f16(f867(a856,a855),x101011),f323(f323(f7(a856,a856,a855),a320),f664(x101015,x101014,x101012,x101011,x101013)))),x101014),f323(f16(f867(a856,a855),x101011),f323(x101015,f552(x101015,x101014,x101012,x101011,x101013))))),f188(f867(f859(x101011),a855))))
% 179.72/179.58 [6291]P101(f323(x62912,x62914))+E(f171(x62911,x62912,f323(f323(f121(x62911),x62913),f323(f323(f144(x62911),x62914),x62915))),f171(x62911,x62912,x62913))
% 179.72/179.58 [6339]~P2(x63392)+E(f323(f323(f323(f110(f867(x63391,x63392)),x63393),x63394),x63395),f323(f323(f110(x63392),f323(x63393,x63395)),f323(x63394,x63395)))
% 179.72/179.58 [6341]~P4(x63412)+E(f323(f323(f323(f22(f867(x63411,x63412)),x63413),x63414),x63415),f323(f323(f22(x63412),f323(x63413,x63415)),f323(x63414,x63415)))
% 179.72/179.58 [6343]~P2(x63432)+E(f323(f323(f323(f101(f867(x63431,x63432)),x63433),x63434),x63435),f323(f323(f101(x63432),f323(x63433,x63435)),f323(x63434,x63435)))
% 179.72/179.58 [6360]E(x63601,x63602)+E(f323(f323(f158(x63603),f323(f323(f152(x63603,x63604),x63601),x63605)),x63602),f323(f323(f158(x63603),x63604),x63602))
% 179.72/179.58 [6622]~E(x66224,f188(f867(x66223,a855)))+E(f323(f323(f110(f867(x66221,a855)),x66222),f323(f323(f39(x66223,f867(x66221,a855)),x66224),x66225)),x66222)
% 179.72/179.58 [6623]~E(x66234,f188(f867(x66233,a855)))+E(f323(f323(f22(f867(x66231,a855)),x66232),f323(f323(f39(x66233,f867(x66231,a855)),x66234),x66235)),x66232)
% 179.72/179.58 [6624]~E(x66244,f188(f867(x66243,a855)))+E(f323(f323(f101(f867(x66241,a855)),x66242),f323(f323(f40(x66243,f867(x66241,a855)),x66244),x66245)),x66242)
% 179.72/179.58 [6638]~E(x66384,f188(f867(x66383,a855)))+E(f323(f323(f301(x66381),x66382),f323(f323(f39(x66383,f867(x66381,a855)),x66384),x66385)),f323(f323(f301(x66381),x66382),f188(f867(x66381,a855))))
% 179.72/179.58 [7421]E(f323(f323(f158(x74211),f323(f323(f147(x74212,x74211),x74213),x74214)),x74215),f323(x74213,f323(f323(f158(x74212),x74214),x74215)))+~P101(f323(f323(f238(a860),x74215),f323(f189(f861(x74212)),x74214)))
% 179.72/179.58 [7486]E(f323(f323(f110(f867(x74861,a855)),f323(x74862,x74863)),f323(f323(f39(x74864,f867(x74861,a855)),x74865),x74862)),f323(f323(f39(x74864,f867(x74861,a855)),x74865),x74862))+~P101(f323(f323(f325(x74864),x74863),x74865))
% 179.72/179.58 [7487]E(f323(f323(f101(f867(x74871,a855)),f323(x74872,x74873)),f323(f323(f40(x74874,f867(x74871,a855)),x74875),x74872)),f323(f323(f40(x74874,f867(x74871,a855)),x74875),x74872))+~P101(f323(f323(f325(x74874),x74873),x74875))
% 179.72/179.58 [8086]~E(x80863,f188(f867(x80861,a855)))+E(f323(f323(f39(x80861,f867(x80862,a855)),x80863),f323(f323(f8(f867(x80862,a855),f867(x80862,a855),x80861),f323(f301(x80862),x80864)),x80865)),f188(f867(x80862,a855)))
% 179.72/179.58 [8091]~P101(f323(f323(f325(x80914),x80913),x80915))+P101(f323(f323(f237(f867(x80911,a855)),f323(x80912,x80913)),f323(f323(f39(x80914,f867(x80911,a855)),x80915),x80912)))
% 179.72/179.58 [8223]~E(f323(x82234,x82232),x82235)+P101(f323(f323(f325(x82231),x82232),f323(f303(x82231,x82233,x82234),f323(f323(f301(x82233),x82235),f188(f867(x82233,a855))))))
% 179.72/179.58 [8269]~P51(x82691,x82692,f323(f278(x82692,x82691),x82693))+E(f323(f323(f101(f867(x82691,a855)),f323(f277(x82692,x82691,x82693),x82694)),f323(f277(x82692,x82691,x82693),x82695)),f323(f277(x82692,x82691,x82693),f323(f323(f101(f867(x82692,a855)),x82694),x82695)))
% 179.72/179.58 [8347]E(x83471,f2(a99))+E(f323(f116(x83472,x83473,f323(x83474,f323(f323(f22(a99),x83471),f76(a99)))),f323(f323(f7(x83472,a99,f862(x83473)),x83475),x83471)),f323(f199(x83472,x83473,x83474,x83475),x83471))
% 179.72/179.58 [8387]E(x83871,f188(f867(x83872,a855)))+E(f323(f323(f39(x83872,f867(x83873,a855)),x83871),f323(f323(f8(f867(x83873,a855),f867(x83873,a855),x83872),f323(f301(x83873),x83874)),x83875)),f323(f323(f301(x83873),x83874),f323(f323(f39(x83872,f867(x83873,a855)),x83871),x83875)))
% 179.72/179.58 [8434]~P27(x84342,x84341,x84343,f246(f867(x84342,a855)))+E(f323(f323(f22(f867(x84341,a855)),f323(f302(x84342,x84341,x84343),x84344)),f323(f302(x84342,x84341,x84343),x84345)),f323(f302(x84342,x84341,x84343),f323(f323(f22(f867(x84342,a855)),x84344),x84345)))
% 179.72/179.58 [8435]~P27(x84352,x84351,x84353,f246(f867(x84352,a855)))+E(f323(f323(f101(f867(x84351,a855)),f323(f302(x84352,x84351,x84353),x84354)),f323(f302(x84352,x84351,x84353),x84355)),f323(f302(x84352,x84351,x84353),f323(f323(f101(f867(x84352,a855)),x84354),x84355)))
% 179.72/179.58 [8501]~P101(f323(f323(f65(x85011,x85012,x85015),x85013),x85014))+P101(f323(f323(f325(f866(x85011,x85012)),f323(f323(f258(x85011,x85012),x85013),x85014)),x85015))
% 179.72/179.58 [8534]P101(f323(f323(f325(x85341),x85342),f323(f254(x85343,x85341),x85344)))+~P101(f323(f323(f325(f866(x85343,x85341)),f323(f323(f258(x85343,x85341),x85345),x85342)),x85344))
% 179.72/179.58 [8536]P101(f323(f323(f325(x85361),x85362),f323(f256(x85361,x85363),x85364)))+~P101(f323(f323(f325(f866(x85361,x85363)),f323(f323(f258(x85361,x85363),x85362),x85365)),x85364))
% 179.72/179.58 [8684]P101(f323(f323(f65(x86841,x86842,x86843),x86844),x86845))+~P101(f323(f323(f325(f866(x86841,x86842)),f323(f323(f258(x86841,x86842),x86844),x86845)),x86843))
% 179.72/179.58 [8723]E(f323(x87231,x87232),x87233)+~P101(f323(f323(f325(x87234),x87232),f323(f303(x87234,x87235,x87231),f323(f323(f301(x87235),x87233),f188(f867(x87235,a855))))))
% 179.72/179.58 [8950]P101(f323(f323(f325(f866(x89501,x89502)),f323(f323(f258(x89501,x89502),x89503),x89504)),f323(f278(x89502,x89501),x89505)))+~P101(f323(f323(f325(f866(x89502,x89501)),f323(f323(f258(x89502,x89501),x89504),x89503)),x89505))
% 179.72/179.58 [8968]~P101(f323(f323(x89681,x89685),x89684))+P101(f323(f323(x89681,f323(f261(x89682,x89683),f323(f323(f258(x89682,x89683),x89684),x89685))),f323(f257(x89682,x89683),f323(f323(f258(x89682,x89683),x89684),x89685))))
% 179.72/179.58 [8998]~P101(f323(f323(f325(f866(x89982,x89981)),f323(f323(f258(x89982,x89981),x89984),x89983)),f323(f278(x89981,x89982),x89985)))+P101(f323(f323(f325(f866(x89981,x89982)),f323(f323(f258(x89981,x89982),x89983),x89984)),x89985))
% 179.72/179.58 [9032]~P101(f323(f323(f325(f866(x90323,x90321)),f323(f323(f258(x90323,x90321),x90325),x90322)),x90324))+P101(f323(f323(f325(x90321),x90322),f323(f277(x90323,x90321,x90324),f323(f323(f301(x90323),x90325),f188(f867(x90323,a855))))))
% 179.72/179.58 [9078]P101(f323(f323(f325(f866(x90781,x90782)),f323(f323(f258(x90781,x90782),x90783),x90784)),x90785))+~P101(f323(f323(f325(x90782),x90784),f323(f277(x90781,x90782,x90785),f323(f323(f301(x90781),x90783),f188(f867(x90781,a855))))))
% 179.72/179.58 [9098]E(f323(f323(f323(f70(x90981,f864(x90982)),f182(x90981,x90982,x90983,x90984)),x90985),f200(x90982)),f182(x90981,x90982,x90983,f323(f323(f22(f867(x90981,a855)),x90984),f323(f323(f301(x90981),x90985),f188(f867(x90981,a855))))))+~P101(f323(f323(f325(x90981),x90985),x90984))
% 179.72/179.58 [9169]~P72(x91691)+E(f323(f323(f6(a860,x91691),x91692),f294(a860,f323(f323(f78(a860),x91693),x91694),f323(f323(f78(a860),x91695),x91694))),f323(f323(f6(a860,x91691),f323(f323(f8(a860,x91691,a860),x91692),f323(f323(f7(a860,a860,a860),f78(a860)),x91694))),f294(a860,x91693,x91695)))
% 179.72/179.58 [9188]~P72(x91881)+E(f323(f323(f6(a860,x91881),x91882),f323(f293(a860,f323(f323(f78(a860),x91883),x91884)),f323(f323(f78(a860),x91885),x91884))),f323(f323(f6(a860,x91881),f323(f323(f8(a860,x91881,a860),x91882),f323(f323(f7(a860,a860,a860),f78(a860)),x91884))),f323(f293(a860,x91883),x91885)))
% 179.72/179.58 [9241]~P27(x92411,x92412,x92413,f246(f867(x92411,a855)))+E(f323(f323(f147(x92411,x92412),x92413),f323(f129(x92411,f323(f323(f8(a855,a855,x92411),a318),f323(a320,x92414))),x92415)),f323(f129(x92412,f323(f323(f8(a855,a855,x92412),a318),f323(a320,f323(x92413,x92414)))),f323(f323(f147(x92411,x92412),x92413),x92415)))
% 179.72/179.58 [9257]~P27(x92571,x92572,x92573,f323(f323(f301(x92571),x92574),f323(f166(x92571),x92575)))+E(f323(f323(f147(x92571,x92572),x92573),f323(f129(x92571,f323(f323(f8(a855,a855,x92571),a318),f323(a320,x92574))),x92575)),f323(f129(x92572,f323(f323(f8(a855,a855,x92572),a318),f323(a320,f323(x92573,x92574)))),f323(f323(f147(x92571,x92572),x92573),x92575)))
% 179.72/179.58 [9412]P101(f323(f323(f325(f866(f861(x94121),f861(x94121))),f323(f323(f258(f861(x94121),f861(x94121)),f323(f323(f144(x94121),x94122),x94123)),f323(f323(f144(x94121),x94124),x94123))),f150(x94121,x94125)))+~P101(f323(f323(f325(f866(x94121,x94121)),f323(f323(f258(x94121,x94121),x94122),x94124)),x94125))
% 179.72/179.58 [9533]E(f323(f323(f301(x95331),f719(x95332,x95333,x95334,x95335,x95331)),f726(x95332,x95333,x95334,x95335,x95331)),f323(f323(f301(x95331),x95334),x95333))+~P101(f323(f60(x95331,x95335,f323(f323(f301(x95331),x95334),x95333)),x95332))
% 179.72/179.58 [9534]E(f323(f323(f301(x95341),f741(x95342,x95343,x95344,x95345,x95341)),f753(x95342,x95343,x95344,x95345,x95341)),f323(f323(f301(x95341),x95344),x95343))+~P101(f323(f60(x95341,x95345,f323(f323(f301(x95341),x95344),x95343)),x95342))
% 179.72/179.58 [9617]P101(f323(f323(f325(x96171),f640(x96172,x96173,x96174,x96175,x96171)),x96174))+P101(f323(f323(f323(f40(x96171,f867(x96175,a855)),x96174),x96173),x96172))
% 179.72/179.58 [9622]P101(f323(f323(f325(x96221),f635(x96222,x96223,x96221,x96224,x96225)),x96223))+P101(f323(f323(f325(x96225),x96224),f323(f323(f40(x96221,f867(x96225,a855)),x96223),x96222)))
% 179.72/179.58 [9630]P101(f323(f323(f325(x96301),f637(x96302,x96303,x96301,x96304,x96305)),x96303))+P101(f323(f323(f237(f867(x96305,a855)),x96304),f323(f323(f40(x96301,f867(x96305,a855)),x96303),x96302)))
% 179.72/179.58 [9632]P101(f323(f323(x96321,f439(x96322,x96321,x96323,x96324,x96325)),x96322))+~P101(f323(f323(f323(f39(x96325,f867(x96324,a855)),x96323),x96321),x96322))
% 179.72/179.58 [9636]P101(f323(f323(f325(x96361),f439(x96362,x96363,x96364,x96365,x96361)),x96364))+~P101(f323(f323(f323(f39(x96361,f867(x96365,a855)),x96364),x96363),x96362))
% 179.72/179.58 [9646]P101(f323(f323(f325(x96461),f450(x96462,x96463,x96461,x96464,x96465)),x96463))+~P101(f323(f323(f325(x96465),x96464),f323(f323(f39(x96461,f867(x96465,a855)),x96463),x96462)))
% 179.72/179.58 [9652]P101(f323(f323(f325(x96521),x96522),f323(x96523,f450(x96523,x96524,x96525,x96522,x96521))))+~P101(f323(f323(f325(x96521),x96522),f323(f323(f39(x96525,f867(x96521,a855)),x96524),x96523)))
% 179.72/179.58 [9746]~P101(f323(f323(x97464,f640(x97465,x97464,x97463,x97462,x97461)),x97465))+P101(f323(f323(f323(f40(x97461,f867(x97462,a855)),x97463),x97464),x97465))
% 179.72/179.58 [9749]~P101(f323(f323(f325(x97491),x97492),f323(x97495,f635(x97495,x97494,x97493,x97492,x97491))))+P101(f323(f323(f325(x97491),x97492),f323(f323(f40(x97493,f867(x97491,a855)),x97494),x97495)))
% 179.72/179.58 [9753]~P101(f323(f323(f237(f867(x97531,a855)),x97532),f323(x97535,f637(x97535,x97534,x97533,x97532,x97531))))+P101(f323(f323(f237(f867(x97531,a855)),x97532),f323(f323(f40(x97533,f867(x97531,a855)),x97534),x97535)))
% 179.72/179.58 [9823]~P101(f323(f323(f325(x98231),f719(x98235,x98234,x98233,x98232,x98231)),f726(x98235,x98234,x98233,x98232,x98231)))+~P101(f323(f60(x98231,x98232,f323(f323(f301(x98231),x98233),x98234)),x98235))
% 179.72/179.58 [9824]~P101(f323(f323(f325(x98241),f741(x98245,x98244,x98243,x98242,x98241)),f753(x98245,x98244,x98243,x98242,x98241)))+~P101(f323(f60(x98241,x98242,f323(f323(f301(x98241),x98243),x98244)),x98245))
% 179.72/179.58 [9825]~P101(f323(f323(f325(f866(x98251,x98251)),f323(f323(f258(x98251,x98251),x98252),x98255)),f323(f323(f183(f866(x98251,x98251),a855),f323(a112,x98254)),x98253)))+P101(f323(f323(f325(f866(x98251,x98251)),f323(f323(f258(x98251,x98251),x98252),f750(x98253,x98254,x98255,x98252,x98251))),f323(f323(f183(f866(x98251,x98251),a855),x98254),x98253)))
% 179.72/179.58 [9832]P101(f323(f64(x98321,x98321,x98322,f719(x98323,x98324,x98325,x98322,x98321),f726(x98323,x98324,x98325,x98322,x98321)),x98323))+~P101(f323(f60(x98321,x98322,f323(f323(f301(x98321),x98325),x98324)),x98323))
% 179.72/179.58 [9833]P101(f323(f64(x98331,x98331,x98332,f741(x98333,x98334,x98335,x98332,x98331),f753(x98333,x98334,x98335,x98332,x98331)),x98333))+~P101(f323(f60(x98331,x98332,f323(f323(f301(x98331),x98335),x98334)),x98333))
% 179.72/179.58 [9845]~P103(x98451)+P16(x98451,f323(f323(f147(x98452,x98451),x98453),f323(f129(x98452,f323(f323(f7(x98452,x98451,a855),f323(f323(f8(x98451,f867(x98451,a855),x98452),a320),x98453)),f323(x98454,x98455))),x98455)))
% 179.72/179.58 [9885]~P101(f323(f323(f325(x98852),x98855),f323(f277(x98851,x98852,x98854),x98853)))+P101(f323(f323(f325(f866(x98851,x98852)),f323(f323(f258(x98851,x98852),f500(x98853,x98854,x98851,x98855,x98852)),x98855)),x98854))
% 179.72/179.58 [9886]~P101(f323(f323(f325(x98862),x98865),f323(f277(x98861,x98862,x98864),x98863)))+P101(f323(f323(f325(f866(x98861,x98862)),f323(f323(f258(x98861,x98862),f526(x98863,x98864,x98861,x98865,x98862)),x98865)),x98864))
% 179.72/179.58 [9906]~P101(f323(f323(f325(f866(x99061,x99061)),f323(f323(f258(x99061,x99061),x99065),x99064)),f323(f323(f183(f866(x99061,x99061),a855),f323(a112,x99063)),x99062)))+P101(f323(f323(f325(f866(x99061,x99061)),f323(f323(f258(x99061,x99061),f750(x99062,x99063,x99064,x99065,x99061)),x99064)),x99062))
% 179.72/179.58 [9909]~P101(f323(f323(f325(f866(x99091,x99091)),f323(f323(f258(x99091,x99091),x99095),x99094)),f323(f323(f183(f866(x99091,x99091),a855),f323(a112,x99093)),x99092)))+P101(f323(f323(f325(f866(x99091,x99091)),f323(f323(f258(x99091,x99091),f748(x99092,x99093,x99094,x99095,x99091)),x99094)),f323(f323(f183(f866(x99091,x99091),a855),x99093),x99092)))
% 179.72/179.58 [9910]~P101(f323(f323(f325(f866(x99101,x99101)),f323(f323(f258(x99101,x99101),x99105),x99104)),f323(f323(f183(f866(x99101,x99101),a855),f323(a112,x99103)),x99102)))+P101(f323(f323(f325(f866(x99101,x99101)),f323(f323(f258(x99101,x99101),f749(x99102,x99103,x99104,x99105,x99101)),x99104)),f323(f323(f183(f866(x99101,x99101),a855),x99103),x99102)))
% 179.72/179.58 [9911]~P101(f323(f323(f325(f866(f861(x99111),f861(x99111))),f323(f323(f258(f861(x99111),f861(x99111)),x99115),f323(f323(f144(x99111),x99114),x99113))),f151(x99111,x99112)))+P101(f323(f323(f325(f866(x99111,x99111)),f323(f323(f258(x99111,x99111),f574(x99112,x99113,x99114,x99115,x99111)),x99114)),x99112))
% 179.72/179.58 [7019]E(x70191,f200(x70192))+E(f177(x70193,x70192,f323(f323(f323(f70(x70193,f864(x70192)),x70194),x70195),x70191)),f323(f323(f301(x70193),x70195),f177(x70193,x70192,x70194)))
% 179.72/179.58 [7507]~E(x75073,f188(f867(x75072,a855)))+E(f323(f323(f110(f867(x75071,a855)),f323(f323(f39(x75072,f867(x75071,a855)),x75073),x75074)),x75075),x75075)
% 179.72/179.58 [7508]~E(x75083,f188(f867(x75082,a855)))+E(f323(f323(f101(f867(x75081,a855)),f323(f323(f40(x75082,f867(x75081,a855)),x75083),x75084)),x75085),x75085)
% 179.72/179.58 [7867]~E(x78675,f200(x78672))+E(f177(x78671,x78672,f323(f323(f323(f70(x78671,f864(x78672)),x78673),x78674),x78675)),f323(f323(f22(f867(x78671,a855)),f177(x78671,x78672,x78673)),f323(f323(f301(x78671),x78674),f188(f867(x78671,a855)))))
% 179.72/179.58 [7934]~E(x79343,f188(f867(x79342,a855)))+E(f323(f323(f22(f867(x79341,a855)),f323(f323(f40(x79342,f867(x79341,a855)),x79343),x79344)),x79345),f323(f323(f22(f867(x79341,a855)),f246(f867(x79341,a855))),x79345))
% 179.72/179.58 [8059]E(f323(f323(f152(x80591,f323(f323(f121(x80591),x80592),x80593)),x80594),x80595),f323(f323(f121(x80591),f323(f323(f152(x80591,x80592),x80594),x80595)),x80593))+~P101(f323(f323(f238(a860),x80594),f323(f189(f861(x80591)),x80592)))
% 179.72/179.58 [8172]P101(f323(f323(f325(x81721),x81725),f323(f166(x81721),x81723)))+E(f323(f323(f179(x81721,x81722),f323(f323(f175(x81721,x81722),x81723),f323(f323(f147(x81721,x81722),x81724),x81723))),x81725),f200(x81722))
% 179.72/179.58 [8297]~P101(f323(f323(f325(x82971),x82975),f323(f166(x82971),x82973)))+E(f323(f323(f179(x82971,x82972),f323(f323(f175(x82971,x82972),x82973),f323(f323(f147(x82971,x82972),x82974),x82973))),x82975),f323(f230(x82972),f323(x82974,x82975)))
% 179.72/179.58 [8337]E(f323(f323(f158(x83371),f323(f323(f147(a860,x83371),x83372),f132(a860,f323(f293(a860,x83373),x83374)))),x83375),f323(x83372,f323(f323(f78(a860),x83373),x83375)))+~P101(f323(f323(f238(a860),x83375),f323(f323(f22(a860),x83374),x83373)))
% 179.72/179.58 [8352]E(x83521,f2(a99))+E(f119(x83522,x83523,f323(x83524,f323(f323(f22(a99),x83521),f76(a99))),f323(f323(f7(x83522,a99,f862(f864(x83523))),x83525),x83521)),f323(f197(x83522,x83523,x83524,x83525),x83521))
% 179.72/179.58 [8377]~E(x83773,f188(f867(x83771,a855)))+E(f323(f323(f39(x83771,f867(x83772,a855)),x83773),f323(f323(f8(f867(x83772,a855),f867(x83772,a855),x83771),f323(f110(f867(x83772,a855)),x83774)),x83775)),f188(f867(x83772,a855)))
% 179.72/179.58 [8378]~E(x83783,f188(f867(x83781,a855)))+E(f323(f323(f40(x83781,f867(x83782,a855)),x83783),f323(f323(f8(f867(x83782,a855),f867(x83782,a855),x83781),f323(f22(f867(x83782,a855)),x83784)),x83785)),f246(f867(x83782,a855)))
% 179.72/179.58 [8379]~E(x83793,f188(f867(x83791,a855)))+E(f323(f323(f40(x83791,f867(x83792,a855)),x83793),f323(f323(f8(f867(x83792,a855),f867(x83792,a855),x83791),f323(f101(f867(x83792,a855)),x83794)),x83795)),f246(f867(x83792,a855)))
% 179.72/179.58 [8381]~P139(x83812)+E(f323(f323(f6(x83811,x83812),f323(f323(f8(x83812,x83812,x83811),f323(f79(x83812),x83813)),x83814)),x83815),f323(f323(f79(x83812),x83813),f323(f323(f6(x83811,x83812),x83814),x83815)))
% 179.72/179.58 [8667]E(x86671,f188(f867(x86672,a855)))+E(f323(f323(f39(x86672,f867(x86673,a855)),x86671),f323(f323(f8(f867(x86673,a855),f867(x86673,a855),x86672),f323(f110(f867(x86673,a855)),x86674)),x86675)),f323(f323(f110(f867(x86673,a855)),x86674),f323(f323(f39(x86672,f867(x86673,a855)),x86671),x86675)))
% 179.72/179.58 [8668]E(x86681,f188(f867(x86682,a855)))+E(f323(f323(f40(x86682,f867(x86683,a855)),x86681),f323(f323(f8(f867(x86683,a855),f867(x86683,a855),x86682),f323(f22(f867(x86683,a855)),x86684)),x86685)),f323(f323(f22(f867(x86683,a855)),x86684),f323(f323(f39(x86682,f867(x86683,a855)),x86681),x86685)))
% 179.72/179.58 [8669]E(x86691,f188(f867(x86692,a855)))+E(f323(f323(f40(x86692,f867(x86693,a855)),x86691),f323(f323(f8(f867(x86693,a855),f867(x86693,a855),x86692),f323(f101(f867(x86693,a855)),x86694)),x86695)),f323(f323(f101(f867(x86693,a855)),x86694),f323(f323(f40(x86692,f867(x86693,a855)),x86691),x86695)))
% 179.72/179.58 [8873]~P101(f323(f323(f238(a860),f323(x88734,x88732)),f323(x88734,x88733)))+P101(f323(f323(f325(f866(x88731,x88731)),f323(f323(f258(x88731,x88731),x88732),x88733)),f146(x88731,f323(f323(f144(f867(x88731,a860)),x88734),x88735))))
% 179.72/179.58 [9132]~P27(x91322,x91321,x91323,f323(f323(f110(f867(x91322,a855)),x91324),x91325))+E(f323(f323(f101(f867(x91321,a855)),f323(f302(x91322,x91321,x91323),f323(f323(f22(f867(x91322,a855)),x91324),x91325))),f323(f302(x91322,x91321,x91323),f323(f323(f22(f867(x91322,a855)),x91325),x91324))),f188(f867(x91321,a855)))
% 179.72/179.58 [9378]~P27(x93783,x93781,x93785,f246(f867(x93783,a855)))+E(f323(f71(x93781,x93782,x93783,f323(f71(x93783,x93782,x93781,x93784),f91(x93783,x93781,f246(f867(x93783,a855)),x93785))),x93785),x93784)
% 179.72/179.58 [9408]~P101(f323(f323(f237(f867(x94083,a855)),f323(f277(x94081,x94083,x94084),x94082)),x94085))+P101(f323(f323(f237(f867(x94081,a855)),x94082),f323(f77(f867(x94081,a855)),f323(f277(x94083,x94081,f323(f278(x94081,x94083),x94084)),f323(f77(f867(x94083,a855)),x94085)))))
% 179.72/179.58 [9435]~P27(x94351,x94352,x94353,f323(f323(f301(x94351),x94354),x94355))+~P101(f323(f323(f325(x94352),f323(x94353,x94354)),f323(f302(x94351,x94352,x94353),f323(f323(f22(f867(x94351,a855)),x94355),f323(f323(f301(x94351),x94354),f188(f867(x94351,a855)))))))
% 179.72/179.58 [9486]P101(f323(f323(f237(f867(x94861,a855)),f323(f277(x94862,x94861,x94863),x94864)),x94865))+~P101(f323(f323(f237(f867(x94862,a855)),x94864),f323(f77(f867(x94862,a855)),f323(f277(x94861,x94862,f323(f278(x94862,x94861),x94863)),f323(f77(f867(x94861,a855)),x94865)))))
% 179.72/179.58 [9562]~P82(x95621)+P101(f323(f323(f237(x95621),f323(f73(x95621),f323(f323(f22(x95621),f323(f323(f78(x95621),x95622),x95623)),f323(f323(f78(x95621),x95624),x95625)))),f323(f323(f78(x95621),f323(f73(x95621),f323(f323(f22(x95621),x95622),x95624))),f323(f73(x95621),f323(f323(f22(x95621),x95623),x95625)))))
% 179.72/179.58 [9667]P101(f323(f323(f325(x96671),f452(x96672,x96673,x96674,x96671,x96675)),x96674))+P101(f323(f323(f237(f867(x96675,a855)),f323(f323(f39(x96671,f867(x96675,a855)),x96674),x96673)),x96672))
% 179.72/179.58 [9863]~P101(f323(f323(f237(f867(x98631,a855)),f323(x98634,f452(x98635,x98634,x98633,x98632,x98631))),x98635))+P101(f323(f323(f237(f867(x98631,a855)),f323(f323(f39(x98632,f867(x98631,a855)),x98633),x98634)),x98635))
% 179.72/179.58 [8481]E(f323(f323(f121(x84811),x84812),f323(f323(f152(x84811,x84813),f323(f323(f22(a860),x84814),f323(f189(f861(x84811)),x84812))),x84815)),f323(f323(f152(x84811,f323(f323(f121(x84811),x84812),x84813)),x84814),x84815))+P101(f323(f323(f238(a860),x84814),f323(f189(f861(x84811)),x84812)))
% 179.72/179.58 [8508]~P136(x85081)+E(f323(f323(f78(x85081),f323(f323(f79(x85081),x85082),x85083)),f323(f323(f78(x85081),f323(f323(f79(x85081),x85084),x85083)),x85085)),f323(f323(f78(x85081),f323(f323(f79(x85081),f323(f323(f78(x85081),x85082),x85084)),x85083)),x85085))
% 179.72/179.58 [9088]~P139(x90881)+E(f323(f159(x90881),f323(f323(f147(x90882,x90881),f323(f323(f8(x90881,x90881,x90882),f323(f79(x90881),x90883)),x90884)),x90885)),f323(f323(f79(x90881),x90883),f323(f159(x90881),f323(f323(f147(x90882,x90881),x90884),x90885))))
% 179.72/179.58 [9256]E(f323(f189(f861(x92561)),f323(f323(f169(x92561),f323(f323(f235(a860),f323(f189(f861(x92561)),x92562)),f323(f189(f861(x92563)),x92564))),x92562)),f323(f189(f861(x92563)),f323(f323(f169(x92563),f323(f323(f235(a860),f323(f189(f861(x92561)),x92562)),f323(f189(f861(x92563)),x92564))),x92564)))+P101(f323(x92565,f323(f323(f175(x92561,x92563),x92562),x92564)))
% 179.72/179.58 [9497]~P139(x94972)+E(f323(f323(f6(x94971,x94972),f323(f323(f7(x94971,x94972,x94972),f323(f323(f8(x94972,f867(x94972,x94972),x94971),f79(x94972)),x94973)),x94974)),x94975),f323(f323(f79(x94972),f323(f323(f6(x94971,x94972),x94973),x94975)),x94974))
% 179.72/179.58 [9498]~P63(x94982)+E(f323(f323(f6(x94981,x94982),f323(f323(f7(x94981,x94982,x94982),f323(f323(f8(x94982,f867(x94982,x94982),x94981),f281(x94982)),x94983)),x94984)),x94985),f323(f323(f281(x94982),f323(f323(f6(x94981,x94982),x94983),x94985)),x94984))
% 179.72/179.58 [9505]~P60(x95052)+E(f323(f323(f6(x95051,x95052),f323(f323(f18(x95051,x95052,x95052),f323(f323(f8(x95052,f867(x95052,x95052),x95051),f22(x95052)),x95053)),x95054)),x95055),f323(f323(f22(x95052),f323(f323(f6(x95051,x95052),x95053),x95055)),f323(f323(f6(x95051,x95052),x95054),x95055)))
% 179.72/179.58 [9506]~P72(x95062)+E(f323(f323(f6(x95061,x95062),f323(f323(f18(x95061,x95062,x95062),f323(f323(f8(x95062,f867(x95062,x95062),x95061),f78(x95062)),x95063)),x95064)),x95065),f323(f323(f78(x95062),f323(f323(f6(x95061,x95062),x95063),x95065)),f323(f323(f6(x95061,x95062),x95064),x95065)))
% 179.72/179.58 [9507]~P68(x95072)+E(f323(f323(f9(x95071,x95072),f323(f323(f18(x95071,x95072,x95072),f323(f323(f8(x95072,f867(x95072,x95072),x95071),f79(x95072)),x95073)),x95074)),x95075),f323(f323(f79(x95072),f323(f323(f9(x95071,x95072),x95073),x95075)),f323(f323(f9(x95071,x95072),x95074),x95075)))
% 179.72/179.58 [9546]~E(x95463,f188(f867(x95461,a855)))+E(f323(f323(f39(x95461,f867(x95462,a855)),x95463),f323(f323(f7(x95461,f867(x95462,a855),f867(x95462,a855)),f323(f323(f8(f867(x95462,a855),f867(f867(x95462,a855),f867(x95462,a855)),x95461),f110(f867(x95462,a855))),x95464)),x95465)),f188(f867(x95462,a855)))
% 179.72/179.58 [9547]~E(x95473,f188(f867(x95471,a855)))+E(f323(f323(f40(x95471,f867(x95472,a855)),x95473),f323(f323(f7(x95471,f867(x95472,a855),f867(x95472,a855)),f323(f323(f8(f867(x95472,a855),f867(f867(x95472,a855),f867(x95472,a855)),x95471),f22(f867(x95472,a855))),x95474)),x95475)),f246(f867(x95472,a855)))
% 179.72/179.58 [9548]~E(x95483,f188(f867(x95481,a855)))+E(f323(f323(f40(x95481,f867(x95482,a855)),x95483),f323(f323(f7(x95481,f867(x95482,a855),f867(x95482,a855)),f323(f323(f8(f867(x95482,a855),f867(f867(x95482,a855),f867(x95482,a855)),x95481),f101(f867(x95482,a855))),x95484)),x95485)),f246(f867(x95482,a855)))
% 179.72/179.58 [9570]E(x95701,f188(f867(x95702,a855)))+E(f323(f323(f39(x95702,f867(x95703,a855)),x95701),f323(f323(f7(x95702,f867(x95703,a855),f867(x95703,a855)),f323(f323(f8(f867(x95703,a855),f867(f867(x95703,a855),f867(x95703,a855)),x95702),f110(f867(x95703,a855))),x95704)),x95705)),f323(f323(f110(f867(x95703,a855)),f323(f323(f39(x95702,f867(x95703,a855)),x95701),x95704)),x95705))
% 179.72/179.58 [9571]E(x95711,f188(f867(x95712,a855)))+E(f323(f323(f40(x95712,f867(x95713,a855)),x95711),f323(f323(f7(x95712,f867(x95713,a855),f867(x95713,a855)),f323(f323(f8(f867(x95713,a855),f867(f867(x95713,a855),f867(x95713,a855)),x95712),f22(f867(x95713,a855))),x95714)),x95715)),f323(f323(f22(f867(x95713,a855)),f323(f323(f40(x95712,f867(x95713,a855)),x95711),x95714)),x95715))
% 179.72/179.58 [9572]E(x95721,f188(f867(x95722,a855)))+E(f323(f323(f40(x95722,f867(x95723,a855)),x95721),f323(f323(f7(x95722,f867(x95723,a855),f867(x95723,a855)),f323(f323(f8(f867(x95723,a855),f867(f867(x95723,a855),f867(x95723,a855)),x95722),f101(f867(x95723,a855))),x95724)),x95725)),f323(f323(f101(f867(x95723,a855)),f323(f323(f40(x95722,f867(x95723,a855)),x95721),x95724)),x95725))
% 179.72/179.58 [9139]~P101(f323(f323(f237(a860),x91391),x91394))+E(f323(f323(f22(a860),f323(f323(f78(a860),f323(f323(f79(a860),x91391),x91392)),x91393)),f323(f323(f78(a860),f323(f323(f79(a860),x91394),x91392)),x91395)),f323(f323(f22(a860),x91393),f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x91394),x91391)),x91392)),x91395)))
% 179.72/179.58 [9727]~P139(x97271)+E(f323(f159(x97271),f323(f323(f147(x97272,x97271),f323(f323(f7(x97272,x97271,x97271),f323(f323(f8(x97271,f867(x97271,x97271),x97272),f79(x97271)),x97273)),x97274)),x97275)),f323(f323(f79(x97271),f323(f159(x97271),f323(f323(f147(x97272,x97271),x97273),x97275))),x97274))
% 179.72/179.58 [9733]~P60(x97331)+E(f323(f159(x97331),f323(f323(f147(x97332,x97331),f323(f323(f18(x97332,x97331,x97331),f323(f323(f8(x97331,f867(x97331,x97331),x97332),f22(x97331)),x97333)),x97334)),x97335)),f323(f323(f22(x97331),f323(f159(x97331),f323(f323(f147(x97332,x97331),x97333),x97335))),f323(f159(x97331),f323(f323(f147(x97332,x97331),x97334),x97335))))
% 179.72/179.58 [9734]~P72(x97341)+E(f323(f159(x97341),f323(f323(f147(x97342,x97341),f323(f323(f18(x97342,x97341,x97341),f323(f323(f8(x97341,f867(x97341,x97341),x97342),f78(x97341)),x97343)),x97344)),x97345)),f323(f323(f78(x97341),f323(f159(x97341),f323(f323(f147(x97342,x97341),x97343),x97345))),f323(f159(x97341),f323(f323(f147(x97342,x97341),x97344),x97345))))
% 179.72/179.58 [9876]P101(f323(x98761,f323(f323(f175(x98762,x98763),x98764),x98765)))+~P101(f323(x98761,f323(f323(f175(x98762,x98763),f323(f323(f169(x98762),f323(f323(f235(a860),f323(f189(f861(x98762)),x98764)),f323(f189(f861(x98763)),x98765))),x98764)),f323(f323(f169(x98763),f323(f323(f235(a860),f323(f189(f861(x98762)),x98764)),f323(f189(f861(x98763)),x98765))),x98765))))
% 179.72/179.58 [10110]~P101(f323(f323(f325(f866(x101102,x101101)),f323(f323(f258(x101102,x101101),x101104),x101105)),f323(f278(x101101,x101102),x101103)))+P101(f323(f323(f247(x101101,x101102,f323(f323(f7(x101101,f867(f866(x101101,x101102),a855),f867(x101102,a855)),f323(f323(f8(f867(x101102,f867(f867(f866(x101101,x101102),a855),a855)),f867(f867(f866(x101101,x101102),a855),f867(x101102,a855)),x101101),f7(x101102,f867(f866(x101101,x101102),a855),a855)),f323(f323(f8(f867(x101102,f866(x101101,x101102)),f867(x101102,f867(f867(f866(x101101,x101102),a855),a855)),x101101),f323(f8(f866(x101101,x101102),f867(f867(f866(x101101,x101102),a855),a855),x101102),f325(f866(x101101,x101102)))),f258(x101101,x101102)))),x101103)),x101104),x101105))
% 179.72/179.58 [10119]P101(f323(f323(f325(f866(x101191,x101192)),f323(f323(f258(x101191,x101192),x101193),x101194)),f323(f278(x101192,x101191),x101195)))+~P101(f323(f323(f247(x101192,x101191,f323(f323(f7(x101192,f867(f866(x101192,x101191),a855),f867(x101191,a855)),f323(f323(f8(f867(x101191,f867(f867(f866(x101192,x101191),a855),a855)),f867(f867(f866(x101192,x101191),a855),f867(x101191,a855)),x101192),f7(x101191,f867(f866(x101192,x101191),a855),a855)),f323(f323(f8(f867(x101191,f866(x101192,x101191)),f867(x101191,f867(f867(f866(x101192,x101191),a855),a855)),x101192),f323(f8(f866(x101192,x101191),f867(f867(f866(x101192,x101191),a855),a855),x101191),f325(f866(x101192,x101191)))),f258(x101192,x101191)))),x101195)),x101193),x101194))
% 179.72/179.58 [9377]~P101(f323(f323(f237(a860),x93774),x93771))+E(f323(f323(f22(a860),f323(f323(f78(a860),f323(f323(f79(a860),x93771),x93772)),x93773)),f323(f323(f78(a860),f323(f323(f79(a860),x93774),x93772)),x93775)),f323(f323(f22(a860),f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x93771),x93774)),x93772)),x93773)),x93775))
% 179.72/179.58 [5235]E(x52351,x52352)+~E(f27(x52353,x52354,x52351),f27(x52355,x52356,x52352))
% 179.72/179.58 [5236]E(x52361,x52362)+~E(f27(x52363,x52361,x52364),f27(x52365,x52362,x52366))
% 179.72/179.58 [5237]E(x52371,x52372)+~E(f27(x52371,x52373,x52374),f27(x52372,x52375,x52376))
% 179.72/179.58 [5238]E(x52381,x52382)+~E(f26(x52383,x52384,x52381),f26(x52385,x52386,x52382))
% 179.72/179.58 [5239]E(x52391,x52392)+~E(f26(x52393,x52391,x52394),f26(x52395,x52392,x52396))
% 179.72/179.58 [5240]E(x52401,x52402)+~E(f26(x52401,x52403,x52404),f26(x52402,x52405,x52406))
% 179.72/179.58 [6665]E(f323(f180(x66651,x66652,x66653,x66654),x66655),f323(f230(x66652),x66656))+~E(f323(x66654,x66655),f323(f230(x66652),x66656))
% 179.72/179.58 [6808]E(f323(f232(f864(x68081),x68082,f200(x68081),x68083),f323(x68084,x68085)),f323(x68083,x68086))+~E(f323(x68084,x68085),f323(f230(x68082),x68086))
% 179.72/179.58 [8322]~P21(x83225,x83221,x83222,x83226)+E(f323(f71(x83221,x83221,x83221,f323(x83222,x83223)),f323(x83222,x83224)),f323(f71(x83221,x83221,x83221,f323(x83222,x83224)),f323(x83222,x83223)))
% 179.72/179.58 [8553]~P53(x85534,x85535,x85532,x85531,x85536)+E(f323(x85531,f323(x85532,x85533)),x85533)
% 179.72/179.58 [8721]P27(x87211,x87212,x87213,x87214)+~P27(x87211,x87215,f323(f71(x87212,x87215,x87211,x87216),x87213),x87214)
% 179.72/179.58 [8808]~P27(x88084,x88082,f323(f71(x88081,x88082,x88084,x88083),x88085),x88086)+P27(x88081,x88082,x88083,f323(f302(x88084,x88081,x88085),x88086))
% 179.72/179.58 [9508]P101(f323(f59(x95081),x95082))+~P101(f323(f64(x95081,x95083,x95084,x95085,x95082),x95086))
% 179.72/179.58 [9517]~P101(f323(f323(f325(x95174),x95173),f291(x95174,x95175,x95171,x95172,x95176)))+P101(f323(f323(x95171,x95172),x95173))
% 179.72/179.58 [9518]~P101(f323(f323(f325(x95184),x95183),f288(x95184,x95181,x95185,x95182,x95186)))+P101(f323(f323(x95181,x95182),x95183))
% 179.72/179.58 [9519]~P101(f323(f323(f325(x95194),x95192),f291(x95194,x95191,x95195,x95196,x95193)))+P101(f323(f323(x95191,x95192),x95193))
% 179.72/179.58 [9520]~P101(f323(f323(f325(x95204),x95202),f288(x95204,x95205,x95201,x95206,x95203)))+P101(f323(f323(x95201,x95202),x95203))
% 179.72/179.58 [5738]E(x57381,x57382)+~E(f323(f323(f258(x57383,x57384),x57385),x57381),f323(f323(f258(x57383,x57384),x57386),x57382))
% 179.72/179.58 [5740]E(x57401,x57402)+~E(f323(f323(f258(x57403,x57404),x57401),x57405),f323(f323(f258(x57403,x57404),x57402),x57406))
% 179.72/179.58 [5864]~P18(x58645,x58646,x58641)+E(f323(f323(x58641,x58642),f323(f323(x58641,x58643),x58644)),f323(f323(x58641,x58643),f323(f323(x58641,x58642),x58644)))
% 179.72/179.58 [7259]~P33(x72594,x72591,f323(f323(f144(x72594),x72592),x72595),f323(f323(f144(x72594),x72593),x72596))+P101(f323(f323(x72591,x72592),x72593))
% 179.72/179.58 [7621]P33(x76211,x76212,x76213,x76214)+~P33(x76211,x76212,f323(f323(f144(x76211),x76215),x76213),f323(f323(f144(x76211),x76216),x76214))
% 179.72/179.58 [8658]~P53(x86585,x86581,x86582,x86586,x86584)+P101(f323(f323(f325(x86581),f323(x86582,x86583)),x86584))
% 179.72/179.58 [8835]E(f323(f74(x88351,x88352,x88353,x88354,x88355),x88356),f323(x88353,x88356))+P101(f323(f323(f325(x88351),x88356),x88355))
% 179.72/179.58 [8856]~E(x88563,f323(f323(f144(x88561),x88565),x88566))+P101(f323(f323(f325(f866(f861(x88561),f861(x88561))),f323(f323(f258(f861(x88561),f861(x88561)),x88562),f323(f323(f121(x88561),x88562),x88563))),f140(x88561,x88564)))
% 179.72/179.58 [8862]E(f323(f74(x88621,x88622,x88623,x88624,x88625),x88626),f323(x88624,x88626))+~P101(f323(f323(f325(x88621),x88626),x88625))
% 179.72/179.58 [8868]E(f323(f181(x88681,x88682,x88683,x88684,x88685),x88686),f323(x88683,x88686))+P101(f323(f323(f325(x88681),x88686),f323(f166(x88681),x88684)))
% 179.72/179.58 [9092]~P35(x90921,x90922,x90923,x90925,x90926)+P35(x90921,x90922,x90923,f323(f323(f169(x90921),x90924),x90925),f323(f323(f169(x90922),x90924),x90926))
% 179.72/179.58 [9093]~P35(x90931,x90932,x90933,x90935,x90936)+P35(x90931,x90932,x90933,f323(f323(f131(x90931),x90934),x90935),f323(f323(f131(x90932),x90934),x90936))
% 179.72/179.58 [9582]~P25(x95824,x95822,x95825,x95823,x95826,x95821)+E(f323(x95821,f188(f867(x95822,a855))),x95823)
% 179.72/179.58 [9826]~E(f323(x98264,f323(f257(x98261,x98263),x98265)),f323(x98266,f323(f257(x98261,x98263),x98265)))+E(f323(f263(x98261,x98262,x98263,x98263,x98264,f32(x98263)),x98265),f323(f263(x98261,x98262,x98263,x98263,x98266,f32(x98263)),x98265))
% 179.72/179.58 [9827]~E(f323(x98274,f323(f261(x98271,x98272),x98275)),f323(x98276,f323(f261(x98271,x98272),x98275)))+E(f323(f263(x98271,x98271,x98272,x98273,f32(x98271),x98274),x98275),f323(f263(x98271,x98271,x98272,x98273,f32(x98271),x98276),x98275))
% 179.72/179.58 [9872]~E(f323(f263(x98722,x98726,x98723,x98723,x98721,f32(x98723)),x98724),f323(f263(x98722,x98726,x98723,x98723,x98725,f32(x98723)),x98724))+E(f323(x98721,f323(f257(x98722,x98723),x98724)),f323(x98725,f323(f257(x98722,x98723),x98724)))
% 179.72/179.58 [9873]~E(f323(f263(x98732,x98732,x98733,x98736,f32(x98732),x98731),x98734),f323(f263(x98732,x98732,x98733,x98736,f32(x98732),x98735),x98734))+E(f323(x98731,f323(f261(x98732,x98733),x98734)),f323(x98735,f323(f261(x98732,x98733),x98734)))
% 179.72/179.58 [8762]P101(f323(f323(f325(x87621),x87622),x87623))+~P101(f323(f323(f325(f866(x87621,x87624)),f323(f323(f258(x87621,x87624),x87622),x87625)),f323(f323(f260(x87621,x87624),x87623),x87626)))
% 179.72/179.58 [8778]P101(f323(f323(f325(x87781),x87782),f323(x87783,x87784)))+~P101(f323(f323(f325(f866(x87785,x87781)),f323(f323(f258(x87785,x87781),x87784),x87782)),f323(f323(f260(x87785,x87781),x87786),x87783)))
% 179.72/179.58 [8865]~E(f323(f189(f861(x88651)),x88654),f323(f189(f861(x88652)),x88655))+E(f181(x88651,x88652,x88653,x88654,f323(f323(f121(x88652),x88655),x88656)),f181(x88651,x88652,x88653,x88654,x88655))
% 179.72/179.58 [8866]~E(f323(f189(f861(x88661)),x88664),f323(f189(f861(x88662)),x88666))+E(f181(x88661,x88662,x88663,f323(f323(f121(x88661),x88664),x88665),x88666),f181(x88661,x88662,x88663,x88664,x88666))
% 179.72/179.58 [9110]P101(f323(f323(f325(x91101),x91104),f177(x91101,x91102,x91106)))+E(f180(x91101,x91102,f323(f323(f323(f70(x91101,f864(x91102)),x91103),x91104),f323(f230(x91102),x91105)),x91106),f323(f323(f323(f70(x91101,f864(x91102)),f180(x91101,x91102,x91103,x91106)),x91104),f323(f230(x91102),x91105)))
% 179.72/179.58 [9209]P101(f323(f323(f325(f866(x92091,x92091)),f323(f323(f258(x92091,x92091),f323(x92092,x92093)),f323(x92092,x92094))),x92095))+~P101(f323(f323(f325(f866(x92096,x92096)),f323(f323(f258(x92096,x92096),x92093),x92094)),f323(f323(f279(x92091,x92096),x92095),x92092)))
% 179.72/179.58 [9228]~P101(f323(f323(f325(f866(x92284,x92284)),f323(f323(f258(x92284,x92284),f323(x92286,x92282)),f323(x92286,x92283))),x92285))+P101(f323(f323(f325(f866(x92281,x92281)),f323(f323(f258(x92281,x92281),x92282),x92283)),f323(f323(f279(x92284,x92281),x92285),x92286)))
% 179.72/179.58 [9875]E(f323(f323(f258(x98751,x98752),f774(x98753,x98754,x98755,x98756,x98752,x98751)),f776(x98753,x98754,x98755,x98756,x98752,x98751)),x98756)+~P101(f323(f323(f325(f866(x98751,x98752)),x98756),f323(f323(f280(x98751,x98755,x98752),x98754),x98753)))
% 179.72/179.58 [10073]~P101(f323(f323(f325(f866(x100731,x100736)),x100735),f323(f323(f280(x100731,x100732,x100736),x100734),x100733)))+P101(f323(f323(f325(f866(x100731,x100732)),f323(f323(f258(x100731,x100732),f774(x100733,x100734,x100732,x100735,x100736,x100731)),f777(x100733,x100734,x100732,x100735,x100736,x100731))),x100734))
% 179.72/179.58 [10074]~P101(f323(f323(f325(f866(x100746,x100742)),x100745),f323(f323(f280(x100746,x100741,x100742),x100744),x100743)))+P101(f323(f323(f325(f866(x100741,x100742)),f323(f323(f258(x100741,x100742),f777(x100743,x100744,x100741,x100745,x100742,x100746)),f776(x100743,x100744,x100741,x100745,x100742,x100746))),x100743))
% 179.72/179.58 [6132]~E(x61326,x61324)+E(f323(f323(f323(f323(f70(x61321,x61322),x61323),x61324),x61325),x61326),x61325)
% 179.72/179.58 [6181]E(x61811,x61812)+E(f323(f323(f323(f323(f70(x61813,x61814),x61815),x61812),x61816),x61811),f323(x61815,x61811))
% 179.72/179.58 [7692]~P6(x76922)+E(f323(f323(f39(x76921,x76922),x76923),f323(f323(f7(x76921,x76924,x76922),x76925),x76926)),f323(f323(f323(f39(x76921,f867(x76924,x76922)),x76923),x76925),x76926))
% 179.72/179.58 [7693]~P6(x76932)+E(f323(f323(f40(x76931,x76932),x76933),f323(f323(f7(x76931,x76934,x76932),x76935),x76936)),f323(f323(f323(f40(x76931,f867(x76934,x76932)),x76933),x76935),x76936))
% 179.72/179.58 [8463]E(f323(f323(f39(x84631,f867(x84632,a855)),x84633),f323(f323(f8(f867(x84632,a855),f867(x84632,a855),x84631),f323(f301(x84632),x84634)),x84635)),f323(f323(f301(x84632),x84634),f323(f323(f39(x84631,f867(x84632,a855)),x84633),x84635)))+~P101(f323(f323(f325(x84631),x84636),x84633))
% 179.72/179.58 [8912]~P6(x89122)+E(f323(f323(f39(x89121,x89122),x89123),f323(f323(f8(f867(x89124,x89122),x89122,x89121),f323(f39(x89124,x89122),x89125)),f323(f7(x89124,x89121,x89122),x89126))),f323(f323(f39(x89124,x89122),x89125),f323(f323(f8(f867(x89121,x89122),x89122,x89124),f323(f39(x89121,x89122),x89123)),x89126)))
% 179.72/179.58 [8913]~P6(x89132)+E(f323(f323(f40(x89131,x89132),x89133),f323(f323(f8(f867(x89134,x89132),x89132,x89131),f323(f40(x89134,x89132),x89135)),f323(f7(x89134,x89131,x89132),x89136))),f323(f323(f40(x89134,x89132),x89135),f323(f323(f8(f867(x89131,x89132),x89132,x89134),f323(f40(x89131,x89132),x89133)),x89136)))
% 179.72/179.58 [9119]P101(f323(f323(f325(x91191),x91192),f323(f166(x91191),x91193)))+~P101(f323(f323(f325(f866(x91194,x91191)),f323(f323(f258(x91194,x91191),x91195),x91192)),f323(f166(f866(x91194,x91191)),f323(f323(f175(x91194,x91191),x91196),x91193))))
% 179.72/179.58 [9120]P101(f323(f323(f325(x91201),x91202),f323(f166(x91201),x91203)))+~P101(f323(f323(f325(f866(x91201,x91204)),f323(f323(f258(x91201,x91204),x91202),x91205)),f323(f166(f866(x91201,x91204)),f323(f323(f175(x91201,x91204),x91203),x91206))))
% 179.72/179.58 [9225]P101(f323(f323(f237(f867(x92251,a855)),f323(f277(x92252,x92251,x92253),x92254)),x92255))+~P101(f323(f323(f237(f867(f866(x92252,x92251),a855)),x92253),f323(f323(f260(x92252,x92251),x92256),f323(f16(f867(x92251,a855),x92252),x92255))))
% 179.72/179.58 [9229]~P28(x92294,x92292,x92295,f246(f867(x92294,a855)),f246(f867(x92292,a855)))+E(f323(f323(f40(x92291,f867(x92292,a855)),x92293),f323(f323(f8(f867(x92294,a855),f867(x92292,a855),x92291),f302(x92294,x92292,x92295)),x92296)),f323(f302(x92294,x92292,x92295),f323(f323(f40(x92291,f867(x92294,a855)),x92293),x92296)))
% 179.72/179.58 [9411]P101(f323(f323(f325(f866(f861(x94111),f861(x94111))),f323(f323(f258(f861(x94111),f861(x94111)),f323(f323(f144(x94111),x94112),x94113)),f323(f323(f144(x94111),x94114),x94115))),f140(x94111,x94116)))+~P101(f323(f323(f325(f866(x94111,x94111)),f323(f323(f258(x94111,x94111),x94112),x94114)),x94116))
% 179.72/179.58 [9871]E(f323(f323(f258(x98711,x98712),f694(x98713,x98714,x98715,x98712,x98711,x98716)),f695(x98713,x98714,x98715,x98712,x98711,x98716)),x98716)+P101(f323(f323(f325(x98715),x98714),f323(f323(f262(x98711,x98712,f867(x98715,a855)),x98713),x98716)))
% 179.72/179.58 [9877]E(f323(f323(f258(x98771,x98772),f696(x98773,x98774,x98772,x98771,x98775,x98776)),f697(x98773,x98774,x98772,x98771,x98775,x98776)),x98773)+~P101(f323(f323(f325(x98776),x98775),f323(f323(f262(x98771,x98772,f867(x98776,a855)),x98774),x98773)))
% 179.72/179.58 [10033]P101(f323(f323(f325(x100331),x100332),f323(f323(x100333,f696(x100334,x100333,x100335,x100336,x100332,x100331)),f697(x100334,x100333,x100335,x100336,x100332,x100331))))+~P101(f323(f323(f325(x100331),x100332),f323(f323(f262(x100336,x100335,f867(x100331,a855)),x100333),x100334)))
% 179.72/179.58 [10051]~P101(f323(f323(f325(x100511),x100512),f323(f323(x100515,f694(x100515,x100512,x100511,x100514,x100513,x100516)),f695(x100515,x100512,x100511,x100514,x100513,x100516))))+P101(f323(f323(f325(x100511),x100512),f323(f323(f262(x100513,x100514,f867(x100511,a855)),x100515),x100516)))
% 179.72/179.58 [7810]P101(f323(f323(f325(x78101),x78104),x78106))+E(f182(x78101,x78102,f323(f323(f323(f70(x78101,f864(x78102)),x78103),x78104),x78105),x78106),f182(x78101,x78102,x78103,x78106))
% 179.72/179.58 [7890]P101(f323(f323(f325(x78901),x78904),x78906))+E(f323(f302(x78901,x78902,f323(f323(f323(f70(x78901,x78902),x78903),x78904),x78905)),x78906),f323(f302(x78901,x78902,x78903),x78906))
% 179.72/179.58 [7918]P101(f323(f323(f325(x79181),x79184),f323(f166(x79181),x79186)))+E(f323(f323(f147(x79181,x79182),f323(f323(f323(f70(x79181,x79182),x79183),x79184),x79185)),x79186),f323(f323(f147(x79181,x79182),x79183),x79186))
% 179.72/179.58 [8369]E(x83691,x83692)+E(f323(f323(f152(x83693,f323(f323(f152(x83693,x83694),x83691),x83695)),x83692),x83696),f323(f323(f152(x83693,f323(f323(f152(x83693,x83694),x83692),x83696)),x83691),x83695))
% 179.72/179.58 [8918]~P101(f323(f323(f325(x89183),x89186),x89185))+E(f323(f323(f301(x89181),x89182),f323(f302(x89183,x89181,x89184),f323(f323(f22(f867(x89183,a855)),x89185),f323(f323(f301(x89183),x89186),f188(f867(x89183,a855)))))),f323(f302(x89183,x89181,f323(f323(f323(f70(x89183,x89181),x89184),x89186),x89182)),x89185))
% 179.72/179.58 [9689]E(f181(x96891,x96892,x96893,f323(f323(f121(x96891),x96894),f323(f323(f144(x96891),x96895),f113(x96891))),x96896),f323(f323(f323(f70(x96891,f864(x96892)),f181(x96891,x96892,x96893,x96894,x96896)),x96895),f323(f230(x96892),f323(f323(f158(x96892),x96896),f323(f189(f861(x96891)),x96894)))))+~P101(f323(f323(f238(a860),f323(f189(f861(x96891)),x96894)),f323(f189(f861(x96892)),x96896)))
% 179.72/179.58 [8702]~E(x87023,x87026)+E(f323(f323(f179(x87021,x87022),f323(f323(f144(f866(x87021,x87022)),f323(f323(f258(x87021,x87022),x87023),x87024)),x87025)),x87026),f323(f230(x87022),x87024))
% 179.72/179.58 [8732]E(x87321,x87322)+E(f323(f323(f179(x87323,x87324),f323(f323(f144(f866(x87323,x87324)),f323(f323(f258(x87323,x87324),x87321),x87325)),x87326)),x87322),f323(f323(f179(x87323,x87324),x87326),x87322))
% 179.72/179.58 [8991]~P101(f323(f323(x89914,x89915),x89916))+P101(f323(f323(f323(f323(f110(f867(x89911,f867(x89912,a855))),x89913),x89914),x89915),x89916))
% 179.72/179.58 [8993]~P101(f323(f323(x89933,x89935),x89936))+P101(f323(f323(f323(f323(f110(f867(x89931,f867(x89932,a855))),x89933),x89934),x89935),x89936))
% 179.72/179.58 [9278]P101(f323(f323(x92781,x92782),x92783))+~P101(f323(f323(f323(f323(f101(f867(x92784,f867(x92785,a855))),x92786),x92781),x92782),x92783))
% 179.72/179.58 [9279]P101(f323(f323(x92791,x92792),x92793))+~P101(f323(f323(f323(f323(f101(f867(x92794,f867(x92795,a855))),x92791),x92796),x92792),x92793))
% 179.72/179.58 [9711]~P72(x97112)+E(f323(f323(f6(x97111,x97112),f323(f323(f7(x97111,f867(x97113,a855),x97112),f323(f323(f8(f867(x97113,x97112),f867(f867(x97113,a855),x97112),x97111),f6(x97113,x97112)),x97114)),x97115)),x97116),f323(f323(f6(f866(x97111,x97113),x97112),f323(f262(x97111,x97113,x97112),x97114)),f323(f323(f260(x97111,x97113),x97116),f323(f16(f867(x97113,a855),x97111),x97115))))
% 179.72/179.58 [9712]~P68(x97122)+E(f323(f323(f9(x97121,x97122),f323(f323(f7(x97121,f867(x97123,a855),x97122),f323(f323(f8(f867(x97123,x97122),f867(f867(x97123,a855),x97122),x97121),f9(x97123,x97122)),x97124)),x97125)),x97126),f323(f323(f9(f866(x97121,x97123),x97122),f323(f262(x97121,x97123,x97122),x97124)),f323(f323(f260(x97121,x97123),x97126),f323(f16(f867(x97123,a855),x97121),x97125))))
% 179.72/179.58 [9854]~P72(x98542)+E(f323(f323(f6(x98541,x98542),f323(f323(f7(x98541,f867(x98543,a855),x98542),f323(f323(f8(f867(x98543,x98542),f867(f867(x98543,a855),x98542),x98541),f6(x98543,x98542)),f323(f7(x98543,x98541,x98542),x98544))),x98545)),x98546),f323(f323(f6(x98543,x98542),f323(f323(f7(x98543,f867(x98541,a855),x98542),f323(f323(f8(f867(x98541,x98542),f867(f867(x98541,a855),x98542),x98543),f6(x98541,x98542)),x98544)),x98546)),x98545))
% 179.72/179.58 [9551]~P101(f323(f323(f325(x95511),x95515),x95514))+E(f323(f323(f323(f70(x95511,f864(x95512)),f182(x95511,x95512,x95513,f323(f323(f22(f867(x95511,a855)),x95514),f323(f323(f301(x95511),x95515),f188(f867(x95511,a855)))))),x95515),x95516),f182(x95511,x95512,f323(f323(f323(f70(x95511,f864(x95512)),x95513),x95515),x95516),x95514))
% 179.72/179.58 [10129]~P101(f323(f323(f325(f866(x101291,x101292)),f323(f323(f258(x101291,x101292),x101295),x101296)),f323(f323(f110(f867(f866(x101291,x101292),a855)),x101293),x101294)))+P101(f323(f323(f323(f323(f110(f867(x101291,f867(x101292,a855))),f323(f323(f7(x101291,f867(f866(x101291,x101292),a855),f867(x101292,a855)),f323(f323(f8(f867(x101292,f867(f867(f866(x101291,x101292),a855),a855)),f867(f867(f866(x101291,x101292),a855),f867(x101292,a855)),x101291),f7(x101292,f867(f866(x101291,x101292),a855),a855)),f323(f323(f8(f867(x101292,f866(x101291,x101292)),f867(x101292,f867(f867(f866(x101291,x101292),a855),a855)),x101291),f323(f8(f866(x101291,x101292),f867(f867(f866(x101291,x101292),a855),a855),x101292),f325(f866(x101291,x101292)))),f258(x101291,x101292)))),x101293)),f323(f323(f7(x101291,f867(f866(x101291,x101292),a855),f867(x101292,a855)),f323(f323(f8(f867(x101292,f867(f867(f866(x101291,x101292),a855),a855)),f867(f867(f866(x101291,x101292),a855),f867(x101292,a855)),x101291),f7(x101292,f867(f866(x101291,x101292),a855),a855)),f323(f323(f8(f867(x101292,f866(x101291,x101292)),f867(x101292,f867(f867(f866(x101291,x101292),a855),a855)),x101291),f323(f8(f866(x101291,x101292),f867(f867(f866(x101291,x101292),a855),a855),x101292),f325(f866(x101291,x101292)))),f258(x101291,x101292)))),x101294)),x101295),x101296))
% 179.72/179.58 [10130]~P101(f323(f323(f325(f866(x101301,x101302)),f323(f323(f258(x101301,x101302),x101305),x101306)),f323(f323(f101(f867(f866(x101301,x101302),a855)),x101303),x101304)))+P101(f323(f323(f323(f323(f101(f867(x101301,f867(x101302,a855))),f323(f323(f7(x101301,f867(f866(x101301,x101302),a855),f867(x101302,a855)),f323(f323(f8(f867(x101302,f867(f867(f866(x101301,x101302),a855),a855)),f867(f867(f866(x101301,x101302),a855),f867(x101302,a855)),x101301),f7(x101302,f867(f866(x101301,x101302),a855),a855)),f323(f323(f8(f867(x101302,f866(x101301,x101302)),f867(x101302,f867(f867(f866(x101301,x101302),a855),a855)),x101301),f323(f8(f866(x101301,x101302),f867(f867(f866(x101301,x101302),a855),a855),x101302),f325(f866(x101301,x101302)))),f258(x101301,x101302)))),x101303)),f323(f323(f7(x101301,f867(f866(x101301,x101302),a855),f867(x101302,a855)),f323(f323(f8(f867(x101302,f867(f867(f866(x101301,x101302),a855),a855)),f867(f867(f866(x101301,x101302),a855),f867(x101302,a855)),x101301),f7(x101302,f867(f866(x101301,x101302),a855),a855)),f323(f323(f8(f867(x101302,f866(x101301,x101302)),f867(x101302,f867(f867(f866(x101301,x101302),a855),a855)),x101301),f323(f8(f866(x101301,x101302),f867(f867(f866(x101301,x101302),a855),a855),x101302),f325(f866(x101301,x101302)))),f258(x101301,x101302)))),x101304)),x101305),x101306))
% 179.72/179.58 [10136]P101(f323(f323(f325(f866(x101361,x101362)),f323(f323(f258(x101361,x101362),x101363),x101364)),f323(f323(f110(f867(f866(x101361,x101362),a855)),x101365),x101366)))+~P101(f323(f323(f323(f323(f110(f867(x101361,f867(x101362,a855))),f323(f323(f7(x101361,f867(f866(x101361,x101362),a855),f867(x101362,a855)),f323(f323(f8(f867(x101362,f867(f867(f866(x101361,x101362),a855),a855)),f867(f867(f866(x101361,x101362),a855),f867(x101362,a855)),x101361),f7(x101362,f867(f866(x101361,x101362),a855),a855)),f323(f323(f8(f867(x101362,f866(x101361,x101362)),f867(x101362,f867(f867(f866(x101361,x101362),a855),a855)),x101361),f323(f8(f866(x101361,x101362),f867(f867(f866(x101361,x101362),a855),a855),x101362),f325(f866(x101361,x101362)))),f258(x101361,x101362)))),x101365)),f323(f323(f7(x101361,f867(f866(x101361,x101362),a855),f867(x101362,a855)),f323(f323(f8(f867(x101362,f867(f867(f866(x101361,x101362),a855),a855)),f867(f867(f866(x101361,x101362),a855),f867(x101362,a855)),x101361),f7(x101362,f867(f866(x101361,x101362),a855),a855)),f323(f323(f8(f867(x101362,f866(x101361,x101362)),f867(x101362,f867(f867(f866(x101361,x101362),a855),a855)),x101361),f323(f8(f866(x101361,x101362),f867(f867(f866(x101361,x101362),a855),a855),x101362),f325(f866(x101361,x101362)))),f258(x101361,x101362)))),x101366)),x101363),x101364))
% 179.72/179.58 [10137]P101(f323(f323(f325(f866(x101371,x101372)),f323(f323(f258(x101371,x101372),x101373),x101374)),f323(f323(f101(f867(f866(x101371,x101372),a855)),x101375),x101376)))+~P101(f323(f323(f323(f323(f101(f867(x101371,f867(x101372,a855))),f323(f323(f7(x101371,f867(f866(x101371,x101372),a855),f867(x101372,a855)),f323(f323(f8(f867(x101372,f867(f867(f866(x101371,x101372),a855),a855)),f867(f867(f866(x101371,x101372),a855),f867(x101372,a855)),x101371),f7(x101372,f867(f866(x101371,x101372),a855),a855)),f323(f323(f8(f867(x101372,f866(x101371,x101372)),f867(x101372,f867(f867(f866(x101371,x101372),a855),a855)),x101371),f323(f8(f866(x101371,x101372),f867(f867(f866(x101371,x101372),a855),a855),x101372),f325(f866(x101371,x101372)))),f258(x101371,x101372)))),x101375)),f323(f323(f7(x101371,f867(f866(x101371,x101372),a855),f867(x101372,a855)),f323(f323(f8(f867(x101372,f867(f867(f866(x101371,x101372),a855),a855)),f867(f867(f866(x101371,x101372),a855),f867(x101372,a855)),x101371),f7(x101372,f867(f866(x101371,x101372),a855),a855)),f323(f323(f8(f867(x101372,f866(x101371,x101372)),f867(x101372,f867(f867(f866(x101371,x101372),a855),a855)),x101371),f323(f8(f866(x101371,x101372),f867(f867(f866(x101371,x101372),a855),a855),x101372),f325(f866(x101371,x101372)))),f258(x101371,x101372)))),x101376)),x101373),x101374))
% 179.72/179.58 [10125]~P101(f323(f323(f325(f866(x101252,x101253)),f323(f323(f258(x101252,x101253),x101255),x101256)),f323(f323(f39(x101251,f867(f866(x101252,x101253),a855)),f246(f867(x101251,a855))),x101254)))+P101(f323(f323(f323(f323(f39(x101251,f867(x101252,f867(x101253,a855))),f246(f867(x101251,a855))),f323(f323(f8(f867(f866(x101252,x101253),a855),f867(x101252,f867(x101253,a855)),x101251),f323(f7(x101252,f867(f866(x101252,x101253),a855),f867(x101253,a855)),f323(f323(f8(f867(x101253,f867(f867(f866(x101252,x101253),a855),a855)),f867(f867(f866(x101252,x101253),a855),f867(x101253,a855)),x101252),f7(x101253,f867(f866(x101252,x101253),a855),a855)),f323(f323(f8(f867(x101253,f866(x101252,x101253)),f867(x101253,f867(f867(f866(x101252,x101253),a855),a855)),x101252),f323(f8(f866(x101252,x101253),f867(f867(f866(x101252,x101253),a855),a855),x101253),f325(f866(x101252,x101253)))),f258(x101252,x101253))))),x101254)),x101255),x101256))
% 179.72/179.58 [10126]~P101(f323(f323(f325(f866(x101262,x101263)),f323(f323(f258(x101262,x101263),x101265),x101266)),f323(f323(f40(x101261,f867(f866(x101262,x101263),a855)),f246(f867(x101261,a855))),x101264)))+P101(f323(f323(f323(f323(f40(x101261,f867(x101262,f867(x101263,a855))),f246(f867(x101261,a855))),f323(f323(f8(f867(f866(x101262,x101263),a855),f867(x101262,f867(x101263,a855)),x101261),f323(f7(x101262,f867(f866(x101262,x101263),a855),f867(x101263,a855)),f323(f323(f8(f867(x101263,f867(f867(f866(x101262,x101263),a855),a855)),f867(f867(f866(x101262,x101263),a855),f867(x101263,a855)),x101262),f7(x101263,f867(f866(x101262,x101263),a855),a855)),f323(f323(f8(f867(x101263,f866(x101262,x101263)),f867(x101263,f867(f867(f866(x101262,x101263),a855),a855)),x101262),f323(f8(f866(x101262,x101263),f867(f867(f866(x101262,x101263),a855),a855),x101263),f325(f866(x101262,x101263)))),f258(x101262,x101263))))),x101264)),x101265),x101266))
% 179.72/179.58 [10133]P101(f323(f323(f325(f866(x101331,x101332)),f323(f323(f258(x101331,x101332),x101333),x101334)),f323(f323(f39(x101335,f867(f866(x101331,x101332),a855)),f246(f867(x101335,a855))),x101336)))+~P101(f323(f323(f323(f323(f39(x101335,f867(x101331,f867(x101332,a855))),f246(f867(x101335,a855))),f323(f323(f8(f867(f866(x101331,x101332),a855),f867(x101331,f867(x101332,a855)),x101335),f323(f7(x101331,f867(f866(x101331,x101332),a855),f867(x101332,a855)),f323(f323(f8(f867(x101332,f867(f867(f866(x101331,x101332),a855),a855)),f867(f867(f866(x101331,x101332),a855),f867(x101332,a855)),x101331),f7(x101332,f867(f866(x101331,x101332),a855),a855)),f323(f323(f8(f867(x101332,f866(x101331,x101332)),f867(x101332,f867(f867(f866(x101331,x101332),a855),a855)),x101331),f323(f8(f866(x101331,x101332),f867(f867(f866(x101331,x101332),a855),a855),x101332),f325(f866(x101331,x101332)))),f258(x101331,x101332))))),x101336)),x101333),x101334))
% 179.72/179.58 [10134]P101(f323(f323(f325(f866(x101341,x101342)),f323(f323(f258(x101341,x101342),x101343),x101344)),f323(f323(f40(x101345,f867(f866(x101341,x101342),a855)),f246(f867(x101345,a855))),x101346)))+~P101(f323(f323(f323(f323(f40(x101345,f867(x101341,f867(x101342,a855))),f246(f867(x101345,a855))),f323(f323(f8(f867(f866(x101341,x101342),a855),f867(x101341,f867(x101342,a855)),x101345),f323(f7(x101341,f867(f866(x101341,x101342),a855),f867(x101342,a855)),f323(f323(f8(f867(x101342,f867(f867(f866(x101341,x101342),a855),a855)),f867(f867(f866(x101341,x101342),a855),f867(x101342,a855)),x101341),f7(x101342,f867(f866(x101341,x101342),a855),a855)),f323(f323(f8(f867(x101342,f866(x101341,x101342)),f867(x101342,f867(f867(f866(x101341,x101342),a855),a855)),x101341),f323(f8(f866(x101341,x101342),f867(f867(f866(x101341,x101342),a855),a855),x101342),f325(f866(x101341,x101342)))),f258(x101341,x101342))))),x101346)),x101343),x101344))
% 179.72/179.58 [7369]E(f323(x73691,f323(x73692,x73693)),f323(x73694,x73693))+~E(f323(f71(x73695,x73696,x73697,x73691),x73692),x73694)
% 179.72/179.58 [9581]~P24(x95813,x95814,x95811,x95815,x95816,x95817)+E(f323(f323(x95811,x95812),x95812),x95812)
% 179.72/179.58 [9951]~E(f323(f232(f864(x99517),x99511,f200(x99517),x99515),f323(x99514,x99513)),f323(f230(x99517),x99512))+E(f323(f230(x99511),f831(x99512,x99513,x99514,x99515,x99516,x99517,x99511)),f323(x99514,x99513))
% 179.72/179.58 [9952]~E(f323(f232(f864(x99526),x99527,f200(x99526),x99521),f323(x99524,x99523)),f323(f230(x99526),x99522))+E(f323(x99521,f831(x99522,x99523,x99524,x99521,x99525,x99526,x99527)),f323(f230(x99526),x99522))
% 179.72/179.58 [5961]~E(f323(f323(f147(x59611,x59615),x59616),x59612),f323(f323(f147(x59613,x59615),x59617),x59614))+E(f323(f189(f861(x59611)),x59612),f323(f189(f861(x59613)),x59614))
% 179.72/179.58 [7445]E(x74451,x74452)+~E(f323(f323(f323(f70(x74453,f864(x74454)),x74455),x74456),f323(f230(x74454),x74451)),f323(f323(f323(f70(x74453,f864(x74454)),x74457),x74456),f323(f230(x74454),x74452)))
% 179.72/179.58 [8401]E(f323(x84011,f323(x84012,x84013)),f323(x84014,x84013))+~E(f323(f71(x84015,x84016,x84017,x84011),x84012),f323(f71(x84016,x84016,x84017,f32(x84016)),x84014))
% 179.72/179.58 [8751]~P35(x87514,x87515,x87511,f323(f323(f144(x87514),x87512),x87516),f323(f323(f144(x87515),x87513),x87517))+P101(f323(f323(x87511,x87512),x87513))
% 179.72/179.58 [9126]P35(x91261,x91262,x91263,x91264,x91265)+~P35(x91261,x91262,x91263,f323(f323(f144(x91261),x91266),x91264),f323(f323(f144(x91262),x91267),x91265))
% 179.72/179.58 [9750]P101(f323(f323(x97501,x97502),f665(x97503,x97502,x97504,x97501)))+~P101(f323(f323(f259(x97505,x97506,x97507,x97501,x97504),x97502),x97503))
% 179.72/179.58 [9771]P101(f323(f323(x97711,f665(x97712,x97713,x97711,x97714)),x97712))+~P101(f323(f323(f259(x97715,x97716,x97717,x97714,x97711),x97713),x97712))
% 179.72/179.58 [6004]E(x60041,x60042)+~E(f323(f323(f323(f90(x60043),x60044),x60045),x60041),f323(f323(f323(f90(x60043),x60046),x60047),x60042))
% 179.72/179.58 [6005]E(x60051,x60052)+~E(f323(f323(f323(f90(x60053),x60054),x60051),x60055),f323(f323(f323(f90(x60053),x60056),x60052),x60057))
% 179.72/179.58 [6006]E(x60061,x60062)+~E(f323(f323(f323(f90(x60063),x60061),x60064),x60065),f323(f323(f323(f90(x60063),x60062),x60066),x60067))
% 179.72/179.58 [8871]~P22(x88716,x88711,x88713,x88717)+E(f323(f71(x88711,x88711,x88712,f323(x88713,x88714)),f323(f71(x88711,x88711,x88712,f323(x88713,x88714)),x88715)),f323(f71(x88711,x88711,x88712,f323(x88713,x88714)),x88715))
% 179.72/179.58 [9232]~P35(x92323,x92322,x92324,f323(f323(f147(x92321,x92323),x92325),x92326),x92327)+P35(x92321,x92322,f323(f323(f8(x92323,f867(x92322,a855),x92321),x92324),x92325),x92326,x92327)
% 179.72/179.58 [9253]P35(x92531,x92532,x92533,f323(f323(f147(x92534,x92531),x92535),x92536),x92537)+~P35(x92534,x92532,f323(f323(f8(x92531,f867(x92532,a855),x92534),x92533),x92535),x92536,x92537)
% 179.72/179.58 [9669]E(f181(x96691,x96692,f323(f323(f323(f70(x96691,f864(x96692)),x96693),x96694),f323(f230(x96692),x96695)),x96696,x96697),f323(f323(f323(f70(x96691,f864(x96692)),f181(x96691,x96692,x96693,x96696,x96697)),x96694),f323(f230(x96692),x96695)))+P101(f323(f323(f325(x96691),x96694),f323(f166(x96691),x96696)))
% 179.72/179.58 [8870]~P101(f323(f323(f325(x88701),x88702),f323(f323(x88705,x88706),x88707)))+P101(f323(f323(f325(x88701),x88702),f323(f323(f262(x88703,x88704,f867(x88701,a855)),x88705),f323(f323(f258(x88703,x88704),x88706),x88707))))
% 179.72/179.58 [9154]P101(f323(f323(f323(x91541,x91542),x91543),x91544))+~P101(f323(f323(f323(f262(x91545,x91546,f867(x91547,a855)),x91541),f323(f323(f258(x91545,x91546),x91542),x91543)),x91544))
% 179.72/179.58 [9293]P101(f323(f323(f325(x92931),f323(f323(x92932,x92933),x92934)),f323(f302(f866(x92935,x92936),x92931,f323(f262(x92935,x92936,x92931),x92932)),x92937)))+~P101(f323(f323(f325(f866(x92935,x92936)),f323(f323(f258(x92935,x92936),x92933),x92934)),x92937))
% 179.72/179.58 [9628]P101(f323(f323(f325(f866(f861(x96281),f861(x96281))),f323(f323(f258(f861(x96281),f861(x96281)),f323(f323(f121(x96281),x96282),f323(f323(f144(x96281),x96283),x96284))),f323(f323(f121(x96281),x96282),f323(f323(f144(x96281),x96285),x96286)))),f140(x96281,x96287)))+~P101(f323(f323(f325(f866(x96281,x96281)),f323(f323(f258(x96281,x96281),x96283),x96285)),x96287))
% 179.72/179.58 [9691]~P35(x96911,x96913,x96914,x96916,f323(f323(f147(x96912,x96913),x96915),x96917))+P35(x96911,x96912,f323(f323(f7(x96911,f867(x96912,x96913),f867(x96912,a855)),f323(f323(f8(f867(x96913,a855),f867(f867(x96912,x96913),f867(x96912,a855)),x96911),f8(x96913,a855,x96912)),x96914)),x96915),x96916,x96917)
% 179.72/179.58 [9775]P35(x97751,x97752,x97753,x97754,f323(f323(f147(x97755,x97752),x97756),x97757))+~P35(x97751,x97755,f323(f323(f7(x97751,f867(x97755,x97752),f867(x97755,a855)),f323(f323(f8(f867(x97752,a855),f867(f867(x97755,x97752),f867(x97755,a855)),x97751),f8(x97752,a855,x97755)),x97753)),x97756),x97754,x97757)
% 179.72/179.58 [9146]E(x91461,x91462)+E(f323(f323(f323(f70(x91463,x91464),f323(f323(f323(f70(x91463,x91464),x91465),x91461),x91466)),x91462),x91467),f323(f323(f323(f70(x91463,x91464),f323(f323(f323(f70(x91463,x91464),x91465),x91462),x91467)),x91461),x91466))
% 179.72/179.58 [9387]E(f181(x93871,x93872,f323(f323(f323(f70(x93871,f864(x93872)),x93873),x93874),f323(f230(x93872),x93875)),x93876,x93877),f181(x93871,x93872,x93873,x93876,x93877))+~P101(f323(f323(f325(x93871),x93874),f323(f166(x93871),f323(f323(f169(x93871),f323(f189(f861(x93872)),x93877)),x93876))))
% 179.72/179.58 [9702]E(f181(x97021,x97022,f323(f323(f323(f70(x97021,f864(x97022)),x97023),x97024),f323(f230(x97022),x97025)),x97026,x97027),f323(f323(f323(f70(x97021,f864(x97022)),f181(x97021,x97022,x97023,x97026,x97027)),x97024),f323(f230(x97022),x97025)))+P101(f323(f323(f325(x97021),x97024),f323(f166(x97021),f323(f323(f169(x97021),f323(f189(f861(x97022)),x97027)),x97026))))
% 179.72/179.58 [10062]P101(f323(f323(f325(x100621),f641(x100622,x100623,x100624,x100625,x100626,x100627,x100621)),x100625))+P101(f323(f323(f323(f323(f40(x100621,f867(x100627,f867(x100626,a855))),x100625),x100624),x100623),x100622))
% 179.72/179.58 [10063]P101(f323(f323(f325(x100631),f465(x100632,x100633,x100634,x100635,x100636,x100637,x100631)),x100635))+~P101(f323(f323(f323(f323(f39(x100631,f867(x100637,f867(x100636,a855))),x100635),x100634),x100633),x100632))
% 179.72/179.58 [10090]P101(f323(f323(f323(x100901,f465(x100902,x100903,x100901,x100904,x100905,x100906,x100907)),x100903),x100902))+~P101(f323(f323(f323(f323(f39(x100907,f867(x100906,f867(x100905,a855))),x100904),x100901),x100903),x100902))
% 179.72/179.58 [10108]~P101(f323(f323(f323(x101085,f641(x101087,x101086,x101085,x101084,x101083,x101082,x101081)),x101086),x101087))+P101(f323(f323(f323(f323(f40(x101081,f867(x101082,f867(x101083,a855))),x101084),x101085),x101086),x101087))
% 179.72/179.58 [10124]~P101(f323(f323(f325(f866(x101241,x101243)),f323(f323(f258(x101241,x101243),x101246),x101247)),f323(f323(f280(x101241,x101242,x101243),x101244),x101245)))+P101(f323(f323(f259(x101241,x101242,x101243,f323(f323(f7(x101241,f867(f866(x101241,x101242),a855),f867(x101242,a855)),f323(f323(f8(f867(x101242,f867(f867(f866(x101241,x101242),a855),a855)),f867(f867(f866(x101241,x101242),a855),f867(x101242,a855)),x101241),f7(x101242,f867(f866(x101241,x101242),a855),a855)),f323(f323(f8(f867(x101242,f866(x101241,x101242)),f867(x101242,f867(f867(f866(x101241,x101242),a855),a855)),x101241),f323(f8(f866(x101241,x101242),f867(f867(f866(x101241,x101242),a855),a855),x101242),f325(f866(x101241,x101242)))),f258(x101241,x101242)))),x101244),f323(f323(f7(x101242,f867(f866(x101242,x101243),a855),f867(x101243,a855)),f323(f323(f8(f867(x101243,f867(f867(f866(x101242,x101243),a855),a855)),f867(f867(f866(x101242,x101243),a855),f867(x101243,a855)),x101242),f7(x101243,f867(f866(x101242,x101243),a855),a855)),f323(f323(f8(f867(x101243,f866(x101242,x101243)),f867(x101243,f867(f867(f866(x101242,x101243),a855),a855)),x101242),f323(f8(f866(x101242,x101243),f867(f867(f866(x101242,x101243),a855),a855),x101243),f325(f866(x101242,x101243)))),f258(x101242,x101243)))),x101245)),x101246),x101247))
% 179.72/179.58 [10132]P101(f323(f323(f325(f866(x101321,x101322)),f323(f323(f258(x101321,x101322),x101323),x101324)),f323(f323(f280(x101321,x101325,x101322),x101326),x101327)))+~P101(f323(f323(f259(x101321,x101325,x101322,f323(f323(f7(x101321,f867(f866(x101321,x101325),a855),f867(x101325,a855)),f323(f323(f8(f867(x101325,f867(f867(f866(x101321,x101325),a855),a855)),f867(f867(f866(x101321,x101325),a855),f867(x101325,a855)),x101321),f7(x101325,f867(f866(x101321,x101325),a855),a855)),f323(f323(f8(f867(x101325,f866(x101321,x101325)),f867(x101325,f867(f867(f866(x101321,x101325),a855),a855)),x101321),f323(f8(f866(x101321,x101325),f867(f867(f866(x101321,x101325),a855),a855),x101325),f325(f866(x101321,x101325)))),f258(x101321,x101325)))),x101326),f323(f323(f7(x101325,f867(f866(x101325,x101322),a855),f867(x101322,a855)),f323(f323(f8(f867(x101322,f867(f867(f866(x101325,x101322),a855),a855)),f867(f867(f866(x101325,x101322),a855),f867(x101322,a855)),x101325),f7(x101322,f867(f866(x101325,x101322),a855),a855)),f323(f323(f8(f867(x101322,f866(x101325,x101322)),f867(x101322,f867(f867(f866(x101325,x101322),a855),a855)),x101325),f323(f8(f866(x101325,x101322),f867(f867(f866(x101325,x101322),a855),a855),x101322),f325(f866(x101325,x101322)))),f258(x101325,x101322)))),x101327)),x101323),x101324))
% 179.72/179.58 [10072]~P139(x100722)+E(f323(f323(f6(x100721,x100722),f323(f323(f7(x100721,f867(x100723,a855),x100722),f323(f323(f8(f867(x100723,x100722),f867(f867(x100723,a855),x100722),x100721),f6(x100723,x100722)),f323(f323(f7(x100721,f867(x100723,x100722),f867(x100723,x100722)),f323(f323(f8(f867(x100722,x100722),f867(f867(x100723,x100722),f867(x100723,x100722)),x100721),f8(x100722,x100722,x100723)),f323(f323(f8(x100722,f867(x100722,x100722),x100721),f79(x100722)),x100724))),x100725))),x100726)),x100727),f323(f323(f79(x100722),f323(f323(f6(x100721,x100722),x100724),x100727)),f323(f323(f6(x100723,x100722),x100725),x100726)))
% 179.72/179.58 [9184]~P21(x91847,x91841,x91843,x91848)+E(f323(f71(x91841,x91841,x91842,f323(x91843,x91844)),f323(f71(x91841,x91841,x91842,f323(x91843,x91845)),x91846)),f323(f71(x91841,x91841,x91842,f323(x91843,x91845)),f323(f71(x91841,x91841,x91842,f323(x91843,x91844)),x91846)))
% 179.72/179.58 [10127]E(f323(f323(f258(x101271,x101272),f323(x101273,f607(x101274,x101275,x101273,x101276,x101277,x101278,x101272,x101271))),f323(x101275,f608(x101274,x101275,x101273,x101276,x101277,x101278,x101272,x101271))),x101278)+~P101(f323(f323(f325(f866(x101271,x101272)),x101278),f323(f302(f866(x101277,x101276),f866(x101271,x101272),f263(x101277,x101271,x101276,x101272,x101273,x101275)),x101274)))
% 179.72/179.58 [10141]~P101(f323(f323(f325(f866(x101418,x101417)),x101416),f323(f302(f866(x101411,x101412),f866(x101418,x101417),f263(x101411,x101418,x101412,x101417,x101415,x101414)),x101413)))+P101(f323(f323(f325(f866(x101411,x101412)),f323(f323(f258(x101411,x101412),f607(x101413,x101414,x101415,x101412,x101411,x101416,x101417,x101418)),f608(x101413,x101414,x101415,x101412,x101411,x101416,x101417,x101418))),x101413))
% 179.72/179.58 [9618]P101(f323(f323(f325(f866(f866(x96181,x96182),f866(x96181,x96182))),f323(f323(f258(f866(x96181,x96182),f866(x96181,x96182)),f323(f323(f258(x96181,x96182),x96183),x96184)),f323(f323(f258(x96181,x96182),x96185),x96186))),f315(x96181,x96182,x96187,x96188)))+~P101(f323(f323(f325(f866(x96181,x96181)),f323(f323(f258(x96181,x96181),x96183),x96185)),x96187))
% 179.72/179.58 [10118]E(f323(f135(x101181,x101182,f323(f7(x101182,x101181,x101181),x101183),f323(x101184,x101185)),x101186),f323(x101184,f323(f135(x101187,x101182,f323(f7(x101182,x101187,x101187),x101188),x101185),x101186)))+P101(f323(f323(f325(x101182),f678(x101185,x101188,x101184,x101183,x101187,x101181,x101186,x101182)),f323(f166(x101182),x101186)))
% 179.72/179.58 [10135]~E(f323(f71(x101351,x101351,x101357,f323(x101353,f678(x101355,x101358,x101354,x101353,x101357,x101351,x101356,x101352))),x101354),f323(f71(x101357,x101351,x101357,x101354),f323(x101358,f678(x101355,x101358,x101354,x101353,x101357,x101351,x101356,x101352))))+E(f323(f135(x101351,x101352,f323(f7(x101352,x101351,x101351),x101353),f323(x101354,x101355)),x101356),f323(x101354,f323(f135(x101357,x101352,f323(f7(x101352,x101357,x101357),x101358),x101355),x101356)))
% 179.72/179.58 [8406]E(f323(x84061,f323(x84062,x84063)),f323(x84064,f323(x84065,x84063)))+~E(f323(f71(x84066,x84067,x84068,x84061),x84062),f323(f71(x84069,x84067,x84068,x84064),x84065))
% 179.72/179.58 [10002]P101(f323(f323(f325(f866(x100021,x100022)),f323(f323(f258(x100021,x100022),f323(x100023,x100024)),f323(x100025,x100026))),f323(f302(f866(x100027,x100028),f866(x100021,x100022),f263(x100027,x100021,x100028,x100022,x100023,x100025)),x100029)))+~P101(f323(f323(f325(f866(x100027,x100028)),f323(f323(f258(x100027,x100028),x100024),x100026)),x100029))
% 179.72/179.58 [8696]~E(f323(x86964,f323(x86965,x86966)),f323(x86969,f323(x869610,x869611)))+E(f323(f323(f71(x86961,x86962,x86963,x86964),x86965),x86966),f323(f323(f71(x86967,x86962,x86968,x86969),x869610),x869611))
% 179.72/179.58 [4576]~P98(x45761)+~P103(x45761)+E(f101(x45761),f235(x45761))
% 179.72/179.58 [4577]~P97(x45771)+~P103(x45771)+E(f110(x45771),f236(x45771))
% 179.72/179.58 [4821]~P116(x48211)+~P90(x48211)+E(f323(f73(x48211),f323(f103(x48211),a97)),f76(x48211))
% 179.72/179.58 [5096]E(x50961,f2(a1))+E(f80(a1,x50961),f323(f77(a1),f76(a1)))+P101(f323(f323(f238(a1),f2(a1)),x50961))
% 179.72/179.58 [5300]E(x53001,f2(a1))+E(f80(a1,x53001),f76(a1))+~P101(f323(f323(f238(a1),f2(a1)),x53001))
% 179.72/179.58 [7263]~P39(x72631)+P101(f323(f59(a1),x72631))+~P101(f323(f59(a860),f323(f302(a1,a860,a104),x72631)))
% 179.72/179.58 [9580]E(x95801,f188(f867(f866(a860,a860),a855)))+~P101(f323(f59(f866(a860,a860)),x95801))+P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),f188(f867(f866(a860,a860),a855))),x95801)),a34))
% 179.72/179.58 [9751]E(x97511,f2(a860))+E(x97511,f323(a112,f2(a860)))+~P101(f323(f323(f238(a860),x97511),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.58 [10030]E(x100301,f2(a99))+E(f323(f323(f78(a1),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(a20,f323(f323(f36(a99),x100301),f323(f103(a99),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))),f76(a1)),f323(a20,x100301))+E(f42(a99,x100301,f323(f103(a99),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f2(a99))
% 179.72/179.58 [9882]E(x98821,f2(a99))+~E(f42(a99,x98821,f323(f103(a99),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f2(a99))+E(f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(a20,f323(f323(f36(a99),x98821),f323(f103(a99),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))),f323(a20,x98821))
% 179.72/179.58 [4648]~P54(x46481,x46482)+P44(x46481,x46482)+~P45(a855)
% 179.72/179.58 [4586]~P140(x45861)+P30(x45861,x45862)+~E(x45862,f2(x45861))
% 179.72/179.58 [4587]~P103(x45871)+P16(x45871,x45872)+~E(x45872,f113(x45871))
% 179.72/179.58 [4596]~P116(x45961)+~E(x45962,f2(x45961))+E(f80(x45961,x45962),f2(x45961))
% 179.72/179.58 [4597]~P85(x45971)+~E(x45972,f2(x45971))+E(f80(x45971,x45972),f2(x45971))
% 179.72/179.58 [4605]~P140(x46052)+~P30(x46052,x46051)+E(x46051,f2(x46052))
% 179.72/179.58 [4639]~P116(x46392)+~E(f80(x46392,x46391),f2(x46392))+E(x46391,f2(x46392))
% 179.72/179.58 [4655]~P5(x46552)+~P5(x46551)+P5(f867(x46551,x46552))
% 179.72/179.58 [4656]~P5(x46562)+~P5(x46561)+P5(f865(x46561,x46562))
% 179.72/179.58 [4657]~P5(x46572)+~P5(x46571)+P5(f866(x46571,x46572))
% 179.72/179.58 [4658]~P61(x46582)+~P61(x46581)+P61(f867(x46581,x46582))
% 179.72/179.58 [4659]~P61(x46592)+~P61(x46591)+P61(f865(x46591,x46592))
% 179.72/179.58 [4660]~P61(x46602)+~P61(x46601)+P61(f866(x46601,x46602))
% 179.72/179.58 [4661]~P7(x46612)+~P7(x46611)+P7(f194(x46611,x46612))
% 179.72/179.58 [4662]~P141(x46622)+~P141(x46621)+P141(f866(x46621,x46622))
% 179.72/179.58 [4663]~P5(x46631)+~P92(x46632)+P92(f867(x46631,x46632))
% 179.72/179.58 [4793]~P103(x47931)+~P16(x47931,x47932)+P16(x47931,f145(x47931,x47932))
% 179.72/179.58 [5027]~P7(x50272)+~P7(x50271)+P7(f42(a1,x50271,x50272))
% 179.72/179.58 [4607]~P74(x46071)+~E(x46072,f2(x46071))+E(f323(f77(x46071),x46072),x46072)
% 179.72/179.58 [4611]~P134(x46111)+~E(x46112,f2(a1))+E(f323(f102(x46111),x46112),f2(x46111))
% 179.72/179.58 [4612]~P89(x46121)+~E(x46122,f2(a1))+E(f323(f102(x46121),x46122),f2(x46121))
% 179.72/179.58 [4636]~P59(x46361)+~E(f2(x46361),x46362)+E(f323(f77(x46361),x46362),f2(x46361))
% 179.72/179.58 [4637]~P59(x46371)+~E(x46372,f2(x46371))+E(f323(f77(x46371),x46372),f2(x46371))
% 179.72/179.58 [4638]~P82(x46381)+~E(x46382,f2(x46381))+E(f323(f73(x46381),x46382),f2(x46381))
% 179.72/179.58 [4665]~P74(x46652)+E(x46651,f2(x46652))+~E(f323(f77(x46652),x46651),x46651)
% 179.72/179.58 [4673]E(x46731,f323(a104,x46732))+~E(x46731,f2(a860))+~E(x46732,f323(f100(a1),x46731))
% 179.72/179.58 [4674]E(f323(a104,x46741),x46742)+~E(x46742,f2(a860))+~E(x46741,f323(f100(a1),x46742))
% 179.72/179.58 [4678]~P89(x46782)+E(x46781,f2(a1))+~E(f323(f102(x46782),x46781),f2(x46782))
% 179.72/179.58 [4683]~P59(x46832)+E(x46831,f2(x46832))+~E(f323(f77(x46832),x46831),f2(x46832))
% 179.72/179.58 [4684]~P82(x46842)+E(x46841,f2(x46842))+~E(f323(f73(x46842),x46841),f2(x46842))
% 179.72/179.58 [4685]~P59(x46851)+E(f2(x46851),x46852)+~E(f323(f77(x46851),x46852),f2(x46851))
% 179.72/179.58 [4867]~P103(x48671)+~P16(x48671,x48672)+P16(x48671,f323(f165(x48671),x48672))
% 179.72/179.58 [4892]~P101(x48922)+~P101(x48921)+P101(f323(f323(a321,x48921),x48922))
% 179.72/179.58 [4926]~E(f76(a860),f2(a860))+E(f323(f35(x49261),x49262),f2(a860))+~P101(f323(f59(x49261),x49262))
% 179.72/179.58 [4959]~P139(x49591)+~P110(x49591)+E(f323(f323(f248(x49591),f2(x49591)),f323(a112,x49592)),f2(x49591))
% 179.72/179.58 [4997]~P103(x49971)+P16(x49971,f132(x49971,x49972))+~P101(f323(f59(x49971),x49972))
% 179.72/179.58 [4998]~P103(x49981)+P16(x49981,f687(x49982,x49981))+~P101(f323(f59(x49981),x49982))
% 179.72/179.58 [5019]~P103(x50191)+E(f323(f166(x50191),f132(x50191,x50192)),x50192)+~P101(f323(f59(x50191),x50192))
% 179.72/179.58 [5020]~P103(x50201)+E(f323(f166(x50201),f687(x50202,x50201)),x50202)+~P101(f323(f59(x50201),x50202))
% 179.72/179.58 [5048]P101(x50481)+P101(x50482)+~P101(f323(f323(a322,x50482),x50481))
% 179.72/179.58 [5060]E(x50601,f188(f867(x50602,a855)))+~E(f323(f35(x50602),x50601),f2(a860))+~P101(f323(f59(x50602),x50601))
% 179.72/179.58 [5065]P101(x50651)+~P101(x50652)+~P101(f323(f323(a326,x50652),x50651))
% 179.72/179.58 [5114]~P71(x51141)+E(f323(f73(x51141),x51142),x51142)+P101(f323(f323(f238(x51141),x51142),f2(x51141)))
% 179.72/179.58 [5176]~P5(x51762)+~P101(f323(f55(x51762),x51761))+P101(f323(x51761,f646(x51761,x51762)))
% 179.72/179.58 [5177]~P5(x51772)+~P101(f323(f55(x51772),x51771))+P101(f323(x51771,f671(x51771,x51772)))
% 179.72/179.58 [5211]E(x52111,f113(x52112))+P101(f323(f130(x52112),f114(x52112,x52111)))+~P101(f323(f130(x52112),x52111))
% 179.72/179.58 [5216]~P103(x52161)+~P101(f323(f59(x52161),x52162))+P101(f323(f130(x52161),f132(x52161,x52162)))
% 179.72/179.58 [5217]~P103(x52171)+~P101(f323(f59(x52171),x52172))+P101(f323(f130(x52171),f687(x52172,x52171)))
% 179.72/179.58 [5223]~P134(x52231)+E(f323(f100(x52231),f323(a104,x52232)),f323(f102(x52231),x52232))+P101(f323(f323(f238(a1),x52232),f2(a1)))
% 179.72/179.58 [5251]P8(x52512,x52511)+E(f323(x52511,f488(x52511)),f323(x52511,f524(x52511)))+P101(f323(f323(x52511,f488(x52511)),f524(x52511)))
% 179.72/179.58 [5265]E(f323(f100(a1),f422(x52651,x52652)),x52651)+P101(f323(x52652,f323(a104,x52651)))+~P101(f323(x52652,f2(a860)))
% 179.72/179.58 [5277]~P5(x52771)+~P101(f323(x52772,f611(x52772,x52771)))+P101(f323(f56(x52771),x52772))
% 179.72/179.58 [5278]~P5(x52781)+~P101(f323(x52782,f648(x52782,x52781)))+P101(f323(f56(x52781),x52782))
% 179.72/179.58 [5293]~P5(x52932)+~P36(x52932,x52931,f53(x52932))+P101(f323(x52931,f782(x52931,x52932)))
% 179.72/179.58 [5309]~P116(x53091)+~E(f80(x53091,x53092),f323(f77(x53091),f76(x53091)))+P101(f323(f323(f238(x53091),x53092),f2(x53091)))
% 179.72/179.58 [5385]~E(x53852,f2(a1))+E(f217(x53851,x53852),f323(f323(f258(a1,a1),f2(a1)),f76(a1)))+P101(f323(f323(f238(a1),x53852),f2(a1)))
% 179.72/179.58 [5386]~E(x53861,f2(a1))+E(f217(x53861,x53862),f323(f323(f258(a1,a1),f2(a1)),f76(a1)))+P101(f323(f323(f238(a1),x53862),f2(a1)))
% 179.72/179.58 [5438]E(f323(f100(a1),f422(x54381,x54382)),x54381)+P101(f323(x54382,f323(a104,x54381)))+P101(f323(f323(f238(a1),x54381),f2(a1)))
% 179.72/179.58 [5501]~P116(x55011)+E(f80(x55011,x55012),f323(f77(x55011),f76(x55011)))+~P101(f323(f323(f238(x55011),x55012),f2(x55011)))
% 179.72/179.58 [5502]~P82(x55021)+E(f323(f73(x55021),x55022),f323(f77(x55021),x55022))+~P101(f323(f323(f237(x55021),x55022),f2(x55021)))
% 179.72/179.58 [5503]~P82(x55031)+E(f323(f73(x55031),x55032),f323(f77(x55031),x55032))+~P101(f323(f323(f238(x55031),x55032),f2(x55031)))
% 179.72/179.58 [5504]~P71(x55041)+E(f323(f73(x55041),x55042),f323(f77(x55041),x55042))+~P101(f323(f323(f238(x55041),x55042),f2(x55041)))
% 179.72/179.58 [5600]~P101(f323(x56001,f422(x56002,x56001)))+P101(f323(x56001,f323(a104,x56002)))+~P101(f323(x56001,f2(a860)))
% 179.72/179.58 [5607]E(x56071,f2(a860))+E(f323(a112,f846(x56072,x56071)),x56071)+~P101(f323(f323(f238(a860),x56071),f323(a112,x56072)))
% 179.72/179.58 [5611]P8(x56111,x56112)+~E(f323(x56112,f488(x56112)),f323(x56112,f524(x56112)))+~P101(f323(f323(x56112,f488(x56112)),f524(x56112)))
% 179.72/179.58 [5631]~P103(x56311)+P16(x56311,x56312)+P101(f323(f323(f237(a860),f559(x56312,x56311)),f560(x56312,x56311)))
% 179.72/179.58 [5632]~P103(x56321)+P16(x56321,x56322)+P101(f323(f323(f237(a860),f601(x56322,x56321)),f604(x56322,x56321)))
% 179.72/179.58 [5718]~P82(x57181)+~E(x57182,f2(x57181))+P101(f323(f323(f237(x57181),f323(f73(x57181),x57182)),f2(x57181)))
% 179.72/179.58 [5797]~P5(x57972)+~P5(x57971)+E(f57(x57971,x57972,f53(x57971),f53(x57972)),f53(f866(x57971,x57972)))
% 179.72/179.58 [5801]~P101(f323(x58011,f422(x58012,x58011)))+P101(f323(x58011,f323(a104,x58012)))+P101(f323(f323(f238(a1),x58012),f2(a1)))
% 179.72/179.58 [5824]~P101(f323(x58241,f323(a104,x58242)))+P101(f323(x58241,f2(a860)))+~P101(f323(f323(f238(a1),x58242),f2(a1)))
% 179.72/179.59 [6153]~P116(x61531)+~P101(f323(f323(f238(x61531),x61532),f2(x61531)))+P101(f323(f323(f238(x61531),f80(x61531,x61532)),f2(x61531)))
% 179.72/179.59 [6266]~P116(x62661)+P101(f323(f323(f237(x62661),f323(f102(x62661),x62662)),f2(x62661)))+~P101(f323(f323(f237(a1),x62662),f2(a1)))
% 179.72/179.59 [6267]~P116(x62671)+P101(f323(f323(f238(x62671),f323(f102(x62671),x62672)),f2(x62671)))+~P101(f323(f323(f238(a1),x62672),f2(a1)))
% 179.72/179.59 [6274]~P82(x62742)+E(x62741,f2(x62742))+~P101(f323(f323(f237(x62742),f323(f73(x62742),x62741)),f2(x62742)))
% 179.72/179.59 [6349]~P134(x63491)+~P101(f323(f323(f325(x63491),x63492),f109(x63491)))+P101(f323(f323(f325(x63491),f323(f77(x63491),x63492)),f109(x63491)))
% 179.72/179.59 [6382]~P116(x63821)+~P101(f323(f323(f238(x63821),f80(x63821,x63822)),f2(x63821)))+P101(f323(f323(f238(x63821),x63822),f2(x63821)))
% 179.72/179.59 [6550]~P116(x65502)+~P101(f323(f323(f237(x65502),f323(f102(x65502),x65501)),f2(x65502)))+P101(f323(f323(f237(a1),x65501),f2(a1)))
% 179.72/179.59 [6551]~P116(x65512)+~P101(f323(f323(f238(x65512),f323(f102(x65512),x65511)),f2(x65512)))+P101(f323(f323(f238(a1),x65511),f2(a1)))
% 179.72/179.59 [7050]~P74(x70501)+~P101(f323(f323(f237(x70501),x70502),f2(x70501)))+P101(f323(f323(f237(x70501),f323(f323(f78(x70501),x70502),x70502)),f2(x70501)))
% 179.72/179.59 [7051]~P116(x70511)+~P101(f323(f323(f238(x70511),x70512),f2(x70511)))+P101(f323(f323(f238(x70511),f323(f323(f78(x70511),x70512),x70512)),f2(x70511)))
% 179.72/179.59 [7052]~P74(x70521)+~P101(f323(f323(f238(x70521),x70522),f2(x70521)))+P101(f323(f323(f238(x70521),f323(f323(f78(x70521),x70522),x70522)),f2(x70521)))
% 179.72/179.59 [7615]~P74(x76151)+~P101(f323(f323(f237(x76151),f323(f323(f78(x76151),x76152),x76152)),f2(x76151)))+P101(f323(f323(f237(x76151),x76152),f2(x76151)))
% 179.72/179.59 [7616]~P116(x76161)+~P101(f323(f323(f238(x76161),f323(f323(f78(x76161),x76162),x76162)),f2(x76161)))+P101(f323(f323(f238(x76161),x76162),f2(x76161)))
% 179.72/179.59 [7617]~P74(x76171)+~P101(f323(f323(f238(x76171),f323(f323(f78(x76171),x76172),x76172)),f2(x76171)))+P101(f323(f323(f238(x76171),x76172),f2(x76171)))
% 179.72/179.59 [4723]~E(x47232,f76(a860))+~E(x47231,f76(a860))+E(f323(f323(f79(a860),x47231),x47232),f76(a860))
% 179.72/179.59 [4724]~E(x47242,f76(a1))+~E(x47241,f76(a1))+E(f323(f323(f79(a1),x47241),x47242),f76(a1))
% 179.72/179.59 [4725]~E(x47252,f2(a860))+~E(x47251,f2(a860))+E(f323(f323(f78(a860),x47251),x47252),f2(a860))
% 179.72/179.59 [4779]~P114(x47792)+E(x47791,f2(x47792))+E(f323(f323(f281(x47792),x47791),x47791),f76(x47792))
% 179.72/179.59 [4780]~P57(x47802)+E(x47801,f2(x47802))+E(f323(f323(f36(x47802),x47801),x47801),f76(x47802))
% 179.72/179.59 [4781]~P115(x47812)+E(x47811,f2(x47812))+E(f323(f323(f281(x47812),x47811),x47811),f76(x47812))
% 179.72/179.59 [4799]~P133(x47991)+~E(x47992,f76(x47991))+E(f323(f323(f79(x47991),x47992),x47992),f76(x47991))
% 179.72/179.59 [4800]~P74(x48001)+~E(x48002,f2(x48001))+E(f323(f323(f78(x48001),x48002),x48002),f2(x48001))
% 179.72/179.59 [4801]~P115(x48011)+~E(x48012,f2(x48011))+E(f323(f323(f281(x48011),x48012),x48012),f2(x48011))
% 179.72/179.59 [4846]~E(x48462,f2(a860))+~E(x48461,f2(a860))+E(f323(f77(a1),f323(f100(a1),x48461)),f323(f100(a1),x48462))
% 179.72/179.59 [4864]E(x48641,f76(a860))+E(x48642,f2(a860))+~E(f323(f323(f79(a860),x48642),x48641),x48642)
% 179.72/179.59 [4874]E(x48741,f2(a860))+E(x48742,f2(a860))+~E(f323(f323(f79(a860),x48742),x48741),f2(a860))
% 179.72/179.59 [4901]~E(x49012,f2(a860))+~E(x49011,f323(a112,f2(a860)))+E(f323(f323(f78(a860),x49011),x49012),f323(a112,f2(a860)))
% 179.72/179.59 [4902]~E(x49021,f2(a860))+~E(x49022,f323(a112,f2(a860)))+E(f323(f323(f78(a860),x49021),x49022),f323(a112,f2(a860)))
% 179.72/179.59 [4909]E(x49091,f76(a1))+E(x49092,f323(f103(a1),a97))+~E(f323(f323(f79(a1),x49091),x49092),f76(a1))
% 179.72/179.59 [4910]E(x49101,f76(a1))+E(x49102,f323(f103(a1),a97))+~E(f323(f323(f79(a1),x49102),x49101),f76(a1))
% 179.72/179.59 [4911]E(x49111,f76(a1))+E(x49111,f323(f103(a1),a97))+~E(f323(f323(f79(a1),x49112),x49111),f76(a1))
% 179.72/179.59 [4913]E(x49131,f76(a1))+E(x49131,f323(f103(a1),a97))+~E(f323(f323(f79(a1),x49131),x49132),f76(a1))
% 179.72/179.59 [4930]~P74(x49302)+E(x49301,f2(x49302))+~E(f323(f323(f78(x49302),x49301),x49301),f2(x49302))
% 179.72/179.59 [4936]~E(x49361,f323(f103(a1),a97))+~E(x49362,f323(f103(a1),a97))+E(f323(f323(f79(a1),x49361),x49362),f76(a1))
% 179.72/179.59 [4948]E(x49481,f2(a860))+E(x49482,f2(a860))+~E(f323(f323(f78(a860),x49482),x49481),f323(a112,f2(a860)))
% 179.72/179.59 [4958]~P62(x49581)+~P90(x49581)+E(f323(f323(f281(x49581),x49582),f323(f103(x49581),a81)),f2(x49581))
% 179.72/179.59 [4964]~P133(x49641)+~E(x49642,f323(f77(x49641),f76(x49641)))+E(f323(f323(f79(x49641),x49642),x49642),f76(x49641))
% 179.72/179.59 [4969]~P7(x49692)+~P7(x49691)+P7(f323(f323(f79(a1),x49691),x49692))
% 179.72/179.59 [4970]~P7(x49702)+~P7(x49701)+P7(f323(f323(f78(a1),x49701),x49702))
% 179.72/179.59 [4971]~P7(x49712)+~P7(x49711)+P7(f323(f323(f36(a1),x49711),x49712))
% 179.72/179.59 [4973]~E(x49732,f2(a1))+E(x49731,f2(a1))+E(f43(x49731,x49732),f323(f323(f258(a1,a1),f2(a1)),x49731))
% 179.72/179.59 [4995]~E(x49952,f323(a112,f2(a860)))+~E(x49951,f323(a112,f2(a860)))+E(f323(f323(f79(a860),x49951),x49952),f323(a112,f2(a860)))
% 179.72/179.59 [5010]E(x50101,f2(a860))+E(x50102,f323(a112,f2(a860)))+~E(f323(f323(f248(a860),x50102),x50101),f323(a112,f2(a860)))
% 179.72/179.59 [5011]E(x50111,f2(a860))+E(x50111,f323(a112,f2(a860)))+~E(f323(f323(f78(a860),x50112),x50111),f323(a112,f2(a860)))
% 179.72/179.59 [5012]E(x50121,f2(a860))+E(x50121,f323(a112,f2(a860)))+~E(f323(f323(f78(a860),x50121),x50122),f323(a112,f2(a860)))
% 179.72/179.59 [5021]~P62(x50211)+~P90(x50211)+E(f323(f323(f281(x50211),x50212),f323(f103(x50211),a97)),f323(f77(x50211),x50212))
% 179.72/179.59 [5040]E(x50401,f323(a104,x50402))+~E(x50401,f2(a860))+P101(f323(f323(f237(a1),f2(a1)),x50402))
% 179.72/179.59 [5041]E(f323(a104,x50411),x50412)+~E(x50412,f2(a860))+P101(f323(f323(f237(a1),f2(a1)),x50411))
% 179.72/179.59 [5056]E(x50561,f323(a112,f2(a860)))+E(x50562,f323(a112,f2(a860)))+~E(f323(f323(f78(a860),x50561),x50562),f323(a112,f2(a860)))
% 179.72/179.59 [5067]~E(x50671,f323(a104,x50672))+E(x50671,f2(a860))+P101(f323(f323(f237(a1),f2(a1)),x50672))
% 179.72/179.59 [5068]~E(f323(a104,x50682),x50681)+E(x50681,f2(a860))+P101(f323(f323(f237(a1),f2(a1)),x50682))
% 179.72/179.59 [5090]~P2(x50901)+E(f323(f61(x50901,f101(x50901)),x50902),f11(x50901,x50902))+~P101(f323(f59(x50901),x50902))
% 179.72/179.59 [5091]~P2(x50911)+E(f323(f61(x50911,f110(x50911)),x50912),f10(x50911,x50912))+~P101(f323(f59(x50911),x50912))
% 179.72/179.59 [5092]~P103(x50921)+E(f323(f61(x50921,f236(x50921)),x50922),f14(x50921,x50922))+~P101(f323(f59(x50921),x50922))
% 179.72/179.59 [5093]~P103(x50931)+E(f323(f61(x50931,f235(x50931)),x50932),f15(x50931,x50932))+~P101(f323(f59(x50931),x50932))
% 179.72/179.59 [5095]~P5(x50951)+~P101(f323(x50952,f200(x50951)))+P101(f323(f55(f864(x50951)),x50952))
% 179.72/179.59 [5169]~P5(x51692)+P101(f323(x51691,f200(x51692)))+~P101(f323(f56(f864(x51692)),x51691))
% 179.72/179.59 [5170]E(x51701,x51702)+~E(f323(f323(f22(a860),x51702),x51701),f2(a860))+~E(f323(f323(f22(a860),x51701),x51702),f2(a860))
% 179.72/179.59 [5184]P7(x51841)+~P39(x51842)+~P101(f323(f323(f325(a1),x51841),x51842))
% 179.72/179.59 [5212]~P116(x52121)+~E(f80(x52121,x52122),f76(x52121))+P101(f323(f323(f238(x52121),f2(x52121)),x52122))
% 179.72/179.59 [5224]~P90(x52241)+E(f323(f100(x52241),f323(f103(a860),x52242)),f323(f103(x52241),x52242))+P101(f323(a193,f323(f103(a1),x52242)))
% 179.72/179.59 [5230]~P44(x52301,x52302)+P45(a855)+P101(f323(f59(f866(x52301,x52301)),x52302))
% 179.72/179.59 [5302]~P103(x53021)+E(f323(f61(x53021,f235(x53021)),x53022),f12(x53021,f235(x53021),x53022))+~P101(f323(f59(x53021),x53022))
% 179.72/179.59 [5303]~P103(x53031)+E(f323(f61(x53031,f236(x53031)),x53032),f13(x53031,f236(x53031),x53032))+~P101(f323(f59(x53031),x53032))
% 179.72/179.59 [5316]E(x53161,x53162)+P101(f323(f323(f238(a860),x53162),x53161))+P101(f323(f323(f238(a860),x53161),x53162))
% 179.72/179.59 [5317]E(x53171,x53172)+P101(f323(f323(f238(a1),x53172),x53171))+P101(f323(f323(f238(a1),x53171),x53172))
% 179.72/179.59 [5372]~P90(x53721)+E(f323(f100(x53721),f323(f103(a860),x53722)),f2(x53721))+~P101(f323(a193,f323(f103(a1),x53722)))
% 179.72/179.59 [5375]~E(x53752,f323(a104,x53751))+E(x53751,f323(f100(a1),x53752))+~P101(f323(f323(f237(a1),f2(a1)),x53751))
% 179.72/179.59 [5376]~E(f323(a104,x53761),x53762)+E(x53761,f323(f100(a1),x53762))+~P101(f323(f323(f237(a1),f2(a1)),x53761))
% 179.72/179.59 [5377]~E(x53771,f323(a104,x53772))+E(f323(f100(a1),x53771),x53772)+~P101(f323(f323(f237(a1),f2(a1)),x53772))
% 179.72/179.59 [5387]E(x53871,f323(a104,x53872))+~E(x53872,f323(f100(a1),x53871))+~P101(f323(f323(f237(a1),f2(a1)),x53872))
% 179.72/179.59 [5388]E(f323(a104,x53881),x53882)+~E(x53881,f323(f100(a1),x53882))+~P101(f323(f323(f237(a1),f2(a1)),x53881))
% 179.72/179.59 [5427]~P82(x54272)+E(x54271,f2(x54272))+P101(f323(f323(f238(x54272),f2(x54272)),f323(f73(x54272),x54271)))
% 179.72/179.59 [5494]~P116(x54941)+E(f80(x54941,x54942),f76(x54941))+~P101(f323(f323(f238(x54941),f2(x54941)),x54942))
% 179.72/179.59 [5498]~P90(x54981)+E(f323(f100(x54981),f323(f103(a860),x54982)),f2(x54981))+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x54982)))
% 179.72/179.59 [5505]~P82(x55051)+E(f323(f73(x55051),x55052),x55052)+~P101(f323(f323(f237(x55051),f2(x55051)),x55052))
% 179.72/179.59 [5506]~P82(x55061)+E(f323(f73(x55061),x55062),x55062)+~P101(f323(f323(f238(x55061),f2(x55061)),x55062))
% 179.72/179.59 [5514]E(x55141,f2(a860))+~E(f132(a860,f323(f293(a860,x55142),x55141)),f113(a860))+P101(f323(f323(f237(a860),x55141),x55142))
% 179.72/179.59 [5524]~P72(x55241)+E(f323(f323(f6(x55241,x55241),f5(x55241)),f323(f166(x55241),x55242)),f323(f159(x55241),x55242))+~P101(f323(f130(x55241),x55242))
% 179.72/179.59 [5527]~P134(x55271)+E(f323(f100(x55271),f323(a104,x55272)),f323(f102(x55271),x55272))+~P101(f323(f323(f237(a1),f2(a1)),x55272))
% 179.72/179.59 [5554]E(x55541,x55542)+P101(f323(f323(f238(a860),x55541),x55542))+~P101(f323(f323(f237(a860),x55541),x55542))
% 179.72/179.59 [5555]E(x55551,x55552)+P101(f323(f323(f238(a1),x55551),x55552))+~P101(f323(f323(f237(a1),x55551),x55552))
% 179.72/179.59 [5558]E(x55581,f76(a1))+~E(f323(f323(f79(a1),x55582),x55581),f76(a1))+~P101(f323(f323(f238(a1),f2(a1)),x55582))
% 179.72/179.59 [5559]E(x55591,f76(a1))+~E(f323(f323(f79(a1),x55591),x55592),f76(a1))+~P101(f323(f323(f238(a1),f2(a1)),x55591))
% 179.72/179.59 [5597]~P39(x55972)+P101(f323(f323(f237(a1),f2(a1)),x55971))+~P101(f323(f323(f325(a1),x55971),x55972))
% 179.72/179.59 [5616]~P54(x56161,x56162)+P38(x56161,x56162)+~P101(f323(f59(f866(x56161,x56161)),x56162))
% 179.72/179.59 [5618]~P54(x56181,x56182)+P44(x56181,x56182)+~P101(f323(f59(f866(x56181,x56181)),x56182))
% 179.72/179.59 [5662]E(x56621,f188(f867(x56622,a855)))+~P101(f323(f59(x56622),x56621))+P101(f323(f323(f238(a860),f2(a860)),f323(f35(x56622),x56621)))
% 179.72/179.59 [5689]~P101(f323(x56891,x56892))+P101(f323(x56891,f2(a860)))+P101(f323(f323(f238(a860),f851(x56892,x56891)),x56892))
% 179.72/179.59 [5712]E(x57121,f2(a860))+~E(f323(f159(a860),x57122),f2(a860))+~P101(f323(f323(f325(a860),x57121),f323(f166(a860),x57122)))
% 179.72/179.59 [5778]E(x57781,x57782)+~P101(f323(f323(f237(a860),x57782),x57781))+~P101(f323(f323(f237(a860),x57781),x57782))
% 179.72/179.59 [5779]E(x57791,x57792)+~P101(f323(f323(f237(a1),x57792),x57791))+~P101(f323(f323(f237(a1),x57791),x57792))
% 179.72/179.59 [5780]E(f323(f35(x57801),x57802),f2(a860))+~P101(f323(f59(x57801),x57802))+P101(f323(f323(f325(x57801),f486(x57802,x57801)),x57802))
% 179.72/179.59 [5789]E(f47(x57891,x57892),f43(x57891,x57892))+P101(f323(f323(f237(a1),f2(a1)),x57891))+~P101(f323(f323(f238(a1),f2(a1)),x57892))
% 179.72/179.59 [5813]~P101(f323(x58131,f420(x58131)))+P101(f323(x58131,f323(a104,x58132)))+~P101(f323(f323(f237(a1),f2(a1)),x58132))
% 179.72/179.59 [5815]P101(f323(f323(f237(a860),x58151),f788(x58152)))+~P101(f323(f59(a860),x58152))+~P101(f323(f323(f325(a860),x58151),x58152))
% 179.72/179.59 [5816]P101(f323(f323(f238(a860),x58161),f811(x58162)))+~P101(f323(f59(a860),x58162))+~P101(f323(f323(f325(a860),x58161),x58162))
% 179.72/179.59 [5845]E(x58451,x58452)+~P101(f323(f323(f238(a860),x58451),f323(a112,x58452)))+P101(f323(f323(f238(a860),x58451),x58452))
% 179.72/179.59 [5877]E(x58771,f323(a112,x58772))+~P101(f323(f323(f237(a860),x58771),f323(a112,x58772)))+P101(f323(f323(f237(a860),x58771),x58772))
% 179.72/179.59 [5890]P101(f323(x58901,f421(x58901)))+~P101(f323(x58901,f323(a104,x58902)))+~P101(f323(f323(f237(a1),f2(a1)),x58902))
% 179.72/179.59 [5904]~P101(f323(x59041,x59042))+~P101(f323(f323(f237(a1),f2(a1)),x59042))+P101(f323(x59041,f323(f100(a1),f381(x59041))))
% 179.72/179.59 [5918]~P82(x59182)+~E(x59181,f2(x59182))+~P101(f323(f323(f238(x59182),f2(x59182)),f323(f73(x59182),x59181)))
% 179.72/179.59 [5942]~P54(x59421,x59422)+P38(x59421,f323(f278(x59421,x59421),x59422))+~P101(f323(f59(f866(x59421,x59421)),x59422))
% 179.72/179.59 [5950]~P90(x59501)+E(f323(f100(x59501),f323(f103(a860),x59502)),f323(f103(x59501),x59502))+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x59502)))
% 179.72/179.59 [5953]E(f323(a112,x59531),x59532)+~P101(f323(f323(f238(a860),x59531),x59532))+P101(f323(f323(f238(a860),f323(a112,x59531)),x59532))
% 179.72/179.59 [5966]E(f323(f323(f36(a1),x59661),x59662),f2(a1))+~P101(f323(f323(f237(a1),x59661),f2(a1)))+~P101(f323(f323(f238(a1),x59662),x59661))
% 179.72/179.59 [5977]E(f42(a1,x59771,x59772),x59771)+~P101(f323(f323(f237(a1),x59771),f2(a1)))+~P101(f323(f323(f238(a1),x59772),x59771))
% 179.72/179.59 [5990]E(f44(x59901,x59902),f43(x59901,x59902))+~P101(f323(f323(f237(a1),f2(a1)),x59901))+~P101(f323(f323(f237(a1),f2(a1)),x59902))
% 179.72/179.59 [5998]E(f323(f323(f36(a1),x59981),x59982),f2(a1))+~P101(f323(f323(f237(a1),f2(a1)),x59981))+~P101(f323(f323(f238(a1),x59981),x59982))
% 179.72/179.59 [6010]E(f42(a860,f323(f103(a860),x60101),f323(f103(a860),x60102)),f323(f103(a860),x60101))+P101(f323(a193,f323(f103(a1),x60101)))+~P101(f323(a193,f323(f103(a1),x60102)))
% 179.72/179.59 [6012]E(f42(a1,x60121,x60122),x60121)+~P101(f323(f323(f237(a1),f2(a1)),x60121))+~P101(f323(f323(f238(a1),x60121),x60122))
% 179.72/179.59 [6013]E(x60131,x60132)+~P101(f323(f323(f238(a860),x60131),f323(a112,x60132)))+~P101(f323(f323(f237(a860),x60132),x60131))
% 179.72/179.59 [6030]~P74(x60301)+~P101(f323(f323(f237(x60301),x60302),f2(x60301)))+P101(f323(f323(f237(x60301),x60302),f323(f77(x60301),x60302)))
% 179.72/179.59 [6031]~P116(x60311)+~P101(f323(f323(f238(x60311),x60312),f2(x60311)))+P101(f323(f323(f238(x60311),x60312),f323(f77(x60311),x60312)))
% 179.72/179.59 [6041]~P6(x60411)+E(f323(f323(f62(x60411,x60411,f110(x60411)),f188(x60411)),x60412),f37(x60411,x60412))+~P101(f323(f59(x60411),x60412))
% 179.72/179.59 [6042]~P6(x60421)+E(f323(f323(f62(x60421,x60421,f101(x60421)),f246(x60421)),x60422),f38(x60421,x60422))+~P101(f323(f59(x60421),x60422))
% 179.72/179.59 [6056]~P116(x60561)+~P101(f323(f323(f237(a1),f2(a1)),x60562))+P101(f323(f323(f237(x60561),f2(x60561)),f323(f102(x60561),x60562)))
% 179.72/179.59 [6057]~P119(x60571)+~P101(f323(f323(f238(a860),f2(a860)),x60572))+P101(f323(f323(f238(x60571),f2(x60571)),f323(f100(x60571),x60572)))
% 179.72/179.59 [6058]~P116(x60581)+~P101(f323(f323(f238(a1),f2(a1)),x60582))+P101(f323(f323(f238(x60581),f2(x60581)),f323(f102(x60581),x60582)))
% 179.72/179.59 [6061]~P7(x60612)+~P7(x60611)+E(f323(f302(a860,a1,f100(a1)),f294(a860,f323(a104,x60611),f323(a104,x60612))),f294(a1,x60611,x60612))
% 179.72/179.59 [6067]P101(f323(x60671,x60672))+~P101(f323(f323(f237(a1),f2(a1)),x60672))+~P101(f323(x60671,f323(f100(a1),f382(x60671))))
% 179.72/179.59 [6092]E(f323(f323(f78(a860),f323(f103(a860),x60921)),f323(f103(a860),x60922)),f323(f103(a860),x60921))+P101(f323(f323(f238(a1),x60921),a81))+~P101(f323(f323(f238(a1),x60922),a81))
% 179.72/179.59 [6096]~P116(x60961)+P101(f323(f323(f238(x60961),f2(x60961)),f80(x60961,x60962)))+~P101(f323(f323(f238(x60961),f2(x60961)),x60962))
% 179.72/179.59 [6107]~P75(x61071)+~P101(f323(f323(f237(x61071),x61072),f2(x61071)))+P101(f323(f323(f237(x61071),f2(x61071)),f323(f77(x61071),x61072)))
% 179.72/179.59 [6108]~P75(x61081)+~P101(f323(f323(f238(x61081),x61082),f2(x61081)))+P101(f323(f323(f238(x61081),f2(x61081)),f323(f77(x61081),x61082)))
% 179.72/179.59 [6111]E(x61111,f246(f867(x61112,a855)))+~E(f323(f35(x61112),x61111),f323(f35(x61112),f246(f867(x61112,a855))))+~P101(f323(f59(x61112),f246(f867(x61112,a855))))
% 179.72/179.59 [6145]~P74(x61451)+P101(f323(f323(f237(x61451),x61452),f2(x61451)))+~P101(f323(f323(f237(x61451),x61452),f323(f77(x61451),x61452)))
% 179.72/179.59 [6146]~P116(x61461)+P101(f323(f323(f238(x61461),x61462),f2(x61461)))+~P101(f323(f323(f238(x61461),x61462),f323(f77(x61461),x61462)))
% 179.72/179.59 [6155]~P90(x61551)+P101(f323(f323(f325(x61551),f323(f103(x61551),x61552)),f186(x61551)))+~P101(f323(f323(f237(a1),a81),x61552))
% 179.72/179.59 [6186]E(x61861,f2(a860))+~P101(f323(f323(f238(a860),x61861),f323(a112,x61862)))+P101(f323(f323(f238(a860),f846(x61862,x61861)),x61862))
% 179.72/179.59 [6208]~P116(x62081)+~P101(f323(f323(f238(x62081),f2(x62081)),f80(x62081,x62082)))+P101(f323(f323(f238(x62081),f2(x62081)),x62082))
% 179.72/179.59 [6210]~E(f323(f103(a860),x62102),f323(f103(a860),x62101))+P101(f323(f323(f237(a1),f323(f103(a1),x62101)),f2(a1)))+~P101(f323(a193,f323(f103(a1),x62102)))
% 179.72/179.59 [6239]E(f323(f257(a1,a1),f47(x62391,x62392)),f323(f323(f36(a1),x62391),x62392))+~P101(f323(f323(f238(a1),x62391),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x62392))
% 179.72/179.59 [6272]E(f323(f261(a1,a1),f47(x62721,x62722)),f42(a1,x62721,x62722))+~P101(f323(f323(f238(a1),x62721),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x62722))
% 179.72/179.59 [6275]~P116(x62752)+~P101(f323(f323(f237(x62752),f2(x62752)),f323(f102(x62752),x62751)))+P101(f323(f323(f237(a1),f2(a1)),x62751))
% 179.72/179.59 [6276]~P119(x62762)+~P101(f323(f323(f238(x62762),f2(x62762)),f323(f100(x62762),x62761)))+P101(f323(f323(f238(a860),f2(a860)),x62761))
% 179.72/179.59 [6277]~P116(x62772)+~P101(f323(f323(f238(x62772),f2(x62772)),f323(f102(x62772),x62771)))+P101(f323(f323(f238(a1),f2(a1)),x62771))
% 179.72/179.59 [6280]E(f323(f257(a1,a1),f44(x62801,x62802)),f323(f323(f36(a1),x62801),x62802))+~P101(f323(f323(f237(a1),f2(a1)),x62802))+~P101(f323(f323(f238(a1),f2(a1)),x62801))
% 179.72/179.59 [6295]E(f323(f261(a1,a1),f44(x62951,x62952)),f42(a1,x62951,x62952))+~P101(f323(f323(f237(a1),f2(a1)),x62952))+~P101(f323(f323(f238(a1),f2(a1)),x62951))
% 179.72/179.59 [6310]~P75(x63101)+P101(f323(f323(f237(x63101),x63102),f2(x63101)))+~P101(f323(f323(f237(x63101),f2(x63101)),f323(f77(x63101),x63102)))
% 179.72/179.59 [6311]~P75(x63111)+P101(f323(f323(f238(x63111),x63112),f2(x63111)))+~P101(f323(f323(f238(x63111),f2(x63111)),f323(f77(x63111),x63112)))
% 179.72/179.59 [6337]P101(f323(f46(x63371,x63372),f47(x63371,x63372)))+~P101(f323(f323(f238(a1),x63371),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x63372))
% 179.72/179.59 [6361]P101(f323(f46(x63611,x63612),f44(x63611,x63612)))+~P101(f323(f323(f237(a1),f2(a1)),x63611))+~P101(f323(f323(f238(a1),f2(a1)),x63612))
% 179.72/179.59 [6404]~P75(x64041)+P101(f323(f323(f237(x64041),f323(f77(x64041),x64042)),f2(x64041)))+~P101(f323(f323(f237(x64041),f2(x64041)),x64042))
% 179.72/179.59 [6405]~P75(x64051)+P101(f323(f323(f238(x64051),f323(f77(x64051),x64052)),f2(x64051)))+~P101(f323(f323(f238(x64051),f2(x64051)),x64052))
% 179.72/179.59 [6421]E(f323(f323(f22(a860),f323(a104,x64211)),f323(a104,x64212)),f323(a104,f194(x64211,x64212)))+~P101(f323(f323(f237(a1),f2(a1)),x64212))+~P101(f323(f323(f237(a1),f2(a1)),x64211))
% 179.72/179.59 [6438]P101(f323(f323(f237(a1),f2(a1)),f194(x64381,x64382)))+~P101(f323(f323(f237(a1),f2(a1)),x64382))+~P101(f323(f323(f237(a1),f2(a1)),x64381))
% 179.72/179.59 [6475]~P101(f323(x64751,x64752))+P101(f323(x64751,f2(a860)))+P101(f323(x64751,f323(f323(f78(a860),f851(x64752,x64751)),f76(a860))))
% 179.72/179.59 [6557]E(f323(f103(a860),x65571),f323(f103(a860),x65572))+~P101(f323(f323(f237(a1),f323(f103(a1),x65572)),f2(a1)))+~P101(f323(a193,f323(f103(a1),x65571)))
% 179.72/179.59 [6567]~E(x65671,f2(a860))+~E(f606(x65672,x65671),f2(a860))+E(f323(f135(a860,a860,f78(a860),x65671),x65672),f2(a860))
% 179.72/179.59 [6592]~P101(f323(f59(x65921),f546(x65922,x65921)))+~P101(f323(f59(f867(x65921,a855)),x65922))+P101(f323(f59(x65921),f37(f867(x65921,a855),x65922)))
% 179.72/179.59 [6598]E(x65981,x65982)+P101(f323(f323(f238(a1),x65981),x65982))+~P101(f323(f323(f238(a1),x65981),f323(f323(f78(a1),x65982),f76(a1))))
% 179.72/179.59 [6599]P101(f323(f323(f237(a860),f323(a104,x65991)),f323(a104,x65992)))+~P101(f323(f323(f237(a1),f2(a1)),x65992))+~P101(f323(f323(f237(a1),x65991),x65992))
% 179.72/179.59 [6600]P101(f323(f323(f237(a860),f323(a104,x66001)),f323(a104,x66002)))+~P101(f323(f323(f238(a1),f2(a1)),x66001))+~P101(f323(f323(f237(a1),x66001),x66002))
% 179.72/179.59 [6602]P101(f323(f323(f238(a860),f323(a104,x66021)),f323(a104,x66022)))+~P101(f323(f323(f237(a1),f2(a1)),x66021))+~P101(f323(f323(f238(a1),x66021),x66022))
% 179.72/179.59 [6603]P101(f323(f323(f238(a860),f323(a104,x66031)),f323(a104,x66032)))+~P101(f323(f323(f238(a1),f2(a1)),x66032))+~P101(f323(f323(f238(a1),x66031),x66032))
% 179.72/179.59 [6614]E(f42(a860,f323(a104,x66141),f323(a104,x66142)),f323(a104,f42(a1,x66141,x66142)))+~P101(f323(f323(f237(a1),f2(a1)),x66142))+~P101(f323(f323(f237(a1),f2(a1)),x66141))
% 179.72/179.59 [6636]~P75(x66361)+~P101(f323(f323(f237(x66361),f323(f77(x66361),x66362)),f2(x66361)))+P101(f323(f323(f237(x66361),f2(x66361)),x66362))
% 179.72/179.59 [6637]~P75(x66371)+~P101(f323(f323(f238(x66371),f323(f77(x66371),x66372)),f2(x66371)))+P101(f323(f323(f238(x66371),f2(x66371)),x66372))
% 179.72/179.59 [6652]~P101(f323(f323(f238(a1),a81),x66522))+~P101(f323(f323(f238(a1),x66521),x66522))+P101(f323(f323(f238(a860),f323(f103(a860),x66521)),f323(f103(a860),x66522)))
% 179.72/179.59 [6742]~P101(f323(f323(f237(a1),f2(a1)),x67421))+P101(f323(f323(f238(a860),f323(a104,x67421)),x67422))+~P101(f323(f323(f238(a1),x67421),f323(f100(a1),x67422)))
% 179.72/179.59 [6759]E(x67591,f2(a1))+E(f42(a1,x67592,x67591),f2(a1))+E(f323(f323(f22(a1),f323(f77(a1),f323(f323(f36(a1),x67592),x67591))),f76(a1)),f323(f323(f36(a1),x67592),f323(f77(a1),x67591)))
% 179.72/179.59 [6775]~P101(f323(f323(f237(a1),f2(a1)),x67751))+~P101(f323(f323(f238(a860),f323(a104,x67751)),x67752))+P101(f323(f323(f238(a1),x67751),f323(f100(a1),x67752)))
% 179.72/179.59 [6810]~P101(f323(f323(f237(a860),f323(a104,x68101)),f323(a104,x68102)))+~P101(f323(f323(f237(a1),f2(a1)),x68102))+P101(f323(f323(f237(a1),x68101),x68102))
% 179.72/179.59 [6811]~P101(f323(f323(f237(a860),f323(a104,x68111)),f323(a104,x68112)))+~P101(f323(f323(f238(a1),f2(a1)),x68111))+P101(f323(f323(f237(a1),x68111),x68112))
% 179.72/179.59 [6839]P101(f323(f323(f237(a1),x68391),x68392))+~P101(f323(f323(f237(a860),f323(f103(a860),x68391)),f323(f103(a860),x68392)))+P101(f323(f323(f237(a1),x68391),a81))
% 179.72/179.59 [6863]P101(f323(f323(f237(a1),f2(a1)),f42(a1,x68631,x68632)))+~P101(f323(f323(f237(a1),f2(a1)),x68632))+~P101(f323(f323(f237(a1),f2(a1)),x68631))
% 179.72/179.59 [6961]P101(f323(f323(f238(a1),a81),x69611))+~P101(f323(f323(f238(a1),x69612),x69611))+~P101(f323(f323(f238(a860),f323(f103(a860),x69612)),f323(f103(a860),x69611)))
% 179.72/179.59 [7012]E(f323(f323(f258(a1,a1),f323(f323(f36(a1),x70121),x70122)),f42(a1,x70121,x70122)),f47(x70121,x70122))+~P101(f323(f323(f238(a1),x70121),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x70122))
% 179.72/179.59 [7033]E(f323(f323(f258(a1,a1),f323(f323(f36(a1),x70331),x70332)),f42(a1,x70331,x70332)),f44(x70331,x70332))+~P101(f323(f323(f237(a1),f2(a1)),x70332))+~P101(f323(f323(f237(a1),f2(a1)),x70331))
% 179.72/179.59 [7084]~P93(x70842)+E(x70841,f113(x70842))+E(f323(f135(x70842,x70842,f79(x70842),f323(f134(x70842),x70841)),f323(f165(x70842),x70841)),f323(f61(x70842,f79(x70842)),f323(f166(x70842),x70841)))
% 179.72/179.59 [7196]~E(x71961,f2(a860))+E(f323(f135(a860,a860,f78(a860),x71961),x71962),f2(a860))+P101(f323(f323(f325(a860),f606(x71962,x71961)),f323(f166(a860),x71962)))
% 179.72/179.59 [7243]~P101(f323(f323(f237(a1),x72431),f2(a1)))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x72431),x72432)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x72432))
% 179.72/179.59 [7244]~P101(f323(f323(f238(a1),x72442),f2(a1)))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x72441),x72442)),f2(a1)))+~P101(f323(f323(f237(a1),f2(a1)),x72441))
% 179.72/179.59 [7245]~P101(f323(f323(f238(a1),x72452),f2(a1)))+P101(f323(f323(f238(a1),f323(f323(f36(a1),x72451),x72452)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x72451))
% 179.72/179.59 [7247]~P101(f323(f323(f238(a1),x72471),f2(a1)))+P101(f323(f323(f238(a1),f323(f323(f36(a1),x72471),x72472)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x72472))
% 179.72/179.59 [7253]P101(f323(f323(f325(f867(x72531,a855)),f546(x72532,x72531)),x72532))+~P101(f323(f59(f867(x72531,a855)),x72532))+P101(f323(f59(x72531),f37(f867(x72531,a855),x72532)))
% 179.72/179.59 [7347]P27(x73471,x73471,x73472,f246(f867(x73471,a855)))+~E(f323(f302(x73471,x73471,x73472),f246(f867(x73471,a855))),f246(f867(x73471,a855)))+~P101(f323(f59(x73471),f246(f867(x73471,a855))))
% 179.72/179.59 [7473]~P27(x74731,x74731,x74732,f246(f867(x74731,a855)))+E(f323(f302(x74731,x74731,x74732),f246(f867(x74731,a855))),f246(f867(x74731,a855)))+~P101(f323(f59(x74731),f246(f867(x74731,a855))))
% 179.72/179.59 [7609]E(f323(f323(f36(a1),x76091),x76092),f323(f103(a1),a97))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x76091),x76092)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x76091))
% 179.72/179.59 [7668]~P101(f323(f323(f238(a1),x76682),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f36(a1),x76681),x76682)),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x76681))
% 179.72/179.59 [7673]E(f323(f323(f78(a1),x76731),x76732),f42(a1,x76731,x76732))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),x76731),x76732)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x76731))
% 179.72/179.59 [7676]P101(f323(f323(f238(a1),x76761),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f36(a1),x76761),x76762)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x76762))
% 179.72/179.59 [8062]~P5(x80621)+~P101(f323(f56(f864(x80621)),x80622))+P101(f323(f56(x80621),f323(f323(f8(f864(x80621),a855,x80621),x80622),f230(x80621))))
% 179.72/179.59 [8374]~P103(x83741)+P16(x83741,x83742)+~P101(f323(f323(f237(x83741),f323(f323(f158(x83741),x83742),f559(x83742,x83741))),f323(f323(f158(x83741),x83742),f560(x83742,x83741))))
% 179.72/179.59 [8375]~P103(x83751)+P16(x83751,x83752)+~P101(f323(f323(f237(x83751),f323(f323(f158(x83751),x83752),f601(x83752,x83751))),f323(f323(f158(x83751),x83752),f604(x83752,x83751))))
% 179.72/179.59 [8520]~P5(x85201)+P101(f323(f55(f864(x85201)),x85202))+~P101(f323(f55(x85201),f323(f323(f8(f864(x85201),a855,x85201),x85202),f230(x85201))))
% 179.72/179.59 [9699]~P5(x96991)+~P5(x96992)+E(f323(f323(f147(f861(x96991),f867(x96992,x96991)),f323(f323(f8(f867(x96992,f864(x96991)),f867(x96992,x96991),f861(x96991)),f71(f864(x96991),x96991,x96992,f234(x96991))),f323(f323(f8(f861(f866(x96992,x96991)),f867(x96992,f864(x96991)),f861(x96991)),f179(x96992,x96991)),f323(f175(x96992,x96991),f53(x96992))))),f52(x96991,f323(f189(f861(x96992)),f53(x96992)),f53(x96991))),f53(f867(x96992,x96991)))
% 179.72/179.59 [5655]E(x56551,f2(a1))+~E(f42(a1,x56552,x56551),f2(a1))+E(f323(f323(f36(a1),x56552),f323(f77(a1),x56551)),f323(f77(a1),f323(f323(f36(a1),x56552),x56551)))
% 179.72/179.59 [5673]~P39(x56732)+~P39(x56731)+P39(f323(f323(f110(f867(a1,a855)),x56731),x56732))
% 179.72/179.59 [5674]~P39(x56742)+~P39(x56741)+P39(f323(f323(f101(f867(a1,a855)),x56741),x56742))
% 179.72/179.59 [5692]~P62(x56921)+~P90(x56921)+E(f323(f77(x56921),f323(f323(f281(x56921),f76(x56921)),x56922)),f323(f323(f281(x56921),f323(f103(x56921),a97)),x56922))
% 179.72/179.59 [5805]E(x58051,f2(a1))+~E(f42(a1,x58052,x58051),f2(a1))+E(f323(f323(f36(a1),f323(f77(a1),x58052)),x58051),f323(f77(a1),f323(f323(f36(a1),x58052),x58051)))
% 179.72/179.59 [5936]~P103(x59361)+P16(x59361,x59362)+P101(f323(f323(f238(a860),f560(x59362,x59361)),f323(f189(f861(x59361)),x59362)))
% 179.72/179.59 [5937]~P103(x59371)+P16(x59371,x59372)+P101(f323(f323(f238(a860),f604(x59372,x59371)),f323(f189(f861(x59371)),x59372)))
% 179.72/179.59 [6088]~P90(x60881)+~E(f323(f103(x60881),x60882),f2(x60881))+P30(x60881,f323(f103(x60881),f323(f323(f78(a1),x60882),f323(f77(a1),a81))))
% 179.72/179.59 [6089]~P90(x60891)+~E(f323(f103(x60891),x60892),f2(x60891))+P30(x60891,f323(f103(x60891),f323(f323(f78(a1),a81),f323(f77(a1),x60892))))
% 179.72/179.59 [6091]E(f323(a48,f44(f323(f77(a1),x60911),f323(f77(a1),x60912))),f43(x60911,x60912))+P101(f323(f323(f237(a1),f2(a1)),x60911))+P101(f323(f323(f238(a1),f2(a1)),x60912))
% 179.72/179.59 [6216]~E(x62162,f2(a860))+~E(x62161,f2(a860))+P101(f323(f323(f237(a1),f323(f100(a1),x62161)),f323(f77(a1),f323(f100(a1),x62162))))
% 179.72/179.59 [6243]E(f323(f323(f78(a860),f323(f103(a860),x62431)),f323(f103(a860),x62432)),f323(f103(a860),f323(f323(f78(a1),x62431),x62432)))+P101(f323(f323(f238(a1),x62431),a81))+P101(f323(f323(f238(a1),x62432),a81))
% 179.72/179.59 [6371]~P74(x63711)+~P101(f323(f323(f237(x63711),f2(x63711)),x63712))+P101(f323(f323(f237(x63711),f323(f77(x63711),x63712)),x63712))
% 179.72/179.59 [6372]~P74(x63721)+~P101(f323(f323(f238(x63721),f2(x63721)),x63722))+P101(f323(f323(f238(x63721),f323(f77(x63721),x63722)),x63722))
% 179.72/179.59 [6543]E(f323(f323(f22(a860),f323(a104,x65431)),f323(a104,x65432)),f323(a104,f323(f323(f22(a1),x65431),x65432)))+~P101(f323(f323(f237(a1),f2(a1)),x65432))+~P101(f323(f323(f237(a1),x65432),x65431))
% 179.72/179.59 [6575]E(f323(a104,f42(a1,f323(f103(a1),x65751),f323(f103(a1),x65752))),f42(a860,f323(f103(a860),x65751),f323(f103(a860),x65752)))+P101(f323(a193,f323(f103(a1),x65751)))+P101(f323(a193,f323(f103(a1),x65752)))
% 179.72/179.59 [6593]~P74(x65931)+P101(f323(f323(f237(x65931),f2(x65931)),x65932))+~P101(f323(f323(f237(x65931),f323(f77(x65931),x65932)),x65932))
% 179.72/179.59 [6594]~P74(x65941)+P101(f323(f323(f238(x65941),f2(x65941)),x65942))+~P101(f323(f323(f238(x65941),f323(f77(x65941),x65942)),x65942))
% 179.72/179.59 [6606]~P74(x66061)+~P101(f323(f323(f237(x66061),f2(x66061)),x66062))+P101(f323(f323(f237(x66061),f2(x66061)),f323(f323(f78(x66061),x66062),x66062)))
% 179.72/179.59 [6608]~P74(x66081)+~P101(f323(f323(f238(x66081),f2(x66081)),x66082))+P101(f323(f323(f238(x66081),f2(x66081)),f323(f323(f78(x66081),x66082),x66082)))
% 179.72/179.59 [6620]E(f323(f323(f78(a860),f323(a104,x66201)),f323(a104,x66202)),f323(a104,f323(f323(f78(a1),x66201),x66202)))+~P101(f323(f323(f237(a1),f2(a1)),x66202))+~P101(f323(f323(f237(a1),f2(a1)),x66201))
% 179.72/179.59 [6631]E(x66311,f2(a860))+P101(f323(f323(f238(a860),f2(a860)),x66312))+~P101(f323(f323(f238(a860),f2(a860)),f323(f323(f248(a860),x66312),x66311)))
% 179.72/179.59 [6661]~P90(x66611)+E(f323(f103(x66611),x66612),f2(x66611))+~P30(x66611,f323(f103(x66611),f323(f323(f78(a1),a81),f323(f77(a1),x66612))))
% 179.72/179.59 [6662]~P90(x66621)+E(f323(f103(x66621),x66622),f2(x66621))+~P30(x66621,f323(f103(x66621),f323(f323(f78(a1),x66622),f323(f77(a1),a81))))
% 179.72/179.59 [6720]~P101(f323(f59(x67201),x67202))+~P101(f323(f59(x67201),f246(f867(x67201,a855))))+P101(f323(f59(x67201),f323(f77(f867(x67201,a855)),x67202)))
% 179.72/179.59 [6743]~P101(f323(f323(f238(a1),f2(a1)),x67432))+~P101(f323(f323(f237(a1),x67432),x67431))+P101(f323(f323(f238(a1),f2(a1)),f323(f323(f36(a1),x67431),x67432)))
% 179.72/179.59 [6744]~P101(f323(f323(f237(a1),x67441),f2(a1)))+~P101(f323(f323(f238(a1),x67442),f2(a1)))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f36(a1),x67441),x67442)))
% 179.72/179.59 [6783]~P101(f323(f323(f237(a1),f2(a1)),x67832))+~P101(f323(f323(f237(a1),f2(a1)),x67831))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f79(a1),x67831),x67832)))
% 179.72/179.59 [6784]~P101(f323(f323(f237(a1),f2(a1)),x67842))+~P101(f323(f323(f237(a1),f2(a1)),x67841))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),x67841),x67842)))
% 179.72/179.59 [6785]~P101(f323(f323(f237(a1),f2(a1)),x67852))+~P101(f323(f323(f237(a1),f2(a1)),x67851))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f36(a1),x67851),x67852)))
% 179.72/179.59 [6786]~P101(f323(f323(f237(a1),f2(a1)),x67861))+~P101(f323(f323(f238(a1),f2(a1)),x67862))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f36(a1),x67861),x67862)))
% 179.72/179.59 [6787]~P101(f323(f323(f238(a860),f2(a860)),x67872))+~P101(f323(f323(f238(a860),f2(a860)),x67871))+P101(f323(f323(f238(a860),f2(a860)),f323(f323(f79(a860),x67871),x67872)))
% 179.72/179.59 [6851]E(x68511,f2(a1))+E(f42(a1,x68512,x68511),f2(a1))+E(f323(f323(f22(a1),f323(f77(a1),f323(f323(f36(a1),x68512),x68511))),f76(a1)),f323(f323(f36(a1),f323(f77(a1),x68512)),x68511))
% 179.72/179.59 [6904]P101(f323(f323(f238(a860),f2(a860)),x69041))+P101(f323(f323(f238(a860),f2(a860)),x69042))+~P101(f323(f323(f238(a860),f2(a860)),f323(f323(f78(a860),x69042),x69041)))
% 179.72/179.59 [6908]~P74(x69081)+P101(f323(f323(f237(x69081),f2(x69081)),x69082))+~P101(f323(f323(f237(x69081),f2(x69081)),f323(f323(f78(x69081),x69082),x69082)))
% 179.72/179.59 [6909]~P74(x69091)+P101(f323(f323(f238(x69091),f2(x69091)),x69092))+~P101(f323(f323(f238(x69091),f2(x69091)),f323(f323(f78(x69091),x69092),x69092)))
% 179.72/179.59 [6962]~P101(f323(f59(x69621),x69622))+P101(f323(f59(x69621),f246(f867(x69621,a855))))+~P101(f323(f59(x69621),f323(f77(f867(x69621,a855)),x69622)))
% 179.72/179.59 [7025]P101(f323(f323(f237(a1),x70251),f2(a1)))+~P101(f323(f323(f238(a1),x70252),f2(a1)))+~P101(f323(f323(f237(a1),f2(a1)),f323(f323(f36(a1),x70251),x70252)))
% 179.72/179.59 [7031]~P101(f323(f323(f238(a1),f2(a1)),x70311))+P101(f323(f323(f237(a1),x70311),x70312))+~P101(f323(f323(f238(a1),f2(a1)),f323(f323(f36(a1),x70312),x70311)))
% 179.72/179.59 [7032]~P101(f323(f323(f237(a1),f2(a1)),x70322))+P101(f323(f323(f237(a1),x70321),x70322))+~P101(f323(f323(f238(a1),f2(a1)),f323(f323(f36(a1),x70322),x70321)))
% 179.72/179.59 [7061]P101(f323(f323(f237(a1),f2(a1)),x70611))+~P101(f323(f323(f238(a1),f2(a1)),x70612))+~P101(f323(f323(f237(a1),f2(a1)),f323(f323(f36(a1),x70611),x70612)))
% 179.72/179.59 [7062]P101(f323(f323(f238(a1),f2(a1)),x70621))+~P101(f323(f323(f237(a1),f2(a1)),x70622))+~P101(f323(f323(f238(a1),f2(a1)),f323(f323(f36(a1),x70622),x70621)))
% 179.72/179.59 [7503]~P101(f323(f59(x75032),f246(f867(x75032,a855))))+~P101(f323(f59(x75031),f246(f867(x75031,a855))))+P101(f323(f59(f865(x75031,x75032)),f246(f867(f865(x75031,x75032),a855))))
% 179.72/179.59 [7504]~P101(f323(f59(x75042),f246(f867(x75042,a855))))+~P101(f323(f59(x75041),f246(f867(x75041,a855))))+P101(f323(f59(f866(x75041,x75042)),f246(f867(f866(x75041,x75042),a855))))
% 179.72/179.59 [7573]~P101(f323(f323(f238(a860),f323(a112,f2(a860))),x75731))+~P101(f323(f323(f238(a860),f323(a112,f2(a860))),x75732))+P101(f323(f323(f238(a860),x75731),f323(f323(f79(a860),x75732),x75731)))
% 179.72/179.59 [7574]~P101(f323(f323(f238(a860),f323(a112,f2(a860))),x75741))+~P101(f323(f323(f238(a860),f323(a112,f2(a860))),x75742))+P101(f323(f323(f238(a860),x75741),f323(f323(f79(a860),x75741),x75742)))
% 179.72/179.59 [7608]E(f323(f35(x76081),f246(f867(x76081,a855))),f323(a112,f2(a860)))+P101(f323(f59(x76082),f246(f867(x76082,a855))))+~P101(f323(f59(f867(x76082,x76081)),f246(f867(f867(x76082,x76081),a855))))
% 179.72/179.59 [7736]~P101(f323(f323(f237(a860),f323(a112,f2(a860))),x77361))+~P101(f323(f323(f237(a860),f323(a112,f2(a860))),x77362))+P101(f323(f323(f237(a860),f323(a112,f2(a860))),f323(f323(f79(a860),x77361),x77362)))
% 179.72/179.59 [7737]~P101(f323(f323(f238(a860),f323(a112,f2(a860))),x77372))+~P101(f323(f323(f238(a860),f323(a112,f2(a860))),x77371))+P101(f323(f323(f238(a860),f323(a112,f2(a860))),f323(f323(f79(a860),x77371),x77372)))
% 179.72/179.59 [8417]E(x84171,f113(x84172))+~P101(f323(f130(x84172),x84171))+E(f171(x84172,f323(f323(f8(a855,a855,x84172),a318),f323(f323(f7(x84172,x84172,a855),a320),f137(x84172,x84171))),x84171),f114(x84172,x84171))
% 179.72/179.59 [8510]~P39(x85102)+~P39(x85101)+E(f323(f302(a860,a1,f100(a1)),f323(f323(f110(f867(a860,a855)),f323(f302(a1,a860,a104),x85101)),f323(f302(a1,a860,a104),x85102))),f323(f323(f110(f867(a1,a855)),x85101),x85102))
% 179.72/179.59 [8511]~P39(x85112)+~P39(x85111)+E(f323(f302(a860,a1,f100(a1)),f323(f323(f101(f867(a860,a855)),f323(f302(a1,a860,a104),x85111)),f323(f302(a1,a860,a104),x85112))),f323(f323(f101(f867(a1,a855)),x85111),x85112))
% 179.72/179.59 [9178]~P90(x91781)+~E(f323(f103(x91781),x91782),f76(x91781))+P30(x91781,f323(f103(x91781),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f77(a1),x91782))))
% 179.72/179.59 [9409]~P90(x94091)+E(f323(f103(x94091),x94092),f76(x94091))+~P30(x94091,f323(f103(x94091),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f77(a1),x94092))))
% 179.72/179.59 [10139]E(x101391,f2(a1))+E(x101392,f2(a1))+E(f323(f263(a1,a1,a1,a1,f32(a1),f323(f79(a1),f80(a1,x101392))),f323(f323(f323(f96(f866(a1,a1)),f323(f323(a320,f80(a1,x101391)),f80(a1,x101392))),f50(x101391,x101392)),f323(f323(f262(a1,a1,f866(a1,a1)),f323(f323(f18(a1,f867(a1,f866(a1,a1)),f867(a1,f866(a1,a1))),f323(f323(f8(f867(a1,f867(f866(a1,a1),f866(a1,a1))),f867(f867(a1,f866(a1,a1)),f867(a1,f866(a1,a1))),a1),f18(a1,f866(a1,a1),f866(a1,a1))),f323(f323(f8(f866(a1,a1),f867(a1,f867(f866(a1,a1),f866(a1,a1))),a1),f323(f7(a1,f866(a1,a1),f867(f866(a1,a1),f866(a1,a1))),f323(f323(f8(a855,f867(f866(a1,a1),f867(f866(a1,a1),f866(a1,a1))),a1),f96(f866(a1,a1))),f323(f323(f7(a1,a1,a855),a320),f2(a1))))),f323(f323(f7(a1,a1,f866(a1,a1)),f323(f323(f8(a1,f867(a1,f866(a1,a1)),a1),f258(a1,a1)),f77(a1))),f2(a1))))),f323(f323(f7(a1,f867(a1,a1),f867(a1,f866(a1,a1))),f323(f323(f8(f867(a1,f866(a1,a1)),f867(f867(a1,a1),f867(a1,f866(a1,a1))),a1),f8(a1,f866(a1,a1),a1)),f323(f323(f8(a1,f867(a1,f866(a1,a1)),a1),f258(a1,a1)),f323(f323(f7(a1,a1,a1),f323(f323(f8(a1,f867(a1,a1),a1),f22(a1)),f77(a1))),f76(a1))))),f323(f22(a1),f323(f73(a1),x101392))))),f50(x101391,x101392)))),f43(x101391,x101392))
% 179.72/179.59 [10140]E(x101401,f2(a1))+E(x101402,f2(a1))+E(f323(f263(a1,a1,a1,a1,f32(a1),f323(f79(a1),f80(a1,x101402))),f323(f323(f323(f96(f866(a1,a1)),f323(f323(a322,f323(f323(a321,f323(f323(f238(a1),f2(a1)),x101402)),f323(f323(f237(a1),f2(a1)),x101401))),f323(f323(a321,f323(f323(f238(a1),x101402),f2(a1))),f323(f323(f238(a1),x101401),f2(a1))))),f50(x101401,x101402)),f323(f323(f262(a1,a1,f866(a1,a1)),f323(f323(f18(a1,f867(a1,f866(a1,a1)),f867(a1,f866(a1,a1))),f323(f323(f8(f867(a1,f867(f866(a1,a1),f866(a1,a1))),f867(f867(a1,f866(a1,a1)),f867(a1,f866(a1,a1))),a1),f18(a1,f866(a1,a1),f866(a1,a1))),f323(f323(f8(f866(a1,a1),f867(a1,f867(f866(a1,a1),f866(a1,a1))),a1),f323(f7(a1,f866(a1,a1),f867(f866(a1,a1),f866(a1,a1))),f323(f323(f8(a855,f867(f866(a1,a1),f867(f866(a1,a1),f866(a1,a1))),a1),f96(f866(a1,a1))),f323(f323(f7(a1,a1,a855),a320),f2(a1))))),f323(f323(f7(a1,a1,f866(a1,a1)),f323(f323(f8(a1,f867(a1,f866(a1,a1)),a1),f258(a1,a1)),f77(a1))),f2(a1))))),f323(f323(f7(a1,f867(a1,a1),f867(a1,f866(a1,a1))),f323(f323(f8(f867(a1,f866(a1,a1)),f867(f867(a1,a1),f867(a1,f866(a1,a1))),a1),f8(a1,f866(a1,a1),a1)),f323(f323(f8(a1,f867(a1,f866(a1,a1)),a1),f258(a1,a1)),f323(f323(f7(a1,a1,a1),f323(f323(f8(a1,f867(a1,a1),a1),f22(a1)),f77(a1))),f76(a1))))),f323(f22(a1),f323(f73(a1),x101402))))),f50(x101401,x101402)))),f43(x101401,x101402))
% 179.72/179.59 [5681]~P116(x56811)+~P90(x56811)+E(f323(f73(x56811),f323(f323(f248(x56811),f323(f103(x56811),a97)),x56812)),f76(x56811))
% 179.72/179.59 [6156]~P134(x61561)+~P101(f323(f323(f238(a1),x61562),f2(a1)))+E(f323(f77(x61561),f323(f100(x61561),f323(a104,f323(f77(a1),x61562)))),f323(f102(x61561),x61562))
% 179.72/179.59 [6354]P101(f323(f323(f237(a99),x63541),f76(a99)))+E(f323(f323(f78(a99),f76(a99)),f271(x63541,f323(f323(f36(a99),x63542),x63541))),f271(x63541,x63542))+P101(f323(f323(f238(a99),x63542),x63541))
% 179.72/179.59 [6949]~P89(x69491)+~P101(f323(f323(f325(x69491),x69492),f109(x69491)))+~E(f323(f323(f78(x69491),f323(f323(f78(x69491),f76(x69491)),x69492)),x69492),f2(x69491))
% 179.72/179.59 [7063]~P101(f323(f323(f237(a1),x70632),f2(a1)))+~P101(f323(f323(f238(a1),x70631),f2(a1)))+E(f323(f257(a1,a1),f323(a48,f44(f323(f77(a1),x70631),f323(f77(a1),x70632)))),f323(f323(f36(a1),x70631),x70632))
% 179.72/179.59 [7080]~P101(f323(f323(f237(a1),x70802),f2(a1)))+~P101(f323(f323(f238(a1),x70801),f2(a1)))+E(f323(f261(a1,a1),f323(a48,f44(f323(f77(a1),x70801),f323(f77(a1),x70802)))),f42(a1,x70801,x70802))
% 179.72/179.59 [7086]~P101(f323(f323(f238(a1),x70862),f2(a1)))+E(f323(f257(a1,a1),f323(a48,f47(f323(f77(a1),x70861),f323(f77(a1),x70862)))),f323(f323(f36(a1),x70861),x70862))+~P101(f323(f323(f238(a1),f2(a1)),x70861))
% 179.72/179.59 [7104]~P101(f323(f323(f238(a1),x71042),f2(a1)))+E(f323(f261(a1,a1),f323(a48,f47(f323(f77(a1),x71041),f323(f77(a1),x71042)))),f42(a1,x71041,x71042))+~P101(f323(f323(f238(a1),f2(a1)),x71041))
% 179.72/179.59 [7157]E(f323(f323(f36(a1),f323(f323(f248(a1),x71571),x71572)),x71571),f323(f323(f248(a1),x71571),f323(f323(f22(a860),x71572),f323(a112,f2(a860)))))+~P101(f323(f323(f238(a860),f2(a860)),x71572))+~P101(f323(f323(f238(a1),f2(a1)),x71571))
% 179.72/179.59 [7250]~P101(f323(f323(f238(a860),f2(a860)),x72501))+~P101(f323(f323(f238(a860),f2(a860)),x72502))+P101(f323(f323(f238(a860),f323(f323(f22(a860),x72501),x72502)),x72501))
% 179.72/179.59 [7251]~P101(f323(f323(f238(a860),f2(a860)),x72511))+~P101(f323(f323(f238(a860),f76(a860)),x72512))+P101(f323(f323(f238(a860),f323(f323(f36(a860),x72511),x72512)),x72511))
% 179.72/179.59 [7252]~P101(f323(f323(f238(a1),f2(a1)),x72521))+~P101(f323(f323(f238(a1),f76(a1)),x72522))+P101(f323(f323(f238(a1),f323(f323(f36(a1),x72521),x72522)),x72521))
% 179.72/179.59 [7396]E(x73961,f2(a860))+~E(x73962,f2(a1))+~P101(f323(f323(f238(a1),f2(a1)),f323(f323(f248(a1),f323(f73(a1),x73962)),x73961)))
% 179.72/179.59 [7814]~E(x78142,f113(f861(x78141)))+E(f323(f189(f861(f861(x78141))),f173(x78141,x78142)),f2(a860))+~P16(a860,f323(f162(a860),f323(f323(f147(f861(x78141),a860),f189(f861(x78141))),x78142)))
% 179.72/179.59 [8061]P101(f323(x80611,x80612))+~P101(f323(x80611,f323(a107,f681(x80611,x80612))))+~P101(f323(f323(f325(f867(f866(a860,a860),a855)),x80612),a98))
% 179.72/179.59 [8079]E(x80791,f113(f861(x80792)))+E(f323(f189(f861(x80792)),f323(f323(f158(f861(x80792)),x80791),f2(a860))),f323(f189(f861(f861(x80792))),f173(x80792,x80791)))+~P16(a860,f323(f162(a860),f323(f323(f147(f861(x80792),a860),f189(f861(x80792))),x80791)))
% 179.72/179.59 [8796]~P101(f323(f59(x87961),f323(f243(x87961),x87962)))+~P101(f323(f59(x87961),f246(f867(x87961,a855))))+P101(f323(f59(x87961),f323(f243(x87961),f323(f323(f8(a855,a855,x87961),a318),x87962))))
% 179.72/179.59 [8857]E(f323(f323(f258(a860,a860),f323(a112,f323(f323(f36(a860),f323(f323(f22(a860),x88571),x88572)),x88572))),f42(a860,f323(f323(f22(a860),x88571),x88572),x88572)),f83(f866(a860,a860),f45(x88571,x88572)))+~P101(f323(f323(f238(a860),f2(a860)),x88572))+~P101(f323(f323(f237(a860),x88572),x88571))
% 179.72/179.59 [9144]~P101(f323(f59(x91441),f323(f243(x91441),x91442)))+P101(f323(f59(x91441),f246(f867(x91441,a855))))+~P101(f323(f59(x91441),f323(f243(x91441),f323(f323(f8(a855,a855,x91441),a318),x91442))))
% 179.72/179.59 [9865]P29(x98651,x98652)+~P38(x98651,f323(f257(f867(f866(x98651,x98651),a855),f867(f866(x98651,x98651),a855)),x98652))+~P101(f323(f323(f237(f867(f866(x98651,x98651),a855)),f323(f323(f280(x98651,x98651,x98651),f323(f257(f867(f866(x98651,x98651),a855),f867(f866(x98651,x98651),a855)),x98652)),f323(f261(f867(f866(x98651,x98651),a855),f867(f866(x98651,x98651),a855)),x98652))),f323(f257(f867(f866(x98651,x98651),a855),f867(f866(x98651,x98651),a855)),x98652)))
% 179.72/179.59 [7183]~P101(f323(f323(f238(a860),f2(a860)),x71832))+P101(f323(f323(f238(a860),x71831),x71832))+E(f323(a112,f323(f323(f36(a860),f323(f323(f22(a860),x71831),x71832)),x71832)),f323(f323(f36(a860),x71831),x71832))
% 179.72/179.59 [7317]~P101(f323(f323(f238(a860),f2(a860)),x73172))+~P101(f323(f323(f237(a860),x73172),x73171))+E(f323(a112,f323(f323(f36(a860),f323(f323(f22(a860),x73171),x73172)),x73172)),f323(f323(f36(a860),x73171),x73172))
% 179.72/179.59 [8290]~P90(x82901)+~P89(x82901)+~P30(x82901,f323(f103(x82901),f323(f323(f22(a1),f323(f323(f78(a1),x82902),x82902)),a97)))
% 179.72/179.59 [9052]E(x90521,f2(a860))+E(f323(f323(f262(a860,a860,f866(a860,a860)),f323(f323(f8(a860,f867(a860,f866(a860,a860)),a860),f258(a860,a860)),a112)),f83(f866(a860,a860),f45(f323(f323(f22(a860),x90522),x90521),x90521))),f83(f866(a860,a860),f45(x90522,x90521)))+P101(f323(f323(f238(a860),x90522),x90521))
% 179.72/179.59 [9474]P101(f323(x94742,f768(x94742,x94741)))+P101(f323(x94741,f768(x94742,x94741)))+E(f323(f243(a1),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),f2(a1)))),x94741)),f323(f243(a1),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),f2(a1)))),x94742)))
% 179.72/179.59 [9478]~P101(f323(x94782,f768(x94782,x94781)))+~P101(f323(x94781,f768(x94782,x94781)))+E(f323(f243(a1),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),f2(a1)))),x94781)),f323(f243(a1),f323(f323(f18(a1,a855,a855),f323(f323(f8(a855,f867(a855,a855),a1),a321),f323(f237(a1),f2(a1)))),x94782)))
% 179.72/179.59 [7531]~P63(x75311)+~P90(x75311)+E(f323(f323(f281(x75311),x75312),f323(f103(x75311),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))),x75312)
% 179.72/179.59 [9177]~P90(x91771)+~E(f323(f103(x91771),x91772),f76(x91771))+P30(x91771,f323(f103(x91771),f323(f323(f78(a1),x91772),f323(f77(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.59 [9353]~P133(x93531)+~E(x93532,f76(x93531))+E(f323(f323(f248(x93531),x93532),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f76(x93531))
% 179.72/179.59 [9354]~P133(x93541)+~E(x93542,f2(x93541))+E(f323(f323(f248(x93541),x93542),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f2(x93541))
% 179.72/179.59 [9367]~P133(x93671)+~E(x93672,f323(f77(x93671),f76(x93671)))+E(f323(f323(f248(x93671),x93672),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f76(x93671))
% 179.72/179.59 [9410]~P90(x94101)+E(f323(f103(x94101),x94102),f76(x94101))+~P30(x94101,f323(f103(x94101),f323(f323(f78(a1),x94102),f323(f77(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.59 [9801]~P116(x98012)+E(x98011,f2(x98012))+P101(f323(f323(f238(x98012),f2(x98012)),f323(f323(f248(x98012),x98011),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))
% 179.72/179.59 [9864]~P116(x98642)+~E(x98641,f2(x98642))+~P101(f323(f323(f238(x98642),f2(x98642)),f323(f323(f248(x98642),x98641),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))
% 179.72/179.59 [9890]P101(f323(f323(f237(a1),x98901),f2(a1)))+P101(f323(f323(f238(a1),x98902),x98901))+E(f323(f41(x98901),f44(x98902,f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98901))),f44(x98902,x98901))
% 179.72/179.59 [9891]~P101(f323(f323(f238(a1),f2(a1)),x98911))+P101(f323(f323(f238(a1),x98912),x98911))+E(f323(f41(x98911),f44(x98912,f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98911))),f44(x98912,x98911))
% 179.72/179.59 [9892]P101(f323(f323(f237(a1),x98921),f2(a1)))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),x98922),x98921)))+E(f323(f41(x98921),f47(x98922,f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98921))),f47(x98922,x98921))
% 179.72/179.59 [9893]~P101(f323(f323(f238(a1),f2(a1)),x98931))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),x98932),x98931)))+E(f323(f41(x98931),f47(x98932,f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98931))),f47(x98932,x98931))
% 179.72/179.59 [9894]~P140(x98941)+~P101(f323(f323(f237(a1),f2(a1)),x98942))+E(f323(f100(x98941),f323(a104,f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x98942))),f323(f323(f78(x98941),f323(f100(x98941),f323(a104,x98942))),f323(f100(x98941),f323(a104,x98942))))
% 179.72/179.59 [5028]~P142(x50281,x50282,x50283)+~E(x50283,f2(a1))+P101(f323(x50281,x50282))
% 179.72/179.59 [5148]~P103(x51481)+~P16(x51481,x51483)+P16(x51481,f164(x51481,x51482,x51483))
% 179.72/179.59 [5149]~P103(x51491)+~P16(x51491,x51493)+P16(x51491,f171(x51491,x51492,x51493))
% 179.72/179.59 [4734]~P59(x47342)+~E(x47343,f323(f77(x47342),x47341))+E(x47341,f323(f77(x47342),x47343))
% 179.72/179.59 [4736]~P59(x47361)+~E(f323(f77(x47361),x47363),x47362)+E(f323(f77(x47361),x47362),x47363)
% 179.72/179.59 [4811]~P87(x48113)+E(x48111,x48112)+~E(f323(f77(x48113),x48111),f323(f77(x48113),x48112))
% 179.72/179.59 [4812]~P59(x48123)+E(x48121,x48122)+~E(f323(f77(x48123),x48121),f323(f77(x48123),x48122))
% 179.72/179.59 [4813]~P103(x48133)+E(x48131,x48132)+~E(f323(f244(x48133),x48131),f323(f244(x48133),x48132))
% 179.72/179.59 [4814]~P99(x48143)+E(x48141,x48142)+~E(f323(f100(x48143),x48141),f323(f100(x48143),x48142))
% 179.72/179.59 [4815]~P103(x48153)+E(x48151,x48152)+~E(f323(f295(x48153),x48151),f323(f295(x48153),x48152))
% 179.72/179.59 [4816]~P103(x48163)+E(x48161,x48162)+~E(f323(f245(x48163),x48161),f323(f245(x48163),x48162))
% 179.72/179.59 [4817]~P89(x48173)+E(x48171,x48172)+~E(f323(f102(x48173),x48171),f323(f102(x48173),x48172))
% 179.72/179.59 [4818]~P103(x48183)+E(x48181,x48182)+~E(f323(f292(x48183),x48181),f323(f292(x48183),x48182))
% 179.72/179.59 [4917]~P5(x49171)+~P101(f323(x49172,x49173))+P101(f323(f55(x49171),x49172))
% 179.72/179.59 [4950]~P5(x49503)+P101(f323(x49501,x49502))+~P101(f323(f56(x49503),x49501))
% 179.72/179.59 [5047]~P143(x50471,x50473,x50472)+~E(x50472,f2(a1))+P101(f323(x50471,f2(a1)))
% 179.72/179.59 [5085]~E(x50851,f2(a860))+E(f781(x50851,x50852,x50853),f188(f867(x50853,a855)))+~E(f323(f35(x50853),x50852),f323(a112,x50851))
% 179.72/179.59 [5229]~E(x52292,f2(a860))+E(f323(f257(a860,a860),x52291),f2(a860))+~P101(f323(f45(x52293,x52292),x52291))
% 179.72/179.59 [5274]P101(f323(x52741,x52742))+~E(x52743,f323(f100(a1),x52742))+~P101(f323(x52741,f323(a104,x52743)))
% 179.72/179.59 [5744]~E(x57443,f2(a860))+~P101(f323(x57441,x57442))+P101(f323(x57441,f42(a860,x57442,x57443)))
% 179.72/179.59 [5905]~P5(x59053)+~P12(x59053,x59051,x59052)+P101(f323(x59051,f539(x59052,x59051,x59053)))
% 179.72/179.59 [6139]~E(x61393,f2(a860))+P101(f323(x61391,x61392))+~P101(f323(x61391,f42(a860,x61392,x61393)))
% 179.72/179.59 [6286]~P5(x62861)+P13(x62861,x62862,x62863)+~P101(f323(x62862,f540(x62863,x62862,x62861)))
% 179.72/179.59 [6809]E(x68091,f2(a860))+~P101(f323(x68092,f490(x68091,x68093,x68092)))+P101(f323(x68092,f42(a860,x68093,x68091)))
% 179.72/179.59 [6914]~P6(x69141)+~P101(f323(f323(f237(x69141),x69142),f642(x69143,x69142,x69141)))+P101(f323(f323(f237(x69141),x69142),f38(x69141,x69143)))
% 179.72/179.59 [6916]~P101(f323(x69161,x69162))+~P101(f323(x69161,f490(x69163,x69162,x69161)))+P101(f323(x69161,f42(a860,x69162,x69163)))
% 179.72/179.59 [7018]E(x70181,f113(x70182))+E(f323(f323(f144(x70182),f623(x70183,x70181,x70182)),f627(x70183,x70181,x70182)),x70181)+~P101(f323(f323(f325(f861(x70182)),x70181),f154(x70182,x70183)))
% 179.72/179.59 [7049]~P134(x70491)+~P101(f323(f323(f325(x70491),x70492),f109(x70491)))+P101(f323(f323(f325(x70491),f323(f323(f248(x70491),x70492),x70493)),f109(x70491)))
% 179.72/179.59 [7366]P38(x73661,x73662)+~P101(f323(f323(f325(x73661),x73663),f730(x73662,x73661)))+P101(f323(f323(f325(x73661),f767(x73662,x73661,x73663)),f730(x73662,x73661)))
% 179.72/179.59 [7635]E(x76351,f113(x76352))+~P101(f323(f323(f325(f861(x76352)),x76351),f154(x76352,x76353)))+P101(f323(f323(f325(f861(x76352)),f627(x76353,x76351,x76352)),f154(x76352,x76353)))
% 179.72/179.59 [7688]E(x76881,f2(a860))+E(f323(f323(f78(a860),f323(f323(f79(a860),x76881),f491(x76881,x76882,x76883))),f490(x76881,x76882,x76883)),x76882)+P101(f323(x76883,f42(a860,x76882,x76881)))
% 179.72/179.59 [7731]~P101(f323(x77313,x77312))+E(f323(f323(f78(a860),f323(f323(f79(a860),x77311),f491(x77311,x77312,x77313))),f490(x77311,x77312,x77313)),x77312)+P101(f323(x77313,f42(a860,x77312,x77311)))
% 179.72/179.59 [7872]P101(f323(f323(f238(a1),x78721),f480(x78722,x78723,x78721)))+P101(f323(f323(x78723,f323(f323(f36(a1),x78722),x78721)),f42(a1,x78722,x78721)))+~P101(f323(f323(f238(a1),x78721),f2(a1)))
% 179.72/179.59 [8139]P101(f323(f323(x81392,f323(f323(f36(a1),x81391),x81393)),f42(a1,x81391,x81393)))+~P101(f323(f323(f238(a1),x81393),f2(a1)))+P101(f323(f323(f237(a1),f480(x81391,x81392,x81393)),f2(a1)))
% 179.72/179.59 [8326]E(f323(f323(f78(a1),f323(f323(f79(a1),x83261),f481(x83262,x83263,x83261))),f480(x83262,x83263,x83261)),x83262)+P101(f323(f323(x83263,f323(f323(f36(a1),x83262),x83261)),f42(a1,x83262,x83261)))+~P101(f323(f323(f238(a1),x83261),f2(a1)))
% 179.72/179.59 [8559]~P101(f323(f323(x85591,f481(x85592,x85591,x85593)),f480(x85592,x85591,x85593)))+P101(f323(f323(x85591,f323(f323(f36(a1),x85592),x85593)),f42(a1,x85592,x85593)))+~P101(f323(f323(f238(a1),x85593),f2(a1)))
% 179.72/179.59 [8806]~P103(x88061)+~P16(x88061,x88063)+P16(x88061,f142(x88061,x88061,f5(x88061),x88062,x88063))
% 179.72/179.59 [9303]~P120(x93032)+E(x93031,f2(x93032))+~P101(f323(f323(f237(x93032),f323(f323(f78(x93032),f323(f323(f79(x93032),x93033),x93033)),f323(f323(f79(x93032),x93031),x93031))),f2(x93032)))
% 179.72/179.59 [9304]~P120(x93042)+E(x93041,f2(x93042))+~P101(f323(f323(f237(x93042),f323(f323(f78(x93042),f323(f323(f79(x93042),x93041),x93041)),f323(f323(f79(x93042),x93043),x93043))),f2(x93042)))
% 179.72/179.59 [10079]~P116(x100791)+~P101(f323(f323(f238(x100791),x100792),f2(x100791)))+P101(f323(f323(f238(x100791),f323(f323(f248(x100791),x100792),f323(a112,f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x100793)))),f2(x100791)))
% 179.72/179.59 [10088]~P116(x100882)+E(x100881,f2(x100882))+~P101(f323(f323(f237(x100882),f323(f323(f78(x100882),f323(f323(f248(x100882),x100883),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x100882),x100881),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))),f2(x100882)))
% 179.72/179.59 [10089]~P116(x100892)+E(x100891,f2(x100892))+~P101(f323(f323(f237(x100892),f323(f323(f78(x100892),f323(f323(f248(x100892),x100891),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x100892),x100893),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))),f2(x100892)))
% 179.72/179.59 [4768]~E(x47682,x47683)+~P59(x47681)+E(f323(f323(f22(x47681),x47682),x47683),f2(x47681))
% 179.72/179.59 [4769]~E(x47692,x47693)+~P60(x47691)+E(f323(f323(f22(x47691),x47692),x47693),f2(x47691))
% 179.72/179.59 [4782]~P135(x47821)+~E(x47823,f2(x47821))+E(f323(f323(f78(x47821),x47822),x47823),x47822)
% 179.72/179.59 [4797]~P137(x47971)+~E(x47973,f2(x47971))+E(f323(f323(f79(x47971),x47972),x47973),f2(x47971))
% 179.72/179.59 [4798]~P137(x47981)+~E(x47982,f2(x47981))+E(f323(f323(f79(x47981),x47982),x47983),f2(x47981))
% 179.72/179.59 [4820]~E(x48203,f113(x48201))+~E(x48202,f113(x48201))+E(f323(f323(f121(x48201),x48202),x48203),f113(x48201))
% 179.72/179.59 [4907]~P135(x49072)+E(x49071,f2(x49072))+~E(f323(f323(f78(x49072),x49073),x49071),x49073)
% 179.72/179.59 [4908]~P59(x49081)+~E(x49082,f323(f77(x49081),x49083))+E(f323(f323(f78(x49081),x49082),x49083),f2(x49081))
% 179.72/179.59 [4915]E(x49151,f113(x49152))+E(x49153,f2(a860))+~E(f323(f323(f169(x49152),x49153),x49151),f113(x49152))
% 179.72/179.59 [4921]~P59(x49213)+E(x49211,x49212)+~E(f323(f323(f22(x49213),x49211),x49212),f2(x49213))
% 179.72/179.59 [4922]~P60(x49223)+E(x49221,x49222)+~E(f323(f323(f22(x49223),x49221),x49222),f2(x49223))
% 179.72/179.59 [4931]~P133(x49312)+E(x49311,f2(x49312))+~E(f323(f323(f248(x49312),x49311),x49313),f2(x49312))
% 179.72/179.59 [4932]~P3(x49322)+E(x49321,f188(x49322))+~E(f323(f323(f110(x49322),x49323),x49321),f188(x49322))
% 179.72/179.59 [4933]~P3(x49332)+E(x49331,f188(x49332))+~E(f323(f323(f110(x49332),x49331),x49333),f188(x49332))
% 179.72/179.59 [4934]~P95(x49342)+E(x49341,f246(x49342))+~E(f323(f323(f101(x49342),x49343),x49341),f246(x49342))
% 179.72/179.59 [4935]~P95(x49352)+E(x49351,f246(x49352))+~E(f323(f323(f101(x49352),x49351),x49353),f246(x49352))
% 179.72/179.59 [5001]~P59(x50012)+E(x50011,f323(f77(x50012),x50013))+~E(f323(f323(f78(x50012),x50011),x50013),f2(x50012))
% 179.72/179.59 [5002]~P59(x50021)+E(f323(f77(x50021),x50022),x50023)+~E(f323(f323(f78(x50021),x50022),x50023),f2(x50021))
% 179.72/179.59 [5004]~E(x50042,x50043)+~P102(x50041)+P101(f323(f323(f237(x50041),x50042),x50043))
% 179.72/179.59 [5006]~E(x50062,x50063)+~P105(x50061)+P101(f323(f323(f237(x50061),x50062),x50063))
% 179.72/179.59 [5007]~E(x50072,x50073)+~P92(x50071)+P101(f323(f323(f89(x50071),x50072),x50073))
% 179.72/179.59 [5101]~P108(x51011)+~E(x51012,f323(f77(x51011),x51013))+E(f323(f323(f79(x51011),x51012),x51012),f323(f323(f79(x51011),x51013),x51013))
% 179.72/179.59 [5109]~P103(x51091)+~P16(x51091,x51093)+P16(x51091,f323(f323(f169(x51091),x51092),x51093))
% 179.72/179.59 [5110]~P103(x51101)+~P16(x51101,x51103)+P16(x51101,f323(f323(f131(x51101),x51102),x51103))
% 179.72/179.59 [5146]E(x51461,x51462)+E(x51463,f2(a860))+~E(f323(f323(f79(a860),x51463),x51461),f323(f323(f79(a860),x51463),x51462))
% 179.72/179.59 [5147]E(x51471,x51472)+E(x51473,f2(a860))+~E(f323(f323(f79(a860),x51471),x51473),f323(f323(f79(a860),x51472),x51473))
% 179.72/179.59 [5220]~E(x52202,x52203)+~P105(x52201)+E(f294(x52201,x52202,x52203),f323(f323(f301(x52201),x52202),f188(f867(x52201,a855))))
% 179.72/179.59 [5261]E(x52611,x52612)+~P92(x52613)+~P101(f323(f323(f89(x52613),x52611),x52612))
% 179.72/179.59 [5272]~E(x52721,x52722)+~P103(x52723)+~P101(f323(f323(f238(x52723),x52721),x52722))
% 179.72/179.59 [5273]~E(x52731,x52732)+~P105(x52733)+~P101(f323(f323(f238(x52733),x52731),x52732))
% 179.72/179.59 [5283]~P105(x52831)+E(f323(f293(x52831,x52832),x52833),f188(f867(x52831,a855)))+P101(f323(f323(f238(x52831),x52832),x52833))
% 179.72/179.59 [5330]~P105(x53301)+E(f294(x53301,x53302,x53303),f188(f867(x53301,a855)))+P101(f323(f323(f237(x53301),x53302),x53303))
% 179.72/179.59 [5331]~P105(x53311)+E(f296(x53311,x53312,x53313),f188(f867(x53311,a855)))+P101(f323(f323(f238(x53311),x53312),x53313))
% 179.72/179.59 [5332]~P105(x53321)+E(f188(f867(x53321,a855)),f294(x53321,x53322,x53323))+P101(f323(f323(f237(x53321),x53322),x53323))
% 179.72/179.59 [5333]~P105(x53331)+E(f188(f867(x53331,a855)),f296(x53331,x53332,x53333))+P101(f323(f323(f238(x53331),x53332),x53333))
% 179.72/179.59 [5341]~P97(x53411)+~E(f323(f323(f110(x53411),x53412),x53413),x53413)+P101(f323(f323(f237(x53411),x53412),x53413))
% 179.72/179.59 [5342]~P98(x53421)+~E(f323(f323(f101(x53421),x53422),x53423),x53422)+P101(f323(f323(f237(x53421),x53422),x53423))
% 179.72/179.59 [5343]~P103(x53431)+~E(f323(f323(f235(x53431),x53432),x53433),x53432)+P101(f323(f323(f237(x53431),x53432),x53433))
% 179.72/179.59 [5344]~P103(x53441)+~E(f323(f323(f236(x53441),x53442),x53443),x53443)+P101(f323(f323(f237(x53441),x53442),x53443))
% 179.72/179.59 [5364]~P103(x53641)+P16(x53641,x53642)+~P16(x53641,f323(f323(f144(x53641),x53643),x53642))
% 179.72/179.59 [5365]~P103(x53651)+P16(x53651,x53652)+~P16(x53651,f323(f323(f121(x53651),x53653),x53652))
% 179.72/179.59 [5366]~P103(x53661)+P16(x53661,x53662)+~P16(x53661,f323(f323(f121(x53661),x53662),x53663))
% 179.72/179.59 [5431]~P103(x54311)+P101(f323(f323(f237(x54311),x54313),x54312))+P101(f323(f323(f237(x54311),x54312),x54313))
% 179.72/179.59 [5436]~P103(x54361)+P101(f323(f323(f238(x54361),x54363),x54362))+P101(f323(f323(f237(x54361),x54362),x54363))
% 179.72/179.59 [5474]~P97(x54741)+E(f323(f323(f110(x54741),x54742),x54743),x54742)+~P101(f323(f323(f237(x54741),x54743),x54742))
% 179.72/179.59 [5476]~P97(x54761)+E(f323(f323(f110(x54761),x54762),x54763),x54763)+~P101(f323(f323(f237(x54761),x54762),x54763))
% 179.72/179.59 [5477]~P98(x54771)+E(f323(f323(f101(x54771),x54772),x54773),x54773)+~P101(f323(f323(f237(x54771),x54773),x54772))
% 179.72/179.59 [5479]~P98(x54791)+E(f323(f323(f101(x54791),x54792),x54793),x54792)+~P101(f323(f323(f237(x54791),x54792),x54793))
% 179.72/179.59 [5480]~P103(x54801)+E(f323(f323(f235(x54801),x54802),x54803),x54803)+~P101(f323(f323(f237(x54801),x54803),x54802))
% 179.72/179.59 [5482]~P103(x54821)+E(f323(f323(f235(x54821),x54822),x54823),x54822)+~P101(f323(f323(f237(x54821),x54822),x54823))
% 179.72/179.59 [5483]~P103(x54831)+E(f323(f323(f236(x54831),x54832),x54833),x54832)+~P101(f323(f323(f237(x54831),x54833),x54832))
% 179.72/179.59 [5485]~P103(x54851)+E(f323(f323(f236(x54851),x54852),x54853),x54853)+~P101(f323(f323(f237(x54851),x54852),x54853))
% 179.72/179.59 [5492]~P114(x54922)+E(x54921,f2(x54922))+E(f323(f323(f281(x54922),f323(f77(x54922),x54923)),f323(f77(x54922),x54921)),f323(f323(f281(x54922),x54923),x54921))
% 179.72/179.59 [5538]~P105(x55381)+E(f323(f293(x55381,x55382),x55383),f188(f867(x55381,a855)))+~P101(f323(f323(f237(x55381),x55383),x55382))
% 179.72/179.59 [5570]~P105(x55701)+E(f294(x55701,x55702,x55703),f188(f867(x55701,a855)))+~P101(f323(f323(f238(x55701),x55703),x55702))
% 179.72/179.59 [5571]~P105(x55711)+E(f297(x55711,x55712,x55713),f188(f867(x55711,a855)))+~P101(f323(f323(f237(x55711),x55713),x55712))
% 179.72/179.59 [5572]~P105(x55721)+E(f296(x55721,x55722,x55723),f188(f867(x55721,a855)))+~P101(f323(f323(f237(x55721),x55723),x55722))
% 179.72/179.59 [5623]~E(f323(f323(f22(a860),x56231),x56233),x56232)+E(x56231,f323(f323(f78(a860),x56232),x56233))+~P101(f323(f323(f237(a860),x56233),x56231))
% 179.72/179.59 [5624]~E(x56241,f323(f323(f78(a860),x56243),x56242))+E(f323(f323(f22(a860),x56241),x56242),x56243)+~P101(f323(f323(f237(a860),x56242),x56241))
% 179.72/179.59 [5670]~P101(f323(x56701,x56703))+P101(f323(x56701,f365(x56701,x56702)))+~P101(f323(f323(f237(a860),x56703),x56702))
% 179.72/179.59 [5671]~P101(f323(x56711,x56713))+P101(f323(x56711,f383(x56711,x56712)))+~P101(f323(f323(f238(a860),x56713),x56712))
% 179.72/179.59 [5679]~P105(x56791)+~E(f323(f293(x56791,x56792),x56793),f188(f867(x56791,a855)))+~P101(f323(f323(f238(x56791),x56792),x56793))
% 179.72/179.59 [5684]~P102(x56841)+~P101(f323(f323(f238(x56841),x56842),x56843))+P101(f323(f323(f237(x56841),x56842),x56843))
% 179.72/179.59 [5686]~P105(x56861)+~P101(f323(f323(f238(x56861),x56862),x56863))+P101(f323(f323(f237(x56861),x56862),x56863))
% 179.72/179.59 [5792]~P105(x57921)+~E(f294(x57921,x57922,x57923),f188(f867(x57921,a855)))+~P101(f323(f323(f237(x57921),x57922),x57923))
% 179.72/179.59 [5793]~P105(x57931)+~E(f296(x57931,x57932,x57933),f188(f867(x57931,a855)))+~P101(f323(f323(f238(x57931),x57932),x57933))
% 179.72/179.59 [5794]~P105(x57941)+~E(f188(f867(x57941,a855)),f294(x57941,x57942,x57943))+~P101(f323(f323(f237(x57941),x57942),x57943))
% 179.72/179.59 [5795]~P105(x57951)+~E(f188(f867(x57951,a855)),f296(x57951,x57952,x57953))+~P101(f323(f323(f238(x57951),x57952),x57953))
% 179.72/179.59 [5803]P101(f323(x58031,x58032))+~P101(f323(x58031,f376(x58031,x58033)))+~P101(f323(f323(f237(a860),x58032),x58033))
% 179.72/179.59 [5804]P101(f323(x58041,x58042))+~P101(f323(x58041,f384(x58041,x58043)))+~P101(f323(f323(f238(a860),x58042),x58043))
% 179.72/179.59 [5812]~E(x58121,f323(a112,x58123))+P101(f323(f323(f238(a860),x58121),f323(a112,x58122)))+~P101(f323(f323(f238(a860),x58123),x58122))
% 179.72/179.59 [5828]E(x58281,x58282)+~E(f323(f323(f79(a860),x58283),x58281),f323(f323(f79(a860),x58283),x58282))+~P101(f323(f323(f238(a860),f2(a860)),x58283))
% 179.72/179.59 [5884]E(f323(x58841,f352(x58841,x58842,x58843)),f76(a860))+~E(f323(f323(f6(x58843,a860),x58841),x58842),f76(a860))+~P101(f323(f59(x58843),x58842))
% 179.72/179.59 [5896]~P6(x58961)+P101(f323(f323(f237(x58961),x58962),f37(x58961,x58963)))+~P101(f323(f323(f325(x58961),x58962),x58963))
% 179.72/179.59 [5922]~P102(x59221)+~P101(f323(f323(f238(x59221),x59223),x59222))+~P101(f323(f323(f237(x59221),x59222),x59223))
% 179.72/179.59 [5926]~P102(x59261)+~P101(f323(f323(f238(x59261),x59263),x59262))+~P101(f323(f323(f238(x59261),x59262),x59263))
% 179.72/179.59 [5929]~P103(x59291)+~P101(f323(f323(f238(x59291),x59293),x59292))+~P101(f323(f323(f237(x59291),x59292),x59293))
% 179.72/179.59 [5930]~P103(x59301)+~P101(f323(f323(f238(x59301),x59303),x59302))+~P101(f323(f323(f238(x59301),x59302),x59303))
% 179.72/179.59 [5931]~P105(x59311)+~P101(f323(f323(f238(x59311),x59313),x59312))+~P101(f323(f323(f238(x59311),x59312),x59313))
% 179.72/179.59 [5956]~E(f323(x59562,f353(x59562,x59563,x59561)),f2(a860))+E(f323(f323(f6(x59561,a860),x59562),x59563),f2(a860))+~P101(f323(f59(x59561),x59563))
% 179.72/179.59 [5957]~E(f323(x59572,f453(x59572,x59573,x59571)),f76(a860))+E(f323(f323(f9(x59571,a860),x59572),x59573),f76(a860))+~P101(f323(f59(x59571),x59573))
% 179.72/179.59 [5970]~P104(x59701)+~P101(f323(f323(f238(x59701),x59703),x59702))+P101(f323(f323(f325(x59701),x59702),f323(f295(x59701),x59703)))
% 179.72/179.59 [5971]~P104(x59711)+~P101(f323(f323(f237(x59711),x59713),x59712))+P101(f323(f323(f325(x59711),x59712),f323(f245(x59711),x59713)))
% 179.72/179.59 [5972]~P104(x59721)+~P101(f323(f323(f238(x59721),x59722),x59723))+P101(f323(f323(f325(x59721),x59722),f323(f244(x59721),x59723)))
% 179.72/179.59 [5973]~P104(x59731)+~P101(f323(f323(f237(x59731),x59732),x59733))+P101(f323(f323(f325(x59731),x59732),f323(f292(x59731),x59733)))
% 179.72/179.59 [5985]E(f323(x59851,f355(x59851,x59852,x59853)),f323(a112,f2(a860)))+~E(f323(f323(f6(x59853,a860),x59851),x59852),f323(a112,f2(a860)))+~P101(f323(f59(x59853),x59852))
% 179.72/179.59 [6068]~P6(x60681)+~P101(f323(f323(f325(x60681),x60683),x60682))+P101(f323(f323(f237(x60681),f38(x60681,x60682)),x60683))
% 179.72/179.59 [6085]~P101(f323(f323(f237(a860),x60851),x60853))+P101(f323(f323(f237(a860),x60851),x60852))+~P101(f323(f323(f237(a860),x60853),x60852))
% 179.72/179.59 [6086]~P101(f323(f323(f237(a1),x60861),x60863))+P101(f323(f323(f237(a1),x60861),x60862))+~P101(f323(f323(f237(a1),x60863),x60862))
% 179.72/179.59 [6103]~P104(x61031)+~P101(f323(f323(f325(x61031),x61033),f323(f245(x61031),x61032)))+P101(f323(f323(f237(x61031),x61032),x61033))
% 179.72/179.59 [6104]~P104(x61041)+~P101(f323(f323(f325(x61041),x61042),f323(f292(x61041),x61043)))+P101(f323(f323(f237(x61041),x61042),x61043))
% 179.72/179.59 [6105]~P104(x61051)+~P101(f323(f323(f325(x61051),x61053),f323(f295(x61051),x61052)))+P101(f323(f323(f238(x61051),x61052),x61053))
% 179.72/179.59 [6106]~P104(x61061)+~P101(f323(f323(f325(x61061),x61062),f323(f244(x61061),x61063)))+P101(f323(f323(f238(x61061),x61062),x61063))
% 179.72/179.59 [6320]~P64(x63201)+P101(f323(f323(f238(x63201),f2(x63201)),f467(x63203,x63202,x63201)))+P101(f323(f323(f237(x63201),x63202),x63203))
% 179.72/179.59 [6387]~P75(x63871)+~P101(f323(f323(f237(x63871),x63873),f323(f77(x63871),x63872)))+P101(f323(f323(f237(x63871),x63872),f323(f77(x63871),x63873)))
% 179.72/179.59 [6389]~P75(x63891)+~P101(f323(f323(f238(x63891),x63893),f323(f77(x63891),x63892)))+P101(f323(f323(f238(x63891),x63892),f323(f77(x63891),x63893)))
% 179.72/179.59 [6401]~P101(f323(f323(f238(a860),x64011),x64013))+~P101(f323(f323(f238(a860),x64013),x64012))+P101(f323(f323(f238(a860),f323(a112,x64011)),x64012))
% 179.72/179.59 [6426]~P119(x64261)+P101(f323(f323(f237(x64261),f323(f100(x64261),x64262)),f323(f100(x64261),x64263)))+~P101(f323(f323(f237(a860),x64262),x64263))
% 179.72/179.59 [6427]~P116(x64271)+P101(f323(f323(f237(x64271),f323(f102(x64271),x64272)),f323(f102(x64271),x64273)))+~P101(f323(f323(f237(a1),x64272),x64273))
% 179.72/179.59 [6429]~P116(x64291)+P101(f323(f323(f238(x64291),f323(f102(x64291),x64292)),f323(f102(x64291),x64293)))+~P101(f323(f323(f238(a1),x64292),x64293))
% 179.72/179.59 [6430]~P119(x64301)+P101(f323(f323(f238(x64301),f323(f100(x64301),x64302)),f323(f100(x64301),x64303)))+~P101(f323(f323(f238(a860),x64302),x64303))
% 179.72/179.59 [6436]~P103(x64361)+E(f323(f323(f110(f867(x64361,a855)),f323(f244(x64361),x64362)),f323(f293(x64361,x64362),x64363)),f323(f244(x64361),x64363))+~P101(f323(f323(f237(x64361),x64362),x64363))
% 179.72/179.59 [6466]~P75(x64661)+~P101(f323(f323(f237(x64661),x64663),x64662))+P101(f323(f323(f237(x64661),f323(f77(x64661),x64662)),f323(f77(x64661),x64663)))
% 179.72/179.59 [6468]~P87(x64681)+~P101(f323(f323(f237(x64681),x64683),x64682))+P101(f323(f323(f237(x64681),f323(f77(x64681),x64682)),f323(f77(x64681),x64683)))
% 179.72/179.59 [6469]~P75(x64691)+~P101(f323(f323(f238(x64691),x64693),x64692))+P101(f323(f323(f238(x64691),f323(f77(x64691),x64692)),f323(f77(x64691),x64693)))
% 179.72/179.59 [6502]~P103(x65021)+E(f323(f323(f110(f867(x65021,a855)),f323(f244(x65021),x65022)),f294(x65021,x65022,x65023)),f323(f292(x65021),x65023))+~P101(f323(f323(f237(x65021),x65022),x65023))
% 179.72/179.59 [6503]~P103(x65031)+E(f323(f323(f110(f867(x65031,a855)),f323(f292(x65031),x65032)),f297(x65031,x65032,x65033)),f323(f244(x65031),x65033))+~P101(f323(f323(f238(x65031),x65032),x65033))
% 179.72/179.59 [6504]~P103(x65041)+E(f323(f323(f110(f867(x65041,a855)),f323(f292(x65041),x65042)),f296(x65041,x65042,x65043)),f323(f292(x65041),x65043))+~P101(f323(f323(f237(x65041),x65042),x65043))
% 179.72/179.59 [6538]~P103(x65381)+E(f323(f323(f110(f867(x65381,a855)),f323(f293(x65381,x65382),x65383)),f323(f245(x65381),x65383)),f323(f245(x65381),x65382))+~P101(f323(f323(f237(x65381),x65382),x65383))
% 179.72/179.59 [6691]~P103(x66911)+E(f323(f323(f110(f867(x66911,a855)),f294(x66911,x66912,x66913)),f323(f295(x66911),x66913)),f323(f245(x66911),x66912))+~P101(f323(f323(f237(x66911),x66912),x66913))
% 179.72/179.59 [6692]~P103(x66921)+E(f323(f323(f110(f867(x66921,a855)),f297(x66921,x66922,x66923)),f323(f245(x66921),x66923)),f323(f295(x66921),x66922))+~P101(f323(f323(f238(x66921),x66922),x66923))
% 179.72/179.59 [6693]~P103(x66931)+E(f323(f323(f110(f867(x66931,a855)),f296(x66931,x66932,x66933)),f323(f295(x66931),x66933)),f323(f295(x66931),x66932))+~P101(f323(f323(f237(x66931),x66932),x66933))
% 179.72/179.59 [6711]P101(f323(x67111,x67112))+~P101(f323(f323(f237(a860),x67112),x67113))+P101(f323(f323(f325(a860),f376(x67111,x67113)),f294(a860,f2(a860),x67113)))
% 179.72/179.59 [6745]E(x67451,x67452)+~E(f323(f323(f158(x67453),x67451),f531(x67453,x67452,x67451)),f323(f323(f158(x67453),x67452),f531(x67453,x67452,x67451)))+~E(f323(f189(f861(x67453)),x67451),f323(f189(f861(x67453)),x67452))
% 179.72/179.59 [6750]~E(x67503,f323(f323(f36(a860),x67501),x67502))+~P101(f323(f323(f238(a860),f2(a860)),x67502))+P101(f323(f323(f238(a860),x67501),f323(f323(f79(a860),x67502),f323(a112,x67503))))
% 179.72/179.59 [6767]~P101(f323(x67671,x67673))+~P101(f323(f323(f237(a860),x67673),x67672))+P101(f323(f323(f325(a860),f365(x67671,x67672)),f294(a860,f2(a860),x67672)))
% 179.72/179.59 [6806]~P101(f323(x68061,x68063))+P101(f323(x68061,f379(x68061,x68062)))+~P101(f323(f323(f325(a860),x68063),f294(a860,f2(a860),x68062)))
% 179.72/179.59 [6825]~P119(x68253)+~P101(f323(f323(f237(x68253),f323(f100(x68253),x68251)),f323(f100(x68253),x68252)))+P101(f323(f323(f237(a860),x68251),x68252))
% 179.72/179.59 [6826]~P116(x68263)+~P101(f323(f323(f237(x68263),f323(f102(x68263),x68261)),f323(f102(x68263),x68262)))+P101(f323(f323(f237(a1),x68261),x68262))
% 179.72/179.59 [6828]~P119(x68283)+~P101(f323(f323(f238(x68283),f323(f100(x68283),x68281)),f323(f100(x68283),x68282)))+P101(f323(f323(f238(a860),x68281),x68282))
% 179.72/179.59 [6829]~P116(x68293)+~P101(f323(f323(f238(x68293),f323(f102(x68293),x68291)),f323(f102(x68293),x68292)))+P101(f323(f323(f238(a1),x68291),x68292))
% 179.72/179.59 [6845]~P119(x68451)+~P101(f323(f323(f238(x68451),f76(x68451)),x68452))+P101(f323(f323(f238(x68451),f76(x68451)),f323(f323(f248(x68451),x68452),f323(a112,x68453))))
% 179.72/179.59 [6847]~P75(x68471)+~P101(f323(f323(f237(x68471),f323(f77(x68471),x68473)),f323(f77(x68471),x68472)))+P101(f323(f323(f237(x68471),x68472),x68473))
% 179.72/179.59 [6848]~P87(x68481)+~P101(f323(f323(f237(x68481),f323(f77(x68481),x68483)),f323(f77(x68481),x68482)))+P101(f323(f323(f237(x68481),x68482),x68483))
% 179.72/179.59 [6849]~P75(x68491)+~P101(f323(f323(f238(x68491),f323(f77(x68491),x68493)),f323(f77(x68491),x68492)))+P101(f323(f323(f238(x68491),x68492),x68493))
% 179.72/179.59 [6873]P101(f323(x68731,x68732))+~P101(f323(x68731,f377(x68731,x68733)))+~P101(f323(f323(f325(a860),x68732),f294(a860,f2(a860),x68733)))
% 179.72/179.59 [6892]~P64(x68921)+P101(f323(f323(f238(x68921),f467(x68923,x68922,x68921)),f76(x68921)))+P101(f323(f323(f237(x68921),x68922),x68923))
% 179.72/179.59 [6911]~E(f42(a860,x69113,x69112),f42(a860,x69111,x69112))+E(f323(f323(f78(a860),x69111),f323(f323(f79(a860),x69112),f492(x69111,x69112,x69113))),x69113)+~P101(f323(f323(f237(a860),x69111),x69113))
% 179.72/179.59 [6930]E(f323(x69301,f454(x69301,x69302,x69303)),f200(x69302))+~P101(f323(f59(x69303),f177(x69303,x69302,x69301)))+P101(f323(f59(x69303),f246(f867(x69303,a855))))
% 179.72/179.59 [6969]E(f323(f323(f6(x69691,a860),x69692),x69693),f2(a860))+~P101(f323(f59(x69691),x69693))+P101(f323(f323(f325(x69691),f353(x69692,x69693,x69691)),x69693))
% 179.72/179.59 [6970]E(f323(f323(f9(x69701,a860),x69702),x69703),f76(a860))+~P101(f323(f59(x69701),x69703))+P101(f323(f323(f325(x69701),f453(x69702,x69703,x69701)),x69703))
% 179.72/179.59 [6992]~P103(x69921)+~P101(f323(f323(f237(x69921),x69922),x69923))+P101(f323(f323(f237(f867(x69921,a855)),f323(f244(x69921),x69922)),f323(f244(x69921),x69923)))
% 179.72/179.59 [6993]~P103(x69931)+~P101(f323(f323(f237(x69931),x69933),x69932))+P101(f323(f323(f237(f867(x69931,a855)),f323(f295(x69931),x69932)),f323(f295(x69931),x69933)))
% 179.72/179.59 [6994]~P105(x69941)+~P101(f323(f323(f237(x69941),x69943),x69942))+P101(f323(f323(f237(f867(x69941,a855)),f323(f245(x69941),x69942)),f323(f245(x69941),x69943)))
% 179.72/179.59 [6995]~P105(x69951)+~P101(f323(f323(f237(x69951),x69952),x69953))+P101(f323(f323(f237(f867(x69951,a855)),f323(f292(x69951),x69952)),f323(f292(x69951),x69953)))
% 179.72/179.59 [6996]~P103(x69961)+~P101(f323(f323(f238(x69961),x69962),x69963))+P101(f323(f323(f238(f867(x69961,a855)),f323(f244(x69961),x69962)),f323(f244(x69961),x69963)))
% 179.72/179.59 [7004]~P6(x70041)+P101(f323(f323(f237(x70041),x70042),f38(x70041,x70043)))+P101(f323(f323(f325(x70041),f642(x70043,x70042,x70041)),x70043))
% 179.72/179.59 [7010]~P75(x70101)+P101(f323(f323(f237(x70101),f323(f323(f22(x70101),x70102),x70103)),f2(x70101)))+~P101(f323(f323(f237(x70101),x70102),x70103))
% 179.72/179.59 [7011]~P75(x70111)+P101(f323(f323(f238(x70111),f323(f323(f22(x70111),x70112),x70113)),f2(x70111)))+~P101(f323(f323(f238(x70111),x70112),x70113))
% 179.72/179.59 [7053]P101(f323(x70531,x70532))+P101(f323(f323(f237(a860),f377(x70531,x70533)),x70533))+~P101(f323(f323(f325(a860),x70532),f294(a860,f2(a860),x70533)))
% 179.72/179.59 [7093]~E(f323(f323(f6(x70931,a860),x70932),x70933),f76(a860))+~P101(f323(f59(x70931),x70933))+P101(f323(f323(f325(x70931),f352(x70932,x70933,x70931)),x70933))
% 179.72/179.59 [7094]~P101(f323(x70941,x70943))+P101(f323(f323(f237(a860),f379(x70941,x70942)),x70942))+~P101(f323(f323(f325(a860),x70943),f294(a860,f2(a860),x70942)))
% 179.72/179.59 [7134]~P6(x71341)+P101(f323(f323(f325(x71341),f548(x71343,x71342,x71341)),x71342))+P101(f323(f323(f237(x71341),f37(x71341,x71342)),x71343))
% 179.72/179.59 [7165]~E(f323(f323(f6(x71651,a860),x71652),x71653),f323(a112,f2(a860)))+~P101(f323(f59(x71651),x71653))+P101(f323(f323(f325(x71651),f355(x71652,x71653,x71651)),x71653))
% 179.72/179.59 [7176]E(x71761,f2(a860))+P101(f323(x71762,f42(a860,x71763,x71761)))+P101(f323(f323(f238(a860),f490(x71761,x71763,x71762)),x71761))
% 179.72/179.59 [7281]~P101(f323(x72811,x72812))+P101(f323(x72811,f42(a860,x72812,x72813)))+P101(f323(f323(f238(a860),f490(x72813,x72812,x72811)),x72813))
% 179.72/179.59 [7400]E(x74001,f113(x74002))+~P101(f323(f323(f325(f861(x74002)),x74001),f154(x74002,x74003)))+P101(f323(f323(f325(x74002),f623(x74003,x74001,x74002)),x74003))
% 179.72/179.59 [7422]~P103(x74221)+E(f323(f323(f110(f867(x74221,a855)),f323(f323(f301(x74221),x74222),f188(f867(x74221,a855)))),f297(x74221,x74222,x74223)),f323(f293(x74221,x74222),x74223))+~P101(f323(f323(f238(x74221),x74222),x74223))
% 179.72/179.59 [7447]~P103(x74471)+E(f323(f323(f110(f867(x74471,a855)),f323(f323(f301(x74471),x74472),f188(f867(x74471,a855)))),f296(x74471,x74472,x74473)),f294(x74471,x74472,x74473))+~P101(f323(f323(f237(x74471),x74472),x74473))
% 179.72/179.59 [7553]~P103(x75531)+P101(f323(f323(f237(x75531),x75532),x75533))+~P101(f323(f323(f237(f867(x75531,a855)),f323(f295(x75531),x75533)),f323(f295(x75531),x75532)))
% 179.72/179.59 [7554]~P105(x75541)+P101(f323(f323(f237(x75541),x75542),x75543))+~P101(f323(f323(f237(f867(x75541,a855)),f323(f245(x75541),x75543)),f323(f245(x75541),x75542)))
% 179.72/179.59 [7555]~P103(x75551)+P101(f323(f323(f237(x75551),x75552),x75553))+~P101(f323(f323(f237(f867(x75551,a855)),f323(f244(x75551),x75552)),f323(f244(x75551),x75553)))
% 179.72/179.59 [7556]~P105(x75561)+P101(f323(f323(f237(x75561),x75562),x75563))+~P101(f323(f323(f237(f867(x75561,a855)),f323(f292(x75561),x75562)),f323(f292(x75561),x75563)))
% 179.72/179.59 [7557]~P103(x75571)+P101(f323(f323(f238(x75571),x75572),x75573))+~P101(f323(f323(f238(f867(x75571,a855)),f323(f244(x75571),x75572)),f323(f244(x75571),x75573)))
% 179.72/179.59 [7580]~P75(x75801)+~P101(f323(f323(f237(x75801),f323(f323(f22(x75801),x75802),x75803)),f2(x75801)))+P101(f323(f323(f237(x75801),x75802),x75803))
% 179.72/179.59 [7581]~P75(x75811)+~P101(f323(f323(f238(x75811),f323(f323(f22(x75811),x75812),x75813)),f2(x75811)))+P101(f323(f323(f238(x75811),x75812),x75813))
% 179.72/179.59 [7738]E(x77381,f2(a860))+~E(f323(f135(a860,a860,f78(a860),x77382),x77383),f2(a860))+~P101(f323(f323(f325(a860),x77381),f323(f166(a860),x77383)))
% 179.72/179.59 [7742]~P6(x77421)+~P101(f323(f323(f237(x77421),f548(x77423,x77422,x77421)),x77423))+P101(f323(f323(f237(x77421),f37(x77421,x77422)),x77423))
% 179.72/179.59 [7899]P101(f323(f323(f237(a1),f2(a1)),f483(x78991,x78992,x78993)))+P101(f323(f323(x78992,f323(f323(f36(a1),x78991),x78993)),f42(a1,x78991,x78993)))+~P101(f323(f323(f238(a1),f2(a1)),x78993))
% 179.72/179.59 [7986]E(x79861,x79862)+~E(f323(f189(f861(x79863)),x79861),f323(f189(f861(x79863)),x79862))+~P101(f323(f323(f262(x79863,x79863,a855),a320),f582(x79863,x79861,x79862)))
% 179.72/179.59 [8052]~P38(x80522,x80523)+E(x80521,f188(f867(x80522,a855)))+~P101(f323(f323(f237(f867(x80522,a855)),x80521),f323(f277(x80522,x80522,x80523),x80521)))
% 179.72/179.59 [8120]P40(x81201,x81202,x81203)+P101(f323(f323(f325(x81201),f587(x81203,x81202,x81201)),x81202))+P101(f323(f323(f325(f866(x81201,x81201)),f588(x81203,x81202,x81201)),x81203))
% 179.72/179.59 [8142]P101(f323(f323(x81422,f323(f323(f36(a1),x81421),x81423)),f42(a1,x81421,x81423)))+~P101(f323(f323(f238(a1),f2(a1)),x81423))+P101(f323(f323(f238(a1),f483(x81421,x81422,x81423)),x81423))
% 179.72/179.59 [8166]E(f323(f302(a860,a860,f323(f323(f7(a860,a860,a860),f22(a860)),x81661)),f323(f293(a860,x81662),x81663)),f188(f867(a860,a855)))+P101(f323(f323(f238(a860),x81661),x81663))+P101(f323(f323(f238(a860),x81662),x81663))
% 179.72/179.59 [8276]E(f323(f302(a860,a860,f323(f323(f7(a860,a860,a860),f22(a860)),x82761)),f323(f293(a860,x82762),x82763)),f323(f323(f301(a860),f2(a860)),f188(f867(a860,a855))))+P101(f323(f323(f238(a860),x82761),x82763))+~P101(f323(f323(f238(a860),x82762),x82763))
% 179.72/179.59 [8293]~P103(x82931)+E(f142(x82931,x82931,f5(x82931),x82932,x82933),x82933)+~P101(f323(f323(f325(x82931),x82932),f323(f166(x82931),x82933)))
% 179.72/179.59 [8307]P27(x83071,x83071,x83072,x83073)+~P101(f323(f59(x83071),x83073))+~P101(f323(f323(f237(f867(x83071,a855)),x83073),f323(f302(x83071,x83071,x83072),x83073)))
% 179.72/179.59 [8333]E(f323(f323(f78(a1),f323(f323(f79(a1),x83331),f484(x83332,x83333,x83331))),f483(x83332,x83333,x83331)),x83332)+P101(f323(f323(x83333,f323(f323(f36(a1),x83332),x83331)),f42(a1,x83332,x83331)))+~P101(f323(f323(f238(a1),f2(a1)),x83331))
% 179.72/179.59 [8567]~P101(f323(f323(x85671,f484(x85672,x85671,x85673)),f483(x85672,x85671,x85673)))+P101(f323(f323(x85671,f323(f323(f36(a1),x85672),x85673)),f42(a1,x85672,x85673)))+~P101(f323(f323(f238(a1),f2(a1)),x85673))
% 179.72/179.59 [9442]~P101(f323(f59(x94421),x94422))+~P101(f323(f323(f325(x94421),x94423),x94422))+P101(f323(f323(f238(a860),f323(f35(x94421),f323(f323(f22(f867(x94421,a855)),x94422),f323(f323(f301(x94421),x94423),f188(f867(x94421,a855)))))),f323(f35(x94421),x94422)))
% 179.72/179.59 [10039]P40(x100391,x100392,x100393)+~P101(f323(f323(f262(x100391,x100391,a855),f323(f323(f7(x100391,f867(x100391,a855),f867(x100391,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x100391,a855),f867(x100391,a855)),x100391),f8(a855,a855,x100391)),f323(f323(f8(a855,f867(a855,a855),x100391),a321),f323(f323(f7(x100391,f867(x100391,a855),a855),f325(x100391)),x100392)))),f323(f323(f7(x100391,f867(x100391,a855),a855),f325(x100391)),x100392))),f588(x100393,x100392,x100391)))+P101(f323(f323(f325(x100391),f587(x100393,x100392,x100391)),x100392))
% 179.72/179.59 [5453]~P114(x54532)+E(x54531,f2(x54532))+E(f323(f323(f281(x54532),x54533),f323(f77(x54532),x54531)),f323(f77(x54532),f323(f323(f281(x54532),x54533),x54531)))
% 179.72/179.59 [5586]~E(x55863,f188(f867(x55861,a855)))+~E(x55862,f188(f867(x55861,a855)))+E(f323(f323(f110(f867(x55861,a855)),x55862),x55863),f188(f867(x55861,a855)))
% 179.72/179.59 [5644]~E(x56443,f2(a860))+~P101(f323(x56441,f2(a860)))+P101(f323(x56441,f323(f323(f36(a860),x56442),x56443)))
% 179.72/179.59 [5784]~P65(x57842)+E(x57841,f2(x57842))+E(f323(f323(f281(x57842),f323(f73(x57842),x57843)),f323(f73(x57842),x57841)),f323(f73(x57842),f323(f323(f281(x57842),x57843),x57841)))
% 179.72/179.59 [5946]~P101(f323(f59(x59461),x59463))+E(f323(f35(x59461),f323(f323(f301(x59461),x59462),x59463)),f323(a112,f323(f35(x59461),x59463)))+P101(f323(f323(f325(x59461),x59462),x59463))
% 179.72/179.59 [6017]~E(x60172,f2(a860))+P101(f323(x60171,f2(a860)))+~P101(f323(x60171,f323(f323(f36(a860),x60173),x60172)))
% 179.72/179.59 [6036]~P101(f323(f59(x60361),x60363))+E(f323(f35(x60361),f323(f323(f301(x60361),x60362),x60363)),f323(f35(x60361),x60363))+~P101(f323(f323(f325(x60361),x60362),x60363))
% 179.72/179.59 [6070]~P101(f323(f59(x60701),x60703))+E(f323(f35(x60701),f323(f323(f301(x60701),x60702),x60703)),f323(f323(f78(a860),f76(a860)),f323(f35(x60701),x60703)))+P101(f323(f323(f325(x60701),x60702),x60703))
% 179.72/179.59 [6184]E(f323(f323(f78(a860),x61841),f847(x61841,x61842,x61843)),x61842)+~P101(f323(x61843,f2(a860)))+P101(f323(x61843,f323(f323(f22(a860),x61842),x61841)))
% 179.72/179.59 [6185]E(f323(f323(f78(a860),x61851),f848(x61851,x61852,x61853)),x61852)+~P101(f323(x61853,f2(a860)))+P101(f323(x61853,f323(f323(f22(a860),x61852),x61851)))
% 179.72/179.59 [6231]~P6(x62311)+~P101(f323(f59(x62311),x62313))+E(f323(f323(f62(x62311,x62311,f110(x62311)),x62312),x62313),f323(f323(f110(x62311),x62312),f37(x62311,x62313)))
% 179.72/179.59 [6232]~P6(x62321)+~P101(f323(f59(x62321),x62323))+E(f323(f323(f62(x62321,x62321,f101(x62321)),x62322),x62323),f323(f323(f101(x62321),x62322),f38(x62321,x62323)))
% 179.72/179.59 [6238]~P90(x62381)+~E(f323(f103(x62381),x62382),f323(f103(x62381),x62383))+P30(x62381,f323(f103(x62381),f323(f323(f78(a1),x62382),f323(f77(a1),x62383))))
% 179.72/179.59 [6245]~P134(x62451)+E(f323(f323(f22(x62451),f323(f100(x62451),x62452)),f323(f100(x62451),x62453)),f323(f100(x62451),f323(f323(f22(a860),x62452),x62453)))+~P101(f323(f323(f237(a860),x62453),x62452))
% 179.72/179.59 [6330]E(f323(f323(f78(a860),x63301),f847(x63301,x63302,x63303)),x63302)+P101(f323(f323(f238(a860),x63302),x63301))+P101(f323(x63303,f323(f323(f22(a860),x63302),x63301)))
% 179.72/179.59 [6331]E(f323(f323(f78(a860),x63311),f848(x63311,x63312,x63313)),x63312)+P101(f323(f323(f238(a860),x63312),x63311))+P101(f323(x63313,f323(f323(f22(a860),x63312),x63311)))
% 179.72/179.59 [6346]~P116(x63461)+E(f323(f323(f79(x63461),f323(f73(x63461),x63462)),x63463),f323(f73(x63461),f323(f323(f79(x63461),x63462),x63463)))+~P101(f323(f323(f237(x63461),f2(x63461)),x63463))
% 179.72/179.59 [6347]~P64(x63471)+E(f323(f323(f281(x63471),f323(f73(x63471),x63472)),x63473),f323(f73(x63471),f323(f323(f281(x63471),x63472),x63473)))+~P101(f323(f323(f238(x63471),f2(x63471)),x63473))
% 179.72/179.59 [6355]~P2(x63551)+~P101(f323(f59(x63551),x63553))+E(f323(f323(f62(x63551,x63551,f101(x63551)),x63552),x63553),f11(x63551,f323(f323(f301(x63551),x63552),x63553)))
% 179.72/179.59 [6356]~P2(x63561)+~P101(f323(f59(x63561),x63563))+E(f323(f323(f62(x63561,x63561,f110(x63561)),x63562),x63563),f10(x63561,f323(f323(f301(x63561),x63562),x63563)))
% 179.72/179.59 [6357]~P103(x63571)+~P101(f323(f59(x63571),x63573))+E(f323(f323(f62(x63571,x63571,f236(x63571)),x63572),x63573),f14(x63571,f323(f323(f301(x63571),x63572),x63573)))
% 179.72/179.59 [6358]~P103(x63581)+~P101(f323(f59(x63581),x63583))+E(f323(f323(f62(x63581,x63581,f235(x63581)),x63582),x63583),f15(x63581,f323(f323(f301(x63581),x63582),x63583)))
% 179.72/179.59 [6403]E(x64031,f113(x64032))+~E(f173(x64032,x64033),f113(f861(x64032)))+~P101(f323(f323(f325(f861(x64032)),x64031),f323(f166(f861(x64032)),x64033)))
% 179.72/179.59 [6444]~P101(f323(f130(x64441),x64443))+P101(f323(f323(f325(x64441),x64442),f323(f166(x64441),x64443)))+P101(f323(f130(x64441),f323(f323(f144(x64441),x64442),x64443)))
% 179.72/179.59 [6455]~P93(x64551)+~P101(f323(f59(x64551),x64553))+E(f323(f61(x64551,f79(x64551)),f323(f323(f301(x64551),x64552),x64553)),f323(f323(f62(x64551,x64551,f79(x64551)),x64552),x64553))
% 179.72/179.59 [6477]~P103(x64771)+~P101(f323(f59(x64771),x64773))+E(f12(x64771,f235(x64771),f323(f323(f301(x64771),x64772),x64773)),f323(f323(f62(x64771,x64771,f235(x64771)),x64772),x64773))
% 179.72/179.59 [6478]~P103(x64781)+~P101(f323(f59(x64781),x64783))+E(f13(x64781,f236(x64781),f323(f323(f301(x64781),x64782),x64783)),f323(f323(f62(x64781,x64781,f236(x64781)),x64782),x64783))
% 179.72/179.59 [6480]P101(f323(x64801,f2(a860)))+~P101(f323(f323(f238(a860),x64802),x64803))+~P101(f323(x64801,f323(f323(f22(a860),x64802),x64803)))
% 179.72/179.59 [6500]~P82(x65001)+P101(f323(f323(f237(x65001),x65002),x65003))+~P101(f323(f323(f237(x65001),f323(f73(x65001),x65002)),x65003))
% 179.72/179.59 [6501]~P116(x65011)+P101(f323(f323(f238(x65011),x65012),x65013))+~P101(f323(f323(f238(x65011),f323(f73(x65011),x65012)),x65013))
% 179.72/179.59 [6518]E(x65181,f113(x65182))+E(f323(f134(x65182),f323(f323(f131(x65182),x65183),x65181)),f323(f323(f158(x65182),x65181),x65183))+~P101(f323(f323(f238(a860),x65183),f323(f189(f861(x65182)),x65181)))
% 179.72/179.59 [6569]~P101(f323(x65691,x65693))+P101(f323(x65691,f385(x65691,x65692)))+~P101(f323(f323(f325(a860),x65693),f323(f293(a860,f2(a860)),x65692)))
% 179.72/179.59 [6590]P101(f323(x65901,x65902))+~P101(f323(f323(f238(a860),x65902),x65903))+P101(f323(f323(f325(a860),f384(x65901,x65903)),f323(f293(a860,f2(a860)),x65903)))
% 179.72/179.59 [6605]~P119(x66051)+~P101(f323(f323(f237(x66051),f76(x66051)),x66052))+P101(f323(f323(f237(x66051),f76(x66051)),f323(f323(f248(x66051),x66052),x66053)))
% 179.72/179.59 [6607]~P119(x66071)+~P101(f323(f323(f237(x66071),f2(x66071)),x66072))+P101(f323(f323(f237(x66071),f2(x66071)),f323(f323(f248(x66071),x66072),x66073)))
% 179.72/179.59 [6609]~P119(x66091)+~P101(f323(f323(f238(x66091),f2(x66091)),x66092))+P101(f323(f323(f238(x66091),f2(x66091)),f323(f323(f248(x66091),x66092),x66093)))
% 179.72/179.59 [6633]~P101(f323(x66331,x66333))+~P101(f323(f323(f238(a860),x66333),x66332))+P101(f323(f323(f325(a860),f383(x66331,x66332)),f323(f293(a860,f2(a860)),x66332)))
% 179.72/179.59 [6640]P101(f323(f59(x66401),x66402))+~P101(f323(f59(x66401),x66403))+~P101(f323(f323(f237(f867(x66401,a855)),x66402),x66403))
% 179.72/179.59 [6648]P101(f323(x66481,x66482))+~P101(f323(x66481,f386(x66481,x66483)))+~P101(f323(f323(f325(a860),x66482),f323(f293(a860,f2(a860)),x66483)))
% 179.72/179.59 [6659]E(x66591,f2(a860))+P101(f323(x66592,f468(x66591,x66593,x66592)))+~P101(f323(x66592,f323(f323(f36(a860),x66593),x66591)))
% 179.72/179.59 [6667]~P120(x66672)+E(x66671,f2(x66672))+~E(f323(f323(f78(x66672),f323(f323(f79(x66672),x66673),x66673)),f323(f323(f79(x66672),x66671),x66671)),f2(x66672))
% 179.72/179.59 [6668]~P120(x66682)+E(x66681,f2(x66682))+~E(f323(f323(f78(x66682),f323(f323(f79(x66682),x66681),x66681)),f323(f323(f79(x66682),x66683),x66683)),f2(x66682))
% 179.72/179.59 [6712]E(x67121,f2(a860))+~P101(f323(x67122,f469(x67121,x67123,x67122)))+P101(f323(x67122,f323(f323(f36(a860),x67123),x67121)))
% 179.72/179.59 [6717]~P103(x67171)+~P16(x67171,x67173)+P16(x67171,f323(f323(f141(x67171,x67171,f5(x67171)),x67172),x67173))
% 179.72/179.59 [6760]P101(f323(x67601,f468(x67602,x67603,x67601)))+P101(f323(x67601,f2(a860)))+~P101(f323(x67601,f323(f323(f36(a860),x67603),x67602)))
% 179.72/179.59 [6766]~P90(x67661)+E(f323(f103(x67661),x67662),f323(f103(x67661),x67663))+~P30(x67661,f323(f103(x67661),f323(f323(f78(a1),x67662),f323(f77(a1),x67663))))
% 179.72/179.59 [6832]E(x68321,f2(a1))+E(x68322,f2(a1))+~P101(f323(f46(x68322,x68322),f323(f323(f258(a1,a1),x68323),x68321)))
% 179.72/179.59 [6833]E(x68331,f76(a1))+E(x68332,f2(a1))+~P101(f323(f46(x68332,x68332),f323(f323(f258(a1,a1),x68331),x68333)))
% 179.72/179.59 [6846]P101(f323(x68461,x68462))+P101(f323(f323(f238(a860),f386(x68461,x68463)),x68463))+~P101(f323(f323(f325(a860),x68462),f323(f293(a860,f2(a860)),x68463)))
% 179.72/179.59 [6868]~P101(f323(x68681,f847(x68683,x68682,x68681)))+~P101(f323(x68681,f2(a860)))+P101(f323(x68681,f323(f323(f22(a860),x68682),x68683)))
% 179.72/179.59 [6869]~P101(f323(x68691,f848(x68693,x68692,x68691)))+~P101(f323(x68691,f2(a860)))+P101(f323(x68691,f323(f323(f22(a860),x68692),x68693)))
% 179.72/179.59 [6870]~P101(f323(x68701,f469(x68703,x68702,x68701)))+~P101(f323(x68701,f2(a860)))+P101(f323(x68701,f323(f323(f36(a860),x68702),x68703)))
% 179.72/179.59 [6888]~P101(f323(x68881,x68883))+P101(f323(f323(f238(a860),f385(x68881,x68882)),x68882))+~P101(f323(f323(f325(a860),x68883),f323(f293(a860,f2(a860)),x68882)))
% 179.72/179.59 [6889]E(f323(f323(f22(a860),f323(f323(f22(a860),x68891),x68892)),f323(f323(f22(a860),x68893),x68892)),f323(f323(f22(a860),x68891),x68893))+~P101(f323(f323(f237(a860),x68892),x68891))+~P101(f323(f323(f237(a860),x68892),x68893))
% 179.72/179.59 [6924]~P75(x69241)+~P101(f323(f323(f237(x69241),f323(f77(x69241),x69243)),x69242))+P101(f323(f323(f237(x69241),f323(f77(x69241),x69242)),x69243))
% 179.72/179.59 [6926]~P82(x69261)+~P101(f323(f323(f237(x69261),f323(f73(x69261),x69262)),x69263))+P101(f323(f323(f237(x69261),f323(f77(x69261),x69262)),x69263))
% 179.72/179.59 [6928]~P75(x69281)+~P101(f323(f323(f238(x69281),f323(f77(x69281),x69283)),x69282))+P101(f323(f323(f238(x69281),f323(f77(x69281),x69282)),x69283))
% 179.72/179.59 [6929]~P116(x69291)+~P101(f323(f323(f238(x69291),f323(f73(x69291),x69292)),x69293))+P101(f323(f323(f238(x69291),f323(f77(x69291),x69292)),x69293))
% 179.72/179.59 [6963]~P101(f323(x69633,f847(x69632,x69631,x69633)))+P101(f323(f323(f238(a860),x69631),x69632))+P101(f323(x69633,f323(f323(f22(a860),x69631),x69632)))
% 179.72/179.59 [6964]~P101(f323(x69643,f848(x69642,x69641,x69643)))+P101(f323(f323(f238(a860),x69641),x69642))+P101(f323(x69643,f323(f323(f22(a860),x69641),x69642)))
% 179.72/179.59 [7014]~E(f551(x70143,x70142,x70141),f550(x70143,x70142,x70141))+E(f323(f323(f101(f867(x70141,a855)),x70142),f37(f867(x70141,a855),x70143)),f188(f867(x70141,a855)))+P101(f323(f323(f325(f867(x70141,a855)),x70142),x70143))
% 179.72/179.59 [7023]~P101(f323(f59(x70231),x70233))+P101(f323(f59(x70231),f38(f867(x70231,a855),x70232)))+~P101(f323(f323(f325(f867(x70231,a855)),x70233),x70232))
% 179.72/179.59 [7082]~P103(x70821)+E(f323(f323(f110(f867(x70821,a855)),f323(f293(x70821,x70822),x70823)),f323(f323(f301(x70821),x70823),f188(f867(x70821,a855)))),f294(x70821,x70822,x70823))+~P101(f323(f323(f237(x70821),x70822),x70823))
% 179.72/179.59 [7083]E(x70831,f2(a860))+P101(f323(f323(f238(a860),f479(x70831,x70833,x70832)),x70831))+P101(f323(x70832,f323(f323(f36(a860),x70833),x70831)))
% 179.72/179.59 [7118]E(x71181,x71182)+~P101(f323(f323(f237(f867(x71183,a855)),x71181),x71182))+P101(f323(f323(f238(f867(x71183,a855)),x71181),x71182))
% 179.72/179.59 [7131]E(x71311,x71312)+~E(f323(f189(f861(x71313)),x71311),f323(f189(f861(x71313)),x71312))+P101(f323(f323(f238(a860),f531(x71313,x71311,x71312)),f323(f189(f861(x71313)),x71312)))
% 179.72/179.59 [7177]P9(x71771,x71772,x71773)+~E(f323(f256(x71771,x71771),x71773),x71772)+~E(f323(f323(f280(x71771,x71771,x71771),f323(f278(x71771,x71771),x71773)),x71773),x71773)
% 179.72/179.59 [7249]~P101(f323(x72491,f2(a860)))+P101(f323(f323(f238(a860),f479(x72493,x72492,x72491)),x72493))+P101(f323(x72491,f323(f323(f36(a860),x72492),x72493)))
% 179.72/179.59 [7258]~P103(x72581)+E(f323(f323(f110(f867(x72581,a855)),f297(x72581,x72582,x72583)),f323(f323(f301(x72581),x72583),f188(f867(x72581,a855)))),f296(x72581,x72582,x72583))+~P101(f323(f323(f238(x72581),x72582),x72583))
% 179.72/179.59 [7355]~P101(f323(f59(x73551),x73553))+P101(f323(f323(f237(a860),f323(f35(x73551),x73552)),f323(f35(x73551),x73553)))+~P101(f323(f323(f237(f867(x73551,a855)),x73552),x73553))
% 179.72/179.59 [7356]~P101(f323(f59(x73561),x73563))+P101(f323(f323(f238(a860),f323(f35(x73561),x73562)),f323(f35(x73561),x73563)))+~P101(f323(f323(f238(f867(x73561,a855)),x73562),x73563))
% 179.72/179.59 [7491]E(x74911,x74912)+~P101(f323(f323(f237(f867(x74913,a855)),x74912),x74911))+~P101(f323(f323(f237(f867(x74913,a855)),x74911),x74912))
% 179.72/179.59 [7494]~P103(x74941)+P16(x74941,x74942)+~P16(x74941,f323(f323(f141(x74941,x74941,f5(x74941)),x74943),x74942))
% 179.72/179.59 [7562]~P101(f323(f323(f238(a860),x75623),x75622))+~P101(f323(f323(f238(a860),x75623),x75621))+P101(f323(f323(f238(a860),f323(f323(f22(a860),x75621),x75622)),f323(f323(f22(a860),x75621),x75623)))
% 179.72/179.59 [7563]~P101(f323(f323(f237(a860),x75632),x75631))+~P101(f323(f323(f238(a860),x75631),x75633))+P101(f323(f323(f238(a860),f323(f323(f22(a860),x75631),x75632)),f323(f323(f22(a860),x75633),x75632)))
% 179.72/179.59 [7578]~P101(f323(f323(f238(a1),x75782),f2(a1)))+~P101(f323(f323(f237(a1),x75783),x75781))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x75781),x75782)),f323(f323(f36(a1),x75783),x75782)))
% 179.72/179.59 [7596]~P101(f323(f323(f238(a860),f2(a860)),x75963))+~P101(f323(f323(f237(a860),x75963),x75962))+P101(f323(f323(f237(a860),f323(f323(f36(a860),x75961),x75962)),f323(f323(f36(a860),x75961),x75963)))
% 179.72/179.59 [7597]~P101(f323(f323(f238(a1),f2(a1)),x75972))+~P101(f323(f323(f237(a1),x75971),x75973))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x75971),x75972)),f323(f323(f36(a1),x75973),x75972)))
% 179.72/179.59 [7601]~P101(f323(f323(f238(a860),f2(a860)),x76012))+~P101(f323(f323(f238(a860),x76011),x76013))+P101(f323(f323(f238(a860),f323(f323(f79(a860),x76011),x76012)),f323(f323(f79(a860),x76013),x76012)))
% 179.72/179.59 [7602]~P101(f323(f323(f238(a860),f2(a860)),x76021))+~P101(f323(f323(f238(a860),x76022),x76023))+P101(f323(f323(f238(a860),f323(f323(f79(a860),x76021),x76022)),f323(f323(f79(a860),x76021),x76023)))
% 179.72/179.59 [7603]~P101(f323(f323(f238(a1),f2(a1)),x76031))+~P101(f323(f323(f238(a1),x76032),x76033))+P101(f323(f323(f238(a1),f323(f323(f79(a1),x76031),x76032)),f323(f323(f79(a1),x76031),x76033)))
% 179.72/179.59 [7653]E(x76531,f2(a860))+E(f323(f323(f78(a860),f323(f323(f79(a860),x76531),f469(x76531,x76532,x76533))),f479(x76531,x76532,x76533)),x76532)+P101(f323(x76533,f323(f323(f36(a860),x76532),x76531)))
% 179.72/179.59 [7711]E(f323(f323(f78(a860),f323(f323(f79(a860),x77111),f469(x77111,x77112,x77113))),f479(x77111,x77112,x77113)),x77112)+~P101(f323(x77113,f2(a860)))+P101(f323(x77113,f323(f323(f36(a860),x77112),x77111)))
% 179.72/179.59 [7729]~P101(f323(f59(x77291),x77293))+P101(f323(f323(f325(x77291),f470(x77292,x77293,x77291)),x77293))+P101(f323(f323(f238(a860),f2(a860)),f323(f323(f9(x77291,a860),x77292),x77293)))
% 179.72/179.59 [7730]~P101(f323(f59(x77301),x77303))+P101(f323(f323(f325(x77301),f487(x77302,x77303,x77301)),x77303))+P101(f323(f323(f238(a860),f2(a860)),f323(f323(f9(x77301,a860),x77302),x77303)))
% 179.72/179.59 [8019]E(x80191,f188(f867(x80192,a855)))+E(x80191,f323(f323(f301(x80192),x80193),f188(f867(x80192,a855))))+~P101(f323(f323(f237(f867(x80192,a855)),x80191),f323(f323(f301(x80192),x80193),f188(f867(x80192,a855)))))
% 179.72/179.59 [8036]~P5(x80361)+P13(x80361,x80362,x80363)+P101(f323(f323(f325(f861(x80361)),f540(x80363,x80362,x80361)),f323(f166(f861(x80361)),f52(x80361,x80363,f53(x80361)))))
% 179.72/179.59 [8054]~P101(f323(f323(f238(a860),f2(a860)),x80543))+P101(f323(f323(f237(a860),x80541),x80542))+~P101(f323(f323(f237(a860),f323(f323(f79(a860),x80543),x80541)),f323(f323(f79(a860),x80543),x80542)))
% 179.72/179.59 [8055]~P101(f323(f323(f238(a860),f2(a860)),x80553))+P101(f323(f323(f237(a860),x80551),x80552))+~P101(f323(f323(f237(a860),f323(f323(f79(a860),x80551),x80553)),f323(f323(f79(a860),x80552),x80553)))
% 179.72/179.59 [8057]~P101(f323(f323(f238(a860),f2(a860)),x80573))+P101(f323(f323(f238(a860),x80571),x80572))+~P101(f323(f323(f238(a860),f323(f323(f248(a860),x80573),x80571)),f323(f323(f248(a860),x80573),x80572)))
% 179.72/179.59 [8082]~P5(x80821)+~P12(x80821,x80823,x80822)+P101(f323(f323(f325(f861(x80821)),f539(x80822,x80823,x80821)),f323(f166(f861(x80821)),f52(x80821,x80822,f53(x80821)))))
% 179.72/179.59 [8098]~E(f323(f323(f101(f867(x80981,a855)),f550(x80983,x80982,x80981)),f551(x80983,x80982,x80981)),f188(f867(x80981,a855)))+E(f323(f323(f101(f867(x80981,a855)),x80982),f37(f867(x80981,a855),x80983)),f188(f867(x80981,a855)))+P101(f323(f323(f325(f867(x80981,a855)),x80982),x80983))
% 179.72/179.59 [8115]E(x81151,f113(x81152))+~E(f323(f135(f861(x81152),f861(x81152),f121(x81152),f113(x81152)),x81153),f113(x81152))+~P101(f323(f323(f325(f861(x81152)),x81151),f323(f166(f861(x81152)),x81153)))
% 179.72/179.59 [8171]E(x81711,f188(f867(f867(x81712,a855),a855)))+P101(f323(f323(f325(f867(x81712,a855)),f659(x81713,x81711,x81712)),x81711))+P101(f323(f323(f237(f867(x81712,a855)),f38(f867(x81712,a855),x81711)),x81713))
% 179.72/179.59 [8179]~P68(x81791)+~P72(x81791)+E(f323(f323(f6(a1,x81791),f323(f323(f8(a860,x81791,a1),x81792),a104)),f323(f302(a860,a1,f100(a1)),x81793)),f323(f323(f6(a860,x81791),x81792),x81793))
% 179.72/179.59 [8180]~P68(x81801)+~P72(x81801)+E(f323(f323(f9(a1,x81801),f323(f323(f8(a860,x81801,a1),x81802),a104)),f323(f302(a860,a1,f100(a1)),x81803)),f323(f323(f9(a860,x81801),x81802),x81803))
% 179.72/179.59 [8221]~P101(f323(f59(x82211),x82213))+~P101(f323(f323(f238(a860),f2(a860)),f323(x82212,f470(x82212,x82213,x82211))))+P101(f323(f323(f238(a860),f2(a860)),f323(f323(f9(x82211,a860),x82212),x82213)))
% 179.72/179.59 [8222]~P101(f323(f59(x82221),x82223))+~P101(f323(f323(f238(a860),f2(a860)),f323(x82222,f487(x82222,x82223,x82221))))+P101(f323(f323(f238(a860),f2(a860)),f323(f323(f9(x82221,a860),x82222),x82223)))
% 179.72/179.59 [8257]~P63(x82572)+E(x82571,f76(x82572))+E(f323(f323(f281(x82572),f323(f323(f22(x82572),f323(f323(f248(x82572),x82571),x82573)),f76(x82572))),f323(f323(f22(x82572),x82571),f76(x82572))),f323(f323(f6(a860,x82572),f323(f248(x82572),x82571)),f323(f293(a860,f2(a860)),x82573)))
% 179.72/179.59 [8318]E(x83181,f2(a860))+~P101(f323(x83183,f323(f323(f36(a860),x83182),x83181)))+P101(f323(f323(f238(a860),x83182),f323(f323(f79(a860),x83181),f323(a112,f468(x83181,x83182,x83183)))))
% 179.72/179.59 [8336]P101(f323(x83361,f2(a860)))+~P101(f323(x83361,f323(f323(f36(a860),x83362),x83363)))+P101(f323(f323(f238(a860),x83362),f323(f323(f79(a860),x83363),f323(a112,f468(x83363,x83362,x83361)))))
% 179.72/179.59 [8376]E(x83761,f2(a860))+~P101(f323(x83763,f323(f323(f36(a860),x83762),x83761)))+P101(f323(f323(f237(a860),f323(f323(f79(a860),x83761),f468(x83761,x83762,x83763))),x83762))
% 179.72/179.59 [8408]P101(f323(x84081,f2(a860)))+~P101(f323(x84081,f323(f323(f36(a860),x84083),x84082)))+P101(f323(f323(f237(a860),f323(f323(f79(a860),x84082),f468(x84082,x84083,x84081))),x84083))
% 179.72/179.59 [8411]~P103(x84111)+E(f323(f323(f141(x84111,x84111,f5(x84111)),x84112),x84113),f142(x84111,x84111,f5(x84111),x84112,x84113))+P101(f323(f323(f325(x84111),x84112),f323(f166(x84111),x84113)))
% 179.72/179.59 [8446]~E(f323(x84463,f688(x84462,x84463,x84461)),f323(x84463,f690(x84462,x84463,x84461)))+~P56(x84461,f323(x84463,f689(x84462,x84463,x84461)))+P56(x84461,f323(f323(f39(x84462,f867(x84461,f867(x84461,a855))),f246(f867(x84462,a855))),x84463))
% 179.72/179.59 [8454]E(x84541,f188(f867(f867(x84542,a855),a855)))+~P101(f323(f323(f237(f867(x84542,a855)),f659(x84543,x84541,x84542)),x84543))+P101(f323(f323(f237(f867(x84542,a855)),f38(f867(x84542,a855),x84541)),x84543))
% 179.72/179.59 [8513]~P65(x85131)+~P101(f323(f323(f238(x85131),x85132),x85133))+P101(f323(f323(f238(x85131),x85132),f323(f323(f281(x85131),f323(f323(f78(x85131),x85132),x85133)),f323(f323(f78(x85131),f76(x85131)),f76(x85131)))))
% 179.72/179.59 [8573]~P101(f323(f323(x85731,f512(x85731,x85733,x85732)),f513(x85731,x85733,x85732)))+P101(f323(f323(x85731,x85732),x85733))+~P101(f323(f311(f866(a1,a1),a49),f323(f323(f258(a1,a1),x85732),x85733)))
% 179.72/179.59 [8574]~P101(f323(f323(x85741,f514(x85741,x85743,x85742)),f515(x85741,x85743,x85742)))+P101(f323(f323(x85741,x85742),x85743))+~P101(f323(f311(f866(a1,a1),a54),f323(f323(f258(a1,a1),x85742),x85743)))
% 179.72/179.59 [8575]~P101(f323(f323(x85751,f520(x85751,x85753,x85752)),f521(x85751,x85753,x85752)))+P101(f323(f323(x85751,x85752),x85753))+~P101(f323(f311(f866(a1,a1),a226),f323(f323(f258(a1,a1),x85752),x85753)))
% 179.72/179.59 [8576]~P101(f323(f323(x85761,f522(x85761,x85763,x85762)),f523(x85761,x85763,x85762)))+P101(f323(f323(x85761,x85762),x85763))+~P101(f323(f311(f866(a860,a860),a221),f323(f323(f258(a860,a860),x85762),x85763)))
% 179.72/179.59 [8577]~P101(f323(f323(x85771,f563(x85771,x85773,x85772)),f567(x85771,x85773,x85772)))+P101(f323(f323(x85771,x85772),x85773))+~P101(f323(f311(f866(a1,a1),a176),f323(f323(f258(a1,a1),x85772),x85773)))
% 179.72/179.59 [8847]P101(f323(f323(x88471,x88472),x88473))+P101(f323(f311(f866(a860,a860),a221),f323(f323(f258(a860,a860),f522(x88471,x88473,x88472)),f523(x88471,x88473,x88472))))+~P101(f323(f311(f866(a860,a860),a221),f323(f323(f258(a860,a860),x88472),x88473)))
% 179.72/179.59 [8848]P101(f323(f323(x88481,x88482),x88483))+P101(f323(f311(f866(a1,a1),a49),f323(f323(f258(a1,a1),f512(x88481,x88483,x88482)),f513(x88481,x88483,x88482))))+~P101(f323(f311(f866(a1,a1),a49),f323(f323(f258(a1,a1),x88482),x88483)))
% 179.72/179.59 [8849]P101(f323(f323(x88491,x88492),x88493))+P101(f323(f311(f866(a1,a1),a54),f323(f323(f258(a1,a1),f514(x88491,x88493,x88492)),f515(x88491,x88493,x88492))))+~P101(f323(f311(f866(a1,a1),a54),f323(f323(f258(a1,a1),x88492),x88493)))
% 179.72/179.59 [8850]P101(f323(f323(x88501,x88502),x88503))+P101(f323(f311(f866(a1,a1),a226),f323(f323(f258(a1,a1),f520(x88501,x88503,x88502)),f521(x88501,x88503,x88502))))+~P101(f323(f311(f866(a1,a1),a226),f323(f323(f258(a1,a1),x88502),x88503)))
% 179.72/179.59 [8851]P101(f323(f323(x88511,x88512),x88513))+P101(f323(f311(f866(a1,a1),a176),f323(f323(f258(a1,a1),f563(x88511,x88513,x88512)),f567(x88511,x88513,x88512))))+~P101(f323(f311(f866(a1,a1),a176),f323(f323(f258(a1,a1),x88512),x88513)))
% 179.72/179.59 [9189]~P101(f323(f59(x91891),x91893))+P101(f323(f323(f325(f866(f867(x91891,a855),f867(x91891,a855))),f323(f323(f258(f867(x91891,a855),f867(x91891,a855)),x91892),x91893)),f298(x91891)))+~P101(f323(f323(f238(f867(x91891,a855)),x91892),x91893))
% 179.72/179.59 [9258]~P56(x92581,f323(x92583,f689(x92582,x92583,x92581)))+P56(x92581,f323(f323(f39(x92582,f867(x92581,f867(x92581,a855))),f246(f867(x92582,a855))),x92583))+~E(f323(f323(f101(f867(x92581,a855)),f252(x92581,x92581,f323(x92583,f688(x92582,x92583,x92581)))),f253(x92581,x92581,f323(x92583,f690(x92582,x92583,x92581)))),f188(f867(x92581,a855)))
% 179.72/179.59 [9455]P40(x94551,x94552,x94553)+P101(f323(f323(f325(f866(x94551,x94551)),f588(x94553,x94552,x94551)),x94553))+~P101(f323(f323(f325(f866(x94551,x94551)),f323(f323(f258(x94551,x94551),f587(x94553,x94552,x94551)),f587(x94553,x94552,x94551))),x94553))
% 179.72/179.59 [10040]P40(x100401,x100402,x100403)+~P101(f323(f323(f262(x100401,x100401,a855),f323(f323(f7(x100401,f867(x100401,a855),f867(x100401,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x100401,a855),f867(x100401,a855)),x100401),f8(a855,a855,x100401)),f323(f323(f8(a855,f867(a855,a855),x100401),a321),f323(f323(f7(x100401,f867(x100401,a855),a855),f325(x100401)),x100402)))),f323(f323(f7(x100401,f867(x100401,a855),a855),f325(x100401)),x100402))),f588(x100403,x100402,x100401)))+~P101(f323(f323(f325(f866(x100401,x100401)),f323(f323(f258(x100401,x100401),f587(x100403,x100402,x100401)),f587(x100403,x100402,x100401))),x100403))
% 179.72/179.59 [5625]~P57(x56252)+E(x56251,f2(x56252))+E(f323(f323(f36(x56252),f323(f323(f79(x56252),x56253),x56251)),x56251),x56253)
% 179.72/179.59 [5626]~P57(x56262)+E(x56261,f2(x56262))+E(f323(f323(f36(x56262),f323(f323(f79(x56262),x56261),x56263)),x56261),x56263)
% 179.72/179.59 [6402]~P72(x64021)+~E(f323(x64022,f2(a860)),f2(x64021))+E(f323(f323(f6(a860,x64021),x64022),f323(f293(a860,f323(a112,f2(a860))),x64023)),f323(f323(f6(a860,x64021),x64022),f323(f293(a860,f2(a860)),x64023)))
% 179.72/179.59 [6530]~P57(x65302)+E(x65301,f2(x65302))+E(f323(f323(f36(x65302),f323(f323(f78(x65302),x65303),x65301)),x65301),f323(f323(f78(x65302),f323(f323(f36(x65302),x65303),x65301)),f76(x65302)))
% 179.72/179.59 [6531]~P57(x65312)+E(x65311,f2(x65312))+E(f323(f323(f36(x65312),f323(f323(f78(x65312),x65311),x65313)),x65311),f323(f323(f78(x65312),f323(f323(f36(x65312),x65313),x65311)),f76(x65312)))
% 179.72/179.59 [6748]~P101(f323(x67483,f2(a1)))+P101(f323(f323(f237(a860),x67481),x67482))+P101(f323(x67483,f323(f100(a1),f323(f323(f22(a860),x67482),x67481))))
% 179.72/179.59 [6852]P101(f323(f323(f238(a860),x68522),x68521))+P101(f323(f323(f237(a860),x68521),x68522))+P101(f323(x68523,f323(f100(a1),f323(f323(f22(a860),x68522),x68521))))
% 179.72/179.59 [6922]E(f323(f323(f78(a860),f323(f103(a860),x69221)),f323(f323(f78(a860),f323(f103(a860),x69222)),x69223)),f323(f323(f78(a860),f323(f103(a860),x69221)),x69223))+P101(f323(a193,f323(f103(a1),x69221)))+~P101(f323(a193,f323(f103(a1),x69222)))
% 179.72/179.59 [7001]~E(x70012,f323(f323(f36(a860),x70013),x70011))+~P101(f323(f323(f238(a860),f2(a860)),x70011))+P101(f323(f323(f237(a860),f323(f323(f79(a860),x70011),x70012)),x70013))
% 179.72/179.59 [7115]~P101(f323(f59(x71151),x71153))+~P101(f323(f59(x71151),x71152))+P101(f323(f59(x71151),f323(f323(f110(f867(x71151,a855)),x71152),x71153)))
% 179.72/179.59 [7406]~P103(x74061)+~P101(f323(f59(x74061),x74062))+E(f132(x74061,f323(f323(f22(f867(x74061,a855)),x74062),f323(f323(f301(x74061),x74063),f188(f867(x74061,a855))))),f164(x74061,x74063,f132(x74061,x74062)))
% 179.72/179.59 [7471]P101(f323(x74711,f2(a1)))+~P101(f323(f323(f238(a860),x74712),x74713))+~P101(f323(x74711,f323(f100(a1),f323(f323(f22(a860),x74712),x74713))))
% 179.72/179.59 [7488]~P101(f323(f59(x74881),x74882))+E(f323(f35(x74881),f323(f323(f22(f867(x74881,a855)),x74882),f323(f323(f301(x74881),x74883),f188(f867(x74881,a855))))),f323(f35(x74881),x74882))+P101(f323(f323(f325(x74881),x74883),x74882))
% 179.72/179.59 [7618]~P119(x76181)+~P101(f323(f323(f238(x76181),f76(x76181)),x76182))+P101(f323(f323(f238(x76181),f76(x76181)),f323(f323(f79(x76181),x76182),f323(f323(f248(x76181),x76182),x76183))))
% 179.72/179.59 [7663]~P101(f323(f59(x76631),x76633))+E(f323(f323(f22(a860),f323(f35(x76631),x76632)),f323(f35(x76631),x76633)),f323(f35(x76631),f323(f323(f22(f867(x76631,a855)),x76632),x76633)))+~P101(f323(f323(f237(f867(x76631,a855)),x76633),x76632))
% 179.72/179.59 [7720]~P101(f323(f323(f237(a860),x77202),x77203))+~P101(f323(f323(f237(a860),x77201),f323(f323(f22(a860),x77203),x77202)))+P101(f323(f323(f237(a860),f323(f323(f78(a860),x77201),x77202)),x77203))
% 179.72/179.59 [7771]P101(f323(f59(x77711),x77712))+~P101(f323(f59(x77711),x77713))+~P101(f323(f59(x77711),f323(f323(f22(f867(x77711,a855)),x77712),x77713)))
% 179.72/179.59 [7777]~P101(f323(f59(x77771),x77772))+E(f323(f35(x77771),f323(f323(f22(f867(x77771,a855)),x77772),f323(f323(f301(x77771),x77773),f188(f867(x77771,a855))))),f323(f323(f22(a860),f323(f35(x77771),x77772)),f76(a860)))+~P101(f323(f323(f325(x77771),x77773),x77772))
% 179.72/179.59 [7854]P56(x78541,x78542)+~P56(x78541,x78543)+~P101(f323(f323(f237(f867(x78541,f867(x78541,a855))),x78542),x78543))
% 179.72/179.59 [7898]~P101(f323(f323(f237(a860),x78983),x78982))+P101(f323(f323(f237(a860),x78981),f323(f323(f22(a860),x78982),x78983)))+~P101(f323(f323(f237(a860),f323(f323(f78(a860),x78981),x78983)),x78982))
% 179.72/179.59 [7916]P38(x79161,x79162)+~P38(x79161,x79163)+~P101(f323(f323(f237(f867(f866(x79161,x79161),a855)),x79162),x79163))
% 179.72/179.59 [7917]P54(x79171,x79172)+~P54(x79171,x79173)+~P101(f323(f323(f237(f867(f866(x79171,x79171),a855)),x79172),x79173))
% 179.72/179.59 [8149]~P119(x81491)+~P101(f323(f323(f238(x81491),f76(x81491)),x81492))+P101(f323(f323(f238(x81491),f323(f323(f248(x81491),x81492),x81493)),f323(f323(f79(x81491),x81492),f323(f323(f248(x81491),x81492),x81493))))
% 179.72/179.59 [8239]~P101(f323(x82391,f2(a1)))+~P101(f323(x82391,f323(f323(f22(a1),f323(f100(a1),x82392)),f323(f100(a1),x82393))))+P101(f323(x82391,f323(f100(a1),f323(f323(f22(a860),x82392),x82393))))
% 179.72/179.59 [8254]~P101(f323(f323(f237(a860),x82543),x82542))+P101(f323(x82541,f323(f323(f22(a1),f323(f100(a1),x82542)),f323(f100(a1),x82543))))+~P101(f323(x82541,f323(f100(a1),f323(f323(f22(a860),x82542),x82543))))
% 179.72/179.59 [8273]P101(f323(f323(f238(a860),x82731),x82732))+~P101(f323(x82733,f323(f323(f22(a1),f323(f100(a1),x82731)),f323(f100(a1),x82732))))+P101(f323(x82733,f323(f100(a1),f323(f323(f22(a860),x82731),x82732))))
% 179.72/179.59 [8330]~P120(x83302)+E(x83301,f2(x83302))+P101(f323(f323(f238(x83302),f2(x83302)),f323(f323(f78(x83302),f323(f323(f79(x83302),x83303),x83303)),f323(f323(f79(x83302),x83301),x83301))))
% 179.72/179.59 [8331]~P120(x83312)+E(x83311,f2(x83312))+P101(f323(f323(f238(x83312),f2(x83312)),f323(f323(f78(x83312),f323(f323(f79(x83312),x83311),x83311)),f323(f323(f79(x83312),x83313),x83313))))
% 179.72/179.59 [8429]~P101(f323(f323(f238(a860),f2(a860)),x84291))+~P101(f323(f323(f238(a1),x84292),x84293))+P101(f323(f323(f238(a1),f323(f323(f79(a1),f323(f100(a1),x84291)),x84292)),f323(f323(f79(a1),f323(f100(a1),x84291)),x84293)))
% 179.72/179.59 [8483]E(f323(f323(f101(f867(x84831,a855)),x84832),f37(f867(x84831,a855),x84833)),f188(f867(x84831,a855)))+P101(f323(f323(f325(f867(x84831,a855)),x84832),x84833))+P101(f323(f323(f325(f867(x84831,a855)),f550(x84833,x84832,x84831)),f323(f323(f301(f867(x84831,a855)),x84832),x84833)))
% 179.72/179.59 [8484]E(f323(f323(f101(f867(x84841,a855)),x84842),f37(f867(x84841,a855),x84843)),f188(f867(x84841,a855)))+P101(f323(f323(f325(f867(x84841,a855)),x84842),x84843))+P101(f323(f323(f325(f867(x84841,a855)),f551(x84843,x84842,x84841)),f323(f323(f301(f867(x84841,a855)),x84842),x84843)))
% 179.72/179.59 [8512]E(x85121,x85122)+~E(f323(f189(f861(x85123)),x85121),f323(f189(f861(x85123)),x85122))+P101(f323(f323(f325(f866(x85123,x85123)),f582(x85123,x85121,x85122)),f323(f166(f866(x85123,x85123)),f323(f323(f175(x85123,x85123),x85122),x85121))))
% 179.72/179.59 [8765]E(f299(x87651,x87652),f299(x87651,x87653))+~P101(f323(f323(f237(f867(f866(x87651,x87651),a855)),x87653),f299(x87651,x87652)))+~P101(f323(f323(f237(f867(f866(x87651,x87651),a855)),x87652),x87653))
% 179.72/179.59 [8826]~P40(x88261,f246(f867(x88261,a855)),x88263)+P101(f323(f323(f237(f867(f866(f861(x88261),f861(x88261)),a855)),f150(x88261,x88262)),f151(x88261,x88263)))+~P101(f323(f323(f237(f867(f866(x88261,x88261),a855)),x88262),x88263))
% 179.72/179.59 [9027]P38(x90271,x90272)+~P101(f323(f323(f325(x90271),x90273),f730(x90272,x90271)))+P101(f323(f323(f325(f866(x90271,x90271)),f323(f323(f258(x90271,x90271),f767(x90272,x90271,x90273)),x90273)),x90272))
% 179.72/179.59 [9062]~P101(f323(f59(x90621),x90622))+P101(f323(f59(f867(x90621,a855)),f323(f323(f58(x90621),x90622),x90623)))+~P101(f323(f323(f237(f867(f866(x90621,x90621),a855)),x90623),f323(f323(f260(x90621,x90621),x90622),f323(f16(f867(x90621,a855),x90621),x90622))))
% 179.72/179.59 [9096]P40(x90961,x90962,x90963)+P101(f323(f323(f325(x90961),f609(x90963,x90962,x90961)),x90962))+~P101(f323(f323(f237(f867(f866(x90961,x90961),a855)),x90963),f323(f323(f260(x90961,x90961),x90962),f323(f16(f867(x90961,a855),x90961),x90962))))
% 179.72/179.59 [9097]P40(x90971,x90972,x90973)+P101(f323(f323(f325(x90971),f615(x90972,x90973,x90971)),x90972))+~P101(f323(f323(f237(f867(f866(x90971,x90971),a855)),x90973),f323(f323(f260(x90971,x90971),x90972),f323(f16(f867(x90971,a855),x90971),x90972))))
% 179.72/179.59 [9131]~P65(x91311)+~P101(f323(f323(f238(x91311),x91312),x91313))+P101(f323(f323(f238(x91311),f323(f323(f281(x91311),f323(f323(f78(x91311),x91312),x91313)),f323(f323(f78(x91311),f76(x91311)),f76(x91311)))),x91313))
% 179.72/179.59 [9164]~P64(x91641)+P101(f323(f323(f237(x91641),x91642),x91643))+~P101(f323(f323(f237(x91641),f323(f323(f79(x91641),f467(x91643,x91642,x91641)),x91642)),x91643))
% 179.72/179.59 [9294]E(f323(f189(f861(f861(x92941))),f323(f129(f861(x92941),f323(f323(f8(a860,a855,f861(x92941)),f323(f238(a860),x92942)),f189(f861(x92941)))),f173(x92941,x92943))),f323(f189(f861(x92941)),f323(f323(f158(f861(x92941)),x92943),x92942)))+~P16(a860,f323(f162(a860),f323(f323(f147(f861(x92941),a860),f189(f861(x92941))),x92943)))+~P101(f323(f323(f238(a860),x92942),f323(f189(f861(f861(x92941))),x92943)))
% 179.72/179.59 [9400]~P38(x94001,x94002)+P29(x94001,f323(f323(f258(f867(f866(x94001,x94001),a855),f867(f866(x94001,x94001),a855)),x94002),x94003))+~P101(f323(f323(f237(f867(f866(x94001,x94001),a855)),f323(f323(f280(x94001,x94001,x94001),x94002),x94003)),x94002))
% 179.72/179.59 [9407]E(f323(f323(f147(f861(x94071),x94071),f323(f323(f7(f861(x94071),a860,x94071),f158(x94071)),x94072)),f323(f129(f861(x94071),f323(f323(f8(a860,a855,f861(x94071)),f323(f238(a860),x94072)),f189(f861(x94071)))),f173(x94071,x94073))),f323(f323(f158(f861(x94071)),x94073),x94072))+~P16(a860,f323(f162(a860),f323(f323(f147(f861(x94071),a860),f189(f861(x94071))),x94073)))+~P101(f323(f323(f238(a860),x94072),f323(f189(f861(f861(x94071))),x94073)))
% 179.72/179.59 [9544]P40(x95441,x95442,x95443)+~P101(f323(f323(f325(f866(x95441,x95441)),f323(f323(f258(x95441,x95441),f609(x95443,x95442,x95441)),f609(x95443,x95442,x95441))),x95443))+~P101(f323(f323(f237(f867(f866(x95441,x95441),a855)),x95443),f323(f323(f260(x95441,x95441),x95442),f323(f16(f867(x95441,a855),x95441),x95442))))
% 179.72/179.59 [9545]P40(x95451,x95452,x95453)+~P101(f323(f323(f325(f866(x95451,x95451)),f323(f323(f258(x95451,x95451),f615(x95452,x95453,x95451)),f615(x95452,x95453,x95451))),x95453))+~P101(f323(f323(f237(f867(f866(x95451,x95451),a855)),x95453),f323(f323(f260(x95451,x95451),x95452),f323(f16(f867(x95451,a855),x95451),x95452))))
% 179.72/179.59 [9722]~P134(x97221)+~P118(x97221)+E(f323(f323(f281(x97221),f323(f102(x97221),f323(f323(f71(f866(a1,a1),a1,x97222,f257(a1,a1)),f214(x97222)),x97223))),f323(f102(x97221),f323(f323(f71(f866(a1,a1),a1,x97222,f261(a1,a1)),f214(x97222)),x97223))),f227(x97222,x97221,x97223))
% 179.72/179.59 [9922]~E(x99223,f2(a860))+~E(f323(f189(f861(x99221)),f323(f323(f158(f861(x99221)),x99222),f566(x99223,x99221,x99222))),x99223)+E(f323(f323(f147(a860,f861(x99221)),f323(f323(f7(a860,f861(a860),f861(x99221)),f323(f323(f8(f867(a860,x99221),f867(f861(a860),f861(x99221)),a860),f147(a860,x99221)),f323(f7(a860,a860,x99221),f323(f323(f8(f861(x99221),f867(a860,x99221),a860),f158(x99221)),f323(f158(f861(x99221)),x99222))))),f132(a860,f323(f293(a860,f2(a860)),f323(f189(f861(f861(x99221))),x99222))))),f132(a860,f323(f293(a860,f2(a860)),x99223))),f173(x99221,x99222))
% 179.72/179.59 [9923]E(x99231,f113(f861(x99232)))+~E(f323(f189(f861(x99232)),f323(f323(f158(f861(x99232)),x99231),f566(x99233,x99232,x99231))),x99233)+E(f323(f323(f147(a860,f861(x99232)),f323(f323(f7(a860,f861(a860),f861(x99232)),f323(f323(f8(f867(a860,x99232),f867(f861(a860),f861(x99232)),a860),f147(a860,x99232)),f323(f7(a860,a860,x99232),f323(f323(f8(f861(x99232),f867(a860,x99232),a860),f158(x99232)),f323(f158(f861(x99232)),x99231))))),f132(a860,f323(f293(a860,f2(a860)),f323(f189(f861(f861(x99232))),x99231))))),f132(a860,f323(f293(a860,f2(a860)),x99233))),f173(x99232,x99231))
% 179.72/179.59 [9924]~E(x99243,f2(a860))+E(f323(f323(f147(a860,f861(x99241)),f323(f323(f7(a860,f861(a860),f861(x99241)),f323(f323(f8(f867(a860,x99241),f867(f861(a860),f861(x99241)),a860),f147(a860,x99241)),f323(f7(a860,a860,x99241),f323(f323(f8(f861(x99241),f867(a860,x99241),a860),f158(x99241)),f323(f158(f861(x99241)),x99242))))),f132(a860,f323(f293(a860,f2(a860)),f323(f189(f861(f861(x99241))),x99242))))),f132(a860,f323(f293(a860,f2(a860)),x99243))),f173(x99241,x99242))+P101(f323(f323(f238(a860),f566(x99243,x99241,x99242)),f323(f189(f861(f861(x99241))),x99242)))
% 179.72/179.59 [9925]E(x99251,f113(f861(x99252)))+E(f323(f323(f147(a860,f861(x99252)),f323(f323(f7(a860,f861(a860),f861(x99252)),f323(f323(f8(f867(a860,x99252),f867(f861(a860),f861(x99252)),a860),f147(a860,x99252)),f323(f7(a860,a860,x99252),f323(f323(f8(f861(x99252),f867(a860,x99252),a860),f158(x99252)),f323(f158(f861(x99252)),x99251))))),f132(a860,f323(f293(a860,f2(a860)),f323(f189(f861(f861(x99252))),x99251))))),f132(a860,f323(f293(a860,f2(a860)),x99253))),f173(x99252,x99251))+P101(f323(f323(f238(a860),f566(x99253,x99252,x99251)),f323(f189(f861(f861(x99252))),x99251)))
% 179.72/179.59 [7660]E(f323(f323(f78(a860),f323(f103(a860),x76601)),f323(f323(f78(a860),f323(f103(a860),x76602)),x76603)),f323(f323(f78(a860),f323(f103(a860),f323(f323(f78(a1),x76601),x76602))),x76603))+P101(f323(a193,f323(f103(a1),x76601)))+P101(f323(a193,f323(f103(a1),x76602)))
% 179.72/179.59 [8420]~P101(f323(f59(x84201),x84202))+~P101(f323(f323(f325(x84201),x84203),x84202))+E(f323(a112,f323(f35(x84201),f323(f323(f22(f867(x84201,a855)),x84202),f323(f323(f301(x84201),x84203),f188(f867(x84201,a855)))))),f323(f35(x84201),x84202))
% 179.72/179.59 [8436]~P101(f323(f59(x84361),x84362))+~P101(f323(f323(f325(x84361),x84363),x84362))+E(f323(f323(f78(a860),f76(a860)),f323(f35(x84361),f323(f323(f22(f867(x84361,a855)),x84362),f323(f323(f301(x84361),x84363),f188(f867(x84361,a855)))))),f323(f35(x84361),x84362))
% 179.72/179.59 [8522]~P103(x85221)+~P101(f323(f59(x85221),x85223))+E(f323(f323(f141(x85221,x85221,f5(x85221)),x85222),f132(x85221,f323(f323(f22(f867(x85221,a855)),x85223),f323(f323(f301(x85221),x85222),f188(f867(x85221,a855)))))),f132(x85221,f323(f323(f301(x85221),x85222),x85223)))
% 179.72/179.59 [8689]~P101(f323(f59(x86891),x86893))+~P101(f323(f59(x86891),x86892))+E(f323(f323(f78(a860),f323(f35(x86891),f323(f323(f110(f867(x86891,a855)),x86892),x86893))),f323(f35(x86891),f323(f323(f101(f867(x86891,a855)),x86892),x86893))),f323(f323(f78(a860),f323(f35(x86891),x86892)),f323(f35(x86891),x86893)))
% 179.72/179.59 [9870]~P27(x98701,f867(f867(x98701,a855),a855),f323(f323(f7(x98701,f867(f866(x98701,x98701),a855),f867(f867(x98701,a855),a855)),f323(f323(f8(f867(x98701,a855),f867(f867(f866(x98701,x98701),a855),f867(f867(x98701,a855),a855)),x98701),f58(x98701)),f323(f323(f7(x98701,f867(x98701,a855),f867(x98701,a855)),f301(x98701)),f188(f867(x98701,a855))))),x98703),x98702)+~P101(f323(f59(x98701),x98702))+E(f323(f35(f867(x98701,a855)),f323(f323(f58(x98701),x98702),x98703)),f323(f35(x98701),x98702))
% 179.72/179.59 [7929]~P90(x79291)+P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x79293)))+E(f323(f323(f248(x79291),x79292),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),x79293),x79293)),a97))),f76(x79291))
% 179.72/179.59 [9385]~P90(x93851)+~P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),x93853)))+E(f323(f323(f248(x93851),x93852),f323(f103(a860),f323(f323(f22(a1),f323(f323(f78(a1),x93853),x93853)),a97))),f323(f323(f84(x93851,x93851),f323(f323(f248(x93851),x93852),f323(f103(a860),x93853))),f323(f323(f18(x93851,x93851,x93851),f323(f323(f8(x93851,f867(x93851,x93851),x93851),f79(x93851)),f323(f79(x93851),x93852))),f5(x93851))))
% 179.72/179.59 [9782]~P101(f323(f130(x97821),x97823))+~P101(f323(f323(f325(x97821),x97822),f323(f166(x97821),x97823)))+E(f323(f323(f131(x97821),f323(f189(f861(x97821)),f171(x97821,f323(f323(f8(a855,a855,x97821),a318),f323(f323(f7(x97821,x97821,a855),a320),x97822)),f323(f162(x97821),x97823)))),f323(f162(x97821),x97823)),f323(f323(f144(x97821),x97822),f323(f162(x97821),f171(x97821,f323(f323(f8(a855,a855,x97821),a318),f323(f323(f7(x97821,x97821,a855),a320),x97822)),x97823))))
% 179.72/179.59 [9851]P101(f323(f323(f237(f867(f866(x98511,x98511),a855)),f299(x98511,x98512)),x98513))+~P101(f323(f323(f237(f867(f866(x98511,x98511),a855)),f299(x98511,f188(f867(f866(x98511,x98511),a855)))),x98513))+~P101(f323(f323(f237(f867(f866(x98511,x98511),a855)),f323(f323(f280(x98511,x98511,x98511),f323(f323(f101(f867(f866(x98511,x98511),a855)),f299(x98511,x98512)),x98513)),x98512)),x98513))
% 179.72/179.59 [9693]~P101(f323(f59(x96931),f323(f243(x96931),x96933)))+~P101(f323(f59(x96931),f323(f243(x96931),x96932)))+P101(f323(f59(x96931),f323(f243(x96931),f323(f323(f18(x96931,a855,a855),f323(f323(f8(a855,f867(a855,a855),x96931),a322),x96932)),x96933))))
% 179.72/179.59 [9984]P101(f323(f323(f237(f867(f866(x99841,x99841),a855)),f323(f323(f280(x99841,x99841,x99841),x99842),f299(x99841,x99842))),x99843))+~P101(f323(f323(f237(f867(f866(x99841,x99841),a855)),x99842),x99843))+~P101(f323(f323(f237(f867(f866(x99841,x99841),a855)),f323(f323(f280(x99841,x99841,x99841),f323(f323(f101(f867(f866(x99841,x99841),a855)),f323(f323(f280(x99841,x99841,x99841),x99842),f299(x99841,x99842))),x99843)),x99842)),x99843))
% 179.72/179.59 [9938]~P116(x99382)+E(x99381,f2(x99382))+~E(f323(f323(f78(x99382),f323(f323(f248(x99382),x99383),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x99382),x99381),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f2(x99382))
% 179.72/179.59 [9939]~P116(x99392)+E(x99391,f2(x99392))+~E(f323(f323(f78(x99392),f323(f323(f248(x99392),x99391),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x99392),x99393),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f2(x99392))
% 179.72/179.59 [9944]~P101(f323(f130(x99441),x99443))+~P101(f323(f323(f325(x99441),x99442),f323(f166(x99441),x99443)))+E(f323(f162(x99441),f323(f165(x99441),f323(f323(f131(x99441),f323(f189(f861(x99441)),f171(x99441,f323(f323(f8(a855,a855,x99441),a318),f323(f323(f7(x99441,x99441,a855),a320),x99442)),x99443))),x99443))),f171(x99441,f323(f323(f8(a855,a855,x99441),a318),f323(f323(f7(x99441,x99441,a855),a320),x99442)),f323(f162(x99441),x99443)))
% 179.72/179.59 [10028]~P116(x100282)+E(x100281,f2(x100282))+P101(f323(f323(f238(x100282),f2(x100282)),f323(f323(f78(x100282),f323(f323(f248(x100282),x100283),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x100282),x100281),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))))
% 179.72/179.59 [10029]~P116(x100292)+E(x100291,f2(x100292))+P101(f323(f323(f238(x100292),f2(x100292)),f323(f323(f78(x100292),f323(f323(f248(x100292),x100291),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x100292),x100293),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))))
% 179.72/179.59 [10070]~P116(x100701)+P101(f323(f323(f237(x100701),f2(x100701)),x100702))+~P101(f323(f323(f237(x100701),f2(x100701)),f323(f323(f248(x100701),x100702),f323(a112,f323(f323(f79(a860),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),x100703)))))
% 179.72/179.59 [5466]~P26(x54661,x54664,x54663)+P26(x54661,x54662,x54663)+~P26(x54661,x54662,x54664)
% 179.72/179.59 [4941]~E(x49412,f88(x49413,x49411))+P101(f323(x49411,x49412))+~P101(f323(x49411,x49414))
% 179.72/179.59 [6660]~P38(x66602,x66604)+~P38(x66601,x66603)+P38(f866(x66601,x66602),f315(x66601,x66602,x66603,x66604))
% 179.72/179.59 [5120]~P8(x51204,x51201)+~E(f323(x51201,x51202),f323(x51201,x51203))+P101(f323(f323(x51201,x51202),x51203))
% 179.72/179.59 [5281]~P8(x52814,x52811)+E(f323(x52811,x52812),f323(x52811,x52813))+~P101(f323(f323(x52811,x52812),x52813))
% 179.72/179.59 [5373]~P20(x53733,x53734,x53731)+E(f323(x53731,x53732),f323(f61(x53733,x53734),x53732))+~P101(f323(f59(x53733),x53732))
% 179.72/179.59 [5374]~P10(x53743,x53744,x53741)+E(f323(x53741,x53742),f323(f61(x53743,x53744),x53742))+~P101(f323(f59(x53743),x53742))
% 179.72/179.59 [5499]~P8(x54994,x54991)+~P101(f323(f323(x54991,x54993),x54992))+P101(f323(f323(x54991,x54992),x54993))
% 179.72/179.59 [5568]E(x55681,x55682)+~E(f323(f257(x55683,x55684),x55681),f323(f257(x55683,x55684),x55682))+~E(f323(f261(x55683,x55684),x55681),f323(f261(x55683,x55684),x55682))
% 179.72/179.59 [5593]E(x55931,x55932)+~P101(f323(f45(x55933,x55934),x55932))+~P101(f323(f45(x55933,x55934),x55931))
% 179.72/179.59 [5783]~P72(x57832)+E(f228(x57831,x57832,x57833,x57834),f2(x57832))+P101(f323(f59(x57831),x57834))
% 179.72/179.59 [5917]~P101(f323(f311(x59171,x59172),x59174))+P101(f323(f311(x59171,x59172),x59173))+~P101(f323(f323(x59172,x59173),x59174))
% 179.72/179.59 [6334]P50(x63341,x63342,x63343,x63344)+P101(f323(f323(x63342,x63344),x63343))+~P101(f323(f323(x63342,x63343),x63344))
% 179.72/179.59 [7766]E(x77661,f2(a860))+~P101(f323(x77662,x77663))+P101(f323(x77662,f797(x77662,x77663,x77661,x77664)))
% 179.72/179.59 [7849]~P103(x78492)+~P101(f323(f130(x78491),x78494))+P101(f323(f130(x78491),f143(x78491,x78492,x78493,x78494)))
% 179.72/179.59 [8070]~P101(f323(f59(x80702),x80704))+~P101(f323(f59(x80701),x80703))+P101(f323(f59(f865(x80701,x80702)),f310(x80701,x80702,x80703,x80704)))
% 179.72/179.59 [8071]~P101(f323(f130(x80712),x80714))+~P101(f323(f130(x80711),x80713))+P101(f323(f130(f866(x80711,x80712)),f57(x80711,x80712,x80713,x80714)))
% 179.72/179.59 [8075]P101(f323(f323(f325(f861(x80751)),f323(f323(f121(x80751),x80752),x80753)),f154(x80751,x80754)))+~P101(f323(f323(f325(f861(x80751)),x80753),f154(x80751,x80754)))+~P101(f323(f323(f325(f861(x80751)),x80752),f154(x80751,x80754)))
% 179.72/179.59 [8361]E(x83611,f2(a860))+P101(f323(x83612,x83613))+~P101(f323(x83612,f799(x83612,x83613,x83611,x83614)))
% 179.72/179.59 [8400]~P103(x84003)+~P101(f323(f130(x84001),f143(x84001,x84003,x84004,x84002)))+P101(f323(f130(x84001),x84002))
% 179.72/179.59 [8678]~P101(f323(f323(f325(f866(x86781,x86781)),f323(f323(f258(x86781,x86781),x86782),x86784)),f299(x86781,x86783)))+P101(f323(f323(f325(x86781),x86782),f312(x86781,x86783)))+~P101(f323(f323(f325(x86781),x86784),f312(x86781,x86783)))
% 179.72/179.59 [5104]~P72(x51042)+E(f323(f323(f6(x51041,x51042),x51043),x51044),f2(x51042))+P101(f323(f59(x51041),x51044))
% 179.72/179.59 [5107]~P68(x51072)+E(f323(f323(f9(x51071,x51072),x51073),x51074),f76(x51072))+P101(f323(f59(x51071),x51074))
% 179.72/179.59 [5245]~P69(x52453)+E(x52451,x52452)+~E(f323(f323(f78(x52453),x52454),x52451),f323(f323(f78(x52453),x52454),x52452))
% 179.72/179.59 [5246]~P70(x52463)+E(x52461,x52462)+~E(f323(f323(f78(x52463),x52464),x52461),f323(f323(f78(x52463),x52464),x52462))
% 179.72/179.59 [5248]~P69(x52483)+E(x52481,x52482)+~E(f323(f323(f78(x52483),x52481),x52484),f323(f323(f78(x52483),x52482),x52484))
% 179.72/179.59 [5369]~P6(x53693)+E(x53691,f188(f867(x53692,a855)))+E(f323(f323(f39(x53692,x53693),x53691),f323(f16(x53693,x53692),x53694)),x53694)
% 179.72/179.59 [5370]~P6(x53703)+E(x53701,f188(f867(x53702,a855)))+E(f323(f323(f40(x53702,x53703),x53701),f323(f16(x53703,x53702),x53704)),x53704)
% 179.72/179.59 [5581]~P105(x55813)+E(x55811,x55812)+~E(f294(x55813,x55814,x55811),f323(f323(f301(x55813),x55812),f188(f867(x55813,a855))))
% 179.72/179.59 [5582]~P105(x55823)+E(x55821,x55822)+~E(f294(x55823,x55821,x55822),f323(f323(f301(x55823),x55824),f188(f867(x55823,a855))))
% 179.72/179.59 [5642]~P36(x56423,x56421,x56424)+P36(x56423,x56421,f323(f323(f144(x56423),x56422),x56424))+P101(f323(x56421,x56422))
% 179.72/179.59 [5743]~P32(x57431,x57432,x57434)+~P101(f323(x57432,x57433))+P32(x57431,x57432,f323(f323(f144(x57431),x57433),x57434))
% 179.72/179.59 [5874]P101(f323(x58741,x58742))+~P101(f323(f251(x58743,x58741),x58744))+~P101(f323(f323(f325(x58743),x58742),x58744))
% 179.72/179.59 [5883]~P32(x58831,x58832,x58834)+~P32(x58831,x58832,x58833)+P32(x58831,x58832,f323(f323(f121(x58831),x58833),x58834))
% 179.72/179.59 [5893]P34(x58931,x58932,x58933)+~P34(x58931,x58932,f323(f323(f144(x58931),x58934),x58933))+P101(f323(x58932,x58934))
% 179.72/179.59 [5894]P36(x58941,x58942,x58943)+~P36(x58941,x58942,f323(f323(f144(x58941),x58944),x58943))+P101(f323(x58942,x58944))
% 179.72/179.59 [5967]P34(x59671,x59672,x59673)+P34(x59671,x59672,x59674)+~P34(x59671,x59672,f323(f323(f121(x59671),x59674),x59673))
% 179.72/179.59 [5986]~P72(x59861)+E(f323(f323(f6(a860,x59861),x59862),f323(f293(a860,x59863),f323(a112,x59864))),f2(x59861))+~P101(f323(f323(f238(a860),x59864),x59863))
% 179.72/179.59 [5991]~P58(x59911)+~E(f42(x59911,x59912,x59913),f42(x59911,x59914,x59913))+E(f42(x59911,f323(f77(x59911),x59912),x59913),f42(x59911,f323(f77(x59911),x59914),x59913))
% 179.72/179.59 [6059]P101(f323(x60591,x60592))+~E(f323(f129(x60593,x60591),x60594),x60594)+~P101(f323(f323(f325(x60593),x60592),f323(f166(x60593),x60594)))
% 179.72/179.59 [6078]~E(f323(f323(f78(a860),x60783),x60782),f323(f323(f78(a860),x60781),x60784))+~P101(f323(f323(f238(a860),x60783),x60784))+P101(f323(f323(f238(a860),x60781),x60782))
% 179.72/179.59 [6082]P34(x60821,x60822,x60823)+~P101(f323(x60822,x60824))+~P101(f323(f323(f325(x60821),x60824),f323(f166(x60821),x60823)))
% 179.72/179.59 [6118]~P32(x61183,x61181,x61184)+P101(f323(x61181,x61182))+~P101(f323(f323(f325(x61183),x61182),f323(f166(x61183),x61184)))
% 179.72/179.59 [6120]~E(f323(f129(x61201,x61202),x61203),f113(x61201))+~P101(f323(x61202,x61204))+~P101(f323(f323(f325(x61201),x61204),f323(f166(x61201),x61203)))
% 179.72/179.59 [6121]~E(f171(x61213,x61211,x61214),x61214)+P101(f323(x61211,x61212))+~P101(f323(f323(f325(x61213),x61212),f323(f166(x61213),x61214)))
% 179.72/179.59 [6149]~E(x61494,f188(f867(x61492,a855)))+~E(x61493,f188(f867(x61491,a855)))+E(f310(x61491,x61492,x61493,x61494),f188(f867(f865(x61491,x61492),a855)))
% 179.72/179.59 [6293]P101(f323(x62931,x62932))+~P101(f323(f153(x62933,x62931),x62934))+~P101(f323(f323(f325(x62933),x62932),f323(f166(x62933),x62934)))
% 179.72/179.59 [6559]~P72(x65591)+E(f323(f323(f6(a860,x65591),x65592),f294(a860,x65593,f323(a112,x65594))),f2(x65591))+~P101(f323(f323(f238(a860),f323(a112,x65594)),x65593))
% 179.72/179.59 [6698]~P103(x66981)+E(f323(f323(f22(f867(x66981,a855)),f323(f293(x66981,x66982),x66983)),f323(f293(x66981,x66982),x66984)),f323(f293(x66981,x66984),x66983))+~P101(f323(f323(f237(x66981),x66982),x66984))
% 179.72/179.59 [6770]~E(x67703,x67704)+E(x67701,f2(a860))+P101(f323(f323(f325(x67702),x67703),f323(f166(x67702),f163(x67702,x67701,x67704))))
% 179.72/179.59 [7047]~P101(f323(f323(f325(f861(x70471)),x70474),f154(x70471,x70473)))+P101(f323(f323(f325(x70471),x70472),x70473))+~P101(f323(f323(f325(x70471),x70472),f323(f166(x70471),x70474)))
% 179.72/179.59 [7054]~P38(x70541,x70542)+P101(f323(f323(f325(x70541),f731(x70542,x70541,x70543)),x70543))+~P101(f323(f323(f325(x70541),x70544),x70543))
% 179.72/179.59 [7110]~P72(x71101)+E(f323(f323(f323(f63(x71101,x71102,f78(x71101)),x71103),f2(x71101)),x71104),f323(f323(f6(x71102,x71101),x71103),x71104))+~P101(f323(f59(x71102),x71104))
% 179.72/179.59 [7112]~P68(x71121)+E(f323(f323(f323(f63(x71121,x71122,f79(x71121)),x71123),f76(x71121)),x71124),f323(f323(f9(x71122,x71121),x71123),x71124))+~P101(f323(f59(x71122),x71124))
% 179.72/179.59 [7140]P27(x71401,x71402,x71403,x71404)+~E(f323(f35(x71402),f323(f302(x71401,x71402,x71403),x71404)),f323(f35(x71401),x71404))+~P101(f323(f59(x71401),x71404))
% 179.72/179.59 [7323]~P72(x73231)+E(f323(f323(f78(x73231),f323(x73232,x73233)),f323(f323(f6(a860,x73231),x73232),f296(a860,x73233,x73234))),f323(f323(f6(a860,x73231),x73232),f294(a860,x73233,x73234)))+~P101(f323(f323(f237(a860),x73233),x73234))
% 179.72/179.59 [7333]~P72(x73331)+~P27(x73332,x73331,x73333,x73334)+E(f323(f323(f6(x73331,x73331),f32(x73331)),f323(f302(x73332,x73331,x73333),x73334)),f323(f323(f6(x73332,x73331),x73333),x73334))
% 179.72/179.59 [7334]~P68(x73341)+~P27(x73342,x73341,x73343,x73344)+E(f323(f323(f9(x73341,x73341),f32(x73341)),f323(f302(x73342,x73341,x73343),x73344)),f323(f323(f9(x73342,x73341),x73343),x73344))
% 179.72/179.59 [7387]E(f323(f35(f865(x73871,x73872)),f310(x73871,x73872,x73873,x73874)),f323(f323(f78(a860),f323(f35(x73871),x73873)),f323(f35(x73872),x73874)))+~P101(f323(f59(x73872),x73874))+~P101(f323(f59(x73871),x73873))
% 179.72/179.59 [7472]E(x74721,x74722)+P101(f323(f323(f325(x74723),x74721),f323(f166(x74723),f164(x74723,x74722,x74724))))+~P101(f323(f323(f325(x74723),x74721),f323(f166(x74723),x74724)))
% 179.72/179.59 [7697]~P72(x76971)+E(f323(f323(f78(x76971),f323(f323(f6(a860,x76971),x76972),f323(f293(a860,x76973),x76974))),f323(x76972,x76974)),f323(f323(f6(a860,x76971),x76972),f323(f293(a860,x76973),f323(a112,x76974))))+P101(f323(f323(f238(a860),x76974),x76973))
% 179.72/179.59 [7748]~P27(x77481,x77482,x77483,f246(f867(x77481,a855)))+~P101(f323(f59(x77482),x77484))+P101(f323(f59(x77481),f323(f303(x77481,x77482,x77483),x77484)))
% 179.72/179.59 [7864]P101(f323(f323(f325(f861(x78641)),f323(f323(f144(x78641),x78642),x78643)),f154(x78641,x78644)))+~P101(f323(f323(f325(f861(x78641)),x78643),f154(x78641,x78644)))+~P101(f323(f323(f325(x78641),x78642),x78644))
% 179.72/179.59 [7953]~E(f323(f302(x79533,x79531,x79534),f246(f867(x79533,a855))),f246(f867(x79531,a855)))+P101(f323(f59(x79531),x79532))+~P101(f323(f59(x79533),f323(f303(x79533,x79531,x79534),x79532)))
% 179.72/179.59 [8043]~P27(x80431,x80433,x80434,x80432)+P101(f323(f59(x80431),x80432))+~P101(f323(f59(x80433),f323(f302(x80431,x80433,x80434),x80432)))
% 179.72/179.59 [8064]~E(x80642,x80643)+P101(f323(f323(f325(f866(x80641,x80641)),f323(f323(f258(x80641,x80641),x80642),x80643)),f255(x80641,x80644)))+~P101(f323(f323(f325(x80641),x80642),x80644))
% 179.72/179.59 [8100]~P72(x81001)+E(f323(f323(f78(x81001),f323(f323(f6(a860,x81001),x81002),f294(a860,x81003,x81004))),f323(x81002,f323(a112,x81004))),f323(f323(f6(a860,x81001),x81002),f294(a860,x81003,f323(a112,x81004))))+P101(f323(f323(f238(a860),f323(a112,x81004)),x81003))
% 179.72/179.59 [8163]P101(f323(x81631,x81632))+~P101(f323(x81631,f323(f323(f158(x81633),x81634),f536(x81631,x81634,x81633))))+~P101(f323(f323(f325(x81633),x81632),f323(f166(x81633),x81634)))
% 179.72/179.59 [8306]~P101(f323(f323(f325(x83061),x83062),f312(x83061,x83064)))+P101(f323(f323(f325(f861(x83061)),f323(f323(f144(x83061),x83062),x83063)),f312(f861(x83061),f150(x83061,x83064))))+~P101(f323(f323(f325(f861(x83061)),x83063),f312(f861(x83061),f150(x83061,x83064))))
% 179.72/179.59 [8321]~P27(x83212,x83213,x83214,f669(x83214,x83213,x83212,x83211))+P27(x83212,x83213,x83214,f38(f867(x83212,a855),x83211))+E(x83211,f188(f867(f867(x83212,a855),a855)))
% 179.72/179.59 [8587]E(x85871,x85872)+~P101(f323(f323(f325(f866(x85873,x85873)),f323(f323(f258(x85873,x85873),x85871),x85872)),f299(x85873,x85874)))+P101(f323(f323(f325(x85873),x85871),f323(f256(x85873,x85873),x85874)))
% 179.72/179.59 [8869]E(x88691,f2(a860))+P101(f323(x88692,x88693))+P101(f323(f323(f325(x88694),f799(x88692,x88693,x88691,x88694)),f323(f166(x88694),f163(x88694,x88691,x88693))))
% 179.72/179.59 [8879]E(x88791,f2(a860))+~P101(f323(x88793,x88794))+P101(f323(f323(f325(x88792),f797(x88793,x88794,x88791,x88792)),f323(f166(x88792),f163(x88792,x88791,x88794))))
% 179.72/179.59 [8881]~P28(x88811,x88812,x88813,f246(f867(x88811,a855)),f246(f867(x88812,a855)))+~P101(f323(f59(x88812),x88814))+P101(f323(f59(x88811),f323(f303(x88811,x88812,x88813),x88814)))
% 179.72/179.59 [8885]P27(x88852,x88853,x88854,f38(f867(x88852,a855),x88851))+E(x88851,f188(f867(f867(x88852,a855),a855)))+P101(f323(f323(f325(f867(x88852,a855)),f669(x88854,x88853,x88852,x88851)),x88851))
% 179.72/179.59 [8996]~P28(x89963,x89961,x89964,f246(f867(x89963,a855)),f246(f867(x89961,a855)))+P101(f323(f59(x89961),x89962))+~P101(f323(f59(x89963),f323(f303(x89963,x89961,x89964),x89962)))
% 179.72/179.59 [9014]P101(f323(f59(x90141),x90142))+~P101(f323(f59(x90144),f323(f302(x90141,x90144,x90143),x90142)))+P101(f323(f323(f325(x90141),f351(x90143,x90144,x90142,x90141)),x90142))
% 179.72/179.59 [9108]~P6(x91082)+E(f323(f323(f62(x91081,x91082,f323(f323(f8(x91082,f867(x91082,x91082),x91081),f110(x91082)),x91083)),f188(x91082)),x91084),f323(f323(f39(x91081,x91082),x91084),x91083))+~P101(f323(f59(x91081),x91084))
% 179.72/179.59 [9109]~P6(x91092)+E(f323(f323(f62(x91091,x91092,f323(f323(f8(x91092,f867(x91092,x91092),x91091),f101(x91092)),x91093)),f246(x91092)),x91094),f323(f323(f40(x91091,x91092),x91094),x91093))+~P101(f323(f59(x91091),x91094))
% 179.72/179.59 [9192]P101(f323(x91921,x91922))+~P101(f323(x91921,f323(f323(f158(x91923),x91924),f558(x91922,x91921,x91924,x91923))))+~P101(f323(f323(f325(x91923),x91922),f323(f166(x91923),x91924)))
% 179.72/179.59 [9212]E(x92121,x92122)+~P101(f323(f323(f325(f866(x92123,x92123)),f323(f323(f258(x92123,x92123),x92121),x92122)),f299(x92123,x92124)))+P101(f323(f323(f325(f866(x92123,x92123)),f323(f323(f258(x92123,x92123),x92121),x92122)),f323(f323(f280(x92123,x92123,x92123),x92124),f299(x92123,x92124))))
% 179.72/179.59 [9259]~E(f323(f189(f861(x92591)),x92592),f323(f189(f861(x92591)),x92593))+~P101(f323(f323(f325(f866(f861(x92591),f861(x92591))),f323(f323(f258(f861(x92591),f861(x92591)),x92592),x92593)),f140(x92591,x92594)))+P101(f323(f323(f325(f866(f861(x92591),f861(x92591))),f323(f323(f258(f861(x92591),f861(x92591)),x92592),x92593)),f138(x92591,x92594)))
% 179.72/179.59 [9490]P32(x94901,f323(f323(f18(x94901,a855,a855),f323(f323(f8(a855,f867(a855,a855),x94901),a322),f323(f323(f8(a855,a855,x94901),a318),x94902))),f323(a320,x94903)),x94904)+~P101(f323(x94902,x94903))+~P36(x94901,x94902,f323(f323(f144(x94901),x94903),x94904))
% 179.72/179.59 [9655]~P32(x96551,f323(f323(f18(x96551,a855,a855),f323(f323(f8(a855,f867(a855,a855),x96551),a322),f323(f323(f8(a855,a855,x96551),a318),x96552))),f323(a320,x96553)),x96554)+~P101(f323(x96552,x96553))+P36(x96551,x96552,f323(f323(f144(x96551),x96553),x96554))
% 179.72/179.59 [9659]~P36(x96591,x96592,x96594)+~P32(x96591,f323(f323(f18(x96591,a855,a855),f323(f323(f8(a855,f867(a855,a855),x96591),a322),f323(f323(f8(a855,a855,x96591),a318),x96592))),f323(a320,x96593)),x96594)+P36(x96591,x96592,f323(f323(f144(x96591),x96593),x96594))
% 179.72/179.59 [9696]~P60(x96961)+E(f323(f323(f6(a860,x96961),f323(f323(f18(a860,x96961,x96961),f323(f323(f8(x96961,f867(x96961,x96961),a860),f22(x96961)),x96962)),f323(f323(f8(a860,x96961,a860),x96962),f323(f323(f7(a860,a860,a860),f78(a860)),f76(a860))))),f294(a860,x96963,x96964)),f2(x96961))+P101(f323(f323(f237(a860),x96963),x96964))
% 179.72/179.59 [9937]~P38(x99372,x99374)+~P27(x99372,x99371,x99373,f246(f867(x99372,a855)))+P38(x99371,f323(f302(f866(x99372,x99372),f866(x99371,x99371),f263(x99372,x99371,x99372,x99371,x99373,x99373)),x99374))
% 179.72/179.59 [10099]~E(f323(f189(f861(x100991)),x100993),f323(f189(f861(x100991)),x100992))+P101(f323(f323(f325(f866(f861(x100991),f861(x100991))),f323(f323(f258(f861(x100991),f861(x100991)),x100992),x100993)),f151(x100991,x100994)))+~P101(f323(f323(f262(x100991,x100991,a855),f323(f323(f7(x100991,f867(f866(x100991,x100991),a855),f867(x100991,a855)),f323(f323(f8(f867(x100991,f867(f867(f866(x100991,x100991),a855),a855)),f867(f867(f866(x100991,x100991),a855),f867(x100991,a855)),x100991),f7(x100991,f867(f866(x100991,x100991),a855),a855)),f323(f323(f8(f867(x100991,f866(x100991,x100991)),f867(x100991,f867(f867(f866(x100991,x100991),a855),a855)),x100991),f323(f8(f866(x100991,x100991),f867(f867(f866(x100991,x100991),a855),a855),x100991),f325(f866(x100991,x100991)))),f258(x100991,x100991)))),x100994)),f575(x100994,x100993,x100992,x100991)))
% 179.72/179.59 [6043]~P57(x60431)+~E(x60432,f2(x60431))+E(f323(f323(f36(x60431),f323(f323(f79(x60431),x60432),x60433)),f323(f323(f79(x60431),x60432),x60434)),f2(x60431))
% 179.72/179.59 [6081]E(x60811,f113(x60812))+E(x60813,f323(f323(f22(a860),f323(f189(f861(x60812)),x60811)),f76(a860)))+E(f137(x60812,f323(f323(f152(x60812,x60811),x60813),x60814)),f137(x60812,x60811))
% 179.72/179.59 [6109]E(x61091,x61092)+P101(f323(x61093,x61092))+~P101(f323(f323(f323(f301(x61094),x61091),x61093),x61092))
% 179.72/179.59 [6125]~P72(x61251)+~P101(f323(f130(x61252),x61254))+E(f323(f159(x61251),f323(f323(f147(x61252,x61251),x61253),x61254)),f323(f323(f6(x61252,x61251),x61253),f323(f166(x61252),x61254)))
% 179.72/179.59 [6142]~P68(x61422)+~P101(f323(f59(x61421),x61424))+E(f323(f323(f9(x61421,x61422),f323(f16(x61422,x61421),x61423)),x61424),f323(f323(f248(x61422),x61423),f323(f35(x61421),x61424)))
% 179.72/179.59 [6197]~P62(x61972)+E(x61971,f2(x61972))+E(f323(f323(f281(x61972),f323(f323(f79(x61972),x61973),x61971)),f323(f323(f79(x61972),x61974),x61971)),f323(f323(f281(x61972),x61973),x61974))
% 179.72/179.59 [6198]~P62(x61982)+E(x61981,f2(x61982))+E(f323(f323(f281(x61982),f323(f323(f79(x61982),x61981),x61983)),f323(f323(f79(x61982),x61981),x61984)),f323(f323(f281(x61982),x61983),x61984))
% 179.72/179.59 [6199]~P57(x61992)+E(x61991,f2(x61992))+E(f323(f323(f36(x61992),f323(f323(f79(x61992),x61993),x61991)),f323(f323(f79(x61992),x61994),x61991)),f323(f323(f36(x61992),x61993),x61994))
% 179.72/179.59 [6201]~P57(x62012)+E(x62011,f2(x62012))+E(f323(f323(f36(x62012),f323(f323(f79(x62012),x62011),x62013)),f323(f323(f79(x62012),x62011),x62014)),f323(f323(f36(x62012),x62013),x62014))
% 179.72/179.59 [6263]P101(f323(x62631,x62632))+~E(x62633,f323(f323(f78(a860),x62634),x62632))+~P101(f323(x62631,f323(f323(f22(a860),x62633),x62634)))
% 179.72/179.59 [6345]~P101(f323(x63452,x63453))+~P101(f323(f153(x63451,x63452),x63454))+P101(f323(f153(x63451,x63452),f323(f323(f144(x63451),x63453),x63454)))
% 179.72/179.59 [6385]E(x63851,f113(x63852))+~E(x63853,f323(f323(f22(a860),f323(f189(f861(x63852)),x63851)),f76(a860)))+E(f137(x63852,f323(f323(f152(x63852,x63851),x63853),x63854)),x63854)
% 179.72/179.59 [6408]~P97(x64081)+~P101(f323(f323(f237(x64081),x64082),x64084))+P101(f323(f323(f237(x64081),x64082),f323(f323(f110(x64081),x64083),x64084)))
% 179.72/179.59 [6409]~P97(x64091)+~P101(f323(f323(f237(x64091),x64092),x64093))+P101(f323(f323(f237(x64091),x64092),f323(f323(f110(x64091),x64093),x64094)))
% 179.72/179.59 [6411]~P103(x64111)+~P101(f323(f323(f237(x64111),x64112),x64114))+P101(f323(f323(f237(x64111),x64112),f323(f323(f236(x64111),x64113),x64114)))
% 179.72/179.59 [6413]~P103(x64131)+~P101(f323(f323(f237(x64131),x64132),x64133))+P101(f323(f323(f237(x64131),x64132),f323(f323(f236(x64131),x64133),x64134)))
% 179.72/179.59 [6414]~P97(x64141)+~P101(f323(f323(f238(x64141),x64142),x64144))+P101(f323(f323(f238(x64141),x64142),f323(f323(f110(x64141),x64143),x64144)))
% 179.72/179.59 [6415]~P97(x64151)+~P101(f323(f323(f238(x64151),x64152),x64153))+P101(f323(f323(f238(x64151),x64152),f323(f323(f110(x64151),x64153),x64154)))
% 179.72/179.59 [6417]~P103(x64171)+~P101(f323(f323(f238(x64171),x64172),x64174))+P101(f323(f323(f238(x64171),x64172),f323(f323(f236(x64171),x64173),x64174)))
% 179.72/179.59 [6419]~P103(x64191)+~P101(f323(f323(f238(x64191),x64192),x64193))+P101(f323(f323(f238(x64191),x64192),f323(f323(f236(x64191),x64193),x64194)))
% 179.72/179.59 [6505]~E(f323(f323(f158(x65051),x65052),x65053),x65054)+E(f323(f323(f152(x65051,x65052),x65053),x65054),x65052)+~P101(f323(f323(f238(a860),x65053),f323(f189(f861(x65051)),x65052)))
% 179.72/179.59 [6545]P101(f323(x65451,x65452))+~P101(f323(x65453,x65452))+~P101(f323(f323(f237(f867(x65454,a855)),x65453),x65451))
% 179.72/179.59 [6576]~E(f323(f323(f152(x65761,x65762),x65763),x65764),x65762)+E(f323(f323(f158(x65761),x65762),x65763),x65764)+~P101(f323(f323(f238(a860),x65763),f323(f189(f861(x65761)),x65762)))
% 179.72/179.59 [6591]~P101(f323(f153(x65911,x65912),x65914))+~P101(f323(f153(x65911,x65912),x65913))+P101(f323(f153(x65911,x65912),f323(f323(f121(x65911),x65913),x65914)))
% 179.72/179.59 [6695]E(x66951,f188(f867(x66952,a855)))+E(x66953,f188(f867(x66954,a855)))+~E(f323(f323(f260(x66954,x66952),x66953),f323(f16(f867(x66952,a855),x66954),x66951)),f188(f867(f866(x66954,x66952),a855)))
% 179.72/179.59 [6714]E(x67141,x67142)+P101(f323(f323(f325(x67143),x67141),x67144))+~P101(f323(f323(f325(x67143),x67141),f323(f323(f301(x67143),x67142),x67144)))
% 179.72/179.59 [6731]~P98(x67311)+P101(f323(f323(f237(x67311),x67312),x67313))+~P101(f323(f323(f237(x67311),x67312),f323(f323(f101(x67311),x67314),x67313)))
% 179.72/179.59 [6733]~P98(x67331)+P101(f323(f323(f237(x67331),x67332),x67333))+~P101(f323(f323(f237(x67331),x67332),f323(f323(f101(x67331),x67333),x67334)))
% 179.72/179.59 [6735]~P103(x67351)+P101(f323(f323(f237(x67351),x67352),x67353))+~P101(f323(f323(f237(x67351),x67352),f323(f323(f235(x67351),x67354),x67353)))
% 179.72/179.59 [6737]~P103(x67371)+P101(f323(f323(f237(x67371),x67372),x67373))+~P101(f323(f323(f237(x67371),x67372),f323(f323(f235(x67371),x67373),x67374)))
% 179.72/179.59 [6738]~P103(x67381)+P101(f323(f323(f238(x67381),x67382),x67383))+~P101(f323(f323(f238(x67381),x67382),f323(f323(f235(x67381),x67384),x67383)))
% 179.72/179.59 [6739]~P103(x67391)+P101(f323(f323(f238(x67391),x67392),x67393))+~P101(f323(f323(f238(x67391),x67392),f323(f323(f235(x67391),x67393),x67394)))
% 179.72/179.59 [6761]~E(f323(f323(f158(x67611),x67613),x67614),x67612)+P101(f323(f323(f325(x67611),x67612),f323(f166(x67611),x67613)))+~P101(f323(f323(f238(a860),x67614),f323(f189(f861(x67611)),x67613)))
% 179.72/179.59 [6773]~P103(x67731)+~P16(x67731,f323(f323(f144(x67731),x67732),f323(f323(f144(x67731),x67733),x67734)))+P101(f323(f323(f237(x67731),x67732),x67733))
% 179.72/179.59 [6912]~P32(x69122,x69121,x69123)+P101(f323(x69121,f323(f323(f158(x69122),x69123),x69124)))+~P101(f323(f323(f238(a860),x69124),f323(f189(f861(x69122)),x69123)))
% 179.72/179.59 [6931]E(x69311,f2(a1))+E(f323(f323(f36(a1),x69312),x69311),x69313)+~P101(f323(f46(x69312,x69311),f323(f323(f258(a1,a1),x69313),x69314)))
% 179.72/179.59 [6952]E(f42(a1,x69522,x69521),x69523)+E(x69521,f2(a1))+~P101(f323(f46(x69522,x69521),f323(f323(f258(a1,a1),x69524),x69523)))
% 179.72/179.59 [7071]P101(f323(f323(f325(x70711),x70712),x70713))+~P101(f323(f323(f325(x70711),x70712),x70714))+~P101(f323(f323(f238(f867(x70711,a855)),x70714),x70713))
% 179.72/179.59 [7072]P101(f323(f323(f325(x70721),x70722),x70723))+~P101(f323(f323(f325(x70721),x70722),x70724))+~P101(f323(f323(f237(f867(x70721,a855)),x70724),x70723))
% 179.72/179.59 [7180]P34(x71801,x71802,x71803)+~P101(f323(x71802,f323(f323(f158(x71801),x71803),x71804)))+~P101(f323(f323(f238(a860),x71804),f323(f189(f861(x71801)),x71803)))
% 179.72/179.59 [7289]~P104(x72892)+~P101(f323(f323(f238(f867(x72891,x72892)),x72893),x72894))+P101(f323(f323(f237(f867(x72891,x72892)),x72893),x72894))
% 179.72/179.59 [7375]~P26(x73751,x73752,x73754)+P26(x73751,x73752,f323(f323(f301(f859(x73751)),x73753),x73754))+~P26(x73751,x73752,f323(f323(f301(f859(x73751)),x73753),f188(f867(f859(x73751),a855))))
% 179.72/179.59 [7419]~P101(f323(f323(f325(x74191),x74192),x74194))+P101(f323(f323(f325(x74191),x74192),f37(f867(x74191,a855),x74193)))+~P101(f323(f323(f325(f867(x74191,a855)),x74194),x74193))
% 179.72/179.59 [7450]~P80(x74501)+~P101(f323(f323(f237(x74501),x74503),x74504))+P101(f323(f323(f237(x74501),f323(f323(f78(x74501),x74502),x74503)),f323(f323(f78(x74501),x74502),x74504)))
% 179.72/179.59 [7451]~P81(x74511)+~P101(f323(f323(f237(x74511),x74513),x74514))+P101(f323(f323(f237(x74511),f323(f323(f78(x74511),x74512),x74513)),f323(f323(f78(x74511),x74512),x74514)))
% 179.72/179.59 [7452]~P80(x74521)+~P101(f323(f323(f237(x74521),x74522),x74524))+P101(f323(f323(f237(x74521),f323(f323(f78(x74521),x74522),x74523)),f323(f323(f78(x74521),x74524),x74523)))
% 179.72/179.59 [7453]~P81(x74531)+~P101(f323(f323(f237(x74531),x74532),x74534))+P101(f323(f323(f237(x74531),f323(f323(f78(x74531),x74532),x74533)),f323(f323(f78(x74531),x74534),x74533)))
% 179.72/179.59 [7454]~P80(x74541)+~P101(f323(f323(f238(x74541),x74543),x74544))+P101(f323(f323(f238(x74541),f323(f323(f78(x74541),x74542),x74543)),f323(f323(f78(x74541),x74542),x74544)))
% 179.72/179.59 [7455]~P83(x74551)+~P101(f323(f323(f238(x74551),x74553),x74554))+P101(f323(f323(f238(x74551),f323(f323(f78(x74551),x74552),x74553)),f323(f323(f78(x74551),x74552),x74554)))
% 179.72/179.59 [7456]~P80(x74561)+~P101(f323(f323(f238(x74561),x74562),x74564))+P101(f323(f323(f238(x74561),f323(f323(f78(x74561),x74562),x74563)),f323(f323(f78(x74561),x74564),x74563)))
% 179.72/179.59 [7457]~P83(x74571)+~P101(f323(f323(f238(x74571),x74572),x74574))+P101(f323(f323(f238(x74571),f323(f323(f78(x74571),x74572),x74573)),f323(f323(f78(x74571),x74574),x74573)))
% 179.72/179.59 [7466]~P107(x74661)+~P91(x74661)+E(f323(f323(f22(x74661),f323(f323(f79(x74661),x74662),f323(f103(x74661),x74663))),f323(f323(f79(x74661),x74664),f323(f103(x74661),x74663))),f323(f323(f79(x74661),f323(f323(f22(x74661),x74662),x74664)),f323(f103(x74661),x74663)))
% 179.72/179.59 [7467]~P136(x74671)+~P91(x74671)+E(f323(f323(f78(x74671),f323(f323(f79(x74671),x74672),f323(f103(x74671),x74673))),f323(f323(f79(x74671),x74674),f323(f103(x74671),x74673))),f323(f323(f79(x74671),f323(f323(f78(x74671),x74672),x74674)),f323(f103(x74671),x74673)))
% 179.72/179.59 [7502]~P72(x75021)+E(f323(f323(f78(x75021),f323(x75022,x75023)),f323(f323(f6(a860,x75021),x75022),f294(a860,f323(a112,x75023),x75024))),f323(f323(f6(a860,x75021),x75022),f294(a860,x75023,x75024)))+~P101(f323(f323(f237(a860),x75023),x75024))
% 179.72/179.59 [7513]~P27(x75132,x75131,x75133,f323(f166(x75132),x75134))+~P101(f323(f130(x75132),x75134))+P101(f323(f130(x75131),f323(f323(f147(x75132,x75131),x75133),x75134)))
% 179.72/179.59 [7560]~P101(f323(f323(f237(a860),x75602),x75604))+~P101(f323(f323(f237(a860),x75601),x75603))+P101(f323(f323(f237(a860),f323(f323(f79(a860),x75601),x75602)),f323(f323(f79(a860),x75603),x75604)))
% 179.72/179.59 [7561]~P101(f323(f323(f237(a860),x75612),x75614))+~P101(f323(f323(f237(a860),x75611),x75613))+P101(f323(f323(f237(a860),f323(f323(f78(a860),x75611),x75612)),f323(f323(f78(a860),x75613),x75614)))
% 179.72/179.59 [7564]~P101(f323(f323(f238(a860),x75642),x75644))+~P101(f323(f323(f238(a860),x75641),x75643))+P101(f323(f323(f238(a860),f323(f323(f78(a860),x75641),x75642)),f323(f323(f78(a860),x75643),x75644)))
% 179.72/179.59 [7565]~P101(f323(f323(f237(a1),x75652),x75654))+~P101(f323(f323(f238(a1),x75651),x75653))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x75651),x75652)),f323(f323(f78(a1),x75653),x75654)))
% 179.72/179.59 [7613]P101(f323(f323(f325(x76131),x76132),x76133))+~P101(f323(f323(f325(x76131),x76132),f38(f867(x76131,a855),x76134)))+~P101(f323(f323(f325(f867(x76131,a855)),x76133),x76134))
% 179.72/179.59 [7629]~P101(f323(x76291,f535(x76291,x76293,x76292)))+P101(f323(x76291,f323(f323(f158(x76292),x76293),x76294)))+~P101(f323(f323(f238(a860),x76294),f323(f189(f861(x76292)),x76293)))
% 179.72/179.59 [7634]P101(f323(x76341,x76342))+~P101(f323(f323(f325(x76344),x76342),f323(f166(x76344),x76343)))+P101(f323(f323(f238(a860),f536(x76341,x76343,x76344)),f323(f189(f861(x76344)),x76343)))
% 179.72/179.59 [7682]~P104(x76821)+~P101(f323(f323(f238(f867(x76822,x76821)),x76824),x76823))+~P101(f323(f323(f237(f867(x76822,x76821)),x76823),x76824))
% 179.72/179.59 [7727]~P101(f323(x77274,x77272))+~P101(f323(f323(f325(x77271),x77272),x77273))+P101(f323(f323(f325(x77271),x77272),f323(f323(f101(f867(x77271,a855)),x77273),f323(f243(x77271),x77274))))
% 179.72/179.59 [7873]~P101(f323(f323(f325(x78731),x78733),x78734))+~P101(f323(f323(f238(f867(x78731,a855)),x78732),x78734))+P101(f323(f323(f238(f867(x78731,a855)),x78732),f323(f323(f301(x78731),x78733),x78734)))
% 179.72/179.59 [7875]E(f323(f323(f101(f867(x78751,a855)),x78752),x78753),f188(f867(x78751,a855)))+~E(f323(f323(f101(f867(x78751,a855)),f37(f867(x78751,a855),x78754)),x78753),f188(f867(x78751,a855)))+~P101(f323(f323(f325(f867(x78751,a855)),x78752),x78754))
% 179.72/179.59 [7949]P101(f323(f323(f325(x79491),x79492),x79493))+~P101(f323(f323(f237(f867(x79491,a855)),x79493),f323(f323(f301(x79491),x79492),x79494)))+P101(f323(f323(f237(f867(x79491,a855)),x79493),x79494))
% 179.72/179.59 [7966]P101(f323(f323(f325(x79662),f535(x79661,x79663,x79662)),f323(f166(x79662),x79663)))+P101(f323(x79661,f323(f323(f158(x79662),x79663),x79664)))+~P101(f323(f323(f238(a860),x79664),f323(f189(f861(x79662)),x79663)))
% 179.72/179.59 [7974]~P101(f323(f323(f237(f867(x79741,a855)),x79742),x79744))+P101(f323(f323(f237(f867(x79741,a855)),x79742),x79743))+~P101(f323(f323(f237(f867(x79741,a855)),x79744),x79743))
% 179.72/179.59 [7975]~P101(f323(f323(f238(f867(x79751,a855)),x79752),x79754))+~P101(f323(f323(f237(f867(x79751,a855)),x79754),x79753))+P101(f323(f323(f238(f867(x79751,a855)),x79752),x79753))
% 179.72/179.59 [7976]~P101(f323(f323(f237(f867(x79761,a855)),x79762),x79764))+~P101(f323(f323(f238(f867(x79761,a855)),x79764),x79763))+P101(f323(f323(f238(f867(x79761,a855)),x79762),x79763))
% 179.72/179.59 [7977]~P101(f323(f323(f238(f867(x79771,a855)),x79772),x79774))+P101(f323(f323(f238(f867(x79771,a855)),x79772),x79773))+~P101(f323(f323(f238(f867(x79771,a855)),x79774),x79773))
% 179.72/179.59 [8018]~P101(f323(f323(f325(x80181),x80184),x80183))+~P101(f323(f323(f238(f867(x80181,a855)),x80182),f323(f323(f301(x80181),x80184),x80183)))+P101(f323(f323(f238(f867(x80181,a855)),x80182),x80183))
% 179.72/179.59 [8029]~P80(x80291)+P101(f323(f323(f237(x80291),x80292),x80293))+~P101(f323(f323(f237(x80291),f323(f323(f78(x80291),x80294),x80292)),f323(f323(f78(x80291),x80294),x80293)))
% 179.72/179.59 [8031]~P80(x80311)+P101(f323(f323(f237(x80311),x80312),x80313))+~P101(f323(f323(f237(x80311),f323(f323(f78(x80311),x80312),x80314)),f323(f323(f78(x80311),x80313),x80314)))
% 179.72/179.59 [8033]~P80(x80331)+P101(f323(f323(f238(x80331),x80332),x80333))+~P101(f323(f323(f238(x80331),f323(f323(f78(x80331),x80334),x80332)),f323(f323(f78(x80331),x80334),x80333)))
% 179.72/179.59 [8035]~P80(x80351)+P101(f323(f323(f238(x80351),x80352),x80353))+~P101(f323(f323(f238(x80351),f323(f323(f78(x80351),x80352),x80354)),f323(f323(f78(x80351),x80353),x80354)))
% 179.72/179.59 [8081]P101(f323(x80811,x80812))+~E(f323(f323(f131(x80813),f323(f189(f861(x80813)),f171(x80813,x80811,x80814))),x80814),f113(x80813))+~P101(f323(f323(f325(x80813),x80812),f323(f166(x80813),x80814)))
% 179.72/179.59 [8206]P101(f323(x82061,x82062))+~P101(f323(f323(f325(x82063),x82062),f323(f166(x82063),x82064)))+P101(f323(f323(f238(a860),f323(f189(f861(x82063)),f323(f129(x82063,x82061),x82064))),f323(f189(f861(x82063)),x82064)))
% 179.72/179.59 [8694]~P101(f323(x86941,f714(x86941,x86943,x86942,x86944)))+P101(f323(x86941,f323(f323(f158(x86942),x86943),x86944)))+~P101(f323(f323(f238(a860),x86944),f323(f189(f861(x86942)),x86943)))
% 179.72/179.59 [8718]~P27(x87184,x87183,x87181,f246(f867(x87184,a855)))+E(f323(x87181,f516(x87182,x87181,x87183,x87184)),x87182)+~P101(f323(f323(f325(x87183),x87182),f323(f302(x87184,x87183,x87181),f246(f867(x87184,a855)))))
% 179.72/179.59 [8787]E(f171(x87871,x87872,x87873),f323(f323(f169(x87871),x87874),x87873))+P101(f323(f323(f238(a860),f630(x87872,x87873,x87871,x87874)),x87874))+P101(f323(f323(f238(a860),x87874),f323(f189(f861(x87871)),x87873)))
% 179.72/179.59 [8790]E(f171(x87901,x87902,x87903),f323(f323(f169(x87901),x87904),x87903))+P101(f323(f323(f238(a860),f630(x87902,x87903,x87901,x87904)),x87904))+P101(f323(x87902,f323(f323(f158(x87901),x87903),x87904)))
% 179.72/179.59 [8819]P101(f323(x88191,x88192))+~P101(f323(f323(f325(x88194),x88192),f323(f166(x88194),x88193)))+P101(f323(f323(f238(a860),f558(x88192,x88191,x88193,x88194)),f323(f189(f861(x88194)),x88193)))
% 179.72/179.59 [8821]E(f171(x88211,x88212,x88213),f323(f323(f169(x88211),x88214),x88213))+P101(f323(f323(f238(a860),x88214),f323(f189(f861(x88211)),x88213)))+P101(f323(f323(f238(a860),f630(x88212,x88213,x88211,x88214)),f323(f189(f861(x88211)),x88213)))
% 179.72/179.59 [8828]E(f171(x88281,x88282,x88283),f323(f323(f169(x88281),x88284),x88283))+P101(f323(x88282,f323(f323(f158(x88281),x88283),x88284)))+P101(f323(f323(f238(a860),f630(x88282,x88283,x88281,x88284)),f323(f189(f861(x88281)),x88283)))
% 179.72/179.59 [8854]~P119(x88544)+P101(f323(f323(f325(x88541),f778(x88542,x88543,x88541,x88544)),x88543))+P101(f323(f323(f238(x88544),f2(x88544)),f323(f323(f9(x88541,x88544),x88542),x88543)))
% 179.72/179.59 [8855]~P119(x88554)+P101(f323(f323(f325(x88551),f784(x88552,x88553,x88551,x88554)),x88553))+P101(f323(f323(f237(x88554),f2(x88554)),f323(f323(f9(x88551,x88554),x88552),x88553)))
% 179.72/179.59 [8887]~P101(f323(f59(x88871),x88874))+P101(f323(f323(f325(x88871),f614(x88872,x88873,x88874,x88871)),x88874))+P101(f323(f59(f866(x88871,x88873)),f323(f323(f260(x88871,x88873),x88874),x88872)))
% 179.72/179.59 [8915]P101(f323(f323(f325(x89152),f714(x89151,x89153,x89152,x89154)),f323(f166(x89152),x89153)))+P101(f323(x89151,f323(f323(f158(x89152),x89153),x89154)))+~P101(f323(f323(f238(a860),x89154),f323(f189(f861(x89152)),x89153)))
% 179.72/179.59 [9047]P101(f323(f323(f237(a860),x90474),f323(f189(f861(x90472)),f171(x90472,x90473,x90471))))+P101(f323(f323(f238(a860),f632(x90471,x90472,x90473,x90474)),x90474))+~P101(f323(f323(f237(a860),x90474),f323(f189(f861(x90472)),x90471)))
% 179.72/179.59 [9151]~E(f323(f323(f179(x91511,x91512),x91513),f683(x91514,x91513,x91512,x91511)),f323(f323(f179(x91511,x91512),x91514),f683(x91514,x91513,x91512,x91511)))+E(f323(f179(x91511,x91512),x91513),f323(f179(x91511,x91512),x91514))+~E(f323(f166(x91511),f323(f323(f147(f866(x91511,x91512),x91511),f257(x91511,x91512)),x91513)),f323(f166(x91511),f323(f323(f147(f866(x91511,x91512),x91511),f257(x91511,x91512)),x91514)))
% 179.72/179.59 [9195]E(f171(x91951,x91952,x91953),f323(f323(f169(x91951),x91954),x91953))+~P101(f323(x91952,f323(f323(f158(x91951),x91953),f630(x91952,x91953,x91951,x91954))))+P101(f323(f323(f238(a860),x91954),f323(f189(f861(x91951)),x91953)))
% 179.72/179.59 [9199]E(f171(x91991,x91992,x91993),f323(f323(f169(x91991),x91994),x91993))+~P101(f323(x91992,f323(f323(f158(x91991),x91993),f630(x91992,x91993,x91991,x91994))))+P101(f323(x91992,f323(f323(f158(x91991),x91993),x91994)))
% 179.72/179.59 [9206]~P101(f323(f59(x92061),x92063))+~P101(f323(f59(x92062),f323(x92064,f614(x92064,x92062,x92063,x92061))))+P101(f323(f59(f866(x92061,x92062)),f323(f323(f260(x92061,x92062),x92063),x92064)))
% 179.72/179.59 [9214]~P119(x92141)+~P101(f323(f323(f237(x92141),f2(x92141)),f323(x92143,f784(x92143,x92144,x92142,x92141))))+P101(f323(f323(f237(x92141),f2(x92141)),f323(f323(f9(x92142,x92141),x92143),x92144)))
% 179.72/179.59 [9215]~P119(x92151)+~P101(f323(f323(f238(x92151),f2(x92151)),f323(x92153,f778(x92153,x92154,x92152,x92151))))+P101(f323(f323(f238(x92151),f2(x92151)),f323(f323(f9(x92152,x92151),x92153),x92154)))
% 179.72/179.59 [9223]~E(f323(f189(f861(x92234)),x92232),f323(f189(f861(x92234)),x92233))+P101(f323(f323(f325(f866(f861(x92234),f861(x92234))),f323(f323(f258(f861(x92234),f861(x92234)),x92233),x92232)),f151(x92234,x92231)))+P101(f323(f323(f238(a860),f569(x92231,x92232,x92233,x92234)),f323(f189(f861(x92234)),x92233)))
% 179.72/179.59 [9273]~P101(f323(x92733,f323(f323(f158(x92732),x92734),f632(x92734,x92732,x92733,x92731))))+P101(f323(f323(f237(a860),x92731),f323(f189(f861(x92732)),f171(x92732,x92733,x92734))))+~P101(f323(f323(f237(a860),x92731),f323(f189(f861(x92732)),x92734)))
% 179.72/179.59 [9350]E(f323(f323(f169(x93501),f586(x93502,x93503,x93504,x93501)),x93503),f323(f323(f169(x93501),f586(x93502,x93503,x93504,x93501)),x93504))+~P101(f323(f323(f325(f866(f861(x93501),f861(x93501))),f323(f323(f258(f861(x93501),f861(x93501)),x93504),x93503)),f140(x93501,x93502)))+P101(f323(f323(f238(a860),f323(f189(f861(x93501)),x93504)),f323(f189(f861(x93501)),x93503)))
% 179.72/179.59 [9403]~P101(f323(f323(f238(a860),f2(a860)),x94033))+~P101(f323(f323(f238(a860),x94034),x94031))+P101(f323(f323(f238(a860),f323(f323(f78(a860),f323(f323(f79(a860),x94031),f42(a860,x94032,x94033))),x94034)),f323(f323(f79(a860),x94031),x94033)))
% 179.72/179.59 [9598]~P104(x95982)+~P101(f323(f323(f237(x95982),f323(x95983,f485(x95984,x95983,x95981,x95982))),f323(x95984,f485(x95984,x95983,x95981,x95982))))+P101(f323(f323(f237(f867(x95981,x95982)),x95983),x95984))
% 179.72/179.59 [9703]~P60(x97031)+E(f323(f323(f6(a860,x97031),f323(f323(f18(a860,x97031,x97031),f323(f323(f8(x97031,f867(x97031,x97031),a860),f22(x97031)),x97032)),f323(f323(f8(a860,x97031,a860),x97032),f323(f323(f7(a860,a860,a860),f78(a860)),f76(a860))))),f294(a860,x97033,x97034)),f323(f323(f22(x97031),f323(x97032,x97033)),f323(x97032,f323(f323(f78(a860),x97034),f76(a860)))))+~P101(f323(f323(f237(a860),x97033),x97034))
% 179.72/179.59 [6765]E(f323(f323(f121(x67651),x67652),x67653),x67654)+~E(x67653,f323(f323(f131(x67651),f323(f189(f861(x67651)),x67652)),x67654))+~E(f323(f323(f169(x67651),f323(f189(f861(x67651)),x67652)),x67654),x67652)
% 179.72/179.59 [6821]~P63(x68212)+E(x68211,f2(x68212))+E(f323(f323(f281(x68212),f323(f323(f248(x68212),x68213),x68214)),f323(f323(f248(x68212),x68211),x68214)),f323(f323(f248(x68212),f323(f323(f281(x68212),x68213),x68211)),x68214))
% 179.72/179.59 [6954]~E(f323(f189(f861(x69541)),x69543),f323(f189(f861(x69542)),x69544))+~P101(f323(f130(x69541),x69543))+E(f177(x69541,x69542,f323(f179(x69541,x69542),f323(f323(f175(x69541,x69542),x69543),x69544))),f323(f166(x69541),x69543))
% 179.72/179.59 [6971]~P98(x69711)+~P101(f323(f323(f237(x69711),x69713),x69714))+P101(f323(f323(f237(x69711),f323(f323(f101(x69711),x69712),x69713)),x69714))
% 179.72/179.59 [6972]~P98(x69721)+~P101(f323(f323(f237(x69721),x69722),x69724))+P101(f323(f323(f237(x69721),f323(f323(f101(x69721),x69722),x69723)),x69724))
% 179.72/179.59 [6974]~P103(x69741)+~P101(f323(f323(f237(x69741),x69743),x69744))+P101(f323(f323(f237(x69741),f323(f323(f235(x69741),x69742),x69743)),x69744))
% 179.72/179.59 [6976]~P103(x69761)+~P101(f323(f323(f237(x69761),x69762),x69764))+P101(f323(f323(f237(x69761),f323(f323(f235(x69761),x69762),x69763)),x69764))
% 179.72/179.59 [6977]~P98(x69771)+~P101(f323(f323(f238(x69771),x69773),x69774))+P101(f323(f323(f238(x69771),f323(f323(f101(x69771),x69772),x69773)),x69774))
% 179.72/179.59 [6978]~P98(x69781)+~P101(f323(f323(f238(x69781),x69782),x69784))+P101(f323(f323(f238(x69781),f323(f323(f101(x69781),x69782),x69783)),x69784))
% 179.72/179.59 [6980]~P103(x69801)+~P101(f323(f323(f238(x69801),x69803),x69804))+P101(f323(f323(f238(x69801),f323(f323(f235(x69801),x69802),x69803)),x69804))
% 179.72/179.59 [6982]~P103(x69821)+~P101(f323(f323(f238(x69821),x69822),x69824))+P101(f323(f323(f238(x69821),f323(f323(f235(x69821),x69822),x69823)),x69824))
% 179.72/179.59 [7002]~P101(f323(x70023,x70024))+~P101(f323(x70022,x70024))+P101(f323(f323(f323(f101(f867(x70021,a855)),x70022),x70023),x70024))
% 179.72/179.59 [7126]P26(x71261,x71262,x71263)+~P26(x71261,x71264,x71263)+~P101(f323(f323(f237(f867(f859(x71261),a855)),x71264),x71262))
% 179.72/179.59 [7127]P26(x71271,x71272,x71273)+~P26(x71271,x71272,x71274)+~P101(f323(f323(f237(f867(f859(x71271),a855)),x71273),x71274))
% 179.72/179.59 [7492]~P72(x74921)+E(f323(f323(f78(x74921),f323(x74922,x74923)),f323(f323(f6(a860,x74921),x74922),f323(f293(a860,f323(a112,x74923)),x74924))),f323(f323(f6(a860,x74921),x74922),f323(f293(a860,x74923),x74924)))+~P101(f323(f323(f238(a860),x74923),x74924))
% 179.72/179.59 [7521]~P97(x75211)+P101(f323(f323(f237(x75211),x75212),x75213))+~P101(f323(f323(f237(x75211),f323(f323(f110(x75211),x75214),x75212)),x75213))
% 179.72/179.59 [7523]~P97(x75231)+P101(f323(f323(f237(x75231),x75232),x75233))+~P101(f323(f323(f237(x75231),f323(f323(f110(x75231),x75232),x75234)),x75233))
% 179.72/179.59 [7525]~P103(x75251)+P101(f323(f323(f237(x75251),x75252),x75253))+~P101(f323(f323(f237(x75251),f323(f323(f236(x75251),x75254),x75252)),x75253))
% 179.72/179.59 [7527]~P103(x75271)+P101(f323(f323(f237(x75271),x75272),x75273))+~P101(f323(f323(f237(x75271),f323(f323(f236(x75271),x75272),x75274)),x75273))
% 179.72/179.59 [7528]~P103(x75281)+P101(f323(f323(f238(x75281),x75282),x75283))+~P101(f323(f323(f238(x75281),f323(f323(f236(x75281),x75284),x75282)),x75283))
% 179.72/179.59 [7529]~P103(x75291)+P101(f323(f323(f238(x75291),x75292),x75293))+~P101(f323(f323(f238(x75291),f323(f323(f236(x75291),x75292),x75294)),x75293))
% 179.72/179.59 [7605]~P101(f323(f323(f325(x76051),x76052),x76054))+P101(f323(f323(f325(x76051),x76052),x76053))+P101(f323(f323(f325(x76051),x76052),f323(f323(f22(f867(x76051,a855)),x76054),x76053)))
% 179.72/179.59 [7689]P101(f323(x76891,x76892))+P101(f323(x76893,x76892))+~P101(f323(f323(f323(f110(f867(x76894,a855)),x76893),x76891),x76892))
% 179.72/179.59 [7700]~P101(f323(f323(f325(x77001),x77002),x77004))+~P101(f323(f323(f325(x77001),x77002),x77003))+P101(f323(f323(f325(x77001),x77002),f323(f323(f101(f867(x77001,a855)),x77003),x77004)))
% 179.72/179.59 [7749]~P97(x77491)+~P101(f323(f59(x77491),x77494))+E(f323(f323(f62(x77491,x77491,f110(x77491)),x77492),f323(f323(f301(x77491),x77493),x77494)),f323(f323(f110(x77491),x77493),f323(f323(f62(x77491,x77491,f110(x77491)),x77492),x77494)))
% 179.72/179.59 [7750]~P98(x77501)+~P101(f323(f59(x77501),x77504))+E(f323(f323(f62(x77501,x77501,f101(x77501)),x77502),f323(f323(f301(x77501),x77503),x77504)),f323(f323(f101(x77501),x77503),f323(f323(f62(x77501,x77501,f101(x77501)),x77502),x77504)))
% 179.72/179.59 [7751]~P103(x77511)+~P101(f323(f59(x77511),x77514))+E(f323(f323(f62(x77511,x77511,f235(x77511)),x77512),f323(f323(f301(x77511),x77513),x77514)),f323(f323(f235(x77511),x77513),f323(f323(f62(x77511,x77511,f235(x77511)),x77512),x77514)))
% 179.72/179.59 [7752]~P103(x77521)+~P101(f323(f59(x77521),x77524))+E(f323(f323(f62(x77521,x77521,f236(x77521)),x77522),f323(f323(f301(x77521),x77523),x77524)),f323(f323(f236(x77521),x77523),f323(f323(f62(x77521,x77521,f236(x77521)),x77522),x77524)))
% 179.72/179.59 [7753]~P107(x77531)+~P91(x77531)+E(f323(f323(f22(x77531),f323(f323(f79(x77531),f323(f103(x77531),x77532)),x77533)),f323(f323(f79(x77531),f323(f103(x77531),x77532)),x77534)),f323(f323(f79(x77531),f323(f103(x77531),x77532)),f323(f323(f22(x77531),x77533),x77534)))
% 179.72/179.59 [7754]~P136(x77541)+~P91(x77541)+E(f323(f323(f78(x77541),f323(f323(f79(x77541),f323(f103(x77541),x77542)),x77543)),f323(f323(f79(x77541),f323(f103(x77541),x77542)),x77544)),f323(f323(f79(x77541),f323(f103(x77541),x77542)),f323(f323(f78(x77541),x77543),x77544)))
% 179.72/179.59 [7871]E(x78711,x78712)+P101(f323(f323(f325(x78713),x78711),f323(f166(x78713),x78714)))+~P101(f323(f323(f325(x78713),x78711),f323(f166(x78713),f323(f323(f144(x78713),x78712),x78714))))
% 179.72/179.59 [7897]~P5(x78971)+~E(f323(f189(f861(x78972)),x78973),f323(f189(f861(x78971)),f53(x78971)))+E(f323(f323(f179(x78971,x78972),f323(f323(f175(x78971,x78972),f53(x78971)),x78973)),x78974),f323(f230(x78972),f542(x78974,x78973,x78972,x78971)))
% 179.72/179.59 [8041]P51(x80411,x80412,x80413)+~P51(x80411,x80412,x80414)+~P101(f323(f323(f237(f867(f866(x80411,x80412),a855)),x80413),x80414))
% 179.72/179.59 [8084]P101(f323(f323(f325(x80841),x80842),x80843))+P101(f323(f323(f325(x80841),x80842),x80844))+~P101(f323(f323(f325(x80841),x80842),f323(f323(f110(f867(x80841,a855)),x80844),x80843)))
% 179.72/179.59 [8094]~P40(x80941,x80944,x80943)+~P101(f323(f323(f325(x80941),x80942),x80944))+P101(f323(f323(f325(f866(x80941,x80941)),f323(f323(f258(x80941,x80941),x80942),x80942)),x80943))
% 179.72/179.59 [8109]~P101(f323(f59(x81092),x81094))+~P101(f323(f59(x81091),x81093))+P101(f323(f59(f866(x81091,x81092)),f323(f323(f260(x81091,x81092),x81093),f323(f16(f867(x81092,a855),x81091),x81094))))
% 179.72/179.59 [8110]~P101(f323(f323(f325(x81101),x81102),x81104))+~P101(f323(f323(f237(f867(x81101,a855)),x81103),x81104))+P101(f323(f323(f237(f867(x81101,a855)),f323(f323(f301(x81101),x81102),x81103)),x81104))
% 179.72/179.59 [8118]~P68(x81182)+~P140(x81182)+E(f323(f323(f9(x81181,x81182),f323(f323(f8(a860,x81182,x81181),f100(x81182)),x81183)),x81184),f323(f100(x81182),f323(f323(f9(x81181,a860),x81183),x81184)))
% 179.72/179.59 [8119]~P68(x81192)+~P134(x81192)+E(f323(f323(f9(x81191,x81192),f323(f323(f8(a1,x81192,x81191),f102(x81192)),x81193)),x81194),f323(f102(x81192),f323(f323(f9(x81191,a1),x81193),x81194)))
% 179.72/179.59 [8144]E(f323(f323(f22(f867(x81441,a855)),x81442),f323(f323(f22(f867(x81441,a855)),x81443),x81444)),x81444)+~P101(f323(f323(f237(f867(x81441,a855)),x81442),x81443))+~P101(f323(f323(f237(f867(x81441,a855)),x81444),x81442))
% 179.72/179.59 [8240]~P101(f323(f59(x82401),x82404))+E(f323(f323(f22(a860),f323(f323(f6(x82401,a860),x82402),x82403)),f323(f323(f6(x82401,a860),x82402),x82404)),f323(f323(f6(x82401,a860),x82402),f323(f323(f22(f867(x82401,a855)),x82403),x82404)))+~P101(f323(f323(f237(f867(x82401,a855)),x82404),x82403))
% 179.72/179.59 [8396]~P9(x83961,x83964,x83963)+~P101(f323(f323(f325(x83961),x83962),x83964))+P101(f323(f323(f325(x83961),x83962),f323(f277(x83961,x83961,x83963),f323(f323(f301(x83961),x83962),f188(f867(x83961,a855))))))
% 179.72/179.59 [8452]~P101(f323(f323(f237(f867(x84521,a855)),x84522),x84523))+~P101(f323(f323(f237(f867(x84521,a855)),x84522),x84524))+P101(f323(f323(f237(f867(x84521,a855)),x84522),f323(f323(f101(f867(x84521,a855)),x84523),x84524)))
% 179.72/179.59 [8554]E(x85541,f188(f867(x85542,a855)))+P101(f323(f59(x85543),x85544))+~P101(f323(f59(f866(x85543,x85542)),f323(f323(f260(x85543,x85542),x85544),f323(f16(f867(x85542,a855),x85543),x85541))))
% 179.72/179.59 [8555]E(x85551,f188(f867(x85552,a855)))+P101(f323(f59(x85553),x85554))+~P101(f323(f59(f866(x85552,x85553)),f323(f323(f260(x85552,x85553),x85551),f323(f16(f867(x85553,a855),x85552),x85554))))
% 179.72/179.59 [8629]P101(f323(f323(f325(x86291),x86292),f312(x86291,x86293)))+~P101(f323(f323(f325(x86291),x86294),f312(x86291,x86293)))+~P101(f323(f323(f325(f866(x86291,x86291)),f323(f323(f258(x86291,x86291),x86292),x86294)),x86293))
% 179.72/179.59 [8686]~P38(x86861,x86864)+P101(f323(f323(f325(f866(x86861,x86861)),f323(f323(f258(x86861,x86861),x86863),x86862)),f299(x86861,x86864)))+P38(x86861,f323(f323(f301(f866(x86861,x86861)),f323(f323(f258(x86861,x86861),x86862),x86863)),x86864))
% 179.72/179.59 [8687]~P54(x86871,x86874)+P101(f323(f323(f325(f866(x86871,x86871)),f323(f323(f258(x86871,x86871),x86873),x86872)),f299(x86871,x86874)))+P54(x86871,f323(f323(f301(f866(x86871,x86871)),f323(f323(f258(x86871,x86871),x86872),x86873)),x86874))
% 179.72/179.59 [8770]~E(x87702,x87703)+~P101(f323(f323(f325(x87701),x87702),f323(f166(x87701),x87704)))+P101(f323(f323(f325(f866(x87701,x87701)),f323(f323(f258(x87701,x87701),x87702),x87703)),f323(f166(f866(x87701,x87701)),f323(f323(f175(x87701,x87701),x87704),x87704))))
% 179.72/179.59 [8852]~E(x88523,x88524)+P101(f323(f323(f262(x88521,x88521,a855),a320),x88522))+~P101(f323(f323(f325(f866(x88521,x88521)),x88522),f323(f166(f866(x88521,x88521)),f323(f323(f175(x88521,x88521),x88523),x88524))))
% 179.72/179.59 [8902]P101(f323(f323(f325(f866(f861(x89021),f861(x89021))),f323(f323(f258(f861(x89021),f861(x89021)),x89022),x89023)),f140(x89021,x89024)))+~E(f323(f323(f169(x89021),f323(f189(f861(x89021)),x89022)),x89023),x89022)+~P101(f323(f323(f238(a860),f323(f189(f861(x89021)),x89022)),f323(f189(f861(x89021)),x89023)))
% 179.72/179.59 [8994]~P101(f323(f59(x89941),x89944))+P101(f323(f323(f325(x89941),f444(x89942,x89943,x89944,x89941)),x89944))+P101(f323(f59(x89943),f323(f323(f39(x89941,f867(x89943,a855)),x89944),x89942)))
% 179.72/179.59 [8995]~P101(f323(f59(x89951),x89954))+P101(f323(f323(f325(x89951),f456(x89952,x89953,x89954,x89951)),x89954))+P101(f323(f59(x89953),f323(f323(f39(x89951,f867(x89953,a855)),x89954),x89952)))
% 179.72/179.59 [9082]P101(f323(f323(f325(f866(x90821,x90821)),x90822),f323(f323(f280(x90821,x90821,x90821),x90823),f299(x90821,x90823))))+~P101(f323(f323(f238(a860),f2(a860)),x90824))+~P101(f323(f323(f325(f866(x90821,x90821)),x90822),f323(f323(f183(f866(x90821,x90821),a855),x90824),x90823)))
% 179.72/179.59 [9090]~P38(x90901,x90902)+~P101(f323(f323(f325(f866(x90901,x90901)),f323(f323(f258(x90901,x90901),x90904),x90903)),x90902))+~P101(f323(f323(f325(f866(x90901,x90901)),f323(f323(f258(x90901,x90901),x90903),x90904)),x90902))
% 179.72/179.59 [9213]~P101(f323(f59(x92131),x92134))+E(f323(f323(f6(x92131,a860),f323(f323(f8(f867(x92132,a855),a860,x92131),f35(x92132)),x92133)),x92134),f323(f35(f866(x92131,x92132)),f323(f323(f260(x92131,x92132),x92134),x92133)))+P101(f323(f323(f325(x92131),f617(x92133,x92132,x92134,x92131)),x92134))
% 179.72/179.59 [9217]~P101(f323(f130(x92171),x92172))+P101(f323(f130(x92171),f323(f323(f152(x92171,x92172),x92173),x92174)))+P101(f323(f323(f325(x92171),x92174),f323(f323(f22(f867(x92171,a855)),f323(f166(x92171),x92172)),f323(f323(f301(x92171),f323(f323(f158(x92171),x92172),x92173)),f188(f867(x92171,a855))))))
% 179.72/179.59 [9233]~P101(f323(f59(x92332),x92333))+~P101(f323(f59(x92331),f323(x92334,f444(x92334,x92331,x92333,x92332))))+P101(f323(f59(x92331),f323(f323(f39(x92332,f867(x92331,a855)),x92333),x92334)))
% 179.72/179.59 [9234]~P101(f323(f59(x92342),x92343))+~P101(f323(f59(x92341),f323(x92344,f456(x92344,x92341,x92343,x92342))))+P101(f323(f59(x92341),f323(f323(f39(x92342,f867(x92341,a855)),x92343),x92344)))
% 179.72/179.59 [9311]~P101(f323(f323(f325(f866(x93111,x93111)),x93112),f323(f323(f280(x93111,x93111,x93111),x93114),f299(x93111,x93114))))+P101(f323(f323(f325(f866(x93111,x93111)),x93112),f323(f323(f280(x93111,x93111,x93111),x93113),f299(x93111,x93113))))+~P101(f323(f323(f237(f867(f866(x93111,x93111),a855)),x93114),x93113))
% 179.72/179.59 [9319]E(f323(f323(f169(x93191),f586(x93194,x93193,x93192,x93191)),x93193),f323(f323(f169(x93191),f586(x93194,x93193,x93192,x93191)),x93192))+~P101(f323(f323(f325(f866(f861(x93191),f861(x93191))),f323(f323(f258(f861(x93191),f861(x93191)),x93192),x93193)),f140(x93191,x93194)))+E(f323(f323(f169(x93191),f323(f189(f861(x93191)),x93192)),x93193),x93192)
% 179.72/179.59 [9335]~P101(f323(f59(x93351),x93354))+E(f323(f323(f6(x93351,a860),f323(f323(f8(f867(x93352,a855),a860,x93351),f35(x93352)),x93353)),x93354),f323(f35(f866(x93351,x93352)),f323(f323(f260(x93351,x93352),x93354),x93353)))+~P101(f323(f59(x93352),f323(x93353,f617(x93353,x93352,x93354,x93351))))
% 179.72/179.59 [9339]~E(f323(f189(f861(x93391)),x93393),f323(f189(f861(x93391)),x93392))+P101(f323(f323(f325(f866(f861(x93391),f861(x93391))),f323(f323(f258(f861(x93391),f861(x93391)),x93392),x93393)),f151(x93391,x93394)))+P101(f323(f323(f325(f866(x93391,x93391)),f575(x93394,x93393,x93392,x93391)),f323(f166(f866(x93391,x93391)),f323(f323(f175(x93391,x93391),x93392),x93393))))
% 179.72/179.59 [9415]~P101(f323(f323(f325(f866(f861(x94151),f861(x94151))),f323(f323(f258(f861(x94151),f861(x94151)),x94152),x94153)),f140(x94151,x94154)))+E(f323(f323(f169(x94151),f323(f189(f861(x94151)),x94152)),x94153),x94152)+P101(f323(f323(f238(a860),f586(x94154,x94153,x94152,x94151)),f323(f323(f235(a860),f323(f189(f861(x94151)),x94152)),f323(f189(f861(x94151)),x94153))))
% 179.72/179.59 [9416]E(f323(f179(x94161,x94162),x94163),f323(f179(x94161,x94162),x94164))+~E(f323(f166(x94161),f323(f323(f147(f866(x94161,x94162),x94161),f257(x94161,x94162)),x94163)),f323(f166(x94161),f323(f323(f147(f866(x94161,x94162),x94161),f257(x94161,x94162)),x94164)))+P101(f323(f323(f325(x94161),f683(x94163,x94164,x94162,x94161)),f323(f166(x94161),f323(f323(f147(f866(x94161,x94162),x94161),f257(x94161,x94162)),x94164))))
% 179.72/179.59 [9440]~P101(f323(f323(f325(f866(f861(x94401),f861(x94401))),f323(f323(f258(f861(x94401),f861(x94401)),x94402),x94403)),f140(x94401,x94404)))+P101(f323(f323(f238(a860),f323(f189(f861(x94401)),x94402)),f323(f189(f861(x94401)),x94403)))+P101(f323(f323(f238(a860),f586(x94404,x94403,x94402,x94401)),f323(f323(f235(a860),f323(f189(f861(x94401)),x94402)),f323(f189(f861(x94401)),x94403))))
% 179.72/179.59 [9740]~P101(f323(f323(f323(x97401,f517(x97401,x97404,x97403,x97402)),f518(x97401,x97404,x97403,x97402)),f519(x97401,x97404,x97403,x97402)))+P101(f323(f323(f323(x97401,x97402),x97403),x97404))+~P101(f323(f311(f866(f867(a1,f864(f861(a319))),f866(a1,a1)),a309),f323(f323(f258(f867(a1,f864(f861(a319))),f866(a1,a1)),x97402),f323(f323(f258(a1,a1),x97403),x97404))))
% 179.72/179.59 [9818]P101(f323(f323(f323(x98181,x98182),x98183),x98184))+P101(f323(f311(f866(f867(a1,f864(f861(a319))),f866(a1,a1)),a309),f323(f323(f258(f867(a1,f864(f861(a319))),f866(a1,a1)),f517(x98181,x98184,x98183,x98182)),f323(f323(f258(a1,a1),f518(x98181,x98184,x98183,x98182)),f519(x98181,x98184,x98183,x98182)))))+~P101(f323(f311(f866(f867(a1,f864(f861(a319))),f866(a1,a1)),a309),f323(f323(f258(f867(a1,f864(f861(a319))),f866(a1,a1)),x98182),f323(f323(f258(a1,a1),x98183),x98184))))
% 179.72/179.59 [9857]~P101(f323(f323(f325(f866(f861(x98571),f861(x98571))),f323(f323(f258(f861(x98571),f861(x98571)),x98572),x98573)),f140(x98571,x98574)))+E(f323(f323(f169(x98571),f323(f189(f861(x98571)),x98572)),x98573),x98572)+P101(f323(f323(f325(f866(x98571,x98571)),f323(f323(f258(x98571,x98571),f323(f323(f158(x98571),x98572),f586(x98574,x98573,x98572,x98571))),f323(f323(f158(x98571),x98573),f586(x98574,x98573,x98572,x98571)))),x98574))
% 179.72/179.59 [9858]~P101(f323(f323(f325(f866(f861(x98581),f861(x98581))),f323(f323(f258(f861(x98581),f861(x98581)),x98582),x98583)),f140(x98581,x98584)))+P101(f323(f323(f238(a860),f323(f189(f861(x98581)),x98582)),f323(f189(f861(x98581)),x98583)))+P101(f323(f323(f325(f866(x98581,x98581)),f323(f323(f258(x98581,x98581),f323(f323(f158(x98581),x98582),f586(x98584,x98583,x98582,x98581))),f323(f323(f158(x98581),x98583),f586(x98584,x98583,x98582,x98581)))),x98584))
% 179.72/179.59 [9915]~E(f323(f189(f861(x99151)),x99152),f323(f189(f861(x99151)),x99153))+P101(f323(f323(f325(f866(f861(x99151),f861(x99151))),f323(f323(f258(f861(x99151),f861(x99151)),x99152),x99153)),f151(x99151,x99154)))+~P101(f323(f323(f325(f866(x99151,x99151)),f323(f323(f258(x99151,x99151),f323(f323(f158(x99151),x99152),f569(x99154,x99153,x99152,x99151))),f323(f323(f158(x99151),x99153),f569(x99154,x99153,x99152,x99151)))),x99154))
% 179.72/179.59 [10048]~P72(x100481)+~P101(f323(f59(x100482),x100484))+E(f323(f159(x100481),f323(f323(f147(x100482,x100481),x100483),f88(f861(x100482),f323(f323(f18(f861(x100482),a855,a855),f323(f323(f8(a855,f867(a855,a855),f861(x100482)),a321),f323(f323(f7(f861(x100482),f867(x100482,a855),a855),f323(f323(f8(f867(x100482,a855),f867(f867(x100482,a855),a855),f861(x100482)),a320),f166(x100482))),x100484))),f130(x100482))))),f228(x100482,x100481,x100483,x100484))
% 179.72/179.59 [7335]~P62(x73352)+E(x73351,f2(x73352))+E(f323(f323(f281(x73352),f323(f323(f78(x73352),x73353),f323(f323(f79(x73352),x73354),x73351))),x73351),f323(f323(f78(x73352),x73354),f323(f323(f281(x73352),x73353),x73351)))
% 179.72/179.59 [7336]~P57(x73362)+E(x73361,f2(x73362))+E(f323(f323(f36(x73362),f323(f323(f78(x73362),x73363),f323(f323(f79(x73362),x73364),x73361))),x73361),f323(f323(f78(x73362),x73364),f323(f323(f36(x73362),x73363),x73361)))
% 179.72/179.59 [7337]~P57(x73372)+E(x73371,f2(x73372))+E(f323(f323(f36(x73372),f323(f323(f78(x73372),x73373),f323(f323(f79(x73372),x73371),x73374))),x73371),f323(f323(f78(x73372),x73374),f323(f323(f36(x73372),x73373),x73371)))
% 179.72/179.59 [7568]~P63(x75682)+E(x75681,f2(x75682))+E(f323(f323(f281(x75682),f323(f323(f22(x75682),x75683),f323(f323(f79(x75682),x75681),x75684))),x75681),f323(f323(f22(x75682),f323(f323(f281(x75682),x75683),x75681)),x75684))
% 179.72/179.59 [7569]~P62(x75692)+E(x75691,f2(x75692))+E(f323(f323(f281(x75692),f323(f323(f78(x75692),x75693),f323(f323(f79(x75692),x75694),x75691))),x75691),f323(f323(f78(x75692),f323(f323(f281(x75692),x75693),x75691)),x75694))
% 179.72/179.59 [7570]~P63(x75702)+E(x75701,f2(x75702))+E(f323(f323(f281(x75702),f323(f323(f78(x75702),x75703),f323(f323(f79(x75702),x75701),x75704))),x75701),f323(f323(f78(x75702),f323(f323(f281(x75702),x75703),x75701)),x75704))
% 179.72/179.59 [8271]~P101(f323(f153(x82711,x82713),x82714))+~P101(f323(f153(x82711,x82712),x82714))+P101(f323(f153(x82711,f323(f323(f101(f867(x82711,a855)),x82712),x82713)),x82714))
% 179.72/179.59 [8644]~E(f323(f323(f280(x86441,x86441,x86441),x86442),x86444),f188(f867(f866(x86441,x86441),a855)))+~E(f323(f323(f280(x86441,x86441,x86441),x86442),x86443),f188(f867(f866(x86441,x86441),a855)))+E(f323(f323(f280(x86441,x86441,x86441),x86442),f323(f323(f110(f867(f866(x86441,x86441),a855)),x86443),x86444)),f188(f867(f866(x86441,x86441),a855)))
% 179.72/179.59 [8771]~P101(f323(f323(f237(f867(x87711,a855)),x87713),x87714))+~P101(f323(f323(f237(f867(x87711,a855)),x87712),x87714))+P101(f323(f323(f237(f867(x87711,a855)),f323(f323(f110(f867(x87711,a855)),x87712),x87713)),x87714))
% 179.72/179.59 [9145]~P101(f323(f59(x91451),x91454))+~P101(f323(f59(x91451),x91453))+E(f323(f323(f22(a860),f323(f323(f78(a860),f323(f323(f6(x91451,a860),x91452),x91453)),f323(f323(f6(x91451,a860),x91452),x91454))),f323(f323(f6(x91451,a860),x91452),f323(f323(f101(f867(x91451,a855)),x91453),x91454))),f323(f323(f6(x91451,a860),x91452),f323(f323(f110(f867(x91451,a855)),x91453),x91454)))
% 179.72/179.59 [9230]~P101(f323(f323(f325(x92301),x92303),x92302))+~P101(f323(f323(f237(f867(x92301,a855)),x92302),f323(f323(f301(x92301),x92303),x92304)))+P101(f323(f323(f237(f867(x92301,a855)),f323(f323(f22(f867(x92301,a855)),x92302),f323(f323(f301(x92301),x92303),f188(f867(x92301,a855))))),x92304))
% 179.72/179.59 [9389]~P101(f323(f323(f325(x93891),x93893),x93892))+P101(f323(f323(f237(f867(x93891,a855)),x93892),f323(f323(f301(x93891),x93893),x93894)))+~P101(f323(f323(f237(f867(x93891,a855)),f323(f323(f22(f867(x93891,a855)),x93892),f323(f323(f301(x93891),x93893),f188(f867(x93891,a855))))),x93894))
% 179.72/179.59 [9479]~P101(f323(f323(f237(a860),x94791),x94793))+~P101(f323(f323(f238(a860),x94792),x94794))+P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),f323(f323(f258(a860,a860),x94791),x94792)),f323(f323(f258(a860,a860),x94793),x94794))),a33))
% 179.72/179.59 [9480]~P101(f323(f323(f237(a860),x94802),x94804))+~P101(f323(f323(f237(a860),x94801),x94803))+P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),f323(f323(f258(a860,a860),x94801),x94802)),f323(f323(f258(a860,a860),x94803),x94804))),a68))
% 179.72/179.59 [9780]~P101(f323(f323(f325(f861(x97801)),x97804),f154(x97801,x97803)))+~P101(f323(f323(f325(f861(x97801)),x97804),f154(x97801,x97802)))+P101(f323(f153(x97801,f323(f323(f101(f867(x97801,a855)),f323(f323(f7(x97801,f867(x97801,a855),a855),f325(x97801)),x97802)),f323(f323(f7(x97801,f867(x97801,a855),a855),f325(x97801)),x97803))),x97804))
% 179.72/179.59 [9880]~P27(x98801,f867(f867(x98801,a855),a855),f323(f323(f7(x98801,f867(f866(x98801,x98801),a855),f867(f867(x98801,a855),a855)),f323(f323(f8(f867(x98801,a855),f867(f867(f866(x98801,x98801),a855),f867(f867(x98801,a855),a855)),x98801),f58(x98801)),f323(f323(f7(x98801,f867(x98801,a855),f867(x98801,a855)),f301(x98801)),f188(f867(x98801,a855))))),x98803),x98802)+~P101(f323(f323(f325(x98801),x98804),x98802))+E(f323(f323(f22(f867(f867(x98801,a855),a855)),f323(f323(f58(x98801),x98802),x98803)),f323(f323(f58(x98801),f323(f323(f301(x98801),x98804),f188(f867(x98801,a855)))),x98803)),f323(f323(f58(x98801),f323(f323(f22(f867(x98801,a855)),x98802),f323(f323(f301(x98801),x98804),f188(f867(x98801,a855))))),x98803))
% 179.72/179.59 [10013]~P40(x100131,x100132,x100134)+~P101(f323(f323(f325(f866(x100131,x100131)),x100133),x100134))+P101(f323(f323(f262(x100131,x100131,a855),f323(f323(f7(x100131,f867(x100131,a855),f867(x100131,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x100131,a855),f867(x100131,a855)),x100131),f8(a855,a855,x100131)),f323(f323(f8(a855,f867(a855,a855),x100131),a321),f323(f323(f7(x100131,f867(x100131,a855),a855),f325(x100131)),x100132)))),f323(f323(f7(x100131,f867(x100131,a855),a855),f325(x100131)),x100132))),x100133))
% 179.72/179.59 [10025]P101(f323(f59(x100251),x100252))+~P101(f323(f59(x100253),f323(f302(x100251,x100253,x100254),x100252)))+~P101(f323(f59(x100251),f323(f243(x100251),f323(f323(f18(x100251,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100251),a321),f323(f323(f7(x100251,f867(x100251,a855),a855),f325(x100251)),x100252))),f323(f323(f7(x100251,x100253,a855),f323(f323(f8(x100253,f867(x100253,a855),x100251),a320),x100254)),f323(x100254,f351(x100254,x100253,x100252,x100251)))))))
% 179.72/179.59 [8024]~P63(x80242)+E(x80241,f2(x80242))+E(f323(f323(f281(x80242),f323(f323(f22(x80242),f323(f323(f79(x80242),x80241),x80243)),x80244)),x80241),f323(f323(f22(x80242),x80243),f323(f323(f281(x80242),x80244),x80241)))
% 179.72/179.59 [8025]~P63(x80252)+E(x80251,f2(x80252))+E(f323(f323(f281(x80252),f323(f323(f78(x80252),f323(f323(f79(x80252),x80251),x80253)),x80254)),x80251),f323(f323(f78(x80252),x80253),f323(f323(f281(x80252),x80254),x80251)))
% 179.72/179.59 [8929]~E(f323(f323(f280(x89291,x89291,x89291),x89293),x89294),f188(f867(f866(x89291,x89291),a855)))+~E(f323(f323(f280(x89291,x89291,x89291),x89292),x89294),f188(f867(f866(x89291,x89291),a855)))+E(f323(f323(f280(x89291,x89291,x89291),f323(f323(f110(f867(f866(x89291,x89291),a855)),x89292),x89293)),x89294),f188(f867(f866(x89291,x89291),a855)))
% 179.72/179.59 [9957]~P141(x99571)+~P141(x99572)+E(f323(f323(f308(x99571),f323(f323(f7(x99571,a99,f864(f861(a319))),f323(f323(f8(f867(x99572,f864(f861(a319))),f867(a99,f864(f861(a319))),x99571),f308(x99572)),f323(f323(f8(f867(x99572,f866(x99571,x99572)),f867(x99572,f864(f861(a319))),x99571),f323(f8(f866(x99571,x99572),f864(f861(a319)),x99572),x99573)),f258(x99571,x99572)))),x99574)),x99574),f323(f323(f308(f866(x99571,x99572)),x99573),x99574))
% 179.72/179.59 [9688]~P101(f323(f153(x96881,x96883),x96884))+~P101(f323(f153(x96881,x96882),x96884))+P101(f323(f153(x96881,f323(f323(f18(x96881,a855,a855),f323(f323(f8(a855,f867(a855,a855),x96881),a321),x96882)),x96883)),x96884))
% 179.72/179.59 [9949]P101(f323(x99491,f829(x99492,x99493,x99491,x99494)))+~P101(f323(f59(x99494),f323(f243(x99494),x99491)))+P101(f323(f59(x99493),f323(f243(x99493),f323(f323(f8(f867(x99494,a855),a855,x99493),f85(x99494)),f323(f323(f8(f867(x99494,a855),f867(x99494,a855),x99493),f323(f18(x99494,a855,a855),f323(f323(f8(a855,f867(a855,a855),x99494),a321),x99491))),x99492)))))
% 179.72/179.59 [9970]~P101(f323(f59(x99702),f323(f243(x99702),x99703)))+~P101(f323(f59(x99701),f323(f243(x99701),f323(f323(f7(x99701,x99702,a855),x99704),f829(x99704,x99701,x99703,x99702)))))+P101(f323(f59(x99701),f323(f243(x99701),f323(f323(f8(f867(x99702,a855),a855,x99701),f85(x99702)),f323(f323(f8(f867(x99702,a855),f867(x99702,a855),x99701),f323(f18(x99702,a855,a855),f323(f323(f8(a855,f867(a855,a855),x99702),a321),x99703))),x99704)))))
% 179.72/179.59 [5016]~E(x50162,x50164)+E(f163(x50161,x50162,x50163),f163(x50161,x50164,x50165))+~E(x50162,f2(a860))
% 179.72/179.59 [5264]E(x52641,x52642)+~E(f163(x52644,x52643,x52641),f163(x52644,x52645,x52642))+E(x52643,f2(a860))
% 179.72/179.59 [6485]E(x64851,x64852)+~E(f323(x64853,x64851),f323(x64853,x64852))+~P27(x64854,x64855,x64853,f246(f867(x64854,a855)))
% 179.72/179.59 [6644]~E(f323(x66443,x66445),f200(x66442))+~E(f323(x66444,x66445),f200(x66442))+E(f323(f180(x66441,x66442,x66443,x66444),x66445),f200(x66442))
% 179.72/179.59 [7370]E(x73701,x73702)+~P27(x73703,x73704,x73705,f246(f867(x73703,a855)))+~E(f323(f302(x73703,x73704,x73705),x73701),f323(f302(x73703,x73704,x73705),x73702))
% 179.72/179.59 [7622]P27(x76222,x76223,f581(x76224,x76223,x76222,x76221),x76221)+~E(f323(f302(x76223,x76222,x76225),x76224),x76221)+E(x76221,f188(f867(x76222,a855)))
% 179.72/179.59 [8155]~P101(f323(f323(x81553,x81552),x81555))+~P101(f323(f323(x81553,x81554),x81552))+P101(f323(f323(f325(x81551),x81552),f290(x81551,x81553,x81554,x81555)))
% 179.72/179.59 [8156]~P101(f323(f323(x81563,x81562),x81565))+~P101(f323(f323(x81563,x81564),x81562))+P101(f323(f323(f325(x81561),x81562),f287(x81561,x81563,x81564,x81565)))
% 179.72/179.59 [8460]~P27(x84601,x84602,x84603,x84604)+P28(x84601,x84602,x84603,x84604,x84605)+~E(f323(f302(x84601,x84602,x84603),x84604),x84605)
% 179.72/179.59 [8593]~P28(x85931,x85933,x85934,x85932,x85935)+~P101(f323(f59(x85933),x85935))+P101(f323(f59(x85931),x85932))
% 179.72/179.59 [8594]~P28(x85943,x85941,x85944,x85945,x85942)+~P101(f323(f59(x85943),x85945))+P101(f323(f59(x85941),x85942))
% 179.72/179.59 [8727]~P27(x87271,x87273,x87275,f246(f867(x87271,a855)))+~P27(x87273,x87272,x87274,f246(f867(x87273,a855)))+P27(x87271,x87272,f323(f71(x87273,x87272,x87271,x87274),x87275),f246(f867(x87271,a855)))
% 179.72/179.59 [9288]P101(f323(f323(f325(f866(x92881,x92881)),f323(f323(f258(x92881,x92881),x92882),x92883)),f299(x92881,x92884)))+~P101(f323(f323(f325(f866(x92881,x92881)),f323(f323(f258(x92881,x92881),x92882),x92885)),f299(x92881,x92884)))+~P101(f323(f323(f325(f866(x92881,x92881)),f323(f323(f258(x92881,x92881),x92885),x92883)),f299(x92881,x92884)))
% 179.72/179.59 [9326]~P103(x93262)+~P101(f323(f130(x93261),x93265))+P101(f323(f130(x93261),f142(x93261,x93262,x93263,x93264,x93265)))
% 179.72/179.59 [5335]~E(x53352,f113(x53351))+E(f323(f323(f121(x53351),x53352),x53353),f323(f323(f144(x53351),x53354),x53355))+~E(x53353,f323(f323(f144(x53351),x53354),x53355))
% 179.72/179.59 [5336]~E(x53362,f113(x53361))+E(f323(f323(f121(x53361),x53362),x53363),f323(f323(f144(x53361),x53364),x53365))+~E(f323(f323(f144(x53361),x53364),x53365),x53363)
% 179.72/179.59 [6442]~E(f323(f189(f861(x64421)),x64425),f323(f189(f861(x64422)),x64424))+E(f323(f323(f147(f866(x64421,x64422),x64422),f261(x64421,x64422)),x64423),x64424)+~E(f323(f323(f175(x64421,x64422),x64425),x64424),x64423)
% 179.72/179.59 [6443]~E(f323(f189(f861(x64431)),x64434),f323(f189(f861(x64432)),x64435))+E(f323(f323(f147(f866(x64431,x64432),x64431),f257(x64431,x64432)),x64433),x64434)+~E(f323(f323(f175(x64431,x64432),x64434),x64435),x64433)
% 179.72/179.59 [6913]~P103(x69131)+~P16(x69131,f323(f323(f147(x69132,x69131),x69133),x69135))+P16(x69131,f323(f323(f147(x69132,x69131),x69133),f323(f129(x69132,x69134),x69135)))
% 179.72/179.59 [6958]~P101(f323(x69583,x69585))+~P101(f323(f323(x69582,x69584),x69585))+P101(f323(f323(f92(x69581,x69582,x69583),x69584),x69585))
% 179.72/179.59 [7055]~P103(x70551)+P16(x70551,f323(f323(f147(x70552,x70551),x70553),f164(x70552,x70554,x70555)))+~P16(x70551,f323(f323(f147(x70552,x70551),x70553),x70555))
% 179.72/179.59 [7078]~P51(x70783,x70782,x70785)+~P51(x70781,x70783,x70784)+P51(x70781,x70782,f323(f323(f280(x70781,x70783,x70782),x70784),x70785))
% 179.72/179.59 [7170]E(x71701,x71702)+~P27(x71703,x71704,x71705,f246(f867(x71703,a855)))+~E(f323(f323(f147(x71703,x71704),x71705),x71701),f323(f323(f147(x71703,x71704),x71705),x71702))
% 179.72/179.59 [7321]~P101(f323(f323(f237(a860),x73211),f323(x73213,x73215)))+P101(f323(f323(f237(a860),x73211),f148(x73212,x73213,x73214)))+~P101(f323(f323(f325(x73212),x73215),f323(f166(x73212),x73214)))
% 179.72/179.59 [7322]~P101(f323(f323(f238(a860),x73221),f323(x73223,x73225)))+P101(f323(f323(f238(a860),x73221),f148(x73222,x73223,x73224)))+~P101(f323(f323(f325(x73222),x73225),f323(f166(x73222),x73224)))
% 179.72/179.59 [7721]P101(f323(x77211,x77212))+~P101(f323(x77211,x77213))+~P101(f323(f323(f325(x77214),x77212),f323(f166(x77214),f163(x77214,x77215,x77213))))
% 179.72/179.59 [7722]P101(f323(x77221,x77222))+~P101(f323(x77221,x77223))+~P101(f323(f323(f325(x77224),x77223),f323(f166(x77224),f163(x77224,x77225,x77222))))
% 179.72/179.59 [7726]~P105(x77261)+P101(f323(f323(f237(f867(x77261,a855)),f294(x77261,x77262,x77263)),f294(x77261,x77264,x77265)))+P101(f323(f323(f237(x77261),x77262),x77263))
% 179.72/179.59 [7747]~P6(x77471)+P101(f323(f323(f237(x77471),f323(f323(f40(x77472,x77471),x77473),x77474)),f323(x77474,x77475)))+~P101(f323(f323(f325(x77472),x77475),x77473))
% 179.72/179.59 [7815]~P27(x78151,x78152,x78154,x78153)+E(f323(f75(x78151,x78152,x78153,x78154),f323(x78154,x78155)),x78155)+~P101(f323(f323(f325(x78151),x78155),x78153))
% 179.72/179.59 [7816]~P27(x78161,x78162,x78164,x78163)+E(f323(f91(x78161,x78162,x78163,x78164),f323(x78164,x78165)),x78165)+~P101(f323(f323(f325(x78161),x78165),x78163))
% 179.72/179.59 [8013]~P101(f323(x80131,x80135))+P101(f323(x80131,f388(x80131,x80132,x80133,x80134)))+~P101(f323(f323(f325(x80134),x80135),x80133))
% 179.72/179.59 [8014]~P101(f323(x80141,x80145))+P101(f323(x80141,f388(x80141,x80142,x80143,x80144)))+~P101(f323(f323(f325(x80144),x80145),x80142))
% 179.72/179.59 [8107]P101(f323(f59(x81071),x81072))+~P101(f323(f59(x81073),x81074))+~P101(f323(f323(f237(f867(x81071,a855)),x81072),f323(f302(x81073,x81071,x81075),x81074)))
% 179.72/179.59 [8275]E(x82751,x82752)+~P27(x82753,x82754,x82755,f323(f323(f110(f867(x82753,a855)),f323(f166(x82753),x82751)),f323(f166(x82753),x82752)))+~E(f323(f323(f147(x82753,x82754),x82755),x82751),f323(f323(f147(x82753,x82754),x82755),x82752))
% 179.72/179.59 [8332]~P105(x83321)+~P101(f323(f323(f238(f867(x83321,a855)),f294(x83321,x83324,x83325)),f294(x83321,x83322,x83323)))+P101(f323(f323(f237(x83321),x83322),x83323))
% 179.72/179.59 [8395]~P27(x83951,x83954,x83955,f246(f867(x83951,a855)))+~P101(f323(f323(f325(x83954),f323(x83955,x83952)),f323(f302(x83951,x83954,x83955),x83953)))+P101(f323(f323(f325(x83951),x83952),x83953))
% 179.72/179.59 [8466]P101(f323(x84661,x84662))+~P101(f323(x84661,f404(x84661,x84663,x84664,x84665)))+~P101(f323(f323(f325(x84665),x84662),x84664))
% 179.72/179.59 [8467]P101(f323(x84671,x84672))+~P101(f323(x84671,f404(x84671,x84673,x84674,x84675)))+~P101(f323(f323(f325(x84675),x84672),x84673))
% 179.72/179.59 [8768]~P27(x87682,x87683,x87681,x87684)+E(f323(x87681,f323(f75(x87682,x87683,x87684,x87681),x87685)),x87685)+~P101(f323(f323(f325(x87683),x87685),f323(f302(x87682,x87683,x87681),x87684)))
% 179.72/179.59 [8874]E(x88741,f113(x88742))+E(f323(f323(f144(x88742),x88743),f568(x88744,x88743,x88745,x88741,x88742)),x88741)+~E(f323(f323(f121(x88742),x88741),x88745),f323(f323(f144(x88742),x88743),x88744))
% 179.72/179.59 [8875]E(x88751,f113(x88752))+E(f323(f323(f144(x88752),x88753),f570(x88754,x88751,x88755,x88753,x88752)),x88751)+~E(f323(f323(f121(x88752),x88751),x88754),f323(f323(f144(x88752),x88753),x88755))
% 179.72/179.59 [8891]E(f323(f323(f144(x88912),x88913),f568(x88914,x88913,x88911,x88915,x88912)),x88915)+~E(f323(f323(f121(x88912),x88915),x88911),f323(f323(f144(x88912),x88913),x88914))+E(x88911,f323(f323(f144(x88912),x88913),x88914))
% 179.72/179.59 [8892]E(f323(f323(f144(x88921),x88922),f570(x88924,x88925,x88923,x88922,x88921)),x88925)+~E(f323(f323(f121(x88921),x88925),x88924),f323(f323(f144(x88921),x88922),x88923))+E(f323(f323(f144(x88921),x88922),x88923),x88924)
% 179.72/179.59 [8965]~E(f323(f302(x89653,x89652,x89654),f246(f867(x89653,a855))),f246(f867(x89652,a855)))+~E(f323(f302(x89651,x89653,x89655),f246(f867(x89651,a855))),f246(f867(x89653,a855)))+E(f323(f302(x89651,x89652,f323(f71(x89653,x89652,x89651,x89654),x89655)),f246(f867(x89651,a855))),f246(f867(x89652,a855)))
% 179.72/179.59 [9332]E(x93321,f113(x93322))+~E(f323(f323(f121(x93322),x93321),x93323),f323(f323(f144(x93322),x93325),x93324))+E(f323(f323(f121(x93322),f570(x93323,x93321,x93324,x93325,x93322)),x93323),x93324)
% 179.72/179.59 [9333]E(x93331,f113(x93332))+~E(f323(f323(f121(x93332),x93331),x93335),f323(f323(f144(x93332),x93334),x93333))+E(f323(f323(f121(x93332),f568(x93333,x93334,x93335,x93331,x93332)),x93335),x93333)
% 179.72/179.59 [9340]E(f323(f323(f121(x93402),f568(x93404,x93403,x93401,x93405,x93402)),x93401),x93404)+~E(f323(f323(f121(x93402),x93405),x93401),f323(f323(f144(x93402),x93403),x93404))+E(x93401,f323(f323(f144(x93402),x93403),x93404))
% 179.72/179.59 [9341]~E(f323(f323(f121(x93411),x93415),x93414),f323(f323(f144(x93411),x93412),x93413))+E(f323(f323(f121(x93411),f570(x93414,x93415,x93413,x93412,x93411)),x93414),x93413)+E(f323(f323(f144(x93411),x93412),x93413),x93414)
% 179.72/179.59 [9342]E(f323(f323(f121(x93421),x93425),f573(x93423,x93422,x93424,x93425,x93421)),x93422)+E(f323(f323(f121(x93421),x93422),f572(x93423,x93422,x93424,x93425,x93421)),x93425)+~E(f323(f323(f121(x93421),x93425),x93424),f323(f323(f121(x93421),x93422),x93423))
% 179.72/179.59 [9374]~P103(x93741)+P16(x93741,f323(f323(f147(x93742,x93741),x93743),f142(x93742,x93741,x93743,x93744,x93745)))+~P16(x93741,f323(f323(f147(x93742,x93741),x93743),x93745))
% 179.72/179.59 [9386]~P55(x93865,x93861,x93864,x93863)+P101(f323(f323(x93861,x93862),f667(x93863,x93864,x93861,x93865,x93862)))+~P101(f323(f323(f325(x93865),x93862),x93864))
% 179.72/179.59 [9491]~P101(f323(f323(f325(f866(x94911,x94911)),f323(f323(f258(x94911,x94911),x94915),x94913)),f299(x94911,x94914)))+P101(f323(f323(f325(f866(x94911,x94911)),f323(f323(f258(x94911,x94911),x94912),x94913)),f323(f323(f280(x94911,x94911,x94911),x94914),f299(x94911,x94914))))+~P101(f323(f323(f325(f866(x94911,x94911)),f323(f323(f258(x94911,x94911),x94912),x94915)),f323(f323(f280(x94911,x94911,x94911),x94914),f299(x94911,x94914))))
% 179.72/179.59 [9492]~P101(f323(f323(f325(f866(x94921,x94921)),f323(f323(f258(x94921,x94921),x94922),x94925)),f299(x94921,x94924)))+P101(f323(f323(f325(f866(x94921,x94921)),f323(f323(f258(x94921,x94921),x94922),x94923)),f323(f323(f280(x94921,x94921,x94921),x94924),f299(x94921,x94924))))+~P101(f323(f323(f325(f866(x94921,x94921)),f323(f323(f258(x94921,x94921),x94925),x94923)),f323(f323(f280(x94921,x94921,x94921),x94924),f299(x94921,x94924))))
% 179.72/179.59 [9495]P101(f323(f323(f325(f866(f861(x94951),f861(x94951))),f323(f323(f258(f861(x94951),f861(x94951)),x94952),x94953)),f151(x94951,f299(x94951,x94954))))+~P101(f323(f323(f325(f866(f861(x94951),f861(x94951))),f323(f323(f258(f861(x94951),f861(x94951)),x94952),x94955)),f151(x94951,f299(x94951,x94954))))+~P101(f323(f323(f325(f866(f861(x94951),f861(x94951))),f323(f323(f258(f861(x94951),f861(x94951)),x94955),x94953)),f151(x94951,f299(x94951,x94954))))
% 179.72/179.59 [9499]E(f323(f323(f121(x94991),x94992),f572(x94993,x94992,x94994,x94995,x94991)),x94995)+E(f323(f323(f121(x94991),f573(x94993,x94992,x94994,x94995,x94991)),x94993),x94994)+~E(f323(f323(f121(x94991),x94992),x94993),f323(f323(f121(x94991),x94995),x94994))
% 179.72/179.59 [9500]E(f323(f323(f121(x95001),x95002),f573(x95003,x95004,x95005,x95002,x95001)),x95004)+E(f323(f323(f121(x95001),f572(x95003,x95004,x95005,x95002,x95001)),x95005),x95003)+~E(f323(f323(f121(x95001),x95002),x95005),f323(f323(f121(x95001),x95004),x95003))
% 179.72/179.59 [9556]P101(f323(f323(f325(f866(x95561,x95561)),f323(f323(f258(x95561,x95561),x95562),x95563)),f323(f323(f280(x95561,x95561,x95561),x95564),f299(x95561,x95564))))+~P101(f323(f323(f325(f866(x95561,x95561)),f323(f323(f258(x95561,x95561),x95562),x95565)),f323(f323(f280(x95561,x95561,x95561),x95564),f299(x95561,x95564))))+~P101(f323(f323(f325(f866(x95561,x95561)),f323(f323(f258(x95561,x95561),x95565),x95563)),f323(f323(f280(x95561,x95561,x95561),x95564),f299(x95561,x95564))))
% 179.72/179.59 [9583]P35(x95831,x95832,x95833,x95834,x95835)+~E(f323(f189(f861(x95831)),x95834),f323(f189(f861(x95832)),x95835))+~P101(f323(f323(f262(x95831,x95832,a855),x95833),f645(x95835,x95834,x95833,x95832,x95831)))
% 179.72/179.59 [9584]P35(x95841,x95842,x95843,x95844,x95845)+~E(f323(f189(f861(x95841)),x95844),f323(f189(f861(x95842)),x95845))+~P101(f323(f323(f262(x95841,x95842,a855),x95843),f656(x95843,x95845,x95844,x95842,x95841)))
% 179.72/179.59 [9589]E(f323(f323(f121(x95891),f572(x95892,x95893,x95894,x95895,x95891)),x95894),x95892)+~E(f323(f323(f121(x95891),x95893),x95892),f323(f323(f121(x95891),x95895),x95894))+E(f323(f323(f121(x95891),f573(x95892,x95893,x95894,x95895,x95891)),x95892),x95894)
% 179.72/179.59 [9604]~P103(x96042)+E(f323(f323(f141(x96041,x96042,x96043),x96044),x96045),f323(f323(f144(x96041),x96044),x96045))+P101(f323(f323(f325(x96041),f699(x96044,x96043,x96045,x96041,x96042)),f323(f166(x96041),x96045)))
% 179.72/179.59 [9609]~P55(x96091,x96094,x96093,x96092)+~P101(f323(f323(f325(x96091),x96095),x96093))+P101(f323(f323(f325(x96091),f667(x96092,x96093,x96094,x96091,x96095)),x96092))
% 179.72/179.59 [9731]~P101(f323(f323(f325(f866(f867(x97311,a855),f867(x97311,a855))),f323(f323(f258(f867(x97311,a855),f867(x97311,a855)),x97314),x97313)),f314(x97311,x97312)))+~P101(f323(f323(f325(x97311),x97315),x97314))+P101(f323(f323(f325(x97311),f716(x97312,x97313,x97314,x97311,x97315)),x97313))
% 179.72/179.59 [9743]~P103(x97432)+E(f323(f323(f141(x97431,x97432,x97433),x97434),x97435),f323(f323(f144(x97431),x97434),x97435))+~P101(f323(f323(f237(x97432),f323(x97433,x97434)),f323(x97433,f699(x97434,x97433,x97435,x97431,x97432))))
% 179.72/179.59 [9789]~P27(x97893,x97894,x97895,f246(f867(x97893,a855)))+P101(f323(x97891,x97892))+~P101(f323(x97891,f323(f91(x97893,x97894,f246(f867(x97893,a855)),x97895),f709(x97892,x97891,x97895,x97894,x97893))))
% 179.72/179.59 [9932]P35(x99321,x99322,x99323,x99324,x99325)+~E(f323(f189(f861(x99321)),x99324),f323(f189(f861(x99322)),x99325))+~P101(f323(f323(x99323,f323(f323(f158(x99321),x99324),f657(x99325,x99324,x99323,x99322,x99321))),f323(f323(f158(x99322),x99325),f657(x99325,x99324,x99323,x99322,x99321))))
% 179.72/179.59 [9933]P35(x99331,x99332,x99333,x99334,x99335)+~E(f323(f189(f861(x99331)),x99334),f323(f189(f861(x99332)),x99335))+~P101(f323(f323(x99333,f323(f323(f158(x99331),x99334),f693(x99333,x99335,x99332,x99334,x99331))),f323(f323(f158(x99332),x99335),f693(x99333,x99335,x99332,x99334,x99331))))
% 179.72/179.59 [6514]~P19(x65142,x65145,x65141)+~P101(f323(f59(x65142),x65144))+E(f323(x65141,f323(f323(f301(x65142),x65143),x65144)),f323(f323(f62(x65142,x65142,x65145),x65143),x65144))
% 179.72/179.59 [6515]~E(x65153,x65154)+~E(x65152,x65155)+E(f323(f323(f301(x65151),x65152),f323(f323(f301(x65151),x65153),f188(f867(x65151,a855)))),f323(f323(f301(x65151),x65154),f323(f323(f301(x65151),x65155),f188(f867(x65151,a855)))))
% 179.72/179.59 [6525]P101(f323(x65252,x65255))+E(f171(x65251,x65252,f323(f323(f121(x65251),x65253),x65254)),f171(x65251,x65252,x65253))+~P101(f323(f323(f325(x65251),x65255),f323(f166(x65251),x65253)))
% 179.72/179.59 [6562]E(f323(x65621,x65622),f188(f867(x65623,a855)))+~E(f323(f323(f39(x65624,f867(x65623,a855)),x65625),x65621),f188(f867(x65623,a855)))+~P101(f323(f323(f325(x65624),x65622),x65625))
% 179.72/179.59 [6563]E(f323(x65631,x65632),f246(f867(x65633,a855)))+~E(f323(f323(f40(x65634,f867(x65633,a855)),x65635),x65631),f246(f867(x65633,a855)))+~P101(f323(f323(f325(x65634),x65632),x65635))
% 179.72/179.59 [7065]~E(x70652,x70654)+~P135(x70651)+E(f323(f323(f78(x70651),f323(f323(f79(x70651),x70652),x70653)),f323(f323(f79(x70651),x70654),x70655)),f323(f323(f78(x70651),f323(f323(f79(x70651),x70652),x70655)),f323(f323(f79(x70651),x70654),x70653)))
% 179.72/179.59 [7125]~P6(x71251)+~P101(f323(f323(f325(x71254),x71253),x71255))+P101(f323(f323(f237(x71251),f323(x71252,x71253)),f323(f323(f39(x71254,x71251),x71255),x71252)))
% 179.72/179.59 [7175]~P104(x71751)+P101(f323(f323(f237(x71751),f323(x71752,x71753)),f323(x71754,x71753)))+~P101(f323(f323(f237(f867(x71755,x71751)),x71752),x71754))
% 179.72/179.59 [7290]E(x72901,x72902)+E(x72903,x72901)+~E(f323(f323(f301(x72904),x72901),f323(f323(f301(x72904),x72905),f188(f867(x72904,a855)))),f323(f323(f301(x72904),x72902),f323(f323(f301(x72904),x72903),f188(f867(x72904,a855)))))
% 179.72/179.59 [7291]E(x72911,x72912)+E(x72913,x72911)+~E(f323(f323(f301(x72914),x72913),f323(f323(f301(x72914),x72912),f188(f867(x72914,a855)))),f323(f323(f301(x72914),x72915),f323(f323(f301(x72914),x72911),f188(f867(x72914,a855)))))
% 179.72/179.59 [7292]E(x72921,x72922)+E(x72921,x72923)+~E(f323(f323(f301(x72924),x72923),f323(f323(f301(x72924),x72922),f188(f867(x72924,a855)))),f323(f323(f301(x72924),x72925),f323(f323(f301(x72924),x72921),f188(f867(x72924,a855)))))
% 179.72/179.59 [7293]E(x72931,x72932)+E(x72931,x72933)+~E(f323(f323(f301(x72934),x72931),f323(f323(f301(x72934),x72935),f188(f867(x72934,a855)))),f323(f323(f301(x72934),x72932),f323(f323(f301(x72934),x72933),f188(f867(x72934,a855)))))
% 179.72/179.59 [7826]P27(x78261,x78262,x78263,x78264)+~P27(x78261,x78262,x78263,x78265)+~P101(f323(f323(f237(f867(x78261,a855)),x78264),x78265))
% 179.72/179.59 [7855]~E(f323(x78553,x78555),x78554)+~P27(x78551,x78552,x78553,f246(f867(x78551,a855)))+E(f323(f91(x78551,x78552,f246(f867(x78551,a855)),x78553),x78554),x78555)
% 179.72/179.59 [8004]E(x80041,x80042)+~E(f323(f302(x80043,x80044,x80045),x80041),f323(f302(x80043,x80044,x80045),x80042))+~P27(x80043,x80044,x80045,f323(f323(f110(f867(x80043,a855)),x80041),x80042))
% 179.72/179.59 [8074]P101(f323(x80742,x80744))+E(f323(f323(f131(x80741),f323(f189(f861(x80741)),f171(x80741,x80742,x80743))),x80743),f323(f323(f144(x80741),x80744),x80745))+~E(f323(f323(f121(x80741),f171(x80741,x80742,x80743)),f323(f323(f144(x80741),x80744),x80745)),x80743)
% 179.72/179.59 [8104]~P27(x81041,x81042,x81043,x81045)+~P27(x81041,x81042,x81043,x81044)+P27(x81041,x81042,x81043,f323(f323(f101(f867(x81041,a855)),x81044),x81045))
% 179.72/179.59 [8215]~P72(x82151)+E(f323(f323(f78(x82151),f323(x82152,x82153)),f323(f159(x82151),f323(f323(f147(x82154,x82151),x82152),f164(x82154,x82153,x82155)))),f323(f159(x82151),f323(f323(f147(x82154,x82151),x82152),x82155)))+~P101(f323(f323(f325(x82154),x82153),f323(f166(x82154),x82155)))
% 179.72/179.59 [8305]~P103(x83051)+~P16(x83051,f323(f323(f147(x83052,x83051),x83053),x83055))+P16(x83051,f323(f323(f147(x83052,x83051),x83053),f323(f323(f141(x83052,x83051,x83053),x83054),x83055)))
% 179.72/179.59 [8391]~P6(x83911)+P101(f323(f323(f237(x83911),f323(f323(f39(x83912,x83911),x83913),x83914)),f323(f323(f39(x83912,x83911),x83915),x83914)))+~P101(f323(f323(f237(f867(x83912,a855)),x83913),x83915))
% 179.72/179.59 [8392]~P6(x83921)+P101(f323(f323(f237(x83921),f323(f323(f40(x83922,x83921),x83923),x83924)),f323(f323(f40(x83922,x83921),x83925),x83924)))+~P101(f323(f323(f237(f867(x83922,a855)),x83925),x83923))
% 179.72/179.59 [8422]~P103(x84223)+P101(f323(f130(x84221),x84222))+~P101(f323(f130(x84221),f323(f323(f141(x84221,x84223,x84224),x84225),x84222)))
% 179.72/179.59 [8566]~P103(x85661)+~P101(f323(f323(f325(x85662),x85663),f323(f166(x85662),x85664)))+~P101(f323(f130(x85662),f323(f323(f141(x85662,x85661,x85665),x85663),x85664)))
% 179.72/179.59 [8656]~P103(x86561)+P16(x86561,f323(f323(f147(x86562,x86561),x86563),x86564))+~P16(x86561,f323(f323(f147(x86562,x86561),x86563),f323(f323(f141(x86562,x86561,x86563),x86565),x86564)))
% 179.72/179.59 [8703]~P27(x87032,x87031,x87034,x87033)+E(f323(f302(x87031,x87032,f91(x87032,x87031,x87033,x87034)),f323(f302(x87032,x87031,x87034),x87035)),x87035)+~P101(f323(f323(f237(f867(x87032,a855)),x87035),x87033))
% 179.72/179.59 [8756]~P103(x87562)+E(f323(f323(f141(x87561,x87562,x87563),x87564),x87565),f142(x87561,x87562,x87563,x87564,x87565))+P101(f323(f323(f325(x87562),f323(x87563,x87564)),f323(f302(x87561,x87562,x87563),f323(f166(x87561),x87565))))
% 179.72/179.59 [8831]~P103(x88312)+E(f142(x88311,x88312,x88313,x88314,x88315),x88315)+~P101(f323(f323(f325(x88312),f323(x88313,x88314)),f323(f302(x88311,x88312,x88313),f323(f166(x88311),x88315))))
% 179.72/179.59 [8846]~P27(x88462,x88461,x88463,x88465)+P101(f323(f323(f238(f867(x88461,a855)),f323(f302(x88462,x88461,x88463),x88464)),f323(f302(x88462,x88461,x88463),x88465)))+~P101(f323(f323(f238(f867(x88462,a855)),x88464),x88465))
% 179.72/179.59 [9007]~P27(x90071,x90072,x90073,f246(f867(x90071,a855)))+~P101(f323(f323(f237(f867(x90072,a855)),x90074),f323(f302(x90071,x90072,x90073),x90075)))+P101(f323(f323(f237(f867(x90071,a855)),f323(f303(x90071,x90072,x90073),x90074)),x90075))
% 179.72/179.59 [9031]~E(f323(f302(x90313,x90311,x90314),f246(f867(x90313,a855))),f246(f867(x90311,a855)))+P101(f323(f323(f237(f867(x90311,a855)),x90312),f323(f302(x90313,x90311,x90314),x90315)))+~P101(f323(f323(f237(f867(x90313,a855)),f323(f303(x90313,x90311,x90314),x90312)),x90315))
% 179.72/179.59 [9056]~E(f323(f230(x90562),x90564),f323(f323(f179(x90561,x90562),x90565),x90563))+~P101(f323(f130(x90561),f323(f323(f147(f866(x90561,x90562),x90561),f257(x90561,x90562)),x90565)))+P101(f323(f323(f325(f866(x90561,x90562)),f323(f323(f258(x90561,x90562),x90563),x90564)),f323(f166(f866(x90561,x90562)),x90565)))
% 179.72/179.59 [9136]~P27(x91361,x91364,x91365,f246(f867(x91361,a855)))+~P101(f323(f323(f237(f867(x91364,a855)),f323(f302(x91361,x91364,x91365),x91362)),f323(f302(x91361,x91364,x91365),x91363)))+P101(f323(f323(f237(f867(x91361,a855)),x91362),x91363))
% 179.72/179.59 [9200]E(f323(f230(x92001),x92002),f323(f323(f179(x92003,x92001),x92004),x92005))+~P101(f323(f130(x92003),f323(f323(f147(f866(x92003,x92001),x92003),f257(x92003,x92001)),x92004)))+~P101(f323(f323(f325(f866(x92003,x92001)),f323(f323(f258(x92003,x92001),x92005),x92002)),f323(f166(f866(x92003,x92001)),x92004)))
% 179.72/179.59 [9202]E(f323(f323(f179(x92021,x92022),x92023),x92024),f323(f230(x92022),x92025))+~P101(f323(f130(x92021),f323(f323(f147(f866(x92021,x92022),x92021),f257(x92021,x92022)),x92023)))+~P101(f323(f323(f325(f866(x92021,x92022)),f323(f323(f258(x92021,x92022),x92024),x92025)),f323(f166(f866(x92021,x92022)),x92023)))
% 179.72/179.59 [9255]~P78(x92551)+~E(f323(x92553,f565(x92553,x92554,x92555,x92552,x92551)),f2(x92551))+E(f323(f159(x92551),f323(f323(f147(x92552,x92551),x92553),f323(f129(x92552,x92554),x92555))),f323(f159(x92551),f323(f323(f147(x92552,x92551),x92553),x92555)))
% 179.72/179.59 [9283]~P28(x92831,x92832,x92833,f246(f867(x92831,a855)),f246(f867(x92832,a855)))+~P101(f323(f323(f237(f867(x92832,a855)),x92834),f323(f302(x92831,x92832,x92833),x92835)))+P101(f323(f323(f237(f867(x92831,a855)),f323(f303(x92831,x92832,x92833),x92834)),x92835))
% 179.72/179.59 [9312]~P28(x93123,x93121,x93124,f246(f867(x93123,a855)),f246(f867(x93121,a855)))+P101(f323(f323(f237(f867(x93121,a855)),x93122),f323(f302(x93123,x93121,x93124),x93125)))+~P101(f323(f323(f237(f867(x93123,a855)),f323(f303(x93123,x93121,x93124),x93122)),x93125))
% 179.72/179.59 [9434]~P18(x94341,x94342,x94343)+~P101(f323(f59(x94341),x94345))+P101(f323(f64(x94341,x94342,x94343,x94344,x94345),f323(f323(f62(x94341,x94342,x94343),x94344),x94345)))
% 179.72/179.59 [9512]~P28(x95122,x95121,x95124,f246(f867(x95122,a855)),f246(f867(x95121,a855)))+~P28(x95121,x95123,x95125,f246(f867(x95121,a855)),f246(f867(x95123,a855)))+E(f323(f71(x95121,x95122,x95123,f91(x95122,x95121,f246(f867(x95122,a855)),x95124)),f91(x95121,x95123,f246(f867(x95121,a855)),x95125)),f91(x95122,x95123,f246(f867(x95122,a855)),f323(f71(x95121,x95123,x95122,x95125),x95124)))
% 179.72/179.59 [9513]P101(f323(x95131,f618(x95132,x95131,x95133,x95134,x95135)))+~P101(f323(f323(f237(f867(x95135,a855)),x95134),x95133))+P101(f323(f323(f237(f867(x95135,a855)),f323(f323(f101(f867(x95135,a855)),x95134),f323(f243(x95135),x95131))),f323(f323(f101(f867(x95135,a855)),x95133),f323(f243(x95135),x95132))))
% 179.72/179.59 [9527]~P78(x95271)+~P101(f323(x95274,f565(x95273,x95274,x95275,x95272,x95271)))+E(f323(f159(x95271),f323(f323(f147(x95272,x95271),x95273),f323(f129(x95272,x95274),x95275))),f323(f159(x95271),f323(f323(f147(x95272,x95271),x95273),x95275)))
% 179.72/179.59 [9607]~P6(x96075)+P101(f323(f323(f325(x96071),f634(x96072,x96073,x96071,x96074,x96075)),x96073))+P101(f323(f323(f237(x96075),x96074),f323(f323(f40(x96071,x96075),x96073),x96072)))
% 179.72/179.59 [9610]~P78(x96101)+E(f323(f159(x96101),f323(f323(f147(x96102,x96101),x96103),f323(f129(x96102,x96104),x96105))),f323(f159(x96101),f323(f323(f147(x96102,x96101),x96103),x96105)))+P101(f323(f323(f325(x96102),f565(x96103,x96104,x96105,x96102,x96101)),f323(f166(x96102),x96105)))
% 179.72/179.59 [9620]~P101(f323(x96205,f618(x96205,x96203,x96204,x96202,x96201)))+~P101(f323(f323(f237(f867(x96201,a855)),x96202),x96204))+P101(f323(f323(f237(f867(x96201,a855)),f323(f323(f101(f867(x96201,a855)),x96202),f323(f243(x96201),x96203))),f323(f323(f101(f867(x96201,a855)),x96204),f323(f243(x96201),x96205))))
% 179.72/179.59 [9635]~P27(x96355,x96353,x96354,f246(f867(x96355,a855)))+P101(f323(x96351,x96352))+P101(f323(f323(f325(x96353),f709(x96352,x96351,x96354,x96353,x96355)),f323(f302(x96355,x96353,x96354),f246(f867(x96355,a855)))))
% 179.72/179.59 [9656]P35(x96561,x96562,x96563,x96564,x96565)+~E(f323(f189(f861(x96562)),x96565),f323(f189(f861(x96561)),x96564))+P101(f323(f323(f238(a860),f657(x96565,x96564,x96563,x96562,x96561)),f323(f189(f861(x96561)),x96564)))
% 179.72/179.59 [9657]P35(x96571,x96572,x96573,x96574,x96575)+~E(f323(f189(f861(x96572)),x96575),f323(f189(f861(x96571)),x96574))+P101(f323(f323(f238(a860),f693(x96573,x96575,x96572,x96574,x96571)),f323(f189(f861(x96571)),x96574)))
% 179.72/179.59 [9690]P101(f323(f323(f325(x96901),f618(x96902,x96903,x96904,x96905,x96901)),x96905))+~P101(f323(f323(f237(f867(x96901,a855)),x96905),x96904))+P101(f323(f323(f237(f867(x96901,a855)),f323(f323(f101(f867(x96901,a855)),x96905),f323(f243(x96901),x96903))),f323(f323(f101(f867(x96901,a855)),x96904),f323(f243(x96901),x96902))))
% 179.72/179.59 [9744]~P6(x97441)+~P101(f323(f323(f237(x97441),x97442),f323(x97445,f634(x97445,x97444,x97443,x97442,x97441))))+P101(f323(f323(f237(x97441),x97442),f323(f323(f40(x97443,x97441),x97444),x97445)))
% 179.72/179.59 [9778]~P68(x97781)+~P101(f323(f59(x97782),x97785))+E(f323(f323(f323(f63(x97781,x97782,f79(x97781)),f323(f323(f18(x97782,x97781,x97781),f323(f323(f8(x97781,f867(x97781,x97781),x97782),f79(x97781)),x97783)),x97784)),f76(x97781)),x97785),f323(f323(f79(x97781),f323(f323(f323(f63(x97781,x97782,f79(x97781)),x97783),f76(x97781)),x97785)),f323(f323(f323(f63(x97781,x97782,f79(x97781)),x97784),f76(x97781)),x97785)))
% 179.72/179.59 [9839]~P101(f323(f323(f325(f866(f867(x98391,a855),f867(x98391,a855))),f323(f323(f258(f867(x98391,a855),f867(x98391,a855)),x98395),x98394)),f314(x98391,x98393)))+~P101(f323(f323(f325(x98391),x98392),x98395))+P101(f323(f323(f325(f866(x98391,x98391)),f323(f323(f258(x98391,x98391),x98392),f716(x98393,x98394,x98395,x98391,x98392))),x98393))
% 179.72/179.59 [9967]~P101(f323(f323(f325(f866(f861(x99671),f861(x99671))),f323(f323(f258(f861(x99671),f861(x99671)),f323(f323(f121(x99671),x99675),x99672)),f323(f323(f121(x99671),x99675),x99673))),f140(x99671,x99674)))+P101(f323(f323(f325(f866(f861(x99671),f861(x99671))),f323(f323(f258(f861(x99671),f861(x99671)),x99672),x99673)),f140(x99671,x99674)))+P101(f323(f323(f325(f866(x99671,x99671)),f323(f323(f258(x99671,x99671),f593(x99674,x99673,x99672,x99675,x99671)),f593(x99674,x99673,x99672,x99675,x99671))),x99674))
% 179.72/179.59 [7105]~E(f323(f189(f861(x71051)),x71053),f323(f189(f861(x71052)),x71054))+E(f323(f323(f179(x71051,x71052),f323(f323(f175(x71051,x71052),x71053),x71054)),x71055),f200(x71052))+P101(f323(f323(f325(x71051),x71055),f323(f166(x71051),x71053)))
% 179.72/179.59 [7178]~E(x71783,x71785)+E(f323(f323(f158(x71781),f323(f323(f152(x71781,x71782),x71783),x71784)),x71785),x71784)+~P101(f323(f323(f238(a860),x71783),f323(f189(f861(x71781)),x71782)))
% 179.72/179.59 [7287]~E(f323(f323(f121(x72871),x72872),x72874),f323(f323(f121(x72871),x72873),x72875))+E(f323(f323(f169(x72871),f323(f189(f861(x72871)),x72872)),x72873),x72872)+P101(f323(f323(f237(a860),f323(f189(f861(x72871)),x72873)),f323(f189(f861(x72871)),x72872)))
% 179.72/179.59 [7785]~E(f323(f323(f121(x77851),x77852),x77854),f323(f323(f121(x77851),x77853),x77855))+E(f323(f323(f169(x77851),f323(f189(f861(x77851)),x77852)),x77853),x77852)+~P101(f323(f323(f237(a860),f323(f189(f861(x77851)),x77852)),f323(f189(f861(x77851)),x77853)))
% 179.72/179.59 [7809]~P101(f323(f59(x78091),f323(x78094,x78095)))+~P101(f323(f323(f325(x78092),x78095),x78093))+P101(f323(f59(x78091),f323(f323(f40(x78092,f867(x78091,a855)),x78093),x78094)))
% 179.72/179.59 [7865]~E(f323(f189(f861(x78651)),x78652),f323(f189(f861(x78653)),x78654))+~E(f323(f323(f179(x78651,x78653),f323(f323(f175(x78651,x78653),x78652),x78654)),x78655),f200(x78653))+~P101(f323(f323(f325(x78651),x78655),f323(f166(x78651),x78652)))
% 179.72/179.59 [7988]~P40(x79881,x79883,x79885)+~P40(x79881,x79882,x79884)+P40(x79881,f323(f323(f110(f867(x79881,a855)),x79882),x79883),f323(f323(f110(f867(f866(x79881,x79881),a855)),x79884),x79885))
% 179.72/179.59 [7989]~P40(x79891,x79893,x79895)+~P40(x79891,x79892,x79894)+P40(x79891,f323(f323(f101(f867(x79891,a855)),x79892),x79893),f323(f323(f101(f867(f866(x79891,x79891),a855)),x79894),x79895))
% 179.72/179.59 [8344]E(f323(f323(f258(x83441,x83442),f323(f323(f158(x83441),x83443),x83444)),f323(f323(f158(x83442),x83445),x83444)),f323(f323(f158(f866(x83441,x83442)),f323(f323(f175(x83441,x83442),x83443),x83445)),x83444))+~P101(f323(f323(f238(a860),x83444),f323(f189(f861(x83441)),x83443)))+~P101(f323(f323(f238(a860),x83444),f323(f189(f861(x83442)),x83445)))
% 179.72/179.59 [8494]~P40(x84941,x84943,x84944)+P101(f323(f323(f325(x84941),x84942),x84943))+~P101(f323(f323(f325(f866(x84941,x84941)),f323(f323(f258(x84941,x84941),x84945),x84942)),x84944))
% 179.72/179.59 [8495]~P40(x84951,x84953,x84954)+P101(f323(f323(f325(x84951),x84952),x84953))+~P101(f323(f323(f325(f866(x84951,x84951)),f323(f323(f258(x84951,x84951),x84952),x84955)),x84954))
% 179.72/179.59 [8496]~P9(x84961,x84963,x84964)+P101(f323(f323(f325(x84961),x84962),x84963))+~P101(f323(f323(f325(f866(x84961,x84961)),f323(f323(f258(x84961,x84961),x84965),x84962)),x84964))
% 179.72/179.59 [8497]~P9(x84971,x84973,x84974)+P101(f323(f323(f325(x84971),x84972),x84973))+~P101(f323(f323(f325(f866(x84971,x84971)),f323(f323(f258(x84971,x84971),x84972),x84975)),x84974))
% 179.72/179.59 [8780]~P9(x87801,x87805,x87802)+E(f323(f277(x87801,x87801,x87802),f323(f323(f301(x87801),x87803),f188(f867(x87801,a855)))),f323(f277(x87801,x87801,x87802),f323(f323(f301(x87801),x87804),f188(f867(x87801,a855)))))+~P101(f323(f323(f325(f866(x87801,x87801)),f323(f323(f258(x87801,x87801),x87803),x87804)),x87802))
% 179.72/179.59 [8962]P101(f323(x89621,x89622))+~P101(f323(f323(f325(x89623),x89622),x89625))+P101(f323(f323(f325(x89623),f404(x89621,x89624,x89625,x89623)),f323(f323(f110(f867(x89623,a855)),x89625),x89624)))
% 179.72/179.59 [8963]P101(f323(x89631,x89632))+~P101(f323(f323(f325(x89633),x89632),x89634))+P101(f323(f323(f325(x89633),f404(x89631,x89634,x89635,x89633)),f323(f323(f110(f867(x89633,a855)),x89635),x89634)))
% 179.72/179.59 [8971]~P101(f323(x89712,x89715))+~P101(f323(f323(f325(x89711),x89715),x89714))+P101(f323(f323(f325(x89711),f388(x89712,x89713,x89714,x89711)),f323(f323(f110(f867(x89711,a855)),x89714),x89713)))
% 179.72/179.59 [8972]~P101(f323(x89722,x89725))+~P101(f323(f323(f325(x89721),x89725),x89723))+P101(f323(f323(f325(x89721),f388(x89722,x89723,x89724,x89721)),f323(f323(f110(f867(x89721,a855)),x89724),x89723)))
% 179.72/179.59 [8987]~P101(f323(f323(f237(f867(x89871,a855)),x89873),x89875))+~P101(f323(f323(f237(f867(x89871,a855)),x89872),x89874))+P101(f323(f323(f237(f867(x89871,a855)),f323(f323(f110(f867(x89871,a855)),x89872),x89873)),f323(f323(f110(f867(x89871,a855)),x89874),x89875)))
% 179.72/179.59 [8988]~P101(f323(f323(f237(f867(x89881,a855)),x89885),x89883))+~P101(f323(f323(f237(f867(x89881,a855)),x89882),x89884))+P101(f323(f323(f237(f867(x89881,a855)),f323(f323(f22(f867(x89881,a855)),x89882),x89883)),f323(f323(f22(f867(x89881,a855)),x89884),x89885)))
% 179.72/179.59 [8989]~P101(f323(f323(f237(f867(x89891,a855)),x89893),x89895))+~P101(f323(f323(f237(f867(x89891,a855)),x89892),x89894))+P101(f323(f323(f237(f867(x89891,a855)),f323(f323(f101(f867(x89891,a855)),x89892),x89893)),f323(f323(f101(f867(x89891,a855)),x89894),x89895)))
% 179.72/179.59 [9081]~E(f323(f189(f861(x90811)),x90813),f323(f189(f861(x90812)),x90814))+E(f323(f323(f179(x90811,x90812),f323(f323(f175(x90811,x90812),x90813),x90814)),x90815),f323(f230(x90812),f532(x90815,x90814,x90812,x90813,x90811)))+~P101(f323(f323(f325(x90811),x90815),f323(f166(x90811),x90813)))
% 179.72/179.59 [9085]P101(f323(f323(f325(f866(x90851,x90851)),f323(f323(f258(x90851,x90851),x90852),x90853)),f317(x90851,x90854,x90855)))+~P101(f323(f323(f237(a860),f323(x90854,x90852)),f323(x90854,x90853)))+~P101(f323(f323(f325(f866(x90851,x90851)),f323(f323(f258(x90851,x90851),x90852),x90853)),x90855))
% 179.72/179.59 [9265]P101(f323(f323(f325(f866(x92651,x92651)),f323(f323(f258(x92651,x92651),x92652),x92653)),f299(x92651,x92654)))+~P101(f323(f323(f325(f866(x92651,x92651)),f323(f323(f258(x92651,x92651),x92652),x92655)),f299(x92651,x92654)))+~P101(f323(f323(f325(f866(x92651,x92651)),f323(f323(f258(x92651,x92651),x92655),x92653)),x92654))
% 179.72/179.59 [9266]P101(f323(f323(f325(f866(x92661,x92661)),f323(f323(f258(x92661,x92661),x92662),x92663)),f299(x92661,x92664)))+~P101(f323(f323(f325(f866(x92661,x92661)),f323(f323(f258(x92661,x92661),x92665),x92663)),f299(x92661,x92664)))+~P101(f323(f323(f325(f866(x92661,x92661)),f323(f323(f258(x92661,x92661),x92662),x92665)),x92664))
% 179.72/179.59 [9363]E(x93631,x93632)+E(f323(a112,f737(x93633,x93634,x93631,x93632,x93635)),x93634)+~P101(f323(f323(f325(f866(x93635,x93635)),f323(f323(f258(x93635,x93635),x93632),x93631)),f323(f323(f183(f866(x93635,x93635),a855),x93634),x93633)))
% 179.72/179.59 [9364]E(x93641,x93642)+E(f323(a112,f739(x93643,x93644,x93641,x93642,x93645)),x93644)+~P101(f323(f323(f325(f866(x93645,x93645)),f323(f323(f258(x93645,x93645),x93642),x93641)),f323(f323(f183(f866(x93645,x93645),a855),x93644),x93643)))
% 179.72/179.59 [9365]E(x93651,f2(a860))+E(f323(a112,f737(x93652,x93651,x93653,x93654,x93655)),x93651)+~P101(f323(f323(f325(f866(x93655,x93655)),f323(f323(f258(x93655,x93655),x93654),x93653)),f323(f323(f183(f866(x93655,x93655),a855),x93651),x93652)))
% 179.72/179.59 [9366]E(x93661,f2(a860))+E(f323(a112,f739(x93662,x93661,x93663,x93664,x93665)),x93661)+~P101(f323(f323(f325(f866(x93665,x93665)),f323(f323(f258(x93665,x93665),x93664),x93663)),f323(f323(f183(f866(x93665,x93665),a855),x93661),x93662)))
% 179.72/179.59 [9383]P101(f323(f323(f325(f866(x93831,x93831)),f323(f323(f258(x93831,x93831),x93832),x93833)),f323(f323(f280(x93831,x93831,x93831),x93834),f299(x93831,x93834))))+~P101(f323(f323(f325(f866(x93831,x93831)),f323(f323(f258(x93831,x93831),x93832),x93835)),x93834))+~P101(f323(f323(f325(f866(x93831,x93831)),f323(f323(f258(x93831,x93831),x93835),x93833)),x93834))
% 179.72/179.59 [9390]~P101(f323(f323(f325(f866(x93901,x93901)),f323(f323(f258(x93901,x93901),x93902),x93905)),f299(x93901,x93904)))+P101(f323(f323(f325(f866(x93901,x93901)),f323(f323(f258(x93901,x93901),x93902),x93903)),f323(f323(f280(x93901,x93901,x93901),x93904),f299(x93901,x93904))))+~P101(f323(f323(f325(f866(x93901,x93901)),f323(f323(f258(x93901,x93901),x93905),x93903)),x93904))
% 179.72/179.59 [9428]~P9(x94281,x94285,x94282)+~P101(f323(f323(f325(f866(x94281,x94281)),f323(f323(f258(x94281,x94281),x94283),x94284)),x94282))+P101(f323(f323(f237(f867(x94281,a855)),f323(f277(x94281,x94281,x94282),f323(f323(f301(x94281),x94283),f188(f867(x94281,a855))))),f323(f277(x94281,x94281,x94282),f323(f323(f301(x94281),x94284),f188(f867(x94281,a855))))))
% 179.72/179.59 [9484]P101(f323(f323(f325(f866(x94841,x94841)),f323(f323(f258(x94841,x94841),x94842),x94843)),f323(f323(f280(x94841,x94841,x94841),x94844),f299(x94841,x94844))))+~P101(f323(f323(f325(f866(x94841,x94841)),f323(f323(f258(x94841,x94841),x94842),x94845)),f323(f323(f280(x94841,x94841,x94841),x94844),f299(x94841,x94844))))+~P101(f323(f323(f325(f866(x94841,x94841)),f323(f323(f258(x94841,x94841),x94845),x94843)),x94844))
% 179.72/179.59 [9485]P101(f323(f323(f325(f866(x94851,x94851)),f323(f323(f258(x94851,x94851),x94852),x94853)),f323(f323(f280(x94851,x94851,x94851),x94854),f299(x94851,x94854))))+~P101(f323(f323(f325(f866(x94851,x94851)),f323(f323(f258(x94851,x94851),x94855),x94853)),f323(f323(f280(x94851,x94851,x94851),x94854),f299(x94851,x94854))))+~P101(f323(f323(f325(f866(x94851,x94851)),f323(f323(f258(x94851,x94851),x94852),x94855)),x94854))
% 179.72/179.59 [9536]~P101(f323(f64(x95361,x95361,x95364,x95362,x95363),x95365))+P101(f323(f323(f325(x95361),x95362),x95363))+P101(f323(f60(x95361,x95364,f323(f323(f301(x95361),x95362),x95363)),x95365))
% 179.72/179.59 [9576]~E(f323(f302(x95763,x95762,x95765),x95764),x95761)+E(x95761,f188(f867(x95762,a855)))+P101(f323(f323(f237(f867(x95763,a855)),f323(f302(x95762,x95763,f581(x95764,x95763,x95762,x95761)),x95761)),x95764))
% 179.72/179.59 [9623]~P6(x96235)+P101(f323(f323(f325(x96231),f449(x96232,x96233,x96234,x96231,x96235)),x96234))+P101(f323(f323(f237(x96235),f323(f323(f39(x96231,x96235),x96234),x96233)),x96232))
% 179.72/179.59 [9676]P35(x96761,x96762,x96763,x96764,x96765)+~E(f323(f189(f861(x96761)),x96764),f323(f189(f861(x96762)),x96765))+P101(f323(f323(f325(f866(x96761,x96762)),f645(x96765,x96764,x96763,x96762,x96761)),f323(f166(f866(x96761,x96762)),f323(f323(f175(x96761,x96762),x96764),x96765))))
% 179.72/179.59 [9677]P35(x96771,x96772,x96773,x96774,x96775)+~E(f323(f189(f861(x96771)),x96774),f323(f189(f861(x96772)),x96775))+P101(f323(f323(f325(f866(x96771,x96772)),f656(x96773,x96775,x96774,x96772,x96771)),f323(f166(f866(x96771,x96772)),f323(f323(f175(x96771,x96772),x96774),x96775))))
% 179.72/179.59 [9816]E(x98161,x98162)+P101(f323(f323(f325(f866(x98163,x98163)),f323(f323(f258(x98163,x98163),x98161),f738(x98164,x98165,x98162,x98161,x98163))),x98164))+~P101(f323(f323(f325(f866(x98163,x98163)),f323(f323(f258(x98163,x98163),x98161),x98162)),f323(f323(f183(f866(x98163,x98163),a855),x98165),x98164)))
% 179.72/179.59 [9817]E(x98171,f2(a860))+P101(f323(f323(f325(f866(x98172,x98172)),f323(f323(f258(x98172,x98172),x98173),f738(x98174,x98171,x98175,x98173,x98172))),x98174))+~P101(f323(f323(f325(f866(x98172,x98172)),f323(f323(f258(x98172,x98172),x98173),x98175)),f323(f323(f183(f866(x98172,x98172),a855),x98171),x98174)))
% 179.72/179.59 [9860]~P6(x98601)+~P101(f323(f323(f237(x98601),f323(x98604,f449(x98605,x98604,x98603,x98602,x98601))),x98605))+P101(f323(f323(f237(x98601),f323(f323(f39(x98602,x98601),x98603),x98604)),x98605))
% 179.72/179.59 [9902]E(x99021,x99022)+P101(f323(f323(f325(f866(x99023,x99023)),f323(f323(f258(x99023,x99023),f740(x99024,x99025,x99021,x99022,x99023)),x99021)),x99024))+~P101(f323(f323(f325(f866(x99023,x99023)),f323(f323(f258(x99023,x99023),x99022),x99021)),f323(f323(f183(f866(x99023,x99023),a855),x99025),x99024)))
% 179.72/179.59 [9903]E(x99031,f2(a860))+P101(f323(f323(f325(f866(x99032,x99032)),f323(f323(f258(x99032,x99032),f740(x99033,x99031,x99034,x99035,x99032)),x99034)),x99033))+~P101(f323(f323(f325(f866(x99032,x99032)),f323(f323(f258(x99032,x99032),x99035),x99034)),f323(f323(f183(f866(x99032,x99032),a855),x99031),x99033)))
% 179.72/179.59 [9907]E(x99071,x99072)+P101(f323(f323(f325(f866(x99073,x99073)),f323(f323(f258(x99073,x99073),x99071),f740(x99074,x99075,x99072,x99071,x99073))),f323(f323(f183(f866(x99073,x99073),a855),f739(x99074,x99075,x99072,x99071,x99073)),x99074)))+~P101(f323(f323(f325(f866(x99073,x99073)),f323(f323(f258(x99073,x99073),x99071),x99072)),f323(f323(f183(f866(x99073,x99073),a855),x99075),x99074)))
% 179.72/179.59 [9908]E(x99081,f2(a860))+P101(f323(f323(f325(f866(x99082,x99082)),f323(f323(f258(x99082,x99082),x99083),f740(x99084,x99081,x99085,x99083,x99082))),f323(f323(f183(f866(x99082,x99082),a855),f739(x99084,x99081,x99085,x99083,x99082)),x99084)))+~P101(f323(f323(f325(f866(x99082,x99082)),f323(f323(f258(x99082,x99082),x99083),x99085)),f323(f323(f183(f866(x99082,x99082),a855),x99081),x99084)))
% 179.72/179.59 [9958]E(x99581,x99582)+P101(f323(f323(f325(f866(x99583,x99583)),f323(f323(f258(x99583,x99583),f738(x99584,x99585,x99581,x99582,x99583)),x99581)),f323(f323(f183(f866(x99583,x99583),a855),f737(x99584,x99585,x99581,x99582,x99583)),x99584)))+~P101(f323(f323(f325(f866(x99583,x99583)),f323(f323(f258(x99583,x99583),x99582),x99581)),f323(f323(f183(f866(x99583,x99583),a855),x99585),x99584)))
% 179.72/179.59 [9959]E(x99591,f2(a860))+P101(f323(f323(f325(f866(x99592,x99592)),f323(f323(f258(x99592,x99592),f738(x99593,x99591,x99594,x99595,x99592)),x99594)),f323(f323(f183(f866(x99592,x99592),a855),f737(x99593,x99591,x99594,x99595,x99592)),x99593)))+~P101(f323(f323(f325(f866(x99592,x99592)),f323(f323(f258(x99592,x99592),x99595),x99594)),f323(f323(f183(f866(x99592,x99592),a855),x99591),x99593)))
% 179.72/179.59 [9992]~P72(x99922)+~P101(f323(f59(x99921),x99925))+E(f323(f323(f6(x99921,x99922),f323(f323(f7(x99921,x99922,x99922),f323(f323(f18(x99921,x99922,f867(x99922,x99922)),f323(f323(f8(a855,f867(x99922,f867(x99922,x99922)),x99921),f96(x99922)),f323(f323(f7(x99921,f867(x99921,a855),a855),f325(x99921)),x99923))),x99924)),f2(x99922))),x99925),f323(f323(f6(x99921,x99922),x99924),f323(f323(f101(f867(x99921,a855)),x99925),x99923)))
% 179.72/179.59 [8562]~P72(x85621)+~P101(f323(f59(x85624),x85625))+E(f323(f323(f78(x85621),f323(x85622,x85623)),f323(f323(f6(x85624,x85621),x85622),f323(f323(f22(f867(x85624,a855)),x85625),f323(f323(f301(x85624),x85623),f188(f867(x85624,a855)))))),f323(f323(f6(x85624,x85621),x85622),f323(f323(f301(x85624),x85623),x85625)))
% 179.72/179.59 [8563]~P68(x85631)+~P101(f323(f59(x85634),x85635))+E(f323(f323(f79(x85631),f323(x85632,x85633)),f323(f323(f9(x85634,x85631),x85632),f323(f323(f22(f867(x85634,a855)),x85635),f323(f323(f301(x85634),x85633),f188(f867(x85634,a855)))))),f323(f323(f9(x85634,x85631),x85632),f323(f323(f301(x85634),x85633),x85635)))
% 179.72/179.59 [8897]~P103(x88972)+~P16(x88972,f323(f162(x88972),f323(f323(f147(x88971,x88972),x88974),x88975)))+E(f323(f129(x88971,f323(f323(f8(x88972,a855,x88971),f323(f238(x88972),x88973)),x88974)),x88975),f171(x88971,f323(f323(f8(x88972,a855,x88971),f323(f238(x88972),x88973)),x88974),x88975))
% 179.72/179.59 [8919]~P72(x89191)+E(f323(f323(f78(x89191),f323(f323(f6(a860,x89191),x89192),f294(a860,x89193,x89194))),f323(f323(f6(a860,x89191),x89192),f294(a860,f323(f323(f78(a860),x89194),f76(a860)),f323(f323(f78(a860),x89194),x89195)))),f323(f323(f6(a860,x89191),x89192),f294(a860,x89193,f323(f323(f78(a860),x89194),x89195))))+~P101(f323(f323(f237(a860),x89193),f323(f323(f78(a860),x89194),f76(a860))))
% 179.72/179.59 [8920]~P101(f323(f323(f325(x89201),x89204),x89205))+~P101(f323(f323(f237(f867(x89201,a855)),f323(f166(x89201),x89202)),x89205))+P101(f323(f323(f237(f867(x89201,a855)),f323(f166(x89201),f323(f323(f152(x89201,x89202),x89203),x89204))),x89205))
% 179.72/179.59 [9147]~P6(x91472)+~P101(f323(f59(x91471),x91475))+E(f323(f323(f62(x91471,x91472,f323(f323(f8(x91472,f867(x91472,x91472),x91471),f110(x91472)),x91473)),x91474),x91475),f323(f323(f110(x91472),x91474),f323(f323(f39(x91471,x91472),x91475),x91473)))
% 179.72/179.59 [9148]~P6(x91482)+~P101(f323(f59(x91481),x91485))+E(f323(f323(f62(x91481,x91482,f323(f323(f8(x91482,f867(x91482,x91482),x91481),f101(x91482)),x91483)),x91484),x91485),f323(f323(f101(x91482),x91484),f323(f323(f40(x91481,x91482),x91485),x91483)))
% 179.72/179.59 [9193]E(f323(x91931,x91932),f323(x91931,x91933))+P101(f323(f323(f238(a860),f323(x91931,x91932)),f323(x91931,x91933)))+~P101(f323(f323(f325(f866(x91934,x91934)),f323(f323(f258(x91934,x91934),x91932),x91933)),f146(x91934,f323(f323(f144(f867(x91934,a860)),x91931),x91935))))
% 179.72/179.59 [9226]~E(f323(x92264,x92262),f323(x92264,x92263))+~P101(f323(f323(f325(f866(x92261,x92261)),f323(f323(f258(x92261,x92261),x92262),x92263)),f146(x92261,x92265)))+P101(f323(f323(f325(f866(x92261,x92261)),f323(f323(f258(x92261,x92261),x92262),x92263)),f146(x92261,f323(f323(f144(f867(x92261,a860)),x92264),x92265))))
% 179.72/179.59 [9245]~P27(x92451,x92452,x92453,x92455)+P27(x92451,x92452,x92453,f323(f323(f301(x92451),x92454),x92455))+P101(f323(f323(f325(x92452),f323(x92453,x92454)),f323(f302(x92451,x92452,x92453),f323(f323(f22(f867(x92451,a855)),x92455),f323(f323(f301(x92451),x92454),f188(f867(x92451,a855)))))))
% 179.72/179.59 [9248]P101(f323(x92482,x92485))+~P101(f323(f323(f325(x92481),x92485),f323(f166(x92481),x92483)))+E(f323(f323(f131(x92481),f323(f189(f861(x92481)),f171(x92481,x92482,f323(f323(f121(x92481),x92483),x92484)))),f323(f323(f121(x92481),x92483),x92484)),f323(f323(f121(x92481),f323(f323(f131(x92481),f323(f189(f861(x92481)),f171(x92481,x92482,x92483))),x92483)),x92484))
% 179.72/179.59 [9251]~P101(f323(f323(f325(f866(x92511,x92511)),f323(f323(f258(x92511,x92511),x92512),x92513)),f146(x92511,x92515)))+~P101(f323(f323(f237(a860),f323(x92514,x92512)),f323(x92514,x92513)))+P101(f323(f323(f325(f866(x92511,x92511)),f323(f323(f258(x92511,x92511),x92512),x92513)),f146(x92511,f323(f323(f144(f867(x92511,a860)),x92514),x92515))))
% 179.72/179.59 [9317]P101(f323(f323(f325(f866(x93174,x93174)),f323(f323(f258(x93174,x93174),x93172),x93173)),f146(x93174,x93175)))+P101(f323(f323(f238(a860),f323(x93171,x93172)),f323(x93171,x93173)))+~P101(f323(f323(f325(f866(x93174,x93174)),f323(f323(f258(x93174,x93174),x93172),x93173)),f146(x93174,f323(f323(f144(f867(x93174,a860)),x93171),x93175))))
% 179.72/179.59 [9457]~P101(f323(f323(f325(f866(f861(x94571),f861(x94571))),f323(f323(f258(f861(x94571),f861(x94571)),x94572),x94574)),f151(x94571,x94575)))+~P101(f323(f323(f238(a860),x94573),f323(f189(f861(x94571)),x94572)))+P101(f323(f323(f325(f866(x94571,x94571)),f323(f323(f258(x94571,x94571),f323(f323(f158(x94571),x94572),x94573)),f323(f323(f158(x94571),x94574),x94573))),x94575))
% 179.72/179.59 [9704]E(x97041,f2(a1))+~P101(f323(f46(x97043,x97041),f323(f323(f258(a1,a1),x97044),x97045)))+P101(f323(f46(f323(f323(f79(a1),x97042),x97043),x97041),f323(f323(f258(a1,a1),f323(f323(f78(a1),f323(f323(f79(a1),x97042),x97044)),f323(f323(f36(a1),f323(f323(f79(a1),x97042),x97045)),x97041))),f42(a1,f323(f323(f79(a1),x97042),x97045),x97041))))
% 179.72/179.59 [9706]~P101(f323(f323(f238(a860),f2(a860)),x97063))+~P101(f323(f45(x97062,x97063),f323(f323(f258(a860,a860),x97064),x97065)))+P101(f323(f45(f323(f323(f79(a860),x97061),x97062),x97063),f323(f323(f258(a860,a860),f323(f323(f78(a860),f323(f323(f79(a860),x97061),x97064)),f323(f323(f36(a860),f323(f323(f79(a860),x97061),x97065)),x97063))),f42(a860,f323(f323(f79(a860),x97061),x97065),x97063))))
% 179.72/179.59 [10014]~P72(x100142)+~P101(f323(f59(x100141),x100144))+E(f323(f323(f6(x100141,x100142),x100143),f323(f243(x100141),f323(f323(f18(x100141,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100141),a321),f323(f323(f7(x100141,f867(x100141,a855),a855),f325(x100141)),x100144))),f323(f323(f7(x100141,f867(x100141,a855),a855),f325(x100141)),x100145)))),f323(f323(f6(x100141,x100142),f323(f323(f7(x100141,x100142,x100142),f323(f323(f18(x100141,x100142,f867(x100142,x100142)),f323(f323(f8(a855,f867(x100142,f867(x100142,x100142)),x100141),f96(x100142)),f323(f323(f7(x100141,f867(x100141,a855),a855),f325(x100141)),x100145))),x100143)),f2(x100142))),x100144))
% 179.72/179.59 [8195]~E(f323(f323(f121(x81951),x81952),x81955),f323(f323(f121(x81951),x81953),x81954))+E(f323(f323(f121(x81951),f323(f323(f131(x81951),f323(f189(f861(x81951)),x81952)),x81953)),x81954),x81955)+P101(f323(f323(f237(a860),f323(f189(f861(x81951)),x81953)),f323(f189(f861(x81951)),x81952)))
% 179.72/179.59 [8394]~E(f323(f323(f121(x83942),x83943),x83941),f323(f323(f121(x83942),x83944),x83945))+E(x83941,f323(f323(f121(x83942),f323(f323(f131(x83942),f323(f189(f861(x83942)),x83943)),x83944)),x83945))+~P101(f323(f323(f237(a860),f323(f189(f861(x83942)),x83943)),f323(f189(f861(x83942)),x83944)))
% 179.72/179.59 [8477]~E(f323(f323(f78(a860),f323(f323(f79(a860),x84773),x84774)),x84771),f323(f323(f78(a860),f323(f323(f79(a860),x84772),x84774)),x84775))+~P101(f323(f323(f237(a860),x84773),x84772))+E(x84771,f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x84772),x84773)),x84774)),x84775))
% 179.72/179.59 [8478]~E(f323(f323(f78(a860),f323(f323(f79(a860),x84781),x84783)),x84784),f323(f323(f78(a860),f323(f323(f79(a860),x84782),x84783)),x84785))+~P101(f323(f323(f237(a860),x84782),x84781))+E(f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x84781),x84782)),x84783)),x84784),x84785)
% 179.72/179.59 [8647]E(f323(f323(f78(a860),f323(f323(f79(a860),x86471),x86472)),x86473),f323(f323(f78(a860),f323(f323(f79(a860),x86474),x86472)),x86475))+~P101(f323(f323(f237(a860),x86474),x86471))+~E(x86475,f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x86471),x86474)),x86472)),x86473))
% 179.72/179.59 [8648]E(f323(f323(f78(a860),f323(f323(f79(a860),x86481),x86482)),x86483),f323(f323(f78(a860),f323(f323(f79(a860),x86484),x86482)),x86485))+~P101(f323(f323(f237(a860),x86484),x86481))+~E(f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x86481),x86484)),x86482)),x86483),x86485)
% 179.72/179.59 [9511]~P62(x95112)+~P101(f323(f59(x95111),x95115))+E(f323(f323(f9(x95111,x95112),f323(f323(f18(x95111,x95112,x95112),f323(f323(f8(x95112,f867(x95112,x95112),x95111),f281(x95112)),x95113)),x95114)),x95115),f323(f323(f281(x95112),f323(f323(f9(x95111,x95112),x95113),x95115)),f323(f323(f9(x95111,x95112),x95114),x95115)))
% 179.72/179.59 [9639]~E(f744(x96395,x96394,x96393,x96392,x96391),f745(x96395,x96394,x96393,x96392,x96391))+P101(f323(f323(f325(f866(x96391,x96391)),f323(f323(f258(x96391,x96391),x96392),x96393)),f299(x96391,x96394)))+~P101(f323(f323(f325(f866(x96391,x96391)),f323(f323(f258(x96391,x96391),x96392),x96393)),f299(x96391,f323(f323(f110(f867(f866(x96391,x96391),a855)),x96394),x96395))))
% 179.72/179.59 [9640]~E(f746(x96405,x96404,x96403,x96402,x96401),f747(x96405,x96404,x96403,x96402,x96401))+P101(f323(f323(f325(f866(x96401,x96401)),f323(f323(f258(x96401,x96401),x96402),x96403)),f299(x96401,x96404)))+~P101(f323(f323(f325(f866(x96401,x96401)),f323(f323(f258(x96401,x96401),x96402),x96403)),f299(x96401,f323(f323(f110(f867(f866(x96401,x96401),a855)),x96404),x96405))))
% 179.72/179.59 [9850]P101(f323(f323(f325(f866(x98501,x98501)),f323(f323(f258(x98501,x98501),x98502),f747(x98505,x98504,x98503,x98502,x98501))),f299(x98501,x98504)))+P101(f323(f323(f325(f866(x98501,x98501)),f323(f323(f258(x98501,x98501),x98502),x98503)),f299(x98501,x98504)))+~P101(f323(f323(f325(f866(x98501,x98501)),f323(f323(f258(x98501,x98501),x98502),x98503)),f299(x98501,f323(f323(f110(f867(f866(x98501,x98501),a855)),x98504),x98505))))
% 179.72/179.59 [9929]P101(f323(f323(f325(f866(x99291,x99291)),f323(f323(f258(x99291,x99291),f745(x99295,x99294,x99293,x99292,x99291)),x99293)),f299(x99291,x99294)))+P101(f323(f323(f325(f866(x99291,x99291)),f323(f323(f258(x99291,x99291),x99292),x99293)),f299(x99291,x99294)))+~P101(f323(f323(f325(f866(x99291,x99291)),f323(f323(f258(x99291,x99291),x99292),x99293)),f299(x99291,f323(f323(f110(f867(f866(x99291,x99291),a855)),x99294),x99295))))
% 179.72/179.59 [9965]P101(f323(f323(f325(f866(x99651,x99651)),f323(f323(f258(x99651,x99651),x99652),x99653)),f299(x99651,x99654)))+P101(f323(f323(f325(f866(x99651,x99651)),f323(f323(f258(x99651,x99651),f744(x99655,x99654,x99653,x99652,x99651)),f745(x99655,x99654,x99653,x99652,x99651))),x99655))+~P101(f323(f323(f325(f866(x99651,x99651)),f323(f323(f258(x99651,x99651),x99652),x99653)),f299(x99651,f323(f323(f110(f867(f866(x99651,x99651),a855)),x99654),x99655))))
% 179.72/179.59 [9966]P101(f323(f323(f325(f866(x99661,x99661)),f323(f323(f258(x99661,x99661),x99662),x99663)),f299(x99661,x99664)))+P101(f323(f323(f325(f866(x99661,x99661)),f323(f323(f258(x99661,x99661),f747(x99665,x99664,x99663,x99662,x99661)),f746(x99665,x99664,x99663,x99662,x99661))),x99665))+~P101(f323(f323(f325(f866(x99661,x99661)),f323(f323(f258(x99661,x99661),x99662),x99663)),f299(x99661,f323(f323(f110(f867(f866(x99661,x99661),a855)),x99664),x99665))))
% 179.72/179.59 [10086]~P101(f323(f323(f325(f866(f861(x100861),f861(x100861))),f323(f323(f258(f861(x100861),f861(x100861)),x100864),x100865)),f151(x100861,x100862)))+~P101(f323(f323(f325(f866(x100861,x100861)),x100863),f323(f166(f866(x100861,x100861)),f323(f323(f175(x100861,x100861),x100864),x100865))))+P101(f323(f323(f262(x100861,x100861,a855),f323(f323(f7(x100861,f867(f866(x100861,x100861),a855),f867(x100861,a855)),f323(f323(f8(f867(x100861,f867(f867(f866(x100861,x100861),a855),a855)),f867(f867(f866(x100861,x100861),a855),f867(x100861,a855)),x100861),f7(x100861,f867(f866(x100861,x100861),a855),a855)),f323(f323(f8(f867(x100861,f866(x100861,x100861)),f867(x100861,f867(f867(f866(x100861,x100861),a855),a855)),x100861),f323(f8(f866(x100861,x100861),f867(f867(f866(x100861,x100861),a855),a855),x100861),f325(f866(x100861,x100861)))),f258(x100861,x100861)))),x100862)),x100863))
% 179.72/179.59 [9540]~P101(f323(f323(f237(a860),x95403),x95402))+~P101(f323(f323(f237(a860),f323(f323(f78(a860),f323(f323(f79(a860),x95403),x95404)),x95401)),f323(f323(f78(a860),f323(f323(f79(a860),x95402),x95404)),x95405)))+P101(f323(f323(f237(a860),x95401),f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x95402),x95403)),x95404)),x95405)))
% 179.72/179.59 [9541]~P101(f323(f323(f237(a860),x95413),x95412))+~P101(f323(f323(f238(a860),f323(f323(f78(a860),f323(f323(f79(a860),x95413),x95414)),x95411)),f323(f323(f78(a860),f323(f323(f79(a860),x95412),x95414)),x95415)))+P101(f323(f323(f238(a860),x95411),f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x95412),x95413)),x95414)),x95415)))
% 179.72/179.59 [9560]~P101(f323(f323(f237(a860),x95601),x95604))+P101(f323(f323(f237(a860),f323(f323(f78(a860),f323(f323(f79(a860),x95601),x95602)),x95603)),f323(f323(f78(a860),f323(f323(f79(a860),x95604),x95602)),x95605)))+~P101(f323(f323(f237(a860),x95603),f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x95604),x95601)),x95602)),x95605)))
% 179.72/179.59 [9561]~P101(f323(f323(f237(a860),x95611),x95614))+P101(f323(f323(f238(a860),f323(f323(f78(a860),f323(f323(f79(a860),x95611),x95612)),x95613)),f323(f323(f78(a860),f323(f323(f79(a860),x95614),x95612)),x95615)))+~P101(f323(f323(f238(a860),x95613),f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x95614),x95611)),x95612)),x95615)))
% 179.72/179.59 [9674]~P101(f323(f323(f237(a860),x96742),x96741))+~P101(f323(f323(f237(a860),f323(f323(f78(a860),f323(f323(f79(a860),x96741),x96743)),x96744)),f323(f323(f78(a860),f323(f323(f79(a860),x96742),x96743)),x96745)))+P101(f323(f323(f237(a860),f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x96741),x96742)),x96743)),x96744)),x96745))
% 179.72/179.59 [9675]~P101(f323(f323(f237(a860),x96752),x96751))+~P101(f323(f323(f238(a860),f323(f323(f78(a860),f323(f323(f79(a860),x96751),x96753)),x96754)),f323(f323(f78(a860),f323(f323(f79(a860),x96752),x96753)),x96755)))+P101(f323(f323(f238(a860),f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x96751),x96752)),x96753)),x96754)),x96755))
% 179.72/179.59 [9728]~P101(f323(f323(f237(a860),x97284),x97281))+P101(f323(f323(f237(a860),f323(f323(f78(a860),f323(f323(f79(a860),x97281),x97282)),x97283)),f323(f323(f78(a860),f323(f323(f79(a860),x97284),x97282)),x97285)))+~P101(f323(f323(f237(a860),f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x97281),x97284)),x97282)),x97283)),x97285))
% 179.72/179.59 [9729]~P101(f323(f323(f237(a860),x97294),x97291))+P101(f323(f323(f238(a860),f323(f323(f78(a860),f323(f323(f79(a860),x97291),x97292)),x97293)),f323(f323(f78(a860),f323(f323(f79(a860),x97294),x97292)),x97295)))+~P101(f323(f323(f238(a860),f323(f323(f78(a860),f323(f323(f79(a860),f323(f323(f22(a860),x97291),x97294)),x97292)),x97293)),x97295))
% 179.72/179.59 [9950]~P14(x99501,x99502,x99505,x99503)+~P101(f323(f323(f325(f866(x99501,x99501)),x99504),x99505))+P101(f323(f323(f262(x99501,x99501,a855),f323(f323(f7(x99501,f867(x99501,x99502),f867(x99501,a855)),f323(f323(f8(f867(x99502,a855),f867(f867(x99501,x99502),f867(x99501,a855)),x99501),f8(x99502,a855,x99501)),f323(f323(f8(x99502,f867(x99502,a855),x99501),a320),x99503))),x99503)),x99504))
% 179.72/179.59 [6753]~E(f323(x67534,x67535),f200(x67532))+E(f323(f180(x67531,x67532,x67533,x67534),x67535),f323(f230(x67532),x67536))+~E(f323(x67533,x67535),f323(f230(x67532),x67536))
% 179.72/179.59 [6853]~E(f323(x68533,x68536),f200(x68531))+E(f323(f232(f864(x68531),x68532,f200(x68531),x68533),f323(x68534,x68535)),f200(x68531))+~E(f323(x68534,x68535),f323(f230(x68532),x68536))
% 179.72/179.59 [7430]E(f323(x74301,x74302),f200(x74303))+~E(f323(f180(x74305,x74303,x74306,x74301),x74302),f323(f230(x74303),x74304))+E(f323(x74301,x74302),f323(f230(x74303),x74304))
% 179.72/179.59 [7465]~E(f323(f180(x74656,x74653,x74655,x74651),x74652),f323(f230(x74653),x74654))+E(f323(x74651,x74652),f323(f230(x74653),x74654))+E(f323(x74655,x74652),f323(f230(x74653),x74654))
% 179.72/179.59 [8357]~P21(x83576,x83571,x83572,x83574)+E(f323(f71(x83571,x83571,x83571,f323(x83572,x83573)),f323(x83574,x83575)),f323(f71(x83571,x83571,x83571,f323(x83574,x83575)),f323(x83572,x83573)))+~P101(f323(f59(x83576),x83575))
% 179.72/179.59 [8792]~P27(x87921,x87923,x87925,x87926)+~P27(x87923,x87922,x87924,f323(f302(x87921,x87923,x87925),x87926))+P27(x87921,x87922,f323(f71(x87923,x87922,x87921,x87924),x87925),x87926)
% 179.72/179.59 [9348]~P101(f323(f323(x93483,x93482),x93486))+~P101(f323(f323(x93484,x93485),x93482))+P101(f323(f323(f325(x93481),x93482),f291(x93481,x93483,x93484,x93485,x93486)))
% 179.72/179.59 [9349]~P101(f323(f323(x93494,x93492),x93496))+~P101(f323(f323(x93493,x93495),x93492))+P101(f323(f323(f325(x93491),x93492),f288(x93491,x93493,x93494,x93495,x93496)))
% 179.72/179.59 [9458]E(x94581,x94582)+E(x94583,x94584)+~P101(f323(f323(f325(f866(f861(x94585),f861(x94585))),f323(f323(f258(f861(x94585),f861(x94585)),f323(f323(f144(x94585),x94583),x94581)),f323(f323(f144(x94585),x94584),x94582))),f150(x94585,x94586)))
% 179.72/179.59 [9468]~E(x94682,x94684)+P101(f323(f323(f325(f866(f861(x94681),f861(x94681))),f323(f323(f258(f861(x94681),f861(x94681)),f323(f323(f144(x94681),x94682),x94683)),f323(f323(f144(x94681),x94684),x94685))),f138(x94681,x94686)))+~P101(f323(f323(f325(f866(f861(x94681),f861(x94681))),f323(f323(f258(f861(x94681),f861(x94681)),x94683),x94685)),f138(x94681,x94686)))
% 179.72/179.59 [9469]~E(x94692,x94694)+P101(f323(f323(f325(f866(f861(x94691),f861(x94691))),f323(f323(f258(f861(x94691),f861(x94691)),f323(f323(f144(x94691),x94692),x94693)),f323(f323(f144(x94691),x94694),x94695))),f140(x94691,x94696)))+~P101(f323(f323(f325(f866(f861(x94691),f861(x94691))),f323(f323(f258(f861(x94691),f861(x94691)),x94693),x94695)),f140(x94691,x94696)))
% 179.72/179.59 [9470]~E(x94702,x94704)+P101(f323(f323(f325(f866(f861(x94701),f861(x94701))),f323(f323(f258(f861(x94701),f861(x94701)),f323(f323(f144(x94701),x94702),x94703)),f323(f323(f144(x94701),x94704),x94705))),f150(x94701,x94706)))+~P101(f323(f323(f325(f866(f861(x94701),f861(x94701))),f323(f323(f258(f861(x94701),f861(x94701)),x94703),x94705)),f150(x94701,x94706)))
% 179.72/179.59 [9471]~E(x94712,x94714)+P101(f323(f323(f325(f866(f861(x94711),f861(x94711))),f323(f323(f258(f861(x94711),f861(x94711)),f323(f323(f121(x94711),x94712),x94713)),f323(f323(f121(x94711),x94714),x94715))),f150(x94711,x94716)))+~P101(f323(f323(f325(f866(f861(x94711),f861(x94711))),f323(f323(f258(f861(x94711),f861(x94711)),x94713),x94715)),f150(x94711,x94716)))
% 179.72/179.59 [9472]~E(x94723,x94725)+P101(f323(f323(f325(f866(f861(x94721),f861(x94721))),f323(f323(f258(f861(x94721),f861(x94721)),f323(f323(f121(x94721),x94722),x94723)),f323(f323(f121(x94721),x94724),x94725))),f150(x94721,x94726)))+~P101(f323(f323(f325(f866(f861(x94721),f861(x94721))),f323(f323(f258(f861(x94721),f861(x94721)),x94722),x94724)),f150(x94721,x94726)))
% 179.72/179.59 [9528]E(x95281,x95282)+P101(f323(f323(f325(f866(f861(x95283),f861(x95283))),f323(f323(f258(f861(x95283),f861(x95283)),x95281),x95282)),f150(x95283,x95284)))+~P101(f323(f323(f325(f866(f861(x95283),f861(x95283))),f323(f323(f258(f861(x95283),f861(x95283)),f323(f323(f144(x95283),x95285),x95281)),f323(f323(f144(x95283),x95286),x95282))),f150(x95283,x95284)))
% 179.72/179.59 [9678]~E(x96783,x96785)+P101(f323(f323(f325(f866(f861(x96781),f861(x96781))),f323(f323(f258(f861(x96781),f861(x96781)),f323(f323(f121(x96781),x96782),f323(f323(f144(x96781),x96783),f113(x96781)))),f323(f323(f121(x96781),x96784),f323(f323(f144(x96781),x96785),f113(x96781))))),f150(x96781,x96786)))+~P101(f323(f323(f325(f866(f861(x96781),f861(x96781))),f323(f323(f258(f861(x96781),f861(x96781)),x96782),x96784)),f150(x96781,x96786)))
% 179.72/179.59 [9694]E(f323(x96941,x96942),f200(x96943))+~E(f323(f232(f864(x96946),x96943,f200(x96946),x96944),f323(x96941,x96942)),f200(x96946))+E(f323(x96944,f837(x96942,x96941,x96944,x96945,x96946,x96943)),f200(x96946))
% 179.72/179.59 [9695]E(f323(x96951,x96952),f200(x96953))+~E(f323(f232(f864(x96956),x96953,f200(x96956),x96954),f323(x96951,x96952)),f200(x96956))+E(f323(f230(x96953),f837(x96952,x96951,x96954,x96955,x96956,x96953)),f323(x96951,x96952))
% 179.72/179.59 [9732]E(x97321,x97322)+E(x97323,x97324)+~P101(f323(f323(f325(f866(f861(x97325),f861(x97325))),f323(f323(f258(f861(x97325),f861(x97325)),f323(f323(f121(x97325),x97323),f323(f323(f144(x97325),x97321),f113(x97325)))),f323(f323(f121(x97325),x97324),f323(f323(f144(x97325),x97322),f113(x97325))))),f150(x97325,x97326)))
% 179.72/179.59 [9757]E(x97571,x97572)+~P101(f323(f323(f325(f866(f861(x97573),f861(x97573))),f323(f323(f258(f861(x97573),f861(x97573)),f323(f323(f121(x97573),x97571),f323(f323(f144(x97573),x97575),f113(x97573)))),f323(f323(f121(x97573),x97572),f323(f323(f144(x97573),x97576),f113(x97573))))),f150(x97573,x97574)))+P101(f323(f323(f325(f866(f861(x97573),f861(x97573))),f323(f323(f258(f861(x97573),f861(x97573)),x97571),x97572)),f150(x97573,x97574)))
% 179.72/179.59 [9795]~P101(f323(f323(f325(f866(f867(x97951,a855),f867(x97951,a855))),f323(f323(f258(f867(x97951,a855),f867(x97951,a855)),x97952),x97954)),f314(x97951,x97956)))+~P101(f323(f323(f325(f866(f867(x97951,a855),f867(x97951,a855))),f323(f323(f258(f867(x97951,a855),f867(x97951,a855)),x97953),x97955)),f314(x97951,x97956)))+P101(f323(f323(f325(f866(f867(x97951,a855),f867(x97951,a855))),f323(f323(f258(f867(x97951,a855),f867(x97951,a855)),f323(f323(f110(f867(x97951,a855)),x97952),x97953)),f323(f323(f110(f867(x97951,a855)),x97954),x97955))),f314(x97951,x97956)))
% 179.72/179.59 [5221]~E(f323(x52213,x52216),x52215)+~E(x52214,f323(f230(x52211),x52216))+E(f323(f323(f201(x52211,x52212),x52213),x52214),f323(f230(x52212),x52215))
% 179.72/179.59 [5634]~E(f323(f323(f121(x56341),x56346),x56343),x56345)+E(f323(f323(f121(x56341),x56342),x56343),f323(f323(f144(x56341),x56344),x56345))+~E(x56342,f323(f323(f144(x56341),x56344),x56346))
% 179.72/179.59 [5635]~E(f323(f323(f121(x56351),x56356),x56353),x56355)+E(f323(f323(f121(x56351),x56352),x56353),f323(f323(f121(x56351),x56354),x56355))+~E(x56352,f323(f323(f121(x56351),x56354),x56356))
% 179.72/179.59 [5637]E(f323(f323(f121(x56371),x56372),x56373),f323(f323(f144(x56371),x56374),x56375))+~E(f323(f323(f144(x56371),x56374),x56376),x56372)+~E(x56375,f323(f323(f121(x56371),x56376),x56373))
% 179.72/179.59 [5639]~E(f323(f323(f121(x56391),x56392),x56396),x56394)+E(f323(f323(f121(x56391),x56392),x56393),f323(f323(f121(x56391),x56394),x56395))+~E(x56393,f323(f323(f121(x56391),x56396),x56395))
% 179.72/179.59 [6747]E(f323(x67471,x67472),f323(x67473,x67472))+~E(f323(f323(f147(x67474,x67475),x67471),x67476),f323(f323(f147(x67474,x67475),x67473),x67476))+~P101(f323(f323(f325(x67474),x67472),f323(f166(x67474),x67476)))
% 179.72/179.59 [7128]~P21(x71284,x71285,x71286,x71281)+E(f323(f323(x71281,x71282),x71283),f323(f323(f62(x71284,x71285,x71286),x71283),x71282))+~P101(f323(f59(x71284),x71282))
% 179.72/179.59 [7194]~E(x71942,f323(x71944,x71946))+~P101(f323(f323(f325(x71943),x71946),x71945))+P101(f323(f323(f325(x71941),x71942),f323(f302(x71943,x71941,x71944),x71945)))
% 179.72/179.59 [7195]~E(f323(x71954,x71952),x71956)+~P101(f323(f323(f325(x71953),x71956),x71955))+P101(f323(f323(f325(x71951),x71952),f323(f303(x71951,x71953,x71954),x71955)))
% 179.72/179.59 [7644]~P33(x76441,x76442,x76444,x76446)+P33(x76441,x76442,f323(f323(f144(x76441),x76443),x76444),f323(f323(f144(x76441),x76445),x76446))+~P101(f323(f323(x76442,x76443),x76445))
% 179.72/179.59 [8657]~P53(x86574,x86575,x86571,x86572,x86576)+E(f323(x86571,f323(x86572,x86573)),x86573)+~P101(f323(f323(f325(x86575),x86573),x86576))
% 179.72/179.59 [9158]~P28(x91582,x91581,x91585,x91584,x91583)+E(f323(f91(x91581,x91582,x91583,f91(x91582,x91581,x91584,x91585)),x91586),f323(x91585,x91586))+~P101(f323(f323(f325(x91582),x91586),x91584))
% 179.72/179.59 [9460]E(x94601,x94602)+E(f323(f189(f861(x94603)),x94604),f323(f189(f861(x94603)),x94605))+~P101(f323(f323(f325(f866(f861(x94603),f861(x94603))),f323(f323(f258(f861(x94603),f861(x94603)),f323(f323(f144(x94603),x94601),x94604)),f323(f323(f144(x94603),x94602),x94605))),f138(x94603,x94606)))
% 179.72/179.59 [9523]~P18(x95231,x95232,x95233)+E(f323(f323(f62(x95231,x95232,x95233),x95234),x95235),x95236)+~P101(f323(f64(x95231,x95232,x95233,x95234,x95235),x95236))
% 179.72/179.59 [9531]E(f323(f189(f861(x95311)),x95312),f323(f189(f861(x95311)),x95313))+P101(f323(f323(f325(f866(f861(x95311),f861(x95311))),f323(f323(f258(f861(x95311),f861(x95311)),x95312),x95313)),f138(x95311,x95314)))+~P101(f323(f323(f325(f866(f861(x95311),f861(x95311))),f323(f323(f258(f861(x95311),f861(x95311)),f323(f323(f144(x95311),x95315),x95312)),f323(f323(f144(x95311),x95316),x95313))),f138(x95311,x95314)))
% 179.72/179.59 [9554]~P101(f323(f323(f325(f866(x95541,x95541)),f323(f323(f258(x95541,x95541),x95542),x95544)),f299(x95541,x95546)))+P101(f323(f323(f325(f866(f861(x95541),f861(x95541))),f323(f323(f258(f861(x95541),f861(x95541)),f323(f323(f144(x95541),x95542),x95543)),f323(f323(f144(x95541),x95544),x95545))),f299(f861(x95541),f150(x95541,x95546))))+~P101(f323(f323(f325(f866(f861(x95541),f861(x95541))),f323(f323(f258(f861(x95541),f861(x95541)),x95543),x95545)),f299(f861(x95541),f150(x95541,x95546))))
% 179.72/179.59 [9738]~P101(f323(x97382,x97386))+~E(f323(f129(x97381,x97382),x97383),f323(f323(f144(x97381),x97384),x97385))+~P101(f323(f323(f325(x97381),x97386),f323(f166(x97381),f708(x97385,x97384,x97383,x97382,x97381))))
% 179.72/179.59 [9739]~P101(f323(x97394,x97396))+~E(f323(f323(f144(x97391),x97392),x97393),f323(f129(x97391,x97394),x97395))+~P101(f323(f323(f325(x97391),x97396),f323(f166(x97391),f707(x97395,x97394,x97393,x97392,x97391))))
% 179.72/179.59 [10041]~P72(x100412)+E(f323(f323(f6(x100411,x100412),f323(f323(f8(f867(x100413,a855),x100412,x100411),f323(f6(x100413,x100412),x100414)),f323(f323(f8(f867(x100413,a855),f867(x100413,a855),x100411),f243(x100413)),f323(f323(f8(f867(x100413,a855),f867(x100413,a855),x100411),f323(f18(x100413,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100413),a321),f323(f323(f7(x100413,f867(x100413,a855),a855),f325(x100413)),x100415)))),f323(f7(x100413,x100411,a855),f323(f323(f8(x100411,f867(x100411,a855),x100413),a320),x100416)))))),f323(f302(x100413,x100411,x100416),x100415)),f323(f323(f6(x100413,x100412),x100414),x100415))+~P101(f323(f59(x100413),x100415))
% 179.72/179.59 [6805]~P103(x68053)+P101(f323(x68052,x68055))+E(f323(f129(x68051,x68052),f323(f323(f141(x68051,x68053,x68054),x68055),x68056)),f323(f129(x68051,x68052),x68056))
% 179.72/179.59 [6807]P101(f323(x68071,x68072))+~E(f160(x68073,x68071,x68074),f323(f323(f258(f861(x68073),f861(x68073)),x68075),x68076))+~P101(f323(f323(f325(x68073),x68072),f323(f166(x68073),x68075)))
% 179.72/179.59 [6850]~P101(f323(x68502,x68506))+~E(f160(x68501,x68502,x68503),f323(f323(f258(f861(x68501),f861(x68501)),x68504),x68505))+~P101(f323(f323(f325(x68501),x68506),f323(f166(x68501),x68505)))
% 179.72/179.59 [7509]~P17(x75091,x75092,x75093)+~P101(f323(f59(x75091),x75096))+E(f323(f323(f62(x75091,x75092,x75093),x75094),f323(f323(f301(x75091),x75095),x75096)),f323(f323(f62(x75091,x75092,x75093),f323(f323(x75093,x75095),x75094)),x75096))
% 179.72/179.59 [7559]~P103(x75592)+~P101(f323(f323(f237(x75592),f323(x75593,x75594)),f323(x75593,x75595)))+E(f323(f323(f141(x75591,x75592,x75593),x75594),f323(f323(f144(x75591),x75595),x75596)),f323(f323(f144(x75591),x75594),f323(f323(f144(x75591),x75595),x75596)))
% 179.72/179.59 [7674]E(x76741,x76742)+~E(f323(f323(f260(x76743,x76744),x76741),f323(f16(f867(x76744,a855),x76743),x76745)),f323(f323(f260(x76743,x76744),x76742),f323(f16(f867(x76744,a855),x76743),x76745)))+~P101(f323(f323(f325(x76744),x76746),x76745))
% 179.72/179.59 [7739]~P17(x77391,x77392,x77393)+~P101(f323(f59(x77391),x77396))+E(f323(f323(f62(x77391,x77392,x77393),x77394),f323(f323(f301(x77391),x77395),x77396)),f323(f323(x77393,x77395),f323(f323(f62(x77391,x77392,x77393),x77394),x77396)))
% 179.72/179.59 [7856]~P18(x78561,x78562,x78563)+~P101(f323(f59(x78561),x78566))+E(f323(f323(f62(x78561,x78562,x78563),f323(f323(x78563,x78564),x78565)),x78566),f323(f323(x78563,x78564),f323(f323(f62(x78561,x78562,x78563),x78565),x78566)))
% 179.72/179.59 [7927]~P22(x79272,x79275,x79276,x79271)+~P101(f323(f59(x79272),x79274))+E(f323(x79271,f323(f323(f301(x79272),x79273),x79274)),f323(f71(x79275,x79275,x79275,f323(x79271,x79274)),f323(x79276,x79273)))
% 179.72/179.59 [7959]~P103(x79592)+P101(f323(f323(f237(x79592),f323(x79593,x79594)),f323(x79593,x79595)))+E(f323(f323(f141(x79591,x79592,x79593),x79594),f323(f323(f144(x79591),x79595),x79596)),f323(f323(f144(x79591),x79595),f323(f323(f141(x79591,x79592,x79593),x79594),x79596)))
% 179.72/179.59 [8096]~E(f323(f189(f861(x80961)),x80965),f323(f189(f861(x80962)),x80966))+~E(f323(f189(f861(x80961)),x80963),f323(f189(f861(x80962)),x80964))+E(f323(f323(f121(f866(x80961,x80962)),f323(f323(f175(x80961,x80962),x80963),x80964)),f323(f323(f175(x80961,x80962),x80965),x80966)),f323(f323(f175(x80961,x80962),f323(f323(f121(x80961),x80963),x80965)),f323(f323(f121(x80962),x80964),x80966)))
% 179.72/179.59 [8210]~E(x82102,f323(f302(x82103,x82101,x82104),x82106))+P101(f323(f323(f237(f867(x82101,a855)),x82102),f323(f302(x82103,x82101,x82104),x82105)))+~P101(f323(f323(f237(f867(x82103,a855)),x82106),x82105))
% 179.72/179.59 [8316]~P103(x83165)+E(f323(x83161,x83162),f323(x83161,x83163))+E(f323(f323(f141(x83164,x83165,x83161),x83162),f323(f323(f141(x83164,x83165,x83161),x83163),x83166)),f323(f323(f141(x83164,x83165,x83161),x83163),f323(f323(f141(x83164,x83165,x83161),x83162),x83166)))
% 179.72/179.59 [8350]~P27(x83503,x83501,x83504,x83505)+P27(x83503,x83501,f323(f323(f323(f70(x83503,x83501),x83504),x83506),x83502),x83505)+P101(f323(f323(f325(x83501),x83502),f323(f302(x83503,x83501,x83504),x83505)))
% 179.72/179.59 [8486]~P101(f323(f323(f325(x84862),x84864),f323(x84866,x84863)))+~P101(f323(f323(f325(x84861),x84863),x84865))+P101(f323(f323(f325(f866(x84861,x84862)),f323(f323(f258(x84861,x84862),x84863),x84864)),f323(f323(f260(x84861,x84862),x84865),x84866)))
% 179.72/179.59 [8960]~P72(x89602)+~P27(x89604,x89601,x89605,x89606)+E(f323(f323(f6(x89601,x89602),x89603),f323(f302(x89604,x89601,x89605),x89606)),f323(f323(f6(x89604,x89602),f323(f71(x89601,x89602,x89604,x89603),x89605)),x89606))
% 179.72/179.59 [8961]~P68(x89612)+~P27(x89614,x89611,x89615,x89616)+E(f323(f323(f9(x89611,x89612),x89613),f323(f302(x89614,x89611,x89615),x89616)),f323(f323(f9(x89614,x89612),f323(f71(x89611,x89612,x89614,x89613),x89615)),x89616))
% 179.72/179.59 [9009]~P35(x90092,x90095,x90091,x90093,x90096)+P101(f323(f323(x90091,f323(f323(f158(x90092),x90093),x90094)),f323(f323(f158(x90095),x90096),x90094)))+~P101(f323(f323(f238(a860),x90094),f323(f189(f861(x90095)),x90096)))
% 179.72/179.59 [9010]~P35(x90102,x90105,x90101,x90103,x90106)+P101(f323(f323(x90101,f323(f323(f158(x90102),x90103),x90104)),f323(f323(f158(x90105),x90106),x90104)))+~P101(f323(f323(f238(a860),x90104),f323(f189(f861(x90102)),x90103)))
% 179.72/179.59 [9021]~E(f323(f302(x90211,x90212,x90213),x90214),x90216)+E(f323(f302(x90211,x90212,x90213),f323(f302(x90212,x90211,f91(x90211,x90212,x90214,x90213)),x90215)),x90215)+~P101(f323(f323(f237(f867(x90212,a855)),x90215),x90216))
% 179.72/179.59 [9221]~P21(x92213,x92211,x92216,x92212)+~P101(f323(f59(x92213),x92214))+E(f323(f71(x92211,x92211,x92211,f323(x92212,f323(f323(f22(f867(x92213,a855)),x92214),f323(f323(f301(x92213),x92215),f188(f867(x92213,a855)))))),f323(x92216,x92215)),f323(x92212,f323(f323(f301(x92213),x92215),x92214)))
% 179.72/179.59 [9830]~E(f323(f302(x98302,x98304,x98306),f246(f867(x98302,a855))),f246(f867(x98304,a855)))+~E(f323(f302(x98301,x98303,x98305),f246(f867(x98301,a855))),f246(f867(x98303,a855)))+E(f323(f302(f866(x98301,x98302),f866(x98303,x98304),f263(x98301,x98303,x98302,x98304,x98305,x98306)),f246(f867(f866(x98301,x98302),a855))),f246(f867(f866(x98303,x98304),a855)))
% 179.72/179.59 [9878]~P27(x98783,x98784,x98785,f323(x98786,f684(x98786,x98785,x98784,x98783,x98782,x98781)))+P27(x98783,x98784,x98785,f323(f323(f40(x98782,f867(x98783,a855)),x98781),x98786))+E(x98781,f188(f867(x98782,a855)))
% 179.72/179.59 [9936]P27(x99366,x99365,x99364,f323(f323(f40(x99362,f867(x99366,a855)),x99361),x99363))+E(x99361,f188(f867(x99362,a855)))+P101(f323(f323(f325(x99362),f684(x99363,x99364,x99365,x99366,x99362,x99361)),x99361))
% 179.72/179.59 [9941]P101(f323(f323(f325(x99411),f711(x99412,x99413,x99414,x99415,x99416,x99411)),x99416))+P101(f323(f323(f237(f867(f866(x99411,x99414),a855)),f323(f323(f260(x99411,x99414),x99416),x99413)),f323(f323(f260(x99411,x99414),x99415),x99412)))+~P101(f323(f323(f237(f867(x99411,a855)),x99416),x99415))
% 179.72/179.59 [9979]P26(x99796,x99795,f323(f323(f301(f859(x99796)),f323(f323(f323(f90(x99796),x99794),x99793),x99792)),f188(f867(f859(x99796),a855))))+~P26(x99796,x99795,f323(f323(f301(f859(x99796)),f323(f323(f323(f90(x99796),x99794),x99793),x99791)),f188(f867(f859(x99796),a855))))+P101(f323(f323(x99791,f775(x99792,x99791,x99793,x99794,x99795,x99796)),f817(x99792,x99791,x99793,x99794,x99795,x99796)))
% 179.72/179.59 [9980]P26(x99806,x99805,f323(f323(f301(f859(x99806)),f323(f323(f323(f90(x99806),x99801),x99803),x99802)),f188(f867(f859(x99806),a855))))+~P26(x99806,x99805,f323(f323(f301(f859(x99806)),f323(f323(f323(f90(x99806),x99804),x99803),x99802)),f188(f867(f859(x99806),a855))))+P101(f323(f323(x99801,f830(x99801,x99802,x99803,x99804,x99805,x99806)),f839(x99801,x99802,x99803,x99804,x99805,x99806)))
% 179.72/179.59 [10017]~P26(x100171,x100172,f323(f323(f301(f859(x100171)),f323(f323(f323(f90(x100171),x100173),x100174),x100176)),f188(f867(f859(x100171),a855))))+P26(x100171,x100172,f323(f323(f301(f859(x100171)),f323(f323(f323(f90(x100171),x100173),x100174),x100175)),f188(f867(f859(x100171),a855))))+~P101(f323(f323(x100175,f775(x100175,x100176,x100174,x100173,x100172,x100171)),f817(x100175,x100176,x100174,x100173,x100172,x100171)))
% 179.72/179.59 [10018]~P26(x100181,x100182,f323(f323(f301(f859(x100181)),f323(f323(f323(f90(x100181),x100186),x100184),x100185)),f188(f867(f859(x100181),a855))))+P26(x100181,x100182,f323(f323(f301(f859(x100181)),f323(f323(f323(f90(x100181),x100183),x100184),x100185)),f188(f867(f859(x100181),a855))))+~P101(f323(f323(x100186,f830(x100183,x100185,x100184,x100186,x100182,x100181)),f839(x100183,x100185,x100184,x100186,x100182,x100181)))
% 179.72/179.59 [10052]~P101(f323(f323(f237(f867(x100522,a855)),f323(x100524,f711(x100526,x100524,x100522,x100525,x100523,x100521))),f323(x100526,f711(x100526,x100524,x100522,x100525,x100523,x100521))))+~P101(f323(f323(f237(f867(x100521,a855)),x100523),x100525))+P101(f323(f323(f237(f867(f866(x100521,x100522),a855)),f323(f323(f260(x100521,x100522),x100523),x100524)),f323(f323(f260(x100521,x100522),x100525),x100526)))
% 179.72/179.59 [7694]~P101(f323(x76941,x76945))+~P101(f323(x76946,x76944))+P101(f323(x76941,f323(f261(x76942,x76943),f323(f323(f258(x76942,x76943),x76944),x76945))))
% 179.72/179.59 [7695]~P101(f323(x76951,x76954))+~P101(f323(x76956,x76955))+P101(f323(x76951,f323(f257(x76952,x76953),f323(f323(f258(x76952,x76953),x76954),x76955))))
% 179.72/179.59 [7716]~E(f323(f189(f861(x77161)),x77163),f323(f189(f861(x77164)),x77165))+~E(f323(f323(f179(x77161,x77164),f323(f323(f175(x77161,x77164),x77163),x77165)),x77162),f323(f230(x77164),x77166))+P101(f323(f323(f325(x77161),x77162),f323(f166(x77161),x77163)))
% 179.72/179.59 [7744]~P101(f323(f323(x77444,x77446),x77445))+~P101(f323(f323(f325(x77441),x77446),x77443))+P101(f323(f323(f323(f39(x77441,f867(x77442,a855)),x77443),x77444),x77445))
% 179.72/179.59 [8047]~P101(f323(f323(f325(x80471),x80472),f323(x80475,x80476)))+~P101(f323(f323(f325(x80473),x80476),x80474))+P101(f323(f323(f325(x80471),x80472),f323(f323(f39(x80473,f867(x80471,a855)),x80474),x80475)))
% 179.72/179.59 [8089]P101(f323(f323(x80891,x80892),x80893))+~P101(f323(f323(x80894,x80892),x80893))+~P101(f323(f323(f237(f867(x80895,f867(x80896,a855))),x80894),x80891))
% 179.72/179.59 [8234]P101(f323(f323(x82341,x82342),x82343))+~P101(f323(f323(f325(x82344),x82342),x82345))+~P101(f323(f323(f323(f40(x82344,f867(x82346,a855)),x82345),x82341),x82343))
% 179.72/179.59 [8373]P101(f323(f323(f325(x83731),x83732),f323(x83733,x83734)))+~P101(f323(f323(f325(x83735),x83734),x83736))+~P101(f323(f323(f325(x83731),x83732),f323(f323(f40(x83735,f867(x83731,a855)),x83736),x83733)))
% 179.72/179.59 [8636]~P14(x86364,x86365,x86366,x86361)+E(f323(x86361,x86362),f323(x86361,x86363))+~P101(f323(f323(f325(f866(x86364,x86364)),f323(f323(f258(x86364,x86364),x86362),x86363)),x86366))
% 179.72/179.59 [8670]P101(f323(f323(f237(f867(x86701,a855)),x86702),f323(x86703,x86704)))+~P101(f323(f323(f325(x86705),x86704),x86706))+~P101(f323(f323(f237(f867(x86701,a855)),x86702),f323(f323(f40(x86705,f867(x86701,a855)),x86706),x86703)))
% 179.72/179.59 [8704]~P51(x87043,x87044,f323(f278(x87044,x87043),x87045))+E(x87041,f188(f867(x87042,a855)))+E(f323(f323(f40(x87042,f867(x87043,a855)),x87041),f323(f323(f8(f867(x87044,a855),f867(x87043,a855),x87042),f277(x87044,x87043,x87045)),x87046)),f323(f277(x87044,x87043,x87045),f323(f323(f40(x87042,f867(x87044,a855)),x87041),x87046)))
% 179.72/179.59 [8783]P101(f323(f323(f325(x87831),x87832),f323(f277(x87833,x87831,x87834),x87835)))+~P101(f323(f323(f325(x87833),x87836),x87835))+~P101(f323(f323(f325(f866(x87833,x87831)),f323(f323(f258(x87833,x87831),x87836),x87832)),x87834))
% 179.72/179.59 [9087]P101(f323(f323(f237(f867(x90871,a855)),f323(f277(x90872,x90871,x90873),x90874)),f323(f277(x90872,x90871,x90875),x90876)))+~P101(f323(f323(f237(f867(x90872,a855)),x90874),x90876))+~P101(f323(f323(f237(f867(f866(x90872,x90871),a855)),x90873),x90875))
% 179.72/179.59 [9267]~P101(f323(f323(f325(x92672),x92676),x92674))+~P101(f323(f323(f237(f867(x92671,a855)),x92673),x92675))+P101(f323(f323(f237(f867(f866(x92671,x92672),a855)),f323(f323(f260(x92671,x92672),x92673),f323(f16(f867(x92672,a855),x92671),x92674))),f323(f323(f260(x92671,x92672),x92675),f323(f16(f867(x92672,a855),x92671),x92674))))
% 179.72/179.59 [9280]~P35(x92801,x92802,x92803,x92805,x92806)+P101(f323(f323(f262(x92801,x92802,a855),x92803),x92804))+~P101(f323(f323(f325(f866(x92801,x92802)),x92804),f323(f166(f866(x92801,x92802)),f323(f323(f175(x92801,x92802),x92805),x92806))))
% 179.72/179.59 [9413]~E(x94133,x94135)+P101(f323(f323(f325(f866(f861(x94131),f861(x94131))),f323(f323(f258(f861(x94131),f861(x94131)),f323(f323(f144(x94131),x94132),x94133)),f323(f323(f144(x94131),x94134),x94135))),f150(x94131,x94136)))+~P101(f323(f323(f325(f866(x94131,x94131)),f323(f323(f258(x94131,x94131),x94132),x94134)),x94136))
% 179.72/179.59 [9420]~E(f323(f189(f861(x94201)),x94205),f323(f189(f861(x94202)),x94206))+E(f181(x94201,x94202,f182(x94201,x94202,x94203,f323(f323(f22(f867(x94201,a855)),x94204),f323(f166(x94201),x94205))),x94205,x94206),f182(x94201,x94202,f181(x94201,x94202,x94203,x94205,x94206),x94204))+~P101(f323(f323(f237(f867(x94201,a855)),f323(f166(x94201),x94205)),x94204))
% 179.72/179.59 [9421]~E(f323(f189(f861(x94211)),x94213),f323(f189(f861(x94211)),x94215))+P101(f323(f323(f325(f866(f861(x94211),f861(x94211))),f323(f323(f258(f861(x94211),f861(x94211)),f323(f323(f144(x94211),x94212),x94213)),f323(f323(f144(x94211),x94214),x94215))),f138(x94211,x94216)))+~P101(f323(f323(f325(f866(x94211,x94211)),f323(f323(f258(x94211,x94211),x94212),x94214)),x94216))
% 179.72/179.59 [9452]P101(f323(f323(f325(f866(x94521,x94521)),f323(f323(f258(x94521,x94521),x94522),x94523)),f323(f323(f183(f866(x94521,x94521),a855),f323(a112,x94524)),x94525)))+~P101(f323(f323(f325(f866(x94521,x94521)),f323(f323(f258(x94521,x94521),x94526),x94523)),x94525))+~P101(f323(f323(f325(f866(x94521,x94521)),f323(f323(f258(x94521,x94521),x94522),x94526)),f323(f323(f183(f866(x94521,x94521),a855),x94524),x94525)))
% 179.72/179.59 [9453]P101(f323(f323(f325(f866(x94531,x94531)),f323(f323(f258(x94531,x94531),x94532),x94533)),f323(f323(f183(f866(x94531,x94531),a855),f323(a112,x94534)),x94535)))+~P101(f323(f323(f325(f866(x94531,x94531)),f323(f323(f258(x94531,x94531),x94532),x94536)),x94535))+~P101(f323(f323(f325(f866(x94531,x94531)),f323(f323(f258(x94531,x94531),x94536),x94533)),f323(f323(f183(f866(x94531,x94531),a855),x94534),x94535)))
% 179.72/179.59 [9456]~P101(f323(f323(f325(x94564),x94565),x94566))+P101(f323(f323(f237(f867(x94561,a855)),x94562),x94563))+~P101(f323(f323(f237(f867(f866(x94561,x94564),a855)),f323(f323(f260(x94561,x94564),x94562),f323(f16(f867(x94564,a855),x94561),x94566))),f323(f323(f260(x94561,x94564),x94563),f323(f16(f867(x94564,a855),x94561),x94566))))
% 179.72/179.59 [9501]E(x95011,x95012)+~P101(f323(f323(f325(f866(f861(x95013),f861(x95013))),f323(f323(f258(f861(x95013),f861(x95013)),f323(f323(f144(x95013),x95011),x95015)),f323(f323(f144(x95013),x95012),x95016))),f138(x95013,x95014)))+P101(f323(f323(f325(f866(x95013,x95013)),f323(f323(f258(x95013,x95013),x95011),x95012)),x95014))
% 179.72/179.59 [9502]E(x95021,x95022)+~P101(f323(f323(f325(f866(f861(x95023),f861(x95023))),f323(f323(f258(f861(x95023),f861(x95023)),f323(f323(f144(x95023),x95021),x95025)),f323(f323(f144(x95023),x95022),x95026))),f140(x95023,x95024)))+P101(f323(f323(f325(f866(x95023,x95023)),f323(f323(f258(x95023,x95023),x95021),x95022)),x95024))
% 179.72/179.59 [9503]E(x95031,x95032)+~P101(f323(f323(f325(f866(f861(x95033),f861(x95033))),f323(f323(f258(f861(x95033),f861(x95033)),f323(f323(f144(x95033),x95031),x95035)),f323(f323(f144(x95033),x95032),x95036))),f150(x95033,x95034)))+P101(f323(f323(f325(f866(x95033,x95033)),f323(f323(f258(x95033,x95033),x95031),x95032)),x95034))
% 179.72/179.59 [9539]P101(f323(f323(f325(f866(f861(x95391),f861(x95391))),f323(f323(f258(f861(x95391),f861(x95391)),f323(f323(f144(x95391),x95392),x95393)),f323(f323(f144(x95391),x95394),x95395))),f151(x95391,x95396)))+~P101(f323(f323(f325(f866(f861(x95391),f861(x95391))),f323(f323(f258(f861(x95391),f861(x95391)),x95393),x95395)),f151(x95391,x95396)))+~P101(f323(f323(f325(f866(x95391,x95391)),f323(f323(f258(x95391,x95391),x95392),x95394)),x95396))
% 179.72/179.59 [9558]P101(f323(x95581,x95582))+~P101(f323(x95581,f446(x95581,x95583,x95584,x95585,x95586)))+~P101(f323(f323(f325(x95586),x95582),f323(f323(f39(x95585,f867(x95586,a855)),x95584),x95583)))
% 179.72/179.59 [9563]~P101(f323(f323(f325(f866(f861(x95631),f861(x95631))),f323(f323(f258(f861(x95631),f861(x95631)),f323(f323(f144(x95631),x95632),x95635)),f323(f323(f144(x95631),x95633),x95636))),f138(x95631,x95634)))+P101(f323(f323(f325(f866(f861(x95631),f861(x95631))),f323(f323(f258(f861(x95631),f861(x95631)),x95635),x95636)),f138(x95631,x95634)))+P101(f323(f323(f325(f866(x95631,x95631)),f323(f323(f258(x95631,x95631),x95632),x95633)),x95634))
% 179.72/179.59 [9564]~P101(f323(f323(f325(f866(f861(x95641),f861(x95641))),f323(f323(f258(f861(x95641),f861(x95641)),f323(f323(f144(x95641),x95642),x95645)),f323(f323(f144(x95641),x95643),x95646))),f140(x95641,x95644)))+P101(f323(f323(f325(f866(f861(x95641),f861(x95641))),f323(f323(f258(f861(x95641),f861(x95641)),x95645),x95646)),f140(x95641,x95644)))+P101(f323(f323(f325(f866(x95641,x95641)),f323(f323(f258(x95641,x95641),x95642),x95643)),x95644))
% 179.72/179.59 [9565]~P101(f323(f323(f325(f866(f861(x95651),f861(x95651))),f323(f323(f258(f861(x95651),f861(x95651)),f323(f323(f144(x95651),x95652),x95655)),f323(f323(f144(x95651),x95653),x95656))),f150(x95651,x95654)))+P101(f323(f323(f325(f866(f861(x95651),f861(x95651))),f323(f323(f258(f861(x95651),f861(x95651)),x95655),x95656)),f150(x95651,x95654)))+P101(f323(f323(f325(f866(x95651,x95651)),f323(f323(f258(x95651,x95651),x95652),x95653)),x95654))
% 179.72/179.59 [9650]P101(f323(x96501,x96502))+P101(f323(f323(f325(x96503),f447(x96501,x96504,x96505,x96503,x96506)),x96505))+~P101(f323(f323(f325(x96506),x96502),f323(f323(f39(x96503,f867(x96506,a855)),x96505),x96504)))
% 179.72/179.59 [9661]~E(x96612,x96614)+P101(f323(f323(f325(f866(f861(x96611),f861(x96611))),f323(f323(f258(f861(x96611),f861(x96611)),f323(f323(f121(x96611),x96612),f323(f323(f144(x96611),x96613),f113(x96611)))),f323(f323(f121(x96611),x96614),f323(f323(f144(x96611),x96615),f113(x96611))))),f150(x96611,x96616)))+~P101(f323(f323(f325(f866(x96611,x96611)),f323(f323(f258(x96611,x96611),x96613),x96615)),x96616))
% 179.72/179.59 [9748]E(x97481,x97482)+~P101(f323(f323(f325(f866(f861(x97483),f861(x97483))),f323(f323(f258(f861(x97483),f861(x97483)),f323(f323(f121(x97483),x97485),f323(f323(f144(x97483),x97481),f113(x97483)))),f323(f323(f121(x97483),x97486),f323(f323(f144(x97483),x97482),f113(x97483))))),f150(x97483,x97484)))+P101(f323(f323(f325(f866(x97483,x97483)),f323(f323(f258(x97483,x97483),x97481),x97482)),x97484))
% 179.72/179.59 [9776]~P101(f323(f323(f325(f866(f861(x97761),f861(x97761))),f323(f323(f258(f861(x97761),f861(x97761)),f323(f323(f121(x97761),x97765),f323(f323(f144(x97761),x97762),f113(x97761)))),f323(f323(f121(x97761),x97766),f323(f323(f144(x97761),x97763),f113(x97761))))),f150(x97761,x97764)))+P101(f323(f323(f325(f866(f861(x97761),f861(x97761))),f323(f323(f258(f861(x97761),f861(x97761)),x97765),x97766)),f150(x97761,x97764)))+P101(f323(f323(f325(f866(x97761,x97761)),f323(f323(f258(x97761,x97761),x97762),x97763)),x97764))
% 179.72/179.59 [9796]P101(f323(x97961,x97962))+P101(f323(f323(f325(x97963),f446(x97961,x97964,x97965,x97966,x97963)),f323(x97964,f447(x97961,x97964,x97965,x97966,x97963))))+~P101(f323(f323(f325(x97963),x97962),f323(f323(f39(x97966,f867(x97963,a855)),x97965),x97964)))
% 179.72/179.59 [8798]~P18(x87983,x87984,x87981)+~P101(f323(f59(x87983),x87986))+E(f323(f323(x87981,x87982),f323(f323(f62(x87983,x87984,x87981),x87985),f323(f323(f22(f867(x87983,a855)),x87986),f323(f323(f301(x87983),x87982),f188(f867(x87983,a855)))))),f323(f323(f62(x87983,x87984,x87981),x87985),f323(f323(f301(x87983),x87982),x87986)))
% 179.72/179.59 [8882]~E(f323(f323(f179(x88821,x88822),x88824),x88825),f323(f230(x88822),x88826))+~P101(f323(f323(x88823,x88825),x88826))+E(f323(f323(f179(x88821,x88822),f323(f129(f866(x88821,x88822),f323(f262(x88821,x88822,a855),x88823)),x88824)),x88825),f323(f230(x88822),x88826))
% 179.72/179.59 [9094]~P101(f323(f323(f325(x90945),x90943),x90946))+P101(f323(f323(f237(f867(x90941,a855)),f323(x90942,x90943)),x90944))+~P101(f323(f323(f237(f867(x90941,a855)),f323(f323(f39(x90945,f867(x90941,a855)),x90946),x90942)),x90944))
% 179.72/179.59 [9721]~P9(x97211,x97215,x97214)+P101(f323(f323(f325(f866(x97211,x97211)),f323(f323(f258(x97211,x97211),x97212),x97213)),x97214))+~P101(f323(f323(f325(x97211),x97216),f323(f323(f101(f867(x97211,a855)),f323(f277(x97211,x97211,x97214),f323(f323(f301(x97211),x97212),f188(f867(x97211,a855))))),f323(f277(x97211,x97211,x97214),f323(f323(f301(x97211),x97213),f188(f867(x97211,a855)))))))
% 179.72/179.59 [8523]~P107(x85232)+~E(f323(f323(f78(x85232),f323(f323(f79(x85232),x85234),x85235)),x85231),f323(f323(f78(x85232),f323(f323(f79(x85232),x85233),x85235)),x85236))+E(x85231,f323(f323(f78(x85232),f323(f323(f79(x85232),f323(f323(f22(x85232),x85233),x85234)),x85235)),x85236))
% 179.72/179.59 [8524]~P107(x85241)+~E(f323(f323(f78(x85241),f323(f323(f79(x85241),x85242),x85244)),x85245),f323(f323(f78(x85241),f323(f323(f79(x85241),x85243),x85244)),x85246))+E(f323(f323(f78(x85241),f323(f323(f79(x85241),f323(f323(f22(x85241),x85242),x85243)),x85244)),x85245),x85246)
% 179.72/179.59 [8707]~P107(x87071)+E(f323(f323(f78(x87071),f323(f323(f79(x87071),x87072),x87073)),x87074),f323(f323(f78(x87071),f323(f323(f79(x87071),x87075),x87073)),x87076))+~E(x87076,f323(f323(f78(x87071),f323(f323(f79(x87071),f323(f323(f22(x87071),x87072),x87075)),x87073)),x87074))
% 179.72/179.59 [8708]~P107(x87081)+E(f323(f323(f78(x87081),f323(f323(f79(x87081),x87082),x87083)),x87084),f323(f323(f78(x87081),f323(f323(f79(x87081),x87085),x87083)),x87086))+~E(f323(f323(f78(x87081),f323(f323(f79(x87081),f323(f323(f22(x87081),x87082),x87085)),x87083)),x87084),x87086)
% 179.72/179.59 [9033]~P101(f323(f323(x90334,x90335),x90336))+~P101(f323(f323(x90333,x90335),x90336))+P101(f323(f323(f323(f323(f101(f867(x90331,f867(x90332,a855))),x90333),x90334),x90335),x90336))
% 179.72/179.59 [9289]P101(f323(f323(x92891,x92892),x92893))+P101(f323(f323(x92894,x92892),x92893))+~P101(f323(f323(f323(f323(f110(f867(x92895,f867(x92896,a855))),x92894),x92891),x92892),x92893))
% 179.72/179.59 [9578]~P122(x95781)+~P101(f323(f323(f237(x95781),f323(f323(f78(x95781),f323(f323(f79(x95781),x95784),x95785)),x95782)),f323(f323(f78(x95781),f323(f323(f79(x95781),x95783),x95785)),x95786)))+P101(f323(f323(f237(x95781),x95782),f323(f323(f78(x95781),f323(f323(f79(x95781),f323(f323(f22(x95781),x95783),x95784)),x95785)),x95786)))
% 179.72/179.59 [9579]~P122(x95791)+~P101(f323(f323(f238(x95791),f323(f323(f78(x95791),f323(f323(f79(x95791),x95794),x95795)),x95792)),f323(f323(f78(x95791),f323(f323(f79(x95791),x95793),x95795)),x95796)))+P101(f323(f323(f238(x95791),x95792),f323(f323(f78(x95791),f323(f323(f79(x95791),f323(f323(f22(x95791),x95793),x95794)),x95795)),x95796)))
% 179.72/179.59 [9602]~P122(x96021)+P101(f323(f323(f237(x96021),f323(f323(f78(x96021),f323(f323(f79(x96021),x96022),x96023)),x96024)),f323(f323(f78(x96021),f323(f323(f79(x96021),x96025),x96023)),x96026)))+~P101(f323(f323(f237(x96021),x96024),f323(f323(f78(x96021),f323(f323(f79(x96021),f323(f323(f22(x96021),x96025),x96022)),x96023)),x96026)))
% 179.72/179.59 [9603]~P122(x96031)+P101(f323(f323(f238(x96031),f323(f323(f78(x96031),f323(f323(f79(x96031),x96032),x96033)),x96034)),f323(f323(f78(x96031),f323(f323(f79(x96031),x96035),x96033)),x96036)))+~P101(f323(f323(f238(x96031),x96034),f323(f323(f78(x96031),f323(f323(f79(x96031),f323(f323(f22(x96031),x96035),x96032)),x96033)),x96036)))
% 179.72/179.59 [9709]~P122(x97091)+~P101(f323(f323(f237(x97091),f323(f323(f78(x97091),f323(f323(f79(x97091),x97092),x97094)),x97095)),f323(f323(f78(x97091),f323(f323(f79(x97091),x97093),x97094)),x97096)))+P101(f323(f323(f237(x97091),f323(f323(f78(x97091),f323(f323(f79(x97091),f323(f323(f22(x97091),x97092),x97093)),x97094)),x97095)),x97096))
% 179.72/179.59 [9710]~P122(x97101)+~P101(f323(f323(f238(x97101),f323(f323(f78(x97101),f323(f323(f79(x97101),x97102),x97104)),x97105)),f323(f323(f78(x97101),f323(f323(f79(x97101),x97103),x97104)),x97106)))+P101(f323(f323(f238(x97101),f323(f323(f78(x97101),f323(f323(f79(x97101),f323(f323(f22(x97101),x97102),x97103)),x97104)),x97105)),x97106))
% 179.72/179.59 [9759]~P122(x97591)+P101(f323(f323(f237(x97591),f323(f323(f78(x97591),f323(f323(f79(x97591),x97592),x97593)),x97594)),f323(f323(f78(x97591),f323(f323(f79(x97591),x97595),x97593)),x97596)))+~P101(f323(f323(f237(x97591),f323(f323(f78(x97591),f323(f323(f79(x97591),f323(f323(f22(x97591),x97592),x97595)),x97593)),x97594)),x97596))
% 179.72/179.59 [9760]~P122(x97601)+P101(f323(f323(f238(x97601),f323(f323(f78(x97601),f323(f323(f79(x97601),x97602),x97603)),x97604)),f323(f323(f78(x97601),f323(f323(f79(x97601),x97605),x97603)),x97606)))+~P101(f323(f323(f238(x97601),f323(f323(f78(x97601),f323(f323(f79(x97601),f323(f323(f22(x97601),x97602),x97605)),x97603)),x97604)),x97606))
% 179.72/179.59 [9930]~P72(x99302)+~P101(f323(f59(x99301),x99306))+E(f323(f323(f6(x99301,x99302),f323(f323(f18(x99301,x99302,x99302),f323(f323(f18(x99301,x99302,f867(x99302,x99302)),f323(f323(f8(a855,f867(x99302,f867(x99302,x99302)),x99301),f96(x99302)),x99303)),x99304)),x99305)),x99306),f323(f323(f78(x99302),f323(f323(f6(x99301,x99302),x99304),f323(f323(f101(f867(x99301,a855)),x99306),f323(f243(x99301),x99303)))),f323(f323(f6(x99301,x99302),x99305),f323(f323(f101(f867(x99301,a855)),x99306),f323(f77(f867(x99301,a855)),f323(f243(x99301),x99303))))))
% 179.72/179.59 [9988]P101(f323(f323(f325(x99882),x99884),x99886))+P101(f323(f323(f325(x99882),x99885),x99886))+E(f323(f303(x99881,x99882,f323(f323(f7(x99881,x99882,x99882),f323(f323(f7(x99881,x99882,f867(x99882,x99882)),f323(f323(f8(a855,f867(x99882,f867(x99882,x99882)),x99881),f96(x99882)),f323(f323(f7(x99881,f867(x99881,a855),a855),f325(x99881)),x99883))),x99884)),x99885)),x99886),f188(f867(x99881,a855)))
% 179.72/179.59 [9989]P101(f323(f323(f325(x99892),x99895),x99896))+~P101(f323(f323(f325(x99892),x99894),x99896))+E(f323(f303(x99891,x99892,f323(f323(f7(x99891,x99892,x99892),f323(f323(f7(x99891,x99892,f867(x99892,x99892)),f323(f323(f8(a855,f867(x99892,f867(x99892,x99892)),x99891),f96(x99892)),f323(f323(f7(x99891,f867(x99891,a855),a855),f325(x99891)),x99893))),x99894)),x99895)),x99896),x99893)
% 179.72/179.59 [9990]P101(f323(f323(f325(x99902),x99904),x99906))+~P101(f323(f323(f325(x99902),x99905),x99906))+E(f323(f303(x99901,x99902,f323(f323(f7(x99901,x99902,x99902),f323(f323(f7(x99901,x99902,f867(x99902,x99902)),f323(f323(f8(a855,f867(x99902,f867(x99902,x99902)),x99901),f96(x99902)),f323(f323(f7(x99901,f867(x99901,a855),a855),f325(x99901)),x99903))),x99904)),x99905)),x99906),f323(f77(f867(x99901,a855)),x99903))
% 179.72/179.59 [9991]~P101(f323(f323(f325(x99912),x99914),x99916))+~P101(f323(f323(f325(x99912),x99915),x99916))+E(f323(f303(x99911,x99912,f323(f323(f7(x99911,x99912,x99912),f323(f323(f7(x99911,x99912,f867(x99912,x99912)),f323(f323(f8(a855,f867(x99912,f867(x99912,x99912)),x99911),f96(x99912)),f323(f323(f7(x99911,f867(x99911,a855),a855),f325(x99911)),x99913))),x99914)),x99915)),x99916),f246(f867(x99911,a855)))
% 179.72/179.59 [8556]E(x85561,x85562)+~P53(x85564,x85565,x85563,x85566,x85567)+~E(f323(x85563,x85561),f323(x85563,x85562))
% 179.72/179.59 [6956]E(f323(f232(f864(x69561),x69562,f200(x69561),x69563),f323(x69564,x69565)),f323(f230(x69561),x69566))+~E(f323(x69564,x69565),f323(f230(x69562),x69567))+~E(f323(x69563,x69567),f323(f230(x69561),x69566))
% 179.72/179.59 [8585]~P11(x85856,x85855,x85857,x85854,x85851)+E(f323(f323(x85851,x85852),x85853),x85854)+P101(f323(f59(x85855),x85853))
% 179.72/179.59 [9443]P43(x94431,x94432,x94433,x94434,x94435,f323(f323(x94433,x94436),x94437))+~E(f323(f323(x94433,x94436),x94437),x94434)+~E(x94435,f188(f867(x94431,a855)))
% 179.72/179.59 [9624]~P101(f323(x96246,x96243))+~P101(f323(f323(f325(f866(x96242,x96242)),f323(f323(f258(x96242,x96242),x96244),x96245)),f323(x96247,x96243)))+P101(f323(f323(f325(f866(f866(x96241,x96242),f866(x96241,x96242))),f323(f323(f258(f866(x96241,x96242),f866(x96241,x96242)),f323(f323(f258(x96241,x96242),x96243),x96244)),f323(f323(f258(x96241,x96242),x96243),x96245))),f275(x96241,x96242,x96246,x96247)))
% 179.72/179.59 [10043]~P43(x100432,x100437,x100433,x100436,x100431,f323(f323(x100433,x100435),x100434))+E(f323(f323(x100433,f597(x100434,x100435,x100431,x100436,x100433,x100437,x100432)),f605(x100434,x100435,x100431,x100436,x100433,x100437,x100432)),f323(f323(x100433,x100435),x100434))+E(x100431,f188(f867(x100432,a855)))
% 179.72/179.59 [10044]~P43(x100447,x100446,x100441,x100444,x100445,f323(f323(x100441,x100442),x100443))+E(f323(f323(x100441,f597(x100443,x100442,x100445,x100444,x100441,x100446,x100447)),f605(x100443,x100442,x100445,x100444,x100441,x100446,x100447)),f323(f323(x100441,x100442),x100443))+E(f323(f323(x100441,x100442),x100443),x100444)
% 179.72/179.59 [9129]~P35(x91291,x91292,x91293,x91295,x91297)+P35(x91291,x91292,x91293,f323(f323(f144(x91291),x91294),x91295),f323(f323(f144(x91292),x91296),x91297))+~P101(f323(f323(x91293,x91294),x91296))
% 179.72/179.59 [9149]P35(x91491,x91492,x91493,x91494,x91495)+~P35(x91491,x91492,x91493,f323(f323(f121(x91491),x91496),x91494),f323(f323(f121(x91492),x91497),x91495))+~E(f323(f189(f861(x91491)),x91496),f323(f189(f861(x91492)),x91497))
% 179.72/179.59 [9150]P35(x91501,x91502,x91503,x91504,x91505)+~P35(x91501,x91502,x91503,f323(f323(f121(x91501),x91504),x91506),f323(f323(f121(x91502),x91505),x91507))+~E(f323(f189(f861(x91501)),x91504),f323(f189(f861(x91502)),x91505))
% 179.72/179.59 [9351]~P35(x93511,x93512,x93513,x93515,x93517)+~P35(x93511,x93512,x93513,x93514,x93516)+P35(x93511,x93512,x93513,f323(f323(f121(x93511),x93514),x93515),f323(f323(f121(x93512),x93516),x93517))
% 179.72/179.59 [9698]~P101(f323(f64(x96981,x96984,x96985,x96986,x96983),x96987))+P101(f323(f64(x96981,x96984,x96985,x96986,f323(f323(f301(x96981),x96982),x96983)),f323(f323(x96985,x96982),x96987)))+P101(f323(f323(f325(x96981),x96982),x96983))
% 179.72/179.59 [9828]~P27(x98283,x98281,x98284,f246(f867(x98283,a855)))+E(f323(f323(f179(x98281,x98282),f323(f323(f147(f866(x98283,x98282),f866(x98281,x98282)),f323(f262(x98283,x98282,f866(x98281,x98282)),f323(f323(f8(x98281,f867(x98282,f866(x98281,x98282)),x98283),f258(x98281,x98282)),x98284))),x98285)),f323(x98284,x98286)),f323(f230(x98282),x98287))+~E(f323(f323(f179(x98283,x98282),x98285),x98286),f323(f230(x98282),x98287))
% 179.72/179.59 [10064]~P43(x100642,x100647,x100646,x100645,x100641,f323(f323(x100646,x100644),x100643))+E(x100641,f188(f867(x100642,a855)))+P101(f323(f323(f325(x100642),f597(x100643,x100644,x100641,x100645,x100646,x100647,x100642)),x100641))
% 179.72/179.59 [10065]~P43(x100655,x100657,x100651,x100654,x100656,f323(f323(x100651,x100652),x100653))+E(f323(f323(x100651,x100652),x100653),x100654)+P101(f323(f323(f325(x100655),f597(x100653,x100652,x100656,x100654,x100651,x100657,x100655)),x100656))
% 179.72/179.59 [6746]~E(x67465,x67467)+~E(x67466,x67464)+E(f323(f323(f323(f323(f70(x67461,f864(x67462)),x67463),x67464),f323(f230(x67462),x67465)),x67466),f323(f230(x67462),x67467))
% 179.72/179.59 [6872]E(x68721,x68722)+~E(f323(x68725,x68721),f323(f230(x68724),x68727))+E(f323(f323(f323(f323(f70(x68723,f864(x68724)),x68725),x68722),f323(f230(x68724),x68726)),x68721),f323(f230(x68724),x68727))
% 179.72/179.59 [7584]E(x75841,x75842)+~E(x75843,x75844)+~E(f323(f323(f323(f323(f70(x75845,f864(x75846)),x75847),x75844),f323(f230(x75846),x75841)),x75843),f323(f230(x75846),x75842))
% 179.72/179.59 [7650]E(x76501,x76502)+E(f323(x76503,x76504),f323(f230(x76505),x76501))+~E(f323(f323(f323(f323(f70(x76506,f864(x76505)),x76503),x76507),f323(f230(x76505),x76502)),x76504),f323(f230(x76505),x76501))
% 179.72/179.59 [7651]E(x76511,x76512)+E(f323(x76513,x76511),f323(f230(x76514),x76515))+~E(f323(f323(f323(f323(f70(x76516,f864(x76514)),x76513),x76512),f323(f230(x76514),x76517)),x76511),f323(f230(x76514),x76515))
% 179.72/179.59 [8822]~P23(x88224,x88225,x88226,x88227,x88221)+~P101(f323(f59(x88225),x88223))+E(f323(f323(x88221,x88222),x88223),f323(f323(f323(f63(x88224,x88225,x88226),x88222),x88227),x88223))
% 179.72/179.59 [8823]~P11(x88234,x88235,x88236,x88237,x88231)+~P101(f323(f59(x88235),x88233))+E(f323(f323(x88231,x88232),x88233),f323(f323(f323(f63(x88234,x88235,x88236),x88232),x88237),x88233))
% 179.72/179.59 [9406]~P26(x94061,x94062,f323(f323(f301(f859(x94061)),f323(f323(f323(f90(x94061),x94063),x94064),x94067)),f188(f867(f859(x94061),a855))))+P26(x94061,x94062,f323(f323(f301(f859(x94061)),f323(f323(f323(f90(x94061),x94063),f30(x94064,x94065)),x94066)),f188(f867(f859(x94061),a855))))+~P26(x94061,x94062,f323(f323(f301(f859(x94061)),f323(f323(f323(f90(x94061),x94067),x94065),x94066)),f188(f867(f859(x94061),a855))))
% 179.72/179.59 [9597]~P25(x95973,x95974,x95975,x95977,x95976,x95971)+~P101(f323(f59(x95974),x95972))+E(f323(x95971,x95972),f323(f323(f323(f63(x95973,x95974,x95975),x95976),x95977),x95972))
% 179.72/179.59 [9754]P43(x97541,x97542,x97543,x97544,x97545,f323(f323(x97543,x97546),x97547))+~P43(x97541,x97542,x97543,x97544,f323(f323(f22(f867(x97541,a855)),x97545),f323(f323(f301(x97541),x97546),f188(f867(x97541,a855)))),x97547)+~P101(f323(f323(f325(x97541),x97546),x97545))
% 179.72/179.59 [10019]~P26(x100191,x100192,f323(f323(f301(f859(x100191)),f323(f323(f323(f90(x100191),f92(x100191,x100193,x100194)),x100195),x100197)),f188(f867(f859(x100191),a855))))+P26(x100191,x100192,f323(f323(f301(f859(x100191)),f323(f323(f323(f90(x100191),x100193),f27(x100194,x100195,x100196)),x100197)),f188(f867(f859(x100191),a855))))+~P26(x100191,x100192,f323(f323(f301(f859(x100191)),f323(f323(f323(f90(x100191),f92(x100191,x100193,f323(f71(a855,a855,a856,a318),x100194))),x100196),x100197)),f188(f867(f859(x100191),a855))))
% 179.72/179.59 [10082]P26(x100827,x100826,f323(f323(f301(f859(x100827)),f323(f323(f323(f90(x100827),x100821),x100824),x100822)),f188(f867(f859(x100827),a855))))+~P26(x100827,x100826,f323(f323(f301(f859(x100827)),f323(f323(f323(f90(x100827),x100825),x100824),x100823)),f188(f867(f859(x100827),a855))))+P101(f323(f323(x100821,f845(x100822,x100821,x100823,x100824,x100825,x100826,x100827)),f853(x100822,x100821,x100823,x100824,x100825,x100826,x100827)))
% 179.72/179.59 [10091]~P43(x100912,x100913,x100914,x100915,x100911,f323(f323(x100914,x100917),x100916))+P43(x100912,x100913,x100914,x100915,f323(f323(f22(f867(x100912,a855)),x100911),f323(f323(f301(x100912),f597(x100916,x100917,x100911,x100915,x100914,x100913,x100912)),f188(f867(x100912,a855)))),f605(x100916,x100917,x100911,x100915,x100914,x100913,x100912))+E(x100911,f188(f867(x100912,a855)))
% 179.72/179.59 [10092]~P43(x100925,x100926,x100921,x100924,x100927,f323(f323(x100921,x100922),x100923))+P43(x100925,x100926,x100921,x100924,f323(f323(f22(f867(x100925,a855)),x100927),f323(f323(f301(x100925),f597(x100923,x100922,x100927,x100924,x100921,x100926,x100925)),f188(f867(x100925,a855)))),f605(x100923,x100922,x100927,x100924,x100921,x100926,x100925))+E(f323(f323(x100921,x100922),x100923),x100924)
% 179.72/179.59 [10093]~P26(x100931,x100932,f323(f323(f301(f859(x100931)),f323(f323(f323(f90(x100931),x100937),x100934),x100936)),f188(f867(f859(x100931),a855))))+P26(x100931,x100932,f323(f323(f301(f859(x100931)),f323(f323(f323(f90(x100931),x100933),x100934),x100935)),f188(f867(f859(x100931),a855))))+~P101(f323(f323(x100935,f845(x100935,x100933,x100936,x100934,x100937,x100932,x100931)),f345(x100935,x100933,x100936,x100934,x100937,x100932,x100931)))
% 179.72/179.59 [9137]E(f181(x91371,x91372,x91373,x91374,f323(f323(f152(x91372,x91375),x91376),x91377)),f181(x91371,x91372,x91373,x91374,x91375))+~P101(f323(f323(f238(a860),x91376),f323(f189(f861(x91372)),x91375)))+~P101(f323(f323(f237(a860),f323(f189(f861(x91371)),x91374)),x91376))
% 179.72/179.59 [9429]P101(f323(f323(f237(f867(f866(x94291,x94292),a855)),f323(f323(f280(x94291,x94293,x94292),x94294),x94295)),f323(f323(f280(x94291,x94293,x94292),x94296),x94297)))+~P101(f323(f323(f237(f867(f866(x94293,x94292),a855)),x94295),x94297))+~P101(f323(f323(f237(f867(f866(x94291,x94293),a855)),x94294),x94296))
% 179.72/179.59 [9765]~P101(f323(f323(f325(x97651),x97656),x97655))+P101(f323(f64(x97651,x97652,x97653,x97654,x97655),f323(f323(x97653,x97656),x97657)))+~P101(f323(f64(x97651,x97652,x97653,x97654,f323(f323(f22(f867(x97651,a855)),x97655),f323(f323(f301(x97651),x97656),f188(f867(x97651,a855))))),x97657))
% 179.72/179.59 [10146]~P139(x101461)+~P27(f866(x101462,x101463),x101461,f323(f262(x101462,x101463,x101461),f323(f323(f7(x101462,f867(x101463,x101461),f867(x101463,x101461)),f323(f323(f8(f867(x101461,x101461),f867(f867(x101463,x101461),f867(x101463,x101461)),x101462),f8(x101461,x101461,x101463)),f323(f323(f8(x101461,f867(x101461,x101461),x101462),f79(x101461)),x101464))),x101465)),f323(f323(f260(x101462,x101463),x101466),f323(f16(f867(x101463,a855),x101462),x101467)))+E(f323(f323(f6(x101461,x101461),f32(x101461)),f323(f243(x101461),f323(f323(f8(f867(x101462,a855),a855,x101461),f85(x101462)),f323(f323(f8(f867(x101462,f867(x101463,a855)),f867(x101462,a855),x101461),f323(f8(f867(x101463,a855),a855,x101462),f85(x101463))),f323(f323(f7(x101461,f867(x101462,f867(x101463,a855)),f867(x101462,f867(x101463,a855))),f323(f323(f8(f867(x101462,f867(f867(x101463,a855),f867(x101463,a855))),f867(f867(x101462,f867(x101463,a855)),f867(x101462,f867(x101463,a855))),x101461),f18(x101462,f867(x101463,a855),f867(x101463,a855))),f323(f323(f8(f867(x101462,f867(x101463,f867(a855,a855))),f867(x101462,f867(f867(x101463,a855),f867(x101463,a855))),x101461),f323(f8(f867(x101463,f867(a855,a855)),f867(f867(x101463,a855),f867(x101463,a855)),x101462),f18(x101463,a855,a855))),f323(f323(f8(f867(x101462,f867(x101463,a855)),f867(x101462,f867(x101463,f867(a855,a855))),x101461),f323(f8(f867(x101463,a855),f867(x101463,f867(a855,a855)),x101462),f323(f8(a855,f867(a855,a855),x101463),a321))),f323(f323(f7(x101461,f867(x101462,f867(x101463,x101461)),f867(x101462,f867(x101463,a855))),f323(f323(f8(f867(f867(x101463,x101461),f867(x101463,a855)),f867(f867(x101462,f867(x101463,x101461)),f867(x101462,f867(x101463,a855))),x101461),f8(f867(x101463,x101461),f867(x101463,a855),x101462)),f323(f323(f8(f867(x101461,a855),f867(f867(x101463,x101461),f867(x101463,a855)),x101461),f8(x101461,a855,x101463)),a320))),f323(f323(f7(x101462,f867(x101463,x101461),f867(x101463,x101461)),f323(f323(f8(f867(x101461,x101461),f867(f867(x101463,x101461),f867(x101463,x101461)),x101462),f8(x101461,x101461,x101463)),f323(f323(f8(x101461,f867(x101461,x101461),x101462),f79(x101461)),x101464))),x101465)))))),f323(f323(f7(x101462,f867(x101463,a855),f867(x101463,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x101463,a855),f867(x101463,a855)),x101462),f8(a855,a855,x101463)),f323(f323(f8(a855,f867(a855,a855),x101462),a321),f323(f323(f7(x101462,f867(x101462,a855),a855),f325(x101462)),x101466)))),f323(f323(f7(x101463,f867(x101463,a855),a855),f325(x101463)),x101467))))))),f323(f323(f79(x101461),f323(f323(f6(x101462,x101461),x101464),x101466)),f323(f323(f6(x101463,x101461),x101465),x101467)))
% 179.72/179.59 [9433]~P28(x94331,x94333,x94335,x94336,x94338)+~P28(x94333,x94332,x94334,x94338,x94337)+P28(x94331,x94332,f323(f71(x94333,x94332,x94331,x94334),x94335),x94336,x94337)
% 179.72/179.59 [9462]P28(x94621,x94622,x94623,x94624,x94625)+~P28(x94626,x94621,x94627,x94628,x94624)+~P28(x94626,x94622,f323(f71(x94621,x94622,x94626,x94623),x94627),x94628,x94625)
% 179.72/179.59 [9595]~P101(f323(f323(x95954,x95956),x95958))+~P101(f323(f323(x95955,x95958),x95957))+P101(f323(f323(f259(x95951,x95952,x95953,x95954,x95955),x95956),x95957))
% 179.72/179.59 [9197]~P21(x91978,x91971,x91973,x91975)+~P101(f323(f59(x91978),x91976))+E(f323(f71(x91971,x91971,x91972,f323(x91973,x91974)),f323(f71(x91971,x91971,x91972,f323(x91975,x91976)),x91977)),f323(f71(x91971,x91971,x91972,f323(x91975,x91976)),f323(f71(x91971,x91971,x91972,f323(x91973,x91974)),x91977)))
% 179.72/179.59 [9585]~P24(x95857,x95852,x95855,x95858,x95856,x95851)+~P101(f323(f59(x95852),x95854))+E(f323(x95851,f323(f323(f301(x95852),x95853),x95854)),f323(f323(x95855,f323(x95856,x95853)),f323(x95851,x95854)))
% 179.72/179.59 [9707]~P27(x97072,x97074,x97076,x97078)+~P27(x97071,x97073,x97075,x97077)+P27(f866(x97071,x97072),f866(x97073,x97074),f263(x97071,x97073,x97072,x97074,x97075,x97076),f323(f323(f260(x97071,x97072),x97077),f323(f16(f867(x97072,a855),x97071),x97078)))
% 179.72/179.59 [9375]P101(f323(f323(f325(f866(x93751,x93752)),f323(f323(f258(x93751,x93752),x93753),x93754)),f323(f323(f280(x93751,x93755,x93752),x93756),x93757)))+~P101(f323(f323(f325(f866(x93751,x93755)),f323(f323(f258(x93751,x93755),x93753),x93758)),x93756))+~P101(f323(f323(f325(f866(x93755,x93752)),f323(f323(f258(x93755,x93752),x93758),x93754)),x93757))
% 179.72/179.59 [9566]~P101(f323(f323(f237(f867(f866(x95663,x95662),a855)),x95665),f323(f323(f260(x95663,x95662),x95668),f323(f16(f867(x95662,a855),x95663),x95667))))+~P101(f323(f323(f237(f867(f866(x95661,x95663),a855)),x95664),f323(f323(f260(x95661,x95663),x95666),f323(f16(f867(x95663,a855),x95661),x95668))))+P101(f323(f323(f237(f867(f866(x95661,x95662),a855)),f323(f323(f280(x95661,x95663,x95662),x95664),x95665)),f323(f323(f260(x95661,x95662),x95666),f323(f16(f867(x95662,a855),x95661),x95667))))
% 179.72/179.59 [9619]~E(x96193,x96195)+P101(f323(f323(f325(f866(f866(x96191,x96192),f866(x96191,x96192))),f323(f323(f258(f866(x96191,x96192),f866(x96191,x96192)),f323(f323(f258(x96191,x96192),x96193),x96194)),f323(f323(f258(x96191,x96192),x96195),x96196))),f315(x96191,x96192,x96197,x96198)))+~P101(f323(f323(f325(f866(x96192,x96192)),f323(f323(f258(x96192,x96192),x96194),x96196)),x96198))
% 179.72/179.59 [9730]E(x97301,x97302)+~P101(f323(f323(f325(f866(f866(x97303,x97305),f866(x97303,x97305))),f323(f323(f258(f866(x97303,x97305),f866(x97303,x97305)),f323(f323(f258(x97303,x97305),x97301),x97306)),f323(f323(f258(x97303,x97305),x97302),x97307))),f315(x97303,x97305,x97304,x97308)))+P101(f323(f323(f325(f866(x97303,x97303)),f323(f323(f258(x97303,x97303),x97301),x97302)),x97304))
% 179.72/179.59 [9747]~P101(f323(f323(f325(f866(f866(x97471,x97475),f866(x97471,x97475))),f323(f323(f258(f866(x97471,x97475),f866(x97471,x97475)),f323(f323(f258(x97471,x97475),x97472),x97476)),f323(f323(f258(x97471,x97475),x97473),x97477))),f315(x97471,x97475,x97474,x97478)))+P101(f323(f323(f325(f866(x97471,x97471)),f323(f323(f258(x97471,x97471),x97472),x97473)),x97474))+P101(f323(f323(f325(f866(x97475,x97475)),f323(f323(f258(x97475,x97475),x97476),x97477)),x97478))
% 179.72/179.59 [9651]~P25(x96517,x96515,x96511,x96518,x96512,x96514)+~P101(f323(f59(x96515),x96516))+E(f323(f323(x96511,f323(x96512,x96513)),f323(x96514,f323(f323(f22(f867(x96515,a855)),x96516),f323(f323(f301(x96515),x96513),f188(f867(x96515,a855)))))),f323(x96514,f323(f323(f301(x96515),x96513),x96516)))
% 179.72/179.59 [9157]~P101(f323(f323(f323(x91575,x91578),x91576),x91577))+~P101(f323(f323(f325(x91571),x91578),x91574))+P101(f323(f323(f323(f323(f39(x91571,f867(x91572,f867(x91573,a855))),x91574),x91575),x91576),x91577))
% 179.72/179.59 [9362]P101(f323(f323(f323(x93621,x93622),x93623),x93624))+~P101(f323(f323(f325(x93625),x93622),x93626))+~P101(f323(f323(f323(f323(f40(x93625,f867(x93627,f867(x93628,a855))),x93626),x93621),x93623),x93624))
% 179.72/179.59 [9559]~P23(x95593,x95592,x95594,x95598,x95591)+~P101(f323(f59(x95592),x95597))+E(f323(f323(x95591,f323(f323(f18(x95592,x95593,x95593),f323(f323(f8(x95593,f867(x95593,x95593),x95592),x95594),x95595)),x95596)),x95597),f323(f323(x95594,f323(f323(x95591,x95595),x95597)),f323(f323(x95591,x95596),x95597)))
% 179.72/179.59 [9836]~E(f323(f302(x98362,x98364,x98366),x98368),x983610)+~E(f323(f302(x98361,x98363,x98365),x98367),x98369)+E(f323(f302(f866(x98361,x98362),f866(x98363,x98364),f263(x98361,x98363,x98362,x98364,x98365,x98366)),f323(f323(f260(x98361,x98362),x98367),f323(f16(f867(x98362,a855),x98361),x98368))),f323(f323(f260(x98363,x98364),x98369),f323(f16(f867(x98364,a855),x98363),x983610)))
% 179.72/179.59 [4826]~P103(x48262)+~P16(x48262,x48261)+P16(x48262,f114(x48262,x48261))+E(x48261,f113(x48262))
% 179.72/179.59 [4827]~P103(x48272)+~P16(x48272,x48271)+P16(x48272,f610(x48271,x48272))+E(x48271,f113(x48272))
% 179.72/179.59 [5058]~P6(x50582)+E(f10(x50582,x50581),f37(x50582,x50581))+E(x50581,f188(f867(x50582,a855)))+~P101(f323(f59(x50582),x50581))
% 179.72/179.59 [5059]~P6(x50592)+E(f11(x50592,x50591),f38(x50592,x50591))+E(x50591,f188(f867(x50592,a855)))+~P101(f323(f59(x50592),x50591))
% 179.72/179.59 [5209]~P103(x52092)+~P16(x52092,x52091)+E(x52091,f113(x52092))+E(f323(f323(f144(x52092),f647(x52091,x52092)),f610(x52091,x52092)),x52091)
% 179.72/179.59 [5995]~P2(x59952)+E(x59951,f188(f867(x59952,a855)))+P101(f323(f323(f237(x59952),f11(x59952,x59951)),f10(x59952,x59951)))+~P101(f323(f59(x59952),x59951))
% 179.72/179.59 [6007]~P39(x60072)+~P39(x60071)+E(x60071,x60072)+~E(f323(f302(a1,a860,a104),x60071),f323(f302(a1,a860,a104),x60072))
% 179.72/179.59 [9011]~P116(x90111)+~P101(f323(f323(f325(x90111),x90112),f109(x90111)))+P101(f323(f323(f238(x90111),f323(f323(f78(x90111),f323(f323(f78(x90111),f76(x90111)),x90112)),x90112)),f2(x90111)))+~P101(f323(f323(f238(x90111),x90112),f2(x90111)))
% 179.72/179.59 [9250]~P116(x92501)+~P101(f323(f323(f325(x92501),x92502),f109(x92501)))+~P101(f323(f323(f238(x92501),f323(f323(f78(x92501),f323(f323(f78(x92501),f76(x92501)),x92502)),x92502)),f2(x92501)))+P101(f323(f323(f238(x92501),x92502),f2(x92501)))
% 179.72/179.59 [4882]~P139(x48822)+~P110(x48822)+E(x48821,f2(a860))+E(f323(f323(f248(x48822),f2(x48822)),x48821),f2(x48822))
% 179.72/179.59 [4885]~P139(x48851)+~P110(x48851)+~E(x48852,f2(a860))+E(f323(f323(f248(x48851),f2(x48851)),x48852),f76(x48851))
% 179.72/179.59 [5045]~P133(x50452)+E(x50451,f76(x50452))+E(x50451,f323(f77(x50452),f76(x50452)))+~E(f323(f323(f79(x50452),x50451),x50451),f76(x50452))
% 179.72/179.59 [5291]~P85(x52912)+E(x52911,f2(x52912))+E(f80(x52912,x52911),f323(f77(x52912),f76(x52912)))+P101(f323(f323(f238(x52912),f2(x52912)),x52911))
% 179.72/179.59 [5525]~P85(x55252)+E(f80(x55252,x55251),f76(x55252))+E(x55251,f2(x55252))+~P101(f323(f323(f238(x55252),f2(x55252)),x55251))
% 179.72/179.59 [5534]E(x55341,x55342)+~E(f323(f103(a860),x55341),f323(f103(a860),x55342))+P101(f323(a193,f323(f103(a1),x55342)))+P101(f323(a193,f323(f103(a1),x55341)))
% 179.72/179.59 [5584]~P89(x55841)+~E(x55842,f2(x55841))+E(f323(f323(f78(x55841),x55842),x55842),f2(x55841))+~P101(f323(f323(f325(x55841),x55842),f109(x55841)))
% 179.72/179.59 [5622]E(x56221,f2(a1))+~E(f323(f323(f36(a1),x56222),x56221),f2(a1))+P101(f323(f323(f238(a1),x56221),x56222))+P101(f323(f323(f238(a1),x56222),x56221))
% 179.72/179.59 [5653]E(x56531,f2(a1))+~E(f323(f323(f36(a1),x56532),x56531),f2(a1))+P101(f323(f323(f237(a1),x56532),f2(a1)))+P101(f323(f323(f238(a1),x56532),x56531))
% 179.72/179.59 [5687]E(x56871,f2(a1))+~E(f323(f323(f36(a1),x56872),x56871),f2(a1))+P101(f323(f323(f237(a1),f2(a1)),x56872))+P101(f323(f323(f238(a1),x56871),x56872))
% 179.72/179.59 [5721]~P89(x57212)+E(x57211,f2(x57212))+~E(f323(f323(f78(x57212),x57211),x57211),f2(x57212))+~P101(f323(f323(f325(x57212),x57211),f109(x57212)))
% 179.72/179.59 [5781]E(f323(f103(a860),x57811),f323(f103(a860),x57812))+~E(f323(f103(a1),x57812),f2(a1))+P101(f323(a193,f323(f103(a1),x57812)))+~P101(f323(a193,f323(f103(a1),x57811)))
% 179.72/179.59 [5808]~E(f323(f103(a860),x58082),f323(f103(a860),x58081))+E(f323(f103(a1),x58081),f2(a1))+P101(f323(a193,f323(f103(a1),x58081)))+~P101(f323(a193,f323(f103(a1),x58082)))
% 179.72/179.59 [5817]~P103(x58172)+E(x58171,f188(f867(x58172,a855)))+~P101(f323(f59(x58172),x58171))+P101(f323(f323(f325(x58172),f14(x58172,x58171)),x58171))
% 179.72/179.59 [5818]~P103(x58182)+E(x58181,f188(f867(x58182,a855)))+~P101(f323(f59(x58182),x58181))+P101(f323(f323(f325(x58182),f15(x58182,x58181)),x58181))
% 179.72/179.59 [5975]~P116(x59751)+~P90(x59751)+P101(f323(f323(f237(x59751),f2(x59751)),f323(f103(x59751),x59752)))+~P101(f323(f323(f237(a1),a81),x59752))
% 179.72/179.59 [5976]~P116(x59761)+~P90(x59761)+P101(f323(f323(f238(x59761),f2(x59761)),f323(f103(x59761),x59762)))+~P101(f323(f323(f238(a1),a81),x59762))
% 179.72/179.59 [5994]~P116(x59941)+~P90(x59941)+E(f323(f73(x59941),f323(f103(x59941),x59942)),f323(f103(x59941),x59942))+P101(f323(f323(f238(x59941),f323(f103(x59941),x59942)),f2(x59941)))
% 179.72/179.59 [6034]E(x60341,x60342)+~E(f323(a104,x60341),f323(a104,x60342))+~P101(f323(f323(f237(a1),f2(a1)),x60342))+~P101(f323(f323(f237(a1),f2(a1)),x60341))
% 179.72/179.59 [6223]~P90(x62232)+~P116(x62232)+~P101(f323(f323(f237(x62232),f2(x62232)),f323(f103(x62232),x62231)))+P101(f323(f323(f237(a1),a81),x62231))
% 179.72/179.59 [6224]~P90(x62242)+~P116(x62242)+~P101(f323(f323(f238(x62242),f2(x62242)),f323(f103(x62242),x62241)))+P101(f323(f323(f238(a1),a81),x62241))
% 179.72/179.59 [6229]~P116(x62291)+~P90(x62291)+P101(f323(f323(f237(x62291),f323(f103(x62291),x62292)),f2(x62291)))+~P101(f323(f323(f237(a1),x62292),a81))
% 179.72/179.59 [6230]~P116(x62301)+~P90(x62301)+P101(f323(f323(f238(x62301),f323(f103(x62301),x62302)),f2(x62301)))+~P101(f323(f323(f238(a1),x62302),a81))
% 179.72/179.59 [6536]~P90(x65362)+~P116(x65362)+~P101(f323(f323(f237(x65362),f323(f103(x65362),x65361)),f2(x65362)))+P101(f323(f323(f237(a1),x65361),a81))
% 179.72/179.59 [6537]~P90(x65372)+~P116(x65372)+~P101(f323(f323(f238(x65372),f323(f103(x65372),x65371)),f2(x65372)))+P101(f323(f323(f238(a1),x65371),a81))
% 179.72/179.59 [6627]~P116(x66271)+~P90(x66271)+E(f323(f73(x66271),f323(f103(x66271),x66272)),f323(f77(x66271),f323(f103(x66271),x66272)))+~P101(f323(f323(f238(x66271),f323(f103(x66271),x66272)),f2(x66271)))
% 179.72/179.59 [6645]E(f323(f103(a860),x66451),f323(f103(a860),x66452))+~E(f323(f103(a1),x66452),f2(a1))+~P101(f323(f323(f237(a1),f323(f103(a1),x66451)),f2(a1)))+~P101(f323(a193,f323(f103(a1),x66451)))
% 179.72/179.59 [7515]~P103(x75152)+E(x75151,f188(f867(x75152,a855)))+~P101(f323(f59(x75152),x75151))+P101(f323(f323(f237(x75152),f12(x75152,f235(x75152),x75151)),f13(x75152,f236(x75152),x75151)))
% 179.72/179.59 [7832]~P7(x78321)+~P39(x78322)+P101(f323(f323(f325(a1),x78321),x78322))+~P101(f323(f323(f325(a860),f323(a104,x78321)),f323(f302(a1,a860,a104),x78322)))
% 179.72/179.59 [8099]~P5(x80992)+P101(f323(x80991,f200(x80992)))+~P101(f323(f55(f864(x80992)),x80991))+P101(f323(f55(x80992),f323(f323(f8(f864(x80992),a855,x80992),x80991),f230(x80992))))
% 179.72/179.59 [8565]~P5(x85651)+~P101(f323(x85652,f200(x85651)))+P101(f323(f56(f864(x85651)),x85652))+~P101(f323(f56(x85651),f323(f323(f8(f864(x85651),a855,x85651),x85652),f230(x85651))))
% 179.72/179.59 [5814]~P134(x58142)+E(x58141,f2(a1))+E(f323(f77(x58142),f323(f102(x58142),f323(f77(a1),x58141))),f323(f102(x58142),x58141))+~P101(f323(f323(f238(a1),x58141),f2(a1)))
% 179.72/179.59 [5885]~P89(x58851)+~P90(x58851)+~P30(x58851,f323(f103(x58851),x58852))+P30(x58851,f323(f103(x58851),f323(f323(f78(a1),x58852),x58852)))
% 179.72/179.59 [6212]~P74(x62122)+E(x62121,f188(f867(x62122,a855)))+E(f15(x62122,f323(f302(x62122,x62122,f77(x62122)),x62121)),f323(f77(x62122),f14(x62122,x62121)))+~P101(f323(f59(x62122),x62121))
% 179.72/179.59 [6213]~P74(x62132)+E(x62131,f188(f867(x62132,a855)))+E(f14(x62132,f323(f302(x62132,x62132,f77(x62132)),x62131)),f323(f77(x62132),f15(x62132,x62131)))+~P101(f323(f59(x62132),x62131))
% 179.72/179.59 [6244]~P89(x62441)+~P90(x62441)+P30(x62441,f323(f103(x62441),x62442))+~P30(x62441,f323(f103(x62441),f323(f323(f78(a1),x62442),x62442)))
% 179.72/179.59 [6332]E(x63321,f2(a1))+E(f323(a48,f47(f323(f77(a1),x63321),f323(f77(a1),x63322))),f43(x63321,x63322))+P101(f323(f323(f237(a1),f2(a1)),x63322))+~P101(f323(f323(f237(a1),f2(a1)),x63321))
% 179.72/179.59 [8614]~P39(x86142)+~P39(x86141)+P101(f323(f323(f238(f867(a860,a855)),f323(f302(a1,a860,a104),x86141)),f323(f302(a1,a860,a104),x86142)))+~P101(f323(f323(f238(f867(a1,a855)),x86141),x86142))
% 179.72/179.59 [8841]~E(f652(x88412,x88411),f653(x88412,x88411))+~P101(f323(f130(x88411),f654(x88412,x88411)))+~P101(f323(f130(f861(x88411)),x88412))+P101(f323(f130(x88411),f323(f135(f861(x88411),f861(x88411),f121(x88411),f113(x88411)),x88412)))
% 179.72/179.59 [8930]~P39(x89302)+~P39(x89301)+~P101(f323(f323(f237(f867(a860,a855)),f323(f302(a1,a860,a104),x89301)),f323(f302(a1,a860,a104),x89302)))+P101(f323(f323(f237(f867(a1,a855)),x89301),x89302))
% 179.72/179.59 [8931]~P39(x89312)+~P39(x89311)+~P101(f323(f323(f238(f867(a860,a855)),f323(f302(a1,a860,a104),x89311)),f323(f302(a1,a860,a104),x89312)))+P101(f323(f323(f238(f867(a1,a855)),x89311),x89312))
% 179.72/179.59 [8937]~E(f652(x89372,x89371),f653(x89372,x89371))+~P101(f323(f130(f861(x89371)),x89372))+P101(f323(f130(x89371),f323(f135(f861(x89371),f861(x89371),f121(x89371),f113(x89371)),x89372)))+P101(f323(f323(f325(f861(x89371)),f654(x89372,x89371)),f323(f166(f861(x89371)),x89372)))
% 179.72/179.59 [8978]~P101(f323(f130(x89781),f654(x89782,x89781)))+~P101(f323(f130(f861(x89781)),x89782))+P101(f323(f130(x89781),f323(f135(f861(x89781),f861(x89781),f121(x89781),f113(x89781)),x89782)))+P101(f323(f323(f325(f861(x89781)),f653(x89782,x89781)),f323(f166(f861(x89781)),x89782)))
% 179.72/179.59 [8979]~P101(f323(f130(x89791),f654(x89792,x89791)))+~P101(f323(f130(f861(x89791)),x89792))+P101(f323(f130(x89791),f323(f135(f861(x89791),f861(x89791),f121(x89791),f113(x89791)),x89792)))+P101(f323(f323(f325(f861(x89791)),f652(x89792,x89791)),f323(f166(f861(x89791)),x89792)))
% 179.72/179.59 [9059]~P101(f323(f130(f861(x90591)),x90592))+P101(f323(f130(x90591),f323(f135(f861(x90591),f861(x90591),f121(x90591),f113(x90591)),x90592)))+P101(f323(f323(f325(f861(x90591)),f653(x90592,x90591)),f323(f166(f861(x90591)),x90592)))+P101(f323(f323(f325(f861(x90591)),f654(x90592,x90591)),f323(f166(f861(x90591)),x90592)))
% 179.72/179.59 [9060]~P101(f323(f130(f861(x90601)),x90602))+P101(f323(f130(x90601),f323(f135(f861(x90601),f861(x90601),f121(x90601),f113(x90601)),x90602)))+P101(f323(f323(f325(f861(x90601)),f652(x90602,x90601)),f323(f166(f861(x90601)),x90602)))+P101(f323(f323(f325(f861(x90601)),f654(x90602,x90601)),f323(f166(f861(x90601)),x90602)))
% 179.72/179.59 [9073]~E(f323(f323(f101(f867(x90731,a855)),f323(f166(x90731),f653(x90732,x90731))),f323(f166(x90731),f652(x90732,x90731))),f188(f867(x90731,a855)))+~P101(f323(f130(x90731),f654(x90732,x90731)))+~P101(f323(f130(f861(x90731)),x90732))+P101(f323(f130(x90731),f323(f135(f861(x90731),f861(x90731),f121(x90731),f113(x90731)),x90732)))
% 179.72/179.59 [9133]~E(f323(f323(f101(f867(x91331,a855)),f323(f166(x91331),f653(x91332,x91331))),f323(f166(x91331),f652(x91332,x91331))),f188(f867(x91331,a855)))+~P101(f323(f130(f861(x91331)),x91332))+P101(f323(f130(x91331),f323(f135(f861(x91331),f861(x91331),f121(x91331),f113(x91331)),x91332)))+P101(f323(f323(f325(f861(x91331)),f654(x91332,x91331)),f323(f166(f861(x91331)),x91332)))
% 179.72/179.59 [9398]E(x93981,f2(a1))+E(x93982,f2(a1))+E(f323(f323(f84(a1,f866(a1,a1)),f323(f323(a219,x93982),x93981)),f323(f323(f18(a1,a1,f866(a1,a1)),f323(f323(f8(a1,f867(a1,f866(a1,a1)),a1),f258(a1,a1)),f323(f36(a1),x93982))),f323(f36(a1),x93981))),f217(x93982,x93981))+P101(f323(f323(f238(a1),x93981),f2(a1)))
% 179.72/179.59 [8159]~P90(x81592)+~P116(x81592)+~P101(f323(f323(f237(x81592),f323(f103(x81592),x81591)),f76(x81592)))+P101(f323(f323(f237(a1),x81591),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))
% 179.72/179.59 [8160]~P90(x81602)+~P116(x81602)+~P101(f323(f323(f238(x81602),f323(f103(x81602),x81601)),f76(x81602)))+P101(f323(f323(f238(a1),x81601),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))
% 179.72/179.59 [8431]~P116(x84311)+~P90(x84311)+P101(f323(f323(f237(x84311),f323(f103(x84311),x84312)),f76(x84311)))+~P101(f323(f323(f237(a1),x84312),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))
% 179.72/179.59 [8432]~P116(x84321)+~P90(x84321)+P101(f323(f323(f238(x84321),f323(f103(x84321),x84322)),f76(x84321)))+~P101(f323(f323(f238(a1),x84322),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))
% 179.72/179.59 [8642]~P90(x86422)+~P116(x86422)+~P101(f323(f323(f237(x86422),f76(x86422)),f323(f103(x86422),x86421)))+P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),x86421))
% 179.72/179.59 [8643]~P90(x86432)+~P116(x86432)+~P101(f323(f323(f238(x86432),f76(x86432)),f323(f103(x86432),x86431)))+P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),x86431))
% 179.72/179.59 [9017]~P116(x90171)+~P90(x90171)+P101(f323(f323(f237(x90171),f76(x90171)),f323(f103(x90171),x90172)))+~P101(f323(f323(f237(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),x90172))
% 179.72/179.59 [9018]~P116(x90181)+~P90(x90181)+P101(f323(f323(f238(x90181),f76(x90181)),f323(f103(x90181),x90182)))+~P101(f323(f323(f238(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),x90182))
% 179.72/179.59 [9530]~P133(x95302)+E(x95301,f76(x95302))+E(x95301,f323(f77(x95302),f76(x95302)))+~E(f323(f323(f248(x95302),x95301),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f76(x95302))
% 179.72/179.59 [9806]~P64(x98061)+~P90(x98061)+~P101(f323(f323(f238(x98061),f2(x98061)),x98062))+P101(f323(f323(f238(x98061),f2(x98061)),f323(f323(f281(x98061),x98062),f323(f103(x98061),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))
% 179.72/179.59 [9866]~P64(x98661)+~P90(x98661)+P101(f323(f323(f238(x98661),f2(x98661)),x98662))+~P101(f323(f323(f238(x98661),f2(x98661)),f323(f323(f281(x98661),x98662),f323(f103(x98661),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))
% 179.72/179.59 [10120]~P134(x101202)+E(x101201,f2(a1))+P101(f323(f323(f238(a1),x101201),f2(a1)))+E(f323(f323(f262(a1,a1,x101202),f323(f323(f7(a1,f867(a1,f867(x101202,x101202)),f867(a1,x101202)),f323(f323(f8(f867(f867(x101202,x101202),x101202),f867(f867(a1,f867(x101202,x101202)),f867(a1,x101202)),a1),f8(f867(x101202,x101202),x101202,a1)),f323(f323(f8(x101202,f867(f867(x101202,x101202),x101202),a1),f84(x101202,x101202)),f102(x101202)))),f323(f323(f7(a1,f867(x101202,x101202),f867(x101202,x101202)),f323(f323(f8(f867(x101202,f867(x101202,x101202)),f867(f867(x101202,x101202),f867(x101202,x101202)),a1),f18(x101202,x101202,x101202)),f323(f323(f7(a1,f867(x101202,x101202),f867(x101202,f867(x101202,x101202))),f323(f323(f8(f867(x101202,f867(x101202,x101202)),f867(f867(x101202,x101202),f867(x101202,f867(x101202,x101202))),a1),f8(x101202,f867(x101202,x101202),x101202)),f323(f323(f8(a855,f867(x101202,f867(x101202,x101202)),a1),f96(x101202)),f323(f323(f7(a1,a1,a855),a320),f2(a1))))),f323(f323(f18(x101202,x101202,x101202),f78(x101202)),f5(x101202))))),f323(f323(f7(x101202,x101202,x101202),f323(f323(f8(x101202,f867(x101202,x101202),x101202),f78(x101202)),f323(f323(f18(x101202,x101202,x101202),f78(x101202)),f5(x101202)))),f76(x101202))))),f43(x101201,f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f102(x101202),x101201))
% 179.72/179.59 [5204]~P5(x52043)+~P36(x52043,x52042,f53(x52043))+E(x52041,f782(x52042,x52043))+~P101(f323(x52042,x52041))
% 179.72/179.59 [5361]~P5(x53611)+P36(x53611,x53612,f53(x53611))+~E(f783(x53612,x53611,x53613),x53613)+~P101(f323(x53612,x53613))
% 179.72/179.59 [4853]~P89(x48533)+~P90(x48533)+E(x48531,x48532)+~E(f323(f103(x48533),x48531),f323(f103(x48533),x48532))
% 179.72/179.59 [5974]~P5(x59741)+P36(x59741,x59742,f53(x59741))+~P101(f323(x59742,x59743))+P101(f323(x59742,f783(x59742,x59741,x59743)))
% 179.72/179.59 [5984]~P101(f323(x59841,x59842))+~P101(f323(x59841,x59843))+~P101(f323(f323(f237(a860),x59843),f851(x59842,x59841)))+P101(f323(x59841,f2(a860)))
% 179.72/179.59 [6395]P143(x63952,x63953,x63951)+E(x63951,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f791(x63951,x63953,x63952)))+P101(f323(f323(f238(a1),x63951),f2(a1)))
% 179.72/179.59 [6396]P142(x63962,x63963,x63961)+E(x63961,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f803(x63961,x63963,x63962)))+P101(f323(f323(f238(a1),x63961),f2(a1)))
% 179.72/179.59 [6516]P142(x65161,x65162,x65163)+~P101(f323(x65161,x65162))+P101(f323(f323(f237(a1),f2(a1)),f803(x65163,x65162,x65161)))+P101(f323(f323(f238(a1),x65163),f2(a1)))
% 179.72/179.59 [6542]P143(x65421,x65422,x65423)+P101(f323(f323(f237(a1),f2(a1)),f791(x65423,x65422,x65421)))+~P101(f323(x65421,f2(a1)))+P101(f323(f323(f238(a1),x65423),f2(a1)))
% 179.72/179.59 [6570]P143(x65702,x65703,x65701)+E(x65701,f2(a1))+~P101(f323(x65702,f792(x65701,x65703,x65702)))+P101(f323(f323(f238(a1),x65701),f2(a1)))
% 179.72/179.59 [6571]P142(x65712,x65713,x65711)+E(x65711,f2(a1))+~P101(f323(x65712,f803(x65711,x65713,x65712)))+P101(f323(f323(f238(a1),x65711),f2(a1)))
% 179.72/179.59 [6670]~P103(x66701)+~P6(x66701)+~P101(f323(f323(f238(x66701),x66702),f37(x66701,x66703)))+P101(f323(f323(f238(x66701),x66702),f547(x66703,x66702,x66701)))
% 179.72/179.59 [6679]P142(x66791,x66792,x66793)+~P101(f323(x66791,x66792))+~P101(f323(x66791,f803(x66793,x66792,x66791)))+P101(f323(f323(f238(a1),x66793),f2(a1)))
% 179.72/179.59 [6710]P143(x67101,x67102,x67103)+~P101(f323(x67101,f792(x67103,x67102,x67101)))+~P101(f323(x67101,f2(a1)))+P101(f323(f323(f238(a1),x67103),f2(a1)))
% 179.72/179.59 [6959]P143(x69592,x69593,x69591)+E(x69591,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f791(x69591,x69593,x69592)))+P101(f323(f323(f238(a1),x69591),f790(x69591,x69593,x69592)))
% 179.72/179.59 [6960]P142(x69602,x69603,x69601)+E(x69601,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f803(x69601,x69603,x69602)))+P101(f323(f323(f238(a1),x69601),f802(x69601,x69603,x69602)))
% 179.72/179.59 [7077]P142(x70771,x70772,x70773)+~P101(f323(x70771,x70772))+P101(f323(f323(f237(a1),f2(a1)),f803(x70773,x70772,x70771)))+P101(f323(f323(f238(a1),x70773),f802(x70773,x70772,x70771)))
% 179.72/179.59 [7096]P143(x70961,x70962,x70963)+P101(f323(f323(f237(a1),f2(a1)),f791(x70963,x70962,x70961)))+P101(f323(f323(f238(a1),x70963),f790(x70963,x70962,x70961)))+~P101(f323(x70961,f2(a1)))
% 179.72/179.59 [7129]P143(x71292,x71293,x71291)+E(x71291,f2(a1))+~P101(f323(x71292,f792(x71291,x71293,x71292)))+P101(f323(f323(f238(a1),x71291),f790(x71291,x71293,x71292)))
% 179.72/179.59 [7130]P142(x71302,x71303,x71301)+E(x71301,f2(a1))+~P101(f323(x71302,f803(x71301,x71303,x71302)))+P101(f323(f323(f238(a1),x71301),f802(x71301,x71303,x71302)))
% 179.72/179.59 [7171]P143(x71712,x71713,x71711)+E(x71711,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f791(x71711,x71713,x71712)))+~P101(f323(x71712,f801(x71711,x71713,x71712)))
% 179.72/179.59 [7172]P142(x71722,x71723,x71721)+E(x71721,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f803(x71721,x71723,x71722)))+~P101(f323(x71722,f802(x71721,x71723,x71722)))
% 179.72/179.59 [7260]P142(x72601,x72602,x72603)+~P101(f323(x72601,x72602))+~P101(f323(x72601,f803(x72603,x72602,x72601)))+P101(f323(f323(f238(a1),x72603),f802(x72603,x72602,x72601)))
% 179.72/179.59 [7276]P143(x72761,x72762,x72763)+~P101(f323(x72761,f792(x72763,x72762,x72761)))+P101(f323(f323(f238(a1),x72763),f790(x72763,x72762,x72761)))+~P101(f323(x72761,f2(a1)))
% 179.72/179.59 [7280]P142(x72801,x72802,x72803)+~P101(f323(x72801,x72802))+P101(f323(f323(f237(a1),f2(a1)),f803(x72803,x72802,x72801)))+~P101(f323(x72801,f802(x72803,x72802,x72801)))
% 179.72/179.59 [7296]P143(x72961,x72962,x72963)+P101(f323(f323(f237(a1),f2(a1)),f791(x72963,x72962,x72961)))+~P101(f323(x72961,f801(x72963,x72962,x72961)))+~P101(f323(x72961,f2(a1)))
% 179.72/179.59 [7319]P143(x73192,x73193,x73191)+E(x73191,f2(a1))+~P101(f323(x73192,f792(x73191,x73193,x73192)))+~P101(f323(x73192,f801(x73191,x73193,x73192)))
% 179.72/179.59 [7320]P142(x73202,x73203,x73201)+E(x73201,f2(a1))+~P101(f323(x73202,f803(x73201,x73203,x73202)))+~P101(f323(x73202,f802(x73201,x73203,x73202)))
% 179.72/179.59 [7411]P142(x74111,x74112,x74113)+~P101(f323(x74111,x74112))+~P101(f323(x74111,f803(x74113,x74112,x74111)))+~P101(f323(x74111,f802(x74113,x74112,x74111)))
% 179.72/179.59 [7428]P143(x74281,x74282,x74283)+~P101(f323(x74281,f792(x74283,x74282,x74281)))+~P101(f323(x74281,f801(x74283,x74282,x74281)))+~P101(f323(x74281,f2(a1)))
% 179.72/179.59 [7475]P143(x74752,x74753,x74751)+E(x74751,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f791(x74751,x74753,x74752)))+P101(f323(f323(f237(a1),f790(x74751,x74753,x74752)),f2(a1)))
% 179.72/179.59 [7476]P142(x74762,x74763,x74761)+E(x74761,f2(a1))+P101(f323(f323(f237(a1),f2(a1)),f803(x74761,x74763,x74762)))+P101(f323(f323(f237(a1),f802(x74761,x74763,x74762)),f2(a1)))
% 179.72/179.59 [7477]~P134(x74771)+~P101(f323(f323(f325(x74771),x74773),f109(x74771)))+~P101(f323(f323(f325(x74771),x74772),f109(x74771)))+P101(f323(f323(f325(x74771),f323(f323(f22(x74771),x74772),x74773)),f109(x74771)))
% 179.72/179.59 [7478]~P134(x74781)+~P101(f323(f323(f325(x74781),x74783),f109(x74781)))+~P101(f323(f323(f325(x74781),x74782),f109(x74781)))+P101(f323(f323(f325(x74781),f323(f323(f79(x74781),x74782),x74783)),f109(x74781)))
% 179.72/179.59 [7479]~P140(x74791)+~P101(f323(f323(f325(x74791),x74793),f186(x74791)))+~P101(f323(f323(f325(x74791),x74792),f186(x74791)))+P101(f323(f323(f325(x74791),f323(f323(f79(x74791),x74792),x74793)),f186(x74791)))
% 179.72/179.59 [7480]~P134(x74801)+~P101(f323(f323(f325(x74801),x74803),f109(x74801)))+~P101(f323(f323(f325(x74801),x74802),f109(x74801)))+P101(f323(f323(f325(x74801),f323(f323(f78(x74801),x74802),x74803)),f109(x74801)))
% 179.72/179.59 [7481]~P140(x74811)+~P101(f323(f323(f325(x74811),x74813),f186(x74811)))+~P101(f323(f323(f325(x74811),x74812),f186(x74811)))+P101(f323(f323(f325(x74811),f323(f323(f78(x74811),x74812),x74813)),f186(x74811)))
% 179.72/179.59 [7482]~P84(x74821)+~P101(f323(f323(f237(x74821),x74823),f2(x74821)))+~P101(f323(f323(f237(x74821),x74822),f2(x74821)))+P101(f323(f323(f237(x74821),f323(f323(f78(x74821),x74822),x74823)),f2(x74821)))
% 179.72/179.59 [7483]~P84(x74831)+~P101(f323(f323(f237(x74831),x74833),f2(x74831)))+~P101(f323(f323(f238(x74831),x74832),f2(x74831)))+P101(f323(f323(f238(x74831),f323(f323(f78(x74831),x74832),x74833)),f2(x74831)))
% 179.72/179.59 [7484]~P84(x74841)+~P101(f323(f323(f237(x74841),x74842),f2(x74841)))+~P101(f323(f323(f238(x74841),x74843),f2(x74841)))+P101(f323(f323(f238(x74841),f323(f323(f78(x74841),x74842),x74843)),f2(x74841)))
% 179.72/179.59 [7485]~P84(x74851)+~P101(f323(f323(f238(x74851),x74853),f2(x74851)))+~P101(f323(f323(f238(x74851),x74852),f2(x74851)))+P101(f323(f323(f238(x74851),f323(f323(f78(x74851),x74852),x74853)),f2(x74851)))
% 179.72/179.59 [7511]P143(x75113,x75112,x75111)+E(x75111,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x75111),f792(x75111,x75112,x75113))),f791(x75111,x75112,x75113)),x75112)+P101(f323(f323(f238(a1),x75111),f2(a1)))
% 179.72/179.59 [7512]P142(x75123,x75122,x75121)+E(x75121,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x75121),f804(x75121,x75122,x75123))),f803(x75121,x75122,x75123)),x75122)+P101(f323(f323(f238(a1),x75121),f2(a1)))
% 179.72/179.59 [7594]P142(x75941,x75942,x75943)+~P101(f323(x75941,x75942))+P101(f323(f323(f237(a1),f2(a1)),f803(x75943,x75942,x75941)))+P101(f323(f323(f237(a1),f802(x75943,x75942,x75941)),f2(a1)))
% 179.72/179.59 [7623]P143(x76231,x76232,x76233)+P101(f323(f323(f237(a1),f2(a1)),f791(x76233,x76232,x76231)))+~P101(f323(x76231,f2(a1)))+P101(f323(f323(f237(a1),f790(x76233,x76232,x76231)),f2(a1)))
% 179.72/179.59 [7632]P142(x76323,x76322,x76321)+~P101(f323(x76323,x76322))+E(f323(f323(f78(a1),f323(f323(f79(a1),x76321),f804(x76321,x76322,x76323))),f803(x76321,x76322,x76323)),x76322)+P101(f323(f323(f238(a1),x76321),f2(a1)))
% 179.72/179.59 [7639]P143(x76392,x76393,x76391)+E(x76391,f2(a1))+~P101(f323(x76392,f792(x76391,x76393,x76392)))+P101(f323(f323(f237(a1),f790(x76391,x76393,x76392)),f2(a1)))
% 179.72/179.59 [7640]P142(x76402,x76403,x76401)+E(x76401,f2(a1))+~P101(f323(x76402,f803(x76401,x76403,x76402)))+P101(f323(f323(f237(a1),f802(x76401,x76403,x76402)),f2(a1)))
% 179.72/179.59 [7645]P143(x76453,x76452,x76451)+E(f323(f323(f78(a1),f323(f323(f79(a1),x76451),f792(x76451,x76452,x76453))),f791(x76451,x76452,x76453)),x76452)+~P101(f323(x76453,f2(a1)))+P101(f323(f323(f238(a1),x76451),f2(a1)))
% 179.72/179.59 [7701]P142(x77011,x77012,x77013)+~P101(f323(x77011,x77012))+~P101(f323(x77011,f803(x77013,x77012,x77011)))+P101(f323(f323(f237(a1),f802(x77013,x77012,x77011)),f2(a1)))
% 179.72/179.59 [7705]P143(x77051,x77052,x77053)+~P101(f323(x77051,f792(x77053,x77052,x77051)))+~P101(f323(x77051,f2(a1)))+P101(f323(f323(f237(a1),f790(x77053,x77052,x77051)),f2(a1)))
% 179.72/179.59 [7772]~P120(x77721)+~P101(f323(f323(f237(x77721),f323(f323(f79(x77721),x77723),x77722)),f2(x77721)))+P101(f323(f323(f237(x77721),x77722),f2(x77721)))+P101(f323(f323(f237(x77721),x77723),f2(x77721)))
% 179.72/179.59 [7773]~P64(x77731)+~P101(f323(f323(f237(x77731),f323(f323(f281(x77731),x77733),x77732)),f2(x77731)))+P101(f323(f323(f237(x77731),x77732),f2(x77731)))+P101(f323(f323(f237(x77731),x77733),f2(x77731)))
% 179.72/179.59 [7774]~P64(x77741)+~P101(f323(f323(f238(x77741),f323(f323(f281(x77741),x77743),x77742)),f2(x77741)))+P101(f323(f323(f238(x77741),x77742),f2(x77741)))+P101(f323(f323(f238(x77741),x77743),f2(x77741)))
% 179.72/179.59 [7891]P143(x78913,x78912,x78911)+E(x78911,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x78911),f792(x78911,x78912,x78913))),f791(x78911,x78912,x78913)),x78912)+P101(f323(f323(f238(a1),x78911),f790(x78911,x78912,x78913)))
% 179.72/179.59 [7892]P142(x78923,x78922,x78921)+E(x78921,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x78921),f804(x78921,x78922,x78923))),f803(x78921,x78922,x78923)),x78922)+P101(f323(f323(f238(a1),x78921),f802(x78921,x78922,x78923)))
% 179.72/179.59 [7905]P143(x79053,x79052,x79051)+E(x79051,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79051),f801(x79051,x79052,x79053))),f790(x79051,x79052,x79053)),x79052)+P101(f323(f323(f237(a1),f2(a1)),f791(x79051,x79052,x79053)))
% 179.72/179.59 [7906]P142(x79063,x79062,x79061)+E(x79061,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79061),f805(x79061,x79062,x79063))),f802(x79061,x79062,x79063)),x79062)+P101(f323(f323(f237(a1),f2(a1)),f803(x79061,x79062,x79063)))
% 179.72/179.59 [7947]P142(x79473,x79472,x79471)+~P101(f323(x79473,x79472))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79471),f804(x79471,x79472,x79473))),f803(x79471,x79472,x79473)),x79472)+P101(f323(f323(f238(a1),x79471),f802(x79471,x79472,x79473)))
% 179.72/179.59 [7956]P143(x79563,x79562,x79561)+E(f323(f323(f78(a1),f323(f323(f79(a1),x79561),f792(x79561,x79562,x79563))),f791(x79561,x79562,x79563)),x79562)+P101(f323(f323(f238(a1),x79561),f790(x79561,x79562,x79563)))+~P101(f323(x79563,f2(a1)))
% 179.72/179.59 [7962]P142(x79623,x79622,x79621)+~P101(f323(x79623,x79622))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79621),f805(x79621,x79622,x79623))),f802(x79621,x79622,x79623)),x79622)+P101(f323(f323(f237(a1),f2(a1)),f803(x79621,x79622,x79623)))
% 179.72/179.59 [7968]P143(x79683,x79682,x79681)+E(f323(f323(f78(a1),f323(f323(f79(a1),x79681),f801(x79681,x79682,x79683))),f790(x79681,x79682,x79683)),x79682)+P101(f323(f323(f237(a1),f2(a1)),f791(x79681,x79682,x79683)))+~P101(f323(x79683,f2(a1)))
% 179.72/179.59 [7979]P143(x79793,x79792,x79791)+E(x79791,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79791),f792(x79791,x79792,x79793))),f791(x79791,x79792,x79793)),x79792)+~P101(f323(x79793,f801(x79791,x79792,x79793)))
% 179.72/179.59 [7980]P142(x79803,x79802,x79801)+E(x79801,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79801),f804(x79801,x79802,x79803))),f803(x79801,x79802,x79803)),x79802)+~P101(f323(x79803,f802(x79801,x79802,x79803)))
% 179.72/179.59 [7981]P143(x79813,x79812,x79811)+E(x79811,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79811),f801(x79811,x79812,x79813))),f790(x79811,x79812,x79813)),x79812)+~P101(f323(x79813,f792(x79811,x79812,x79813)))
% 179.72/179.59 [7982]P142(x79823,x79822,x79821)+E(x79821,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x79821),f805(x79821,x79822,x79823))),f802(x79821,x79822,x79823)),x79822)+~P101(f323(x79823,f803(x79821,x79822,x79823)))
% 179.72/179.59 [8039]P142(x80393,x80392,x80391)+~P101(f323(x80393,x80392))+E(f323(f323(f78(a1),f323(f323(f79(a1),x80391),f804(x80391,x80392,x80393))),f803(x80391,x80392,x80393)),x80392)+~P101(f323(x80393,f802(x80391,x80392,x80393)))
% 179.72/179.59 [8040]P142(x80403,x80402,x80401)+~P101(f323(x80403,x80402))+E(f323(f323(f78(a1),f323(f323(f79(a1),x80401),f805(x80401,x80402,x80403))),f802(x80401,x80402,x80403)),x80402)+~P101(f323(x80403,f803(x80401,x80402,x80403)))
% 179.72/179.59 [8050]P143(x80503,x80502,x80501)+E(f323(f323(f78(a1),f323(f323(f79(a1),x80501),f792(x80501,x80502,x80503))),f791(x80501,x80502,x80503)),x80502)+~P101(f323(x80503,f801(x80501,x80502,x80503)))+~P101(f323(x80503,f2(a1)))
% 179.72/179.59 [8051]P143(x80513,x80512,x80511)+E(f323(f323(f78(a1),f323(f323(f79(a1),x80511),f801(x80511,x80512,x80513))),f790(x80511,x80512,x80513)),x80512)+~P101(f323(x80513,f792(x80511,x80512,x80513)))+~P101(f323(x80513,f2(a1)))
% 179.72/179.59 [8152]P143(x81523,x81522,x81521)+E(x81521,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x81521),f792(x81521,x81522,x81523))),f791(x81521,x81522,x81523)),x81522)+P101(f323(f323(f237(a1),f790(x81521,x81522,x81523)),f2(a1)))
% 179.72/179.59 [8153]P142(x81533,x81532,x81531)+E(x81531,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x81531),f804(x81531,x81532,x81533))),f803(x81531,x81532,x81533)),x81532)+P101(f323(f323(f237(a1),f802(x81531,x81532,x81533)),f2(a1)))
% 179.72/179.59 [8194]P142(x81943,x81942,x81941)+~P101(f323(x81943,x81942))+E(f323(f323(f78(a1),f323(f323(f79(a1),x81941),f804(x81941,x81942,x81943))),f803(x81941,x81942,x81943)),x81942)+P101(f323(f323(f237(a1),f802(x81941,x81942,x81943)),f2(a1)))
% 179.72/179.59 [8199]P143(x81993,x81992,x81991)+E(f323(f323(f78(a1),f323(f323(f79(a1),x81991),f792(x81991,x81992,x81993))),f791(x81991,x81992,x81993)),x81992)+~P101(f323(x81993,f2(a1)))+P101(f323(f323(f237(a1),f790(x81991,x81992,x81993)),f2(a1)))
% 179.72/179.59 [8334]P143(x83343,x83342,x83341)+E(x83341,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x83341),f801(x83341,x83342,x83343))),f790(x83341,x83342,x83343)),x83342)+E(f323(f323(f78(a1),f323(f323(f79(a1),x83341),f792(x83341,x83342,x83343))),f791(x83341,x83342,x83343)),x83342)
% 179.72/179.59 [8335]P142(x83353,x83352,x83351)+E(x83351,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x83351),f805(x83351,x83352,x83353))),f802(x83351,x83352,x83353)),x83352)+E(f323(f323(f78(a1),f323(f323(f79(a1),x83351),f804(x83351,x83352,x83353))),f803(x83351,x83352,x83353)),x83352)
% 179.72/179.59 [8356]P142(x83563,x83562,x83561)+~P101(f323(x83563,x83562))+E(f323(f323(f78(a1),f323(f323(f79(a1),x83561),f805(x83561,x83562,x83563))),f802(x83561,x83562,x83563)),x83562)+E(f323(f323(f78(a1),f323(f323(f79(a1),x83561),f804(x83561,x83562,x83563))),f803(x83561,x83562,x83563)),x83562)
% 179.72/179.59 [8368]P143(x83683,x83682,x83681)+E(f323(f323(f78(a1),f323(f323(f79(a1),x83681),f801(x83681,x83682,x83683))),f790(x83681,x83682,x83683)),x83682)+E(f323(f323(f78(a1),f323(f323(f79(a1),x83681),f792(x83681,x83682,x83683))),f791(x83681,x83682,x83683)),x83682)+~P101(f323(x83683,f2(a1)))
% 179.72/179.59 [9026]~P120(x90261)+~E(x90263,f2(x90261))+~E(x90262,f2(x90261))+P101(f323(f323(f237(x90261),f323(f323(f78(x90261),f323(f323(f79(x90261),x90262),x90262)),f323(f323(f79(x90261),x90263),x90263))),f2(x90261)))
% 179.72/179.59 [10067]~P116(x100671)+~E(x100673,f2(x100671))+~E(x100672,f2(x100671))+P101(f323(f323(f237(x100671),f323(f323(f78(x100671),f323(f323(f248(x100671),x100672),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x100671),x100673),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))),f2(x100671)))
% 179.72/179.59 [4802]~E(x48023,x48021)+~P114(x48022)+E(x48021,f2(x48022))+E(f323(f323(f281(x48022),x48023),x48021),f76(x48022))
% 179.72/179.59 [4854]~P3(x48541)+~E(x48543,f188(x48541))+~E(x48542,f188(x48541))+E(f323(f323(f110(x48541),x48542),x48543),f188(x48541))
% 179.72/179.59 [4855]~P95(x48551)+~E(x48553,f246(x48551))+~E(x48552,f246(x48551))+E(f323(f323(f101(x48551),x48552),x48553),f246(x48551))
% 179.72/179.59 [4942]~P114(x49423)+E(x49421,x49422)+E(x49422,f2(x49423))+~E(f323(f323(f281(x49423),x49421),x49422),f76(x49423))
% 179.72/179.59 [4961]~P123(x49612)+E(x49611,f2(x49612))+E(x49613,f2(x49612))+~E(f323(f323(f79(x49612),x49613),x49611),f2(x49612))
% 179.72/179.59 [4962]~P137(x49622)+E(x49621,f2(x49622))+E(x49623,f2(x49622))+~E(f323(f323(f79(x49622),x49623),x49621),f2(x49622))
% 179.72/179.59 [5328]~P108(x53283)+E(x53281,x53282)+E(x53281,f323(f77(x53283),x53282))+~E(f323(f323(f79(x53283),x53281),x53281),f323(f323(f79(x53283),x53282),x53282))
% 179.72/179.59 [5368]~P87(x53681)+E(f323(f77(x53681),x53682),x53683)+~E(f323(f323(f110(x53681),x53682),x53683),f246(x53681))+~E(f323(f323(f101(x53681),x53682),x53683),f188(x53681))
% 179.72/179.59 [5447]~P116(x54473)+E(x54471,x54472)+P101(f323(f323(f238(x54473),x54472),x54471))+P101(f323(f323(f238(x54473),x54471),x54472))
% 179.72/179.59 [5448]~P103(x54483)+E(x54481,x54482)+P101(f323(f323(f238(x54483),x54482),x54481))+P101(f323(f323(f238(x54483),x54481),x54482))
% 179.72/179.59 [5449]~E(x54492,x54493)+~P103(x54491)+P101(f323(f323(f238(x54491),x54492),x54493))+P101(f323(f323(f237(x54491),x54492),x54493))
% 179.72/179.59 [5703]~P105(x57033)+E(x57031,x57032)+~P101(f323(f323(f237(x57033),x57032),x57031))+P101(f323(f323(f238(x57033),x57032),x57031))
% 179.72/179.59 [5705]~P103(x57053)+E(x57051,x57052)+~P101(f323(f323(f237(x57053),x57051),x57052))+P101(f323(f323(f238(x57053),x57051),x57052))
% 179.72/179.59 [5711]~P105(x57113)+E(x57111,x57112)+~P101(f323(f323(f237(x57113),x57111),x57112))+P101(f323(f323(f238(x57113),x57111),x57112))
% 179.72/179.59 [5811]P142(x58111,x58112,x58113)+~P101(f323(x58111,x58112))+P101(f323(f323(f238(a1),x58113),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x58113))
% 179.72/179.59 [5858]P143(x58581,x58582,x58583)+~P101(f323(x58581,f2(a1)))+P101(f323(f323(f238(a1),x58583),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x58583))
% 179.72/179.59 [5862]~P2(x58621)+E(f323(f323(f110(x58621),x58622),f11(x58621,x58623)),x58622)+~P101(f323(f59(x58621),x58623))+~P101(f323(f323(f325(x58621),x58622),x58623))
% 179.72/179.59 [5863]~P2(x58631)+E(f323(f323(f101(x58631),x58632),f10(x58631,x58633)),x58632)+~P101(f323(f59(x58631),x58633))+~P101(f323(f323(f325(x58631),x58632),x58633))
% 179.72/179.59 [5897]~P2(x58971)+E(f323(f323(f110(x58971),x58972),f10(x58971,x58973)),f10(x58971,x58973))+~P101(f323(f59(x58971),x58973))+~P101(f323(f323(f325(x58971),x58972),x58973))
% 179.72/179.59 [5898]~P2(x58981)+E(f323(f323(f101(x58981),x58982),f11(x58981,x58983)),f11(x58981,x58983))+~P101(f323(f59(x58981),x58983))+~P101(f323(f323(f325(x58981),x58982),x58983))
% 179.72/179.59 [5899]~P103(x58991)+E(f323(f323(f235(x58991),x58992),f15(x58991,x58993)),f15(x58991,x58993))+~P101(f323(f59(x58991),x58993))+~P101(f323(f323(f325(x58991),x58992),x58993))
% 179.72/179.59 [5900]~P103(x59001)+E(f323(f323(f236(x59001),x59002),f14(x59001,x59003)),f14(x59001,x59003))+~P101(f323(f59(x59001),x59003))+~P101(f323(f323(f325(x59001),x59002),x59003))
% 179.72/179.59 [5941]E(x59411,x59412)+~P105(x59413)+~P101(f323(f323(f237(x59413),x59412),x59411))+~P101(f323(f323(f237(x59413),x59411),x59412))
% 179.72/179.59 [6079]~P102(x60791)+P101(f323(f323(f238(x60791),x60793),x60792))+~P101(f323(f323(f237(x60791),x60793),x60792))+P101(f323(f323(f237(x60791),x60792),x60793))
% 179.72/179.59 [6100]~P103(x61001)+~P101(f323(f59(x61001),x61003))+P101(f323(f323(f237(x61001),x61002),f14(x61001,x61003)))+~P101(f323(f323(f325(x61001),x61002),x61003))
% 179.72/179.59 [6147]~P103(x61471)+E(f323(f323(f235(x61471),x61472),f13(x61471,f236(x61471),x61473)),x61472)+~P101(f323(f59(x61471),x61473))+~P101(f323(f323(f325(x61471),x61472),x61473))
% 179.72/179.59 [6148]~P103(x61481)+E(f323(f323(f236(x61481),x61482),f12(x61481,f235(x61481),x61483)),x61482)+~P101(f323(f59(x61481),x61483))+~P101(f323(f323(f325(x61481),x61482),x61483))
% 179.72/179.59 [6285]E(x62851,x62852)+~E(f323(f323(f22(a860),x62851),x62853),f323(f323(f22(a860),x62852),x62853))+~P101(f323(f323(f237(a860),x62853),x62851))+~P101(f323(f323(f237(a860),x62853),x62852))
% 179.72/179.59 [6312]~P103(x63121)+~P101(f323(f59(x63121),x63122))+~P101(f323(f323(f325(x63121),x63123),x63122))+P101(f323(f323(f237(x63121),f15(x63121,x63122)),x63123))
% 179.72/179.59 [6375]P143(x63752,x63753,x63751)+E(x63751,f2(a1))+P101(f323(f323(f238(a1),x63751),f790(x63751,x63753,x63752)))+P101(f323(f323(f238(a1),f2(a1)),x63751))
% 179.72/179.59 [6376]P142(x63762,x63763,x63761)+E(x63761,f2(a1))+P101(f323(f323(f238(a1),x63761),f802(x63761,x63763,x63762)))+P101(f323(f323(f238(a1),f2(a1)),x63761))
% 179.72/179.59 [6377]~P103(x63771)+E(f323(f323(f235(x63771),x63772),f12(x63771,f235(x63771),x63773)),f12(x63771,f235(x63771),x63773))+~P101(f323(f59(x63771),x63773))+~P101(f323(f323(f325(x63771),x63772),x63773))
% 179.72/179.59 [6378]~P103(x63781)+E(f323(f323(f236(x63781),x63782),f13(x63781,f236(x63781),x63783)),f13(x63781,f236(x63781),x63783))+~P101(f323(f59(x63781),x63783))+~P101(f323(f323(f325(x63781),x63782),x63783))
% 179.72/179.59 [6383]~P101(f323(x63831,x63832))+P101(f323(x63831,f489(x63832,x63831,x63833)))+P101(f323(x63831,f2(a860)))+~P101(f323(f323(f238(a860),x63832),x63833))
% 179.72/179.59 [6437]~P101(f323(x64371,x64372))+~P101(f323(f59(x64373),x64372))+P101(f323(x64371,f813(x64371,x64372,x64373)))+P101(f323(x64371,f188(f867(x64373,a855))))
% 179.72/179.59 [6450]~P116(x64501)+~P90(x64501)+P101(f323(f323(f237(x64501),f323(f103(x64501),x64502)),f323(f103(x64501),x64503)))+~P101(f323(f323(f237(a1),x64502),x64503))
% 179.72/179.59 [6451]~P116(x64511)+~P90(x64511)+P101(f323(f323(f238(x64511),f323(f103(x64511),x64512)),f323(f103(x64511),x64513)))+~P101(f323(f323(f238(a1),x64512),x64513))
% 179.72/179.59 [6454]~P101(f323(x64541,x64543))+~P101(f323(f59(x64542),x64543))+P101(f323(f59(x64542),f813(x64541,x64543,x64542)))+P101(f323(x64541,f188(f867(x64542,a855))))
% 179.72/179.59 [6487]P142(x64871,x64872,x64873)+~P101(f323(x64871,x64872))+P101(f323(f323(f238(a1),x64873),f802(x64873,x64872,x64871)))+P101(f323(f323(f238(a1),f2(a1)),x64873))
% 179.72/179.59 [6522]P143(x65221,x65222,x65223)+P101(f323(f323(f238(a1),x65223),f790(x65223,x65222,x65221)))+~P101(f323(x65221,f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x65223))
% 179.72/179.59 [6553]~P104(x65531)+~P91(x65531)+E(f323(f323(f235(x65531),f323(f103(x65531),x65532)),f323(f103(x65531),x65533)),f323(f103(x65531),x65533))+P101(f323(f323(f237(x65531),f323(f103(x65531),x65532)),f323(f103(x65531),x65533)))
% 179.72/179.59 [6554]~P104(x65541)+~P91(x65541)+E(f323(f323(f236(x65541),f323(f103(x65541),x65542)),f323(f103(x65541),x65543)),f323(f103(x65541),x65542))+P101(f323(f323(f237(x65541),f323(f103(x65541),x65542)),f323(f103(x65541),x65543)))
% 179.72/179.59 [6611]P143(x66112,x66113,x66111)+E(x66111,f2(a1))+~P101(f323(x66112,f801(x66111,x66113,x66112)))+P101(f323(f323(f238(a1),f2(a1)),x66111))
% 179.72/179.59 [6612]P142(x66122,x66123,x66121)+E(x66121,f2(a1))+~P101(f323(x66122,f802(x66121,x66123,x66122)))+P101(f323(f323(f238(a1),f2(a1)),x66121))
% 179.72/179.59 [6616]P101(f323(x66161,x66162))+~P101(f323(f59(x66163),x66162))+P101(f323(x66161,f793(x66161,x66162,x66163)))+~P101(f323(x66161,f188(f867(x66163,a855))))
% 179.72/179.59 [6635]P101(f323(x66351,x66352))+P101(f323(f59(x66353),f793(x66351,x66352,x66353)))+~P101(f323(f59(x66353),x66352))+~P101(f323(x66351,f188(f867(x66353,a855))))
% 179.72/179.59 [6699]P142(x66991,x66992,x66993)+~P101(f323(x66991,x66992))+~P101(f323(x66991,f802(x66993,x66992,x66991)))+P101(f323(f323(f238(a1),f2(a1)),x66993))
% 179.72/179.59 [6729]P143(x67291,x67292,x67293)+~P101(f323(x67291,f801(x67293,x67292,x67291)))+~P101(f323(x67291,f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x67293))
% 179.72/179.59 [6837]~P90(x68373)+~P116(x68373)+~P101(f323(f323(f237(x68373),f323(f103(x68373),x68371)),f323(f103(x68373),x68372)))+P101(f323(f323(f237(a1),x68371),x68372))
% 179.72/179.59 [6838]~P90(x68383)+~P116(x68383)+~P101(f323(f323(f238(x68383),f323(f103(x68383),x68381)),f323(f103(x68383),x68382)))+P101(f323(f323(f238(a1),x68381),x68382))
% 179.72/179.59 [6864]~P103(x68641)+~P16(x68641,x68643)+P16(x68641,f323(f323(f144(x68641),x68642),x68643))+~P101(f323(f323(f237(x68641),x68642),f594(x68643,x68642,x68641)))
% 179.72/179.59 [6865]~P103(x68651)+~P16(x68651,x68653)+P16(x68651,f323(f323(f144(x68651),x68652),x68653))+~P101(f323(f323(f237(x68651),x68652),f598(x68653,x68652,x68651)))
% 179.72/179.59 [6866]~P103(x68661)+~P16(x68661,x68663)+P16(x68661,f323(f323(f144(x68661),x68662),x68663))+~P101(f323(f323(f237(x68661),x68662),f703(x68662,x68663,x68661)))
% 179.72/179.59 [6950]P143(x69502,x69503,x69501)+E(x69501,f2(a1))+P101(f323(f323(f238(a1),x69501),f2(a1)))+P101(f323(f323(f238(a1),f791(x69501,x69503,x69502)),x69501))
% 179.72/179.59 [6951]P142(x69512,x69513,x69511)+E(x69511,f2(a1))+P101(f323(f323(f238(a1),x69511),f2(a1)))+P101(f323(f323(f238(a1),f803(x69511,x69513,x69512)),x69511))
% 179.72/179.59 [6990]P143(x69902,x69903,x69901)+E(x69901,f2(a1))+P101(f323(f323(f237(a1),f790(x69901,x69903,x69902)),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x69901))
% 179.72/179.59 [6991]P142(x69912,x69913,x69911)+E(x69911,f2(a1))+P101(f323(f323(f237(a1),f802(x69911,x69913,x69912)),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x69911))
% 179.72/179.59 [7013]~P103(x70131)+~P16(x70131,x70133)+E(f323(f323(f141(x70131,x70131,f5(x70131)),x70132),f164(x70131,x70132,x70133)),x70133)+~P101(f323(f323(f325(x70131),x70132),f323(f166(x70131),x70133)))
% 179.72/179.59 [7060]P142(x70601,x70602,x70603)+~P101(f323(x70601,x70602))+P101(f323(f323(f238(a1),x70603),f2(a1)))+P101(f323(f323(f238(a1),f803(x70603,x70602,x70601)),x70603))
% 179.72/179.59 [7066]~P104(x70661)+~P91(x70661)+E(f323(f323(f235(x70661),f323(f103(x70661),x70662)),f323(f103(x70661),x70663)),f323(f103(x70661),x70662))+~P101(f323(f323(f237(x70661),f323(f103(x70661),x70662)),f323(f103(x70661),x70663)))
% 179.72/179.59 [7067]~P104(x70671)+~P91(x70671)+E(f323(f323(f236(x70671),f323(f103(x70671),x70672)),f323(f103(x70671),x70673)),f323(f103(x70671),x70673))+~P101(f323(f323(f237(x70671),f323(f103(x70671),x70672)),f323(f103(x70671),x70673)))
% 179.72/179.59 [7081]P143(x70811,x70812,x70813)+~P101(f323(x70811,f2(a1)))+P101(f323(f323(f238(a1),x70813),f2(a1)))+P101(f323(f323(f238(a1),f791(x70813,x70812,x70811)),x70813))
% 179.72/179.59 [7089]P142(x70891,x70892,x70893)+~P101(f323(x70891,x70892))+P101(f323(f323(f237(a1),f802(x70893,x70892,x70891)),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x70893))
% 179.72/179.59 [7113]P143(x71131,x71132,x71133)+~P101(f323(x71131,f2(a1)))+P101(f323(f323(f237(a1),f790(x71133,x71132,x71131)),f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x71133))
% 179.72/179.59 [7141]~P101(f323(x71411,x71412))+P101(f323(x71411,f2(a860)))+~P101(f323(f323(f238(a860),x71412),x71413))+P101(f323(f323(f238(a860),f489(x71412,x71411,x71413)),x71413))
% 179.72/179.59 [7158]~P103(x71581)+~P16(x71581,x71583)+P16(x71581,f323(f323(f144(x71581),x71582),x71583))+P101(f323(f323(f325(x71581),f594(x71583,x71582,x71581)),f323(f166(x71581),x71583)))
% 179.72/179.59 [7159]~P103(x71591)+~P16(x71591,x71593)+P16(x71591,f323(f323(f144(x71591),x71592),x71593))+P101(f323(f323(f325(x71591),f598(x71593,x71592,x71591)),f323(f166(x71591),x71593)))
% 179.72/179.59 [7160]~P103(x71601)+~P16(x71601,x71603)+P16(x71601,f323(f323(f144(x71601),x71602),x71603))+P101(f323(f323(f325(x71601),f703(x71602,x71603,x71601)),f323(f166(x71601),x71603)))
% 179.72/179.59 [7264]~P103(x72641)+~P6(x72641)+~P101(f323(f323(f238(x72641),x72643),f37(x72641,x72642)))+P101(f323(f323(f325(x72641),f547(x72642,x72643,x72641)),x72642))
% 179.72/179.59 [7426]~P103(x74261)+~P6(x74261)+~P101(f323(f323(f238(x74261),f38(x74261,x74263)),x74262))+P101(f323(f323(f325(x74261),f643(x74262,x74263,x74261)),x74263))
% 179.72/179.59 [7427]~P103(x74271)+~P6(x74271)+~P101(f323(f323(f238(x74271),f38(x74271,x74273)),x74272))+P101(f323(f323(f238(x74271),f643(x74272,x74273,x74271)),x74272))
% 179.72/179.59 [7441]P143(x74412,x74413,x74411)+E(x74411,f2(a1))+P101(f323(f323(f238(a1),x74411),f790(x74411,x74413,x74412)))+P101(f323(f323(f238(a1),f791(x74411,x74413,x74412)),x74411))
% 179.72/179.59 [7442]P142(x74422,x74423,x74421)+E(x74421,f2(a1))+P101(f323(f323(f238(a1),x74421),f802(x74421,x74423,x74422)))+P101(f323(f323(f238(a1),f803(x74421,x74423,x74422)),x74421))
% 179.72/179.59 [7532]P143(x75323,x75322,x75321)+E(x75321,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x75321),f801(x75321,x75322,x75323))),f790(x75321,x75322,x75323)),x75322)+P101(f323(f323(f238(a1),f2(a1)),x75321))
% 179.72/179.59 [7533]P142(x75333,x75332,x75331)+E(x75331,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x75331),f805(x75331,x75332,x75333))),f802(x75331,x75332,x75333)),x75332)+P101(f323(f323(f238(a1),f2(a1)),x75331))
% 179.72/179.59 [7535]~P120(x75351)+~P101(f323(f323(f237(x75351),x75353),f2(x75351)))+P101(f323(f323(f237(x75351),f323(f323(f79(x75351),x75352),x75353)),f2(x75351)))+~P101(f323(f323(f237(x75351),f2(x75351)),x75352))
% 179.72/179.59 [7536]~P120(x75361)+~P101(f323(f323(f237(x75361),x75362),f2(x75361)))+P101(f323(f323(f237(x75361),f323(f323(f79(x75361),x75362),x75363)),f2(x75361)))+~P101(f323(f323(f237(x75361),f2(x75361)),x75363))
% 179.72/179.59 [7538]~P129(x75381)+~P101(f323(f323(f237(x75381),x75383),f2(x75381)))+P101(f323(f323(f237(x75381),f323(f323(f79(x75381),x75382),x75383)),f2(x75381)))+~P101(f323(f323(f237(x75381),f2(x75381)),x75382))
% 179.72/179.59 [7540]~P129(x75401)+~P101(f323(f323(f237(x75401),x75402),f2(x75401)))+P101(f323(f323(f237(x75401),f323(f323(f79(x75401),x75402),x75403)),f2(x75401)))+~P101(f323(f323(f237(x75401),f2(x75401)),x75403))
% 179.72/179.59 [7541]~P65(x75411)+~P101(f323(f323(f237(x75411),x75412),f2(x75411)))+P101(f323(f323(f237(x75411),f323(f323(f281(x75411),x75412),x75413)),f2(x75411)))+~P101(f323(f323(f238(x75411),f2(x75411)),x75413))
% 179.72/179.59 [7542]~P65(x75421)+~P101(f323(f323(f238(x75421),x75423),f2(x75421)))+P101(f323(f323(f237(x75421),f323(f323(f281(x75421),x75422),x75423)),f2(x75421)))+~P101(f323(f323(f237(x75421),f2(x75421)),x75422))
% 179.72/179.59 [7543]~P64(x75431)+~P101(f323(f323(f237(x75431),x75433),f2(x75431)))+P101(f323(f323(f237(x75431),f323(f323(f281(x75431),x75432),x75433)),f2(x75431)))+~P101(f323(f323(f237(x75431),f2(x75431)),x75432))
% 179.72/179.59 [7544]~P64(x75441)+~P101(f323(f323(f237(x75441),x75442),f2(x75441)))+P101(f323(f323(f237(x75441),f323(f323(f281(x75441),x75442),x75443)),f2(x75441)))+~P101(f323(f323(f237(x75441),f2(x75441)),x75443))
% 179.72/179.59 [7546]~P125(x75461)+~P101(f323(f323(f238(x75461),x75463),f2(x75461)))+P101(f323(f323(f238(x75461),f323(f323(f79(x75461),x75462),x75463)),f2(x75461)))+~P101(f323(f323(f238(x75461),f2(x75461)),x75462))
% 179.72/179.59 [7547]~P125(x75471)+~P101(f323(f323(f238(x75471),x75472),f2(x75471)))+P101(f323(f323(f238(x75471),f323(f323(f79(x75471),x75472),x75473)),f2(x75471)))+~P101(f323(f323(f238(x75471),f2(x75471)),x75473))
% 179.72/179.59 [7548]~P65(x75481)+~P101(f323(f323(f238(x75481),x75483),f2(x75481)))+P101(f323(f323(f238(x75481),f323(f323(f281(x75481),x75482),x75483)),f2(x75481)))+~P101(f323(f323(f238(x75481),f2(x75481)),x75482))
% 179.72/179.59 [7549]~P65(x75491)+~P101(f323(f323(f238(x75491),x75492),f2(x75491)))+P101(f323(f323(f238(x75491),f323(f323(f281(x75491),x75492),x75493)),f2(x75491)))+~P101(f323(f323(f238(x75491),f2(x75491)),x75493))
% 179.72/179.59 [7550]~P64(x75501)+~P101(f323(f323(f238(x75501),x75503),f2(x75501)))+P101(f323(f323(f238(x75501),f323(f323(f281(x75501),x75502),x75503)),f2(x75501)))+~P101(f323(f323(f238(x75501),f2(x75501)),x75502))
% 179.72/179.59 [7551]~P64(x75511)+~P101(f323(f323(f238(x75511),x75512),f2(x75511)))+P101(f323(f323(f238(x75511),f323(f323(f281(x75511),x75512),x75513)),f2(x75511)))+~P101(f323(f323(f238(x75511),f2(x75511)),x75513))
% 179.72/179.59 [7566]P142(x75661,x75662,x75663)+~P101(f323(x75661,x75662))+P101(f323(f323(f238(a1),x75663),f802(x75663,x75662,x75661)))+P101(f323(f323(f238(a1),f803(x75663,x75662,x75661)),x75663))
% 179.72/179.59 [7579]P143(x75791,x75792,x75793)+P101(f323(f323(f238(a1),x75793),f790(x75793,x75792,x75791)))+~P101(f323(x75791,f2(a1)))+P101(f323(f323(f238(a1),f791(x75793,x75792,x75791)),x75793))
% 179.72/179.59 [7630]P143(x76302,x76303,x76301)+E(x76301,f2(a1))+~P101(f323(x76302,f801(x76301,x76303,x76302)))+P101(f323(f323(f238(a1),f791(x76301,x76303,x76302)),x76301))
% 179.72/179.59 [7631]P142(x76312,x76313,x76311)+E(x76311,f2(a1))+~P101(f323(x76312,f802(x76311,x76313,x76312)))+P101(f323(f323(f238(a1),f803(x76311,x76313,x76312)),x76311))
% 179.72/179.59 [7642]P142(x76423,x76422,x76421)+~P101(f323(x76423,x76422))+E(f323(f323(f78(a1),f323(f323(f79(a1),x76421),f805(x76421,x76422,x76423))),f802(x76421,x76422,x76423)),x76422)+P101(f323(f323(f238(a1),f2(a1)),x76421))
% 179.72/179.59 [7659]P143(x76593,x76592,x76591)+E(f323(f323(f78(a1),f323(f323(f79(a1),x76591),f801(x76591,x76592,x76593))),f790(x76591,x76592,x76593)),x76592)+~P101(f323(x76593,f2(a1)))+P101(f323(f323(f238(a1),f2(a1)),x76591))
% 179.72/179.59 [7685]~P101(f323(x76851,x76853))+~P101(f323(f59(x76852),x76853))+P101(f323(f323(f325(x76852),f814(x76851,x76853,x76852)),f813(x76851,x76853,x76852)))+P101(f323(x76851,f188(f867(x76852,a855))))
% 179.72/179.59 [7696]P142(x76961,x76962,x76963)+~P101(f323(x76961,x76962))+~P101(f323(x76961,f802(x76963,x76962,x76961)))+P101(f323(f323(f238(a1),f803(x76963,x76962,x76961)),x76963))
% 179.72/179.59 [7702]P143(x77021,x77022,x77023)+~P101(f323(x77021,f801(x77023,x77022,x77021)))+~P101(f323(x77021,f2(a1)))+P101(f323(f323(f238(a1),f791(x77023,x77022,x77021)),x77023))
% 179.72/179.59 [7803]~P120(x78031)+~P101(f323(f323(f237(x78031),f323(f323(f79(x78031),x78033),x78032)),f2(x78031)))+P101(f323(f323(f237(x78031),x78032),f2(x78031)))+P101(f323(f323(f237(x78031),f2(x78031)),x78032))
% 179.72/179.59 [7804]~P120(x78041)+~P101(f323(f323(f237(x78041),f323(f323(f79(x78041),x78042),x78043)),f2(x78041)))+P101(f323(f323(f237(x78041),x78042),f2(x78041)))+P101(f323(f323(f237(x78041),f2(x78041)),x78042))
% 179.72/179.59 [7805]~P64(x78051)+~P101(f323(f323(f237(x78051),f323(f323(f281(x78051),x78053),x78052)),f2(x78051)))+P101(f323(f323(f237(x78051),x78052),f2(x78051)))+P101(f323(f323(f237(x78051),f2(x78051)),x78052))
% 179.72/179.59 [7806]~P64(x78061)+~P101(f323(f323(f237(x78061),f323(f323(f281(x78061),x78062),x78063)),f2(x78061)))+P101(f323(f323(f237(x78061),x78062),f2(x78061)))+P101(f323(f323(f237(x78061),f2(x78061)),x78062))
% 179.72/179.59 [7807]~P64(x78071)+~P101(f323(f323(f238(x78071),f323(f323(f281(x78071),x78073),x78072)),f2(x78071)))+P101(f323(f323(f238(x78071),x78072),f2(x78071)))+P101(f323(f323(f238(x78071),f2(x78071)),x78072))
% 179.72/179.59 [7808]~P64(x78081)+~P101(f323(f323(f238(x78081),f323(f323(f281(x78081),x78082),x78083)),f2(x78081)))+P101(f323(f323(f238(x78081),x78082),f2(x78081)))+P101(f323(f323(f238(x78081),f2(x78081)),x78082))
% 179.72/179.59 [7833]~P120(x78331)+~P101(f323(f323(f237(x78331),f323(f323(f79(x78331),x78332),x78333)),f2(x78331)))+P101(f323(f323(f237(x78331),f2(x78331)),x78332))+P101(f323(f323(f237(x78331),f2(x78331)),x78333))
% 179.72/179.59 [7834]~P64(x78341)+~P101(f323(f323(f237(x78341),f323(f323(f281(x78341),x78342),x78343)),f2(x78341)))+P101(f323(f323(f237(x78341),f2(x78341)),x78342))+P101(f323(f323(f237(x78341),f2(x78341)),x78343))
% 179.72/179.59 [7835]~P64(x78351)+~P101(f323(f323(f238(x78351),f323(f323(f281(x78351),x78352),x78353)),f2(x78351)))+P101(f323(f323(f238(x78351),f2(x78351)),x78352))+P101(f323(f323(f238(x78351),f2(x78351)),x78353))
% 179.72/179.59 [7857]P143(x78572,x78573,x78571)+E(x78571,f2(a1))+P101(f323(f323(f237(a1),f790(x78571,x78573,x78572)),f2(a1)))+P101(f323(f323(f238(a1),f791(x78571,x78573,x78572)),x78571))
% 179.72/179.59 [7858]P142(x78582,x78583,x78581)+E(x78581,f2(a1))+P101(f323(f323(f237(a1),f802(x78581,x78583,x78582)),f2(a1)))+P101(f323(f323(f238(a1),f803(x78581,x78583,x78582)),x78581))
% 179.72/179.59 [7866]~P119(x78661)+~P101(f323(f323(f238(x78661),x78662),f76(x78661)))+P101(f323(f323(f238(x78661),f323(f323(f248(x78661),x78662),f323(a112,x78663))),f76(x78661)))+~P101(f323(f323(f238(x78661),f2(x78661)),x78662))
% 179.72/179.59 [7922]~P103(x79221)+~E(x79223,f113(x79221))+~P16(x79221,f323(f162(x79221),x79223))+E(f323(f135(x79221,x79221,f323(f7(x79221,x79221,x79221),f236(x79221)),x79222),f323(f162(x79221),x79223)),x79222)
% 179.72/179.59 [7924]P142(x79241,x79242,x79243)+~P101(f323(x79241,x79242))+P101(f323(f323(f237(a1),f802(x79243,x79242,x79241)),f2(a1)))+P101(f323(f323(f238(a1),f803(x79243,x79242,x79241)),x79243))
% 179.72/179.59 [7931]P143(x79311,x79312,x79313)+~P101(f323(x79311,f2(a1)))+P101(f323(f323(f237(a1),f790(x79313,x79312,x79311)),f2(a1)))+P101(f323(f323(f238(a1),f791(x79313,x79312,x79311)),x79313))
% 179.72/179.59 [8147]P143(x81473,x81472,x81471)+E(x81471,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x81471),f801(x81471,x81472,x81473))),f790(x81471,x81472,x81473)),x81472)+P101(f323(f323(f238(a1),f791(x81471,x81472,x81473)),x81471))
% 179.72/179.59 [8148]P142(x81483,x81482,x81481)+E(x81481,f2(a1))+E(f323(f323(f78(a1),f323(f323(f79(a1),x81481),f805(x81481,x81482,x81483))),f802(x81481,x81482,x81483)),x81482)+P101(f323(f323(f238(a1),f803(x81481,x81482,x81483)),x81481))
% 179.72/179.59 [8185]P142(x81853,x81852,x81851)+~P101(f323(x81853,x81852))+E(f323(f323(f78(a1),f323(f323(f79(a1),x81851),f805(x81851,x81852,x81853))),f802(x81851,x81852,x81853)),x81852)+P101(f323(f323(f238(a1),f803(x81851,x81852,x81853)),x81851))
% 179.72/179.59 [8186]~P68(x81861)+~P72(x81861)+~P39(x81863)+E(f323(f323(f6(a860,x81861),f323(f323(f8(a1,x81861,a860),x81862),f100(a1))),f323(f302(a1,a860,a104),x81863)),f323(f323(f6(a1,x81861),x81862),x81863))
% 179.72/179.59 [8187]~P68(x81871)+~P72(x81871)+~P39(x81873)+E(f323(f323(f9(a860,x81871),f323(f323(f8(a1,x81871,a860),x81872),f100(a1))),f323(f302(a1,a860,a104),x81873)),f323(f323(f9(a1,x81871),x81872),x81873))
% 179.72/179.59 [8196]P143(x81963,x81962,x81961)+E(f323(f323(f78(a1),f323(f323(f79(a1),x81961),f801(x81961,x81962,x81963))),f790(x81961,x81962,x81963)),x81962)+~P101(f323(x81963,f2(a1)))+P101(f323(f323(f238(a1),f791(x81961,x81962,x81963)),x81961))
% 179.72/179.59 [8217]~E(x82172,f2(a860))+~E(f323(f257(a860,a860),x82173),f2(a860))+~E(x82171,f323(f323(f78(a860),f323(f323(f79(a860),f323(f257(a860,a860),x82173)),x82172)),f323(f261(a860,a860),x82173)))+P101(f323(f45(x82171,x82172),x82173))
% 179.72/179.59 [8272]P101(f323(x82721,x82722))+~P101(f323(f323(f325(x82723),f795(x82721,x82722,x82723)),f793(x82721,x82722,x82723)))+~P101(f323(f59(x82723),x82722))+~P101(f323(x82721,f188(f867(x82723,a855))))
% 179.72/179.59 [8898]P101(f323(x88981,x88982))+~P101(f323(f59(x88983),x88982))+~P101(f323(x88981,f323(f323(f301(x88983),f795(x88981,x88982,x88983)),f793(x88981,x88982,x88983))))+~P101(f323(x88981,f188(f867(x88983,a855))))
% 179.72/179.59 [9128]P101(f323(f323(f237(a1),x91281),f2(a1)))+~P101(f323(f323(f238(a1),f323(f323(f78(a1),f323(f323(f79(a1),x91283),x91281)),x91282)),f2(a1)))+~P101(f323(f323(f237(a1),f2(a1)),x91282))+~P101(f323(f323(f238(a1),f2(a1)),x91283))
% 179.72/179.59 [5772]~P2(x57722)+E(x57721,f188(f867(x57722,a855)))+~P101(f323(f59(x57722),x57721))+E(f11(x57722,f323(f323(f301(x57722),x57723),x57721)),f323(f323(f101(x57722),x57723),f11(x57722,x57721)))
% 179.72/179.59 [5773]~P2(x57732)+E(x57731,f188(f867(x57732,a855)))+~P101(f323(f59(x57732),x57731))+E(f10(x57732,f323(f323(f301(x57732),x57733),x57731)),f323(f323(f110(x57732),x57733),f10(x57732,x57731)))
% 179.72/179.59 [5774]~P103(x57742)+E(x57741,f188(f867(x57742,a855)))+~P101(f323(f59(x57742),x57741))+E(f14(x57742,f323(f323(f301(x57742),x57743),x57741)),f323(f323(f236(x57742),x57743),f14(x57742,x57741)))
% 179.72/179.59 [5775]~P103(x57752)+E(x57751,f188(f867(x57752,a855)))+~P101(f323(f59(x57752),x57751))+E(f15(x57752,f323(f323(f301(x57752),x57753),x57751)),f323(f323(f235(x57752),x57753),f15(x57752,x57751)))
% 179.72/179.59 [6076]~P120(x60761)+~E(x60763,f2(x60761))+~E(x60762,f2(x60761))+E(f323(f323(f78(x60761),f323(f323(f79(x60761),x60762),x60762)),f323(f323(f79(x60761),x60763),x60763)),f2(x60761))
% 179.72/179.59 [6141]~P93(x61412)+E(x61411,f188(f867(x61412,a855)))+~P101(f323(f59(x61412),x61411))+E(f323(f61(x61412,f79(x61412)),f323(f323(f301(x61412),x61413),x61411)),f323(f323(f79(x61412),x61413),f323(f61(x61412,f79(x61412)),x61411)))
% 179.72/179.59 [6264]~P103(x62642)+E(x62641,f188(f867(x62642,a855)))+~P101(f323(f59(x62642),x62641))+E(f12(x62642,f235(x62642),f323(f323(f301(x62642),x62643),x62641)),f323(f323(f235(x62642),x62643),f12(x62642,f235(x62642),x62641)))
% 179.72/179.59 [6265]~P103(x62652)+E(x62651,f188(f867(x62652,a855)))+~P101(f323(f59(x62652),x62651))+E(f13(x62652,f236(x62652),f323(f323(f301(x62652),x62653),x62651)),f323(f323(f236(x62652),x62653),f13(x62652,f236(x62652),x62651)))
% 179.72/179.59 [6764]~P66(x67641)+~P101(f323(f59(x67641),x67643))+E(f323(f61(x67641,f79(x67641)),f323(f323(f301(x67641),x67642),x67643)),f323(f323(f62(x67641,x67641,f79(x67641)),x67642),x67643))+P101(f323(f323(f325(x67641),x67642),x67643))
% 179.72/179.59 [6844]~E(f323(f323(f78(a1),x68442),f323(f323(f79(a1),x68443),x68441)),x68443)+~P101(f323(f323(f238(a1),f2(a1)),x68443))+P101(f323(f323(f237(a1),f76(a1)),x68441))+~P101(f323(f323(f238(a1),x68442),x68443))
% 179.72/179.59 [6871]~E(f323(f323(f78(a1),x68712),f323(f323(f79(a1),x68713),x68711)),x68713)+P101(f323(f323(f237(a1),x68711),f76(a1)))+~P101(f323(f323(f237(a1),f2(a1)),x68712))+~P101(f323(f323(f238(a1),f2(a1)),x68713))
% 179.72/179.59 [6887]E(x68871,f2(a860))+~P101(f323(f45(x68873,x68871),x68872))+~P101(f323(f323(f238(a860),f2(a860)),x68871))+P101(f323(f323(f238(a860),f323(f261(a860,a860),x68872)),x68871))
% 179.72/179.59 [6917]~P132(x69171)+~P101(f323(f323(f237(x69171),x69172),f2(x69171)))+~P101(f323(f323(f237(x69171),x69173),f2(x69171)))+E(f323(f323(f79(x69171),f323(f73(x69171),x69172)),f323(f73(x69171),x69173)),f323(f73(x69171),f323(f323(f79(x69171),x69172),x69173)))
% 179.72/179.59 [6967]~P132(x69671)+~P101(f323(f323(f237(x69671),x69672),f2(x69671)))+E(f323(f323(f79(x69671),f323(f73(x69671),x69672)),f323(f73(x69671),x69673)),f323(f73(x69671),f323(f323(f79(x69671),x69672),x69673)))+~P101(f323(f323(f237(x69671),f2(x69671)),x69673))
% 179.72/179.59 [6968]~P132(x69681)+~P101(f323(f323(f237(x69681),x69683),f2(x69681)))+E(f323(f323(f79(x69681),f323(f73(x69681),x69682)),f323(f73(x69681),x69683)),f323(f73(x69681),f323(f323(f79(x69681),x69682),x69683)))+~P101(f323(f323(f237(x69681),f2(x69681)),x69682))
% 179.72/179.59 [7022]~P132(x70221)+E(f323(f323(f79(x70221),f323(f73(x70221),x70222)),f323(f73(x70221),x70223)),f323(f73(x70221),f323(f323(f79(x70221),x70222),x70223)))+~P101(f323(f323(f237(x70221),f2(x70221)),x70222))+~P101(f323(f323(f237(x70221),f2(x70221)),x70223))
% 179.72/179.59 [7039]~P122(x70391)+~P101(f323(f323(f237(x70391),x70393),f2(x70391)))+~P101(f323(f323(f237(x70391),x70392),f2(x70391)))+P101(f323(f323(f237(x70391),f2(x70391)),f323(f323(f79(x70391),x70392),x70393)))
% 179.72/179.59 [7040]~P120(x70401)+~P101(f323(f323(f237(x70401),x70403),f2(x70401)))+~P101(f323(f323(f237(x70401),x70402),f2(x70401)))+P101(f323(f323(f237(x70401),f2(x70401)),f323(f323(f79(x70401),x70402),x70403)))
% 179.72/179.59 [7041]~P65(x70411)+~P101(f323(f323(f238(x70411),x70413),f2(x70411)))+~P101(f323(f323(f237(x70411),x70412),f2(x70411)))+P101(f323(f323(f237(x70411),f2(x70411)),f323(f323(f281(x70411),x70412),x70413)))
% 179.72/179.59 [7042]~P64(x70421)+~P101(f323(f323(f237(x70421),x70423),f2(x70421)))+~P101(f323(f323(f237(x70421),x70422),f2(x70421)))+P101(f323(f323(f237(x70421),f2(x70421)),f323(f323(f281(x70421),x70422),x70423)))
% 179.72/179.59 [7043]~P120(x70431)+~P101(f323(f323(f238(x70431),x70433),f2(x70431)))+~P101(f323(f323(f238(x70431),x70432),f2(x70431)))+P101(f323(f323(f238(x70431),f2(x70431)),f323(f323(f79(x70431),x70432),x70433)))
% 179.72/179.59 [7044]~P65(x70441)+~P101(f323(f323(f238(x70441),x70443),f2(x70441)))+~P101(f323(f323(f238(x70441),x70442),f2(x70441)))+P101(f323(f323(f238(x70441),f2(x70441)),f323(f323(f281(x70441),x70442),x70443)))
% 179.72/179.59 [7045]~P64(x70451)+~P101(f323(f323(f238(x70451),x70453),f2(x70451)))+~P101(f323(f323(f238(x70451),x70452),f2(x70451)))+P101(f323(f323(f238(x70451),f2(x70451)),f323(f323(f281(x70451),x70452),x70453)))
% 179.72/179.59 [7046]~P119(x70461)+~P101(f323(f323(f238(a860),f2(a860)),x70463))+~P101(f323(f323(f238(x70461),f76(x70461)),x70462))+P101(f323(f323(f238(x70461),f76(x70461)),f323(f323(f248(x70461),x70462),x70463)))
% 179.72/179.59 [7142]~P122(x71421)+~P101(f323(f323(f237(x71421),f2(x71421)),x71423))+~P101(f323(f323(f237(x71421),f2(x71421)),x71422))+P101(f323(f323(f237(x71421),f2(x71421)),f323(f323(f79(x71421),x71422),x71423)))
% 179.72/179.59 [7143]~P120(x71431)+~P101(f323(f323(f237(x71431),f2(x71431)),x71433))+~P101(f323(f323(f237(x71431),f2(x71431)),x71432))+P101(f323(f323(f237(x71431),f2(x71431)),f323(f323(f79(x71431),x71432),x71433)))
% 179.72/179.59 [7144]~P129(x71441)+~P101(f323(f323(f237(x71441),f2(x71441)),x71443))+~P101(f323(f323(f237(x71441),f2(x71441)),x71442))+P101(f323(f323(f237(x71441),f2(x71441)),f323(f323(f79(x71441),x71442),x71443)))
% 179.72/179.59 [7146]~P65(x71461)+~P101(f323(f323(f238(x71461),f2(x71461)),x71463))+~P101(f323(f323(f237(x71461),f2(x71461)),x71462))+P101(f323(f323(f237(x71461),f2(x71461)),f323(f323(f281(x71461),x71462),x71463)))
% 179.72/179.59 [7147]~P64(x71471)+~P101(f323(f323(f237(x71471),f2(x71471)),x71473))+~P101(f323(f323(f237(x71471),f2(x71471)),x71472))+P101(f323(f323(f237(x71471),f2(x71471)),f323(f323(f281(x71471),x71472),x71473)))
% 179.72/179.59 [7148]~P119(x71481)+~P101(f323(f323(f238(x71481),f76(x71481)),x71483))+~P101(f323(f323(f238(x71481),f76(x71481)),x71482))+P101(f323(f323(f238(x71481),f76(x71481)),f323(f323(f79(x71481),x71482),x71483)))
% 179.72/179.59 [7149]~P125(x71491)+~P101(f323(f323(f238(x71491),f2(x71491)),x71493))+~P101(f323(f323(f238(x71491),f2(x71491)),x71492))+P101(f323(f323(f238(x71491),f2(x71491)),f323(f323(f79(x71491),x71492),x71493)))
% 179.72/179.59 [7152]~P84(x71521)+~P101(f323(f323(f238(x71521),f2(x71521)),x71523))+~P101(f323(f323(f238(x71521),f2(x71521)),x71522))+P101(f323(f323(f238(x71521),f2(x71521)),f323(f323(f78(x71521),x71522),x71523)))
% 179.72/179.59 [7153]~P65(x71531)+~P101(f323(f323(f238(x71531),f2(x71531)),x71533))+~P101(f323(f323(f238(x71531),f2(x71531)),x71532))+P101(f323(f323(f238(x71531),f2(x71531)),f323(f323(f281(x71531),x71532),x71533)))
% 179.72/179.59 [7154]~P64(x71541)+~P101(f323(f323(f238(x71541),f2(x71541)),x71543))+~P101(f323(f323(f238(x71541),f2(x71541)),x71542))+P101(f323(f323(f238(x71541),f2(x71541)),f323(f323(f281(x71541),x71542),x71543)))
% 179.72/179.59 [7225]~P2(x72251)+~P101(f323(f59(x72251),x72253))+E(f11(x72251,f323(f323(f301(x72251),x72252),x72253)),x72252)+~E(f323(f323(f22(f867(x72251,a855)),x72253),f323(f323(f301(x72251),x72252),f188(f867(x72251,a855)))),f188(f867(x72251,a855)))
% 179.72/179.59 [7226]~P2(x72261)+~P101(f323(f59(x72261),x72263))+E(f10(x72261,f323(f323(f301(x72261),x72262),x72263)),x72262)+~E(f323(f323(f22(f867(x72261,a855)),x72263),f323(f323(f301(x72261),x72262),f188(f867(x72261,a855)))),f188(f867(x72261,a855)))
% 179.72/179.59 [7227]~P103(x72271)+~P101(f323(f59(x72271),x72273))+E(f14(x72271,f323(f323(f301(x72271),x72272),x72273)),x72272)+~E(f323(f323(f22(f867(x72271,a855)),x72273),f323(f323(f301(x72271),x72272),f188(f867(x72271,a855)))),f188(f867(x72271,a855)))
% 179.72/179.59 [7228]~P103(x72281)+~P101(f323(f59(x72281),x72283))+E(f15(x72281,f323(f323(f301(x72281),x72282),x72283)),x72282)+~E(f323(f323(f22(f867(x72281,a855)),x72283),f323(f323(f301(x72281),x72282),f188(f867(x72281,a855)))),f188(f867(x72281,a855)))
% 179.72/179.59 [7229]~P120(x72291)+P101(f323(f323(f237(x72291),x72292),f2(x72291)))+P101(f323(f323(f237(x72291),f2(x72291)),x72293))+~P101(f323(f323(f237(x72291),f2(x72291)),f323(f323(f79(x72291),x72293),x72292)))
% 179.72/179.59 [7230]~P120(x72301)+P101(f323(f323(f237(x72301),x72302),f2(x72301)))+P101(f323(f323(f237(x72301),f2(x72301)),x72303))+~P101(f323(f323(f237(x72301),f2(x72301)),f323(f323(f79(x72301),x72302),x72303)))
% 179.72/179.59 [7231]~P64(x72311)+P101(f323(f323(f237(x72311),x72312),f2(x72311)))+P101(f323(f323(f237(x72311),f2(x72311)),x72313))+~P101(f323(f323(f237(x72311),f2(x72311)),f323(f323(f281(x72311),x72313),x72312)))
% 179.72/179.59 [7232]~P64(x72321)+P101(f323(f323(f237(x72321),x72322),f2(x72321)))+P101(f323(f323(f237(x72321),f2(x72321)),x72323))+~P101(f323(f323(f237(x72321),f2(x72321)),f323(f323(f281(x72321),x72322),x72323)))
% 179.72/179.59 [7233]~P120(x72331)+P101(f323(f323(f237(x72331),x72332),f2(x72331)))+P101(f323(f323(f237(x72331),f2(x72331)),x72332))+~P101(f323(f323(f237(x72331),f2(x72331)),f323(f323(f79(x72331),x72333),x72332)))
% 179.72/179.59 [7234]~P120(x72341)+P101(f323(f323(f237(x72341),x72342),f2(x72341)))+P101(f323(f323(f237(x72341),f2(x72341)),x72342))+~P101(f323(f323(f237(x72341),f2(x72341)),f323(f323(f79(x72341),x72342),x72343)))
% 179.72/179.59 [7235]~P64(x72351)+P101(f323(f323(f237(x72351),x72352),f2(x72351)))+P101(f323(f323(f237(x72351),f2(x72351)),x72352))+~P101(f323(f323(f237(x72351),f2(x72351)),f323(f323(f281(x72351),x72353),x72352)))
% 179.72/179.59 [7236]~P64(x72361)+P101(f323(f323(f237(x72361),x72362),f2(x72361)))+P101(f323(f323(f237(x72361),f2(x72361)),x72362))+~P101(f323(f323(f237(x72361),f2(x72361)),f323(f323(f281(x72361),x72362),x72363)))
% 179.72/179.59 [7237]~P64(x72371)+P101(f323(f323(f238(x72371),x72372),f2(x72371)))+P101(f323(f323(f238(x72371),f2(x72371)),x72373))+~P101(f323(f323(f238(x72371),f2(x72371)),f323(f323(f281(x72371),x72373),x72372)))
% 179.72/179.59 [7238]~P64(x72381)+P101(f323(f323(f238(x72381),x72382),f2(x72381)))+P101(f323(f323(f238(x72381),f2(x72381)),x72383))+~P101(f323(f323(f238(x72381),f2(x72381)),f323(f323(f281(x72381),x72382),x72383)))
% 179.72/179.59 [7239]~P64(x72391)+P101(f323(f323(f238(x72391),x72392),f2(x72391)))+P101(f323(f323(f238(x72391),f2(x72391)),x72392))+~P101(f323(f323(f238(x72391),f2(x72391)),f323(f323(f281(x72391),x72393),x72392)))
% 179.72/179.59 [7240]~P64(x72401)+P101(f323(f323(f238(x72401),x72402),f2(x72401)))+P101(f323(f323(f238(x72401),f2(x72401)),x72402))+~P101(f323(f323(f238(x72401),f2(x72401)),f323(f323(f281(x72401),x72402),x72403)))
% 179.72/179.59 [7327]~E(f323(f323(f101(f867(x73271,a855)),f323(f166(x73271),x73272)),f323(f166(x73271),x73273)),f188(f867(x73271,a855)))+~P101(f323(f130(x73271),x73273))+~P101(f323(f130(x73271),x73272))+P101(f323(f130(x73271),f323(f323(f121(x73271),x73272),x73273)))
% 179.72/179.59 [7328]~P103(x73281)+~P101(f323(f59(x73281),x73283))+E(f12(x73281,f235(x73281),f323(f323(f301(x73281),x73282),x73283)),x73282)+~E(f323(f323(f22(f867(x73281,a855)),x73283),f323(f323(f301(x73281),x73282),f188(f867(x73281,a855)))),f188(f867(x73281,a855)))
% 179.72/179.59 [7329]~P103(x73291)+~P101(f323(f59(x73291),x73293))+E(f13(x73291,f236(x73291),f323(f323(f301(x73291),x73292),x73293)),x73292)+~E(f323(f323(f22(f867(x73291,a855)),x73293),f323(f323(f301(x73291),x73292),f188(f867(x73291,a855)))),f188(f867(x73291,a855)))
% 179.72/179.59 [7345]~P82(x73451)+~P101(f323(f323(f237(x73451),x73452),x73453))+~P101(f323(f323(f237(x73451),f323(f77(x73451),x73452)),x73453))+P101(f323(f323(f237(x73451),f323(f73(x73451),x73452)),x73453))
% 179.72/179.59 [7346]~P116(x73461)+~P101(f323(f323(f238(x73461),x73462),x73463))+~P101(f323(f323(f238(x73461),f323(f77(x73461),x73462)),x73463))+P101(f323(f323(f238(x73461),f323(f73(x73461),x73462)),x73463))
% 179.72/179.59 [7416]~P125(x74161)+P101(f323(f323(f238(x74161),f2(x74161)),x74162))+~P101(f323(f323(f238(x74161),f2(x74161)),x74163))+~P101(f323(f323(f238(x74161),f2(x74161)),f323(f323(f79(x74161),x74163),x74162)))
% 179.72/179.59 [7417]~P125(x74171)+P101(f323(f323(f238(x74171),f2(x74171)),x74172))+~P101(f323(f323(f238(x74171),f2(x74171)),x74173))+~P101(f323(f323(f238(x74171),f2(x74171)),f323(f323(f79(x74171),x74172),x74173)))
% 179.72/179.59 [7718]E(x77181,x77182)+~P101(f323(f59(x77183),x77181))+~P101(f323(f323(f237(a860),f323(f35(x77183),x77181)),f323(f35(x77183),x77182)))+~P101(f323(f323(f237(f867(x77183,a855)),x77182),x77181))
% 179.72/179.59 [7862]~P101(f323(f323(f238(a1),x78621),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x78622))+~P101(f323(f323(f237(a1),x78622),x78623))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x78621),x78622)),f323(f323(f36(a1),x78621),x78623)))
% 179.72/179.59 [7874]~P101(f323(f323(f237(a1),f2(a1)),x78741))+~P101(f323(f323(f238(a1),f2(a1)),x78743))+~P101(f323(f323(f237(a1),x78743),x78742))+P101(f323(f323(f237(a1),f323(f323(f36(a1),x78741),x78742)),f323(f323(f36(a1),x78741),x78743)))
% 179.72/179.59 [8009]E(f323(x80091,f431(x80092,x80091,x80093)),x80092)+~P101(f323(f323(f237(a1),x80092),f323(x80091,x80093)))+P101(f323(f323(f238(a860),f432(x80092,x80091,x80093)),x80093))+~P101(f323(f323(f237(a1),f323(x80091,f2(a860))),x80092))
% 179.72/179.59 [8010]E(f323(x80101,f437(x80102,x80101,x80103)),x80102)+~P101(f323(f323(f237(a1),x80102),f323(x80101,x80103)))+P101(f323(f323(f238(a860),f438(x80102,x80101,x80103)),x80103))+~P101(f323(f323(f237(a1),f323(x80101,f2(a860))),x80102))
% 179.72/179.59 [8108]~P101(f323(f59(x81081),x81083))+~P101(f323(f323(f238(a860),f323(f35(x81081),x81082)),f323(f35(x81081),x81083)))+~P101(f323(f323(f237(f867(x81081,a855)),x81082),x81083))+P101(f323(f323(f238(f867(x81081,a855)),x81082),x81083))
% 179.72/179.59 [8137]E(f323(f323(f78(a1),f397(x81373,x81371,x81372)),f398(x81373,x81371,x81372)),x81371)+E(f323(f323(f22(a1),x81371),x81372),x81371)+~P101(f323(f323(f238(a1),f2(a1)),x81372))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x81371),f76(a1))),x81373))
% 179.72/179.59 [8138]E(f323(f323(f22(a1),f399(x81383,x81381,x81382)),f400(x81383,x81381,x81382)),x81381)+E(f323(f323(f78(a1),x81381),x81382),x81381)+~P101(f323(f323(f238(a1),f2(a1)),x81382))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x81381),f76(a1))),x81383))
% 179.72/179.59 [8191]~P101(f323(f323(f237(a860),x81913),x81911))+P101(f323(f323(f237(a860),x81911),x81912))+~P101(f323(f323(f237(a860),x81913),x81912))+~P101(f323(f323(f237(a860),f323(f323(f22(a860),x81911),x81913)),f323(f323(f22(a860),x81912),x81913)))
% 179.72/179.59 [8192]~P101(f323(f323(f237(a860),x81923),x81921))+P101(f323(f323(f238(a860),x81921),x81922))+~P101(f323(f323(f237(a860),x81923),x81922))+~P101(f323(f323(f238(a860),f323(f323(f22(a860),x81921),x81923)),f323(f323(f22(a860),x81922),x81923)))
% 179.72/179.59 [8208]~P103(x82082)+E(x82081,f113(x82082))+~P16(x82082,f323(f162(x82082),x82081))+E(f323(f135(x82082,x82082,f323(f7(x82082,x82082,x82082),f236(x82082)),x82083),f323(f162(x82082),x82081)),f323(f323(f236(x82082),f323(f323(f158(x82082),x82081),f2(a860))),x82083))
% 179.72/179.59 [8277]E(f323(f323(f22(a1),x82771),x82772),x82771)+~P101(f323(f323(f238(a1),f2(a1)),x82772))+P101(f323(f323(f325(a1),f397(x82773,x82771,x82772)),x82773))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x82771),f76(a1))),x82773))
% 179.72/179.59 [8278]E(f323(f323(f78(a1),x82781),x82782),x82781)+~P101(f323(f323(f238(a1),f2(a1)),x82782))+P101(f323(f323(f325(a1),f399(x82783,x82781,x82782)),x82783))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x82781),f76(a1))),x82783))
% 179.72/179.59 [8354]~P101(f323(f323(f237(a1),x83541),f323(x83542,x83543)))+P101(f323(f323(f238(a860),f432(x83541,x83542,x83543)),x83543))+P101(f323(f323(f237(a860),f431(x83541,x83542,x83543)),x83543))+~P101(f323(f323(f237(a1),f323(x83542,f2(a860))),x83541))
% 179.72/179.59 [8355]~P101(f323(f323(f237(a1),x83551),f323(x83552,x83553)))+P101(f323(f323(f238(a860),f438(x83551,x83552,x83553)),x83553))+P101(f323(f323(f237(a860),f437(x83551,x83552,x83553)),x83553))+~P101(f323(f323(f237(a1),f323(x83552,f2(a860))),x83551))
% 179.72/179.59 [8425]E(f323(f323(f22(a1),x84251),x84252),x84251)+~P101(f323(f323(f238(a1),f2(a1)),x84252))+P101(f323(f323(f325(a1),f398(x84253,x84251,x84252)),f294(a1,f76(a1),x84252)))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x84251),f76(a1))),x84253))
% 179.72/179.59 [8426]E(f323(f323(f78(a1),x84261),x84262),x84261)+~P101(f323(f323(f238(a1),f2(a1)),x84262))+P101(f323(f323(f325(a1),f400(x84263,x84261,x84262)),f294(a1,f76(a1),x84262)))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x84261),f76(a1))),x84263))
% 179.72/179.59 [8557]~P119(x85571)+~P101(f323(f323(f238(x85571),x85572),f76(x85571)))+~P101(f323(f323(f238(x85571),f2(x85571)),x85572))+P101(f323(f323(f238(x85571),f323(f323(f79(x85571),x85572),f323(f323(f248(x85571),x85572),x85573))),f323(f323(f248(x85571),x85572),x85573)))
% 179.72/179.59 [8651]~P101(f323(x86511,x86512))+P101(f323(x86511,f2(a860)))+~P101(f323(f323(f238(a860),x86512),x86513))+~P101(f323(x86511,f42(a860,f323(a112,f489(x86512,x86511,x86513)),x86513)))
% 179.72/179.59 [8799]E(f523(x87991,x87992,x87993),f2(a860))+P101(f323(f323(x87991,x87993),x87992))+P101(f323(f323(x87991,f523(x87991,x87992,x87993)),f42(a860,f522(x87991,x87992,x87993),f523(x87991,x87992,x87993))))+~P101(f323(f311(f866(a860,a860),a221),f323(f323(f258(a860,a860),x87993),x87992)))
% 179.72/179.59 [8836]~P27(x88361,x88361,x88362,x88363)+E(f323(f302(x88361,x88361,x88362),x88363),x88363)+~P101(f323(f59(x88361),x88363))+~P101(f323(f323(f237(f867(x88361,a855)),f323(f302(x88361,x88361,x88362),x88363)),x88363))
% 179.72/179.59 [9072]P101(f323(f323(x90721,x90722),x90723))+~P101(f323(f323(f238(a1),f521(x90721,x90723,x90722)),f2(a1)))+P101(f323(f323(x90721,f323(f77(a1),f520(x90721,x90723,x90722))),f323(f77(a1),f521(x90721,x90723,x90722))))+~P101(f323(f311(f866(a1,a1),a226),f323(f323(f258(a1,a1),x90722),x90723)))
% 179.72/179.59 [9254]P101(f323(f323(x92541,x92542),x92543))+P101(f323(f323(x92541,f323(f323(f78(a1),f563(x92541,x92543,x92542)),f76(a1))),f567(x92541,x92543,x92542)))+~P101(f323(f323(f237(a1),f563(x92541,x92543,x92542)),f567(x92541,x92543,x92542)))+~P101(f323(f311(f866(a1,a1),a176),f323(f323(f258(a1,a1),x92542),x92543)))
% 179.72/179.59 [9683]~P5(x96832)+~P5(x96831)+~P101(f323(f56(f866(x96831,x96832)),x96833))+P101(f323(f56(x96831),f323(f323(f8(f867(x96832,a855),a855,x96831),f56(x96832)),f323(f323(f8(f867(x96832,f866(x96831,x96832)),f867(x96832,a855),x96831),f323(f8(f866(x96831,x96832),a855,x96832),x96833)),f258(x96831,x96832)))))
% 179.72/179.59 [9684]~P5(x96842)+~P5(x96841)+~P101(f323(f55(f866(x96841,x96842)),x96843))+P101(f323(f55(x96841),f323(f323(f8(f867(x96842,a855),a855,x96841),f55(x96842)),f323(f323(f8(f867(x96842,f866(x96841,x96842)),f867(x96842,a855),x96841),f323(f8(f866(x96841,x96842),a855,x96842),x96843)),f258(x96841,x96842)))))
% 179.72/179.59 [9787]~P5(x97872)+~P5(x97871)+P101(f323(f56(f866(x97871,x97872)),x97873))+~P101(f323(f56(x97871),f323(f323(f8(f867(x97872,a855),a855,x97871),f56(x97872)),f323(f323(f8(f867(x97872,f866(x97871,x97872)),f867(x97872,a855),x97871),f323(f8(f866(x97871,x97872),a855,x97872),x97873)),f258(x97871,x97872)))))
% 179.72/179.59 [9788]~P5(x97882)+~P5(x97881)+P101(f323(f55(f866(x97881,x97882)),x97883))+~P101(f323(f55(x97881),f323(f323(f8(f867(x97882,a855),a855,x97881),f55(x97882)),f323(f323(f8(f867(x97882,f866(x97881,x97882)),f867(x97882,a855),x97881),f323(f8(f866(x97881,x97882),a855,x97882),x97883)),f258(x97881,x97882)))))
% 179.72/179.59 [9955]E(f323(x99551,f431(x99552,x99551,x99553)),x99552)+~P101(f323(f323(f237(a1),x99552),f323(x99551,x99553)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x99551,f323(f323(f78(a860),f432(x99552,x99551,x99553)),f76(a860)))),f323(x99551,f432(x99552,x99551,x99553))))),f76(a1)))+~P101(f323(f323(f237(a1),f323(x99551,f2(a860))),x99552))
% 179.72/179.59 [9956]E(f323(x99561,f437(x99562,x99561,x99563)),x99562)+~P101(f323(f323(f237(a1),x99562),f323(x99561,x99563)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x99561,f323(f323(f78(a860),f438(x99562,x99561,x99563)),f76(a860)))),f323(x99561,f438(x99562,x99561,x99563))))),f76(a1)))+~P101(f323(f323(f237(a1),f323(x99561,f2(a860))),x99562))
% 179.72/179.59 [9960]~P101(f323(f323(f237(a1),x99601),f323(x99602,x99603)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x99602,f323(f323(f78(a860),f432(x99601,x99602,x99603)),f76(a860)))),f323(x99602,f432(x99601,x99602,x99603))))),f76(a1)))+P101(f323(f323(f237(a860),f431(x99601,x99602,x99603)),x99603))+~P101(f323(f323(f237(a1),f323(x99602,f2(a860))),x99601))
% 179.72/179.59 [9961]~P101(f323(f323(f237(a1),x99611),f323(x99612,x99613)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x99612,f323(f323(f78(a860),f438(x99611,x99612,x99613)),f76(a860)))),f323(x99612,f438(x99611,x99612,x99613))))),f76(a1)))+P101(f323(f323(f237(a860),f437(x99611,x99612,x99613)),x99613))+~P101(f323(f323(f237(a1),f323(x99612,f2(a860))),x99611))
% 179.72/179.59 [10015]E(x100151,x100152)+~E(f323(f135(f861(x100153),f861(x100153),f121(x100153),f113(x100153)),x100151),f323(f135(f861(x100153),f861(x100153),f121(x100153),f113(x100153)),x100152))+~E(f323(f189(f861(f861(x100153))),x100151),f323(f189(f861(f861(x100153))),x100152))+~P101(f323(f323(f262(f861(x100153),f861(x100153),a855),f323(f323(f7(f861(x100153),f867(f861(x100153),a860),f867(f861(x100153),a855)),f323(f323(f8(f867(a860,a855),f867(f867(f861(x100153),a860),f867(f861(x100153),a855)),f861(x100153)),f8(a860,a855,f861(x100153))),f323(f323(f8(a860,f867(a860,a855),f861(x100153)),a320),f189(f861(x100153))))),f189(f861(x100153)))),f595(x100151,x100152,x100153)))
% 179.72/179.59 [10016]E(x100161,x100162)+~E(f323(f135(f861(x100163),f861(x100163),f121(x100163),f113(x100163)),x100161),f323(f135(f861(x100163),f861(x100163),f121(x100163),f113(x100163)),x100162))+~E(f323(f189(f861(f861(x100163))),x100161),f323(f189(f861(f861(x100163))),x100162))+~P101(f323(f323(f262(f861(x100163),f861(x100163),a855),f323(f323(f7(f861(x100163),f867(f861(x100163),a860),f867(f861(x100163),a855)),f323(f323(f8(f867(a860,a855),f867(f867(f861(x100163),a860),f867(f861(x100163),a855)),f861(x100163)),f8(a860,a855,f861(x100163))),f323(f323(f8(a860,f867(a860,a855),f861(x100163)),a320),f189(f861(x100163))))),f189(f861(x100163)))),f596(x100162,x100161,x100163)))
% 179.72/179.59 [6751]~E(f76(a860),f2(a860))+~P101(f323(f59(x67511),x67513))+~P101(f323(f59(x67511),x67512))+E(f323(f323(f78(a860),f323(f35(x67511),x67512)),f323(f35(x67511),x67513)),f323(f35(x67511),f323(f323(f110(f867(x67511,a855)),x67512),x67513)))
% 179.72/179.59 [7161]~P98(x71611)+~P101(f323(f59(x71611),x71612))+~P101(f323(f323(f325(x71611),x71613),x71612))+P101(f323(f323(f237(x71611),f323(f61(x71611,f101(x71611)),x71612)),x71613))
% 179.72/179.59 [7162]~P103(x71621)+~P101(f323(f59(x71621),x71622))+~P101(f323(f323(f325(x71621),x71623),x71622))+P101(f323(f323(f237(x71621),f323(f61(x71621,f235(x71621)),x71622)),x71623))
% 179.72/179.59 [7410]~P101(f323(f59(x74101),x74103))+~P101(f323(f59(x74101),x74102))+~E(f323(f323(f101(f867(x74101,a855)),x74102),x74103),f188(f867(x74101,a855)))+E(f323(f323(f78(a860),f323(f35(x74101),x74102)),f323(f35(x74101),x74103)),f323(f35(x74101),f323(f323(f110(f867(x74101,a855)),x74102),x74103)))
% 179.72/179.59 [8197]~P38(x81971,x81973)+~P38(x81971,x81972)+~E(f323(f323(f101(f867(x81971,a855)),f323(f256(x81971,x81971),x81972)),f323(f254(x81971,x81971),x81973)),f188(f867(x81971,a855)))+P38(x81971,f323(f323(f110(f867(f866(x81971,x81971),a855)),x81972),x81973))
% 179.72/179.59 [8292]E(x82921,f323(f323(f36(a860),x82922),x82923))+~P101(f323(f323(f238(a860),f2(a860)),x82923))+~P101(f323(f323(f238(a860),x82922),f323(f323(f79(a860),x82923),f323(a112,x82921))))+~P101(f323(f323(f237(a860),f323(f323(f79(a860),x82923),x82921)),x82922))
% 179.72/179.59 [8423]~P101(f323(f59(x84231),x84232))+~P101(f323(f59(x84231),x84233))+E(f323(f323(f78(a860),f323(f35(x84231),x84232)),f323(f35(x84231),x84233)),f323(f35(x84231),f323(f323(f110(f867(x84231,a855)),x84232),x84233)))+P101(f323(f323(f325(x84231),f850(x84233,x84232,x84231)),f323(f323(f101(f867(x84231,a855)),x84232),x84233)))
% 179.72/179.59 [8811]~P120(x88112)+~E(x88111,f2(x88112))+~E(x88113,f2(x88112))+~P101(f323(f323(f238(x88112),f2(x88112)),f323(f323(f78(x88112),f323(f323(f79(x88112),x88113),x88113)),f323(f323(f79(x88112),x88111),x88111))))
% 179.72/179.59 [9334]~P38(x93341,x93343)+~P38(x93341,x93342)+P38(x93341,f323(f323(f110(f867(f866(x93341,x93341),a855)),x93342),x93343))+~P101(f323(f323(f237(f867(f866(x93341,x93341),a855)),f323(f323(f280(x93341,x93341,x93341),x93342),x93343)),x93342))
% 179.72/179.59 [9459]~P101(f323(x94591,x94593))+~P101(f323(f59(x94592),x94593))+P101(f323(x94591,f188(f867(x94592,a855))))+~P101(f323(x94591,f323(f323(f22(f867(x94592,a855)),f813(x94591,x94593,x94592)),f323(f323(f301(x94592),f814(x94591,x94593,x94592)),f188(f867(x94592,a855))))))
% 179.72/179.59 [9713]~P5(x97131)+~P5(x97132)+P12(x97131,f323(f323(f8(f867(x97132,x97131),a855,f861(x97131)),x97133),f323(f323(f8(f867(x97132,f864(x97131)),f867(x97132,x97131),f861(x97131)),f71(f864(x97131),x97131,x97132,f234(x97131))),f323(f323(f8(f861(f866(x97132,x97131)),f867(x97132,f864(x97131)),f861(x97131)),f179(x97132,x97131)),f323(f175(x97132,x97131),f53(x97132))))),f323(f189(f861(x97132)),f53(x97132)))+~P101(f323(f55(f867(x97132,x97131)),x97133))
% 179.72/179.59 [9714]~P5(x97141)+~P5(x97142)+P13(x97141,f323(f323(f8(f867(x97142,x97141),a855,f861(x97141)),x97143),f323(f323(f8(f867(x97142,f864(x97141)),f867(x97142,x97141),f861(x97141)),f71(f864(x97141),x97141,x97142,f234(x97141))),f323(f323(f8(f861(f866(x97142,x97141)),f867(x97142,f864(x97141)),f861(x97141)),f179(x97142,x97141)),f323(f175(x97142,x97141),f53(x97142))))),f323(f189(f861(x97142)),f53(x97142)))+~P101(f323(f56(f867(x97142,x97141)),x97143))
% 179.72/179.59 [9809]~P5(x98091)+~P5(x98092)+~P13(x98092,f323(f323(f8(f867(x98091,x98092),a855,f861(x98092)),x98093),f323(f323(f8(f867(x98091,f864(x98092)),f867(x98091,x98092),f861(x98092)),f71(f864(x98092),x98092,x98091,f234(x98092))),f323(f323(f8(f861(f866(x98091,x98092)),f867(x98091,f864(x98092)),f861(x98092)),f179(x98091,x98092)),f323(f175(x98091,x98092),f53(x98091))))),f323(f189(f861(x98091)),f53(x98091)))+P101(f323(f56(f867(x98091,x98092)),x98093))
% 179.72/179.59 [9810]~P5(x98101)+~P5(x98102)+~P12(x98102,f323(f323(f8(f867(x98101,x98102),a855,f861(x98102)),x98103),f323(f323(f8(f867(x98101,f864(x98102)),f867(x98101,x98102),f861(x98102)),f71(f864(x98102),x98102,x98101,f234(x98102))),f323(f323(f8(f861(f866(x98101,x98102)),f867(x98101,f864(x98102)),f861(x98102)),f179(x98101,x98102)),f323(f175(x98101,x98102),f53(x98101))))),f323(f189(f861(x98101)),f53(x98101)))+P101(f323(f55(f867(x98101,x98102)),x98103))
% 179.72/179.59 [8597]~P101(f323(f323(f238(a1),f2(a1)),x85973))+P101(f323(f323(f237(a1),f2(a1)),x85971))+~P101(f323(f323(f238(a1),x85972),x85973))+~P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),f323(f323(f79(a1),x85973),x85971)),x85972)))
% 179.72/179.59 [8622]~P2(x86221)+~P101(f323(f59(x86221),x86222))+E(f323(f323(f22(f867(x86221,a855)),x86222),f323(f323(f301(x86221),x86223),f188(f867(x86221,a855)))),f188(f867(x86221,a855)))+E(f323(f323(f101(x86221),x86223),f11(x86221,f323(f323(f22(f867(x86221,a855)),x86222),f323(f323(f301(x86221),x86223),f188(f867(x86221,a855)))))),f11(x86221,f323(f323(f301(x86221),x86223),x86222)))
% 179.72/179.59 [8623]~P2(x86231)+~P101(f323(f59(x86231),x86232))+E(f323(f323(f22(f867(x86231,a855)),x86232),f323(f323(f301(x86231),x86233),f188(f867(x86231,a855)))),f188(f867(x86231,a855)))+E(f323(f323(f110(x86231),x86233),f10(x86231,f323(f323(f22(f867(x86231,a855)),x86232),f323(f323(f301(x86231),x86233),f188(f867(x86231,a855)))))),f10(x86231,f323(f323(f301(x86231),x86233),x86232)))
% 179.72/179.59 [8624]~P103(x86241)+~P101(f323(f59(x86241),x86242))+E(f323(f323(f22(f867(x86241,a855)),x86242),f323(f323(f301(x86241),x86243),f188(f867(x86241,a855)))),f188(f867(x86241,a855)))+E(f323(f323(f236(x86241),x86243),f14(x86241,f323(f323(f22(f867(x86241,a855)),x86242),f323(f323(f301(x86241),x86243),f188(f867(x86241,a855)))))),f14(x86241,f323(f323(f301(x86241),x86243),x86242)))
% 179.72/179.59 [8625]~P103(x86251)+~P101(f323(f59(x86251),x86252))+E(f323(f323(f22(f867(x86251,a855)),x86252),f323(f323(f301(x86251),x86253),f188(f867(x86251,a855)))),f188(f867(x86251,a855)))+E(f323(f323(f235(x86251),x86253),f15(x86251,f323(f323(f22(f867(x86251,a855)),x86252),f323(f323(f301(x86251),x86253),f188(f867(x86251,a855)))))),f15(x86251,f323(f323(f301(x86251),x86253),x86252)))
% 179.72/179.59 [8697]~P103(x86971)+~P101(f323(f59(x86971),x86972))+E(f323(f323(f22(f867(x86971,a855)),x86972),f323(f323(f301(x86971),x86973),f188(f867(x86971,a855)))),f188(f867(x86971,a855)))+E(f323(f323(f235(x86971),x86973),f12(x86971,f235(x86971),f323(f323(f22(f867(x86971,a855)),x86972),f323(f323(f301(x86971),x86973),f188(f867(x86971,a855)))))),f12(x86971,f235(x86971),f323(f323(f301(x86971),x86973),x86972)))
% 179.72/179.59 [8698]~P103(x86981)+~P101(f323(f59(x86981),x86982))+E(f323(f323(f22(f867(x86981,a855)),x86982),f323(f323(f301(x86981),x86983),f188(f867(x86981,a855)))),f188(f867(x86981,a855)))+E(f323(f323(f236(x86981),x86983),f13(x86981,f236(x86981),f323(f323(f22(f867(x86981,a855)),x86982),f323(f323(f301(x86981),x86983),f188(f867(x86981,a855)))))),f13(x86981,f236(x86981),f323(f323(f301(x86981),x86983),x86982)))
% 179.72/179.59 [9274]E(x92741,x92742)+~E(f323(f135(f861(x92743),f861(x92743),f121(x92743),f113(x92743)),x92741),f323(f135(f861(x92743),f861(x92743),f121(x92743),f113(x92743)),x92742))+~E(f323(f189(f861(f861(x92743))),x92741),f323(f189(f861(f861(x92743))),x92742))+P101(f323(f323(f325(f866(f861(x92743),f861(x92743))),f595(x92741,x92742,x92743)),f323(f166(f866(f861(x92743),f861(x92743))),f323(f323(f175(f861(x92743),f861(x92743)),x92742),x92741))))
% 179.72/179.59 [9275]E(x92751,x92752)+~E(f323(f135(f861(x92753),f861(x92753),f121(x92753),f113(x92753)),x92751),f323(f135(f861(x92753),f861(x92753),f121(x92753),f113(x92753)),x92752))+~E(f323(f189(f861(f861(x92753))),x92751),f323(f189(f861(f861(x92753))),x92752))+P101(f323(f323(f325(f866(f861(x92753),f861(x92753))),f596(x92752,x92751,x92753)),f323(f166(f866(f861(x92753),f861(x92753))),f323(f323(f175(f861(x92753),f861(x92753)),x92751),x92752))))
% 179.72/179.59 [10102]~P96(x101022)+E(x101021,f188(f867(x101022,a855)))+~P101(f323(f59(x101022),x101021))+E(f11(x101022,f323(f243(x101022),f323(f323(f8(f867(x101022,a855),a855,x101022),f85(x101022)),f323(f323(f7(x101022,f867(x101022,a855),f867(x101022,a855)),f323(f323(f8(f867(x101022,f867(a855,a855)),f867(f867(x101022,a855),f867(x101022,a855)),x101022),f18(x101022,a855,a855)),f323(f323(f8(f867(x101022,a855),f867(x101022,f867(a855,a855)),x101022),f323(f8(a855,f867(a855,a855),x101022),a321)),f323(f323(f7(x101022,f867(x101022,x101022),f867(x101022,a855)),f323(f323(f8(f867(x101022,a855),f867(f867(x101022,x101022),f867(x101022,a855)),x101022),f8(x101022,a855,x101022)),a320)),f323(f110(x101022),x101023))))),f323(f323(f7(x101022,f867(x101022,a855),a855),f325(x101022)),x101021))))),f323(f323(f110(x101022),x101023),f11(x101022,x101021)))
% 179.72/179.59 [10103]~P96(x101032)+E(x101031,f188(f867(x101032,a855)))+~P101(f323(f59(x101032),x101031))+E(f10(x101032,f323(f243(x101032),f323(f323(f8(f867(x101032,a855),a855,x101032),f85(x101032)),f323(f323(f7(x101032,f867(x101032,a855),f867(x101032,a855)),f323(f323(f8(f867(x101032,f867(a855,a855)),f867(f867(x101032,a855),f867(x101032,a855)),x101032),f18(x101032,a855,a855)),f323(f323(f8(f867(x101032,a855),f867(x101032,f867(a855,a855)),x101032),f323(f8(a855,f867(a855,a855),x101032),a321)),f323(f323(f7(x101032,f867(x101032,x101032),f867(x101032,a855)),f323(f323(f8(f867(x101032,a855),f867(f867(x101032,x101032),f867(x101032,a855)),x101032),f8(x101032,a855,x101032)),a320)),f323(f101(x101032),x101033))))),f323(f323(f7(x101032,f867(x101032,a855),a855),f325(x101032)),x101031))))),f323(f323(f101(x101032),x101033),f10(x101032,x101031)))
% 179.72/179.59 [10104]~P73(x101042)+E(x101041,f188(f867(x101042,a855)))+~P101(f323(f59(x101042),x101041))+E(f14(x101042,f323(f243(x101042),f323(f323(f8(f867(x101042,a855),a855,x101042),f85(x101042)),f323(f323(f7(x101042,f867(x101042,a855),f867(x101042,a855)),f323(f323(f8(f867(x101042,f867(a855,a855)),f867(f867(x101042,a855),f867(x101042,a855)),x101042),f18(x101042,a855,a855)),f323(f323(f8(f867(x101042,a855),f867(x101042,f867(a855,a855)),x101042),f323(f8(a855,f867(a855,a855),x101042),a321)),f323(f323(f7(x101042,f867(x101042,x101042),f867(x101042,a855)),f323(f323(f8(f867(x101042,a855),f867(f867(x101042,x101042),f867(x101042,a855)),x101042),f8(x101042,a855,x101042)),a320)),f323(f78(x101042),x101043))))),f323(f323(f7(x101042,f867(x101042,a855),a855),f325(x101042)),x101041))))),f323(f323(f78(x101042),x101043),f14(x101042,x101041)))
% 179.72/179.59 [10105]~P73(x101052)+E(x101051,f188(f867(x101052,a855)))+~P101(f323(f59(x101052),x101051))+E(f15(x101052,f323(f243(x101052),f323(f323(f8(f867(x101052,a855),a855,x101052),f85(x101052)),f323(f323(f7(x101052,f867(x101052,a855),f867(x101052,a855)),f323(f323(f8(f867(x101052,f867(a855,a855)),f867(f867(x101052,a855),f867(x101052,a855)),x101052),f18(x101052,a855,a855)),f323(f323(f8(f867(x101052,a855),f867(x101052,f867(a855,a855)),x101052),f323(f8(a855,f867(a855,a855),x101052),a321)),f323(f323(f7(x101052,f867(x101052,x101052),f867(x101052,a855)),f323(f323(f8(f867(x101052,a855),f867(f867(x101052,x101052),f867(x101052,a855)),x101052),f8(x101052,a855,x101052)),a320)),f323(f78(x101052),x101053))))),f323(f323(f7(x101052,f867(x101052,a855),a855),f325(x101052)),x101051))))),f323(f323(f78(x101052),x101053),f15(x101052,x101051)))
% 179.72/179.59 [10106]~P103(x101062)+E(x101061,f188(f867(x101062,a855)))+~P101(f323(f59(x101062),x101061))+E(f13(x101062,f236(x101062),f323(f243(x101062),f323(f323(f8(f867(x101062,a855),a855,x101062),f85(x101062)),f323(f323(f7(x101062,f867(x101062,a855),f867(x101062,a855)),f323(f323(f8(f867(x101062,f867(a855,a855)),f867(f867(x101062,a855),f867(x101062,a855)),x101062),f18(x101062,a855,a855)),f323(f323(f8(f867(x101062,a855),f867(x101062,f867(a855,a855)),x101062),f323(f8(a855,f867(a855,a855),x101062),a321)),f323(f323(f7(x101062,f867(x101062,x101062),f867(x101062,a855)),f323(f323(f8(f867(x101062,a855),f867(f867(x101062,x101062),f867(x101062,a855)),x101062),f8(x101062,a855,x101062)),a320)),f323(f235(x101062),x101063))))),f323(f323(f7(x101062,f867(x101062,a855),a855),f325(x101062)),x101061))))),f323(f323(f235(x101062),x101063),f13(x101062,f236(x101062),x101061)))
% 179.72/179.59 [10107]~P103(x101072)+E(x101071,f188(f867(x101072,a855)))+~P101(f323(f59(x101072),x101071))+E(f12(x101072,f235(x101072),f323(f243(x101072),f323(f323(f8(f867(x101072,a855),a855,x101072),f85(x101072)),f323(f323(f7(x101072,f867(x101072,a855),f867(x101072,a855)),f323(f323(f8(f867(x101072,f867(a855,a855)),f867(f867(x101072,a855),f867(x101072,a855)),x101072),f18(x101072,a855,a855)),f323(f323(f8(f867(x101072,a855),f867(x101072,f867(a855,a855)),x101072),f323(f8(a855,f867(a855,a855),x101072),a321)),f323(f323(f7(x101072,f867(x101072,x101072),f867(x101072,a855)),f323(f323(f8(f867(x101072,a855),f867(f867(x101072,x101072),f867(x101072,a855)),x101072),f8(x101072,a855,x101072)),a320)),f323(f236(x101072),x101073))))),f323(f323(f7(x101072,f867(x101072,a855),a855),f325(x101072)),x101071))))),f323(f323(f236(x101072),x101073),f12(x101072,f235(x101072),x101071)))
% 179.72/179.59 [9859]~P116(x98591)+~E(x98593,f2(x98591))+~E(x98592,f2(x98591))+E(f323(f323(f78(x98591),f323(f323(f248(x98591),x98592),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x98591),x98593),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f2(x98591))
% 179.72/179.59 [9999]~P119(x99991)+~P101(f323(f323(f237(x99991),f2(x99991)),x99993))+P101(f323(f323(f237(x99991),x99992),x99993))+~P101(f323(f323(f237(x99991),f323(f323(f248(x99991),x99992),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x99991),x99993),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))))
% 179.72/179.59 [10045]~P116(x100452)+~E(x100451,f2(x100452))+~E(x100453,f2(x100452))+~P101(f323(f323(f238(x100452),f2(x100452)),f323(f323(f78(x100452),f323(f323(f248(x100452),x100453),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97))))),f323(f323(f248(x100452),x100451),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))))
% 179.72/179.59 [8532]P28(x85321,x85322,f833(x85323,x85322,x85324,x85321),x85324,x85323)+~E(f323(f35(x85321),x85324),f323(f35(x85322),x85323))+~P101(f323(f59(x85322),x85323))+~P101(f323(f59(x85321),x85324))
% 179.72/179.59 [9238]E(x92381,x92382)+~E(f624(x92381,x92382,x92384,x92383),f626(x92381,x92382,x92384,x92383))+P101(f323(f323(f325(f866(f861(x92383),f861(x92383))),f323(f323(f258(f861(x92383),f861(x92383)),x92382),x92381)),f140(x92383,x92384)))+P101(f323(f323(f325(f866(f861(x92383),f861(x92383))),f323(f323(f258(f861(x92383),f861(x92383)),x92381),x92382)),f140(x92383,x92384)))
% 179.72/179.59 [4840]~P62(x48402)+~E(x48404,f2(x48402))+~E(x48401,f2(x48402))+E(x48401,f323(f323(f281(x48402),x48403),x48404))
% 179.72/179.59 [4841]~P62(x48411)+~E(x48413,f2(x48411))+~E(x48414,f2(x48411))+E(f323(f323(f281(x48411),x48412),x48413),x48414)
% 179.72/179.59 [4951]~P62(x49512)+E(x49511,f2(x49512))+~E(x49513,f2(x49512))+~E(x49511,f323(f323(f281(x49512),x49514),x49513))
% 179.72/179.59 [4952]~P62(x49522)+E(x49521,f2(x49522))+~E(x49523,f2(x49522))+~E(f323(f323(f281(x49522),x49524),x49523),x49521)
% 179.72/179.59 [5127]~P114(x51272)+E(x51271,f2(x51272))+~E(f323(f323(f281(x51272),x51273),x51271),x51274)+E(x51273,f323(f323(f79(x51272),x51274),x51271))
% 179.72/179.59 [5129]~P114(x51292)+E(x51291,f2(x51292))+~E(f323(f323(f79(x51292),x51293),x51291),x51294)+E(x51293,f323(f323(f281(x51292),x51294),x51291))
% 179.72/179.59 [5130]~P62(x51302)+E(x51301,f2(x51302))+~E(f323(f323(f281(x51302),x51303),x51301),x51304)+E(x51303,f323(f323(f79(x51302),x51304),x51301))
% 179.72/179.59 [5131]~P62(x51312)+E(x51311,f2(x51312))+~E(f323(f323(f79(x51312),x51313),x51311),x51314)+E(x51313,f323(f323(f281(x51312),x51314),x51311))
% 179.72/179.59 [5132]~P114(x51322)+E(x51321,f2(x51322))+~E(x51323,f323(f323(f281(x51322),x51324),x51321))+E(f323(f323(f79(x51322),x51323),x51321),x51324)
% 179.72/179.59 [5134]~P114(x51342)+E(x51341,f2(x51342))+~E(x51343,f323(f323(f79(x51342),x51344),x51341))+E(f323(f323(f281(x51342),x51343),x51341),x51344)
% 179.72/179.59 [5135]~P62(x51352)+E(x51351,f2(x51352))+~E(x51353,f323(f323(f281(x51352),x51354),x51351))+E(f323(f323(f79(x51352),x51353),x51351),x51354)
% 179.72/179.59 [5136]~P62(x51362)+E(x51361,f2(x51362))+~E(x51363,f323(f323(f79(x51362),x51364),x51361))+E(f323(f323(f281(x51362),x51363),x51361),x51364)
% 179.72/179.59 [5160]~P62(x51602)+~E(x51601,f2(x51602))+~E(f323(f323(f79(x51602),x51601),x51604),x51603)+E(x51601,f323(f323(f281(x51602),x51603),x51604))
% 179.72/179.59 [5161]~P62(x51611)+~E(x51614,f2(x51611))+~E(x51612,f323(f323(f79(x51611),x51614),x51613))+E(f323(f323(f281(x51611),x51612),x51613),x51614)
% 179.72/179.59 [5232]~E(x52323,x52324)+~E(x52322,x52323)+~P105(x52321)+E(f294(x52321,x52322,x52323),f323(f323(f301(x52321),x52324),f188(f867(x52321,a855))))
% 179.72/179.59 [5437]~E(f137(x54372,x54371),x54374)+~E(f114(x54372,x54371),x54373)+E(x54371,f113(x54372))+E(f323(f323(f121(x54372),x54373),f323(f323(f144(x54372),x54374),f113(x54372))),x54371)
% 179.72/179.59 [6044]~P119(x60443)+E(x60441,x60442)+~E(f323(f323(f248(x60443),x60444),x60441),f323(f323(f248(x60443),x60444),x60442))+~P101(f323(f323(f238(x60443),f76(x60443)),x60444))
% 179.72/179.59 [6045]E(x60451,x60452)+~E(f323(f323(f301(x60453),x60454),x60451),f323(f323(f301(x60453),x60454),x60452))+P101(f323(f323(f325(x60453),x60454),x60452))+P101(f323(f323(f325(x60453),x60454),x60451))
% 179.72/179.59 [6083]E(f323(x60831,x60832),f76(a860))+~E(f323(f323(f9(x60833,a860),x60831),x60834),f76(a860))+~P101(f323(f59(x60833),x60834))+~P101(f323(f323(f325(x60833),x60832),x60834))
% 179.72/179.59 [6084]E(f323(x60841,x60842),f2(a860))+~E(f323(f323(f6(x60843,a860),x60841),x60844),f2(a860))+~P101(f323(f59(x60843),x60844))+~P101(f323(f323(f325(x60843),x60842),x60844))
% 179.72/179.59 [6297]~P105(x62971)+~P101(f323(f323(f237(x62971),x62974),x62973))+P101(f323(f323(f237(x62971),x62972),x62973))+~P101(f323(f323(f237(x62971),x62972),x62974))
% 179.72/179.59 [6298]~P102(x62981)+~P101(f323(f323(f237(x62981),x62982),x62984))+P101(f323(f323(f237(x62981),x62982),x62983))+~P101(f323(f323(f237(x62981),x62984),x62983))
% 179.72/179.59 [6299]~P105(x62991)+~P101(f323(f323(f238(x62991),x62994),x62993))+P101(f323(f323(f238(x62991),x62992),x62993))+~P101(f323(f323(f237(x62991),x62992),x62994))
% 179.72/179.59 [6300]~P105(x63001)+~P101(f323(f323(f238(x63001),x63002),x63004))+P101(f323(f323(f238(x63001),x63002),x63003))+~P101(f323(f323(f237(x63001),x63004),x63003))
% 179.72/179.59 [6301]~P105(x63011)+~P101(f323(f323(f238(x63011),x63014),x63013))+P101(f323(f323(f238(x63011),x63012),x63013))+~P101(f323(f323(f238(x63011),x63012),x63014))
% 179.72/179.59 [6302]~P102(x63021)+~P101(f323(f323(f238(x63021),x63022),x63024))+P101(f323(f323(f238(x63021),x63022),x63023))+~P101(f323(f323(f237(x63021),x63024),x63023))
% 179.72/179.59 [6303]~P102(x63031)+~P101(f323(f323(f238(x63031),x63034),x63033))+P101(f323(f323(f238(x63031),x63032),x63033))+~P101(f323(f323(f237(x63031),x63032),x63034))
% 179.72/179.59 [6304]~P102(x63041)+~P101(f323(f323(f238(x63041),x63042),x63044))+P101(f323(f323(f238(x63041),x63042),x63043))+~P101(f323(f323(f238(x63041),x63044),x63043))
% 179.72/179.59 [6384]~P36(x63844,x63843,x63842)+E(x63841,f789(x63842,x63843,x63844))+~P101(f323(x63843,x63841))+~P101(f323(f323(f325(x63844),x63841),f323(f166(x63844),x63842)))
% 179.72/179.59 [6528]~P6(x65281)+~P101(f323(f323(f237(x65281),x65282),f38(x65281,x65284)))+P101(f323(f323(f237(x65281),x65282),x65283))+~P101(f323(f323(f325(x65281),x65283),x65284))
% 179.72/179.59 [6673]~P103(x66731)+~P16(x66731,f323(f323(f144(x66731),x66732),x66734))+~P101(f323(f323(f325(x66731),x66733),f323(f166(x66731),x66734)))+P101(f323(f323(f237(x66731),x66732),x66733))
% 179.72/179.59 [6762]~P6(x67621)+~P101(f323(f323(f237(x67621),f37(x67621,x67624)),x67623))+P101(f323(f323(f237(x67621),x67622),x67623))+~P101(f323(f323(f325(x67621),x67622),x67624))
% 179.72/179.59 [7164]~P103(x71641)+E(f323(f323(f110(f867(x71641,a855)),f323(f293(x71641,x71642),x71643)),f323(f293(x71641,x71643),x71644)),f323(f293(x71641,x71642),x71644))+~P101(f323(f323(f237(x71641),x71643),x71644))+~P101(f323(f323(f237(x71641),x71642),x71643))
% 179.72/179.59 [7201]P36(x72011,x72012,x72013)+~E(f794(x72013,x72012,x72011,x72014),x72014)+~P101(f323(x72012,x72014))+~P101(f323(f323(f325(x72011),x72014),f323(f166(x72011),x72013)))
% 179.72/179.59 [7275]~P103(x72751)+E(f323(f323(f110(f867(x72751,a855)),f323(f293(x72751,x72752),x72753)),f294(x72751,x72753,x72754)),f294(x72751,x72752,x72754))+~P101(f323(f323(f237(x72751),x72753),x72754))+~P101(f323(f323(f237(x72751),x72752),x72753))
% 179.72/179.59 [7338]~P103(x73381)+E(f323(f323(f110(f867(x73381,a855)),f297(x73381,x73382,x73383)),f323(f293(x73381,x73383),x73384)),f297(x73381,x73382,x73384))+~P101(f323(f323(f237(x73381),x73383),x73384))+~P101(f323(f323(f238(x73381),x73382),x73383))
% 179.72/179.59 [7358]~P103(x73581)+E(f323(f323(f110(f867(x73581,a855)),f294(x73581,x73582,x73583)),f297(x73581,x73583,x73584)),f323(f293(x73581,x73582),x73584))+~P101(f323(f323(f237(x73581),x73582),x73583))+~P101(f323(f323(f238(x73581),x73583),x73584))
% 179.72/179.59 [7390]~P103(x73901)+E(f323(f323(f110(f867(x73901,a855)),f294(x73901,x73902,x73903)),f296(x73901,x73903,x73904)),f294(x73901,x73902,x73904))+~P101(f323(f323(f237(x73901),x73903),x73904))+~P101(f323(f323(f237(x73901),x73902),x73903))
% 179.72/179.59 [7391]~P103(x73911)+E(f323(f323(f110(f867(x73911,a855)),f297(x73911,x73912,x73913)),f294(x73911,x73913,x73914)),f296(x73911,x73912,x73914))+~P101(f323(f323(f237(x73911),x73913),x73914))+~P101(f323(f323(f238(x73911),x73912),x73913))
% 179.72/179.59 [7392]~P103(x73921)+E(f323(f323(f110(f867(x73921,a855)),f296(x73921,x73922,x73923)),f297(x73921,x73923,x73924)),f297(x73921,x73922,x73924))+~P101(f323(f323(f237(x73921),x73922),x73923))+~P101(f323(f323(f238(x73921),x73923),x73924))
% 179.72/179.59 [7393]~P103(x73931)+E(f323(f323(f110(f867(x73931,a855)),f296(x73931,x73932,x73933)),f296(x73931,x73933,x73934)),f296(x73931,x73932,x73934))+~P101(f323(f323(f237(x73931),x73933),x73934))+~P101(f323(f323(f237(x73931),x73932),x73933))
% 179.72/179.59 [8181]P27(x81811,x81812,f832(x81813,x81812,x81814,x81811),x81814)+~P101(f323(f59(x81812),x81813))+~P101(f323(f59(x81811),x81814))+~P101(f323(f323(f237(a860),f323(f35(x81811),x81814)),f323(f35(x81812),x81813)))
% 179.72/179.59 [8202]P36(x82021,x82022,x82023)+~P101(f323(x82022,x82024))+P101(f323(x82022,f794(x82023,x82022,x82021,x82024)))+~P101(f323(f323(f325(x82021),x82024),f323(f166(x82021),x82023)))
% 179.72/179.59 [8255]~P68(x82551)+~E(f323(x82553,f466(x82553,x82554,x82552,x82551)),f76(x82551))+E(f323(f323(f323(f63(x82551,x82552,f79(x82551)),x82553),f76(x82551)),x82554),f76(x82551))+~P101(f323(f59(x82552),x82554))
% 179.72/179.59 [8521]~P119(x85211)+~P101(f323(f323(f237(x85211),f2(x85211)),x85213))+P101(f323(f323(f237(x85211),x85212),x85213))+~P101(f323(f323(f237(x85211),f323(f323(f248(x85211),x85212),f323(a112,x85214))),f323(f323(f248(x85211),x85213),f323(a112,x85214))))
% 179.72/179.59 [8837]P36(x88371,x88372,x88373)+~P101(f323(x88372,x88374))+~P101(f323(f323(f325(x88371),x88374),f323(f166(x88371),x88373)))+P101(f323(f323(f325(x88371),f794(x88373,x88372,x88371,x88374)),f323(f166(x88371),x88373)))
% 179.72/179.59 [8916]~P68(x89161)+E(f323(f323(f323(f63(x89161,x89162,f79(x89161)),x89163),f76(x89161)),x89164),f76(x89161))+~P101(f323(f59(x89162),x89164))+P101(f323(f323(f325(x89162),f466(x89163,x89164,x89162,x89161)),x89164))
% 179.72/179.59 [9399]~P101(f323(f323(f237(a1),x93994),f2(a1)))+P101(f323(f323(f237(a1),f323(f323(f78(a1),f323(f323(f79(a1),x93991),f42(a1,x93992,x93993))),x93994)),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x93993))+~P101(f323(f323(f238(a1),x93991),x93994))
% 179.72/179.59 [9852]~P101(f323(f59(x98521),x98522))+~P101(f323(f323(f325(x98521),x98524),x98522))+~P101(f323(f323(f325(x98521),x98523),x98522))+P101(f323(f323(f238(a860),f323(f35(x98521),f323(f323(f22(f867(x98521,a855)),f323(f323(f22(f867(x98521,a855)),x98522),f323(f323(f301(x98521),x98523),f188(f867(x98521,a855))))),f323(f323(f301(x98521),x98524),f188(f867(x98521,a855)))))),f323(f35(x98521),x98522)))
% 179.72/179.59 [6876]~P98(x68761)+~P101(f323(f323(f237(x68761),x68762),x68764))+~P101(f323(f323(f237(x68761),x68762),x68763))+P101(f323(f323(f237(x68761),x68762),f323(f323(f101(x68761),x68763),x68764)))
% 179.72/179.59 [6879]~P103(x68791)+~P101(f323(f323(f237(x68791),x68792),x68794))+~P101(f323(f323(f237(x68791),x68792),x68793))+P101(f323(f323(f237(x68791),x68792),f323(f323(f235(x68791),x68793),x68794)))
% 179.72/179.59 [6880]~P103(x68801)+~P101(f323(f323(f238(x68801),x68802),x68804))+~P101(f323(f323(f238(x68801),x68802),x68803))+P101(f323(f323(f238(x68801),x68802),f323(f323(f235(x68801),x68803),x68804)))
% 179.72/179.59 [6899]~P63(x68992)+E(x68991,f2(x68992))+E(f323(f323(f281(x68992),f323(f323(f248(x68992),x68991),x68993)),f323(f323(f248(x68992),x68991),x68994)),f323(f323(f248(x68992),x68991),f323(f323(f22(a860),x68993),x68994)))+~P101(f323(f323(f237(a860),x68994),x68993))
% 179.72/179.59 [6944]~P103(x69441)+~P16(x69441,f323(f323(f144(x69441),x69443),x69444))+P16(x69441,f323(f323(f144(x69441),x69442),f323(f323(f144(x69441),x69443),x69444)))+~P101(f323(f323(f237(x69441),x69442),x69443))
% 179.72/179.59 [6983]~P84(x69831)+~P101(f323(f323(f237(x69831),f2(x69831)),x69834))+~P101(f323(f323(f237(x69831),x69832),x69833))+P101(f323(f323(f237(x69831),x69832),f323(f323(f78(x69831),x69833),x69834)))
% 179.72/179.59 [6984]~P84(x69841)+~P101(f323(f323(f237(x69841),f2(x69841)),x69843))+~P101(f323(f323(f237(x69841),x69842),x69844))+P101(f323(f323(f237(x69841),x69842),f323(f323(f78(x69841),x69843),x69844)))
% 179.72/179.59 [6985]~P119(x69851)+~P101(f323(f323(f238(x69851),f2(x69851)),x69853))+~P101(f323(f323(f238(x69851),x69852),x69854))+P101(f323(f323(f238(x69851),x69852),f323(f323(f78(x69851),x69853),x69854)))
% 179.72/179.59 [6986]~P84(x69861)+~P101(f323(f323(f237(x69861),x69862),x69864))+~P101(f323(f323(f238(x69861),f2(x69861)),x69863))+P101(f323(f323(f238(x69861),x69862),f323(f323(f78(x69861),x69863),x69864)))
% 179.72/179.59 [6987]~P84(x69871)+~P101(f323(f323(f237(x69871),f2(x69871)),x69873))+~P101(f323(f323(f238(x69871),x69872),x69874))+P101(f323(f323(f238(x69871),x69872),f323(f323(f78(x69871),x69873),x69874)))
% 179.72/179.59 [7026]~P103(x70261)+P101(f323(f323(f237(x70261),x70262),x70263))+P101(f323(f323(f237(x70261),x70262),x70264))+~P101(f323(f323(f237(x70261),x70262),f323(f323(f236(x70261),x70264),x70263)))
% 179.72/179.59 [7027]~P103(x70271)+P101(f323(f323(f238(x70271),x70272),x70273))+P101(f323(f323(f238(x70271),x70272),x70274))+~P101(f323(f323(f238(x70271),x70272),f323(f323(f236(x70271),x70274),x70273)))
% 179.72/179.59 [7311]~P105(x73112)+~P5(x73111)+~P101(f323(f323(f238(f867(x73111,x73112)),x73113),x73114))+P101(f323(f323(f237(f867(x73111,x73112)),x73113),x73114))
% 179.72/179.59 [7678]~P65(x76781)+~P101(f323(f323(f238(x76781),x76784),f2(x76781)))+~P101(f323(f323(f237(x76781),x76783),f323(f323(f281(x76781),x76782),x76784)))+P101(f323(f323(f237(x76781),x76782),f323(f323(f79(x76781),x76783),x76784)))
% 179.72/179.59 [7679]~P65(x76791)+~P101(f323(f323(f238(x76791),x76794),f2(x76791)))+~P101(f323(f323(f237(x76791),x76793),f323(f323(f79(x76791),x76792),x76794)))+P101(f323(f323(f237(x76791),x76792),f323(f323(f281(x76791),x76793),x76794)))
% 179.72/179.59 [7680]~P65(x76801)+~P101(f323(f323(f238(x76801),x76804),f2(x76801)))+~P101(f323(f323(f238(x76801),x76803),f323(f323(f281(x76801),x76802),x76804)))+P101(f323(f323(f238(x76801),x76802),f323(f323(f79(x76801),x76803),x76804)))
% 179.72/179.59 [7681]~P65(x76811)+~P101(f323(f323(f238(x76811),x76814),f2(x76811)))+~P101(f323(f323(f238(x76811),x76813),f323(f323(f79(x76811),x76812),x76814)))+P101(f323(f323(f238(x76811),x76812),f323(f323(f281(x76811),x76813),x76814)))
% 179.72/179.59 [7786]~P122(x77861)+~P101(f323(f323(f237(x77861),x77862),f2(x77861)))+~P101(f323(f323(f237(x77861),x77864),x77863))+P101(f323(f323(f237(x77861),f323(f323(f79(x77861),x77862),x77863)),f323(f323(f79(x77861),x77862),x77864)))
% 179.72/179.59 [7787]~P120(x77871)+~P101(f323(f323(f238(x77871),x77872),f2(x77871)))+~P101(f323(f323(f237(x77871),x77874),x77873))+P101(f323(f323(f237(x77871),f323(f323(f79(x77871),x77872),x77873)),f323(f323(f79(x77871),x77872),x77874)))
% 179.72/179.59 [7788]~P122(x77881)+~P101(f323(f323(f237(x77881),x77883),f2(x77881)))+~P101(f323(f323(f237(x77881),x77884),x77882))+P101(f323(f323(f237(x77881),f323(f323(f79(x77881),x77882),x77883)),f323(f323(f79(x77881),x77884),x77883)))
% 179.72/179.59 [7789]~P64(x77891)+~P101(f323(f323(f237(x77891),x77893),f2(x77891)))+~P101(f323(f323(f237(x77891),x77894),x77892))+P101(f323(f323(f237(x77891),f323(f323(f281(x77891),x77892),x77893)),f323(f323(f281(x77891),x77894),x77893)))
% 179.72/179.59 [7793]~P120(x77931)+~P101(f323(f323(f238(x77931),x77933),f2(x77931)))+~P101(f323(f323(f238(x77931),x77934),x77932))+P101(f323(f323(f238(x77931),f323(f323(f79(x77931),x77932),x77933)),f323(f323(f79(x77931),x77934),x77933)))
% 179.72/179.59 [7794]~P120(x77941)+~P101(f323(f323(f238(x77941),x77942),f2(x77941)))+~P101(f323(f323(f238(x77941),x77944),x77943))+P101(f323(f323(f238(x77941),f323(f323(f79(x77941),x77942),x77943)),f323(f323(f79(x77941),x77942),x77944)))
% 179.72/179.59 [7795]~P65(x77951)+~P101(f323(f323(f238(x77951),x77953),f2(x77951)))+~P101(f323(f323(f238(x77951),x77954),x77952))+P101(f323(f323(f238(x77951),f323(f323(f281(x77951),x77952),x77953)),f323(f323(f281(x77951),x77954),x77953)))
% 179.72/179.59 [7796]~P119(x77961)+~P101(f323(f323(f238(x77961),f76(x77961)),x77962))+~P101(f323(f323(f237(a860),x77963),x77964))+P101(f323(f323(f237(x77961),f323(f323(f248(x77961),x77962),x77963)),f323(f323(f248(x77961),x77962),x77964)))
% 179.72/179.59 [7797]~P119(x77971)+~P101(f323(f323(f237(x77971),f76(x77971)),x77972))+~P101(f323(f323(f237(a860),x77973),x77974))+P101(f323(f323(f237(x77971),f323(f323(f248(x77971),x77972),x77973)),f323(f323(f248(x77971),x77972),x77974)))
% 179.72/179.59 [7799]~P119(x77991)+~P101(f323(f323(f238(x77991),f76(x77991)),x77992))+~P101(f323(f323(f238(a860),x77993),x77994))+P101(f323(f323(f238(x77991),f323(f323(f248(x77991),x77992),x77993)),f323(f323(f248(x77991),x77992),x77994)))
% 179.72/179.59 [7828]P101(f323(f323(f238(a860),f2(a860)),f323(x78281,x78282)))+~P101(f323(f59(x78283),x78284))+~P101(f323(f323(f325(x78283),x78282),x78284))+~P101(f323(f323(f238(a860),f2(a860)),f323(f323(f9(x78283,a860),x78281),x78284)))
% 179.72/179.59 [7836]~P120(x78361)+~P101(f323(f323(f238(x78361),f2(x78361)),x78362))+~P101(f323(f323(f237(x78361),x78363),x78364))+P101(f323(f323(f237(x78361),f323(f323(f79(x78361),x78362),x78363)),f323(f323(f79(x78361),x78362),x78364)))
% 179.72/179.59 [7837]~P131(x78371)+~P101(f323(f323(f237(x78371),x78373),x78374))+~P101(f323(f323(f237(x78371),f2(x78371)),x78372))+P101(f323(f323(f237(x78371),f323(f323(f79(x78371),x78372),x78373)),f323(f323(f79(x78371),x78372),x78374)))
% 179.72/179.59 [7838]~P130(x78381)+~P101(f323(f323(f237(x78381),x78383),x78384))+~P101(f323(f323(f237(x78381),f2(x78381)),x78382))+P101(f323(f323(f237(x78381),f323(f323(f79(x78381),x78382),x78383)),f323(f323(f79(x78381),x78382),x78384)))
% 179.72/179.59 [7839]~P131(x78391)+~P101(f323(f323(f237(x78391),x78392),x78394))+~P101(f323(f323(f237(x78391),f2(x78391)),x78393))+P101(f323(f323(f237(x78391),f323(f323(f79(x78391),x78392),x78393)),f323(f323(f79(x78391),x78394),x78393)))
% 179.72/179.59 [7840]~P119(x78401)+~P101(f323(f323(f237(x78401),x78402),x78404))+~P101(f323(f323(f237(x78401),f2(x78401)),x78402))+P101(f323(f323(f237(x78401),f323(f323(f248(x78401),x78402),x78403)),f323(f323(f248(x78401),x78404),x78403)))
% 179.72/179.59 [7841]~P64(x78411)+~P101(f323(f323(f237(x78411),x78412),x78414))+~P101(f323(f323(f237(x78411),f2(x78411)),x78413))+P101(f323(f323(f237(x78411),f323(f323(f281(x78411),x78412),x78413)),f323(f323(f281(x78411),x78414),x78413)))
% 179.72/179.59 [7843]~P125(x78431)+~P101(f323(f323(f238(x78431),x78433),x78434))+~P101(f323(f323(f238(x78431),f2(x78431)),x78432))+P101(f323(f323(f238(x78431),f323(f323(f79(x78431),x78432),x78433)),f323(f323(f79(x78431),x78432),x78434)))
% 179.72/179.59 [7844]~P117(x78441)+~P101(f323(f323(f238(x78441),x78443),x78444))+~P101(f323(f323(f238(x78441),f2(x78441)),x78442))+P101(f323(f323(f238(x78441),f323(f323(f79(x78441),x78442),x78443)),f323(f323(f79(x78441),x78442),x78444)))
% 179.72/179.59 [7845]~P120(x78451)+~P101(f323(f323(f238(x78451),x78452),x78454))+~P101(f323(f323(f238(x78451),f2(x78451)),x78453))+P101(f323(f323(f238(x78451),f323(f323(f79(x78451),x78452),x78453)),f323(f323(f79(x78451),x78454),x78453)))
% 179.72/179.59 [7846]~P125(x78461)+~P101(f323(f323(f238(x78461),x78462),x78464))+~P101(f323(f323(f238(x78461),f2(x78461)),x78463))+P101(f323(f323(f238(x78461),f323(f323(f79(x78461),x78462),x78463)),f323(f323(f79(x78461),x78464),x78463)))
% 179.72/179.59 [7847]~P120(x78471)+~P101(f323(f323(f238(x78471),x78473),x78474))+~P101(f323(f323(f238(x78471),f2(x78471)),x78472))+P101(f323(f323(f238(x78471),f323(f323(f79(x78471),x78472),x78473)),f323(f323(f79(x78471),x78472),x78474)))
% 179.72/179.59 [7848]~P65(x78481)+~P101(f323(f323(f238(x78481),x78482),x78484))+~P101(f323(f323(f238(x78481),f2(x78481)),x78483))+P101(f323(f323(f238(x78481),f323(f323(f281(x78481),x78482),x78483)),f323(f323(f281(x78481),x78484),x78483)))
% 179.72/179.59 [7893]~P104(x78932)+P101(f323(f323(f238(f867(x78931,x78932)),x78934),x78933))+~P101(f323(f323(f237(f867(x78931,x78932)),x78934),x78933))+P101(f323(f323(f237(f867(x78931,x78932)),x78933),x78934))
% 179.72/179.59 [7933]P101(f323(f323(f325(x79331),x79332),x79333))+P101(f323(f323(f325(x79331),x79332),x79334))+~P101(f323(f323(f237(f867(x79331,a855)),x79334),x79333))+P101(f323(f323(f238(f867(x79331,a855)),x79334),f323(f323(f301(x79331),x79332),x79333)))
% 179.72/179.59 [8087]P101(f323(f323(f325(x80871),x80872),x80873))+P101(f323(f323(f325(x80871),x80872),x80874))+~P101(f323(f323(f238(f867(x80871,a855)),x80874),f323(f323(f301(x80871),x80872),x80873)))+P101(f323(f323(f237(f867(x80871,a855)),x80874),x80873))
% 179.72/179.59 [8095]~P5(x80951)+P12(x80951,x80952,x80953)+~P101(f323(x80952,x80954))+~P101(f323(f323(f325(f861(x80951)),x80954),f323(f166(f861(x80951)),f52(x80951,x80953,f53(x80951)))))
% 179.72/179.59 [8105]~P13(x81053,x81051,x81054)+~P5(x81053)+P101(f323(x81051,x81052))+~P101(f323(f323(f325(f861(x81053)),x81052),f323(f166(f861(x81053)),f52(x81053,x81054,f53(x81053)))))
% 179.72/179.59 [8157]~P120(x81571)+P101(f323(f323(f238(x81571),x81573),x81572))+P101(f323(f323(f238(x81571),x81572),x81573))+~P101(f323(f323(f238(x81571),f323(f323(f79(x81571),x81574),x81572)),f323(f323(f79(x81571),x81574),x81573)))
% 179.72/179.59 [8158]~P120(x81581)+P101(f323(f323(f238(x81581),x81583),x81582))+P101(f323(f323(f238(x81581),x81582),x81583))+~P101(f323(f323(f238(x81581),f323(f323(f79(x81581),x81582),x81584)),f323(f323(f79(x81581),x81583),x81584)))
% 179.72/179.59 [8169]~P120(x81691)+P101(f323(f323(f238(x81691),x81694),f2(x81691)))+P101(f323(f323(f238(x81691),x81692),x81693))+~P101(f323(f323(f238(x81691),f323(f323(f79(x81691),x81692),x81694)),f323(f323(f79(x81691),x81693),x81694)))
% 179.72/179.59 [8170]~P120(x81701)+P101(f323(f323(f238(x81701),x81704),f2(x81701)))+P101(f323(f323(f238(x81701),x81702),x81703))+~P101(f323(f323(f238(x81701),f323(f323(f79(x81701),x81704),x81702)),f323(f323(f79(x81701),x81704),x81703)))
% 179.72/179.59 [8175]~P120(x81751)+P101(f323(f323(f238(x81751),x81752),x81753))+P101(f323(f323(f238(x81751),f2(x81751)),x81754))+~P101(f323(f323(f238(x81751),f323(f323(f79(x81751),x81754),x81753)),f323(f323(f79(x81751),x81754),x81752)))
% 179.72/179.59 [8176]~P120(x81761)+P101(f323(f323(f238(x81761),x81762),x81763))+P101(f323(f323(f238(x81761),f2(x81761)),x81764))+~P101(f323(f323(f238(x81761),f323(f323(f79(x81761),x81763),x81764)),f323(f323(f79(x81761),x81762),x81764)))
% 179.72/179.59 [8189]~P120(x81891)+P101(f323(f323(f238(x81891),x81892),f2(x81891)))+P101(f323(f323(f238(x81891),f2(x81891)),x81892))+~P101(f323(f323(f238(x81891),f323(f323(f79(x81891),x81893),x81892)),f323(f323(f79(x81891),x81894),x81892)))
% 179.72/179.59 [8190]~P120(x81901)+P101(f323(f323(f238(x81901),x81902),f2(x81901)))+P101(f323(f323(f238(x81901),f2(x81901)),x81902))+~P101(f323(f323(f238(x81901),f323(f323(f79(x81901),x81902),x81903)),f323(f323(f79(x81901),x81902),x81904)))
% 179.72/179.59 [8218]~P120(x82181)+~P101(f323(f323(f238(x82181),x82184),f2(x82181)))+P101(f323(f323(f237(x82181),x82182),x82183))+~P101(f323(f323(f237(x82181),f323(f323(f79(x82181),x82184),x82183)),f323(f323(f79(x82181),x82184),x82182)))
% 179.72/179.59 [8219]~P120(x82191)+~P101(f323(f323(f238(x82191),x82194),f2(x82191)))+P101(f323(f323(f238(x82191),x82192),x82193))+~P101(f323(f323(f238(x82191),f323(f323(f79(x82191),x82194),x82193)),f323(f323(f79(x82191),x82194),x82192)))
% 179.72/179.59 [8229]~P119(x82293)+~P101(f323(f323(f238(x82293),f76(x82293)),x82294))+P101(f323(f323(f237(a860),x82291),x82292))+~P101(f323(f323(f237(x82293),f323(f323(f248(x82293),x82294),x82291)),f323(f323(f248(x82293),x82294),x82292)))
% 179.72/179.59 [8231]~P119(x82313)+~P101(f323(f323(f238(x82313),f76(x82313)),x82314))+P101(f323(f323(f238(a860),x82311),x82312))+~P101(f323(f323(f238(x82313),f323(f323(f248(x82313),x82314),x82311)),f323(f323(f248(x82313),x82314),x82312)))
% 179.72/179.59 [8241]~P120(x82411)+P101(f323(f323(f237(x82411),x82412),x82413))+~P101(f323(f323(f238(x82411),f2(x82411)),x82414))+~P101(f323(f323(f237(x82411),f323(f323(f79(x82411),x82414),x82412)),f323(f323(f79(x82411),x82414),x82413)))
% 179.72/179.59 [8242]~P125(x82421)+P101(f323(f323(f237(x82421),x82422),x82423))+~P101(f323(f323(f238(x82421),f2(x82421)),x82424))+~P101(f323(f323(f237(x82421),f323(f323(f79(x82421),x82424),x82422)),f323(f323(f79(x82421),x82424),x82423)))
% 179.72/179.59 [8243]~P125(x82431)+P101(f323(f323(f237(x82431),x82432),x82433))+~P101(f323(f323(f238(x82431),f2(x82431)),x82434))+~P101(f323(f323(f237(x82431),f323(f323(f79(x82431),x82432),x82434)),f323(f323(f79(x82431),x82433),x82434)))
% 179.72/179.59 [8244]~P120(x82441)+P101(f323(f323(f238(x82441),x82442),x82443))+~P101(f323(f323(f238(x82441),f2(x82441)),x82444))+~P101(f323(f323(f238(x82441),f323(f323(f79(x82441),x82444),x82442)),f323(f323(f79(x82441),x82444),x82443)))
% 179.72/179.59 [8245]~P125(x82451)+P101(f323(f323(f238(x82451),x82452),x82453))+~P101(f323(f323(f237(x82451),f2(x82451)),x82454))+~P101(f323(f323(f238(x82451),f323(f323(f79(x82451),x82454),x82452)),f323(f323(f79(x82451),x82454),x82453)))
% 179.72/179.59 [8246]~P126(x82461)+P101(f323(f323(f238(x82461),x82462),x82463))+~P101(f323(f323(f237(x82461),f2(x82461)),x82464))+~P101(f323(f323(f238(x82461),f323(f323(f79(x82461),x82464),x82462)),f323(f323(f79(x82461),x82464),x82463)))
% 179.72/179.59 [8247]~P119(x82471)+~P101(f323(f323(f237(x82471),f2(x82471)),x82473))+P101(f323(f323(f238(x82471),x82472),x82473))+~P101(f323(f323(f238(x82471),f323(f323(f248(x82471),x82472),x82474)),f323(f323(f248(x82471),x82473),x82474)))
% 179.72/179.59 [8248]~P125(x82481)+P101(f323(f323(f238(x82481),x82482),x82483))+~P101(f323(f323(f237(x82481),f2(x82481)),x82484))+~P101(f323(f323(f238(x82481),f323(f323(f79(x82481),x82482),x82484)),f323(f323(f79(x82481),x82483),x82484)))
% 179.72/179.59 [8249]~P126(x82491)+P101(f323(f323(f238(x82491),x82492),x82493))+~P101(f323(f323(f237(x82491),f2(x82491)),x82494))+~P101(f323(f323(f238(x82491),f323(f323(f79(x82491),x82492),x82494)),f323(f323(f79(x82491),x82493),x82494)))
% 179.72/179.59 [8295]P101(f323(f323(f325(x82951),x82952),x82953))+~P101(f323(f323(f237(f867(x82951,a855)),x82953),x82954))+~P101(f323(f323(f238(f867(x82951,a855)),x82953),x82954))+P101(f323(f323(f238(f867(x82951,a855)),x82953),f323(f323(f301(x82951),x82952),x82954)))
% 179.72/179.59 [8546]~P5(x85461)+~P92(x85462)+~E(f323(x85463,f798(x85464,x85463,x85461,x85462)),f323(x85464,f798(x85464,x85463,x85461,x85462)))+P101(f323(f323(f89(f867(x85461,x85462)),x85463),x85464))
% 179.72/179.59 [8672]E(f323(f323(f22(a1),f389(x86721,x86722,x86723,x86724)),f390(x86721,x86722,x86723,x86724)),x86724)+~P101(f323(f323(f238(a1),f2(a1)),x86723))+~P101(f323(f323(f237(a1),x86721),x86724))+P101(f323(f323(f237(a1),x86721),f323(f323(f78(a1),x86724),x86723)))
% 179.72/179.59 [8673]E(f323(f323(f22(a1),f414(x86731,x86732,x86733,x86734)),f415(x86731,x86732,x86733,x86734)),x86734)+~P101(f323(f323(f238(a1),f2(a1)),x86733))+~P101(f323(f323(f238(a1),x86731),x86734))+P101(f323(f323(f238(a1),x86731),f323(f323(f78(a1),x86734),x86733)))
% 179.72/179.59 [8818]~E(f323(f323(f158(x88181),x88183),f639(x88184,x88183,x88181,x88182)),f323(f323(f158(x88181),x88184),f639(x88184,x88183,x88181,x88182)))+E(f323(f323(f169(x88181),x88182),x88183),f323(f323(f169(x88181),x88182),x88184))+~P101(f323(f323(f237(a860),x88182),f323(f189(f861(x88181)),x88183)))+~P101(f323(f323(f237(a860),x88182),f323(f189(f861(x88181)),x88184)))
% 179.72/179.59 [8888]~P101(f323(f323(f238(a1),f2(a1)),x88883))+~P101(f323(f323(f237(a1),x88881),x88884))+P101(f323(f323(f325(a1),f389(x88881,x88882,x88883,x88884)),x88882))+P101(f323(f323(f237(a1),x88881),f323(f323(f78(a1),x88884),x88883)))
% 179.72/179.59 [8889]~P101(f323(f323(f238(a1),f2(a1)),x88893))+~P101(f323(f323(f238(a1),x88891),x88894))+P101(f323(f323(f325(a1),f414(x88891,x88892,x88893,x88894)),x88892))+P101(f323(f323(f238(a1),x88891),f323(f323(f78(a1),x88894),x88893)))
% 179.72/179.59 [8925]~P98(x89251)+~P101(f323(f59(x89251),x89253))+~P101(f323(f323(f325(x89251),x89254),x89253))+P101(f323(f323(f237(x89251),f323(f323(f62(x89251,x89251,f101(x89251)),x89252),x89253)),f323(f323(f101(x89251),x89254),x89252)))
% 179.72/179.59 [8926]~P103(x89261)+~P101(f323(f59(x89261),x89263))+~P101(f323(f323(f325(x89261),x89264),x89263))+P101(f323(f323(f237(x89261),f323(f323(f62(x89261,x89261,f235(x89261)),x89262),x89263)),f323(f323(f235(x89261),x89264),x89262)))
% 179.72/179.59 [8970]E(f323(f323(f169(x89701),x89702),x89703),f323(f323(f169(x89701),x89702),x89704))+P101(f323(f323(f238(a860),f639(x89703,x89704,x89701,x89702)),x89702))+~P101(f323(f323(f237(a860),x89702),f323(f189(f861(x89701)),x89703)))+~P101(f323(f323(f237(a860),x89702),f323(f189(f861(x89701)),x89704)))
% 179.72/179.59 [8975]~P101(f323(f323(f238(a1),f2(a1)),x89753))+~P101(f323(f323(f237(a1),x89751),x89752))+P101(f323(f323(f325(a1),f390(x89751,x89754,x89753,x89752)),f294(a1,f76(a1),x89753)))+P101(f323(f323(f237(a1),x89751),f323(f323(f78(a1),x89752),x89753)))
% 179.72/179.59 [8976]~P101(f323(f323(f238(a1),f2(a1)),x89763))+~P101(f323(f323(f238(a1),x89761),x89762))+P101(f323(f323(f325(a1),f415(x89761,x89764,x89763,x89762)),f294(a1,f76(a1),x89763)))+P101(f323(f323(f238(a1),x89761),f323(f323(f78(a1),x89762),x89763)))
% 179.72/179.59 [9143]~E(f323(f179(x91431,x91432),x91433),f323(f179(x91431,x91432),x91434))+E(f323(f166(f866(x91431,x91432)),x91433),f323(f166(f866(x91431,x91432)),x91434))+~P101(f323(f130(x91431),f323(f323(f147(f866(x91431,x91432),x91431),f257(x91431,x91432)),x91434)))+~P101(f323(f130(x91431),f323(f323(f147(f866(x91431,x91432),x91431),f257(x91431,x91432)),x91433)))
% 179.72/179.59 [9155]E(f323(f179(x91551,x91552),x91553),f323(f179(x91551,x91552),x91554))+~E(f323(f166(f866(x91551,x91552)),x91553),f323(f166(f866(x91551,x91552)),x91554))+~P101(f323(f130(x91551),f323(f323(f147(f866(x91551,x91552),x91551),f257(x91551,x91552)),x91554)))+~P101(f323(f130(x91551),f323(f323(f147(f866(x91551,x91552),x91551),f257(x91551,x91552)),x91553)))
% 179.72/179.59 [9295]~P103(x92951)+~P101(f323(f59(x92951),x92954))+P101(f323(f323(f325(x92951),f764(x92952,x92953,x92954,x92951)),x92954))+P101(f323(f323(f237(x92951),f323(f323(f62(x92951,x92951,f236(x92951)),x92952),x92954)),f323(f323(f236(x92951),x92953),x92952)))
% 179.72/179.59 [9296]~P97(x92961)+~P101(f323(f59(x92961),x92964))+P101(f323(f323(f325(x92961),f765(x92962,x92963,x92964,x92961)),x92964))+P101(f323(f323(f237(x92961),f323(f323(f62(x92961,x92961,f110(x92961)),x92962),x92964)),f323(f323(f110(x92961),x92963),x92962)))
% 179.72/179.59 [9418]~P97(x94181)+~P101(f323(f59(x94181),x94183))+~P101(f323(f323(f237(x94181),f765(x94182,x94184,x94183,x94181)),x94184))+P101(f323(f323(f237(x94181),f323(f323(f62(x94181,x94181,f110(x94181)),x94182),x94183)),f323(f323(f110(x94181),x94184),x94182)))
% 179.72/179.59 [9419]~P103(x94191)+~P101(f323(f59(x94191),x94193))+~P101(f323(f323(f237(x94191),f764(x94192,x94194,x94193,x94191)),x94194))+P101(f323(f323(f237(x94191),f323(f323(f62(x94191,x94191,f236(x94191)),x94192),x94193)),f323(f323(f236(x94191),x94194),x94192)))
% 179.72/179.59 [9422]~P101(f323(f323(f237(a1),f2(a1)),x94224))+~P101(f323(f323(f238(a1),f2(a1)),x94223))+~P101(f323(f323(f238(a1),x94224),x94221))+P101(f323(f323(f238(a1),f323(f323(f78(a1),f323(f323(f79(a1),x94221),f42(a1,x94222,x94223))),x94224)),f323(f323(f79(a1),x94221),x94223)))
% 179.72/179.59 [9821]E(x98211,x98212)+P101(f323(f323(f325(f866(f861(x98213),f861(x98213))),f323(f323(f258(f861(x98213),f861(x98213)),x98212),x98211)),f140(x98213,x98214)))+P101(f323(f323(f325(f866(f861(x98213),f861(x98213))),f323(f323(f258(f861(x98213),f861(x98213)),x98211),x98212)),f140(x98213,x98214)))+~P101(f323(f323(f325(f866(x98213,x98213)),f323(f323(f258(x98213,x98213),f624(x98211,x98212,x98214,x98213)),f626(x98211,x98212,x98214,x98213))),x98214))
% 179.72/179.59 [9822]E(x98221,x98222)+P101(f323(f323(f325(f866(f861(x98223),f861(x98223))),f323(f323(f258(f861(x98223),f861(x98223)),x98222),x98221)),f140(x98223,x98224)))+P101(f323(f323(f325(f866(f861(x98223),f861(x98223))),f323(f323(f258(f861(x98223),f861(x98223)),x98221),x98222)),f140(x98223,x98224)))+~P101(f323(f323(f325(f866(x98223,x98223)),f323(f323(f258(x98223,x98223),f626(x98221,x98222,x98224,x98223)),f624(x98221,x98222,x98224,x98223))),x98224))
% 179.72/179.59 [7380]~P97(x73801)+~P101(f323(f323(f237(x73801),x73803),x73804))+~P101(f323(f323(f237(x73801),x73802),x73804))+P101(f323(f323(f237(x73801),f323(f323(f110(x73801),x73802),x73803)),x73804))
% 179.72/179.59 [7383]~P103(x73831)+~P101(f323(f323(f237(x73831),x73833),x73834))+~P101(f323(f323(f237(x73831),x73832),x73834))+P101(f323(f323(f237(x73831),f323(f323(f236(x73831),x73832),x73833)),x73834))
% 179.72/179.59 [7384]~P103(x73841)+~P101(f323(f323(f238(x73841),x73843),x73844))+~P101(f323(f323(f238(x73841),x73842),x73844))+P101(f323(f323(f238(x73841),f323(f323(f236(x73841),x73842),x73843)),x73844))
% 179.72/179.59 [7703]~E(x77031,x77033)+E(f132(a860,f323(f293(a860,x77031),x77032)),f323(f323(f144(a860),x77033),x77034))+~E(f132(a860,f323(f293(a860,f323(f323(f78(a860),x77031),f76(a860))),x77032)),x77034)+~P101(f323(f323(f238(a860),x77031),x77032))
% 179.72/179.59 [7712]~P103(x77121)+P101(f323(f323(f237(x77121),x77122),x77123))+P101(f323(f323(f237(x77121),x77124),x77123))+~P101(f323(f323(f237(x77121),f323(f323(f235(x77121),x77124),x77122)),x77123))
% 179.72/179.59 [7713]~P103(x77131)+P101(f323(f323(f238(x77131),x77132),x77133))+P101(f323(f323(f238(x77131),x77134),x77133))+~P101(f323(f323(f238(x77131),f323(f323(f235(x77131),x77134),x77132)),x77133))
% 179.72/179.59 [7991]~P64(x79911)+~P101(f323(f323(f238(x79911),f2(x79911)),x79913))+~P101(f323(f323(f237(x79911),x79912),f323(f323(f281(x79911),x79914),x79913)))+P101(f323(f323(f237(x79911),f323(f323(f79(x79911),x79912),x79913)),x79914))
% 179.72/179.59 [7992]~P65(x79921)+~P101(f323(f323(f238(x79921),f2(x79921)),x79923))+~P101(f323(f323(f237(x79921),x79922),f323(f323(f281(x79921),x79924),x79923)))+P101(f323(f323(f237(x79921),f323(f323(f79(x79921),x79922),x79923)),x79924))
% 179.72/179.59 [7994]~P64(x79941)+~P101(f323(f323(f238(x79941),f2(x79941)),x79943))+~P101(f323(f323(f237(x79941),x79942),f323(f323(f79(x79941),x79944),x79943)))+P101(f323(f323(f237(x79941),f323(f323(f281(x79941),x79942),x79943)),x79944))
% 179.72/179.59 [7995]~P65(x79951)+~P101(f323(f323(f238(x79951),f2(x79951)),x79953))+~P101(f323(f323(f237(x79951),x79952),f323(f323(f79(x79951),x79954),x79953)))+P101(f323(f323(f237(x79951),f323(f323(f281(x79951),x79952),x79953)),x79954))
% 179.72/179.59 [7996]~P64(x79961)+~P101(f323(f323(f238(x79961),f2(x79961)),x79963))+~P101(f323(f323(f238(x79961),x79962),f323(f323(f281(x79961),x79964),x79963)))+P101(f323(f323(f238(x79961),f323(f323(f79(x79961),x79962),x79963)),x79964))
% 179.72/179.59 [7997]~P65(x79971)+~P101(f323(f323(f238(x79971),f2(x79971)),x79973))+~P101(f323(f323(f238(x79971),x79972),f323(f323(f281(x79971),x79974),x79973)))+P101(f323(f323(f238(x79971),f323(f323(f79(x79971),x79972),x79973)),x79974))
% 179.72/179.59 [7999]~P64(x79991)+~P101(f323(f323(f238(x79991),f2(x79991)),x79993))+~P101(f323(f323(f238(x79991),x79992),f323(f323(f79(x79991),x79994),x79993)))+P101(f323(f323(f238(x79991),f323(f323(f281(x79991),x79992),x79993)),x79994))
% 179.72/179.59 [8000]~P65(x80001)+~P101(f323(f323(f238(x80001),f2(x80001)),x80003))+~P101(f323(f323(f238(x80001),x80002),f323(f323(f79(x80001),x80004),x80003)))+P101(f323(f323(f238(x80001),f323(f323(f281(x80001),x80002),x80003)),x80004))
% 179.72/179.59 [8127]~P64(x81271)+~P101(f323(f323(f238(x81271),f2(x81271)),x81274))+P101(f323(f323(f237(x81271),x81272),f323(f323(f79(x81271),x81273),x81274)))+~P101(f323(f323(f237(x81271),f323(f323(f281(x81271),x81272),x81274)),x81273))
% 179.72/179.59 [8129]~P64(x81291)+~P101(f323(f323(f238(x81291),f2(x81291)),x81294))+P101(f323(f323(f237(x81291),x81292),f323(f323(f281(x81291),x81293),x81294)))+~P101(f323(f323(f237(x81291),f323(f323(f79(x81291),x81292),x81294)),x81293))
% 179.72/179.59 [8130]~P65(x81301)+~P101(f323(f323(f238(x81301),f2(x81301)),x81304))+P101(f323(f323(f237(x81301),x81302),f323(f323(f79(x81301),x81303),x81304)))+~P101(f323(f323(f237(x81301),f323(f323(f281(x81301),x81302),x81304)),x81303))
% 179.72/179.59 [8131]~P65(x81311)+~P101(f323(f323(f238(x81311),f2(x81311)),x81314))+P101(f323(f323(f237(x81311),x81312),f323(f323(f281(x81311),x81313),x81314)))+~P101(f323(f323(f237(x81311),f323(f323(f79(x81311),x81312),x81314)),x81313))
% 179.72/179.59 [8132]~P64(x81321)+~P101(f323(f323(f238(x81321),f2(x81321)),x81324))+P101(f323(f323(f238(x81321),x81322),f323(f323(f79(x81321),x81323),x81324)))+~P101(f323(f323(f238(x81321),f323(f323(f281(x81321),x81322),x81324)),x81323))
% 179.72/179.59 [8134]~P64(x81341)+~P101(f323(f323(f238(x81341),f2(x81341)),x81344))+P101(f323(f323(f238(x81341),x81342),f323(f323(f281(x81341),x81343),x81344)))+~P101(f323(f323(f238(x81341),f323(f323(f79(x81341),x81342),x81344)),x81343))
% 179.72/179.59 [8135]~P65(x81351)+~P101(f323(f323(f238(x81351),f2(x81351)),x81354))+P101(f323(f323(f238(x81351),x81352),f323(f323(f79(x81351),x81353),x81354)))+~P101(f323(f323(f238(x81351),f323(f323(f281(x81351),x81352),x81354)),x81353))
% 179.72/179.59 [8136]~P65(x81361)+~P101(f323(f323(f238(x81361),f2(x81361)),x81364))+P101(f323(f323(f238(x81361),x81362),f323(f323(f281(x81361),x81363),x81364)))+~P101(f323(f323(f238(x81361),f323(f323(f79(x81361),x81362),x81364)),x81363))
% 179.72/179.59 [8299]~P65(x82991)+~P101(f323(f323(f238(x82991),x82993),f2(x82991)))+~P101(f323(f323(f237(x82991),f323(f323(f281(x82991),x82994),x82993)),x82992))+P101(f323(f323(f237(x82991),f323(f323(f79(x82991),x82992),x82993)),x82994))
% 179.72/179.59 [8300]~P65(x83001)+~P101(f323(f323(f238(x83001),x83003),f2(x83001)))+~P101(f323(f323(f237(x83001),f323(f323(f79(x83001),x83004),x83003)),x83002))+P101(f323(f323(f237(x83001),f323(f323(f281(x83001),x83002),x83003)),x83004))
% 179.72/179.59 [8301]~P65(x83011)+~P101(f323(f323(f238(x83011),x83013),f2(x83011)))+~P101(f323(f323(f238(x83011),f323(f323(f281(x83011),x83014),x83013)),x83012))+P101(f323(f323(f238(x83011),f323(f323(f79(x83011),x83012),x83013)),x83014))
% 179.72/179.59 [8302]~P65(x83021)+~P101(f323(f323(f238(x83021),x83023),f2(x83021)))+~P101(f323(f323(f238(x83021),f323(f323(f79(x83021),x83024),x83023)),x83022))+P101(f323(f323(f238(x83021),f323(f323(f281(x83021),x83022),x83023)),x83024))
% 179.72/179.59 [8314]~P101(f323(x83141,x83144))+~P101(f323(f323(f238(a860),x83142),f323(f323(f79(a860),x83143),f323(a112,x83144))))+P101(f323(x83141,f323(f323(f36(a860),x83142),x83143)))+~P101(f323(f323(f237(a860),f323(f323(f79(a860),x83143),x83144)),x83142))
% 179.72/179.59 [8518]~P97(x85181)+~P101(f323(f59(x85181),x85184))+~P101(f323(f323(f325(x85181),x85182),x85184))+P101(f323(f323(f237(x85181),f323(f323(f110(x85181),x85182),x85183)),f323(f323(f62(x85181,x85181,f110(x85181)),x85183),x85184)))
% 179.72/179.59 [8519]~P103(x85191)+~P101(f323(f59(x85191),x85194))+~P101(f323(f323(f325(x85191),x85192),x85194))+P101(f323(f323(f237(x85191),f323(f323(f236(x85191),x85192),x85193)),f323(f323(f62(x85191,x85191,f236(x85191)),x85193),x85194)))
% 179.72/179.59 [8674]~P101(f323(f59(x86741),x86742))+E(f323(f35(x86741),f323(f323(f22(f867(x86741,a855)),x86742),f323(f323(f301(x86741),x86743),x86744))),f323(f323(f22(a860),f323(f35(x86741),f323(f323(f22(f867(x86741,a855)),x86742),x86744))),f76(a860)))+P101(f323(f323(f325(x86741),x86743),x86744))+~P101(f323(f323(f325(x86741),x86743),x86742))
% 179.72/179.59 [8752]E(f323(f323(f78(a1),f391(x87521,x87522,x87523,x87524)),f392(x87521,x87522,x87523,x87524)),x87524)+~P101(f323(f323(f238(a1),f2(a1)),x87523))+~P101(f323(f323(f237(a1),x87524),x87521))+P101(f323(f323(f237(a1),f323(f323(f22(a1),x87524),x87523)),x87521))
% 179.72/179.59 [8753]E(f323(f323(f78(a1),f416(x87531,x87532,x87533,x87534)),f417(x87531,x87532,x87533,x87534)),x87534)+~P101(f323(f323(f238(a1),f2(a1)),x87533))+~P101(f323(f323(f238(a1),x87534),x87531))+P101(f323(f323(f238(a1),f323(f323(f22(a1),x87534),x87533)),x87531))
% 179.72/179.59 [8955]~P101(f323(f323(f238(a1),f2(a1)),x89553))+~P101(f323(f323(f237(a1),x89554),x89551))+P101(f323(f323(f325(a1),f391(x89551,x89552,x89553,x89554)),x89552))+P101(f323(f323(f237(a1),f323(f323(f22(a1),x89554),x89553)),x89551))
% 179.72/179.59 [8956]~P101(f323(f323(f238(a1),f2(a1)),x89563))+~P101(f323(f323(f238(a1),x89564),x89561))+P101(f323(f323(f325(a1),f416(x89561,x89562,x89563,x89564)),x89562))+P101(f323(f323(f238(a1),f323(f323(f22(a1),x89564),x89563)),x89561))
% 179.72/179.59 [9045]~P101(f323(f323(f238(a1),f2(a1)),x90452))+~P101(f323(f323(f237(a1),x90451),x90453))+P101(f323(f323(f325(a1),f392(x90453,x90454,x90452,x90451)),f294(a1,f76(a1),x90452)))+P101(f323(f323(f237(a1),f323(f323(f22(a1),x90451),x90452)),x90453))
% 179.72/179.59 [9046]~P101(f323(f323(f238(a1),f2(a1)),x90462))+~P101(f323(f323(f238(a1),x90461),x90463))+P101(f323(f323(f325(a1),f417(x90463,x90464,x90462,x90461)),f294(a1,f76(a1),x90462)))+P101(f323(f323(f238(a1),f323(f323(f22(a1),x90461),x90462)),x90463))
% 179.72/179.59 [9063]~P101(f323(f323(f237(a1),f2(a1)),x90634))+~P101(f323(f323(f238(a1),f2(a1)),x90633))+~P101(f323(f323(f238(a1),x90634),x90631))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),f323(f323(f79(a1),x90631),f42(a1,x90632,x90633))),x90634)))
% 179.72/179.59 [9124]~P98(x91241)+~P101(f323(f59(x91241),x91244))+~P101(f323(f323(f237(x91241),x91242),f762(x91243,x91242,x91244,x91241)))+P101(f323(f323(f237(x91241),f323(f323(f101(x91241),x91242),x91243)),f323(f323(f62(x91241,x91241,f101(x91241)),x91243),x91244)))
% 179.72/179.59 [9125]~P103(x91251)+~P101(f323(f59(x91251),x91254))+~P101(f323(f323(f237(x91251),x91252),f763(x91253,x91252,x91254,x91251)))+P101(f323(f323(f237(x91251),f323(f323(f235(x91251),x91252),x91253)),f323(f323(f62(x91251,x91251,f235(x91251)),x91253),x91254)))
% 179.72/179.59 [9141]~P101(f323(f323(f237(a1),x91414),f2(a1)))+~P101(f323(f323(f238(a1),f2(a1)),x91412))+~P101(f323(f323(f238(a1),x91411),x91414))+P101(f323(f323(f238(a1),f323(f323(f79(a1),x91411),x91412)),f323(f323(f78(a1),f323(f323(f79(a1),x91411),f42(a1,x91413,x91412))),x91414)))
% 179.72/179.59 [9167]P101(f323(f59(x91671),x91672))+~P101(f323(f59(x91671),x91673))+~P101(f323(f323(f325(f867(x91671,a855)),x91672),f323(f323(f58(x91671),x91673),x91674)))+~P101(f323(f323(f237(f867(f866(x91671,x91671),a855)),x91674),f323(f323(f260(x91671,x91671),x91673),f323(f16(f867(x91671,a855),x91671),x91673))))
% 179.72/179.59 [9190]~P103(x91901)+~P101(f323(f59(x91901),x91904))+P101(f323(f323(f325(x91901),f763(x91902,x91903,x91904,x91901)),x91904))+P101(f323(f323(f237(x91901),f323(f323(f235(x91901),x91903),x91902)),f323(f323(f62(x91901,x91901,f235(x91901)),x91902),x91904)))
% 179.72/179.59 [9191]~P98(x91911)+~P101(f323(f59(x91911),x91914))+P101(f323(f323(f325(x91911),f762(x91912,x91913,x91914,x91911)),x91914))+P101(f323(f323(f237(x91911),f323(f323(f101(x91911),x91913),x91912)),f323(f323(f62(x91911,x91911,f101(x91911)),x91912),x91914)))
% 179.72/179.59 [9587]~P101(f323(f59(x95872),x95874))+~P101(f323(f59(x95871),x95873))+~P101(f323(f323(f237(a860),f323(f35(x95872),x95874)),f323(f35(x95871),x95873)))+P101(f323(f323(f237(f867(x95871,a855)),f323(f302(x95872,x95871,f832(x95873,x95871,x95874,x95872)),x95874)),x95873))
% 179.72/179.59 [9237]~P101(f323(f323(f325(x92371),x92372),x92374))+P101(f323(f323(f325(x92371),x92372),x92373))+~P101(f323(f323(f238(f867(x92371,a855)),x92374),f323(f323(f301(x92371),x92372),x92373)))+P101(f323(f323(f238(f867(x92371,a855)),f323(f323(f22(f867(x92371,a855)),x92374),f323(f323(f301(x92371),x92372),f188(f867(x92371,a855))))),x92373))
% 179.72/179.59 [9396]~P101(f323(f323(f325(x93961),x93962),x93964))+P101(f323(f323(f325(x93961),x93962),x93963))+P101(f323(f323(f238(f867(x93961,a855)),x93964),f323(f323(f301(x93961),x93962),x93963)))+~P101(f323(f323(f238(f867(x93961,a855)),f323(f323(f22(f867(x93961,a855)),x93964),f323(f323(f301(x93961),x93962),f188(f867(x93961,a855))))),x93963))
% 179.72/179.59 [9425]P101(f323(f323(f325(x94251),x94252),x94253))+~P101(f323(f323(f237(f867(x94251,a855)),x94254),x94253))+P101(f323(f323(f238(f867(x94251,a855)),x94254),f323(f323(f301(x94251),x94252),x94253)))+~P101(f323(f323(f238(f867(x94251,a855)),f323(f323(f22(f867(x94251,a855)),x94254),f323(f323(f301(x94251),x94252),f188(f867(x94251,a855))))),x94253))
% 179.72/179.59 [9430]~P101(f323(f323(f325(x94301),x94303),x94302))+~P101(f323(f323(f238(f867(x94301,a855)),x94302),x94304))+P101(f323(f323(f238(f867(x94301,a855)),x94302),f323(f323(f301(x94301),x94303),x94304)))+~P101(f323(f323(f238(f867(x94301,a855)),f323(f323(f22(f867(x94301,a855)),x94302),f323(f323(f301(x94301),x94303),f188(f867(x94301,a855))))),x94304))
% 179.72/179.59 [9445]~P101(f323(f323(f237(f867(x94451,a855)),x94452),x94454))+~P101(f323(f323(f238(f867(x94451,a855)),x94452),x94454))+P101(f323(f323(f238(f867(x94451,a855)),x94452),f323(f323(f301(x94451),x94453),x94454)))+~P101(f323(f323(f238(f867(x94451,a855)),f323(f323(f22(f867(x94451,a855)),x94452),f323(f323(f301(x94451),x94453),f188(f867(x94451,a855))))),x94454))
% 179.72/179.59 [9488]~P105(x94882)+~P5(x94881)+~P101(f323(f323(f237(f867(x94881,x94882)),x94883),x94884))+P101(f323(f56(x94881),f323(f323(f18(x94881,x94882,a855),f323(f323(f8(x94882,f867(x94882,a855),x94881),f237(x94882)),x94883)),x94884)))
% 179.72/179.59 [9634]~P105(x96342)+~P5(x96341)+P101(f323(f323(f237(f867(x96341,x96342)),x96343),x96344))+~P101(f323(f56(x96341),f323(f323(f18(x96341,x96342,a855),f323(f323(f8(x96342,f867(x96342,a855),x96341),f237(x96342)),x96343)),x96344)))
% 179.72/179.59 [9807]E(f323(f323(f158(x98071),f323(f323(f158(f861(x98071)),f173(x98071,x98072)),x98073)),x98074),f323(f323(f158(x98071),f323(f323(f158(f861(x98071)),x98072),x98074)),x98073))+~P101(f323(f323(f238(a860),x98073),f323(f189(f861(f861(x98071))),f173(x98071,x98072))))+~P16(a860,f323(f162(a860),f323(f323(f147(f861(x98071),a860),f189(f861(x98071))),x98072)))+~P101(f323(f323(f238(a860),x98074),f323(f189(f861(f861(x98071))),f323(f129(f861(x98071),f323(f323(f8(a860,a855,f861(x98071)),f323(f238(a860),x98073)),f189(f861(x98071)))),x98072))))
% 179.72/179.59 [9834]~P101(f323(f323(f325(f866(a860,a860)),x98344),x98341))+~P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),x98344),x98342)),a33))+~P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),x98341),x98343)),a66))+P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),x98341),f323(f323(f301(f866(a860,a860)),x98342),x98343))),a66))
% 179.72/179.59 [9835]~P101(f323(f323(f325(f866(a860,a860)),x98354),x98351))+~P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),x98354),x98352)),a68))+~P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),x98351),x98353)),a69))+P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),x98351),f323(f323(f301(f866(a860,a860)),x98352),x98353))),a69))
% 179.72/179.59 [9720]~P105(x97202)+~P5(x97201)+~P101(f323(f323(f238(f867(x97201,x97202)),x97203),x97204))+P101(f323(f55(x97201),f323(f323(f8(a855,a855,x97201),a318),f323(f323(f18(x97201,x97202,a855),f323(f323(f8(x97202,f867(x97202,a855),x97201),a320),x97203)),x97204))))
% 179.72/179.59 [9848]~P101(f323(f323(f325(f866(a860,a860)),x98484),x98483))+~P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),x98481),x98484)),a33))+~P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),x98482),x98483)),a34))+P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),f323(f323(f301(f866(a860,a860)),x98481),x98482)),x98483)),a34))
% 179.72/179.59 [9849]~P101(f323(f323(f325(f866(a860,a860)),x98494),x98493))+~P101(f323(f323(f325(f866(f866(a860,a860),f866(a860,a860))),f323(f323(f258(f866(a860,a860),f866(a860,a860)),x98491),x98494)),a68))+~P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),x98492),x98493)),a67))+P101(f323(f323(f325(f866(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855))),f323(f323(f258(f867(f866(a860,a860),a855),f867(f866(a860,a860),a855)),f323(f323(f301(f866(a860,a860)),x98491),x98492)),x98493)),a67))
% 179.72/179.59 [5993]~P8(x59934,x59931)+~P101(f323(f323(x59931,x59932),x59935))+P101(f323(f323(x59931,x59932),x59933))+~P101(f323(f323(x59931,x59935),x59933))
% 179.72/179.59 [5263]~P60(x52635)+E(x52631,x52632)+~E(x52633,x52634)+~E(f323(f323(f22(x52635),x52633),x52634),f323(f323(f22(x52635),x52631),x52632))
% 179.72/179.59 [6101]~P19(x61015,x61011,x61013)+E(f323(f323(x61011,x61012),f323(x61013,x61014)),f323(x61013,x61014))+~P101(f323(f59(x61015),x61014))+~P101(f323(f323(f325(x61015),x61012),x61014))
% 179.72/179.59 [6288]~P75(x62881)+~E(f323(f323(f22(x62881),x62884),x62885),f323(f323(f22(x62881),x62882),x62883))+~P101(f323(f323(f237(x62881),x62884),x62885))+P101(f323(f323(f237(x62881),x62882),x62883))
% 179.72/179.59 [6290]~P75(x62901)+~E(f323(f323(f22(x62901),x62904),x62905),f323(f323(f22(x62901),x62902),x62903))+~P101(f323(f323(f238(x62901),x62904),x62905))+P101(f323(f323(f238(x62901),x62902),x62903))
% 179.72/179.59 [7242]~E(x72422,f323(f323(f144(x72421),x72424),x72425))+P101(f323(f323(f325(f861(x72421)),x72422),f154(x72421,x72423)))+~P101(f323(f323(f325(f861(x72421)),x72425),f154(x72421,x72423)))+~P101(f323(f323(f325(x72421),x72424),x72423))
% 179.72/179.59 [7654]~E(f323(f189(f861(x76541)),x76543),f323(f189(f861(x76542)),x76544))+~E(f323(f323(f147(f866(x76541,x76542),x76542),f261(x76541,x76542)),x76545),x76544)+~E(f323(f323(f147(f866(x76541,x76542),x76541),f257(x76541,x76542)),x76545),x76543)+E(f323(f323(f175(x76541,x76542),x76543),x76544),x76545)
% 179.72/179.59 [7987]~P105(x79871)+P101(f323(f323(f238(f867(x79871,a855)),f294(x79871,x79872,x79873)),f294(x79871,x79874,x79875)))+~P101(f323(f323(f237(x79871),x79874),x79875))+P101(f323(f323(f237(x79871),x79872),x79873))
% 179.72/179.59 [8080]~P105(x80801)+P101(f323(f323(f237(f867(x80801,a855)),f294(x80801,x80802,x80803)),f294(x80801,x80804,x80805)))+~P101(f323(f323(f237(x80801),x80803),x80805))+~P101(f323(f323(f237(x80801),x80804),x80802))
% 179.72/179.59 [8204]~P103(x82041)+P101(f323(f323(f237(x82041),x82042),x82043))+P101(f323(f323(f237(x82041),x82044),x82043))+~P101(f323(f323(f237(f867(x82041,a855)),f323(f293(x82041,x82043),x82042)),f323(f293(x82041,x82044),x82045)))
% 179.72/179.59 [8205]~P103(x82051)+P101(f323(f323(f237(x82051),x82052),x82053))+P101(f323(f323(f237(x82051),x82052),x82054))+~P101(f323(f323(f237(f867(x82051,a855)),f323(f293(x82051,x82053),x82052)),f323(f293(x82051,x82055),x82054)))
% 179.72/179.59 [8437]~P105(x84371)+~P101(f323(f323(f237(f867(x84371,a855)),f294(x84371,x84374,x84372)),f294(x84371,x84375,x84373)))+P101(f323(f323(f237(x84371),x84372),x84373))+~P101(f323(f323(f237(x84371),x84374),x84372))
% 179.72/179.59 [8438]~P105(x84381)+~P101(f323(f323(f238(f867(x84381,a855)),f294(x84381,x84384,x84382)),f294(x84381,x84385,x84383)))+P101(f323(f323(f237(x84381),x84382),x84383))+~P101(f323(f323(f237(x84381),x84384),x84382))
% 179.72/179.59 [8439]~P105(x84391)+~P101(f323(f323(f237(f867(x84391,a855)),f294(x84391,x84393,x84394)),f294(x84391,x84392,x84395)))+P101(f323(f323(f237(x84391),x84392),x84393))+~P101(f323(f323(f237(x84391),x84393),x84394))
% 179.72/179.59 [8440]~P105(x84401)+~P101(f323(f323(f238(f867(x84401,a855)),f294(x84401,x84403,x84404)),f294(x84401,x84402,x84405)))+P101(f323(f323(f237(x84401),x84402),x84403))+~P101(f323(f323(f237(x84401),x84403),x84404))
% 179.72/179.59 [5992]~P19(x59922,x59925,x59923)+E(x59921,f188(f867(x59922,a855)))+~P101(f323(f59(x59922),x59921))+E(f323(x59923,f323(f323(f301(x59922),x59924),x59921)),f323(f323(x59925,x59924),f323(x59923,x59921)))
% 179.72/179.59 [6749]~E(x67491,x67492)+~E(f323(f323(f101(f867(x67493,a855)),x67494),x67495),f188(f867(x67493,a855)))+~P101(f323(f323(f325(x67493),x67492),x67495))+~P101(f323(f323(f325(x67493),x67491),x67494))
% 179.72/179.59 [6831]~P20(x68312,x68315,x68311)+~P101(f323(f59(x68312),x68314))+E(f323(x68311,f323(f323(f301(x68312),x68313),x68314)),f323(f323(f62(x68312,x68312,x68315),x68313),x68314))+P101(f323(f323(f325(x68312),x68313),x68314))
% 179.72/179.59 [6895]~P72(x68952)+~P101(f323(f59(x68951),x68955))+E(f323(f323(f6(x68951,x68952),x68953),f323(f323(f301(x68951),x68954),x68955)),f323(f323(f78(x68952),f323(x68953,x68954)),f323(f323(f6(x68951,x68952),x68953),x68955)))+P101(f323(f323(f325(x68951),x68954),x68955))
% 179.72/179.59 [6897]~P68(x68972)+~P101(f323(f59(x68971),x68975))+E(f323(f323(f9(x68971,x68972),x68973),f323(f323(f301(x68971),x68974),x68975)),f323(f323(f79(x68972),f323(x68973,x68974)),f323(f323(f9(x68971,x68972),x68973),x68975)))+P101(f323(f323(f325(x68971),x68974),x68975))
% 179.72/179.59 [7395]~P20(x73952,x73955,x73951)+~P101(f323(f59(x73952),x73954))+E(f323(x73951,f323(f323(f301(x73952),x73953),x73954)),x73953)+~E(f323(f323(f22(f867(x73952,a855)),x73954),f323(f323(f301(x73952),x73953),f188(f867(x73952,a855)))),f188(f867(x73952,a855)))
% 179.72/179.59 [7756]~P97(x77561)+~P101(f323(f323(f237(x77561),x77563),x77565))+~P101(f323(f323(f237(x77561),x77562),x77564))+P101(f323(f323(f237(x77561),f323(f323(f110(x77561),x77562),x77563)),f323(f323(f110(x77561),x77564),x77565)))
% 179.72/179.59 [7757]~P98(x77571)+~P101(f323(f323(f237(x77571),x77573),x77575))+~P101(f323(f323(f237(x77571),x77572),x77574))+P101(f323(f323(f237(x77571),f323(f323(f101(x77571),x77572),x77573)),f323(f323(f101(x77571),x77574),x77575)))
% 179.72/179.59 [7758]~P81(x77581)+~P101(f323(f323(f237(x77581),x77583),x77585))+~P101(f323(f323(f237(x77581),x77582),x77584))+P101(f323(f323(f237(x77581),f323(f323(f78(x77581),x77582),x77583)),f323(f323(f78(x77581),x77584),x77585)))
% 179.72/179.59 [7759]~P103(x77591)+~P101(f323(f323(f237(x77591),x77593),x77595))+~P101(f323(f323(f237(x77591),x77592),x77594))+P101(f323(f323(f237(x77591),f323(f323(f235(x77591),x77592),x77593)),f323(f323(f235(x77591),x77594),x77595)))
% 179.72/179.59 [7760]~P103(x77601)+~P101(f323(f323(f237(x77601),x77603),x77605))+~P101(f323(f323(f237(x77601),x77602),x77604))+P101(f323(f323(f237(x77601),f323(f323(f236(x77601),x77602),x77603)),f323(f323(f236(x77601),x77604),x77605)))
% 179.72/179.59 [7761]~P83(x77611)+~P101(f323(f323(f237(x77611),x77613),x77615))+~P101(f323(f323(f238(x77611),x77612),x77614))+P101(f323(f323(f238(x77611),f323(f323(f78(x77611),x77612),x77613)),f323(f323(f78(x77611),x77614),x77615)))
% 179.72/179.59 [7762]~P83(x77621)+~P101(f323(f323(f237(x77621),x77622),x77624))+~P101(f323(f323(f238(x77621),x77623),x77625))+P101(f323(f323(f238(x77621),f323(f323(f78(x77621),x77622),x77623)),f323(f323(f78(x77621),x77624),x77625)))
% 179.72/179.59 [7763]~P83(x77631)+~P101(f323(f323(f238(x77631),x77633),x77635))+~P101(f323(f323(f238(x77631),x77632),x77634))+P101(f323(f323(f238(x77631),f323(f323(f78(x77631),x77632),x77633)),f323(f323(f78(x77631),x77634),x77635)))
% 179.72/179.59 [7904]~P135(x79045)+E(x79041,x79042)+E(x79043,x79044)+~E(f323(f323(f78(x79045),f323(f323(f79(x79045),x79043),x79041)),f323(f323(f79(x79045),x79044),x79042)),f323(f323(f78(x79045),f323(f323(f79(x79045),x79043),x79042)),f323(f323(f79(x79045),x79044),x79041)))
% 179.72/179.59 [8102]~P103(x81024)+~P101(f323(f130(x81021),x81023))+P101(f323(f323(f325(x81021),x81022),f323(f166(x81021),x81023)))+P101(f323(f130(x81021),f323(f323(f141(x81021,x81024,x81025),x81022),x81023)))
% 179.72/179.59 [8250]~P60(x82501)+E(f323(f323(f22(x82501),f323(f323(f6(a860,x82501),x82502),f323(f293(a860,x82503),x82504))),f323(f323(f6(a860,x82501),x82502),f323(f293(a860,x82503),x82505))),f323(f323(f6(a860,x82501),x82502),f323(f293(a860,x82505),x82504)))+~P101(f323(f323(f237(a860),x82505),x82504))+~P101(f323(f323(f237(a860),x82503),x82505))
% 179.72/179.59 [8251]~P72(x82511)+E(f323(f323(f78(x82511),f323(f323(f6(a860,x82511),x82512),f323(f293(a860,x82513),x82514))),f323(f323(f6(a860,x82511),x82512),f323(f293(a860,x82514),x82515))),f323(f323(f6(a860,x82511),x82512),f323(f293(a860,x82513),x82515)))+~P101(f323(f323(f237(a860),x82514),x82515))+~P101(f323(f323(f237(a860),x82513),x82514))
% 179.72/179.59 [8579]~P63(x85792)+E(x85791,f2(x85792))+E(x85793,f2(x85792))+E(f323(f323(f281(x85792),f323(f323(f22(x85792),f323(f323(f79(x85792),x85794),x85791)),f323(f323(f79(x85792),x85795),x85793))),f323(f323(f79(x85792),x85793),x85791)),f323(f323(f22(x85792),f323(f323(f281(x85792),x85794),x85793)),f323(f323(f281(x85792),x85795),x85791)))
% 179.72/179.59 [8580]~P63(x85802)+E(x85801,f2(x85802))+E(x85803,f2(x85802))+E(f323(f323(f281(x85802),f323(f323(f78(x85802),f323(f323(f79(x85802),x85804),x85801)),f323(f323(f79(x85802),x85805),x85803))),f323(f323(f79(x85802),x85803),x85801)),f323(f323(f78(x85802),f323(f323(f281(x85802),x85804),x85803)),f323(f323(f281(x85802),x85805),x85801)))
% 179.72/179.59 [8589]~E(x85892,f323(x85893,x85891))+E(x85891,f516(x85892,x85893,x85894,x85895))+~P27(x85895,x85894,x85893,f246(f867(x85895,a855)))+~P101(f323(f323(f325(x85894),x85892),f323(f302(x85895,x85894,x85893),f246(f867(x85895,a855)))))
% 179.72/179.59 [8803]~P116(x88031)+~P101(f323(f323(f238(x88031),f323(f73(x88031),x88032)),x88034))+P101(f323(f323(f238(x88031),f323(f323(f79(x88031),f323(f73(x88031),x88032)),f323(f73(x88031),x88033))),f323(f323(f79(x88031),x88034),x88035)))+~P101(f323(f323(f238(x88031),f323(f73(x88031),x88033)),x88035))
% 179.72/179.59 [8917]~P27(x89171,x89173,x89175,x89172)+~P101(f323(f59(x89173),x89174))+P101(f323(f323(f237(a860),f323(f35(x89171),x89172)),f323(f35(x89173),x89174)))+~P101(f323(f323(f237(f867(x89173,a855)),f323(f302(x89171,x89173,x89175),x89172)),x89174))
% 179.72/179.59 [8984]~P72(x89842)+~P27(x89841,x89841,x89844,x89845)+~P101(f323(f59(x89841),x89845))+E(f323(f323(f6(x89841,x89842),f323(f71(x89841,x89842,x89841,x89843),x89844)),x89845),f323(f323(f6(x89841,x89842),x89843),f323(f302(x89841,x89841,x89844),x89845)))
% 179.72/179.59 [8985]~P68(x89852)+~P27(x89851,x89851,x89854,x89855)+~P101(f323(f59(x89851),x89855))+E(f323(f323(f9(x89851,x89852),f323(f71(x89851,x89852,x89851,x89853),x89854)),x89855),f323(f323(f9(x89851,x89852),x89853),f323(f302(x89851,x89851,x89854),x89855)))
% 179.72/179.59 [9103]~P38(x91031,x91032)+~P101(f323(f323(f325(x91031),x91033),x91034))+~P101(f323(f323(f325(x91031),x91035),x91034))+~P101(f323(f323(f325(f866(x91031,x91031)),f323(f323(f258(x91031,x91031),x91035),f731(x91032,x91031,x91034))),x91032))
% 179.72/179.59 [9140]~P27(x91402,x91403,x91405,x91401)+E(x91401,f188(f867(x91402,a855)))+E(f323(f302(x91403,x91402,f571(x91404,x91403,x91402,x91401)),x91404),x91401)+~P101(f323(f323(f237(f867(x91403,a855)),f323(f302(x91402,x91403,x91405),x91401)),x91404))
% 179.72/179.59 [9616]~P103(x96165)+~P6(x96165)+P101(f323(f323(f325(x96161),f448(x96162,x96163,x96161,x96164,x96165)),x96163))+~P101(f323(f323(f238(x96165),x96164),f323(f323(f39(x96161,x96165),x96163),x96162)))
% 179.72/179.59 [9621]~P103(x96211)+~P6(x96211)+P101(f323(f323(f238(x96211),x96212),f323(x96213,f448(x96213,x96214,x96215,x96212,x96211))))+~P101(f323(f323(f238(x96211),x96212),f323(f323(f39(x96215,x96211),x96214),x96213)))
% 179.72/179.59 [9700]~P66(x97001)+~P101(f323(f64(x97001,x97001,f79(x97001),x97002,x97003),x97005))+P101(f323(f323(f325(x97001),x97002),x97003))+P101(f323(f64(x97001,x97001,f79(x97001),x97004,f323(f323(f301(x97001),x97002),x97003)),f323(f323(f79(x97001),x97004),x97005)))
% 179.72/179.59 [9916]~P72(x99162)+~P101(f323(f59(x99161),x99165))+E(f323(f323(f6(x99161,x99162),f323(f323(f7(x99161,x99162,x99162),f323(f323(f18(x99161,x99162,f867(x99162,x99162)),f323(f323(f8(a855,f867(x99162,f867(x99162,x99162)),x99161),f96(x99162)),f323(a320,x99163))),x99164)),f2(x99162))),x99165),f2(x99162))+P101(f323(f323(f325(x99161),x99163),x99165))
% 179.72/179.59 [9917]~P68(x99172)+~P101(f323(f59(x99171),x99175))+E(f323(f323(f9(x99171,x99172),f323(f323(f7(x99171,x99172,x99172),f323(f323(f18(x99171,x99172,f867(x99172,x99172)),f323(f323(f8(a855,f867(x99172,f867(x99172,x99172)),x99171),f96(x99172)),f323(a320,x99173))),x99174)),f76(x99172))),x99175),f76(x99172))+P101(f323(f323(f325(x99171),x99173),x99175))
% 179.72/179.59 [9918]~P72(x99182)+~P101(f323(f59(x99181),x99185))+E(f323(f323(f6(x99181,x99182),f323(f323(f7(x99181,x99182,x99182),f323(f323(f18(x99181,x99182,f867(x99182,x99182)),f323(f323(f8(a855,f867(x99182,f867(x99182,x99182)),x99181),f96(x99182)),f323(a320,x99183))),x99184)),f2(x99182))),x99185),f323(x99184,x99183))+~P101(f323(f323(f325(x99181),x99183),x99185))
% 179.72/179.59 [9919]~P68(x99192)+~P101(f323(f59(x99191),x99195))+E(f323(f323(f9(x99191,x99192),f323(f323(f7(x99191,x99192,x99192),f323(f323(f18(x99191,x99192,f867(x99192,x99192)),f323(f323(f8(a855,f867(x99192,f867(x99192,x99192)),x99191),f96(x99192)),f323(a320,x99193))),x99194)),f76(x99192))),x99195),f323(x99194,x99193))+~P101(f323(f323(f325(x99191),x99193),x99195))
% 179.72/179.59 [9974]~P72(x99742)+~P101(f323(f59(x99741),x99745))+E(f323(f323(f6(x99741,x99742),f323(f323(f7(x99741,x99742,x99742),f323(f323(f18(x99741,x99742,f867(x99742,x99742)),f323(f323(f8(a855,f867(x99742,f867(x99742,x99742)),x99741),f96(x99742)),f323(f323(f7(x99741,x99741,a855),a320),x99743))),x99744)),f2(x99742))),x99745),f2(x99742))+P101(f323(f323(f325(x99741),x99743),x99745))
% 179.72/179.59 [9975]~P68(x99752)+~P101(f323(f59(x99751),x99755))+E(f323(f323(f9(x99751,x99752),f323(f323(f7(x99751,x99752,x99752),f323(f323(f18(x99751,x99752,f867(x99752,x99752)),f323(f323(f8(a855,f867(x99752,f867(x99752,x99752)),x99751),f96(x99752)),f323(f323(f7(x99751,x99751,a855),a320),x99753))),x99754)),f76(x99752))),x99755),f76(x99752))+P101(f323(f323(f325(x99751),x99753),x99755))
% 179.72/179.59 [9977]~P72(x99772)+~P101(f323(f59(x99771),x99775))+E(f323(f323(f6(x99771,x99772),f323(f323(f7(x99771,x99772,x99772),f323(f323(f18(x99771,x99772,f867(x99772,x99772)),f323(f323(f8(a855,f867(x99772,f867(x99772,x99772)),x99771),f96(x99772)),f323(f323(f7(x99771,x99771,a855),a320),x99773))),x99774)),f2(x99772))),x99775),f323(x99774,x99773))+~P101(f323(f323(f325(x99771),x99773),x99775))
% 179.72/179.59 [9978]~P68(x99782)+~P101(f323(f59(x99781),x99785))+E(f323(f323(f9(x99781,x99782),f323(f323(f7(x99781,x99782,x99782),f323(f323(f18(x99781,x99782,f867(x99782,x99782)),f323(f323(f8(a855,f867(x99782,f867(x99782,x99782)),x99781),f96(x99782)),f323(f323(f7(x99781,x99781,a855),a320),x99783))),x99784)),f76(x99782))),x99785),f323(x99784,x99783))+~P101(f323(f323(f325(x99781),x99783),x99785))
% 179.72/179.59 [7755]~P60(x77552)+~P101(f323(f59(x77551),x77554))+E(f323(f323(f6(x77551,x77552),x77553),f323(f323(f22(f867(x77551,a855)),x77554),f323(f323(f301(x77551),x77555),f188(f867(x77551,a855))))),f323(f323(f6(x77551,x77552),x77553),x77554))+P101(f323(f323(f325(x77551),x77555),x77554))
% 179.72/179.59 [8258]~P107(x82582)+~P101(f323(f59(x82581),x82584))+E(f323(f323(f6(x82581,x82582),x82583),f323(f323(f22(f867(x82581,a855)),x82584),f323(f323(f301(x82581),x82585),f188(f867(x82581,a855))))),f323(f323(f22(x82582),f323(f323(f6(x82581,x82582),x82583),x82584)),f323(x82583,x82585)))+~P101(f323(f323(f325(x82581),x82585),x82584))
% 179.72/179.59 [8259]~P60(x82592)+~P101(f323(f59(x82591),x82594))+E(f323(f323(f6(x82591,x82592),x82593),f323(f323(f22(f867(x82591,a855)),x82594),f323(f323(f301(x82591),x82595),f188(f867(x82591,a855))))),f323(f323(f22(x82592),f323(f323(f6(x82591,x82592),x82593),x82594)),f323(x82593,x82595)))+~P101(f323(f323(f325(x82591),x82595),x82594))
% 179.72/179.59 [8291]~P60(x82911)+~P101(f323(f59(x82912),x82914))+E(f323(f323(f22(x82911),f323(f323(f6(x82912,x82911),x82913),x82914)),f323(f323(f6(x82912,x82911),x82913),x82915)),f323(f323(f6(x82912,x82911),x82913),f323(f323(f22(f867(x82912,a855)),x82914),x82915)))+~P101(f323(f323(f237(f867(x82912,a855)),x82915),x82914))
% 179.72/179.59 [8311]P101(f323(f59(x83111),f323(x83112,x83113)))+~P101(f323(f59(x83114),x83115))+~P101(f323(f323(f325(x83114),x83113),x83115))+~P101(f323(f59(x83111),f323(f323(f39(x83114,f867(x83111,a855)),x83115),x83112)))
% 179.72/179.59 [8764]~P9(x87641,x87645,x87644)+~E(f323(f277(x87641,x87641,x87644),f323(f323(f301(x87641),x87642),f188(f867(x87641,a855)))),f323(f277(x87641,x87641,x87644),f323(f323(f301(x87641),x87643),f188(f867(x87641,a855)))))+~P101(f323(f323(f325(x87641),x87643),x87645))+P101(f323(f323(f325(f866(x87641,x87641)),f323(f323(f258(x87641,x87641),x87642),x87643)),x87644))
% 179.72/179.59 [9061]~P101(f323(x90611,x90615))+P101(f323(x90611,f387(x90611,x90612,x90613,x90614)))+P101(f323(x90611,f378(x90611,x90612,x90613,x90614)))+~P101(f323(f323(f325(x90614),x90615),f323(f323(f110(f867(x90614,a855)),x90613),x90612)))
% 179.72/179.59 [9242]~P101(f323(x92421,x92425))+P101(f323(x92421,f378(x92421,x92422,x92423,x92424)))+P101(f323(f323(f325(x92424),f387(x92421,x92422,x92423,x92424)),x92422))+~P101(f323(f323(f325(x92424),x92425),f323(f323(f110(f867(x92424,a855)),x92423),x92422)))
% 179.72/179.59 [9243]~P101(f323(x92431,x92435))+P101(f323(x92431,f387(x92431,x92432,x92433,x92434)))+P101(f323(f323(f325(x92434),f378(x92431,x92432,x92433,x92434)),x92433))+~P101(f323(f323(f325(x92434),x92435),f323(f323(f110(f867(x92434,a855)),x92433),x92432)))
% 179.72/179.59 [9247]P101(f323(x92471,x92472))+~P101(f323(x92471,f429(x92471,x92473,x92474,x92475)))+~P101(f323(x92471,f418(x92471,x92473,x92474,x92475)))+~P101(f323(f323(f325(x92475),x92472),f323(f323(f110(f867(x92475,a855)),x92474),x92473)))
% 179.72/179.59 [9290]E(x92901,x92902)+~P101(f323(f323(f325(f866(x92903,x92903)),f323(f323(f258(x92903,x92903),x92901),x92902)),f299(x92903,x92905)))+P101(f323(f323(f325(x92903),x92901),x92904))+~P101(f323(f323(f237(f867(f866(x92903,x92903),a855)),x92905),f323(f323(f260(x92903,x92903),x92904),f323(f16(f867(x92903,a855),x92903),x92904))))
% 179.72/179.59 [9308]P101(f323(x93081,x93082))+~P101(f323(x93081,f418(x93081,x93084,x93085,x93083)))+P101(f323(f323(f325(x93083),f429(x93081,x93084,x93085,x93083)),x93084))+~P101(f323(f323(f325(x93083),x93082),f323(f323(f110(f867(x93083,a855)),x93085),x93084)))
% 179.72/179.59 [9309]P101(f323(x93091,x93092))+~P101(f323(x93091,f429(x93091,x93094,x93095,x93093)))+P101(f323(f323(f325(x93093),f418(x93091,x93094,x93095,x93093)),x93095))+~P101(f323(f323(f325(x93093),x93092),f323(f323(f110(f867(x93093,a855)),x93095),x93094)))
% 179.72/179.59 [9370]P101(f323(x93701,x93702))+P101(f323(f323(f325(x93703),f429(x93701,x93704,x93705,x93703)),x93704))+P101(f323(f323(f325(x93703),f418(x93701,x93704,x93705,x93703)),x93705))+~P101(f323(f323(f325(x93703),x93702),f323(f323(f110(f867(x93703,a855)),x93705),x93704)))
% 179.72/179.59 [9372]~P101(f323(x93722,x93725))+P101(f323(f323(f325(x93721),f387(x93722,x93723,x93724,x93721)),x93723))+P101(f323(f323(f325(x93721),f378(x93722,x93723,x93724,x93721)),x93724))+~P101(f323(f323(f325(x93721),x93725),f323(f323(f110(f867(x93721,a855)),x93724),x93723)))
% 179.72/179.59 [9521]~P9(x95211,x95215,x95214)+~P101(f323(f323(f325(x95211),x95213),x95215))+P101(f323(f323(f325(f866(x95211,x95211)),f323(f323(f258(x95211,x95211),x95212),x95213)),x95214))+~P101(f323(f323(f237(f867(x95211,a855)),f323(f277(x95211,x95211,x95214),f323(f323(f301(x95211),x95213),f188(f867(x95211,a855))))),f323(f277(x95211,x95211,x95214),f323(f323(f301(x95211),x95212),f188(f867(x95211,a855))))))
% 179.72/179.59 [9647]~P103(x96475)+~P6(x96475)+P101(f323(f323(f325(x96471),f636(x96472,x96473,x96474,x96471,x96475)),x96474))+~P101(f323(f323(f238(x96475),f323(f323(f40(x96471,x96475),x96474),x96473)),x96472))
% 179.72/179.59 [9680]~P81(x96805)+~P78(x96805)+P101(f323(f323(f325(x96801),f557(x96802,x96803,x96804,x96801,x96805)),f323(f166(x96801),x96804)))+P101(f323(f323(f237(x96805),f323(f159(x96805),f323(f323(f147(x96801,x96805),x96803),x96804))),f323(f159(x96805),f323(f323(f147(x96801,x96805),x96802),x96804))))
% 179.72/179.59 [9797]~P103(x97971)+~P6(x97971)+P101(f323(f323(f238(x97971),f323(x97972,f636(x97973,x97972,x97974,x97975,x97971))),x97973))+~P101(f323(f323(f238(x97971),f323(f323(f40(x97975,x97971),x97974),x97972)),x97973))
% 179.72/179.59 [9934]~P81(x99341)+~P78(x99341)+~P101(f323(f323(f237(x99341),f323(x99343,f557(x99345,x99343,x99344,x99342,x99341))),f323(x99345,f557(x99345,x99343,x99344,x99342,x99341))))+P101(f323(f323(f237(x99341),f323(f159(x99341),f323(f323(f147(x99342,x99341),x99343),x99344))),f323(f159(x99341),f323(f323(f147(x99342,x99341),x99345),x99344))))
% 179.72/179.59 [8602]~P72(x86021)+~P101(f323(f59(x86024),x86025))+~P101(f323(f323(f325(x86024),x86023),x86025))+E(f323(f323(f78(x86021),f323(x86022,x86023)),f323(f323(f6(x86024,x86021),x86022),f323(f323(f22(f867(x86024,a855)),x86025),f323(f323(f301(x86024),x86023),f188(f867(x86024,a855)))))),f323(f323(f6(x86024,x86021),x86022),x86025))
% 179.72/179.59 [8603]~P68(x86031)+~P101(f323(f59(x86034),x86035))+~P101(f323(f323(f325(x86034),x86033),x86035))+E(f323(f323(f79(x86031),f323(x86032,x86033)),f323(f323(f9(x86034,x86031),x86032),f323(f323(f22(f867(x86034,a855)),x86035),f323(f323(f301(x86034),x86033),f188(f867(x86034,a855)))))),f323(f323(f9(x86034,x86031),x86032),x86035))
% 179.72/179.59 [8663]~P20(x86631,x86634,x86635)+~P101(f323(f59(x86631),x86632))+E(f323(f323(f22(f867(x86631,a855)),x86632),f323(f323(f301(x86631),x86633),f188(f867(x86631,a855)))),f188(f867(x86631,a855)))+E(f323(f323(x86634,x86633),f323(x86635,f323(f323(f22(f867(x86631,a855)),x86632),f323(f323(f301(x86631),x86633),f188(f867(x86631,a855)))))),f323(x86635,f323(f323(f301(x86631),x86633),x86632)))
% 179.72/179.59 [9041]~P68(x90411)+~P101(f323(f59(x90412),x90415))+~P101(f323(f59(x90412),x90414))+E(f323(f323(f79(x90411),f323(f323(f9(x90412,x90411),x90413),f323(f323(f110(f867(x90412,a855)),x90414),x90415))),f323(f323(f9(x90412,x90411),x90413),f323(f323(f101(f867(x90412,a855)),x90414),x90415))),f323(f323(f79(x90411),f323(f323(f9(x90412,x90411),x90413),x90414)),f323(f323(f9(x90412,x90411),x90413),x90415)))
% 179.72/179.59 [9042]~P72(x90421)+~P101(f323(f59(x90422),x90425))+~P101(f323(f59(x90422),x90424))+E(f323(f323(f78(x90421),f323(f323(f6(x90422,x90421),x90423),f323(f323(f110(f867(x90422,a855)),x90424),x90425))),f323(f323(f6(x90422,x90421),x90423),f323(f323(f101(f867(x90422,a855)),x90424),x90425))),f323(f323(f78(x90421),f323(f323(f6(x90422,x90421),x90423),x90424)),f323(f323(f6(x90422,x90421),x90423),x90425)))
% 179.72/179.59 [9180]~P60(x91801)+~P101(f323(f59(x91802),x91805))+~P101(f323(f59(x91802),x91804))+E(f323(f323(f22(x91801),f323(f323(f78(x91801),f323(f323(f6(x91802,x91801),x91803),x91804)),f323(f323(f6(x91802,x91801),x91803),x91805))),f323(f323(f6(x91802,x91801),x91803),f323(f323(f101(f867(x91802,a855)),x91804),x91805))),f323(f323(f6(x91802,x91801),x91803),f323(f323(f110(f867(x91802,a855)),x91804),x91805)))
% 179.72/179.59 [9382]~P27(x93821,x93822,x93823,x93825)+~P27(x93821,x93822,x93823,x93824)+P27(x93821,x93822,x93823,f323(f323(f110(f867(x93821,a855)),x93824),x93825))+~E(f323(f323(f101(f867(x93822,a855)),f323(f302(x93821,x93822,x93823),f323(f323(f22(f867(x93821,a855)),x93824),x93825))),f323(f302(x93821,x93822,x93823),f323(f323(f22(f867(x93821,a855)),x93825),x93824))),f188(f867(x93822,a855)))
% 179.72/179.59 [9496]E(x94961,f2(a1))+~P101(f323(f323(f238(a1),f2(a1)),x94963))+~P101(f323(f46(x94962,x94961),f323(f323(f258(a1,a1),x94964),x94965)))+P101(f323(f46(x94962,f323(f323(f79(a1),x94961),x94963)),f323(f323(f258(a1,a1),f323(f323(f36(a1),x94964),x94963)),f323(f323(f78(a1),f323(f323(f79(a1),x94961),f42(a1,x94964,x94963))),x94965))))
% 179.72/179.59 [9504]~P101(f323(f323(f238(a860),f2(a860)),x95043))+~P101(f323(f323(f238(a860),f2(a860)),x95042))+~P101(f323(f45(x95041,x95042),f323(f323(f258(a860,a860),x95044),x95045)))+P101(f323(f45(x95041,f323(f323(f79(a860),x95042),x95043)),f323(f323(f258(a860,a860),f323(f323(f36(a860),x95044),x95043)),f323(f323(f78(a860),f323(f323(f79(a860),x95042),f42(a860,x95044,x95043))),x95045))))
% 179.72/179.59 [9555]~P68(x95551)+~P101(f323(f59(x95552),x95555))+~P101(f323(f59(x95552),x95554))+E(f323(f323(f79(x95551),f323(f323(f323(f63(x95551,x95552,f79(x95551)),x95553),f76(x95551)),f323(f323(f110(f867(x95552,a855)),x95554),x95555))),f323(f323(f323(f63(x95551,x95552,f79(x95551)),x95553),f76(x95551)),f323(f323(f101(f867(x95552,a855)),x95554),x95555))),f323(f323(f79(x95551),f323(f323(f323(f63(x95551,x95552,f79(x95551)),x95553),f76(x95551)),x95554)),f323(f323(f323(f63(x95551,x95552,f79(x95551)),x95553),f76(x95551)),x95555)))
% 179.72/179.59 [9557]~E(f323(f323(f169(x95571),x95575),x95572),f323(f323(f169(x95571),x95575),x95573))+P101(f323(f323(f325(f866(f861(x95571),f861(x95571))),f323(f323(f258(f861(x95571),f861(x95571)),x95572),x95573)),f140(x95571,x95574)))+~P101(f323(f323(f238(a860),x95575),f323(f323(f235(a860),f323(f189(f861(x95571)),x95572)),f323(f189(f861(x95571)),x95573))))+~P101(f323(f323(f325(f866(x95571,x95571)),f323(f323(f258(x95571,x95571),f323(f323(f158(x95571),x95572),x95575)),f323(f323(f158(x95571),x95573),x95575))),x95574))
% 179.72/179.59 [9668]~P81(x96685)+~P140(x96685)+P101(f323(f323(f325(x96681),f375(x96682,x96683,x96684,x96681,x96685)),x96684))+P101(f323(f323(f237(x96685),f323(f323(f6(x96681,x96685),x96683),x96684)),f323(f323(f79(x96685),f323(f100(x96685),f323(f35(x96681),x96684))),x96682)))
% 179.72/179.59 [9862]~P81(x98621)+~P140(x98621)+~P101(f323(f323(f237(x98621),f323(x98623,f375(x98625,x98623,x98624,x98622,x98621))),x98625))+P101(f323(f323(f237(x98621),f323(f323(f6(x98622,x98621),x98623),x98624)),f323(f323(f79(x98621),f323(f100(x98621),f323(f35(x98622),x98624))),x98625)))
% 179.72/179.59 [8632]E(f323(f323(f121(x86321),x86322),x86323),f323(f323(f121(x86321),x86324),x86325))+~E(f323(f323(f169(x86321),f323(f189(f861(x86321)),x86322)),x86324),x86322)+~E(f323(f323(f121(x86321),f323(f323(f131(x86321),f323(f189(f861(x86321)),x86322)),x86324)),x86325),x86323)+P101(f323(f323(f237(a860),f323(f189(f861(x86321)),x86324)),f323(f189(f861(x86321)),x86322)))
% 179.72/179.59 [8763]E(f323(f323(f121(x87631),x87632),x87633),f323(f323(f121(x87631),x87634),x87635))+~E(f323(f323(f169(x87631),f323(f189(f861(x87631)),x87632)),x87634),x87632)+~E(x87633,f323(f323(f121(x87631),f323(f323(f131(x87631),f323(f189(f861(x87631)),x87632)),x87634)),x87635))+~P101(f323(f323(f237(a860),f323(f189(f861(x87631)),x87632)),f323(f189(f861(x87631)),x87634)))
% 179.72/179.59 [9995]~P101(f323(x99955,x99954))+~P101(f323(f59(x99952),f323(f243(x99952),x99955)))+P101(f323(f59(x99951),f323(f243(x99951),f323(f323(f7(x99951,x99952,a855),x99953),x99954))))+~P101(f323(f59(x99951),f323(f243(x99951),f323(f323(f8(f867(x99952,a855),a855,x99951),f85(x99952)),f323(f323(f8(f867(x99952,a855),f867(x99952,a855),x99951),f323(f18(x99952,a855,a855),f323(f323(f8(a855,f867(a855,a855),x99952),a321),x99955))),x99953)))))
% 179.72/179.59 [8418]~P21(x84185,x84181,x84186,x84182)+E(f323(f71(x84181,x84181,x84181,f323(x84182,x84183)),f323(x84182,x84184)),f323(f71(x84181,x84181,x84181,f323(x84182,x84184)),f323(x84182,x84183)))+~P101(f323(f59(x84185),x84184))+~P101(f323(f59(x84185),x84183))
% 179.72/179.59 [7811]~P27(x78111,x78112,x78114,x78113)+~E(f323(x78114,x78116),x78115)+E(f323(f75(x78111,x78112,x78113,x78114),x78115),x78116)+~P101(f323(f323(f325(x78111),x78116),x78113))
% 179.72/179.59 [7812]~P27(x78121,x78122,x78124,x78123)+~E(f323(x78124,x78126),x78125)+E(f323(f91(x78121,x78122,x78123,x78124),x78125),x78126)+~P101(f323(f323(f325(x78121),x78126),x78123))
% 179.72/179.59 [8008]~P22(x80086,x80081,x80084,x80082)+E(f323(f71(x80081,x80081,x80081,f323(x80082,x80083)),f323(x80084,x80085)),f323(x80082,x80083))+~P101(f323(f59(x80086),x80083))+~P101(f323(f323(f325(x80086),x80085),x80083))
% 179.72/179.59 [9130]E(x91301,x91302)+~E(f323(f91(x91303,x91304,x91305,x91306),x91301),f323(f91(x91303,x91304,x91305,x91306),x91302))+~P101(f323(f323(f325(x91304),x91302),f323(f302(x91303,x91304,x91306),x91305)))+~P101(f323(f323(f325(x91304),x91301),f323(f302(x91303,x91304,x91306),x91305)))
% 179.72/179.59 [9227]~P21(x92273,x92271,x92276,x92272)+E(f323(f71(x92271,x92271,x92271,f323(x92272,f323(f323(f22(f867(x92273,a855)),x92274),f323(f323(f301(x92273),x92275),f188(f867(x92273,a855)))))),f323(x92276,x92275)),f323(x92272,x92274))+~P101(f323(f59(x92273),x92274))+~P101(f323(f323(f325(x92273),x92275),x92274))
% 179.72/179.59 [6900]~P58(x69001)+~E(f42(x69001,x69003,x69004),f42(x69001,x69006,x69004))+~E(f42(x69001,x69002,x69004),f42(x69001,x69005,x69004))+E(f42(x69001,f323(f323(f22(x69001),x69002),x69003),x69004),f42(x69001,f323(f323(f22(x69001),x69005),x69006),x69004))
% 179.72/179.59 [6901]~P57(x69011)+~E(f42(x69011,x69013,x69014),f42(x69011,x69016,x69014))+~E(f42(x69011,x69012,x69014),f42(x69011,x69015,x69014))+E(f42(x69011,f323(f323(f79(x69011),x69012),x69013),x69014),f42(x69011,f323(f323(f79(x69011),x69015),x69016),x69014))
% 179.72/179.59 [6902]~P57(x69021)+~E(f42(x69021,x69023,x69024),f42(x69021,x69026,x69024))+~E(f42(x69021,x69022,x69024),f42(x69021,x69025,x69024))+E(f42(x69021,f323(f323(f78(x69021),x69022),x69023),x69024),f42(x69021,f323(f323(f78(x69021),x69025),x69026),x69024))
% 179.72/179.59 [7707]~P18(x77071,x77072,x77073)+~P101(f323(f59(x77071),x77076))+E(f323(f323(f62(x77071,x77072,x77073),x77074),f323(f323(f301(x77071),x77075),x77076)),f323(f323(f62(x77071,x77072,x77073),f323(f323(x77073,x77075),x77074)),x77076))+P101(f323(f323(f325(x77071),x77075),x77076))
% 179.72/179.59 [7769]~P6(x77691)+P101(f323(f323(f237(x77691),x77692),f323(x77693,x77694)))+~P101(f323(f323(f325(x77695),x77694),x77696))+~P101(f323(f323(f237(x77691),x77692),f323(f323(f40(x77695,x77691),x77696),x77693)))
% 179.72/179.59 [7930]~P18(x79301,x79302,x79303)+~P101(f323(f59(x79301),x79306))+E(f323(f323(f62(x79301,x79302,x79303),x79304),f323(f323(f301(x79301),x79305),x79306)),f323(f323(x79303,x79305),f323(f323(f62(x79301,x79302,x79303),x79304),x79306)))+P101(f323(f323(f325(x79301),x79305),x79306))
% 179.72/179.59 [8023]~P103(x80233)+~P101(f323(x80232,x80235))+~P16(x80233,f323(f323(f147(x80231,x80233),x80234),x80236))+E(f323(f129(x80231,x80232),f323(f323(f141(x80231,x80233,x80234),x80235),x80236)),f323(f323(f141(x80231,x80233,x80234),x80235),f323(f129(x80231,x80232),x80236)))
% 179.72/179.59 [8044]E(x80441,x80442)+E(x80443,f2(a1))+~P101(f323(f46(x80444,x80443),f323(f323(f258(a1,a1),x80445),x80442)))+~P101(f323(f46(x80444,x80443),f323(f323(f258(a1,a1),x80446),x80441)))
% 179.72/179.59 [8045]E(x80451,x80452)+E(x80453,f2(a1))+~P101(f323(f46(x80454,x80453),f323(f323(f258(a1,a1),x80452),x80455)))+~P101(f323(f46(x80454,x80453),f323(f323(f258(a1,a1),x80451),x80456)))
% 179.72/179.59 [8065]~P21(x80652,x80655,x80656,x80651)+~P101(f323(f59(x80652),x80654))+E(f323(x80651,f323(f323(f301(x80652),x80653),x80654)),f323(f71(x80655,x80655,x80655,f323(x80651,x80654)),f323(x80656,x80653)))+P101(f323(f323(f325(x80652),x80653),x80654))
% 179.72/179.59 [8294]~P22(x82945,x82941,x82946,x82942)+E(f323(f71(x82941,x82941,x82941,f323(x82942,x82943)),f323(x82942,x82944)),f323(x82942,x82943))+~P101(f323(f59(x82945),x82943))+~P101(f323(f323(f237(f867(x82945,a855)),x82944),x82943))
% 179.72/179.59 [9427]~P27(x94271,x94272,x94274,x94273)+~P101(f323(f323(f325(x94272),x94275),f323(f302(x94271,x94272,x94274),x94273)))+P101(f323(f323(f325(x94271),f323(f75(x94271,x94272,x94273,x94274),x94275)),x94276))+~P101(f323(f323(f237(f867(x94271,a855)),x94273),x94276))
% 179.72/179.59 [9808]~P72(x98082)+~E(f370(x98081,x98083,x98085,x98086,x98084,x98082),f371(x98081,x98083,x98085,x98086,x98084,x98082))+~P101(f323(f59(x98084),x98086))+E(f323(f323(f6(x98081,x98082),x98083),f323(f302(x98084,x98081,x98085),x98086)),f323(f323(f6(x98084,x98082),f323(f71(x98081,x98082,x98084,x98083),x98085)),x98086))
% 179.72/179.59 [9844]~P72(x98446)+E(f323(x98441,f370(x98442,x98443,x98441,x98444,x98445,x98446)),f323(x98441,f371(x98442,x98443,x98441,x98444,x98445,x98446)))+E(f323(f323(f6(x98442,x98446),x98443),f323(f302(x98445,x98442,x98441),x98444)),f323(f323(f6(x98445,x98446),f323(f71(x98442,x98446,x98445,x98443),x98441)),x98444))+~P101(f323(f59(x98445),x98444))
% 179.72/179.59 [9884]~P72(x98842)+~E(f323(x98843,f323(x98845,f371(x98841,x98843,x98845,x98846,x98844,x98842))),f2(x98842))+~P101(f323(f59(x98844),x98846))+E(f323(f323(f6(x98841,x98842),x98843),f323(f302(x98844,x98841,x98845),x98846)),f323(f323(f6(x98844,x98842),f323(f71(x98841,x98842,x98844,x98843),x98845)),x98846))
% 179.72/179.59 [9942]~P72(x99422)+~P101(f323(f59(x99424),x99426))+E(f323(f323(f6(x99421,x99422),x99423),f323(f302(x99424,x99421,x99425),x99426)),f323(f323(f6(x99424,x99422),f323(f71(x99421,x99422,x99424,x99423),x99425)),x99426))+P101(f323(f323(f325(x99424),f371(x99421,x99423,x99425,x99426,x99424,x99422)),x99426))
% 179.72/179.59 [9943]~P72(x99432)+~P101(f323(f59(x99434),x99436))+E(f323(f323(f6(x99431,x99432),x99433),f323(f302(x99434,x99431,x99435),x99436)),f323(f323(f6(x99434,x99432),f323(f71(x99431,x99432,x99434,x99433),x99435)),x99436))+P101(f323(f323(f325(x99434),f370(x99431,x99433,x99435,x99436,x99434,x99432)),x99436))
% 179.72/179.59 [10053]~P68(x100531)+~P101(f323(f59(x100532),x100536))+E(f323(f323(f323(f63(x100531,x100532,f79(x100531)),f323(f323(f18(x100532,f867(x100533,a855),x100531),f323(f323(f7(x100532,x100531,f867(f867(x100533,a855),x100531)),f323(f323(f8(f867(x100533,x100531),f867(x100531,f867(f867(x100533,a855),x100531)),x100532),f63(x100531,x100533,f79(x100531))),x100534)),f76(x100531))),x100535)),f76(x100531)),x100536),f323(f323(f323(f63(x100531,f866(x100532,x100533),f79(x100531)),f323(f262(x100532,x100533,x100531),x100534)),f76(x100531)),f323(f323(f260(x100532,x100533),x100536),x100535)))+P101(f323(f323(f325(x100532),f620(x100534,x100535,x100533,x100536,x100532,x100531)),x100536))
% 179.72/179.59 [10071]~P68(x100711)+~P101(f323(f59(x100712),x100716))+E(f323(f323(f323(f63(x100711,x100712,f79(x100711)),f323(f323(f18(x100712,f867(x100713,a855),x100711),f323(f323(f7(x100712,x100711,f867(f867(x100713,a855),x100711)),f323(f323(f8(f867(x100713,x100711),f867(x100711,f867(f867(x100713,a855),x100711)),x100712),f63(x100711,x100713,f79(x100711))),x100714)),f76(x100711))),x100715)),f76(x100711)),x100716),f323(f323(f323(f63(x100711,f866(x100712,x100713),f79(x100711)),f323(f262(x100712,x100713,x100711),x100714)),f76(x100711)),f323(f323(f260(x100712,x100713),x100716),x100715)))+~P101(f323(f59(x100713),f323(x100715,f620(x100714,x100715,x100713,x100716,x100712,x100711))))
% 179.72/179.59 [8203]~P22(x82032,x82035,x82036,x82031)+~P101(f323(f59(x82032),x82034))+~P101(f323(f59(x82032),x82033))+E(f323(x82031,f323(f323(f110(f867(x82032,a855)),x82033),x82034)),f323(f71(x82035,x82035,x82035,f323(x82031,x82033)),f323(x82031,x82034)))
% 179.72/179.59 [8419]~P6(x84191)+P101(f323(f323(f237(x84191),f323(x84192,x84193)),x84194))+~P101(f323(f323(f325(x84195),x84193),x84196))+~P101(f323(f323(f237(x84191),f323(f323(f39(x84195,x84191),x84196),x84192)),x84194))
% 179.72/179.59 [8844]~P27(x88442,x88441,x88443,x88446)+E(f323(f323(f22(f867(x88441,a855)),f323(f302(x88442,x88441,x88443),x88444)),f323(f302(x88442,x88441,x88443),x88445)),f323(f302(x88442,x88441,x88443),f323(f323(f22(f867(x88442,a855)),x88444),x88445)))+~P101(f323(f323(f237(f867(x88442,a855)),x88445),x88446))+~P101(f323(f323(f237(f867(x88442,a855)),x88444),x88446))
% 179.72/179.59 [8845]~P27(x88452,x88451,x88453,x88456)+E(f323(f323(f101(f867(x88451,a855)),f323(f302(x88452,x88451,x88453),x88454)),f323(f302(x88452,x88451,x88453),x88455)),f323(f302(x88452,x88451,x88453),f323(f323(f101(f867(x88452,a855)),x88454),x88455)))+~P101(f323(f323(f237(f867(x88452,a855)),x88455),x88456))+~P101(f323(f323(f237(f867(x88452,a855)),x88454),x88456))
% 179.72/179.59 [9105]E(x91051,x91052)+~P51(x91053,x91054,x91055)+~P101(f323(f323(f325(f866(x91053,x91054)),f323(f323(f258(x91053,x91054),x91056),x91052)),x91055))+~P101(f323(f323(f325(f866(x91053,x91054)),f323(f323(f258(x91053,x91054),x91056),x91051)),x91055))
% 179.72/179.59 [9879]~P66(x98791)+~E(f323(x98793,f494(x98794,x98796,x98793,x98795,x98792,x98791)),f323(x98796,f494(x98794,x98796,x98793,x98795,x98792,x98791)))+~P101(f323(f59(x98792),x98795))+E(f323(f323(f323(f63(x98791,x98792,f79(x98791)),x98793),x98794),x98795),f323(f323(f323(f63(x98791,x98792,f79(x98791)),x98796),x98794),x98795))
% 179.72/179.59 [9940]~P66(x99401)+~P101(f323(f59(x99402),x99405))+E(f323(f323(f323(f63(x99401,x99402,f79(x99401)),x99403),x99404),x99405),f323(f323(f323(f63(x99401,x99402,f79(x99401)),x99406),x99404),x99405))+P101(f323(f323(f325(x99402),f494(x99404,x99403,x99406,x99405,x99402,x99401)),x99405))
% 179.72/179.59 [8646]~P66(x86461)+~P101(f323(f59(x86462),x86466))+P101(f323(f323(f325(x86462),x86465),x86466))+E(f323(f323(f323(f63(x86461,x86462,f79(x86461)),x86463),x86464),f323(f323(f301(x86462),x86465),x86466)),f323(f323(f79(x86461),f323(x86463,x86465)),f323(f323(f323(f63(x86461,x86462,f79(x86461)),x86463),x86464),x86466)))
% 179.72/179.59 [8699]~P9(x86991,x86996,x86993)+~P14(x86991,f867(x86992,a855),x86993,x86995)+~P101(f323(f323(f325(x86991),x86994),x86996))+E(f323(f323(f39(x86991,f867(x86992,a855)),f323(f277(x86991,x86991,x86993),f323(f323(f301(x86991),x86994),f188(f867(x86991,a855))))),x86995),f323(x86995,x86994))
% 179.72/179.59 [8820]~P18(x88203,x88204,x88201)+~P101(f323(f59(x88203),x88206))+~P101(f323(f323(f325(x88203),x88202),x88206))+E(f323(f323(x88201,x88202),f323(f323(f62(x88203,x88204,x88201),x88205),f323(f323(f22(f867(x88203,a855)),x88206),f323(f323(f301(x88203),x88202),f188(f867(x88203,a855)))))),f323(f323(f62(x88203,x88204,x88201),x88205),x88206))
% 179.72/179.59 [9116]~P21(x91163,x91161,x91166,x91162)+~P101(f323(f59(x91163),x91165))+~P101(f323(f59(x91163),x91164))+E(f323(f71(x91161,x91161,x91161,f323(x91162,f323(f323(f110(f867(x91163,a855)),x91164),x91165))),f323(x91162,f323(f323(f101(f867(x91163,a855)),x91164),x91165))),f323(f71(x91161,x91161,x91161,f323(x91162,x91164)),f323(x91162,x91165)))
% 179.72/179.59 [9449]~E(x94493,f323(f323(f152(x94491,x94492),x94495),x94496))+P101(f323(f323(f325(f866(f861(x94491),f861(x94491))),f323(f323(f258(f861(x94491),f861(x94491)),x94492),x94493)),f150(x94491,x94494)))+~P101(f323(f323(f238(a860),x94495),f323(f189(f861(x94491)),x94492)))+~P101(f323(f323(f325(f866(x94491,x94491)),f323(f323(f258(x94491,x94491),f323(f323(f158(x94491),x94492),x94495)),x94496)),x94494))
% 179.72/179.59 [9953]~P72(x99532)+~P101(f323(f59(x99531),x99536))+P101(f323(f323(f325(x99531),f619(x99534,x99535,x99533,x99536,x99531,x99532)),x99536))+E(f323(f323(f6(x99531,x99532),f323(f323(f18(x99531,f867(x99533,a855),x99532),f323(f323(f8(f867(x99533,x99532),f867(f867(x99533,a855),x99532),x99531),f6(x99533,x99532)),x99534)),x99535)),x99536),f323(f323(f6(f866(x99531,x99533),x99532),f323(f262(x99531,x99533,x99532),x99534)),f323(f323(f260(x99531,x99533),x99536),x99535)))
% 179.72/179.59 [9954]~P68(x99542)+~P101(f323(f59(x99541),x99546))+P101(f323(f323(f325(x99541),f616(x99544,x99545,x99543,x99546,x99541,x99542)),x99546))+E(f323(f323(f9(x99541,x99542),f323(f323(f18(x99541,f867(x99543,a855),x99542),f323(f323(f8(f867(x99543,x99542),f867(f867(x99543,a855),x99542),x99541),f9(x99543,x99542)),x99544)),x99545)),x99546),f323(f323(f9(f866(x99541,x99543),x99542),f323(f262(x99541,x99543,x99542),x99544)),f323(f323(f260(x99541,x99543),x99546),x99545)))
% 179.72/179.59 [9993]~P72(x99932)+~P101(f323(f59(x99931),x99936))+~P101(f323(f59(x99933),f323(x99935,f619(x99934,x99935,x99933,x99936,x99931,x99932))))+E(f323(f323(f6(x99931,x99932),f323(f323(f18(x99931,f867(x99933,a855),x99932),f323(f323(f8(f867(x99933,x99932),f867(f867(x99933,a855),x99932),x99931),f6(x99933,x99932)),x99934)),x99935)),x99936),f323(f323(f6(f866(x99931,x99933),x99932),f323(f262(x99931,x99933,x99932),x99934)),f323(f323(f260(x99931,x99933),x99936),x99935)))
% 179.72/179.59 [9994]~P68(x99942)+~P101(f323(f59(x99941),x99946))+~P101(f323(f59(x99943),f323(x99945,f616(x99944,x99945,x99943,x99946,x99941,x99942))))+E(f323(f323(f9(x99941,x99942),f323(f323(f18(x99941,f867(x99943,a855),x99942),f323(f323(f8(f867(x99943,x99942),f867(f867(x99943,a855),x99942),x99941),f9(x99943,x99942)),x99944)),x99945)),x99946),f323(f323(f9(f866(x99941,x99943),x99942),f323(f262(x99941,x99943,x99942),x99944)),f323(f323(f260(x99941,x99943),x99946),x99945)))
% 179.72/179.59 [9976]~P68(x99762)+~P101(f323(f59(x99761),x99766))+P101(f323(f323(f325(x99761),x99763),x99766))+E(f323(f323(f9(x99761,x99762),f323(f323(f7(x99761,x99762,x99762),f323(f323(f18(x99761,x99762,f867(x99762,x99762)),f323(f323(f8(a855,f867(x99762,f867(x99762,x99762)),x99761),f96(x99762)),f323(f323(f7(x99761,x99761,a855),a320),x99763))),x99764)),x99765)),x99766),f323(f323(f248(x99762),x99765),f323(f35(x99761),x99766)))
% 179.72/179.59 [9981]~P68(x99812)+~P101(f323(f59(x99811),x99816))+~P101(f323(f323(f325(x99811),x99813),x99816))+E(f323(f323(f9(x99811,x99812),f323(f323(f7(x99811,x99812,x99812),f323(f323(f18(x99811,x99812,f867(x99812,x99812)),f323(f323(f8(a855,f867(x99812,f867(x99812,x99812)),x99811),f96(x99812)),f323(f323(f7(x99811,x99811,a855),a320),x99813))),x99814)),x99815)),x99816),f323(f323(f79(x99812),f323(x99814,x99813)),f323(f323(f248(x99812),x99815),f323(f323(f22(a860),f323(f35(x99811),x99816)),f76(a860)))))
% 179.72/179.59 [10046]~P101(f323(f59(x100461),x100465))+~P101(f323(f59(x100462),x100463))+P101(f323(f323(f325(x100462),f372(x100466,x100464,x100463,x100462,x100465,x100461)),x100463))+E(f323(f323(f6(x100461,a860),f323(f323(f8(f867(x100462,a855),a860,x100461),f35(x100462)),f323(f323(f8(f867(x100462,a855),f867(x100462,a855),x100461),f243(x100462)),f323(f323(f8(f867(x100462,a855),f867(x100462,a855),x100461),f323(f18(x100462,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100462),a321),f323(f323(f7(x100462,f867(x100462,a855),a855),f325(x100462)),x100463)))),x100464)))),x100465),f323(f323(f79(a860),x100466),f323(f35(x100462),x100463)))
% 179.72/179.59 [10047]~P101(f323(f59(x100471),x100475))+~P101(f323(f59(x100472),x100473))+P101(f323(f323(f325(x100472),f373(x100476,x100474,x100473,x100472,x100475,x100471)),x100473))+E(f323(f323(f6(x100471,a860),f323(f323(f8(f867(x100472,a855),a860,x100471),f35(x100472)),f323(f323(f8(f867(x100472,a855),f867(x100472,a855),x100471),f243(x100472)),f323(f323(f8(f867(x100472,a855),f867(x100472,a855),x100471),f323(f18(x100472,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100472),a321),f323(f323(f7(x100472,f867(x100472,a855),a855),f325(x100472)),x100473)))),x100474)))),x100475),f323(f323(f6(x100472,a860),x100476),x100473))
% 179.72/179.59 [10078]~P101(f323(f59(x100782),x100783))+~P101(f323(f59(x100781),x100785))+~E(f323(f35(x100781),f323(f243(x100781),f323(f323(f18(x100781,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100781),a321),f323(f323(f7(x100781,f867(x100781,a855),a855),f325(x100781)),x100785))),f323(f323(f7(x100781,x100782,a855),x100784),f372(x100786,x100784,x100783,x100782,x100785,x100781))))),x100786)+E(f323(f323(f6(x100781,a860),f323(f323(f8(f867(x100782,a855),a860,x100781),f35(x100782)),f323(f323(f8(f867(x100782,a855),f867(x100782,a855),x100781),f243(x100782)),f323(f323(f8(f867(x100782,a855),f867(x100782,a855),x100781),f323(f18(x100782,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100782),a321),f323(f323(f7(x100782,f867(x100782,a855),a855),f325(x100782)),x100783)))),x100784)))),x100785),f323(f323(f79(a860),x100786),f323(f35(x100782),x100783)))
% 179.72/179.59 [10080]~P101(f323(f59(x100802),x100803))+~P101(f323(f59(x100801),x100805))+~E(f323(f35(x100801),f323(f243(x100801),f323(f323(f18(x100801,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100801),a321),f323(f323(f7(x100801,f867(x100801,a855),a855),f325(x100801)),x100805))),f323(f323(f7(x100801,x100802,a855),x100804),f373(x100806,x100804,x100803,x100802,x100805,x100801))))),f323(x100806,f373(x100806,x100804,x100803,x100802,x100805,x100801)))+E(f323(f323(f6(x100801,a860),f323(f323(f8(f867(x100802,a855),a860,x100801),f35(x100802)),f323(f323(f8(f867(x100802,a855),f867(x100802,a855),x100801),f243(x100802)),f323(f323(f8(f867(x100802,a855),f867(x100802,a855),x100801),f323(f18(x100802,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100802),a321),f323(f323(f7(x100802,f867(x100802,a855),a855),f325(x100802)),x100803)))),x100804)))),x100805),f323(f323(f6(x100802,a860),x100806),x100803))
% 179.72/179.59 [9735]E(x97351,x97352)+~P18(x97353,x97354,x97355)+~P101(f323(f64(x97353,x97354,x97355,x97356,x97357),x97352))+~P101(f323(f64(x97353,x97354,x97355,x97356,x97357),x97351))
% 179.72/179.59 [9525]P101(f323(x95251,x95252))+~P101(f323(f323(f325(x95257),x95252),f323(x95256,x95254)))+~P101(f323(x95251,f445(x95251,x95256,x95255,x95253,x95257)))+~P101(f323(f323(f325(x95253),x95254),x95255))
% 179.72/179.59 [9968]~P18(x99687,x99686,x99681)+E(f323(f323(x99681,x99682),f760(x99682,x99683,x99684,x99685,x99681,x99686,x99687)),x99683)+~P101(f323(f64(x99687,x99686,x99681,x99685,x99684),x99683))+~P101(f323(f323(f325(x99687),x99682),x99684))
% 179.72/179.59 [10032]~P18(x100321,x100322,x100323)+~P101(f323(f64(x100321,x100322,x100323,x100324,x100325),x100327))+P101(f323(f64(x100321,x100322,x100323,x100324,f323(f323(f22(f867(x100321,a855)),x100325),f323(f323(f301(x100321),x100326),f188(f867(x100321,a855))))),f760(x100326,x100327,x100325,x100324,x100323,x100322,x100321)))+~P101(f323(f323(f325(x100321),x100326),x100325))
% 179.72/179.59 [9187]P28(x91871,x91872,x91873,x91874,x91875)+~P28(x91871,x91872,x91873,x91876,x91877)+~E(f323(f302(x91871,x91872,x91873),x91874),x91875)+~P101(f323(f323(f237(f867(x91871,a855)),x91874),x91876))
% 179.72/179.59 [9417]~P28(x94171,x94172,x94173,x94175,x94177)+~P28(x94171,x94172,x94173,x94174,x94176)+P28(x94171,x94172,x94173,f323(f323(f110(f867(x94171,a855)),x94174),x94175),f323(f323(f110(f867(x94172,a855)),x94176),x94177))+~E(f323(f323(f101(f867(x94172,a855)),x94176),x94177),f188(f867(x94172,a855)))
% 179.72/179.59 [9423]~P66(x94231)+~P27(x94235,x94232,x94236,x94237)+~P101(f323(f59(x94235),x94237))+E(f323(f323(f323(f63(x94231,x94232,f79(x94231)),x94233),x94234),f323(f302(x94235,x94232,x94236),x94237)),f323(f323(f323(f63(x94231,x94235,f79(x94231)),f323(f71(x94232,x94231,x94235,x94233),x94236)),x94234),x94237))
% 179.72/179.59 [9549]~E(f323(f323(f301(x95491),x95495),x95496),f323(f323(f301(x95491),x95492),x95493))+~P101(f323(f64(x95491,x95491,x95494,x95492,x95493),x95497))+P101(f323(f323(f325(x95491),x95492),x95493))+P101(f323(f60(x95491,x95494,f323(f323(f301(x95491),x95495),x95496)),x95497))
% 179.72/179.59 [9633]P101(f323(x96331,x96332))+~P101(f323(f323(f325(x96333),x96332),f323(x96334,x96337)))+~P101(f323(f323(f325(x96336),x96337),x96335))+P101(f323(f323(f325(x96333),f445(x96331,x96334,x96335,x96336,x96333)),f323(f323(f39(x96336,f867(x96333,a855)),x96335),x96334)))
% 179.72/179.59 [9648]~P27(x96482,x96481,x96485,x96484)+~P27(x96481,x96483,x96486,f323(f302(x96482,x96481,x96485),x96484))+E(f323(f323(f71(x96481,x96482,x96483,f75(x96482,x96481,x96484,x96485)),f75(x96481,x96483,f323(f302(x96482,x96481,x96485),x96484),x96486)),x96487),f323(f75(x96482,x96483,x96484,f323(f71(x96481,x96483,x96482,x96486),x96485)),x96487))+~P101(f323(f323(f325(x96483),x96487),f323(f302(x96481,x96483,x96486),f323(f302(x96482,x96481,x96485),x96484))))
% 179.72/179.59 [9649]~P27(x96492,x96491,x96495,x96494)+~P27(x96491,x96493,x96496,f323(f302(x96492,x96491,x96495),x96494))+E(f323(f323(f71(x96491,x96492,x96493,f91(x96492,x96491,x96494,x96495)),f91(x96491,x96493,f323(f302(x96492,x96491,x96495),x96494),x96496)),x96497),f323(f91(x96492,x96493,x96494,f323(f71(x96491,x96493,x96492,x96496),x96495)),x96497))+~P101(f323(f323(f325(x96493),x96497),f323(f302(x96491,x96493,x96496),f323(f302(x96492,x96491,x96495),x96494))))
% 179.72/179.59 [9969]~P18(x99697,x99696,x99691)+E(f323(f323(x99691,x99692),f761(x99693,x99694,x99692,x99695,x99691,x99696,x99697)),x99693)+P101(f323(f323(f325(x99697),x99692),x99694))+~P101(f323(f64(x99697,x99696,x99691,x99695,f323(f323(f301(x99697),x99692),x99694)),x99693))
% 179.72/179.59 [10031]~P18(x100311,x100314,x100315)+P101(f323(f64(x100311,x100314,x100315,x100316,x100313),f761(x100317,x100313,x100312,x100316,x100315,x100314,x100311)))+P101(f323(f323(f325(x100311),x100312),x100313))+~P101(f323(f64(x100311,x100314,x100315,x100316,f323(f323(f301(x100311),x100312),x100313)),x100317))
% 179.72/179.59 [9717]E(x97171,f2(a1))+~P101(f323(f46(x97173,x97171),f323(f323(f258(a1,a1),x97175),x97177)))+~P101(f323(f46(x97172,x97171),f323(f323(f258(a1,a1),x97174),x97176)))+P101(f323(f46(f323(f323(f78(a1),x97172),x97173),x97171),f323(f323(f258(a1,a1),f323(f323(f78(a1),f323(f323(f78(a1),x97174),x97175)),f323(f323(f36(a1),f323(f323(f78(a1),x97176),x97177)),x97171))),f42(a1,f323(f323(f78(a1),x97176),x97177),x97171))))
% 179.72/179.59 [9719]~P101(f323(f323(f238(a860),f2(a860)),x97193))+~P101(f323(f45(x97192,x97193),f323(f323(f258(a860,a860),x97195),x97197)))+~P101(f323(f45(x97191,x97193),f323(f323(f258(a860,a860),x97194),x97196)))+P101(f323(f45(f323(f323(f78(a860),x97191),x97192),x97193),f323(f323(f258(a860,a860),f323(f323(f78(a860),f323(f323(f78(a860),x97194),x97195)),f323(f323(f36(a860),f323(f323(f78(a860),x97196),x97197)),x97193))),f42(a860,f323(f323(f78(a860),x97196),x97197),x97193))))
% 179.72/179.59 [10077]~P72(x100772)+~P101(f323(f59(x100773),x100775))+~P101(f323(f59(x100771),x100777))+E(f323(f323(f6(x100771,x100772),f323(f323(f18(x100771,f867(x100773,a855),x100772),f323(f323(f8(f867(x100773,x100772),f867(f867(x100773,a855),x100772),x100771),f6(x100773,x100772)),x100774)),f323(f323(f8(f867(x100773,a855),f867(x100773,a855),x100771),f243(x100773)),f323(f323(f8(f867(x100773,a855),f867(x100773,a855),x100771),f323(f18(x100773,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100773),a321),f323(f323(f7(x100773,f867(x100773,a855),a855),f325(x100773)),x100775)))),x100776)))),x100777),f323(f323(f6(x100773,x100772),f323(f323(f18(x100773,f867(x100771,a855),x100772),f323(f323(f8(f867(x100771,x100772),f867(f867(x100771,a855),x100772),x100773),f6(x100771,x100772)),f323(f7(x100771,x100773,x100772),x100774))),f323(f323(f8(f867(x100771,a855),f867(x100771,a855),x100773),f243(x100771)),f323(f323(f8(f867(x100771,a855),f867(x100771,a855),x100773),f323(f18(x100771,a855,a855),f323(f323(f8(a855,f867(a855,a855),x100771),a321),f323(f323(f7(x100771,f867(x100771,a855),a855),f325(x100771)),x100777)))),f323(f7(x100771,x100773,a855),x100776))))),x100775))
% 179.72/179.59 [9586]~P24(x95867,x95866,x95861,x95868,x95862,x95864)+E(f323(f323(x95861,f323(x95862,x95863)),f323(x95864,x95865)),f323(x95864,x95865))+~P101(f323(f59(x95866),x95865))+~P101(f323(f323(f325(x95866),x95863),x95865))
% 179.72/179.59 [9590]~P15(x95906,x95901,x95902,x95908,x95903,x95904)+~P9(x95906,x95907,x95908)+P14(x95901,x95902,x95903,f323(x95904,x95905))+~P101(f323(f323(f325(x95906),x95905),x95907))
% 179.72/179.59 [9210]~P21(x92107,x92101,x92108,x92103)+~P101(f323(f59(x92107),x92105))+~P101(f323(f59(x92107),x92104))+E(f323(f71(x92101,x92101,x92102,f323(x92103,x92104)),f323(f71(x92101,x92101,x92102,f323(x92103,x92105)),x92106)),f323(f71(x92101,x92101,x92102,f323(x92103,x92105)),f323(f71(x92101,x92101,x92102,f323(x92103,x92104)),x92106)))
% 179.72/179.59 [9219]~P35(x92191,x92192,x92193,x92194,x92197)+P35(x92191,x92192,x92193,f323(f323(f152(x92191,x92194),x92195),x92196),f323(f323(f152(x92192,x92197),x92195),x92198))+~P101(f323(f323(x92193,x92196),x92198))+~P101(f323(f323(f238(a860),x92195),f323(f189(f861(x92191)),x92194)))
% 179.72/179.59 [9220]~P35(x92201,x92202,x92203,x92204,x92207)+P35(x92201,x92202,x92203,f323(f323(f152(x92201,x92204),x92205),x92206),f323(f323(f152(x92202,x92207),x92205),x92208))+~P101(f323(f323(x92203,x92206),x92208))+~P101(f323(f323(f238(a860),x92205),f323(f189(f861(x92202)),x92207)))
% 179.72/179.59 [9297]~P27(x92972,x92972,x92975,x92976)+~P23(x92973,x92972,x92977,x92978,x92971)+~P101(f323(f59(x92972),x92976))+E(f323(f323(x92971,f323(f71(x92972,x92973,x92972,x92974),x92975)),x92976),f323(f323(x92971,x92974),f323(f302(x92972,x92972,x92975),x92976)))
% 179.72/179.59 [9550]P28(x95501,x95502,x95503,x95504,x95505)+~P28(x95502,x95506,x95507,x95505,x95508)+~P28(x95501,x95506,f323(f71(x95502,x95506,x95501,x95507),x95503),x95504,x95508)+~P101(f323(f323(f237(f867(x95502,a855)),f323(f302(x95501,x95502,x95503),x95504)),x95505))
% 179.72/179.59 [9588]~P25(x95887,x95882,x95885,x95888,x95886,x95881)+~P101(f323(f59(x95882),x95884))+E(f323(x95881,f323(f323(f301(x95882),x95883),x95884)),f323(f323(x95885,f323(x95886,x95883)),f323(x95881,x95884)))+P101(f323(f323(f325(x95882),x95883),x95884))
% 179.72/179.59 [9599]~P24(x95996,x95995,x95991,x95997,x95998,x95992)+E(f323(f323(x95991,f323(x95992,x95993)),f323(x95992,x95994)),f323(x95992,x95994))+~P101(f323(f59(x95995),x95994))+~P101(f323(f323(f237(f867(x95995,a855)),x95993),x95994))
% 179.72/179.59 [10075]P26(x100758,x100757,f323(f323(f301(f859(x100758)),f323(f323(f323(f90(x100758),x100754),x100755),x100753)),f188(f867(f859(x100758),a855))))+~P26(x100758,x100757,f323(f323(f301(f859(x100758)),f323(f323(f323(f90(x100758),x100756),x100755),x100751)),f188(f867(f859(x100758),a855))))+~P101(f323(f323(x100756,x100752),f853(x100753,x100754,x100751,x100755,x100756,x100757,x100758)))+P101(f323(f323(x100751,x100752),f345(x100753,x100754,x100751,x100755,x100756,x100757,x100758)))
% 179.72/179.59 [9196]P101(f323(f323(f325(f866(f861(x91961),f861(x91961))),f323(f323(f258(f861(x91961),f861(x91961)),x91962),x91963)),f150(x91961,x91964)))+~E(x91963,f323(f323(f121(x91961),x91965),f323(f323(f144(x91961),x91966),x91967)))+~E(x91962,f323(f323(f121(x91961),x91965),f323(f323(f144(x91961),x91968),x91967)))+~P101(f323(f323(f325(f866(x91961,x91961)),f323(f323(f258(x91961,x91961),x91968),x91966)),x91964))
% 179.72/179.59 [9593]~P24(x95936,x95932,x95935,x95937,x95938,x95931)+~P101(f323(f59(x95932),x95934))+~P101(f323(f59(x95932),x95933))+E(f323(x95931,f323(f323(f110(f867(x95932,a855)),x95933),x95934)),f323(f323(x95935,f323(x95931,x95933)),f323(x95931,x95934)))
% 179.72/179.59 [10117]~P27(x101174,x101172,x101175,x101178)+E(f323(f323(f40(x101171,f867(x101172,a855)),x101173),f323(f323(f8(f867(x101174,a855),f867(x101172,a855),x101171),f302(x101174,x101172,x101175)),x101176)),f323(f302(x101174,x101172,x101175),f323(f323(f40(x101171,f867(x101174,a855)),x101173),x101176)))+~P101(f323(f323(f325(x101171),x101177),x101173))+P101(f323(f323(f325(x101171),f644(x101177,x101176,x101173,x101171,x101178,x101175,x101172,x101174)),x101173))
% 179.72/179.59 [10138]~P27(x101384,x101382,x101385,x101387)+E(f323(f323(f40(x101381,f867(x101382,a855)),x101383),f323(f323(f8(f867(x101384,a855),f867(x101382,a855),x101381),f302(x101384,x101382,x101385)),x101386)),f323(f302(x101384,x101382,x101385),f323(f323(f40(x101381,f867(x101384,a855)),x101383),x101386)))+~P101(f323(f323(f325(x101381),x101388),x101383))+~P101(f323(f323(f237(f867(x101384,a855)),f323(x101386,f644(x101388,x101386,x101383,x101381,x101387,x101385,x101382,x101384))),x101387))
% 179.72/179.59 [9658]~P25(x96587,x96585,x96581,x96588,x96582,x96584)+~P101(f323(f59(x96585),x96586))+~P101(f323(f323(f325(x96585),x96583),x96586))+E(f323(f323(x96581,f323(x96582,x96583)),f323(x96584,f323(f323(f22(f867(x96585,a855)),x96586),f323(f323(f301(x96585),x96583),f188(f867(x96585,a855)))))),f323(x96584,x96586))
% 179.72/179.59 [9666]~P25(x96666,x96663,x96661,x96667,x96668,x96662)+~P101(f323(f59(x96663),x96665))+~P101(f323(f59(x96663),x96664))+E(f323(f323(x96661,f323(x96662,f323(f323(f110(f867(x96663,a855)),x96664),x96665))),f323(x96662,f323(f323(f101(f867(x96663,a855)),x96664),x96665))),f323(f323(x96661,f323(x96662,x96664)),f323(x96662,x96665)))
% 179.72/179.59 [9758]P43(x97581,x97582,x97583,x97584,x97585,f323(f323(x97583,x97586),x97587))+~P43(x97581,x97582,x97583,x97584,f323(f323(f22(f867(x97581,a855)),x97585),f323(f323(f301(x97581),x97588),f188(f867(x97581,a855)))),x97589)+~E(f323(f323(x97583,x97586),x97587),f323(f323(x97583,x97588),x97589))+~P101(f323(f323(f325(x97581),x97588),x97585))
% 179.72/179.59 [10149]P26(x101491,x101492,f323(f323(f301(f859(x101491)),f323(f323(f323(f90(x101491),f323(x101493,f808(x101494,x101495,x101496,x101497,x101493,x101492,x101491,x101498,x101499))),f323(x101497,f808(x101494,x101495,x101496,x101497,x101493,x101492,x101491,x101498,x101499))),f323(x101496,f808(x101494,x101495,x101496,x101497,x101493,x101492,x101491,x101498,x101499)))),f188(f867(f859(x101491),a855))))+~P101(f323(f59(x101499),x101498))+~P26(x101491,x101492,f323(f302(x101499,f859(x101491),f323(f323(f18(x101499,f867(x101491,f867(a856,a855)),f859(x101491)),f323(f323(f18(x101499,a857,f867(f867(x101491,f867(a856,a855)),f859(x101491))),f323(f323(f8(f867(x101491,f867(a856,a855)),f867(a857,f867(f867(x101491,f867(a856,a855)),f859(x101491))),x101499),f90(x101491)),x101493)),x101497)),x101496)),x101498))+P26(x101491,x101492,f323(f302(x101499,f859(x101491),f323(f323(f18(x101499,f867(x101491,f867(a856,a855)),f859(x101491)),f323(f323(f18(x101499,a857,f867(f867(x101491,f867(a856,a855)),f859(x101491))),f323(f323(f8(f867(x101491,f867(a856,a855)),f867(a857,f867(f867(x101491,f867(a856,a855)),f859(x101491))),x101499),f90(x101491)),x101495)),x101497)),x101494)),x101498))
% 179.72/179.59 [10150]~P26(x101501,x101502,f323(f323(f301(f859(x101501)),f323(f323(f323(f90(x101501),f323(x101504,f808(x101506,x101504,x101508,x101505,x101509,x101502,x101501,x101507,x101503))),f323(x101505,f808(x101506,x101504,x101508,x101505,x101509,x101502,x101501,x101507,x101503))),f323(x101506,f808(x101506,x101504,x101508,x101505,x101509,x101502,x101501,x101507,x101503)))),f188(f867(f859(x101501),a855))))+~P101(f323(f59(x101503),x101507))+~P26(x101501,x101502,f323(f302(x101503,f859(x101501),f323(f323(f18(x101503,f867(x101501,f867(a856,a855)),f859(x101501)),f323(f323(f18(x101503,a857,f867(f867(x101501,f867(a856,a855)),f859(x101501))),f323(f323(f8(f867(x101501,f867(a856,a855)),f867(a857,f867(f867(x101501,f867(a856,a855)),f859(x101501))),x101503),f90(x101501)),x101509)),x101505)),x101508)),x101507))+P26(x101501,x101502,f323(f302(x101503,f859(x101501),f323(f323(f18(x101503,f867(x101501,f867(a856,a855)),f859(x101501)),f323(f323(f18(x101503,a857,f867(f867(x101501,f867(a856,a855)),f859(x101501))),f323(f323(f8(f867(x101501,f867(a856,a855)),f867(a857,f867(f867(x101501,f867(a856,a855)),f859(x101501))),x101503),f90(x101501)),x101504)),x101505)),x101506)),x101507))
% 179.72/179.59 [9692]~P15(x96926,x96927,x96928,x96929,x969210,x96921)+E(f323(f323(x96921,x96922),x96923),f323(f323(x96921,x96924),x96925))+~P101(f323(f323(f325(f866(x96927,x96927)),f323(f323(f258(x96927,x96927),x96923),x96925)),x969210))+~P101(f323(f323(f325(f866(x96926,x96926)),f323(f323(f258(x96926,x96926),x96922),x96924)),x96929))
% 179.72/179.59 [9299]~P2(x92992)+E(x92991,f188(f867(x92992,a855)))+~P101(f323(f59(x92992),x92991))+P101(f323(f323(f325(x92992),f11(x92992,x92991)),x92991))+~P101(f323(f323(f325(x92992),f323(f323(f101(x92992),f816(x92991,x92992)),f818(x92991,x92992))),f323(f323(f301(x92992),f816(x92991,x92992)),f323(f323(f301(x92992),f818(x92991,x92992)),f188(f867(x92992,a855))))))
% 179.72/179.59 [9300]~P2(x93002)+E(x93001,f188(f867(x93002,a855)))+~P101(f323(f59(x93002),x93001))+P101(f323(f323(f325(x93002),f10(x93002,x93001)),x93001))+~P101(f323(f323(f325(x93002),f323(f323(f110(x93002),f819(x93001,x93002)),f820(x93001,x93002))),f323(f323(f301(x93002),f819(x93001,x93002)),f323(f323(f301(x93002),f820(x93001,x93002)),f188(f867(x93002,a855))))))
% 179.72/179.59 [9331]~P66(x93312)+E(x93311,f188(f867(x93312,a855)))+~P101(f323(f59(x93312),x93311))+P101(f323(f323(f325(x93312),f323(f61(x93312,f79(x93312)),x93311)),x93311))+~P101(f323(f323(f325(x93312),f323(f323(f79(x93312),f836(x93311,x93312)),f838(x93311,x93312))),f323(f323(f301(x93312),f836(x93311,x93312)),f323(f323(f301(x93312),f838(x93311,x93312)),f188(f867(x93312,a855))))))
% 179.72/179.59 [9336]~P103(x93362)+E(x93361,f188(f867(x93362,a855)))+~P101(f323(f59(x93362),x93361))+P101(f323(f323(f325(x93362),f12(x93362,f235(x93362),x93361)),x93361))+~P101(f323(f323(f325(x93362),f323(f323(f235(x93362),f338(x93361,x93362)),f341(x93361,x93362))),f323(f323(f301(x93362),f338(x93361,x93362)),f323(f323(f301(x93362),f341(x93361,x93362)),f188(f867(x93362,a855))))))
% 179.72/179.59 [9337]~P103(x93372)+E(x93371,f188(f867(x93372,a855)))+~P101(f323(f59(x93372),x93371))+P101(f323(f323(f325(x93372),f13(x93372,f236(x93372),x93371)),x93371))+~P101(f323(f323(f325(x93372),f323(f323(f236(x93372),f339(x93371,x93372)),f340(x93371,x93372))),f323(f323(f301(x93372),f339(x93371,x93372)),f323(f323(f301(x93372),f340(x93371,x93372)),f188(f867(x93372,a855))))))
% 179.72/179.59 [6473]~P84(x64732)+E(x64731,f2(x64732))+~E(f323(f323(f78(x64732),x64733),x64731),f2(x64732))+~P101(f323(f323(f237(x64732),f2(x64732)),x64733))+~P101(f323(f323(f237(x64732),f2(x64732)),x64731))
% 179.72/179.59 [6474]~P84(x64742)+E(x64741,f2(x64742))+~E(f323(f323(f78(x64742),x64741),x64743),f2(x64742))+~P101(f323(f323(f237(x64742),f2(x64742)),x64743))+~P101(f323(f323(f237(x64742),f2(x64742)),x64741))
% 179.72/179.59 [7000]~P103(x70002)+~P16(x70002,x70001)+E(x70001,f113(x70002))+~P101(f323(f323(f325(x70002),x70003),f323(f166(x70002),f610(x70001,x70002))))+P101(f323(f323(f237(x70002),f647(x70001,x70002)),x70003))
% 179.72/179.59 [7166]~P103(x71661)+E(f15(x71661,x71662),x71663)+~P101(f323(f59(x71661),x71662))+~P101(f323(f323(f237(x71661),x71663),f496(x71663,x71662,x71661)))+~P101(f323(f323(f325(x71661),x71663),x71662))
% 179.72/179.59 [7197]~P103(x71971)+~P16(x71971,x71972)+~P16(x71971,x71973)+P16(x71971,f323(f323(f121(x71971),x71972),x71973))+P101(f323(f323(f325(x71971),f599(x71973,x71972,x71971)),f323(f166(x71971),x71972)))
% 179.72/179.59 [7198]~P103(x71981)+~P16(x71981,x71982)+~P16(x71981,x71983)+P16(x71981,f323(f323(f121(x71981),x71982),x71983))+P101(f323(f323(f325(x71981),f600(x71983,x71982,x71981)),f323(f166(x71981),x71983)))
% 179.72/179.59 [7254]~P103(x72541)+E(f14(x72541,x72542),x72543)+~P101(f323(f59(x72541),x72542))+P101(f323(f323(f325(x72541),f497(x72543,x72542,x72541)),x72542))+~P101(f323(f323(f325(x72541),x72543),x72542))
% 179.72/179.59 [7255]~P103(x72551)+E(f15(x72551,x72552),x72553)+~P101(f323(f59(x72551),x72552))+P101(f323(f323(f325(x72551),f496(x72553,x72552,x72551)),x72552))+~P101(f323(f323(f325(x72551),x72553),x72552))
% 179.72/179.59 [7831]~P103(x78311)+E(f14(x78311,x78312),x78313)+~P101(f323(f59(x78311),x78312))+~P101(f323(f323(f325(x78311),x78313),x78312))+~P101(f323(f323(f237(x78311),f497(x78313,x78312,x78311)),x78313))
% 179.72/179.59 [8150]~P103(x81501)+~P16(x81501,x81502)+~P16(x81501,x81503)+P16(x81501,f323(f323(f121(x81501),x81502),x81503))+~P101(f323(f323(f237(x81501),f599(x81503,x81502,x81501)),f600(x81503,x81502,x81501)))
% 179.72/179.59 [8940]~P2(x89402)+E(x89401,f188(f867(x89402,a855)))+~E(f323(f323(f101(x89402),f323(x89403,f815(x89401,x89403,x89402))),f323(x89403,f821(x89401,x89403,x89402))),f323(x89403,f323(f323(f101(x89402),f815(x89401,x89403,x89402)),f821(x89401,x89403,x89402))))+E(f11(x89402,f323(f302(x89402,x89402,x89403),x89401)),f323(x89403,f11(x89402,x89401)))+~P101(f323(f59(x89402),x89401))
% 179.72/179.59 [8941]~P2(x89412)+E(x89411,f188(f867(x89412,a855)))+~E(f323(f323(f110(x89412),f323(x89413,f822(x89411,x89413,x89412))),f323(x89413,f823(x89411,x89413,x89412))),f323(x89413,f323(f323(f110(x89412),f822(x89411,x89413,x89412)),f823(x89411,x89413,x89412))))+E(f10(x89412,f323(f302(x89412,x89412,x89413),x89411)),f323(x89413,f10(x89412,x89411)))+~P101(f323(f59(x89412),x89411))
% 179.72/179.59 [8942]~P103(x89422)+E(x89421,f188(f867(x89422,a855)))+~E(f323(f323(f236(x89422),f323(x89423,f334(x89421,x89423,x89422))),f323(x89423,f348(x89421,x89423,x89422))),f323(x89423,f323(f323(f236(x89422),f334(x89421,x89423,x89422)),f348(x89421,x89423,x89422))))+E(f14(x89422,f323(f302(x89422,x89422,x89423),x89421)),f323(x89423,f14(x89422,x89421)))+~P101(f323(f59(x89422),x89421))
% 179.72/179.59 [8943]~P103(x89432)+E(x89431,f188(f867(x89432,a855)))+~E(f323(f323(f235(x89432),f323(x89433,f349(x89431,x89433,x89432))),f323(x89433,f350(x89431,x89433,x89432))),f323(x89433,f323(f323(f235(x89432),f349(x89431,x89433,x89432)),f350(x89431,x89433,x89432))))+E(f15(x89432,f323(f302(x89432,x89432,x89433),x89431)),f323(x89433,f15(x89432,x89431)))+~P101(f323(f59(x89432),x89431))
% 179.72/179.59 [9012]~P103(x90122)+E(x90121,f188(f867(x90122,a855)))+~E(f323(f323(f235(x90122),f323(x90123,f335(x90121,x90123,x90122))),f323(x90123,f347(x90121,x90123,x90122))),f323(x90123,f323(f323(f235(x90122),f335(x90121,x90123,x90122)),f347(x90121,x90123,x90122))))+E(f12(x90122,f235(x90122),f323(f302(x90122,x90122,x90123),x90121)),f323(x90123,f12(x90122,f235(x90122),x90121)))+~P101(f323(f59(x90122),x90121))
% 179.72/179.59 [9013]~P103(x90132)+E(x90131,f188(f867(x90132,a855)))+~E(f323(f323(f236(x90132),f323(x90133,f336(x90131,x90133,x90132))),f323(x90133,f346(x90131,x90133,x90132))),f323(x90133,f323(f323(f236(x90132),f336(x90131,x90133,x90132)),f346(x90131,x90133,x90132))))+E(f13(x90132,f236(x90132),f323(f302(x90132,x90132,x90133),x90131)),f323(x90133,f13(x90132,f236(x90132),x90131)))+~P101(f323(f59(x90132),x90131))
% 179.72/179.59 [6489]~P66(x64892)+E(x64891,f188(f867(x64892,a855)))+~P101(f323(f59(x64892),x64891))+E(f323(f61(x64892,f79(x64892)),f323(f323(f301(x64892),x64893),x64891)),f323(f323(f79(x64892),x64893),f323(f61(x64892,f79(x64892)),x64891)))+P101(f323(f323(f325(x64892),x64893),x64891))
% 179.72/179.59 [7006]~P2(x70062)+E(f323(f323(f110(x70062),f10(x70062,x70061)),f10(x70062,x70063)),f10(x70062,x70063))+E(x70061,f188(f867(x70062,a855)))+~P101(f323(f59(x70062),x70063))+~P101(f323(f323(f237(f867(x70062,a855)),x70061),x70063))
% 179.72/179.59 [7007]~P2(x70072)+E(f323(f323(f101(x70072),f11(x70072,x70071)),f11(x70072,x70073)),f11(x70072,x70073))+E(x70071,f188(f867(x70072,a855)))+~P101(f323(f59(x70072),x70073))+~P101(f323(f323(f237(f867(x70072,a855)),x70071),x70073))
% 179.72/179.59 [7008]~P103(x70082)+E(f323(f323(f235(x70082),f15(x70082,x70081)),f15(x70082,x70083)),f15(x70082,x70083))+E(x70081,f188(f867(x70082,a855)))+~P101(f323(f59(x70082),x70083))+~P101(f323(f323(f237(f867(x70082,a855)),x70081),x70083))
% 179.72/179.59 [7009]~P103(x70092)+E(f323(f323(f236(x70092),f14(x70092,x70091)),f14(x70092,x70093)),f14(x70092,x70093))+E(x70091,f188(f867(x70092,a855)))+~P101(f323(f59(x70092),x70093))+~P101(f323(f323(f237(f867(x70092,a855)),x70091),x70093))
% 179.72/179.59 [7303]~P103(x73032)+E(x73031,f188(f867(x73032,a855)))+~P101(f323(f59(x73032),x73033))+P101(f323(f323(f237(x73032),f14(x73032,x73031)),f14(x73032,x73033)))+~P101(f323(f323(f237(f867(x73032,a855)),x73031),x73033))
% 179.72/179.59 [7304]~P103(x73042)+E(x73041,f188(f867(x73042,a855)))+~P101(f323(f59(x73042),x73043))+P101(f323(f323(f237(x73042),f15(x73042,x73043)),f15(x73042,x73041)))+~P101(f323(f323(f237(f867(x73042,a855)),x73041),x73043))
% 179.72/179.59 [7362]~P2(x73621)+E(f11(x73621,x73622),x73623)+~P101(f323(f59(x73621),x73622))+~E(f323(f323(f22(f867(x73621,a855)),x73622),f323(f323(f301(x73621),x73623),f188(f867(x73621,a855)))),f188(f867(x73621,a855)))+~P101(f323(f323(f325(x73621),x73623),x73622))
% 179.72/179.59 [7363]~P2(x73631)+E(f10(x73631,x73632),x73633)+~P101(f323(f59(x73631),x73632))+~E(f323(f323(f22(f867(x73631,a855)),x73632),f323(f323(f301(x73631),x73633),f188(f867(x73631,a855)))),f188(f867(x73631,a855)))+~P101(f323(f323(f325(x73631),x73633),x73632))
% 179.72/179.59 [7364]~P103(x73641)+E(f14(x73641,x73642),x73643)+~P101(f323(f59(x73641),x73642))+~E(f323(f323(f22(f867(x73641,a855)),x73642),f323(f323(f301(x73641),x73643),f188(f867(x73641,a855)))),f188(f867(x73641,a855)))+~P101(f323(f323(f325(x73641),x73643),x73642))
% 179.72/179.59 [7365]~P103(x73651)+E(f15(x73651,x73652),x73653)+~P101(f323(f59(x73651),x73652))+~E(f323(f323(f22(f867(x73651,a855)),x73652),f323(f323(f301(x73651),x73653),f188(f867(x73651,a855)))),f188(f867(x73651,a855)))+~P101(f323(f323(f325(x73651),x73653),x73652))
% 179.72/179.59 [7462]~P103(x74621)+E(f12(x74621,f235(x74621),x74622),x74623)+~P101(f323(f59(x74621),x74622))+~E(f323(f323(f22(f867(x74621,a855)),x74622),f323(f323(f301(x74621),x74623),f188(f867(x74621,a855)))),f188(f867(x74621,a855)))+~P101(f323(f323(f325(x74621),x74623),x74622))
% 179.72/179.59 [7463]~P103(x74631)+E(f13(x74631,f236(x74631),x74632),x74633)+~P101(f323(f59(x74631),x74632))+~E(f323(f323(f22(f867(x74631,a855)),x74632),f323(f323(f301(x74631),x74633),f188(f867(x74631,a855)))),f188(f867(x74631,a855)))+~P101(f323(f323(f325(x74631),x74633),x74632))
% 179.72/179.59 [7499]~P98(x74992)+E(x74991,f188(f867(x74992,a855)))+~P101(f323(f59(x74992),x74991))+~P101(f323(f323(f237(x74992),x74993),f824(x74993,x74991,x74992)))+P101(f323(f323(f237(x74992),x74993),f323(f61(x74992,f101(x74992)),x74991)))
% 179.72/179.59 [7500]~P103(x75002)+E(x75001,f188(f867(x75002,a855)))+~P101(f323(f59(x75002),x75001))+~P101(f323(f323(f237(x75002),x75003),f852(x75003,x75001,x75002)))+P101(f323(f323(f237(x75002),x75003),f323(f61(x75002,f235(x75002)),x75001)))
% 179.72/179.59 [7501]~P103(x75012)+E(x75011,f188(f867(x75012,a855)))+~P101(f323(f59(x75012),x75011))+~P101(f323(f323(f238(x75012),x75013),f331(x75013,x75011,x75012)))+P101(f323(f323(f238(x75012),x75013),f323(f61(x75012,f235(x75012)),x75011)))
% 179.72/179.59 [7586]~P98(x75862)+E(x75861,f188(f867(x75862,a855)))+~P101(f323(f59(x75862),x75861))+P101(f323(f323(f325(x75862),f824(x75863,x75861,x75862)),x75861))+P101(f323(f323(f237(x75862),x75863),f323(f61(x75862,f101(x75862)),x75861)))
% 179.72/179.59 [7587]~P103(x75872)+E(x75871,f188(f867(x75872,a855)))+~P101(f323(f59(x75872),x75871))+P101(f323(f323(f325(x75872),f852(x75873,x75871,x75872)),x75871))+P101(f323(f323(f237(x75872),x75873),f323(f61(x75872,f235(x75872)),x75871)))
% 179.72/179.59 [7588]~P103(x75882)+E(x75881,f188(f867(x75882,a855)))+~P101(f323(f59(x75882),x75881))+P101(f323(f323(f325(x75882),f331(x75883,x75881,x75882)),x75881))+P101(f323(f323(f238(x75882),x75883),f323(f61(x75882,f235(x75882)),x75881)))
% 179.72/179.59 [7709]~P103(x77092)+E(x77091,f188(f867(x77092,a855)))+E(f323(f323(f235(x77092),f12(x77092,f235(x77092),x77091)),f12(x77092,f235(x77092),x77093)),f12(x77092,f235(x77092),x77093))+~P101(f323(f59(x77092),x77093))+~P101(f323(f323(f237(f867(x77092,a855)),x77091),x77093))
% 179.72/179.59 [7710]~P103(x77102)+E(x77101,f188(f867(x77102,a855)))+E(f323(f323(f236(x77102),f13(x77102,f236(x77102),x77101)),f13(x77102,f236(x77102),x77103)),f13(x77102,f236(x77102),x77103))+~P101(f323(f59(x77102),x77103))+~P101(f323(f323(f237(f867(x77102,a855)),x77101),x77103))
% 179.72/179.59 [7912]~E(f554(x79121,x79123,x79122),f555(x79121,x79123,x79122))+~E(f323(f35(x79122),f556(x79121,x79123,x79122)),x79121)+E(f323(f323(f79(a860),x79121),f323(f35(f867(x79122,a855)),x79123)),f323(f35(x79122),f37(f867(x79122,a855),x79123)))+~P101(f323(f59(x79122),f37(f867(x79122,a855),x79123)))+~P101(f323(f59(f867(x79122,a855)),x79123))
% 179.72/179.59 [8085]~P103(x80852)+E(x80851,f188(f867(x80852,a855)))+~P101(f323(f59(x80852),x80853))+P101(f323(f323(f237(x80852),f323(f61(x80852,f235(x80852)),x80853)),f323(f61(x80852,f235(x80852)),x80851)))+~P101(f323(f323(f237(f867(x80852,a855)),x80851),x80853))
% 179.72/179.59 [8393]~E(f554(x83931,x83933,x83932),f555(x83931,x83933,x83932))+E(f323(f323(f79(a860),x83931),f323(f35(f867(x83932,a855)),x83933)),f323(f35(x83932),f37(f867(x83932,a855),x83933)))+P101(f323(f323(f325(f867(x83932,a855)),f556(x83931,x83933,x83932)),x83933))+~P101(f323(f59(x83932),f37(f867(x83932,a855),x83933)))+~P101(f323(f59(f867(x83932,a855)),x83933))
% 179.72/179.59 [8415]~E(f323(f35(x84152),f556(x84151,x84153,x84152)),x84151)+E(f323(f323(f79(a860),x84151),f323(f35(f867(x84152,a855)),x84153)),f323(f35(x84152),f37(f867(x84152,a855),x84153)))+P101(f323(f323(f325(f867(x84152,a855)),f555(x84151,x84153,x84152)),x84153))+~P101(f323(f59(x84152),f37(f867(x84152,a855),x84153)))+~P101(f323(f59(f867(x84152,a855)),x84153))
% 179.72/179.59 [8416]~E(f323(f35(x84162),f556(x84161,x84163,x84162)),x84161)+E(f323(f323(f79(a860),x84161),f323(f35(f867(x84162,a855)),x84163)),f323(f35(x84162),f37(f867(x84162,a855),x84163)))+P101(f323(f323(f325(f867(x84162,a855)),f554(x84161,x84163,x84162)),x84163))+~P101(f323(f59(x84162),f37(f867(x84162,a855),x84163)))+~P101(f323(f59(f867(x84162,a855)),x84163))
% 179.72/179.59 [8441]~E(f323(f35(x84412),f556(x84411,x84413,x84412)),x84411)+~E(f323(f323(f101(f867(x84412,a855)),f555(x84411,x84413,x84412)),f554(x84411,x84413,x84412)),f188(f867(x84412,a855)))+E(f323(f323(f79(a860),x84411),f323(f35(f867(x84412,a855)),x84413)),f323(f35(x84412),f37(f867(x84412,a855),x84413)))+~P101(f323(f59(f867(x84412,a855)),x84413))+~P101(f323(f59(x84412),f37(f867(x84412,a855),x84413)))
% 179.72/179.59 [8705]E(f323(f323(f79(a860),x87051),f323(f35(f867(x87052,a855)),x87053)),f323(f35(x87052),f37(f867(x87052,a855),x87053)))+P101(f323(f323(f325(f867(x87052,a855)),f556(x87051,x87053,x87052)),x87053))+P101(f323(f323(f325(f867(x87052,a855)),f555(x87051,x87053,x87052)),x87053))+~P101(f323(f59(f867(x87052,a855)),x87053))+~P101(f323(f59(x87052),f37(f867(x87052,a855),x87053)))
% 179.72/179.59 [8706]E(f323(f323(f79(a860),x87061),f323(f35(f867(x87062,a855)),x87063)),f323(f35(x87062),f37(f867(x87062,a855),x87063)))+P101(f323(f323(f325(f867(x87062,a855)),f556(x87061,x87063,x87062)),x87063))+P101(f323(f323(f325(f867(x87062,a855)),f554(x87061,x87063,x87062)),x87063))+~P101(f323(f59(f867(x87062,a855)),x87063))+~P101(f323(f59(x87062),f37(f867(x87062,a855),x87063)))
% 179.72/179.59 [8733]~E(f323(f323(f101(f867(x87332,a855)),f555(x87331,x87333,x87332)),f554(x87331,x87333,x87332)),f188(f867(x87332,a855)))+E(f323(f323(f79(a860),x87331),f323(f35(f867(x87332,a855)),x87333)),f323(f35(x87332),f37(f867(x87332,a855),x87333)))+~P101(f323(f59(f867(x87332,a855)),x87333))+P101(f323(f323(f325(f867(x87332,a855)),f556(x87331,x87333,x87332)),x87333))+~P101(f323(f59(x87332),f37(f867(x87332,a855),x87333)))
% 179.72/179.59 [8986]~P93(x89862)+E(x89861,f188(f867(x89862,a855)))+~E(f323(f323(f79(x89862),f323(x89863,f835(x89861,x89863,x89862))),f323(x89863,f840(x89861,x89863,x89862))),f323(x89863,f323(f323(f79(x89862),f835(x89861,x89863,x89862)),f840(x89861,x89863,x89862))))+~P101(f323(f59(x89862),x89861))+E(f323(f61(x89862,f79(x89862)),f323(f302(x89862,x89862,x89863),x89861)),f323(x89863,f323(f61(x89862,f79(x89862)),x89861)))
% 179.72/179.59 [9914]P101(f323(f323(x99141,x99142),x99143))+P101(f323(f323(f238(a1),f514(x99141,x99143,x99142)),f515(x99141,x99143,x99142)))+P101(f323(f323(f237(a1),f515(x99141,x99143,x99142)),f2(a1)))+P101(f323(f323(x99141,f514(x99141,x99143,x99142)),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f515(x99141,x99143,x99142))))+~P101(f323(f311(f866(a1,a1),a54),f323(f323(f258(a1,a1),x99142),x99143)))
% 179.72/179.59 [9920]P101(f323(f323(x99201,x99202),x99203))+P101(f323(f323(f237(a1),f513(x99201,x99203,x99202)),f2(a1)))+P101(f323(f323(x99201,f512(x99201,x99203,x99202)),f323(f323(f79(a1),f323(f103(a1),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f513(x99201,x99203,x99202))))+P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),f512(x99201,x99203,x99202)),f513(x99201,x99203,x99202))))+~P101(f323(f311(f866(a1,a1),a49),f323(f323(f258(a1,a1),x99202),x99203)))
% 179.72/179.59 [7882]~P116(x78821)+~P101(f323(f323(f237(x78821),x78822),f76(x78821)))+~P101(f323(f323(f237(x78821),f2(x78821)),x78822))+~P101(f323(f323(f237(x78821),f2(x78821)),x78823))+P101(f323(f323(f237(x78821),f323(f323(f79(x78821),x78822),x78823)),x78823))
% 179.72/179.59 [7883]~P116(x78831)+~P101(f323(f323(f237(x78831),x78833),f76(x78831)))+~P101(f323(f323(f237(x78831),f2(x78831)),x78833))+~P101(f323(f323(f237(x78831),f2(x78831)),x78832))+P101(f323(f323(f237(x78831),f323(f323(f79(x78831),x78832),x78833)),x78832))
% 179.72/179.59 [8235]~P103(x82352)+E(x82351,f188(f867(x82352,a855)))+~P101(f323(f59(x82352),x82351))+P101(f323(f323(f325(x82352),f332(x82353,x82351,x82352)),x82351))+~P101(f323(f323(f237(x82352),f323(f61(x82352,f235(x82352)),x82351)),x82353))
% 179.72/179.59 [8236]~P103(x82362)+E(x82361,f188(f867(x82362,a855)))+~P101(f323(f59(x82362),x82361))+P101(f323(f323(f325(x82362),f333(x82363,x82361,x82362)),x82361))+~P101(f323(f323(f238(x82362),f323(f61(x82362,f235(x82362)),x82361)),x82363))
% 179.72/179.59 [8237]~P103(x82372)+E(x82371,f188(f867(x82372,a855)))+~P101(f323(f59(x82372),x82371))+P101(f323(f323(f237(x82372),f332(x82373,x82371,x82372)),x82373))+~P101(f323(f323(f237(x82372),f323(f61(x82372,f235(x82372)),x82371)),x82373))
% 179.72/179.59 [8238]~P103(x82382)+E(x82381,f188(f867(x82382,a855)))+~P101(f323(f59(x82382),x82381))+P101(f323(f323(f238(x82382),f333(x82383,x82381,x82382)),x82383))+~P101(f323(f323(f238(x82382),f323(f61(x82382,f235(x82382)),x82381)),x82383))
% 179.72/179.59 [8328]~P101(f323(x83281,x83283))+P101(f323(x83281,f402(x83281,x83282)))+P101(f323(x83281,f401(x83281,x83282)))+~P101(f323(f323(f238(a1),f2(a1)),x83282))+P101(f323(x83281,f323(f323(f22(a1),f401(x83281,x83282)),f323(f323(f79(a1),f403(x83281,x83282)),x83282))))
% 179.72/179.59 [8540]~P101(f323(x85401,x85403))+P101(f323(x85401,f401(x85401,x85402)))+~P101(f323(f323(f238(a1),f2(a1)),x85402))+P101(f323(f323(f325(a1),f402(x85401,x85402)),f294(a1,f76(a1),x85402)))+P101(f323(x85401,f323(f323(f22(a1),f401(x85401,x85402)),f323(f323(f79(a1),f403(x85401,x85402)),x85402))))
% 179.72/179.59 [8755]~P101(f323(x87551,x87553))+~P101(f323(x87551,f401(x87551,x87552)))+P101(f323(x87551,f402(x87551,x87552)))+~P101(f323(f323(f238(a1),f2(a1)),x87552))+~P101(f323(x87551,f323(f323(f22(a1),f401(x87551,x87552)),f323(f323(f79(a1),f403(x87551,x87552)),x87552))))
% 179.72/179.59 [8880]~P101(f323(x88801,x88803))+~P101(f323(x88801,f401(x88801,x88802)))+~P101(f323(f323(f238(a1),f2(a1)),x88802))+P101(f323(f323(f325(a1),f402(x88801,x88802)),f294(a1,f76(a1),x88802)))+~P101(f323(x88801,f323(f323(f22(a1),f401(x88801,x88802)),f323(f323(f79(a1),f403(x88801,x88802)),x88802))))
% 179.72/179.59 [8659]~P2(x86591)+~P101(f323(f59(x86591),x86592))+E(f323(f323(f22(f867(x86591,a855)),x86592),f323(f323(f301(x86591),x86593),f188(f867(x86591,a855)))),f188(f867(x86591,a855)))+~P101(f323(f323(f325(x86591),x86593),x86592))+E(f323(f323(f101(x86591),x86593),f11(x86591,f323(f323(f22(f867(x86591,a855)),x86592),f323(f323(f301(x86591),x86593),f188(f867(x86591,a855)))))),f11(x86591,x86592))
% 179.72/179.59 [8660]~P2(x86601)+~P101(f323(f59(x86601),x86602))+E(f323(f323(f22(f867(x86601,a855)),x86602),f323(f323(f301(x86601),x86603),f188(f867(x86601,a855)))),f188(f867(x86601,a855)))+~P101(f323(f323(f325(x86601),x86603),x86602))+E(f323(f323(f110(x86601),x86603),f10(x86601,f323(f323(f22(f867(x86601,a855)),x86602),f323(f323(f301(x86601),x86603),f188(f867(x86601,a855)))))),f10(x86601,x86602))
% 179.72/179.59 [8661]~P103(x86611)+~P101(f323(f59(x86611),x86612))+E(f323(f323(f22(f867(x86611,a855)),x86612),f323(f323(f301(x86611),x86613),f188(f867(x86611,a855)))),f188(f867(x86611,a855)))+~P101(f323(f323(f325(x86611),x86613),x86612))+E(f323(f323(f236(x86611),x86613),f14(x86611,f323(f323(f22(f867(x86611,a855)),x86612),f323(f323(f301(x86611),x86613),f188(f867(x86611,a855)))))),f14(x86611,x86612))
% 179.72/179.59 [8662]~P103(x86621)+~P101(f323(f59(x86621),x86622))+E(f323(f323(f22(f867(x86621,a855)),x86622),f323(f323(f301(x86621),x86623),f188(f867(x86621,a855)))),f188(f867(x86621,a855)))+~P101(f323(f323(f325(x86621),x86623),x86622))+E(f323(f323(f235(x86621),x86623),f15(x86621,f323(f323(f22(f867(x86621,a855)),x86622),f323(f323(f301(x86621),x86623),f188(f867(x86621,a855)))))),f15(x86621,x86622))
% 179.72/179.59 [8725]~P103(x87251)+~P101(f323(f59(x87251),x87252))+E(f323(f323(f22(f867(x87251,a855)),x87252),f323(f323(f301(x87251),x87253),f188(f867(x87251,a855)))),f188(f867(x87251,a855)))+~P101(f323(f323(f325(x87251),x87253),x87252))+E(f323(f323(f235(x87251),x87253),f12(x87251,f235(x87251),f323(f323(f22(f867(x87251,a855)),x87252),f323(f323(f301(x87251),x87253),f188(f867(x87251,a855)))))),f12(x87251,f235(x87251),x87252))
% 179.72/179.59 [8726]~P103(x87261)+~P101(f323(f59(x87261),x87262))+E(f323(f323(f22(f867(x87261,a855)),x87262),f323(f323(f301(x87261),x87263),f188(f867(x87261,a855)))),f188(f867(x87261,a855)))+~P101(f323(f323(f325(x87261),x87263),x87262))+E(f323(f323(f236(x87261),x87263),f13(x87261,f236(x87261),f323(f323(f22(f867(x87261,a855)),x87262),f323(f323(f301(x87261),x87263),f188(f867(x87261,a855)))))),f13(x87261,f236(x87261),x87262))
% 179.72/179.59 [8742]~P2(x87421)+~P101(f323(f59(x87421),x87423))+~P101(f323(f59(x87421),x87422))+E(f323(f323(f101(f867(x87421,a855)),x87422),x87423),f188(f867(x87421,a855)))+E(f323(f323(f110(x87421),f10(x87421,f323(f323(f110(f867(x87421,a855)),x87422),x87423))),f10(x87421,f323(f323(f101(f867(x87421,a855)),x87422),x87423))),f323(f323(f110(x87421),f10(x87421,x87422)),f10(x87421,x87423)))
% 179.72/179.59 [8743]~P2(x87431)+~P101(f323(f59(x87431),x87433))+~P101(f323(f59(x87431),x87432))+E(f323(f323(f101(f867(x87431,a855)),x87432),x87433),f188(f867(x87431,a855)))+E(f323(f323(f101(x87431),f11(x87431,f323(f323(f110(f867(x87431,a855)),x87432),x87433))),f11(x87431,f323(f323(f101(f867(x87431,a855)),x87432),x87433))),f323(f323(f101(x87431),f11(x87431,x87432)),f11(x87431,x87433)))
% 179.72/179.59 [8744]~P103(x87441)+~P101(f323(f59(x87441),x87443))+~P101(f323(f59(x87441),x87442))+E(f323(f323(f101(f867(x87441,a855)),x87442),x87443),f188(f867(x87441,a855)))+E(f323(f323(f235(x87441),f15(x87441,f323(f323(f110(f867(x87441,a855)),x87442),x87443))),f15(x87441,f323(f323(f101(f867(x87441,a855)),x87442),x87443))),f323(f323(f235(x87441),f15(x87441,x87442)),f15(x87441,x87443)))
% 179.72/179.59 [8745]~P103(x87451)+~P101(f323(f59(x87451),x87453))+~P101(f323(f59(x87451),x87452))+E(f323(f323(f101(f867(x87451,a855)),x87452),x87453),f188(f867(x87451,a855)))+E(f323(f323(f236(x87451),f14(x87451,f323(f323(f110(f867(x87451,a855)),x87452),x87453))),f14(x87451,f323(f323(f101(f867(x87451,a855)),x87452),x87453))),f323(f323(f236(x87451),f14(x87451,x87452)),f14(x87451,x87453)))
% 179.72/179.59 [8958]~P103(x89581)+~P101(f323(f59(x89581),x89583))+~P101(f323(f59(x89581),x89582))+E(f323(f323(f101(f867(x89581,a855)),x89582),x89583),f188(f867(x89581,a855)))+E(f323(f323(f235(x89581),f12(x89581,f235(x89581),f323(f323(f110(f867(x89581,a855)),x89582),x89583))),f12(x89581,f235(x89581),f323(f323(f101(f867(x89581,a855)),x89582),x89583))),f323(f323(f235(x89581),f12(x89581,f235(x89581),x89582)),f12(x89581,f235(x89581),x89583)))
% 179.72/179.59 [8959]~P103(x89591)+~P101(f323(f59(x89591),x89593))+~P101(f323(f59(x89591),x89592))+E(f323(f323(f101(f867(x89591,a855)),x89592),x89593),f188(f867(x89591,a855)))+E(f323(f323(f236(x89591),f13(x89591,f236(x89591),f323(f323(f110(f867(x89591,a855)),x89592),x89593))),f13(x89591,f236(x89591),f323(f323(f101(f867(x89591,a855)),x89592),x89593))),f323(f323(f236(x89591),f13(x89591,f236(x89591),x89592)),f13(x89591,f236(x89591),x89593)))
% 179.72/179.59 [9755]~P119(x97553)+E(x97551,x97552)+~P101(f323(f323(f237(x97553),f2(x97553)),x97552))+~P101(f323(f323(f237(x97553),f2(x97553)),x97551))+~E(f323(f323(f248(x97553),x97551),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))),f323(f323(f248(x97553),x97552),f323(f103(a860),f323(f323(f78(a1),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)),f323(f323(f22(a1),f323(f323(f78(a1),a81),a81)),a97)))))
% 179.72/179.59 [6292]E(f352(x62921,x62922,x62923),x62924)+E(f323(x62921,x62924),f2(a860))+~E(f323(f323(f6(x62923,a860),x62921),x62922),f76(a860))+~P101(f323(f59(x62923),x62922))+~P101(f323(f323(f325(x62923),x62924),x62922))
% 179.72/179.59 [6353]E(f355(x63531,x63532,x63533),x63534)+E(f323(x63531,x63534),f2(a860))+~E(f323(f323(f6(x63533,a860),x63531),x63532),f323(a112,f2(a860)))+~P101(f323(f59(x63533),x63532))+~P101(f323(f323(f325(x63533),x63534),x63532))
% 179.72/179.59 [6458]~P103(x64581)+~P6(x64581)+P101(f323(f323(f238(x64581),x64582),f37(x64581,x64583)))+~P101(f323(f323(f238(x64581),x64582),x64584))+~P101(f323(f323(f325(x64581),x64584),x64583))
% 179.72/179.59 [6630]~P103(x66301)+~P6(x66301)+~P101(f323(f323(f238(x66301),x66304),x66303))+P101(f323(f323(f238(x66301),f38(x66301,x66302)),x66303))+~P101(f323(f323(f325(x66301),x66304),x66302))
% 179.72/179.59 [6886]~P119(x68863)+E(x68861,x68862)+~E(f323(f323(f248(x68863),x68861),f323(a112,x68864)),f323(f323(f248(x68863),x68862),f323(a112,x68864)))+~P101(f323(f323(f237(x68863),f2(x68863)),x68862))+~P101(f323(f323(f237(x68863),f2(x68863)),x68861))
% 179.72/179.59 [7095]~E(f357(x70952,x70953,x70951,x70954),x70954)+~E(f323(x70952,x70954),f76(a860))+E(f323(f323(f6(x70951,a860),x70952),x70953),f76(a860))+~P101(f323(f59(x70951),x70953))+~P101(f323(f323(f325(x70951),x70954),x70953))
% 179.72/179.59 [7102]~P112(x71024)+~P123(x71024)+E(f323(x71021,f460(x71021,x71022,x71023,x71024)),f2(x71024))+~E(f323(f323(f9(x71023,x71024),x71021),x71022),f2(x71024))+~P101(f323(f59(x71023),x71022))
% 179.72/179.59 [7188]~E(f356(x71882,x71883,x71881,x71884),x71884)+~E(f323(x71882,x71884),f323(a112,f2(a860)))+E(f323(f323(f6(x71881,a860),x71882),x71883),f323(a112,f2(a860)))+~P101(f323(f59(x71881),x71883))+~P101(f323(f323(f325(x71881),x71884),x71883))
% 179.72/179.59 [7923]~E(f323(x79232,x79234),f76(a860))+~E(f323(x79232,f357(x79232,x79233,x79231,x79234)),f2(a860))+E(f323(f323(f6(x79231,a860),x79232),x79233),f76(a860))+~P101(f323(f59(x79231),x79233))+~P101(f323(f323(f325(x79231),x79234),x79233))
% 179.72/179.59 [7961]~E(f323(x79612,x79614),f323(a112,f2(a860)))+~E(f323(x79612,f356(x79612,x79613,x79611,x79614)),f2(a860))+E(f323(f323(f6(x79611,a860),x79612),x79613),f323(a112,f2(a860)))+~P101(f323(f59(x79611),x79613))+~P101(f323(f323(f325(x79611),x79614),x79613))
% 179.72/179.59 [8507]~P103(x85071)+~P16(x85071,x85074)+P16(x85071,x85072)+~E(x85072,f323(f323(f144(x85071),x85073),x85074))+~P101(f323(f323(f237(x85071),x85073),f651(x85072,x85071,x85074,x85073)))
% 179.72/179.59 [8544]E(x85441,x85442)+E(f323(f323(f22(a1),f405(x85443,x85442,x85444,x85441)),f406(x85443,x85442,x85444,x85441)),x85441)+~E(f323(f323(f78(a1),x85441),x85444),x85442)+~P101(f323(f323(f238(a1),f2(a1)),x85444))+~P101(f323(f323(f325(a1),x85442),x85443))
% 179.72/179.59 [8545]E(x85451,x85452)+E(f323(f323(f78(a1),f408(x85453,x85452,x85454,x85451)),f409(x85453,x85452,x85454,x85451)),x85451)+~E(f323(f323(f22(a1),x85451),x85454),x85452)+~P101(f323(f323(f238(a1),f2(a1)),x85454))+~P101(f323(f323(f325(a1),x85452),x85453))
% 179.72/179.59 [8740]E(f323(x87401,f751(x87402,x87401,x87403,x87404)),x87402)+P101(f323(f323(f237(a860),x87404),f752(x87402,x87401,x87403,x87404)))+~P101(f323(f323(f237(a1),x87402),f323(x87401,x87403)))+~P101(f323(f323(f238(a860),x87404),x87403))+~P101(f323(f323(f237(a1),f323(x87401,x87404)),x87402))
% 179.72/179.59 [8741]~P103(x87411)+~P16(x87411,x87413)+P16(x87411,x87412)+~E(x87412,f323(f323(f144(x87411),x87414),x87413))+P101(f323(f323(f325(x87411),f651(x87412,x87411,x87413,x87414)),f323(f166(x87411),x87413)))
% 179.72/179.59 [8759]~P112(x87594)+~P123(x87594)+~E(f323(f323(f9(x87591,x87594),x87592),x87593),f2(x87594))+~P101(f323(f59(x87591),x87593))+P101(f323(f323(f325(x87591),f460(x87592,x87593,x87591,x87594)),x87593))
% 179.72/179.59 [8795]~E(f323(x87952,x87954),f76(a860))+E(f323(f323(f6(x87951,a860),x87952),x87953),f76(a860))+~P101(f323(f59(x87951),x87953))+~P101(f323(f323(f325(x87951),x87954),x87953))+P101(f323(f323(f325(x87951),f357(x87952,x87953,x87951,x87954)),x87953))
% 179.72/179.59 [8804]E(x88041,x88042)+~E(f323(f323(f78(a1),x88042),x88044),x88041)+~P101(f323(f323(f238(a1),f2(a1)),x88044))+~P101(f323(f323(f325(a1),x88041),x88043))+P101(f323(f323(f325(a1),f405(x88043,x88041,x88044,x88042)),x88043))
% 179.72/179.59 [8805]E(x88051,x88052)+~E(f323(f323(f22(a1),x88052),x88054),x88051)+~P101(f323(f323(f238(a1),f2(a1)),x88054))+~P101(f323(f323(f325(a1),x88051),x88053))+P101(f323(f323(f325(a1),f408(x88053,x88051,x88054,x88052)),x88053))
% 179.72/179.59 [8807]~E(f323(x88072,x88074),f323(a112,f2(a860)))+E(f323(f323(f6(x88071,a860),x88072),x88073),f323(a112,f2(a860)))+~P101(f323(f59(x88071),x88073))+~P101(f323(f323(f325(x88071),x88074),x88073))+P101(f323(f323(f325(x88071),f356(x88072,x88073,x88071,x88074)),x88073))
% 179.72/179.59 [8812]P55(x88122,x88123,x88124,x88121)+E(x88121,f188(f867(x88122,a855)))+~P101(f323(f59(x88122),x88124))+~P101(f323(f59(x88122),x88121))+P101(f323(f323(f325(x88122),f662(x88121,x88124,x88123,x88122)),x88124))
% 179.72/179.59 [8893]E(x88931,x88932)+~E(f323(f323(f78(a1),x88932),x88934),x88931)+~P101(f323(f323(f238(a1),f2(a1)),x88934))+~P101(f323(f323(f325(a1),x88931),x88933))+P101(f323(f323(f325(a1),f406(x88933,x88931,x88934,x88932)),f294(a1,f76(a1),x88934)))
% 179.72/179.59 [8894]E(x88941,x88942)+~E(f323(f323(f22(a1),x88942),x88944),x88941)+~P101(f323(f323(f238(a1),f2(a1)),x88944))+~P101(f323(f323(f325(a1),x88941),x88943))+P101(f323(f323(f325(a1),f409(x88943,x88941,x88944,x88942)),f294(a1,f76(a1),x88944)))
% 179.72/179.59 [8964]P101(f323(f323(f237(a860),x89641),f751(x89642,x89643,x89644,x89641)))+~P101(f323(f323(f237(a1),x89642),f323(x89643,x89644)))+P101(f323(f323(f237(a860),x89641),f752(x89642,x89643,x89644,x89641)))+~P101(f323(f323(f238(a860),x89641),x89644))+~P101(f323(f323(f237(a1),f323(x89643,x89641)),x89642))
% 179.72/179.59 [9079]E(f323(x90791,f751(x90792,x90791,x90793,x90794)),x90792)+~P101(f323(f323(f237(a1),x90792),f323(x90791,x90793)))+P101(f323(f323(f238(a860),f752(x90792,x90791,x90793,x90794)),x90793))+~P101(f323(f323(f238(a860),x90794),x90793))+~P101(f323(f323(f237(a1),f323(x90791,x90794)),x90792))
% 179.72/179.59 [9207]~P101(f323(f323(f237(a1),x92072),f323(x92073,x92074)))+P101(f323(f323(f237(a860),x92071),f752(x92072,x92073,x92074,x92071)))+P101(f323(f323(f237(a860),f751(x92072,x92073,x92074,x92071)),x92074))+~P101(f323(f323(f238(a860),x92071),x92074))+~P101(f323(f323(f237(a1),f323(x92073,x92071)),x92072))
% 179.72/179.59 [9208]~P101(f323(f323(f237(a1),x92082),f323(x92083,x92084)))+P101(f323(f323(f237(a860),x92081),f751(x92082,x92083,x92084,x92081)))+P101(f323(f323(f238(a860),f752(x92082,x92083,x92084,x92081)),x92084))+~P101(f323(f323(f238(a860),x92081),x92084))+~P101(f323(f323(f237(a1),f323(x92083,x92081)),x92082))
% 179.72/179.59 [9314]~P101(f323(f323(f237(a1),x93141),f323(x93142,x93143)))+P101(f323(f323(f238(a860),f752(x93141,x93142,x93143,x93144)),x93143))+~P101(f323(f323(f238(a860),x93144),x93143))+~P101(f323(f323(f237(a1),f323(x93142,x93144)),x93141))+P101(f323(f323(f237(a860),f751(x93141,x93142,x93143,x93144)),x93143))
% 179.72/179.59 [9392]E(x93921,f188(f867(x93922,a855)))+~P101(f323(f59(x93922),x93924))+~P101(f323(f59(x93922),x93921))+P101(f323(f323(f325(f866(f867(x93922,a855),f867(x93922,a855))),f323(f323(f258(f867(x93922,a855),f867(x93922,a855)),x93924),x93921)),f314(x93922,x93923)))+P101(f323(f323(f325(x93922),f670(x93923,x93921,x93924,x93922)),x93924))
% 179.72/179.59 [9393]E(x93931,f188(f867(x93932,a855)))+~P101(f323(f59(x93932),x93934))+~P101(f323(f59(x93932),x93931))+P101(f323(f323(f325(f866(f867(x93932,a855),f867(x93932,a855))),f323(f323(f258(f867(x93932,a855),f867(x93932,a855)),x93934),x93931)),f314(x93932,x93933)))+P101(f323(f323(f325(x93932),f715(x93933,x93931,x93934,x93932)),x93934))
% 179.72/179.59 [10054]E(f323(x100541,f751(x100542,x100541,x100543,x100544)),x100542)+~P101(f323(f323(f237(a1),x100542),f323(x100541,x100543)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x100541,f323(f323(f78(a860),f752(x100542,x100541,x100543,x100544)),f76(a860)))),f323(x100541,f752(x100542,x100541,x100543,x100544))))),f76(a1)))+~P101(f323(f323(f238(a860),x100544),x100543))+~P101(f323(f323(f237(a1),f323(x100541,x100544)),x100542))
% 179.72/179.59 [10055]~P101(f323(f323(f237(a1),x100552),f323(x100553,x100554)))+P101(f323(f323(f237(a860),x100551),f751(x100552,x100553,x100554,x100551)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x100553,f323(f323(f78(a860),f752(x100552,x100553,x100554,x100551)),f76(a860)))),f323(x100553,f752(x100552,x100553,x100554,x100551))))),f76(a1)))+~P101(f323(f323(f238(a860),x100551),x100554))+~P101(f323(f323(f237(a1),f323(x100553,x100551)),x100552))
% 179.72/179.59 [10056]~P101(f323(f323(f237(a1),x100561),f323(x100562,x100563)))+~P101(f323(f323(f237(a1),f323(f73(a1),f323(f323(f22(a1),f323(x100562,f323(f323(f78(a860),f752(x100561,x100562,x100563,x100564)),f76(a860)))),f323(x100562,f752(x100561,x100562,x100563,x100564))))),f76(a1)))+~P101(f323(f323(f238(a860),x100564),x100563))+~P101(f323(f323(f237(a1),f323(x100562,x100564)),x100561))+P101(f323(f323(f237(a860),f751(x100561,x100562,x100563,x100564)),x100563))
% 179.72/179.59 [7155]~P64(x71551)+P101(f323(f323(f238(x71551),x71552),f2(x71551)))+~P101(f323(f323(f237(x71551),x71553),f2(x71551)))+P101(f323(f323(f238(x71551),f2(x71551)),x71552))+P101(f323(f323(f237(x71551),x71553),f323(f323(f281(x71551),x71554),x71552)))
% 179.72/179.59 [7156]~P64(x71561)+P101(f323(f323(f238(x71561),x71562),f2(x71561)))+~P101(f323(f323(f238(x71561),x71563),f2(x71561)))+P101(f323(f323(f238(x71561),f2(x71561)),x71562))+P101(f323(f323(f238(x71561),x71563),f323(f323(f281(x71561),x71564),x71562)))
% 179.72/179.59 [7401]~P64(x74011)+P101(f323(f323(f237(x74011),x74012),f2(x74011)))+P101(f323(f323(f238(x74011),x74013),f2(x74011)))+P101(f323(f323(f238(x74011),f2(x74011)),x74013))+~P101(f323(f323(f237(x74011),x74012),f323(f323(f281(x74011),x74014),x74013)))
% 179.72/179.59 [7402]~P64(x74021)+P101(f323(f323(f238(x74021),x74022),f2(x74021)))+P101(f323(f323(f238(x74021),x74023),f2(x74021)))+P101(f323(f323(f238(x74021),f2(x74021)),x74023))+~P101(f323(f323(f238(x74021),x74022),f323(f323(f281(x74021),x74024),x74023)))
% 179.72/179.59 [7519]E(x75191,x75192)+~E(f323(f323(f158(x75193),x75194),x75191),f323(f323(f158(x75193),x75194),x75192))+~P101(f323(f130(x75193),x75194))+~P101(f323(f323(f238(a860),x75192),f323(f189(f861(x75193)),x75194)))+~P101(f323(f323(f238(a860),x75191),f323(f189(f861(x75193)),x75194)))
% 179.72/179.59 [7884]~P64(x78841)+~P101(f323(f323(f237(x78841),x78843),f2(x78841)))+P101(f323(f323(f238(x78841),f2(x78841)),x78842))+~P101(f323(f323(f237(x78841),x78844),f323(f323(f79(x78841),x78843),x78842)))+P101(f323(f323(f237(x78841),x78843),f323(f323(f281(x78841),x78844),x78842)))
% 179.72/179.59 [7885]~P64(x78851)+~P101(f323(f323(f238(x78851),x78853),f2(x78851)))+P101(f323(f323(f238(x78851),f2(x78851)),x78852))+~P101(f323(f323(f238(x78851),x78854),f323(f323(f79(x78851),x78853),x78852)))+P101(f323(f323(f238(x78851),x78853),f323(f323(f281(x78851),x78854),x78852)))
% 179.72/179.59 [7886]~P64(x78861)+~P101(f323(f323(f238(x78861),x78862),f2(x78861)))+P101(f323(f323(f238(x78861),f2(x78861)),x78862))+~P101(f323(f323(f237(x78861),x78864),f323(f323(f79(x78861),x78863),x78862)))+P101(f323(f323(f237(x78861),x78863),f323(f323(f281(x78861),x78864),x78862)))
% 179.72/179.59 [7887]~P64(x78871)+~P101(f323(f323(f238(x78871),x78872),f2(x78871)))+P101(f323(f323(f238(x78871),f2(x78871)),x78872))+~P101(f323(f323(f237(x78871),x78874),f323(f323(f281(x78871),x78873),x78872)))+P101(f323(f323(f237(x78871),x78873),f323(f323(f79(x78871),x78874),x78872)))
% 179.72/179.59 [7888]~P64(x78881)+~P101(f323(f323(f238(x78881),x78882),f2(x78881)))+P101(f323(f323(f238(x78881),f2(x78881)),x78882))+~P101(f323(f323(f238(x78881),x78884),f323(f323(f79(x78881),x78883),x78882)))+P101(f323(f323(f238(x78881),x78883),f323(f323(f281(x78881),x78884),x78882)))
% 179.72/179.59 [7889]~P64(x78891)+~P101(f323(f323(f238(x78891),x78892),f2(x78891)))+P101(f323(f323(f238(x78891),f2(x78891)),x78892))+~P101(f323(f323(f238(x78891),x78894),f323(f323(f281(x78891),x78893),x78892)))+P101(f323(f323(f238(x78891),x78893),f323(f323(f79(x78891),x78894),x78892)))
% 179.72/179.59 [8027]~P103(x80271)+~P16(x80271,x80272)+~P101(f323(f323(f237(a860),x80273),x80274))+P101(f323(f323(f237(x80271),f323(f323(f158(x80271),x80272),x80273)),f323(f323(f158(x80271),x80272),x80274)))+~P101(f323(f323(f238(a860),x80274),f323(f189(f861(x80271)),x80272)))
% 179.72/179.59 [8076]~P119(x80761)+~P101(f323(f323(f237(x80761),x80762),f76(x80761)))+~P101(f323(f323(f237(x80761),f2(x80761)),x80762))+~P101(f323(f323(f237(a860),x80764),x80763))+P101(f323(f323(f237(x80761),f323(f323(f248(x80761),x80762),x80763)),f323(f323(f248(x80761),x80762),x80764)))
% 179.72/179.59 [8077]~P119(x80771)+~P101(f323(f323(f238(x80771),x80772),f76(x80771)))+~P101(f323(f323(f238(x80771),f2(x80771)),x80772))+~P101(f323(f323(f238(a860),x80774),x80773))+P101(f323(f323(f238(x80771),f323(f323(f248(x80771),x80772),x80773)),f323(f323(f248(x80771),x80772),x80774)))
% 179.72/179.59 [8078]~P119(x80781)+~P101(f323(f323(f237(x80781),f2(x80781)),x80782))+~P101(f323(f323(f238(a860),f2(a860)),x80783))+~P101(f323(f323(f238(x80781),x80782),x80784))+P101(f323(f323(f238(x80781),f323(f323(f248(x80781),x80782),x80783)),f323(f323(f248(x80781),x80784),x80783)))
% 179.72/179.59 [8097]~P103(x80971)+~P16(x80971,f323(f162(x80971),x80972))+~P101(f323(f323(f237(a860),x80974),x80973))+P101(f323(f323(f237(x80971),f323(f323(f158(x80971),x80972),x80973)),f323(f323(f158(x80971),x80972),x80974)))+~P101(f323(f323(f238(a860),x80973),f323(f189(f861(x80971)),x80972)))
% 179.72/179.59 [8348]~P64(x83481)+~P101(f323(f323(f237(x83481),x83482),f2(x83481)))+~P101(f323(f323(f237(x83481),x83483),x83484))+~P101(f323(f323(f238(x83481),f2(x83481)),f323(f323(f79(x83481),x83483),x83484)))+P101(f323(f323(f237(x83481),f323(f323(f281(x83481),x83482),x83483)),f323(f323(f281(x83481),x83482),x83484)))
% 179.72/179.59 [8349]~P65(x83491)+~P101(f323(f323(f238(x83491),x83492),f2(x83491)))+~P101(f323(f323(f238(x83491),x83493),x83494))+~P101(f323(f323(f238(x83491),f2(x83491)),f323(f323(f79(x83491),x83493),x83494)))+P101(f323(f323(f238(x83491),f323(f323(f281(x83491),x83492),x83493)),f323(f323(f281(x83491),x83492),x83494)))
% 179.72/179.59 [8359]~P65(x83591)+~P101(f323(f323(f237(x83591),x83594),x83593))+~P101(f323(f323(f237(x83591),f2(x83591)),x83592))+~P101(f323(f323(f238(x83591),f2(x83591)),f323(f323(f79(x83591),x83593),x83594)))+P101(f323(f323(f237(x83591),f323(f323(f281(x83591),x83592),x83593)),f323(f323(f281(x83591),x83592),x83594)))
% 179.72/179.59 [8360]~P65(x83601)+~P101(f323(f323(f238(x83601),x83604),x83603))+~P101(f323(f323(f238(x83601),f2(x83601)),x83602))+~P101(f323(f323(f238(x83601),f2(x83601)),f323(f323(f79(x83601),x83603),x83604)))+P101(f323(f323(f238(x83601),f323(f323(f281(x83601),x83602),x83603)),f323(f323(f281(x83601),x83602),x83604)))
% 179.72/179.59 [8456]P101(f323(x84561,x84562))+~P101(f323(f59(x84564),x84562))+P101(f323(x84561,f827(x84561,x84563,x84562,x84564)))+~P101(f323(x84561,f188(f867(x84564,a855))))+~P101(f323(f323(f237(f867(x84564,a855)),x84562),x84563))
% 179.72/179.59 [8465]P101(f323(x84651,x84652))+P101(f323(f59(x84653),f827(x84651,x84654,x84652,x84653)))+~P101(f323(f59(x84653),x84652))+~P101(f323(x84651,f188(f867(x84653,a855))))+~P101(f323(f323(f237(f867(x84653,a855)),x84652),x84654))
% 179.72/179.59 [8735]E(f323(f323(f78(a1),f410(x87351,x87352,x87353,x87354)),f411(x87351,x87352,x87353,x87354)),x87354)+~P101(f323(f323(f238(a1),f2(a1)),x87353))+~P101(f323(f323(f238(a1),x87352),x87354))+~P101(f323(f323(f325(a1),x87352),x87351))+P101(f323(f323(f238(a1),x87352),f323(f323(f22(a1),x87354),x87353)))
% 179.72/179.59 [8946]~P101(f323(f323(f238(a1),f2(a1)),x89463))+~P101(f323(f323(f238(a1),x89462),x89464))+~P101(f323(f323(f325(a1),x89462),x89461))+P101(f323(f323(f325(a1),f410(x89461,x89462,x89463,x89464)),x89461))+P101(f323(f323(f238(a1),x89462),f323(f323(f22(a1),x89464),x89463)))
% 179.72/179.59 [8957]P101(f323(x89571,x89572))+~P101(f323(f59(x89573),x89572))+P101(f323(f323(f325(x89573),f828(x89571,x89574,x89572,x89573)),x89574))+~P101(f323(x89571,f188(f867(x89573,a855))))+~P101(f323(f323(f237(f867(x89573,a855)),x89572),x89574))
% 179.72/179.59 [8974]E(f323(f323(f78(a1),f393(x89741,x89742,x89743,x89744)),f394(x89741,x89742,x89743,x89744)),x89744)+~P101(f323(f323(f238(a1),f2(a1)),x89743))+~P101(f323(f323(f237(a1),x89742),x89744))+P101(f323(f323(f237(a1),x89742),f323(f323(f22(a1),x89744),x89743)))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x89742),f76(a1))),x89741))
% 179.72/179.59 [9030]~P101(f323(f323(f238(a1),f2(a1)),x90303))+~P101(f323(f323(f238(a1),x90301),x90302))+~P101(f323(f323(f325(a1),x90301),x90304))+P101(f323(f323(f325(a1),f411(x90304,x90301,x90303,x90302)),f294(a1,f76(a1),x90303)))+P101(f323(f323(f238(a1),x90301),f323(f323(f22(a1),x90302),x90303)))
% 179.72/179.59 [9123]~P101(f323(f323(f238(a1),f2(a1)),x91233))+~P101(f323(f323(f237(a1),x91232),x91234))+P101(f323(f323(f325(a1),f393(x91231,x91232,x91233,x91234)),x91231))+P101(f323(f323(f237(a1),x91232),f323(f323(f22(a1),x91234),x91233)))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x91232),f76(a1))),x91231))
% 179.72/179.59 [9168]~P101(f323(f323(f238(a1),f2(a1)),x91683))+~P101(f323(f323(f237(a1),x91681),x91682))+P101(f323(f323(f325(a1),f394(x91684,x91681,x91683,x91682)),f294(a1,f76(a1),x91683)))+P101(f323(f323(f237(a1),x91681),f323(f323(f22(a1),x91682),x91683)))+~P101(f323(f323(f325(a1),f323(f323(f22(a1),x91681),f76(a1))),x91684))
% 179.72/179.59 [9395]P101(f323(x93951,x93952))+~P101(f323(f323(f325(x93953),f828(x93951,x93954,x93952,x93953)),f827(x93951,x93954,x93952,x93953)))+~P101(f323(f59(x93953),x93952))+~P101(f323(x93951,f188(f867(x93953,a855))))+~P101(f323(f323(f237(f867(x93953,a855)),x93952),x93954))
% 179.72/179.59 [9613]P101(f323(x96131,x96132))+~P101(f323(f59(x96133),x96132))+~P101(f323(x96131,f323(f323(f301(x96133),f828(x96131,x96134,x96132,x96133)),f827(x96131,x96134,x96132,x96133))))+~P101(f323(x96131,f188(f867(x96133,a855))))+~P101(f323(f323(f237(f867(x96133,a855)),x96132),x96134))
% 179.72/179.59 [7655]~P64(x76551)+P101(f323(f323(f238(x76551),x76552),f2(x76551)))+~P101(f323(f323(f237(x76551),f2(x76551)),x76554))+P101(f323(f323(f238(x76551),f2(x76551)),x76552))+P101(f323(f323(f237(x76551),f323(f323(f281(x76551),x76553),x76552)),x76554))
% 179.72/179.59 [7656]~P64(x76561)+P101(f323(f323(f238(x76561),x76562),f2(x76561)))+P101(f323(f323(f238(x76561),f2(x76561)),x76562))+~P101(f323(f323(f238(x76561),f2(x76561)),x76564))+P101(f323(f323(f238(x76561),f323(f323(f281(x76561),x76563),x76562)),x76564))
% 179.72/179.59 [7936]~P101(f323(f323(f237(a1),x79364),f2(a1)))+~E(x79362,f323(f323(f78(a1),f323(f323(f79(a1),x79361),x79363)),x79364))+P101(f323(f323(f238(a1),f2(a1)),x79361))+~P101(f323(f323(f238(a1),x79361),x79364))+P101(f323(f46(x79362,x79361),f323(f323(f258(a1,a1),x79363),x79364)))
% 179.72/179.59 [7970]~P101(f323(x79701,x79704))+P101(f323(x79701,f426(x79702,x79701,x79703)))+~P101(f323(f323(f237(a1),f2(a1)),x79702))+~P101(f323(f323(f238(a1),f2(a1)),x79703))+P101(f323(x79701,f323(f323(f22(a1),x79704),f323(f323(f79(a1),x79702),x79703))))
% 179.72/179.59 [7971]~P101(f323(x79711,x79714))+P101(f323(x79711,f428(x79712,x79711,x79713)))+~P101(f323(f323(f237(a1),f2(a1)),x79712))+~P101(f323(f323(f238(a1),f2(a1)),x79713))+P101(f323(x79711,f323(f323(f78(a1),x79714),f323(f323(f79(a1),x79712),x79713))))
% 179.72/179.59 [7972]~P64(x79721)+P101(f323(f323(f238(x79721),x79722),f2(x79721)))+P101(f323(f323(f238(x79721),f2(x79721)),x79722))+P101(f323(f323(f237(x79721),f2(x79721)),x79723))+~P101(f323(f323(f237(x79721),f323(f323(f281(x79721),x79724),x79722)),x79723))
% 179.72/179.59 [7973]~P64(x79731)+P101(f323(f323(f238(x79731),x79732),f2(x79731)))+P101(f323(f323(f238(x79731),f2(x79731)),x79732))+P101(f323(f323(f238(x79731),f2(x79731)),x79733))+~P101(f323(f323(f238(x79731),f323(f323(f281(x79731),x79734),x79732)),x79733))
% 179.72/179.59 [8022]~E(x80221,f323(f323(f78(a1),f323(f323(f79(a1),x80222),x80223)),x80224))+~P101(f323(f323(f237(a1),f2(a1)),x80224))+~P101(f323(f323(f238(a1),f2(a1)),x80222))+~P101(f323(f323(f238(a1),x80224),x80222))+P101(f323(f46(x80221,x80222),f323(f323(f258(a1,a1),x80223),x80224)))
% 179.72/179.59 [8140]~P64(x81401)+P101(f323(f323(f238(x81401),x81402),f2(x81401)))+~P101(f323(f323(f237(x81401),f2(x81401)),x81404))+~P101(f323(f323(f237(x81401),x81403),f323(f323(f79(x81401),x81404),x81402)))+P101(f323(f323(f237(x81401),f323(f323(f281(x81401),x81403),x81402)),x81404))
% 179.72/179.59 [8141]~P64(x81411)+P101(f323(f323(f238(x81411),x81412),f2(x81411)))+~P101(f323(f323(f238(x81411),f2(x81411)),x81414))+~P101(f323(f323(f238(x81411),x81413),f323(f323(f79(x81411),x81414),x81412)))+P101(f323(f323(f238(x81411),f323(f323(f281(x81411),x81413),x81412)),x81414))
% 179.72/179.59 [8225]~P64(x82251)+P101(f323(f323(f238(x82251),x82252),f2(x82251)))+~P101(f323(f323(f237(x82251),x82253),f2(x82251)))+P101(f323(f323(f237(x82251),x82253),f323(f323(f281(x82251),x82254),x82252)))+~P101(f323(f323(f237(x82251),f323(f323(f79(x82251),x82253),x82252)),x82254))
% 179.72/179.59 [8226]~P64(x82261)+P101(f323(f323(f238(x82261),x82262),f2(x82261)))+~P101(f323(f323(f238(x82261),x82263),f2(x82261)))+P101(f323(f323(f238(x82261),x82263),f323(f323(f281(x82261),x82264),x82262)))+~P101(f323(f323(f238(x82261),f323(f323(f79(x82261),x82263),x82262)),x82264))
% 179.72/179.59 [8382]~P64(x83821)+~P101(f323(f323(f238(x83821),x83822),f2(x83821)))+P101(f323(f323(f238(x83821),f2(x83821)),x83822))+~P101(f323(f323(f237(x83821),f323(f323(f281(x83821),x83824),x83822)),x83823))+P101(f323(f323(f237(x83821),f323(f323(f79(x83821),x83823),x83822)),x83824))
% 179.72/179.59 [8383]~P64(x83831)+~P101(f323(f323(f238(x83831),x83832),f2(x83831)))+P101(f323(f323(f238(x83831),f2(x83831)),x83832))+~P101(f323(f323(f237(x83831),f323(f323(f79(x83831),x83834),x83832)),x83833))+P101(f323(f323(f237(x83831),f323(f323(f281(x83831),x83833),x83832)),x83834))
% 179.72/179.59 [8384]~P64(x83841)+~P101(f323(f323(f238(x83841),x83842),f2(x83841)))+P101(f323(f323(f238(x83841),f2(x83841)),x83842))+~P101(f323(f323(f238(x83841),f323(f323(f281(x83841),x83844),x83842)),x83843))+P101(f323(f323(f238(x83841),f323(f323(f79(x83841),x83843),x83842)),x83844))
% 179.72/179.59 [8385]~P64(x83851)+~P101(f323(f323(f238(x83851),x83852),f2(x83851)))+P101(f323(f323(f238(x83851),f2(x83851)),x83852))+~P101(f323(f323(f238(x83851),f323(f323(f79(x83851),x83854),x83852)),x83853))+P101(f323(f323(f238(x83851),f323(f323(f281(x83851),x83853),x83852)),x83854))
% 179.72/179.59 [8402]~P64(x84021)+~P101(f323(f323(f237(x84021),f2(x84021)),x84024))+P101(f323(f323(f238(x84021),f2(x84021)),x84022))+~P101(f323(f323(f237(x84021),f323(f323(f79(x84021),x84024),x84022)),x84023))+P101(f323(f323(f237(x84021),f323(f323(f281(x84021),x84023),x84022)),x84024))
% 179.72/179.59 [8403]~P64(x84031)+~P101(f323(f323(f238(x84031),f2(x84031)),x84034))+P101(f323(f323(f238(x84031),f2(x84031)),x84032))+~P101(f323(f323(f238(x84031),f323(f323(f79(x84031),x84034),x84032)),x84033))+P101(f323(f323(f238(x84031),f323(f323(f281(x84031),x84033),x84032)),x84034))
% 179.72/179.59 [8473]~P64(x84731)+~P101(f323(f323(f238(x84731),x84734),f2(x84731)))+~P101(f323(f323(f237(x84731),x84733),f323(f323(f79(x84731),x84732),x84734)))+P101(f323(f323(f237(x84731),x84732),f323(f323(f281(x84731),x84733),x84734)))+~P101(f323(f323(f237(x84731),f323(f323(f79(x84731),x84732),x84734)),x84733))
% 179.72/179.59 [8474]~P64(x84741)+~P101(f323(f323(f237(x84741),x84742),f2(x84741)))+~P101(f323(f323(f237(x84741),x84743),f323(f323(f79(x84741),x84742),x84744)))+P101(f323(f323(f237(x84741),x84742),f323(f323(f281(x84741),x84743),x84744)))+~P101(f323(f323(f237(x84741),f323(f323(f79(x84741),x84742),x84744)),x84743))
% 179.72/179.59 [8475]~P64(x84751)+~P101(f323(f323(f238(x84751),x84754),f2(x84751)))+~P101(f323(f323(f238(x84751),x84753),f323(f323(f79(x84751),x84752),x84754)))+P101(f323(f323(f238(x84751),x84752),f323(f323(f281(x84751),x84753),x84754)))+~P101(f323(f323(f238(x84751),f323(f323(f79(x84751),x84752),x84754)),x84753))
% 179.72/179.59 [8476]~P64(x84761)+~P101(f323(f323(f238(x84761),x84762),f2(x84761)))+~P101(f323(f323(f238(x84761),x84763),f323(f323(f79(x84761),x84762),x84764)))+P101(f323(f323(f238(x84761),x84762),f323(f323(f281(x84761),x84763),x84764)))+~P101(f323(f323(f238(x84761),f323(f323(f79(x84761),x84762),x84764)),x84763))
% 179.72/179.59 [8598]~P64(x85981)+~P101(f323(f323(f238(x85981),x85983),f2(x85981)))+~P101(f323(f323(f237(x85981),x85982),f323(f323(f79(x85981),x85984),x85983)))+~P101(f323(f323(f237(x85981),f323(f323(f79(x85981),x85984),x85983)),x85982))+P101(f323(f323(f237(x85981),f323(f323(f281(x85981),x85982),x85983)),x85984))
% 179.72/179.59 [8599]~P64(x85991)+~P101(f323(f323(f238(x85991),x85993),f2(x85991)))+~P101(f323(f323(f238(x85991),x85992),f323(f323(f79(x85991),x85994),x85993)))+~P101(f323(f323(f238(x85991),f323(f323(f79(x85991),x85994),x85993)),x85992))+P101(f323(f323(f238(x85991),f323(f323(f281(x85991),x85992),x85993)),x85994))
% 179.72/179.59 [8617]~P64(x86171)+~P101(f323(f323(f237(x86171),f2(x86171)),x86174))+~P101(f323(f323(f237(x86171),x86172),f323(f323(f79(x86171),x86174),x86173)))+~P101(f323(f323(f237(x86171),f323(f323(f79(x86171),x86174),x86173)),x86172))+P101(f323(f323(f237(x86171),f323(f323(f281(x86171),x86172),x86173)),x86174))
% 179.72/179.59 [8618]~P64(x86181)+~P101(f323(f323(f238(x86181),f2(x86181)),x86184))+~P101(f323(f323(f238(x86181),x86182),f323(f323(f79(x86181),x86184),x86183)))+~P101(f323(f323(f238(x86181),f323(f323(f79(x86181),x86184),x86183)),x86182))+P101(f323(f323(f238(x86181),f323(f323(f281(x86181),x86182),x86183)),x86184))
% 179.72/179.59 [8797]E(f323(f323(f22(a1),f412(x87971,x87972,x87973,x87974)),f413(x87971,x87972,x87973,x87974)),x87974)+~P101(f323(f323(f238(a1),f2(a1)),x87973))+~P101(f323(f323(f325(a1),x87972),x87971))+~P101(f323(f323(f238(a1),x87974),x87972))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x87974),x87973)),x87972))
% 179.72/179.59 [8876]~P101(f323(x88761,x88762))+~P101(f323(f323(f237(a1),f2(a1)),x88763))+~P101(f323(f323(f238(a1),f2(a1)),x88764))+~P101(f323(x88761,f323(f323(f22(a1),f426(x88763,x88761,x88764)),x88764)))+P101(f323(x88761,f323(f323(f22(a1),x88762),f323(f323(f79(a1),x88763),x88764))))
% 179.72/179.59 [8877]~P101(f323(x88771,x88772))+~P101(f323(f323(f237(a1),f2(a1)),x88773))+~P101(f323(f323(f238(a1),f2(a1)),x88774))+~P101(f323(x88771,f323(f323(f78(a1),f428(x88773,x88771,x88774)),x88774)))+P101(f323(x88771,f323(f323(f78(a1),x88772),f323(f323(f79(a1),x88773),x88774))))
% 179.72/179.59 [9023]~P101(f323(f323(f238(a1),f2(a1)),x90233))+~P101(f323(f323(f325(a1),x90232),x90231))+~P101(f323(f323(f238(a1),x90234),x90232))+P101(f323(f323(f325(a1),f412(x90231,x90232,x90233,x90234)),x90231))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x90234),x90233)),x90232))
% 179.72/179.59 [9044]E(f323(f323(f22(a1),f395(x90441,x90442,x90443,x90444)),f396(x90441,x90442,x90443,x90444)),x90444)+~P101(f323(f323(f238(a1),f2(a1)),x90443))+~P101(f323(f323(f237(a1),x90444),x90442))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x90442),f76(a1))),x90441))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x90444),x90443)),x90442))
% 179.72/179.59 [9071]~P101(f323(f323(f238(a1),f2(a1)),x90712))+~P101(f323(f323(f325(a1),x90713),x90714))+~P101(f323(f323(f238(a1),x90711),x90713))+P101(f323(f323(f325(a1),f413(x90714,x90713,x90712,x90711)),f294(a1,f76(a1),x90712)))+P101(f323(f323(f238(a1),f323(f323(f78(a1),x90711),x90712)),x90713))
% 179.72/179.59 [9163]~P101(f323(f323(f238(a1),f2(a1)),x91633))+~P101(f323(f323(f237(a1),x91634),x91632))+P101(f323(f323(f325(a1),f395(x91631,x91632,x91633,x91634)),x91631))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x91632),f76(a1))),x91631))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x91634),x91633)),x91632))
% 179.72/179.59 [9203]~P101(f323(f323(f238(a1),f2(a1)),x92032))+~P101(f323(f323(f237(a1),x92031),x92033))+P101(f323(f323(f325(a1),f396(x92034,x92033,x92032,x92031)),f294(a1,f76(a1),x92032)))+~P101(f323(f323(f325(a1),f323(f323(f78(a1),x92033),f76(a1))),x92034))+P101(f323(f323(f237(a1),f323(f323(f78(a1),x92031),x92032)),x92033))
% 179.72/179.59 [9487]~P38(x94871,x94873)+~P29(x94871,x94874)+P38(x94871,f323(f323(f110(f867(f866(x94871,x94871),a855)),x94872),x94873))+~P101(f323(f323(f237(f867(f866(x94871,x94871),a855)),x94872),f323(f257(f867(f866(x94871,x94871),a855),f867(f866(x94871,x94871),a855)),x94874)))+~P101(f323(f323(f237(f867(f866(x94871,x94871),a855)),x94873),f323(f261(f867(f866(x94871,x94871),a855),f867(f866(x94871,x94871),a855)),x94874)))
% 179.72/179.59 [9784]~E(f323(f517(x97841,x97844,x97843,x97842),f519(x97841,x97844,x97843,x97842)),f200(f861(a319)))+P101(f323(f323(f238(a1),f518(x97841,x97844,x97843,x97842)),f519(x97841,x97844,x97843,x97842)))+P101(f323(f323(f323(x97841,x97842),x97843),x97844))+P101(f323(f323(f323(x97841,f517(x97841,x97844,x97843,x97842)),f518(x97841,x97844,x97843,x97842)),f323(f323(f78(a1),f519(x97841,x97844,x97843,x97842)),f76(a1))))+~P101(f323(f311(f866(f867(a1,f864(f861(a319))),f866(a1,a1)),a309),f323(f323(f258(f867(a1,f864(f861(a319))),f866(a1,a1)),x97842),f323(f323(f258(a1,a1),x97843),x97844))))
% 179.72/179.59 [9883]~P20(x98832,x98834,x98833)+E(x98831,f188(f867(x98832,a855)))+~P101(f323(f59(x98832),x98831))+P101(f323(f323(f325(x98832),f323(x98833,x98831)),x98831))+~P101(f323(f323(f325(x98832),f323(f323(x98834,f807(x98831,x98833,x98834,x98832)),f809(x98831,x98833,x98834,x98832))),f323(f323(f301(x98832),f807(x98831,x98833,x98834,x98832)),f323(f323(f301(x98832),f809(x98831,x98833,x98834,x98832)),f188(f867(x98832,a855))))))
% 179.72/179.59 [9814]~P105(x98142)+~P5(x98141)+~P101(f323(f323(f237(f867(x98141,x98142)),x98143),x98144))+P101(f323(f323(f238(f867(x98141,x98142)),x98143),x98144))+~P101(f323(f55(x98141),f323(f323(f8(a855,a855,x98141),a318),f323(f323(f18(x98141,x98142,a855),f323(f323(f8(x98142,f867(x98142,a855),x98141),a320),x98143)),x98144))))
% 179.72/179.59 [9401]~P51(x94011,x94011,x94014)+P101(f323(f323(f325(f866(x94011,x94011)),f323(f323(f258(x94011,x94011),x94012),x94013)),f299(x94011,x94014)))+P101(f323(f323(f325(f866(x94011,x94011)),f323(f323(f258(x94011,x94011),x94013),x94012)),f299(x94011,x94014)))+~P101(f323(f323(f325(f866(x94011,x94011)),f323(f323(f258(x94011,x94011),x94015),x94012)),f299(x94011,x94014)))+~P101(f323(f323(f325(f866(x94011,x94011)),f323(f323(f258(x94011,x94011),x94015),x94013)),f299(x94011,x94014)))
% 179.72/179.59 [5591]E(x55911,f2(a860))+~E(f323(f35(x55912),x55915),x55911)+E(f323(f35(x55912),x55913),f323(a112,x55911))+~E(x55913,f323(f323(f301(x55912),x55914),x55915))+P101(f323(f323(f325(x55912),x55914),x55915))
% 179.72/179.59 [5715]~P63(x57152)+E(x57151,f2(x57152))+E(x57153,f2(x57152))+~E(f323(f323(f281(x57152),x57154),x57153),f323(f323(f281(x57152),x57155),x57151))+E(f323(f323(f79(x57152),x57154),x57151),f323(f323(f79(x57152),x57155),x57153))
% 179.72/179.59 [5716]~P63(x57162)+E(x57161,f2(x57162))+E(x57163,f2(x57162))+~E(f323(f323(f79(x57162),x57164),x57163),f323(f323(f79(x57162),x57165),x57161))+E(f323(f323(f281(x57162),x57164),x57161),f323(f323(f281(x57162),x57165),x57163))
% 179.72/179.59 [5782]~E(f323(f35(x57821),x57825),x57823)+~E(x57825,f188(f867(x57821,a855)))+E(f323(f35(x57821),x57822),f323(a112,x57823))+~E(x57822,f323(f323(f301(x57821),x57824),x57825))+P101(f323(f323(f325(x57821),x57824),x57825))
% 179.72/179.59 [6002]~P112(x60022)+~E(f323(x60023,x60025),f2(x60022))+E(f323(f323(f9(x60021,x60022),x60023),x60024),f2(x60022))+~P101(f323(f59(x60021),x60024))+~P101(f323(f323(f325(x60021),x60025),x60024))
% 179.72/179.59 [6366]~P103(x63663)+E(x63661,x63662)+~E(f323(f293(x63663,x63664),x63661),f323(f293(x63663,x63665),x63662))+~P101(f323(f323(f238(x63663),x63665),x63662))+~P101(f323(f323(f238(x63663),x63664),x63661))
% 179.72/179.59 [6367]~P103(x63673)+E(x63671,x63672)+~E(f323(f293(x63673,x63671),x63674),f323(f293(x63673,x63672),x63675))+~P101(f323(f323(f238(x63673),x63672),x63675))+~P101(f323(f323(f238(x63673),x63671),x63674))
% 179.72/179.59 [7418]~P103(x74181)+~P16(x74181,f323(f323(f121(x74181),x74184),x74185))+~P101(f323(f323(f325(x74181),x74183),f323(f166(x74181),x74185)))+~P101(f323(f323(f325(x74181),x74182),f323(f166(x74181),x74184)))+P101(f323(f323(f237(x74181),x74182),x74183))
% 179.72/179.59 [8509]~P105(x85091)+~P101(f323(f323(f238(f867(x85091,a855)),f294(x85091,x85095,x85092)),f294(x85091,x85094,x85093)))+~P101(f323(f323(f237(x85091),x85095),x85092))+P101(f323(f323(f238(x85091),x85092),x85093))+P101(f323(f323(f238(x85091),x85094),x85095))
% 179.72/179.59 [9926]~P19(x99262,x99265,x99263)+E(x99261,f188(f867(x99262,a855)))+~E(f323(f323(x99265,f323(x99264,f842(x99261,x99264,x99263,x99265,x99262))),f323(x99264,f843(x99261,x99264,x99263,x99265,x99262))),f323(x99264,f323(f323(x99265,f842(x99261,x99264,x99263,x99265,x99262)),f843(x99261,x99264,x99263,x99265,x99262))))+E(f323(x99263,f323(f302(x99262,x99262,x99264),x99261)),f323(x99264,f323(x99263,x99261)))+~P101(f323(f59(x99262),x99261))
% 179.72/179.59 [6363]~P20(x63632,x63635,x63633)+E(x63631,f188(f867(x63632,a855)))+~P101(f323(f59(x63632),x63631))+E(f323(x63633,f323(f323(f301(x63632),x63634),x63631)),f323(f323(x63635,x63634),f323(x63633,x63631)))+P101(f323(f323(f325(x63632),x63634),x63631))
% 179.72/179.59 [7179]~P19(x71792,x71793,x71794)+E(f323(f323(x71793,f323(x71794,x71791)),f323(x71794,x71795)),f323(x71794,x71795))+E(x71791,f188(f867(x71792,a855)))+~P101(f323(f59(x71792),x71795))+~P101(f323(f323(f237(f867(x71792,a855)),x71791),x71795))
% 179.72/179.59 [7394]~P5(x73944)+~P92(x73945)+E(f323(x73941,x73942),f323(x73943,x73942))+~P101(f323(f323(f325(x73944),x73942),f323(f166(x73944),f53(x73944))))+~P101(f323(f323(f89(f867(x73944,x73945)),x73941),x73943))
% 179.72/179.59 [7552]~P20(x75524,x75525,x75521)+E(f323(x75521,x75522),x75523)+~P101(f323(f59(x75524),x75522))+~E(f323(f323(f22(f867(x75524,a855)),x75522),f323(f323(f301(x75524),x75523),f188(f867(x75524,a855)))),f188(f867(x75524,a855)))+~P101(f323(f323(f325(x75524),x75523),x75522))
% 179.72/179.59 [7638]E(x76381,x76382)+~E(f323(f189(f861(x76383)),x76382),f323(f189(f861(x76384)),x76385))+~E(f323(f189(f861(x76383)),x76381),f323(f189(f861(x76384)),x76385))+~E(f323(f179(x76384,x76383),f323(f323(f175(x76384,x76383),x76385),x76381)),f323(f179(x76384,x76383),f323(f323(f175(x76384,x76383),x76385),x76382)))+~P101(f323(f130(x76384),x76385))
% 179.72/179.59 [8480]E(x84801,x84802)+~P9(x84803,x84804,x84805)+E(f323(f323(f101(f867(x84803,a855)),x84801),x84802),f188(f867(x84803,a855)))+~P101(f323(f323(f325(f867(x84803,a855)),x84802),f323(f323(f58(x84803),x84804),x84805)))+~P101(f323(f323(f325(f867(x84803,a855)),x84801),f323(f323(f58(x84803),x84804),x84805)))
% 179.72/179.59 [9284]~P72(x92842)+~E(f323(x92843,f433(x92843,x92844,x92845,x92841,x92842)),f2(x92842))+E(f323(f323(f6(x92841,x92842),x92843),x92844),f323(f323(f6(x92841,x92842),x92843),x92845))+~P101(f323(f59(x92841),x92845))+~P101(f323(f323(f237(f867(x92841,a855)),x92844),x92845))
% 179.72/179.59 [9285]~P72(x92852)+~E(f323(x92853,f434(x92853,x92854,x92855,x92851,x92852)),f2(x92852))+E(f323(f323(f6(x92851,x92852),x92853),x92854),f323(f323(f6(x92851,x92852),x92853),x92855))+~P101(f323(f59(x92851),x92855))+~P101(f323(f323(f237(f867(x92851,a855)),x92854),x92855))
% 179.72/179.59 [9286]~P68(x92862)+~E(f323(x92863,f475(x92863,x92864,x92865,x92861,x92862)),f76(x92862))+E(f323(f323(f9(x92861,x92862),x92863),x92864),f323(f323(f9(x92861,x92862),x92863),x92865))+~P101(f323(f59(x92861),x92865))+~P101(f323(f323(f237(f867(x92861,a855)),x92864),x92865))
% 179.72/179.59 [9287]~P68(x92872)+~E(f323(x92873,f478(x92873,x92874,x92875,x92871,x92872)),f76(x92872))+E(f323(f323(f9(x92871,x92872),x92873),x92874),f323(f323(f9(x92871,x92872),x92873),x92875))+~P101(f323(f59(x92871),x92875))+~P101(f323(f323(f237(f867(x92871,a855)),x92874),x92875))
% 179.72/179.59 [9763]~P84(x97631)+~P101(f323(f59(x97632),x97635))+~P101(f323(f323(f237(x97631),f2(x97631)),f323(x97633,f359(x97633,x97634,x97635,x97632,x97631))))+P101(f323(f323(f237(x97631),f323(f323(f6(x97632,x97631),x97633),x97634)),f323(f323(f6(x97632,x97631),x97633),x97635)))+~P101(f323(f323(f237(f867(x97632,a855)),x97634),x97635))
% 179.72/179.59 [7415]E(x74151,f2(a860))+P101(f323(x74152,x74153))+~E(x74154,f323(f323(f78(a860),f323(f323(f79(a860),x74151),x74153)),x74155))+~P101(f323(f323(f238(a860),x74155),x74151))+~P101(f323(x74152,f323(f323(f36(a860),x74154),x74151)))
% 179.72/179.59 [7493]E(x74931,f2(a860))+P101(f323(x74932,x74933))+~P101(f323(x74932,f42(a860,x74934,x74931)))+~E(x74934,f323(f323(f78(a860),f323(f323(f79(a860),x74931),x74935)),x74933))+~P101(f323(f323(f238(a860),x74933),x74931))
% 179.72/179.59 [7782]~P63(x77823)+E(f323(x77821,x77822),f2(x77823))+~P101(f323(f59(x77824),x77825))+E(f323(f323(f9(x77824,x77823),x77821),f323(f323(f22(f867(x77824,a855)),x77825),f323(f323(f301(x77824),x77822),f188(f867(x77824,a855))))),f323(f323(f9(x77824,x77823),x77821),x77825))+P101(f323(f323(f325(x77824),x77822),x77825))
% 179.72/179.59 [8182]~P72(x81821)+~P101(f323(f59(x81822),x81825))+~P101(f323(f59(x81822),x81824))+~E(f323(f323(f101(f867(x81822,a855)),x81824),x81825),f188(f867(x81822,a855)))+E(f323(f323(f78(x81821),f323(f323(f6(x81822,x81821),x81823),x81824)),f323(f323(f6(x81822,x81821),x81823),x81825)),f323(f323(f6(x81822,x81821),x81823),f323(f323(f110(f867(x81822,a855)),x81824),x81825)))
% 179.72/179.59 [8184]~P68(x81841)+~P101(f323(f59(x81842),x81845))+~P101(f323(f59(x81842),x81844))+~E(f323(f323(f101(f867(x81842,a855)),x81844),x81845),f188(f867(x81842,a855)))+E(f323(f323(f79(x81841),f323(f323(f9(x81842,x81841),x81843),x81844)),f323(f323(f9(x81842,x81841),x81843),x81845)),f323(f323(f9(x81842,x81841),x81843),f323(f323(f110(f867(x81842,a855)),x81844),x81845)))
% 179.72/179.59 [8280]~P63(x82803)+E(f323(x82801,x82802),f2(x82803))+~P101(f323(f59(x82804),x82805))+E(f323(f323(f9(x82804,x82803),x82801),f323(f323(f22(f867(x82804,a855)),x82805),f323(f323(f301(x82804),x82802),f188(f867(x82804,a855))))),f323(f323(f281(x82803),f323(f323(f9(x82804,x82803),x82801),x82805)),f323(x82801,x82802)))+~P101(f323(f323(f325(x82804),x82802),x82805))
% 179.72/179.59 [8999]~P9(x89991,x89995,x89994)+~E(f323(f323(f58(x89991),f323(f323(f301(x89991),x89992),f188(f867(x89991,a855)))),x89994),f323(f323(f58(x89991),f323(f323(f301(x89991),x89993),f188(f867(x89991,a855)))),x89994))+~P101(f323(f323(f325(x89991),x89993),x89995))+~P101(f323(f323(f325(x89991),x89992),x89995))+P101(f323(f323(f325(f866(x89991,x89991)),f323(f323(f258(x89991,x89991),x89992),x89993)),x89994))
% 179.72/179.59 [9022]~P9(x90221,x90225,x90223)+E(f323(f323(f58(x90221),f323(f323(f301(x90221),x90222),f188(f867(x90221,a855)))),x90223),f323(f323(f58(x90221),f323(f323(f301(x90221),x90224),f188(f867(x90221,a855)))),x90223))+~P101(f323(f323(f325(x90221),x90224),x90225))+~P101(f323(f323(f325(x90221),x90222),x90225))+~P101(f323(f323(f325(f866(x90221,x90221)),f323(f323(f258(x90221,x90221),x90222),x90224)),x90223))
% 179.72/179.59 [9313]~P68(x93131)+~P101(f323(f59(x93132),x93135))+~P101(f323(f59(x93132),x93134))+~E(f323(f323(f101(f867(x93132,a855)),x93134),x93135),f188(f867(x93132,a855)))+E(f323(f323(f79(x93131),f323(f323(f323(f63(x93131,x93132,f79(x93131)),x93133),f76(x93131)),x93134)),f323(f323(f323(f63(x93131,x93132,f79(x93131)),x93133),f76(x93131)),x93135)),f323(f323(f323(f63(x93131,x93132,f79(x93131)),x93133),f76(x93131)),f323(f323(f110(f867(x93132,a855)),x93134),x93135)))
% 179.72/179.59 [9322]~P72(x93221)+~E(f323(x93223,f358(x93223,x93225,x93224,x93222,x93221)),f2(x93221))+~P101(f323(f59(x93222),x93224))+~P101(f323(f59(x93222),x93225))+E(f323(f323(f78(x93221),f323(f323(f6(x93222,x93221),x93223),x93224)),f323(f323(f6(x93222,x93221),x93223),x93225)),f323(f323(f6(x93222,x93221),x93223),f323(f323(f110(f867(x93222,a855)),x93224),x93225)))
% 179.72/179.59 [9323]~P72(x93231)+~E(f323(x93233,f360(x93233,x93235,x93234,x93232,x93231)),f2(x93231))+~P101(f323(f59(x93232),x93234))+~P101(f323(f59(x93232),x93235))+E(f323(f323(f78(x93231),f323(f323(f6(x93232,x93231),x93233),x93234)),f323(f323(f6(x93232,x93231),x93233),x93235)),f323(f323(f6(x93232,x93231),x93233),f323(f323(f110(f867(x93232,a855)),x93234),x93235)))
% 179.72/179.59 [9324]~P68(x93241)+~E(f323(x93243,f473(x93243,x93245,x93244,x93242,x93241)),f76(x93241))+~P101(f323(f59(x93242),x93244))+~P101(f323(f59(x93242),x93245))+E(f323(f323(f79(x93241),f323(f323(f9(x93242,x93241),x93243),x93244)),f323(f323(f9(x93242,x93241),x93243),x93245)),f323(f323(f9(x93242,x93241),x93243),f323(f323(f110(f867(x93242,a855)),x93244),x93245)))
% 179.72/179.59 [9325]~P68(x93251)+~E(f323(x93253,f474(x93253,x93255,x93254,x93252,x93251)),f76(x93251))+~P101(f323(f59(x93252),x93254))+~P101(f323(f59(x93252),x93255))+E(f323(f323(f79(x93251),f323(f323(f9(x93252,x93251),x93253),x93254)),f323(f323(f9(x93252,x93251),x93253),x93255)),f323(f323(f9(x93252,x93251),x93253),f323(f323(f110(f867(x93252,a855)),x93254),x93255)))
% 179.72/179.59 [9532]~P68(x95321)+~E(f323(x95323,f841(x95323,x95325,x95324,x95322,x95321)),f76(x95321))+~P101(f323(f59(x95322),x95324))+~P101(f323(f59(x95322),x95325))+E(f323(f323(f79(x95321),f323(f323(f323(f63(x95321,x95322,f79(x95321)),x95323),f76(x95321)),x95324)),f323(f323(f323(f63(x95321,x95322,f79(x95321)),x95323),f76(x95321)),x95325)),f323(f323(f323(f63(x95321,x95322,f79(x95321)),x95323),f76(x95321)),f323(f323(f110(f867(x95322,a855)),x95324),x95325)))
% 179.72/179.59 [9641]~P72(x96412)+E(f323(f323(f6(x96411,x96412),x96413),x96414),f323(f323(f6(x96411,x96412),x96413),x96415))+~P101(f323(f59(x96411),x96415))+~P101(f323(f323(f237(f867(x96411,a855)),x96414),x96415))+P101(f323(f323(f325(x96411),f433(x96413,x96414,x96415,x96411,x96412)),f323(f323(f22(f867(x96411,a855)),x96415),x96414)))
% 179.72/179.59 [9642]~P72(x96422)+E(f323(f323(f6(x96421,x96422),x96423),x96424),f323(f323(f6(x96421,x96422),x96423),x96425))+~P101(f323(f59(x96421),x96425))+~P101(f323(f323(f237(f867(x96421,a855)),x96424),x96425))+P101(f323(f323(f325(x96421),f434(x96423,x96424,x96425,x96421,x96422)),f323(f323(f22(f867(x96421,a855)),x96425),x96424)))
% 179.72/179.59 [9643]~P68(x96432)+E(f323(f323(f9(x96431,x96432),x96433),x96434),f323(f323(f9(x96431,x96432),x96433),x96435))+~P101(f323(f59(x96431),x96435))+~P101(f323(f323(f237(f867(x96431,a855)),x96434),x96435))+P101(f323(f323(f325(x96431),f475(x96433,x96434,x96435,x96431,x96432)),f323(f323(f22(f867(x96431,a855)),x96435),x96434)))
% 179.72/179.59 [9644]~P68(x96442)+E(f323(f323(f9(x96441,x96442),x96443),x96444),f323(f323(f9(x96441,x96442),x96443),x96445))+~P101(f323(f59(x96441),x96445))+~P101(f323(f323(f237(f867(x96441,a855)),x96444),x96445))+P101(f323(f323(f325(x96441),f478(x96443,x96444,x96445,x96441,x96442)),f323(f323(f22(f867(x96441,a855)),x96445),x96444)))
% 179.72/179.59 [9662]~P72(x96621)+~P101(f323(f59(x96622),x96624))+~P101(f323(f59(x96622),x96625))+E(f323(f323(f78(x96621),f323(f323(f6(x96622,x96621),x96623),x96624)),f323(f323(f6(x96622,x96621),x96623),x96625)),f323(f323(f6(x96622,x96621),x96623),f323(f323(f110(f867(x96622,a855)),x96624),x96625)))+P101(f323(f323(f325(x96622),f358(x96623,x96625,x96624,x96622,x96621)),f323(f323(f101(f867(x96622,a855)),x96624),x96625)))
% 179.72/179.59 [9663]~P72(x96631)+~P101(f323(f59(x96632),x96634))+~P101(f323(f59(x96632),x96635))+E(f323(f323(f78(x96631),f323(f323(f6(x96632,x96631),x96633),x96634)),f323(f323(f6(x96632,x96631),x96633),x96635)),f323(f323(f6(x96632,x96631),x96633),f323(f323(f110(f867(x96632,a855)),x96634),x96635)))+P101(f323(f323(f325(x96632),f360(x96633,x96635,x96634,x96632,x96631)),f323(f323(f101(f867(x96632,a855)),x96634),x96635)))
% 179.72/179.59 [9664]~P68(x96641)+~P101(f323(f59(x96642),x96644))+~P101(f323(f59(x96642),x96645))+E(f323(f323(f79(x96641),f323(f323(f9(x96642,x96641),x96643),x96644)),f323(f323(f9(x96642,x96641),x96643),x96645)),f323(f323(f9(x96642,x96641),x96643),f323(f323(f110(f867(x96642,a855)),x96644),x96645)))+P101(f323(f323(f325(x96642),f473(x96643,x96645,x96644,x96642,x96641)),f323(f323(f101(f867(x96642,a855)),x96644),x96645)))
% 179.72/179.59 [9665]~P68(x96651)+~P101(f323(f59(x96652),x96654))+~P101(f323(f59(x96652),x96655))+E(f323(f323(f79(x96651),f323(f323(f9(x96652,x96651),x96653),x96654)),f323(f323(f9(x96652,x96651),x96653),x96655)),f323(f323(f9(x96652,x96651),x96653),f323(f323(f110(f867(x96652,a855)),x96654),x96655)))+P101(f323(f323(f325(x96652),f474(x96653,x96655,x96654,x96652,x96651)),f323(f323(f101(f867(x96652,a855)),x96654),x96655)))
% 179.72/179.59 [9672]~P84(x96725)+~P101(f323(f59(x96721),x96724))+P101(f323(f323(f237(x96725),f323(f323(f6(x96721,x96725),x96722),x96723)),f323(f323(f6(x96721,x96725),x96722),x96724)))+~P101(f323(f323(f237(f867(x96721,a855)),x96723),x96724))+P101(f323(f323(f325(x96721),f359(x96722,x96723,x96724,x96721,x96725)),f323(f323(f22(f867(x96721,a855)),x96724),x96723)))
% 179.72/179.59 [9726]~P68(x97261)+~P101(f323(f59(x97262),x97264))+~P101(f323(f59(x97262),x97265))+E(f323(f323(f79(x97261),f323(f323(f323(f63(x97261,x97262,f79(x97261)),x97263),f76(x97261)),x97264)),f323(f323(f323(f63(x97261,x97262,f79(x97261)),x97263),f76(x97261)),x97265)),f323(f323(f323(f63(x97261,x97262,f79(x97261)),x97263),f76(x97261)),f323(f323(f110(f867(x97262,a855)),x97264),x97265)))+P101(f323(f323(f325(x97262),f841(x97263,x97265,x97264,x97262,x97261)),f323(f323(f101(f867(x97262,a855)),x97264),x97265)))
% 179.72/179.59 [8690]~P20(x86901,x86904,x86905)+~P101(f323(f59(x86901),x86902))+E(f323(f323(f22(f867(x86901,a855)),x86902),f323(f323(f301(x86901),x86903),f188(f867(x86901,a855)))),f188(f867(x86901,a855)))+~P101(f323(f323(f325(x86901),x86903),x86902))+E(f323(f323(x86904,x86903),f323(x86905,f323(f323(f22(f867(x86901,a855)),x86902),f323(f323(f301(x86901),x86903),f188(f867(x86901,a855)))))),f323(x86905,x86902))
% 179.72/179.59 [8769]~P20(x87691,x87694,x87695)+~P101(f323(f59(x87691),x87693))+~P101(f323(f59(x87691),x87692))+E(f323(f323(f101(f867(x87691,a855)),x87692),x87693),f188(f867(x87691,a855)))+E(f323(f323(x87694,f323(x87695,f323(f323(f110(f867(x87691,a855)),x87692),x87693))),f323(x87695,f323(f323(f101(f867(x87691,a855)),x87692),x87693))),f323(f323(x87694,f323(x87695,x87692)),f323(x87695,x87693)))
% 179.72/179.59 [9327]~P101(f323(f323(f237(a1),x93274),f2(a1)))+~P101(f323(f323(f238(a1),x93273),x93275))+P101(f323(f323(f237(a1),x93271),x93272))+~P101(f323(f323(f238(a1),x93273),x93274))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),f323(f323(f79(a1),x93273),x93272)),x93275)),f323(f323(f78(a1),f323(f323(f79(a1),x93273),x93271)),x93274)))
% 179.72/179.59 [9329]~P101(f323(f323(f237(a1),f2(a1)),x93295))+P101(f323(f323(f237(a1),x93291),x93292))+~P101(f323(f323(f238(a1),x93293),x93294))+~P101(f323(f323(f238(a1),x93295),x93294))+~P101(f323(f323(f237(a1),f323(f323(f78(a1),f323(f323(f79(a1),x93294),x93291)),x93295)),f323(f323(f78(a1),f323(f323(f79(a1),x93294),x93292)),x93293)))
% 179.72/179.59 [9441]~P63(x94415)+E(f323(x94411,f476(x94411,x94412,x94413,x94414,x94415)),f2(x94415))+~P101(f323(f59(x94414),x94413))+~P101(f323(f59(x94414),x94412))+E(f323(f323(f281(x94415),f323(f323(f79(x94415),f323(f323(f9(x94414,x94415),x94411),x94413)),f323(f323(f9(x94414,x94415),x94411),x94412))),f323(f323(f9(x94414,x94415),x94411),f323(f323(f101(f867(x94414,a855)),x94413),x94412))),f323(f323(f9(x94414,x94415),x94411),f323(f323(f110(f867(x94414,a855)),x94413),x94412)))
% 179.72/179.59 [9718]~P63(x97181)+~P101(f323(f59(x97182),x97184))+~P101(f323(f59(x97182),x97185))+E(f323(f323(f281(x97181),f323(f323(f79(x97181),f323(f323(f9(x97182,x97181),x97183),x97184)),f323(f323(f9(x97182,x97181),x97183),x97185))),f323(f323(f9(x97182,x97181),x97183),f323(f323(f101(f867(x97182,a855)),x97184),x97185))),f323(f323(f9(x97182,x97181),x97183),f323(f323(f110(f867(x97182,a855)),x97184),x97185)))+P101(f323(f323(f325(x97182),f476(x97183,x97185,x97184,x97182,x97181)),f323(f323(f101(f867(x97182,a855)),x97184),x97185)))
% 179.72/179.59 [9043]E(f323(f323(f121(x90431),x90432),x90433),f323(f323(f121(x90431),x90434),x90435))+~E(f323(f323(f169(x90431),f323(f189(f861(x90431)),x90434)),x90432),x90434)+~E(f323(f323(f169(x90431),f323(f189(f861(x90431)),x90432)),x90434),x90432)+~E(x90435,f323(f323(f121(x90431),f323(f323(f131(x90431),f323(f189(f861(x90431)),x90434)),x90432)),x90433))+~E(f323(f323(f121(x90431),f323(f323(f131(x90431),f323(f189(f861(x90431)),x90432)),x90434)),x90435),x90433)
% 179.72/179.59 [9439]~P103(x94392)+E(f323(f323(f141(x94391,x94392,x94393),x94394),f164(x94391,x94394,x94395)),x94395)+~P16(x94392,f323(f323(f147(x94391,x94392),x94393),x94395))+~P101(f323(f323(f325(x94391),x94394),f323(f166(x94391),x94395)))+~E(f323(f134(x94391),f323(f129(x94391,f323(f323(f8(x94392,a855,x94391),f323(a320,f323(x94393,x94394))),x94393)),x94395)),x94394)
% 179.72/179.59 [9781]~P66(x97811)+~P101(f323(f64(x97811,x97811,f79(x97811),x97812,x97813),x97815))+~P101(f323(f323(f325(x97811),x97814),x97813))+P101(f323(f323(f325(x97811),x97812),x97813))+P101(f323(f64(x97811,x97811,f79(x97811),x97814,f323(f323(f301(x97811),x97812),f323(f323(f22(f867(x97811,a855)),x97813),f323(f323(f301(x97811),x97814),f188(f867(x97811,a855)))))),x97815))
% 179.72/179.59 [7187]E(x71871,x71872)+~P27(x71874,x71875,x71873,x71876)+~E(f323(x71873,x71871),f323(x71873,x71872))+~P101(f323(f323(f325(x71874),x71872),x71876))+~P101(f323(f323(f325(x71874),x71871),x71876))
% 179.72/179.59 [6453]~P135(x64534)+E(x64531,x64532)+~E(x64535,x64536)+E(x64533,f2(x64534))+~E(f323(f323(f78(x64534),x64535),f323(f323(f79(x64534),x64533),x64531)),f323(f323(f78(x64534),x64536),f323(f323(f79(x64534),x64533),x64532)))
% 179.72/179.59 [7474]~P103(x74741)+~P6(x74741)+~P101(f323(f323(f238(x74741),x74742),f323(x74745,x74746)))+~P101(f323(f323(f325(x74743),x74746),x74744))+P101(f323(f323(f238(x74741),x74742),f323(f323(f39(x74743,x74741),x74744),x74745)))
% 179.72/179.59 [9777]~P27(x97772,x97771,x97773,x97774)+~P27(x97771,x97772,x97776,x97775)+P28(x97771,x97772,f800(x97773,x97774,x97775,x97776,x97772,x97771),x97775,x97774)+~P101(f323(f323(f237(f867(x97772,a855)),f323(f302(x97771,x97772,x97776),x97775)),x97774))+~P101(f323(f323(f237(f867(x97771,a855)),f323(f302(x97772,x97771,x97773),x97774)),x97775))
% 179.72/179.59 [8151]~P103(x81511)+~P6(x81511)+~P101(f323(f323(f238(x81511),f323(x81514,x81516)),x81515))+~P101(f323(f323(f325(x81512),x81516),x81513))+P101(f323(f323(f238(x81511),f323(f323(f40(x81512,x81511),x81513),x81514)),x81515))
% 179.72/179.59 [8409]~P21(x84092,x84095,x84096,x84091)+~P101(f323(f59(x84092),x84094))+~P101(f323(f59(x84092),x84093))+~E(f323(f323(f101(f867(x84092,a855)),x84093),x84094),f188(f867(x84092,a855)))+E(f323(x84091,f323(f323(f110(f867(x84092,a855)),x84093),x84094)),f323(f71(x84095,x84095,x84095,f323(x84091,x84093)),f323(x84091,x84094)))
% 179.72/179.59 [8739]E(x87391,x87392)+~P53(x87394,x87395,x87396,x87393,x87397)+~E(f323(x87393,x87391),f323(x87393,x87392))+~P101(f323(f323(f325(x87395),x87392),x87397))+~P101(f323(f323(f325(x87395),x87391),x87397))
% 179.72/179.59 [10023]~P101(f323(x100232,x100234))+~E(x100235,f323(f129(x100231,x100232),x100237))+E(f323(f129(x100231,x100232),x100233),f323(f323(f144(x100231),x100234),x100235))+~E(x100233,f323(f323(f121(x100231),x100236),f323(f323(f144(x100231),x100234),x100237)))+P101(f323(x100232,f712(x100235,x100234,x100233,x100232,x100231,x100236,x100237)))
% 179.72/179.59 [10024]~P101(f323(x100244,x100242))+~E(x100243,f323(f129(x100241,x100244),x100247))+E(f323(f323(f144(x100241),x100242),x100243),f323(f129(x100241,x100244),x100245))+~E(x100245,f323(f323(f121(x100241),x100246),f323(f323(f144(x100241),x100242),x100247)))+P101(f323(x100244,f710(x100245,x100244,x100243,x100242,x100241,x100246,x100247)))
% 179.72/179.59 [10057]~P101(f323(x100572,x100574))+~E(x100575,f323(f129(x100571,x100572),x100577))+E(f323(f129(x100571,x100572),x100573),f323(f323(f144(x100571),x100574),x100575))+~E(x100573,f323(f323(f121(x100571),x100576),f323(f323(f144(x100571),x100574),x100577)))+P101(f323(f323(f325(x100571),f712(x100575,x100574,x100573,x100572,x100571,x100576,x100577)),f323(f166(x100571),x100576)))
% 179.72/179.59 [10058]~P101(f323(x100584,x100582))+~E(x100583,f323(f129(x100581,x100584),x100587))+E(f323(f323(f144(x100581),x100582),x100583),f323(f129(x100581,x100584),x100585))+~E(x100585,f323(f323(f121(x100581),x100586),f323(f323(f144(x100581),x100582),x100587)))+P101(f323(f323(f325(x100581),f710(x100585,x100584,x100583,x100582,x100581,x100586,x100587)),f323(f166(x100581),x100586)))
% 179.72/179.59 [10061]~P9(x100611,x100617,x100616)+~P14(x100611,f867(x100615,a855),x100616,x100614)+P101(f323(f323(f325(x100611),f501(x100612,x100613,x100614,x100615,x100616,x100617,x100611)),x100617))+~P101(f323(f323(f325(f867(x100611,a855)),x100613),f323(f323(f58(x100611),x100617),x100616)))+P101(f323(f323(f325(f867(x100615,a855)),f323(f323(f39(x100611,f867(x100615,a855)),x100613),x100614)),x100612))
% 179.72/179.59 [10109]~P9(x101092,x101096,x101097)+~P14(x101092,f867(x101091,a855),x101097,x101094)+~P101(f323(f323(f325(f867(x101092,a855)),x101093),f323(f323(f58(x101092),x101096),x101097)))+~P101(f323(f323(f325(f867(x101091,a855)),f323(x101094,f501(x101095,x101093,x101094,x101091,x101097,x101096,x101092))),x101095))+P101(f323(f323(f325(f867(x101091,a855)),f323(f323(f39(x101092,f867(x101091,a855)),x101093),x101094)),x101095))
% 179.72/179.59 [8327]~P68(x83272)+~P27(x83271,x83275,x83278,x83274)+~E(x83273,f323(f71(x83275,x83272,x83271,x83276),x83278))+~E(x83277,f323(f302(x83271,x83275,x83278),x83274))+E(f323(f323(f9(x83271,x83272),x83273),x83274),f323(f323(f9(x83275,x83272),x83276),x83277))
% 179.72/179.59 [10113]~P68(x101132)+~P27(x101135,x101131,x101138,x101137)+~E(f323(x101136,f477(x101133,x101136,x101134,x101137,x101138,x101131,x101135,x101132)),f323(f323(f71(x101131,x101132,x101135,x101133),x101138),f477(x101133,x101136,x101134,x101137,x101138,x101131,x101135,x101132)))+~E(x101134,f323(f302(x101135,x101131,x101138),x101137))+E(f323(f323(f9(x101131,x101132),x101133),x101134),f323(f323(f9(x101135,x101132),x101136),x101137))
% 179.72/179.59 [10115]~P72(x101152)+~P27(x101151,x101155,x101158,x101154)+~E(x101157,f323(f302(x101151,x101155,x101158),x101154))+E(f323(f323(f6(x101151,x101152),x101153),x101154),f323(f323(f6(x101155,x101152),x101156),x101157))+P101(f323(f323(f325(x101151),f723(x101156,x101153,x101157,x101154,x101158,x101155,x101151,x101152)),x101154))
% 179.72/179.59 [10116]~P68(x101162)+~P27(x101161,x101165,x101168,x101164)+~E(x101167,f323(f302(x101161,x101165,x101168),x101164))+E(f323(f323(f9(x101161,x101162),x101163),x101164),f323(f323(f9(x101165,x101162),x101166),x101167))+P101(f323(f323(f325(x101161),f477(x101166,x101163,x101167,x101164,x101168,x101165,x101161,x101162)),x101164))
% 179.72/179.59 [10121]~P72(x101212)+~P27(x101215,x101211,x101218,x101217)+~E(x101214,f323(f302(x101215,x101211,x101218),x101217))+~E(f323(x101216,f723(x101213,x101216,x101214,x101217,x101218,x101211,x101215,x101212)),f323(x101213,f323(x101218,f723(x101213,x101216,x101214,x101217,x101218,x101211,x101215,x101212))))+E(f323(f323(f6(x101211,x101212),x101213),x101214),f323(f323(f6(x101215,x101212),x101216),x101217))
% 179.72/179.59 [9493]~E(f323(f189(f861(x94932)),x94935),f323(f189(f861(x94931)),x94933))+~E(f323(f189(f861(x94932)),x94934),f323(f189(f861(x94931)),x94933))+~E(f323(f323(f323(f70(x94931,f864(x94932)),f323(f179(x94931,x94932),f323(f323(f175(x94931,x94932),x94933),x94934))),x94936),f323(f230(x94932),x94937)),f323(f323(f323(f70(x94931,f864(x94932)),f323(f179(x94931,x94932),f323(f323(f175(x94931,x94932),x94933),x94935))),x94936),f323(f230(x94932),x94938)))+E(f323(f179(x94931,x94932),f323(f323(f175(x94931,x94932),x94933),x94934)),f323(f179(x94931,x94932),f323(f323(f175(x94931,x94932),x94933),x94935)))+P101(f323(f323(f325(x94931),x94936),f323(f166(x94931),x94933)))
% 179.72/179.59 [9608]~P25(x96086,x96082,x96085,x96087,x96088,x96081)+~P101(f323(f59(x96082),x96084))+~P101(f323(f59(x96082),x96083))+~E(f323(f323(f101(f867(x96082,a855)),x96083),x96084),f188(f867(x96082,a855)))+E(f323(x96081,f323(f323(f110(f867(x96082,a855)),x96083),x96084)),f323(f323(x96085,f323(x96081,x96083)),f323(x96081,x96084)))
% 179.72/179.59 [10010]~P25(x100108,x100102,x100105,x100107,x100106,x100101)+~E(f323(x100106,f844(x100104,x100103,x100101,x100106,x100107,x100105,x100102)),x100107)+~P101(f323(f59(x100102),x100103))+~P101(f323(f59(x100102),x100104))+E(f323(x100101,f323(f323(f110(f867(x100102,a855)),x100103),x100104)),f323(f323(x100105,f323(x100101,x100103)),f323(x100101,x100104)))
% 179.72/179.59 [10066]~P25(x100668,x100662,x100665,x100667,x100666,x100661)+~P101(f323(f59(x100662),x100663))+~P101(f323(f59(x100662),x100664))+E(f323(x100661,f323(f323(f110(f867(x100662,a855)),x100663),x100664)),f323(f323(x100665,f323(x100661,x100663)),f323(x100661,x100664)))+P101(f323(f323(f325(x100662),f844(x100664,x100663,x100661,x100666,x100667,x100665,x100662)),f323(f323(f101(f867(x100662,a855)),x100663),x100664)))
% 179.72/179.59 [9768]~P9(x97684,x97688,x97685)+~P9(x97681,x97689,x97683)+~P15(x97681,x97684,f867(x97682,a855),x97683,x97685,x97687)+P14(x97681,f867(x97682,a855),x97683,f323(f323(f8(f867(x97684,f867(x97682,a855)),f867(x97682,a855),x97681),f323(f39(x97684,f867(x97682,a855)),f323(f277(x97684,x97684,x97685),f323(f323(f301(x97684),x97686),f188(f867(x97684,a855)))))),x97687))+~P101(f323(f323(f325(x97684),x97686),x97688))
% 179.72/179.59 [5397]~P103(x53973)+~P16(x53973,x53971)+E(x53971,f687(x53972,x53973))+~E(f323(f166(x53973),x53971),x53972)+~P101(f323(f59(x53973),x53972))+~P101(f323(f130(x53973),x53971))
% 179.72/179.59 [5029]~P123(x50292)+~P124(x50292)+~P138(x50292)+~P110(x50292)+E(x50291,f2(x50292))+~E(f323(f323(f248(x50292),x50291),x50293),f2(x50292))
% 179.72/179.59 [5030]~P123(x50302)+~P124(x50302)+~P138(x50302)+~P110(x50302)+~E(x50301,f2(a860))+~E(f323(f323(f248(x50302),x50303),x50301),f2(x50302))
% 179.72/179.59 [6435]~P84(x64351)+~E(x64353,f2(x64351))+~E(x64352,f2(x64351))+E(f323(f323(f78(x64351),x64352),x64353),f2(x64351))+~P101(f323(f323(f237(x64351),f2(x64351)),x64353))+~P101(f323(f323(f237(x64351),f2(x64351)),x64352))
% 179.72/179.59 [8802]~E(f323(f257(a860,a860),x88023),f2(a860))+~E(x88021,f323(f323(f78(a860),f323(f323(f79(a860),f323(f257(a860,a860),x88023)),x88022)),f323(f261(a860,a860),x88023)))+P101(f323(f45(x88021,x88022),x88023))+~P101(f323(f323(f237(a860),f323(f261(a860,a860),x88023)),f2(a860)))+P101(f323(f323(f238(a860),f2(a860)),x88022))+~P101(f323(f323(f238(a860),x88022),f323(f261(a860,a860),x88023)))
% 179.72/179.60 [8810]E(x88101,f2(a860))+~E(x88102,f323(f323(f78(a860),f323(f323(f79(a860),f323(f257(a860,a860),x88103)),x88101)),f323(f261(a860,a860),x88103)))+P101(f323(f45(x88102,x88101),x88103))+~P101(f323(f323(f238(a860),f2(a860)),x88101))+~P101(f323(f323(f237(a860),f2(a860)),f323(f261(a860,a860),x88103)))+~P101(f323(f323(f238(a860),f323(f261(a860,a860),x88103)),x88101))
% 179.72/179.60 [8827]~E(f323(f257(a860,a860),x88273),f2(a860))+~E(x88271,f323(f323(f78(a860),f323(f323(f79(a860),f323(f257(a860,a860),x88273)),x88272)),f323(f261(a860,a860),x88273)))+P101(f323(f45(x88271,x88272),x88273))+~P101(f323(f323(f238(a860),f2(a860)),x88272))+~P101(f323(f323(f237(a860),f2(a860)),f323(f261(a860,a860),x88273)))+~P101(f323(f323(f238(a860),f323(f261(a860,a860),x88273)),x88272))
% 179.72/179.60 [6815]~P2(x68152)+E(x68151,f188(f867(x68152,a855)))+E(x68153,f188(f867(x68152,a855)))+~P101(f323(f59(x68152),x68151))+~P101(f323(f59(x68152),x68153))+E(f11(x68152,f323(f323(f110(f867(x68152,a855)),x68153),x68151)),f323(f323(f101(x68152),f11(x68152,x68153)),f11(x68152,x68151)))
% 179.72/179.60 [6816]~P2(x68162)+E(x68161,f188(f867(x68162,a855)))+E(x68163,f188(f867(x68162,a855)))+~P101(f323(f59(x68162),x68161))+~P101(f323(f59(x68162),x68163))+E(f10(x68162,f323(f323(f110(f867(x68162,a855)),x68163),x68161)),f323(f323(f110(x68162),f10(x68162,x68163)),f10(x68162,x68161)))
% 179.72/179.60 [6817]~P103(x68172)+E(x68171,f188(f867(x68172,a855)))+E(x68173,f188(f867(x68172,a855)))+~P101(f323(f59(x68172),x68171))+~P101(f323(f59(x68172),x68173))+E(f14(x68172,f323(f323(f110(f867(x68172,a855)),x68173),x68171)),f323(f323(f236(x68172),f14(x68172,x68173)),f14(x68172,x68171)))
% 179.72/179.60 [6818]~P103(x68182)+E(x68181,f188(f867(x68182,a855)))+E(x68183,f188(f867(x68182,a855)))+~P101(f323(f59(x68182),x68181))+~P101(f323(f59(x68182),x68183))+E(f15(x68182,f323(f323(f110(f867(x68182,a855)),x68183),x68181)),f323(f323(f235(x68182),f15(x68182,x68183)),f15(x68182,x68181)))
% 179.72/179.60 [7449]~P93(x74492)+E(x74491,f188(f867(x74492,a855)))+E(x74493,f188(f867(x74492,a855)))+~P101(f323(f59(x74492),x74491))+~P101(f323(f59(x74492),x74493))+E(f323(f323(f79(x74492),f323(f61(x74492,f79(x74492)),x74493)),f323(f61(x74492,f79(x74492)),x74491)),f323(f61(x74492,f79(x74492)),f323(f323(f110(f867(x74492,a855)),x74493),x74491)))
% 179.72/179.60 [7606]~P103(x76062)+E(x76061,f188(f867(x76062,a855)))+E(x76063,f188(f867(x76062,a855)))+~P101(f323(f59(x76062),x76061))+~P101(f323(f59(x76062),x76063))+E(f323(f323(f235(x76062),f12(x76062,f235(x76062),x76063)),f12(x76062,f235(x76062),x76061)),f12(x76062,f235(x76062),f323(f323(f110(f867(x76062,a855)),x76063),x76061)))
% 179.72/179.60 [7607]~P103(x76072)+E(x76071,f188(f867(x76072,a855)))+E(x76073,f188(f867(x76072,a855)))+~P101(f323(f59(x76072),x76071))+~P101(f323(f59(x76072),x76073))+E(f323(f323(f236(x76072),f13(x76072,f236(x76072),x76073)),f13(x76072,f236(x76072),x76071)),f13(x76072,f236(x76072),f323(f323(f110(f867(x76072,a855)),x76073),x76071)))
% 179.72/179.60 [8639]~P101(f323(x86391,x86393))+P101(f323(x86391,f407(x86391,x86392)))+P101(f323(x86391,f401(x86391,x86392)))+~P101(f323(f323(f238(a1),f2(a1)),x86392))+~P101(f323(f323(f325(a1),x86393),f294(a1,f76(a1),x86392)))+P101(f323(x86391,f323(f323(f22(a1),f401(x86391,x86392)),f323(f323(f79(a1),f403(x86391,x86392)),x86392))))
% 179.72/179.60 [8939]~P101(f323(x89391,x89393))+~P101(f323(x89391,f401(x89391,x89392)))+P101(f323(x89391,f407(x89391,x89392)))+~P101(f323(f323(f238(a1),f2(a1)),x89392))+~P101(f323(f323(f325(a1),x89393),f294(a1,f76(a1),x89392)))+~P101(f323(x89391,f323(f323(f22(a1),f401(x89391,x89392)),f323(f323(f79(a1),f403(x89391,x89392)),x89392))))
% 179.72/179.60 [10142]~P96(x101422)+E(x101421,f188(f867(x101422,a855)))+E(x101423,f188(f867(x101422,a855)))+~P101(f323(f59(x101422),x101421))+~P101(f323(f59(x101422),x101423))+E(f11(x101422,f323(f243(x101422),f323(f323(f8(f867(x101422,a855),a855,x101422),f85(x101422)),f323(f323(f8(f867(x101422,f867(x101422,a855)),f867(x101422,a855),x101422),f323(f8(f867(x101422,a855),a855,x101422),f85(x101422))),f323(f323(f7(x101422,f867(x101422,f867(x101422,a855)),f867(x101422,f867(x101422,a855))),f323(f323(f8(f867(x101422,f867(f867(x101422,a855),f867(x101422,a855))),f867(f867(x101422,f867(x101422,a855)),f867(x101422,f867(x101422,a855))),x101422),f18(x101422,f867(x101422,a855),f867(x101422,a855))),f323(f323(f8(f867(x101422,f867(x101422,f867(a855,a855))),f867(x101422,f867(f867(x101422,a855),f867(x101422,a855))),x101422),f323(f8(f867(x101422,f867(a855,a855)),f867(f867(x101422,a855),f867(x101422,a855)),x101422),f18(x101422,a855,a855))),f323(f323(f8(f867(x101422,f867(x101422,a855)),f867(x101422,f867(x101422,f867(a855,a855))),x101422),f323(f8(f867(x101422,a855),f867(x101422,f867(a855,a855)),x101422),f323(f8(a855,f867(a855,a855),x101422),a321))),f323(f323(f7(x101422,f867(x101422,f867(x101422,x101422)),f867(x101422,f867(x101422,a855))),f323(f323(f8(f867(f867(x101422,x101422),f867(x101422,a855)),f867(f867(x101422,f867(x101422,x101422)),f867(x101422,f867(x101422,a855))),x101422),f8(f867(x101422,x101422),f867(x101422,a855),x101422)),f323(f323(f8(f867(x101422,a855),f867(f867(x101422,x101422),f867(x101422,a855)),x101422),f8(x101422,a855,x101422)),a320))),f110(x101422)))))),f323(f323(f7(x101422,f867(x101422,a855),f867(x101422,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x101422,a855),f867(x101422,a855)),x101422),f8(a855,a855,x101422)),f323(f323(f8(a855,f867(a855,a855),x101422),a321),f323(f323(f7(x101422,f867(x101422,a855),a855),f325(x101422)),x101423)))),f323(f323(f7(x101422,f867(x101422,a855),a855),f325(x101422)),x101421))))))),f323(f323(f110(x101422),f11(x101422,x101423)),f11(x101422,x101421)))
% 179.72/179.60 [10143]~P96(x101432)+E(x101431,f188(f867(x101432,a855)))+E(x101433,f188(f867(x101432,a855)))+~P101(f323(f59(x101432),x101431))+~P101(f323(f59(x101432),x101433))+E(f10(x101432,f323(f243(x101432),f323(f323(f8(f867(x101432,a855),a855,x101432),f85(x101432)),f323(f323(f8(f867(x101432,f867(x101432,a855)),f867(x101432,a855),x101432),f323(f8(f867(x101432,a855),a855,x101432),f85(x101432))),f323(f323(f7(x101432,f867(x101432,f867(x101432,a855)),f867(x101432,f867(x101432,a855))),f323(f323(f8(f867(x101432,f867(f867(x101432,a855),f867(x101432,a855))),f867(f867(x101432,f867(x101432,a855)),f867(x101432,f867(x101432,a855))),x101432),f18(x101432,f867(x101432,a855),f867(x101432,a855))),f323(f323(f8(f867(x101432,f867(x101432,f867(a855,a855))),f867(x101432,f867(f867(x101432,a855),f867(x101432,a855))),x101432),f323(f8(f867(x101432,f867(a855,a855)),f867(f867(x101432,a855),f867(x101432,a855)),x101432),f18(x101432,a855,a855))),f323(f323(f8(f867(x101432,f867(x101432,a855)),f867(x101432,f867(x101432,f867(a855,a855))),x101432),f323(f8(f867(x101432,a855),f867(x101432,f867(a855,a855)),x101432),f323(f8(a855,f867(a855,a855),x101432),a321))),f323(f323(f7(x101432,f867(x101432,f867(x101432,x101432)),f867(x101432,f867(x101432,a855))),f323(f323(f8(f867(f867(x101432,x101432),f867(x101432,a855)),f867(f867(x101432,f867(x101432,x101432)),f867(x101432,f867(x101432,a855))),x101432),f8(f867(x101432,x101432),f867(x101432,a855),x101432)),f323(f323(f8(f867(x101432,a855),f867(f867(x101432,x101432),f867(x101432,a855)),x101432),f8(x101432,a855,x101432)),a320))),f101(x101432)))))),f323(f323(f7(x101432,f867(x101432,a855),f867(x101432,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x101432,a855),f867(x101432,a855)),x101432),f8(a855,a855,x101432)),f323(f323(f8(a855,f867(a855,a855),x101432),a321),f323(f323(f7(x101432,f867(x101432,a855),a855),f325(x101432)),x101433)))),f323(f323(f7(x101432,f867(x101432,a855),a855),f325(x101432)),x101431))))))),f323(f323(f101(x101432),f10(x101432,x101433)),f10(x101432,x101431)))
% 179.72/179.60 [10144]~P103(x101442)+E(x101441,f188(f867(x101442,a855)))+E(x101443,f188(f867(x101442,a855)))+~P101(f323(f59(x101442),x101441))+~P101(f323(f59(x101442),x101443))+E(f13(x101442,f236(x101442),f323(f243(x101442),f323(f323(f8(f867(x101442,a855),a855,x101442),f85(x101442)),f323(f323(f8(f867(x101442,f867(x101442,a855)),f867(x101442,a855),x101442),f323(f8(f867(x101442,a855),a855,x101442),f85(x101442))),f323(f323(f7(x101442,f867(x101442,f867(x101442,a855)),f867(x101442,f867(x101442,a855))),f323(f323(f8(f867(x101442,f867(f867(x101442,a855),f867(x101442,a855))),f867(f867(x101442,f867(x101442,a855)),f867(x101442,f867(x101442,a855))),x101442),f18(x101442,f867(x101442,a855),f867(x101442,a855))),f323(f323(f8(f867(x101442,f867(x101442,f867(a855,a855))),f867(x101442,f867(f867(x101442,a855),f867(x101442,a855))),x101442),f323(f8(f867(x101442,f867(a855,a855)),f867(f867(x101442,a855),f867(x101442,a855)),x101442),f18(x101442,a855,a855))),f323(f323(f8(f867(x101442,f867(x101442,a855)),f867(x101442,f867(x101442,f867(a855,a855))),x101442),f323(f8(f867(x101442,a855),f867(x101442,f867(a855,a855)),x101442),f323(f8(a855,f867(a855,a855),x101442),a321))),f323(f323(f7(x101442,f867(x101442,f867(x101442,x101442)),f867(x101442,f867(x101442,a855))),f323(f323(f8(f867(f867(x101442,x101442),f867(x101442,a855)),f867(f867(x101442,f867(x101442,x101442)),f867(x101442,f867(x101442,a855))),x101442),f8(f867(x101442,x101442),f867(x101442,a855),x101442)),f323(f323(f8(f867(x101442,a855),f867(f867(x101442,x101442),f867(x101442,a855)),x101442),f8(x101442,a855,x101442)),a320))),f235(x101442)))))),f323(f323(f7(x101442,f867(x101442,a855),f867(x101442,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x101442,a855),f867(x101442,a855)),x101442),f8(a855,a855,x101442)),f323(f323(f8(a855,f867(a855,a855),x101442),a321),f323(f323(f7(x101442,f867(x101442,a855),a855),f325(x101442)),x101443)))),f323(f323(f7(x101442,f867(x101442,a855),a855),f325(x101442)),x101441))))))),f323(f323(f235(x101442),f13(x101442,f236(x101442),x101443)),f13(x101442,f236(x101442),x101441)))
% 179.72/179.60 [10145]~P103(x101452)+E(x101451,f188(f867(x101452,a855)))+E(x101453,f188(f867(x101452,a855)))+~P101(f323(f59(x101452),x101451))+~P101(f323(f59(x101452),x101453))+E(f12(x101452,f235(x101452),f323(f243(x101452),f323(f323(f8(f867(x101452,a855),a855,x101452),f85(x101452)),f323(f323(f8(f867(x101452,f867(x101452,a855)),f867(x101452,a855),x101452),f323(f8(f867(x101452,a855),a855,x101452),f85(x101452))),f323(f323(f7(x101452,f867(x101452,f867(x101452,a855)),f867(x101452,f867(x101452,a855))),f323(f323(f8(f867(x101452,f867(f867(x101452,a855),f867(x101452,a855))),f867(f867(x101452,f867(x101452,a855)),f867(x101452,f867(x101452,a855))),x101452),f18(x101452,f867(x101452,a855),f867(x101452,a855))),f323(f323(f8(f867(x101452,f867(x101452,f867(a855,a855))),f867(x101452,f867(f867(x101452,a855),f867(x101452,a855))),x101452),f323(f8(f867(x101452,f867(a855,a855)),f867(f867(x101452,a855),f867(x101452,a855)),x101452),f18(x101452,a855,a855))),f323(f323(f8(f867(x101452,f867(x101452,a855)),f867(x101452,f867(x101452,f867(a855,a855))),x101452),f323(f8(f867(x101452,a855),f867(x101452,f867(a855,a855)),x101452),f323(f8(a855,f867(a855,a855),x101452),a321))),f323(f323(f7(x101452,f867(x101452,f867(x101452,x101452)),f867(x101452,f867(x101452,a855))),f323(f323(f8(f867(f867(x101452,x101452),f867(x101452,a855)),f867(f867(x101452,f867(x101452,x101452)),f867(x101452,f867(x101452,a855))),x101452),f8(f867(x101452,x101452),f867(x101452,a855),x101452)),f323(f323(f8(f867(x101452,a855),f867(f867(x101452,x101452),f867(x101452,a855)),x101452),f8(x101452,a855,x101452)),a320))),f236(x101452)))))),f323(f323(f7(x101452,f867(x101452,a855),f867(x101452,a855)),f323(f323(f8(f867(a855,a855),f867(f867(x101452,a855),f867(x101452,a855)),x101452),f8(a855,a855,x101452)),f323(f323(f8(a855,f867(a855,a855),x101452),a321),f323(f323(f7(x101452,f867(x101452,a855),a855),f325(x101452)),x101453)))),f323(f323(f7(x101452,f867(x101452,a855),a855),f325(x101452)),x101451))))))),f323(f323(f236(x101452),f12(x101452,f235(x101452),x101453)),f12(x101452,f235(x101452),x101451)))
% 179.72/179.60 [7138]~P119(x71383)+E(x71381,x71382)+~E(f323(f323(f248(x71383),x71381),x71384),f323(f323(f248(x71383),x71382),x71384))+~P101(f323(f323(f237(x71383),f2(x71383)),x71382))+~P101(f323(f323(f237(x71383),f2(x71383)),x71381))+~P101(f323(f323(f238(a860),f2(a860)),x71384))
% 179.72/179.60 [7407]~P98(x74072)+E(x74071,f188(f867(x74072,a855)))+~P101(f323(f59(x74072),x74071))+~P101(f323(f323(f325(x74072),x74074),x74071))+P101(f323(f323(f237(x74072),x74073),x74074))+~P101(f323(f323(f237(x74072),x74073),f323(f61(x74072,f101(x74072)),x74071)))
% 179.72/179.60 [7408]~P103(x74082)+E(x74081,f188(f867(x74082,a855)))+~P101(f323(f59(x74082),x74081))+~P101(f323(f323(f325(x74082),x74084),x74081))+P101(f323(f323(f237(x74082),x74083),x74084))+~P101(f323(f323(f237(x74082),x74083),f323(f61(x74082,f235(x74082)),x74081)))
% 179.72/179.60 [7409]~P103(x74092)+E(x74091,f188(f867(x74092,a855)))+~P101(f323(f59(x74092),x74091))+~P101(f323(f323(f325(x74092),x74094),x74091))+P101(f323(f323(f238(x74092),x74093),x74094))+~P101(f323(f323(f238(x74092),x74093),f323(f61(x74092,f235(x74092)),x74091)))
% 179.72/179.60 [7309]E(x73091,f2(a1))+E(f323(f323(f36(a1),x73092),x73091),x73093)+~P101(f323(f323(f237(a1),x73094),f2(a1)))+~E(x73092,f323(f323(f78(a1),f323(f323(f79(a1),x73091),x73093)),x73094))+P101(f323(f323(f238(a1),f2(a1)),x73091))+~P101(f323(f323(f238(a1),x73091),x73094))
% 179.72/179.60 [7324]E(f42(a1,x73242,x73241),x73243)+E(x73241,f2(a1))+~P101(f323(f323(f237(a1),x73243),f2(a1)))+~E(x73242,f323(f323(f78(a1),f323(f323(f79(a1),x73241),x73244)),x73243))+P101(f323(f323(f238(a1),f2(a1)),x73241))+~P101(f323(f323(f238(a1),x73241),x73243))
% 179.72/179.60 [7448]E(x74481,f2(a1))+E(f323(f323(f36(a1),x74482),x74481),x74483)+~E(x74482,f323(f323(f78(a1),f323(f323(f79(a1),x74481),x74483)),x74484))+~P101(f323(f323(f237(a1),f2(a1)),x74484))+~P101(f323(f323(f238(a1),f2(a1)),x74481))+~P101(f323(f323(f238(a1),x74484),x74481))
% 179.72/179.60 [7470]E(f42(a1,x74702,x74701),x74703)+E(x74701,f2(a1))+~E(x74702,f323(f323(f78(a1),f323(f323(f79(a1),x74701),x74704)),x74703))+~P101(f323(f323(f237(a1),f2(a1)),x74703))+~P101(f323(f323(f238(a1),f2(a1)),x74701))+~P101(f323(f323(f238(a1),x74703),x74701))
% 179.72/179.60 [7610]~P103(x76102)+E(x76101,f188(f867(x76102,a855)))+~P101(f323(f59(x76102),x76101))+~P101(f323(f323(f237(x76102),x76104),x76103))+~P101(f323(f323(f325(x76102),x76104),x76101))+P101(f323(f323(f237(x76102),f323(f61(x76102,f235(x76102)),x76101)),x76103))
% 179.72/179.60 [7611]~P103(x76112)+E(x76111,f188(f867(x76112,a855)))+~P101(f323(f59(x76112),x76111))+~P101(f323(f323(f238(x76112),x76114),x76113))+~P101(f323(f323(f325(x76112),x76114),x76111))+P101(f323(f323(f238(x76112),f323(f61(x76112,f235(x76112)),x76111)),x76113))
% 179.72/179.60 [8177]~P101(f323(f323(f237(a1),x81774),f2(a1)))+~E(x81771,f323(f323(f78(a1),f323(f323(f79(a1),x81772),x81773)),x81774))+~P101(f323(f323(f237(a1),f2(a1)),x81774))+~P101(f323(f323(f238(a1),x81774),x81772))+~P101(f323(f323(f238(a1),x81772),x81774))+P101(f323(f46(x81771,x81772),f323(f323(f258(a1,a1),x81773),x81774)))
% 179.72/179.60 [9134]~P5(x91343)+~P5(x91344)+E(x91341,x91342)+~E(f323(f189(f861(x91343)),x91342),f323(f189(f861(x91344)),f53(x91344)))+~E(f323(f189(f861(x91343)),x91341),f323(f189(f861(x91344)),f53(x91344)))+~E(f323(f71(f864(x91343),x91343,x91344,f234(x91343)),f323(f179(x91344,x91343),f323(f323(f175(x91344,x91343),f53(x91344)),x91341))),f323(f71(f864(x91343),x91343,x91344,f234(x91343)),f323(f179(x91344,x91343),f323(f323(f175(x91344,x91343),f53(x91344)),x91342))))
% 179.72/179.60 [8345]~P105(x83451)+P101(f323(f323(f238(f867(x83451,a855)),f294(x83451,x83452,x83453)),f294(x83451,x83454,x83455)))+~P101(f323(f323(f237(x83451),x83454),x83452))+~P101(f323(f323(f237(x83451),x83454),x83455))+~P101(f323(f323(f237(x83451),x83453),x83455))+~P101(f323(f323(f238(x83451),x83453),x83455))
% 179.72/179.60 [8346]~P105(x83461)+P101(f323(f323(f238(f867(x83461,a855)),f294(x83461,x83462,x83463)),f294(x83461,x83464,x83465)))+~P101(f323(f323(f237(x83461),x83463),x83465))+~P101(f323(f323(f237(x83461),x83464),x83465))+~P101(f323(f323(f237(x83461),x83464),x83462))+~P101(f323(f323(f238(x83461),x83464),x83462))
% 179.72/179.60 [9198]P55(x91982,x91983,x91984,x91981)+E(x91981,f188(f867(x91982,a855)))+~P101(f323(f59(x91982),x91984))+~P101(f323(f59(x91982),x91981))+~P101(f323(f323(x91983,f662(x91981,x91984,x91983,x91982)),x91985))+~P101(f323(f323(f325(x91982),x91985),x91981))
% 179.72/179.60 [9345]~E(x93453,x93455)+~P68(x93451)+~P72(x93451)+~P39(x93453)+E(f323(f323(f6(a1,x93451),x93452),x93453),f323(f323(f6(a1,x93451),x93454),x93455))+P101(f323(f323(f237(a1),f2(a1)),f435(x93452,x93454,x93453,x93455,x93451)))
% 179.72/179.60 [9346]~E(x93463,x93465)+~P68(x93461)+~P72(x93461)+~P39(x93463)+E(f323(f323(f9(a1,x93461),x93462),x93463),f323(f323(f9(a1,x93461),x93464),x93465))+P101(f323(f323(f237(a1),f2(a1)),f482(x93462,x93464,x93463,x93465,x93461)))
% 179.72/179.60 [9515]~E(x95155,x95153)+~P68(x95151)+~P72(x95151)+~P39(x95155)+~E(f323(x95152,f435(x95154,x95152,x95155,x95153,x95151)),f323(x95154,f435(x95154,x95152,x95155,x95153,x95151)))+E(f323(f323(f6(a1,x95151),x95152),x95153),f323(f323(f6(a1,x95151),x95154),x95155))
% 179.72/179.60 [9516]~E(x95165,x95163)+~P68(x95161)+~P72(x95161)+~P39(x95165)+~E(f323(x95162,f482(x95164,x95162,x95165,x95163,x95161)),f323(x95164,f482(x95164,x95162,x95165,x95163,x95161)))+E(f323(f323(f9(a1,x95161),x95162),x95163),f323(f323(f9(a1,x95161),x95164),x95165))
% 179.72/179.60 [9605]~P75(x96053)+E(f323(x96051,x96052),f2(x96053))+~E(f323(f323(f6(x96054,x96053),x96051),x96055),f2(x96053))+~P101(f323(f59(x96054),x96055))+P101(f323(f323(f325(x96054),f369(x96052,x96051,x96055,x96054,x96053)),x96055))+~P101(f323(f323(f325(x96054),x96052),x96055))
% 179.72/179.60 [9742]~P75(x97423)+E(f323(x97421,x97422),f2(x97423))+~E(f323(f323(f6(x97424,x97423),x97421),x97425),f2(x97423))+~P101(f323(f59(x97424),x97425))+~P101(f323(f323(f325(x97424),x97422),x97425))+~P101(f323(f323(f237(x97423),f2(x97423)),f323(x97421,f369(x97422,x97421,x97425,x97424,x97423))))
% 179.72/179.60 [8260]~P131(x82601)+~P101(f323(f323(f237(x82601),x82603),x82605))+~P101(f323(f323(f237(x82601),x82602),x82604))+~P101(f323(f323(f237(x82601),f2(x82601)),x82603))+~P101(f323(f323(f237(x82601),f2(x82601)),x82604))+P101(f323(f323(f237(x82601),f323(f323(f79(x82601),x82602),x82603)),f323(f323(f79(x82601),x82604),x82605)))
% 179.72/179.60 [8261]~P131(x82611)+~P101(f323(f323(f237(x82611),x82613),x82615))+~P101(f323(f323(f237(x82611),x82612),x82614))+~P101(f323(f323(f237(x82611),f2(x82611)),x82613))+~P101(f323(f323(f237(x82611),f2(x82611)),x82612))+P101(f323(f323(f237(x82611),f323(f323(f79(x82611),x82612),x82613)),f323(f323(f79(x82611),x82614),x82615)))
% 179.72/179.60 [8262]~P65(x82621)+~P101(f323(f323(f238(x82621),f2(x82621)),x82625))+~P101(f323(f323(f237(x82621),x82625),x82623))+~P101(f323(f323(f237(x82621),x82622),x82624))+~P101(f323(f323(f237(x82621),f2(x82621)),x82622))+P101(f323(f323(f237(x82621),f323(f323(f281(x82621),x82622),x82623)),f323(f323(f281(x82621),x82624),x82625)))
% 179.72/179.60 [8263]~P125(x82631)+~P101(f323(f323(f237(x82631),x82633),x82635))+~P101(f323(f323(f237(x82631),f2(x82631)),x82632))+~P101(f323(f323(f238(x82631),x82632),x82634))+~P101(f323(f323(f238(x82631),f2(x82631)),x82633))+P101(f323(f323(f238(x82631),f323(f323(f79(x82631),x82632),x82633)),f323(f323(f79(x82631),x82634),x82635)))
% 179.72/179.60 [8264]~P125(x82641)+~P101(f323(f323(f237(x82641),x82642),x82644))+~P101(f323(f323(f237(x82641),f2(x82641)),x82643))+~P101(f323(f323(f238(x82641),x82643),x82645))+~P101(f323(f323(f238(x82641),f2(x82641)),x82642))+P101(f323(f323(f238(x82641),f323(f323(f79(x82641),x82642),x82643)),f323(f323(f79(x82641),x82644),x82645)))
% 179.72/179.60 [8265]~P125(x82651)+~P101(f323(f323(f237(x82651),f2(x82651)),x82653))+~P101(f323(f323(f237(x82651),f2(x82651)),x82652))+~P101(f323(f323(f238(x82651),x82653),x82655))+~P101(f323(f323(f238(x82651),x82652),x82654))+P101(f323(f323(f238(x82651),f323(f323(f79(x82651),x82652),x82653)),f323(f323(f79(x82651),x82654),x82655)))
% 179.72/179.60 [8266]~P125(x82661)+~P101(f323(f323(f237(x82661),f2(x82661)),x82663))+~P101(f323(f323(f238(x82661),x82663),x82665))+~P101(f323(f323(f238(x82661),x82662),x82664))+~P101(f323(f323(f238(x82661),f2(x82661)),x82664))+P101(f323(f323(f238(x82661),f323(f323(f79(x82661),x82662),x82663)),f323(f323(f79(x82661),x82664),x82665)))
% 179.72/179.60 [8267]~P65(x82671)+~P101(f323(f323(f237(x82671),x82675),x82673))+~P101(f323(f323(f237(x82671),f2(x82671)),x82672))+~P101(f323(f323(f238(x82671),x82672),x82674))+~P101(f323(f323(f238(x82671),f2(x82671)),x82675))+P101(f323(f323(f238(x82671),f323(f323(f281(x82671),x82672),x82673)),f323(f323(f281(x82671),x82674),x82675)))
% 179.72/179.60 [8268]~P65(x82681)+~P101(f323(f323(f237(x82681),x82682),x82684))+~P101(f323(f323(f238(x82681),x82685),x82683))+~P101(f323(f323(f238(x82681),f2(x82681)),x82685))+~P101(f323(f323(f238(x82681),f2(x82681)),x82682))+P101(f323(f323(f238(x82681),f323(f323(f281(x82681),x82682),x82683)),f323(f323(f281(x82681),x82684),x82685)))
% 179.72/179.60 [9645]~P83(x96455)+~P72(x96455)+E(x96451,f188(f867(x96452,a855)))+~P101(f323(f59(x96452),x96451))+P101(f323(f323(f325(x96452),f436(x96453,x96454,x96451,x96452,x96455)),x96451))+P101(f323(f323(f238(x96455),f323(f323(f6(x96452,x96455),x96454),x96451)),f323(f323(f6(x96452,x96455),x96453),x96451)))
% 179.72/179.60 [9764]~P81(x97641)+~P72(x97641)+~P101(f323(f59(x97642),x97645))+~P101(f323(f323(f237(x97641),f2(x97641)),f323(x97643,f361(x97643,x97644,x97645,x97642,x97641))))+P101(f323(f323(f237(x97641),f323(f323(f6(x97642,x97641),x97643),x97644)),f323(f323(f6(x97642,x97641),x97643),x97645)))+~P101(f323(f323(f237(f867(x97642,a855)),x97644),x97645))
% 179.72/179.60 [9931]~P83(x99313)+~P72(x99313)+E(x99311,f188(f867(x99312,a855)))+~P101(f323(f59(x99312),x99311))+~P101(f323(f323(f238(x99313),f323(x99314,f436(x99315,x99314,x99311,x99312,x99313))),f323(x99315,f436(x99315,x99314,x99311,x99312,x99313))))+P101(f323(f323(f238(x99313),f323(f323(f6(x99312,x99313),x99314),x99311)),f323(f323(f6(x99312,x99313),x99315),x99311)))
% 179.72/179.60 [6997]~P19(x69972,x69975,x69974)+E(x69971,f188(f867(x69972,a855)))+E(x69973,f188(f867(x69972,a855)))+~P101(f323(f59(x69972),x69971))+~P101(f323(f59(x69972),x69973))+E(f323(x69974,f323(f323(f110(f867(x69972,a855)),x69973),x69971)),f323(f323(x69975,f323(x69974,x69973)),f323(x69974,x69971)))
% 179.72/179.60 [7576]~P143(x75761,x75763,x75764)+P101(f323(x75761,x75762))+~P101(f323(f323(f238(a1),x75764),f2(a1)))+~P101(f323(f323(f237(a1),x75765),f2(a1)))+~E(x75763,f323(f323(f78(a1),f323(f323(f79(a1),x75764),x75762)),x75765))+~P101(f323(f323(f238(a1),x75764),x75765))
% 179.72/179.60 [7577]~P142(x75771,x75773,x75774)+P101(f323(x75771,x75772))+~P101(f323(f323(f238(a1),x75774),f2(a1)))+~P101(f323(f323(f237(a1),x75772),f2(a1)))+~E(x75773,f323(f323(f78(a1),f323(f323(f79(a1),x75774),x75775)),x75772))+~P101(f323(f323(f238(a1),x75774),x75772))
% 179.72/179.60 [7619]~P143(x76191,x76193,x76194)+P101(f323(x76191,x76192))+~E(x76193,f323(f323(f78(a1),f323(f323(f79(a1),x76194),x76192)),x76195))+~P101(f323(f323(f237(a1),f2(a1)),x76195))+~P101(f323(f323(f238(a1),f2(a1)),x76194))+~P101(f323(f323(f238(a1),x76195),x76194))
% 179.72/179.60 [7620]~P142(x76201,x76203,x76204)+P101(f323(x76201,x76202))+~E(x76203,f323(f323(f78(a1),f323(f323(f79(a1),x76204),x76205)),x76202))+~P101(f323(f323(f237(a1),f2(a1)),x76202))+~P101(f323(f323(f238(a1),f2(a1)),x76204))+~P101(f323(f323(f238(a1),x76202),x76204))
% 179.72/179.60 [8551]P101(f323(f323(x85511,x85512),x85513))+~P101(f323(f323(x85511,f323(f323(f36(a1),x85514),x85515)),f42(a1,x85514,x85515)))+~P101(f323(f323(f238(a1),x85515),f2(a1)))+~P101(f323(f323(f237(a1),x85513),f2(a1)))+~E(x85514,f323(f323(f78(a1),f323(f323(f79(a1),x85515),x85512)),x85513))+~P101(f323(f323(f238(a1),x85515),x85513))
% 179.72/179.60 [8560]P101(f323(f323(x85601,x85602),x85603))+~P101(f323(f323(x85601,f323(f323(f36(a1),x85604),x85605)),f42(a1,x85604,x85605)))+~E(x85604,f323(f323(f78(a1),f323(f323(f79(a1),x85605),x85602)),x85603))+~P101(f323(f323(f237(a1),f2(a1)),x85603))+~P101(f323(f323(f238(a1),f2(a1)),x85605))+~P101(f323(f323(f238(a1),x85603),x85605))
% 179.72/179.60 [8816]E(x88161,x88162)+~P52(x88163,x88165,x88164)+~P101(f323(f323(f325(x88163),x88162),x88165))+~P101(f323(f323(f325(x88163),x88161),x88165))+P101(f323(f323(f325(f866(x88163,x88163)),f323(f323(f258(x88163,x88163),x88161),x88162)),x88164))+P101(f323(f323(f325(f866(x88163,x88163)),f323(f323(f258(x88163,x88163),x88162),x88161)),x88164))
% 179.72/179.60 [9673]~P81(x96735)+~P72(x96735)+~P101(f323(f59(x96731),x96734))+P101(f323(f323(f237(x96735),f323(f323(f6(x96731,x96735),x96732),x96733)),f323(f323(f6(x96731,x96735),x96732),x96734)))+~P101(f323(f323(f237(f867(x96731,a855)),x96733),x96734))+P101(f323(f323(f325(x96731),f361(x96732,x96733,x96734,x96731,x96735)),f323(f323(f22(f867(x96731,a855)),x96734),x96733)))
% 179.72/179.60 [9772]E(x97721,f188(f867(x97722,a855)))+~P101(f323(f59(x97722),x97723))+~P101(f323(f59(x97722),x97721))+P101(f323(f323(f325(f866(f867(x97722,a855),f867(x97722,a855))),f323(f323(f258(f867(x97722,a855),f867(x97722,a855)),x97723),x97721)),f314(x97722,x97724)))+~P101(f323(f323(f325(x97722),x97725),x97721))+~P101(f323(f323(f325(f866(x97722,x97722)),f323(f323(f258(x97722,x97722),f670(x97724,x97721,x97723,x97722)),x97725)),x97724))
% 179.72/179.60 [9773]E(x97731,f188(f867(x97732,a855)))+~P101(f323(f59(x97732),x97733))+~P101(f323(f59(x97732),x97731))+P101(f323(f323(f325(f866(f867(x97732,a855),f867(x97732,a855))),f323(f323(f258(f867(x97732,a855),f867(x97732,a855)),x97733),x97731)),f314(x97732,x97734)))+~P101(f323(f323(f325(x97732),x97735),x97731))+~P101(f323(f323(f325(f866(x97732,x97732)),f323(f323(f258(x97732,x97732),f715(x97734,x97731,x97733,x97732)),x97735)),x97734))
% 179.72/179.60 [9935]~P75(x99351)+~E(f323(f323(f6(x99355,x99351),x99352),x99356),x99354)+~P101(f323(f59(x99355),x99356))+P101(f323(f323(f325(x99355),f374(x99353,x99354,x99352,x99356,x99355,x99351)),x99356))+P101(f323(f323(f237(x99351),f323(x99352,x99353)),x99354))+~P101(f323(f323(f325(x99355),x99353),x99356))
% 179.72/179.60 [9982]~P75(x99821)+~E(f323(f323(f6(x99825,x99821),x99822),x99826),x99824)+~P101(f323(f59(x99825),x99826))+~P101(f323(f323(f325(x99825),x99823),x99826))+~P101(f323(f323(f237(x99821),f2(x99821)),f323(x99822,f374(x99823,x99824,x99822,x99826,x99825,x99821))))+P101(f323(f323(f237(x99821),f323(x99822,x99823)),x99824))
% 179.72/179.60 [10095]~E(x100955,x100958)+~E(x100954,x100957)+~P104(x100951)+~P72(x100952)+E(f323(f323(f6(x100951,x100952),x100953),f323(f293(x100951,x100954),x100955)),f323(f323(f6(x100951,x100952),x100956),f323(f293(x100951,x100957),x100958)))+P101(f323(f323(f237(x100951),x100954),f722(x100953,x100956,x100955,x100958,x100954,x100957,x100951,x100952)))
% 179.72/179.60 [10112]~E(x101127,x101124)+~E(x101128,x101125)+~P104(x101121)+~P72(x101122)+~E(f323(x101123,f722(x101126,x101123,x101128,x101125,x101127,x101124,x101121,x101122)),f323(x101126,f722(x101126,x101123,x101128,x101125,x101127,x101124,x101121,x101122)))+E(f323(f323(f6(x101121,x101122),x101123),f323(f293(x101121,x101124),x101125)),f323(f323(f6(x101121,x101122),x101126),f323(f293(x101121,x101127),x101128)))
% 179.72/179.60 [10114]~E(x101144,x101147)+~E(x101145,x101148)+~P104(x101141)+~P72(x101142)+E(f323(f323(f6(x101141,x101142),x101143),f323(f293(x101141,x101144),x101145)),f323(f323(f6(x101141,x101142),x101146),f323(f293(x101141,x101147),x101148)))+P101(f323(f323(f238(x101141),f722(x101143,x101146,x101145,x101148,x101144,x101147,x101141,x101142)),x101145))
% 179.72/179.60 [9779]~P9(x97795,x97799,x97796)+~P9(x97791,x977910,x97793)+~P15(x97791,x97795,f867(x97792,a855),x97793,x97796,x97798)+~P101(f323(f323(f325(x97795),x97797),x97799))+~P101(f323(f323(f325(x97791),x97794),x977910))+E(f323(f323(f39(x97791,f867(x97792,a855)),f323(f277(x97791,x97791,x97793),f323(f323(f301(x97791),x97794),f188(f867(x97791,a855))))),f323(f323(f8(f867(x97795,f867(x97792,a855)),f867(x97792,a855),x97791),f323(f39(x97795,f867(x97792,a855)),f323(f277(x97795,x97795,x97796),f323(f323(f301(x97795),x97797),f188(f867(x97795,a855)))))),x97798)),f323(f323(x97798,x97794),x97797))
% 179.72/179.60 [5564]~P103(x55643)+~P16(x55643,x55642)+~P16(x55643,x55641)+E(x55641,x55642)+~E(f323(f166(x55643),x55641),f323(f166(x55643),x55642))+~P101(f323(f130(x55643),x55642))+~P101(f323(f130(x55643),x55641))
% 179.72/179.60 [4914]~P123(x49142)+~P124(x49142)+~P138(x49142)+~P110(x49142)+~E(x49143,f2(x49142))+E(x49141,f2(a860))+E(f323(f323(f248(x49142),x49143),x49141),f2(x49142))
% 179.72/179.60 [9077]E(x90771,f2(a860))+~E(x90772,f323(f323(f78(a860),f323(f323(f79(a860),f323(f257(a860,a860),x90773)),x90771)),f323(f261(a860,a860),x90773)))+P101(f323(f45(x90772,x90771),x90773))+~P101(f323(f323(f237(a860),f323(f261(a860,a860),x90773)),f2(a860)))+~P101(f323(f323(f237(a860),f2(a860)),f323(f261(a860,a860),x90773)))+~P101(f323(f323(f238(a860),x90771),f323(f261(a860,a860),x90773)))+~P101(f323(f323(f238(a860),f323(f261(a860,a860),x90773)),x90771))
% 179.72/179.60 [9086]~E(f323(f257(a860,a860),x90863),f2(a860))+~E(x90861,f323(f323(f78(a860),f323(f323(f79(a860),f323(f257(a860,a860),x90863)),x90862)),f323(f261(a860,a860),x90863)))+P101(f323(f45(x90861,x90862),x90863))+~P101(f323(f323(f237(a860),f323(f261(a860,a860),x90863)),f2(a860)))+~P101(f323(f323(f237(a860),f2(a860)),f323(f261(a860,a860),x90863)))+~P101(f323(f323(f238(a860),x90862),f323(f261(a860,a860),x90863)))+~P101(f323(f323(f238(a860),f323(f261(a860,a860),x90863)),x90862))
% 179.72/179.60 [7932]~P66(x79322)+E(x79321,f188(f867(x79322,a855)))+E(x79323,f188(f867(x79322,a855)))+~P101(f323(f59(x79322),x79321))+~P101(f323(f59(x79322),x79323))+~E(f323(f323(f101(f867(x79322,a855)),x79323),x79321),f188(f867(x79322,a855)))+E(f323(f323(f79(x79322),f323(f61(x79322,f79(x79322)),x79323)),f323(f61(x79322,f79(x79322)),x79321)),f323(f61(x79322,f79(x79322)),f323(f323(f110(f867(x79322,a855)),x79323),x79321)))
% 179.72/179.60 [7715]E(x77151,f2(a1))+E(f323(f323(f36(a1),x77152),x77151),x77153)+~P101(f323(f323(f237(a1),x77154),f2(a1)))+~E(x77152,f323(f323(f78(a1),f323(f323(f79(a1),x77151),x77153)),x77154))+~P101(f323(f323(f237(a1),f2(a1)),x77154))+~P101(f323(f323(f238(a1),x77154),x77151))+~P101(f323(f323(f238(a1),x77151),x77154))
% 179.72/179.60 [7724]E(f42(a1,x77242,x77241),x77243)+E(x77241,f2(a1))+~P101(f323(f323(f237(a1),x77243),f2(a1)))+~E(x77242,f323(f323(f78(a1),f323(f323(f79(a1),x77241),x77244)),x77243))+~P101(f323(f323(f237(a1),f2(a1)),x77243))+~P101(f323(f323(f238(a1),x77243),x77241))+~P101(f323(f323(f238(a1),x77241),x77243))
% 179.72/179.60 [7628]~P20(x76282,x76285,x76284)+E(x76281,f188(f867(x76282,a855)))+E(x76283,f188(f867(x76282,a855)))+~P101(f323(f59(x76282),x76281))+~P101(f323(f59(x76282),x76283))+~E(f323(f323(f101(f867(x76282,a855)),x76283),x76281),f188(f867(x76282,a855)))+E(f323(x76284,f323(f323(f110(f867(x76282,a855)),x76283),x76281)),f323(f323(x76285,f323(x76284,x76283)),f323(x76284,x76281)))
% 179.72/179.60 [9318]~P27(x93183,x93181,x93185,x93184)+~P27(x93181,x93183,x93186,x93182)+E(f323(f35(x93181),x93182),f323(f35(x93183),x93184))+~P101(f323(f59(x93183),x93184))+~P101(f323(f59(x93181),x93182))+~P101(f323(f323(f237(f867(x93183,a855)),f323(f302(x93181,x93183,x93186),x93182)),x93184))+~P101(f323(f323(f237(f867(x93181,a855)),f323(f302(x93183,x93181,x93185),x93184)),x93182))
% 179.72/179.60 [9261]~P101(f323(f323(f238(a1),f323(f323(f78(a1),f323(f323(f79(a1),x92615),x92611)),x92616)),f2(a1)))+~E(f323(f323(f78(a1),f323(f323(f79(a1),x92613),x92612)),x92614),f323(f323(f78(a1),f323(f323(f79(a1),x92615),x92611)),x92616))+~P101(f323(f323(f237(a1),f2(a1)),x92616))+~P101(f323(f323(f238(a1),f2(a1)),x92615))+~P101(f323(f323(f237(a1),x92615),x92613))+~P101(f323(f323(f238(a1),x92614),x92613))+P101(f323(f323(f237(a1),x92611),x92612))
% 179.72/179.60 [9029]~E(f323(f323(f78(a1),f323(f323(f79(a1),x90293),x90291)),x90294),f323(f323(f78(a1),f323(f323(f79(a1),x90295),x90292)),x90296))+~P101(f323(f323(f237(a1),f2(a1)),x90294))+~P101(f323(f323(f238(a1),f2(a1)),x90295))+~P101(f323(f323(f237(a1),x90295),x90293))+~P101(f323(f323(f238(a1),x90296),x90295))+P101(f323(f323(f237(a1),x90291),x90292))+~P101(f323(f323(f237(a1),f2(a1)),f323(f323(f78(a1),f323(f323(f79(a1),x90295),x90292)),x90296)))
% 179.72/179.60 [9204]~P127(x92041)+~E(f323(f323(f78(x92041),x92042),x92044),f76(x92041))+~P101(f323(f323(f237(x92041),x92045),x92046))+~P101(f323(f323(f237(x92041),x92043),x92046))+~P101(f323(f323(f237(x92041),f2(x92041)),x92044))+~P101(f323(f323(f237(x92041),f2(x92041)),x92042))+P101(f323(f323(f237(x92041),f323(f323(f78(x92041),f323(f323(f79(x92041),x92042),x92043)),f323(f323(f79(x92041),x92044),x92045))),x92046))
% 179.72/179.60 [9205]~P128(x92051)+~E(f323(f323(f78(x92051),x92052),x92054),f76(x92051))+~P101(f323(f323(f237(x92051),f2(x92051)),x92054))+~P101(f323(f323(f237(x92051),f2(x92051)),x92052))+~P101(f323(f323(f238(x92051),x92055),x92056))+~P101(f323(f323(f238(x92051),x92053),x92056))+P101(f323(f323(f238(x92051),f323(f323(f78(x92051),f323(f323(f79(x92051),x92052),x92053)),f323(f323(f79(x92051),x92054),x92055))),x92056))
% 179.72/179.60 [10026]~P9(x100267,x100266,x100265)+E(x100261,x100262)+~P14(x100267,f867(x100264,a855),x100265,x100263)+E(f323(x100263,f508(x100261,x100262,x100263,x100264,x100265,x100266,x100267)),f323(x100263,f509(x100261,x100262,x100263,x100264,x100265,x100266,x100267)))+~E(f323(f323(f39(x100267,f867(x100264,a855)),x100261),x100263),f323(f323(f39(x100267,f867(x100264,a855)),x100262),x100263))+~P101(f323(f323(f325(f867(x100267,a855)),x100262),f323(f323(f58(x100267),x100266),x100265)))+~P101(f323(f323(f325(f867(x100267,a855)),x100261),f323(f323(f58(x100267),x100266),x100265)))
% 179.72/179.60 [10059]~P9(x100593,x100597,x100596)+E(x100591,x100592)+~P14(x100593,f867(x100595,a855),x100596,x100594)+~E(f323(f323(f39(x100593,f867(x100595,a855)),x100591),x100594),f323(f323(f39(x100593,f867(x100595,a855)),x100592),x100594))+P101(f323(f323(f325(x100593),f509(x100591,x100592,x100594,x100595,x100596,x100597,x100593)),x100597))+~P101(f323(f323(f325(f867(x100593,a855)),x100592),f323(f323(f58(x100593),x100597),x100596)))+~P101(f323(f323(f325(f867(x100593,a855)),x100591),f323(f323(f58(x100593),x100597),x100596)))
% 179.72/179.60 [10060]~P9(x100603,x100607,x100606)+E(x100601,x100602)+~P14(x100603,f867(x100605,a855),x100606,x100604)+~E(f323(f323(f39(x100603,f867(x100605,a855)),x100601),x100604),f323(f323(f39(x100603,f867(x100605,a855)),x100602),x100604))+P101(f323(f323(f325(x100603),f508(x100601,x100602,x100604,x100605,x100606,x100607,x100603)),x100607))+~P101(f323(f323(f325(f867(x100603,a855)),x100602),f323(f323(f58(x100603),x100607),x100606)))+~P101(f323(f323(f325(f867(x100603,a855)),x100601),f323(f323(f58(x100603),x100607),x100606)))
% 179.72/179.60 [10128]E(x101281,x101282)+~P9(x101283,x101286,x101287)+~P14(x101283,f867(x101284,a855),x101287,x101285)+~E(f323(f323(f39(x101283,f867(x101284,a855)),x101281),x101285),f323(f323(f39(x101283,f867(x101284,a855)),x101282),x101285))+~P101(f323(f323(f325(f866(x101283,x101283)),f323(f323(f258(x101283,x101283),f509(x101281,x101282,x101285,x101284,x101287,x101286,x101283)),f508(x101281,x101282,x101285,x101284,x101287,x101286,x101283))),x101287))+~P101(f323(f323(f325(f867(x101283,a855)),x101282),f323(f323(f58(x101283),x101286),x101287)))+~P101(f323(f323(f325(f867(x101283,a855)),x101281),f323(f323(f58(x101283),x101286),x101287)))
% 179.72/179.60 [9028]~P9(x90281,x90287,x90284)+~E(x90285,x90286)+~P101(f323(f323(f325(x90281),x90283),x90286))+~P101(f323(f323(f325(x90281),x90282),x90285))+~P101(f323(f323(f325(f867(x90281,a855)),x90286),f323(f323(f58(x90281),x90287),x90284)))+~P101(f323(f323(f325(f867(x90281,a855)),x90285),f323(f323(f58(x90281),x90287),x90284)))+P101(f323(f323(f325(f866(x90281,x90281)),f323(f323(f258(x90281,x90281),x90282),x90283)),x90284))
% 179.72/179.60 [9166]E(x91661,x91662)+~P9(x91663,x91664,x91665)+~P101(f323(f323(f325(x91663),x91666),x91662))+~P101(f323(f323(f325(x91663),x91667),x91661))+~P101(f323(f323(f325(f867(x91663,a855)),x91662),f323(f323(f58(x91663),x91664),x91665)))+~P101(f323(f323(f325(f867(x91663,a855)),x91661),f323(f323(f58(x91663),x91664),x91665)))+~P101(f323(f323(f325(f866(x91663,x91663)),f323(f323(f258(x91663,x91663),x91667),x91666)),x91665))
% 179.72/179.60 [10147]~P9(x101479,x101478,x101477)+~P9(x101471,x1014711,x1014710)+~P15(x101471,x101479,f867(x101476,a855),x1014710,x101477,x101475)+P101(f323(f323(f325(x101471),f502(x101472,x101473,x101474,x101475,x101476,x101477,x101478,x101479,x1014710,x1014711,x101471)),x1014711))+~P101(f323(f323(f325(f867(x101479,a855)),x101473),f323(f323(f58(x101479),x101478),x101477)))+~P101(f323(f323(f325(f867(x101471,a855)),x101474),f323(f323(f58(x101471),x1014711),x1014710)))+P101(f323(f323(f325(f867(x101476,a855)),f323(f323(f39(x101471,f867(x101476,a855)),x101474),f323(f323(f8(f867(x101479,f867(x101476,a855)),f867(x101476,a855),x101471),f323(f39(x101479,f867(x101476,a855)),x101473)),x101475))),x101472))
% 179.72/179.60 [10148]~P9(x1014811,x1014810,x101489)+~P9(x101481,x101488,x101487)+~P15(x1014811,x101481,f867(x101486,a855),x101489,x101487,x101485)+P101(f323(f323(f325(x101481),f503(x101482,x101483,x101484,x101485,x101486,x101487,x101488,x101481,x101489,x1014810,x1014811)),x101488))+~P101(f323(f323(f325(f867(x1014811,a855)),x101484),f323(f323(f58(x1014811),x1014810),x101489)))+~P101(f323(f323(f325(f867(x101481,a855)),x101483),f323(f323(f58(x101481),x101488),x101487)))+P101(f323(f323(f325(f867(x101486,a855)),f323(f323(f39(x1014811,f867(x101486,a855)),x101484),f323(f323(f8(f867(x101481,f867(x101486,a855)),f867(x101486,a855),x1014811),f323(f39(x101481,f867(x101486,a855)),x101483)),x101485))),x101482))
% 179.72/179.60 [10151]~P9(x101512,x101518,x101519)+~P9(x101514,x1015110,x1015111)+~P15(x101512,x101514,f867(x101511,a855),x101519,x1015111,x101516)+~P101(f323(f323(f325(f867(x101512,a855)),x101513),f323(f323(f58(x101512),x101518),x101519)))+~P101(f323(f323(f325(f867(x101514,a855)),x101515),f323(f323(f58(x101514),x1015110),x1015111)))+~P101(f323(f323(f325(f867(x101511,a855)),f323(f323(x101516,f502(x101517,x101515,x101513,x101516,x101511,x1015111,x1015110,x101514,x101519,x101518,x101512)),f503(x101517,x101515,x101513,x101516,x101511,x1015111,x1015110,x101514,x101519,x101518,x101512))),x101517))+P101(f323(f323(f325(f867(x101511,a855)),f323(f323(f39(x101512,f867(x101511,a855)),x101513),f323(f323(f8(f867(x101514,f867(x101511,a855)),f867(x101511,a855),x101512),f323(f39(x101514,f867(x101511,a855)),x101515)),x101516))),x101517))
% 179.72/179.60 [9064]E(x90641,x90642)+~P103(x90644)+~P27(x90643,x90644,x90645,f323(f323(f110(f867(x90643,a855)),f323(f166(x90643),x90641)),f323(f166(x90643),x90642)))+~E(f323(f166(x90643),x90641),f323(f166(x90643),x90642))+~P16(x90644,f323(f323(f147(x90643,x90644),x90645),x90642))+~P16(x90644,f323(f323(f147(x90643,x90644),x90645),x90641))+~P101(f323(f130(x90644),f323(f323(f147(x90643,x90644),x90645),x90642)))+~P101(f323(f130(x90644),f323(f323(f147(x90643,x90644),x90645),x90641)))
% 179.72/179.60 %EqnAxiom
% 179.72/179.60 [1]E(x11,x11)
% 179.72/179.60 [2]E(x22,x21)+~E(x21,x22)
% 179.72/179.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 179.72/179.60 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 179.72/179.60 [5]~E(x51,x52)+E(f100(x51),f100(x52))
% 179.72/179.60 [6]~E(x61,x62)+E(f22(x61),f22(x62))
% 179.72/179.60 [7]~E(x71,x72)+E(f188(x71),f188(x72))
% 179.72/179.60 [8]~E(x81,x82)+E(f323(x81,x83),f323(x82,x83))
% 179.72/179.60 [9]~E(x91,x92)+E(f323(x93,x91),f323(x93,x92))
% 179.72/179.60 [10]~E(x101,x102)+E(f28(x101),f28(x102))
% 179.72/179.60 [11]~E(x111,x112)+E(f711(x111,x113,x114,x115,x116,x117),f711(x112,x113,x114,x115,x116,x117))
% 179.72/179.60 [12]~E(x121,x122)+E(f711(x123,x121,x124,x125,x126,x127),f711(x123,x122,x124,x125,x126,x127))
% 179.72/179.60 [13]~E(x131,x132)+E(f711(x133,x134,x131,x135,x136,x137),f711(x133,x134,x132,x135,x136,x137))
% 179.72/179.60 [14]~E(x141,x142)+E(f711(x143,x144,x145,x141,x146,x147),f711(x143,x144,x145,x142,x146,x147))
% 179.72/179.60 [15]~E(x151,x152)+E(f711(x153,x154,x155,x156,x151,x157),f711(x153,x154,x155,x156,x152,x157))
% 179.72/179.60 [16]~E(x161,x162)+E(f711(x163,x164,x165,x166,x167,x161),f711(x163,x164,x165,x166,x167,x162))
% 179.72/179.60 [17]~E(x171,x172)+E(f101(x171),f101(x172))
% 179.72/179.60 [18]~E(x181,x182)+E(f235(x181),f235(x182))
% 179.72/179.60 [19]~E(x191,x192)+E(f110(x191),f110(x192))
% 179.72/179.60 [20]~E(x201,x202)+E(f236(x201),f236(x202))
% 179.72/179.60 [21]~E(x211,x212)+E(f102(x211),f102(x212))
% 179.72/179.60 [22]~E(x221,x222)+E(f32(x221),f32(x222))
% 179.72/179.60 [23]~E(x231,x232)+E(f82(x231),f82(x232))
% 179.72/179.60 [24]~E(x241,x242)+E(f237(x241),f237(x242))
% 179.72/179.60 [25]~E(x251,x252)+E(f867(x251,x253),f867(x252,x253))
% 179.72/179.60 [26]~E(x261,x262)+E(f867(x263,x261),f867(x263,x262))
% 179.72/179.60 [27]~E(x271,x272)+E(f503(x271,x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712),f503(x272,x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712))
% 179.72/179.60 [28]~E(x281,x282)+E(f503(x283,x281,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812),f503(x283,x282,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812))
% 179.72/179.60 [29]~E(x291,x292)+E(f503(x293,x294,x291,x295,x296,x297,x298,x299,x2910,x2911,x2912),f503(x293,x294,x292,x295,x296,x297,x298,x299,x2910,x2911,x2912))
% 179.72/179.60 [30]~E(x301,x302)+E(f503(x303,x304,x305,x301,x306,x307,x308,x309,x3010,x3011,x3012),f503(x303,x304,x305,x302,x306,x307,x308,x309,x3010,x3011,x3012))
% 179.72/179.60 [31]~E(x311,x312)+E(f503(x313,x314,x315,x316,x311,x317,x318,x319,x3110,x3111,x3112),f503(x313,x314,x315,x316,x312,x317,x318,x319,x3110,x3111,x3112))
% 179.72/179.60 [32]~E(x321,x322)+E(f503(x323,x324,x325,x326,x327,x321,x328,x329,x3210,x3211,x3212),f503(x323,x324,x325,x326,x327,x322,x328,x329,x3210,x3211,x3212))
% 179.72/179.60 [33]~E(x331,x332)+E(f503(x333,x334,x335,x336,x337,x338,x331,x339,x3310,x3311,x3312),f503(x333,x334,x335,x336,x337,x338,x332,x339,x3310,x3311,x3312))
% 179.72/179.60 [34]~E(x341,x342)+E(f503(x343,x344,x345,x346,x347,x348,x349,x341,x3410,x3411,x3412),f503(x343,x344,x345,x346,x347,x348,x349,x342,x3410,x3411,x3412))
% 179.72/179.60 [35]~E(x351,x352)+E(f503(x353,x354,x355,x356,x357,x358,x359,x3510,x351,x3511,x3512),f503(x353,x354,x355,x356,x357,x358,x359,x3510,x352,x3511,x3512))
% 179.72/179.60 [36]~E(x361,x362)+E(f503(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x361,x3612),f503(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x362,x3612))
% 179.72/179.60 [37]~E(x371,x372)+E(f503(x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712,x371),f503(x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712,x372))
% 179.72/179.60 [38]~E(x381,x382)+E(f76(x381),f76(x382))
% 179.72/179.60 [39]~E(x391,x392)+E(f352(x391,x393,x394),f352(x392,x393,x394))
% 179.72/179.60 [40]~E(x401,x402)+E(f352(x403,x401,x404),f352(x403,x402,x404))
% 179.72/179.60 [41]~E(x411,x412)+E(f352(x413,x414,x411),f352(x413,x414,x412))
% 179.72/179.60 [42]~E(x421,x422)+E(f502(x421,x423,x424,x425,x426,x427,x428,x429,x4210,x4211,x4212),f502(x422,x423,x424,x425,x426,x427,x428,x429,x4210,x4211,x4212))
% 179.72/179.60 [43]~E(x431,x432)+E(f502(x433,x431,x434,x435,x436,x437,x438,x439,x4310,x4311,x4312),f502(x433,x432,x434,x435,x436,x437,x438,x439,x4310,x4311,x4312))
% 179.72/179.60 [44]~E(x441,x442)+E(f502(x443,x444,x441,x445,x446,x447,x448,x449,x4410,x4411,x4412),f502(x443,x444,x442,x445,x446,x447,x448,x449,x4410,x4411,x4412))
% 179.72/179.60 [45]~E(x451,x452)+E(f502(x453,x454,x455,x451,x456,x457,x458,x459,x4510,x4511,x4512),f502(x453,x454,x455,x452,x456,x457,x458,x459,x4510,x4511,x4512))
% 179.72/179.60 [46]~E(x461,x462)+E(f502(x463,x464,x465,x466,x461,x467,x468,x469,x4610,x4611,x4612),f502(x463,x464,x465,x466,x462,x467,x468,x469,x4610,x4611,x4612))
% 179.72/179.60 [47]~E(x471,x472)+E(f502(x473,x474,x475,x476,x477,x471,x478,x479,x4710,x4711,x4712),f502(x473,x474,x475,x476,x477,x472,x478,x479,x4710,x4711,x4712))
% 179.72/179.60 [48]~E(x481,x482)+E(f502(x483,x484,x485,x486,x487,x488,x481,x489,x4810,x4811,x4812),f502(x483,x484,x485,x486,x487,x488,x482,x489,x4810,x4811,x4812))
% 179.72/179.60 [49]~E(x491,x492)+E(f502(x493,x494,x495,x496,x497,x498,x499,x491,x4910,x4911,x4912),f502(x493,x494,x495,x496,x497,x498,x499,x492,x4910,x4911,x4912))
% 179.72/179.60 [50]~E(x501,x502)+E(f502(x503,x504,x505,x506,x507,x508,x509,x5010,x501,x5011,x5012),f502(x503,x504,x505,x506,x507,x508,x509,x5010,x502,x5011,x5012))
% 179.72/179.60 [51]~E(x511,x512)+E(f502(x513,x514,x515,x516,x517,x518,x519,x5110,x5111,x511,x5112),f502(x513,x514,x515,x516,x517,x518,x519,x5110,x5111,x512,x5112))
% 179.72/179.60 [52]~E(x521,x522)+E(f502(x523,x524,x525,x526,x527,x528,x529,x5210,x5211,x5212,x521),f502(x523,x524,x525,x526,x527,x528,x529,x5210,x5211,x5212,x522))
% 179.72/179.60 [53]~E(x531,x532)+E(f111(x531),f111(x532))
% 179.72/179.60 [54]~E(x541,x542)+E(f325(x541),f325(x542))
% 179.72/179.60 [55]~E(x551,x552)+E(f152(x551,x553),f152(x552,x553))
% 179.72/179.60 [56]~E(x561,x562)+E(f152(x563,x561),f152(x563,x562))
% 179.72/179.60 [57]~E(x571,x572)+E(f4(x571),f4(x572))
% 179.72/179.60 [58]~E(x581,x582)+E(f6(x581,x583),f6(x582,x583))
% 179.72/179.60 [59]~E(x591,x592)+E(f6(x593,x591),f6(x593,x592))
% 179.72/179.60 [60]~E(x601,x602)+E(f859(x601),f859(x602))
% 179.72/179.60 [61]~E(x611,x612)+E(f864(x611),f864(x612))
% 179.72/179.60 [62]~E(x621,x622)+E(f861(x621),f861(x622))
% 179.72/179.60 [63]~E(x631,x632)+E(f862(x631),f862(x632))
% 179.72/179.60 [64]~E(x641,x642)+E(f35(x641),f35(x642))
% 179.72/179.60 [65]~E(x651,x652)+E(f18(x651,x653,x654),f18(x652,x653,x654))
% 179.72/179.60 [66]~E(x661,x662)+E(f18(x663,x661,x664),f18(x663,x662,x664))
% 179.72/179.60 [67]~E(x671,x672)+E(f18(x673,x674,x671),f18(x673,x674,x672))
% 179.72/179.60 [68]~E(x681,x682)+E(f121(x681),f121(x682))
% 179.72/179.60 [69]~E(x691,x692)+E(f144(x691),f144(x692))
% 179.72/179.60 [70]~E(x701,x702)+E(f77(x701),f77(x702))
% 179.72/179.60 [71]~E(x711,x712)+E(f238(x711),f238(x712))
% 179.72/179.60 [72]~E(x721,x722)+E(f189(x721),f189(x722))
% 179.72/179.60 [73]~E(x731,x732)+E(f260(x731,x733),f260(x732,x733))
% 179.72/179.60 [74]~E(x741,x742)+E(f260(x743,x741),f260(x743,x742))
% 179.72/179.60 [75]~E(x751,x752)+E(f103(x751),f103(x752))
% 179.72/179.60 [76]~E(x761,x762)+E(f89(x761),f89(x762))
% 179.72/179.60 [77]~E(x771,x772)+E(f113(x771),f113(x772))
% 179.72/179.60 [78]~E(x781,x782)+E(f311(x781,x783),f311(x782,x783))
% 179.72/179.60 [79]~E(x791,x792)+E(f311(x793,x791),f311(x793,x792))
% 179.72/179.60 [80]~E(x801,x802)+E(f73(x801),f73(x802))
% 179.72/179.60 [81]~E(x811,x812)+E(f78(x811),f78(x812))
% 179.72/179.60 [82]~E(x821,x822)+E(f866(x821,x823),f866(x822,x823))
% 179.72/179.60 [83]~E(x831,x832)+E(f866(x833,x831),f866(x833,x832))
% 179.72/179.60 [84]~E(x841,x842)+E(f147(x841,x843),f147(x842,x843))
% 179.72/179.60 [85]~E(x851,x852)+E(f147(x853,x851),f147(x853,x852))
% 179.72/179.60 [86]~E(x861,x862)+E(f302(x861,x863,x864),f302(x862,x863,x864))
% 179.72/179.60 [87]~E(x871,x872)+E(f302(x873,x871,x874),f302(x873,x872,x874))
% 179.72/179.60 [88]~E(x881,x882)+E(f302(x883,x884,x881),f302(x883,x884,x882))
% 179.72/179.60 [89]~E(x891,x892)+E(f695(x891,x893,x894,x895,x896,x897),f695(x892,x893,x894,x895,x896,x897))
% 179.72/179.60 [90]~E(x901,x902)+E(f695(x903,x901,x904,x905,x906,x907),f695(x903,x902,x904,x905,x906,x907))
% 179.72/179.60 [91]~E(x911,x912)+E(f695(x913,x914,x911,x915,x916,x917),f695(x913,x914,x912,x915,x916,x917))
% 179.72/179.60 [92]~E(x921,x922)+E(f695(x923,x924,x925,x921,x926,x927),f695(x923,x924,x925,x922,x926,x927))
% 179.72/179.60 [93]~E(x931,x932)+E(f695(x933,x934,x935,x936,x931,x937),f695(x933,x934,x935,x936,x932,x937))
% 179.72/179.60 [94]~E(x941,x942)+E(f695(x943,x944,x945,x946,x947,x941),f695(x943,x944,x945,x946,x947,x942))
% 179.72/179.60 [95]~E(x951,x952)+E(f79(x951),f79(x952))
% 179.72/179.60 [96]~E(x961,x962)+E(f694(x961,x963,x964,x965,x966,x967),f694(x962,x963,x964,x965,x966,x967))
% 179.72/179.60 [97]~E(x971,x972)+E(f694(x973,x971,x974,x975,x976,x977),f694(x973,x972,x974,x975,x976,x977))
% 179.72/179.60 [98]~E(x981,x982)+E(f694(x983,x984,x981,x985,x986,x987),f694(x983,x984,x982,x985,x986,x987))
% 179.72/179.60 [99]~E(x991,x992)+E(f694(x993,x994,x995,x991,x996,x997),f694(x993,x994,x995,x992,x996,x997))
% 179.72/179.60 [100]~E(x1001,x1002)+E(f694(x1003,x1004,x1005,x1006,x1001,x1007),f694(x1003,x1004,x1005,x1006,x1002,x1007))
% 179.72/179.60 [101]~E(x1011,x1012)+E(f694(x1013,x1014,x1015,x1016,x1017,x1011),f694(x1013,x1014,x1015,x1016,x1017,x1012))
% 179.72/179.60 [102]~E(x1021,x1022)+E(f27(x1021,x1023,x1024),f27(x1022,x1023,x1024))
% 179.72/179.60 [103]~E(x1031,x1032)+E(f27(x1033,x1031,x1034),f27(x1033,x1032,x1034))
% 179.72/179.60 [104]~E(x1041,x1042)+E(f27(x1043,x1044,x1041),f27(x1043,x1044,x1042))
% 179.72/179.60 [105]~E(x1051,x1052)+E(f58(x1051),f58(x1052))
% 179.72/179.60 [106]~E(x1061,x1062)+E(f262(x1061,x1063,x1064),f262(x1062,x1063,x1064))
% 179.72/179.60 [107]~E(x1071,x1072)+E(f262(x1073,x1071,x1074),f262(x1073,x1072,x1074))
% 179.72/179.60 [108]~E(x1081,x1082)+E(f262(x1083,x1084,x1081),f262(x1083,x1084,x1082))
% 179.72/179.60 [109]~E(x1091,x1092)+E(f59(x1091),f59(x1092))
% 179.72/179.60 [110]~E(x1101,x1102)+E(f7(x1101,x1103,x1104),f7(x1102,x1103,x1104))
% 179.72/179.60 [111]~E(x1111,x1112)+E(f7(x1113,x1111,x1114),f7(x1113,x1112,x1114))
% 179.72/179.60 [112]~E(x1121,x1122)+E(f7(x1123,x1124,x1121),f7(x1123,x1124,x1122))
% 179.72/179.60 [113]~E(x1131,x1132)+E(f9(x1131,x1133),f9(x1132,x1133))
% 179.72/179.60 [114]~E(x1141,x1142)+E(f9(x1143,x1141),f9(x1143,x1142))
% 179.72/179.60 [115]~E(x1151,x1152)+E(f166(x1151),f166(x1152))
% 179.72/179.60 [116]~E(x1161,x1162)+E(f234(x1161),f234(x1162))
% 179.72/179.60 [117]~E(x1171,x1172)+E(f472(x1171,x1173,x1174),f472(x1172,x1173,x1174))
% 179.72/179.60 [118]~E(x1181,x1182)+E(f472(x1183,x1181,x1184),f472(x1183,x1182,x1184))
% 179.72/179.60 [119]~E(x1191,x1192)+E(f472(x1193,x1194,x1191),f472(x1193,x1194,x1192))
% 179.72/179.60 [120]~E(x1201,x1202)+E(f804(x1201,x1203,x1204),f804(x1202,x1203,x1204))
% 179.72/179.60 [121]~E(x1211,x1212)+E(f804(x1213,x1211,x1214),f804(x1213,x1212,x1214))
% 179.72/179.60 [122]~E(x1221,x1222)+E(f804(x1223,x1224,x1221),f804(x1223,x1224,x1222))
% 179.72/179.60 [123]~E(x1231,x1232)+E(f165(x1231),f165(x1232))
% 179.72/179.60 [124]~E(x1241,x1242)+E(f293(x1241,x1243),f293(x1242,x1243))
% 179.72/179.60 [125]~E(x1251,x1252)+E(f293(x1253,x1251),f293(x1253,x1252))
% 179.72/179.60 [126]~E(x1261,x1262)+E(f803(x1261,x1263,x1264),f803(x1262,x1263,x1264))
% 179.72/179.60 [127]~E(x1271,x1272)+E(f803(x1273,x1271,x1274),f803(x1273,x1272,x1274))
% 179.72/179.60 [128]~E(x1281,x1282)+E(f803(x1283,x1284,x1281),f803(x1283,x1284,x1282))
% 179.72/179.60 [129]~E(x1291,x1292)+E(f301(x1291),f301(x1292))
% 179.72/179.60 [130]~E(x1301,x1302)+E(f8(x1301,x1303,x1304),f8(x1302,x1303,x1304))
% 179.72/179.60 [131]~E(x1311,x1312)+E(f8(x1313,x1311,x1314),f8(x1313,x1312,x1314))
% 179.72/179.60 [132]~E(x1321,x1322)+E(f8(x1323,x1324,x1321),f8(x1323,x1324,x1322))
% 179.72/179.60 [133]~E(x1331,x1332)+E(f36(x1331),f36(x1332))
% 179.72/179.60 [134]~E(x1341,x1342)+E(f248(x1341),f248(x1342))
% 179.72/179.60 [135]~E(x1351,x1352)+E(f154(x1351,x1353),f154(x1352,x1353))
% 179.72/179.60 [136]~E(x1361,x1362)+E(f154(x1363,x1361),f154(x1363,x1362))
% 179.72/179.60 [137]~E(x1371,x1372)+E(f44(x1371,x1373),f44(x1372,x1373))
% 179.72/179.60 [138]~E(x1381,x1382)+E(f44(x1383,x1381),f44(x1383,x1382))
% 179.72/179.60 [139]~E(x1391,x1392)+E(f218(x1391,x1393),f218(x1392,x1393))
% 179.72/179.60 [140]~E(x1401,x1402)+E(f218(x1403,x1401),f218(x1403,x1402))
% 179.72/179.60 [141]~E(x1411,x1412)+E(f83(x1411,x1413),f83(x1412,x1413))
% 179.72/179.60 [142]~E(x1421,x1422)+E(f83(x1423,x1421),f83(x1423,x1422))
% 179.72/179.60 [143]~E(x1431,x1432)+E(f230(x1431),f230(x1432))
% 179.72/179.60 [144]~E(x1441,x1442)+E(f42(x1441,x1443,x1444),f42(x1442,x1443,x1444))
% 179.72/179.60 [145]~E(x1451,x1452)+E(f42(x1453,x1451,x1454),f42(x1453,x1452,x1454))
% 179.72/179.60 [146]~E(x1461,x1462)+E(f42(x1463,x1464,x1461),f42(x1463,x1464,x1462))
% 179.72/179.60 [147]~E(x1471,x1472)+E(f151(x1471,x1473),f151(x1472,x1473))
% 179.72/179.60 [148]~E(x1481,x1482)+E(f151(x1483,x1481),f151(x1483,x1482))
% 179.72/179.60 [149]~E(x1491,x1492)+E(f40(x1491,x1493),f40(x1492,x1493))
% 179.72/179.60 [150]~E(x1501,x1502)+E(f40(x1503,x1501),f40(x1503,x1502))
% 179.72/179.60 [151]~E(x1511,x1512)+E(f258(x1511,x1513),f258(x1512,x1513))
% 179.72/179.60 [152]~E(x1521,x1522)+E(f258(x1523,x1521),f258(x1523,x1522))
% 179.72/179.60 [153]~E(x1531,x1532)+E(f281(x1531),f281(x1532))
% 179.72/179.60 [154]~E(x1541,x1542)+E(f15(x1541,x1543),f15(x1542,x1543))
% 179.72/179.60 [155]~E(x1551,x1552)+E(f15(x1553,x1551),f15(x1553,x1552))
% 179.72/179.60 [156]~E(x1561,x1562)+E(f62(x1561,x1563,x1564),f62(x1562,x1563,x1564))
% 179.72/179.60 [157]~E(x1571,x1572)+E(f62(x1573,x1571,x1574),f62(x1573,x1572,x1574))
% 179.72/179.60 [158]~E(x1581,x1582)+E(f62(x1583,x1584,x1581),f62(x1583,x1584,x1582))
% 179.72/179.60 [159]~E(x1591,x1592)+E(f105(x1591),f105(x1592))
% 179.72/179.60 [160]~E(x1601,x1602)+E(f106(x1601),f106(x1602))
% 179.72/179.60 [161]~E(x1611,x1612)+E(f324(x1611),f324(x1612))
% 179.72/179.60 [162]~E(x1621,x1622)+E(f312(x1621,x1623),f312(x1622,x1623))
% 179.72/179.60 [163]~E(x1631,x1632)+E(f312(x1633,x1631),f312(x1633,x1632))
% 179.72/179.60 [164]~E(x1641,x1642)+E(f129(x1641,x1643),f129(x1642,x1643))
% 179.72/179.60 [165]~E(x1651,x1652)+E(f129(x1653,x1651),f129(x1653,x1652))
% 179.72/179.60 [166]~E(x1661,x1662)+E(f244(x1661),f244(x1662))
% 179.72/179.60 [167]~E(x1671,x1672)+E(f181(x1671,x1673,x1674,x1675,x1676),f181(x1672,x1673,x1674,x1675,x1676))
% 179.72/179.60 [168]~E(x1681,x1682)+E(f181(x1683,x1681,x1684,x1685,x1686),f181(x1683,x1682,x1684,x1685,x1686))
% 179.72/179.60 [169]~E(x1691,x1692)+E(f181(x1693,x1694,x1691,x1695,x1696),f181(x1693,x1694,x1692,x1695,x1696))
% 179.72/179.60 [170]~E(x1701,x1702)+E(f181(x1703,x1704,x1705,x1701,x1706),f181(x1703,x1704,x1705,x1702,x1706))
% 179.72/179.60 [171]~E(x1711,x1712)+E(f181(x1713,x1714,x1715,x1716,x1711),f181(x1713,x1714,x1715,x1716,x1712))
% 179.72/179.60 [172]~E(x1721,x1722)+E(f243(x1721),f243(x1722))
% 179.72/179.60 [173]~E(x1731,x1732)+E(f46(x1731,x1733),f46(x1732,x1733))
% 179.72/179.60 [174]~E(x1741,x1742)+E(f46(x1743,x1741),f46(x1743,x1742))
% 179.72/179.60 [175]~E(x1751,x1752)+E(f5(x1751),f5(x1752))
% 179.72/179.60 [176]~E(x1761,x1762)+E(f179(x1761,x1763),f179(x1762,x1763))
% 179.72/179.60 [177]~E(x1771,x1772)+E(f179(x1773,x1771),f179(x1773,x1772))
% 179.72/179.60 [178]~E(x1781,x1782)+E(f299(x1781,x1783),f299(x1782,x1783))
% 179.72/179.60 [179]~E(x1791,x1792)+E(f299(x1793,x1791),f299(x1793,x1792))
% 179.72/179.60 [180]~E(x1801,x1802)+E(f261(x1801,x1803),f261(x1802,x1803))
% 179.72/179.60 [181]~E(x1811,x1812)+E(f261(x1813,x1811),f261(x1813,x1812))
% 179.72/179.60 [182]~E(x1821,x1822)+E(f278(x1821,x1823),f278(x1822,x1823))
% 179.72/179.60 [183]~E(x1831,x1832)+E(f278(x1833,x1831),f278(x1833,x1832))
% 179.72/179.60 [184]~E(x1841,x1842)+E(f213(x1841,x1843,x1844,x1845,x1846,x1847,x1848),f213(x1842,x1843,x1844,x1845,x1846,x1847,x1848))
% 179.72/179.60 [185]~E(x1851,x1852)+E(f213(x1853,x1851,x1854,x1855,x1856,x1857,x1858),f213(x1853,x1852,x1854,x1855,x1856,x1857,x1858))
% 179.72/179.60 [186]~E(x1861,x1862)+E(f213(x1863,x1864,x1861,x1865,x1866,x1867,x1868),f213(x1863,x1864,x1862,x1865,x1866,x1867,x1868))
% 179.72/179.60 [187]~E(x1871,x1872)+E(f213(x1873,x1874,x1875,x1871,x1876,x1877,x1878),f213(x1873,x1874,x1875,x1872,x1876,x1877,x1878))
% 179.72/179.60 [188]~E(x1881,x1882)+E(f213(x1883,x1884,x1885,x1886,x1881,x1887,x1888),f213(x1883,x1884,x1885,x1886,x1882,x1887,x1888))
% 179.72/179.60 [189]~E(x1891,x1892)+E(f213(x1893,x1894,x1895,x1896,x1897,x1891,x1898),f213(x1893,x1894,x1895,x1896,x1897,x1892,x1898))
% 179.72/179.60 [190]~E(x1901,x1902)+E(f213(x1903,x1904,x1905,x1906,x1907,x1908,x1901),f213(x1903,x1904,x1905,x1906,x1907,x1908,x1902))
% 179.72/179.60 [191]~E(x1911,x1912)+E(f135(x1911,x1913,x1914,x1915),f135(x1912,x1913,x1914,x1915))
% 179.72/179.60 [192]~E(x1921,x1922)+E(f135(x1923,x1921,x1924,x1925),f135(x1923,x1922,x1924,x1925))
% 179.72/179.60 [193]~E(x1931,x1932)+E(f135(x1933,x1934,x1931,x1935),f135(x1933,x1934,x1932,x1935))
% 179.72/179.60 [194]~E(x1941,x1942)+E(f135(x1943,x1944,x1945,x1941),f135(x1943,x1944,x1945,x1942))
% 179.72/179.60 [195]~E(x1951,x1952)+E(f865(x1951,x1953),f865(x1952,x1953))
% 179.72/179.60 [196]~E(x1961,x1962)+E(f865(x1963,x1961),f865(x1963,x1962))
% 179.72/179.60 [197]~E(x1971,x1972)+E(f246(x1971),f246(x1972))
% 179.72/179.60 [198]~E(x1981,x1982)+E(f50(x1981,x1983),f50(x1982,x1983))
% 179.72/179.60 [199]~E(x1991,x1992)+E(f50(x1993,x1991),f50(x1993,x1992))
% 179.72/179.60 [200]~E(x2001,x2002)+E(f199(x2001,x2003,x2004,x2005),f199(x2002,x2003,x2004,x2005))
% 179.72/179.60 [201]~E(x2011,x2012)+E(f199(x2013,x2011,x2014,x2015),f199(x2013,x2012,x2014,x2015))
% 179.72/179.60 [202]~E(x2021,x2022)+E(f199(x2023,x2024,x2021,x2025),f199(x2023,x2024,x2022,x2025))
% 179.72/179.60 [203]~E(x2031,x2032)+E(f199(x2033,x2034,x2035,x2031),f199(x2033,x2034,x2035,x2032))
% 179.72/179.60 [204]~E(x2041,x2042)+E(f180(x2041,x2043,x2044,x2045),f180(x2042,x2043,x2044,x2045))
% 179.72/179.60 [205]~E(x2051,x2052)+E(f180(x2053,x2051,x2054,x2055),f180(x2053,x2052,x2054,x2055))
% 179.72/179.60 [206]~E(x2061,x2062)+E(f180(x2063,x2064,x2061,x2065),f180(x2063,x2064,x2062,x2065))
% 179.72/179.60 [207]~E(x2071,x2072)+E(f180(x2073,x2074,x2075,x2071),f180(x2073,x2074,x2075,x2072))
% 179.72/179.60 [208]~E(x2081,x2082)+E(f510(x2081,x2083,x2084),f510(x2082,x2083,x2084))
% 179.72/179.60 [209]~E(x2091,x2092)+E(f510(x2093,x2091,x2094),f510(x2093,x2092,x2094))
% 179.72/179.60 [210]~E(x2101,x2102)+E(f510(x2103,x2104,x2101),f510(x2103,x2104,x2102))
% 179.72/179.60 [211]~E(x2111,x2112)+E(f150(x2111,x2113),f150(x2112,x2113))
% 179.72/179.60 [212]~E(x2121,x2122)+E(f150(x2123,x2121),f150(x2123,x2122))
% 179.72/179.60 [213]~E(x2131,x2132)+E(f10(x2131,x2133),f10(x2132,x2133))
% 179.72/179.60 [214]~E(x2141,x2142)+E(f10(x2143,x2141),f10(x2143,x2142))
% 179.72/179.60 [215]~E(x2151,x2152)+E(f435(x2151,x2153,x2154,x2155,x2156),f435(x2152,x2153,x2154,x2155,x2156))
% 179.72/179.60 [216]~E(x2161,x2162)+E(f435(x2163,x2161,x2164,x2165,x2166),f435(x2163,x2162,x2164,x2165,x2166))
% 179.72/179.60 [217]~E(x2171,x2172)+E(f435(x2173,x2174,x2171,x2175,x2176),f435(x2173,x2174,x2172,x2175,x2176))
% 179.72/179.60 [218]~E(x2181,x2182)+E(f435(x2183,x2184,x2185,x2181,x2186),f435(x2183,x2184,x2185,x2182,x2186))
% 179.72/179.60 [219]~E(x2191,x2192)+E(f435(x2193,x2194,x2195,x2196,x2191),f435(x2193,x2194,x2195,x2196,x2192))
% 179.72/179.60 [220]~E(x2201,x2202)+E(f164(x2201,x2203,x2204),f164(x2202,x2203,x2204))
% 179.72/179.60 [221]~E(x2211,x2212)+E(f164(x2213,x2211,x2214),f164(x2213,x2212,x2214))
% 179.72/179.60 [222]~E(x2221,x2222)+E(f164(x2223,x2224,x2221),f164(x2223,x2224,x2222))
% 179.72/179.60 [223]~E(x2231,x2232)+E(f173(x2231,x2233),f173(x2232,x2233))
% 179.72/179.60 [224]~E(x2241,x2242)+E(f173(x2243,x2241),f173(x2243,x2242))
% 179.72/179.60 [225]~E(x2251,x2252)+E(f71(x2251,x2253,x2254,x2255),f71(x2252,x2253,x2254,x2255))
% 179.72/179.60 [226]~E(x2261,x2262)+E(f71(x2263,x2261,x2264,x2265),f71(x2263,x2262,x2264,x2265))
% 179.72/179.60 [227]~E(x2271,x2272)+E(f71(x2273,x2274,x2271,x2275),f71(x2273,x2274,x2272,x2275))
% 179.72/179.60 [228]~E(x2281,x2282)+E(f71(x2283,x2284,x2285,x2281),f71(x2283,x2284,x2285,x2282))
% 179.72/179.60 [229]~E(x2291,x2292)+E(f263(x2291,x2293,x2294,x2295,x2296,x2297),f263(x2292,x2293,x2294,x2295,x2296,x2297))
% 179.72/179.60 [230]~E(x2301,x2302)+E(f263(x2303,x2301,x2304,x2305,x2306,x2307),f263(x2303,x2302,x2304,x2305,x2306,x2307))
% 179.72/179.60 [231]~E(x2311,x2312)+E(f263(x2313,x2314,x2311,x2315,x2316,x2317),f263(x2313,x2314,x2312,x2315,x2316,x2317))
% 179.72/179.60 [232]~E(x2321,x2322)+E(f263(x2323,x2324,x2325,x2321,x2326,x2327),f263(x2323,x2324,x2325,x2322,x2326,x2327))
% 179.72/179.60 [233]~E(x2331,x2332)+E(f263(x2333,x2334,x2335,x2336,x2331,x2337),f263(x2333,x2334,x2335,x2336,x2332,x2337))
% 179.72/179.60 [234]~E(x2341,x2342)+E(f263(x2343,x2344,x2345,x2346,x2347,x2341),f263(x2343,x2344,x2345,x2346,x2347,x2342))
% 179.72/179.60 [235]~E(x2351,x2352)+E(f840(x2351,x2353,x2354),f840(x2352,x2353,x2354))
% 179.72/179.60 [236]~E(x2361,x2362)+E(f840(x2363,x2361,x2364),f840(x2363,x2362,x2364))
% 179.72/179.60 [237]~E(x2371,x2372)+E(f840(x2373,x2374,x2371),f840(x2373,x2374,x2372))
% 179.72/179.60 [238]~E(x2381,x2382)+E(f11(x2381,x2383),f11(x2382,x2383))
% 179.72/179.60 [239]~E(x2391,x2392)+E(f11(x2393,x2391),f11(x2393,x2392))
% 179.72/179.60 [240]~E(x2401,x2402)+E(f45(x2401,x2403),f45(x2402,x2403))
% 179.72/179.60 [241]~E(x2411,x2412)+E(f45(x2413,x2411),f45(x2413,x2412))
% 179.72/179.60 [242]~E(x2421,x2422)+E(f39(x2421,x2423),f39(x2422,x2423))
% 179.72/179.60 [243]~E(x2431,x2432)+E(f39(x2433,x2431),f39(x2433,x2432))
% 179.72/179.60 [244]~E(x2441,x2442)+E(f153(x2441,x2443),f153(x2442,x2443))
% 179.72/179.60 [245]~E(x2451,x2452)+E(f153(x2453,x2451),f153(x2453,x2452))
% 179.72/179.60 [246]~E(x2461,x2462)+E(f169(x2461),f169(x2462))
% 179.72/179.60 [247]~E(x2471,x2472)+E(f572(x2471,x2473,x2474,x2475,x2476),f572(x2472,x2473,x2474,x2475,x2476))
% 179.72/179.60 [248]~E(x2481,x2482)+E(f572(x2483,x2481,x2484,x2485,x2486),f572(x2483,x2482,x2484,x2485,x2486))
% 179.72/179.60 [249]~E(x2491,x2492)+E(f572(x2493,x2494,x2491,x2495,x2496),f572(x2493,x2494,x2492,x2495,x2496))
% 179.72/179.60 [250]~E(x2501,x2502)+E(f572(x2503,x2504,x2505,x2501,x2506),f572(x2503,x2504,x2505,x2502,x2506))
% 179.72/179.60 [251]~E(x2511,x2512)+E(f572(x2513,x2514,x2515,x2516,x2511),f572(x2513,x2514,x2515,x2516,x2512))
% 179.72/179.60 [252]~E(x2521,x2522)+E(f434(x2521,x2523,x2524,x2525,x2526),f434(x2522,x2523,x2524,x2525,x2526))
% 179.72/179.60 [253]~E(x2531,x2532)+E(f434(x2533,x2531,x2534,x2535,x2536),f434(x2533,x2532,x2534,x2535,x2536))
% 179.72/179.60 [254]~E(x2541,x2542)+E(f434(x2543,x2544,x2541,x2545,x2546),f434(x2543,x2544,x2542,x2545,x2546))
% 179.72/179.60 [255]~E(x2551,x2552)+E(f434(x2553,x2554,x2555,x2551,x2556),f434(x2553,x2554,x2555,x2552,x2556))
% 179.72/179.60 [256]~E(x2561,x2562)+E(f434(x2563,x2564,x2565,x2566,x2561),f434(x2563,x2564,x2565,x2566,x2562))
% 179.72/179.60 [257]~E(x2571,x2572)+E(f354(x2571,x2573),f354(x2572,x2573))
% 179.72/179.60 [258]~E(x2581,x2582)+E(f354(x2583,x2581),f354(x2583,x2582))
% 179.72/179.60 [259]~E(x2591,x2592)+E(f37(x2591,x2593),f37(x2592,x2593))
% 179.72/179.60 [260]~E(x2601,x2602)+E(f37(x2603,x2601),f37(x2603,x2602))
% 179.72/179.60 [261]~E(x2611,x2612)+E(f267(x2611,x2613),f267(x2612,x2613))
% 179.72/179.60 [262]~E(x2621,x2622)+E(f267(x2623,x2621),f267(x2623,x2622))
% 179.72/179.60 [263]~E(x2631,x2632)+E(f61(x2631,x2633),f61(x2632,x2633))
% 179.72/179.60 [264]~E(x2641,x2642)+E(f61(x2643,x2641),f61(x2643,x2642))
% 179.72/179.60 [265]~E(x2651,x2652)+E(f280(x2651,x2653,x2654),f280(x2652,x2653,x2654))
% 179.72/179.60 [266]~E(x2661,x2662)+E(f280(x2663,x2661,x2664),f280(x2663,x2662,x2664))
% 179.72/179.60 [267]~E(x2671,x2672)+E(f280(x2673,x2674,x2671),f280(x2673,x2674,x2672))
% 179.72/179.60 [268]~E(x2681,x2682)+E(f131(x2681),f131(x2682))
% 179.72/179.60 [269]~E(x2691,x2692)+E(f201(x2691,x2693),f201(x2692,x2693))
% 179.72/179.60 [270]~E(x2701,x2702)+E(f201(x2703,x2701),f201(x2703,x2702))
% 179.72/179.60 [271]~E(x2711,x2712)+E(f145(x2711,x2713),f145(x2712,x2713))
% 179.72/179.60 [272]~E(x2721,x2722)+E(f145(x2723,x2721),f145(x2723,x2722))
% 179.72/179.60 [273]~E(x2731,x2732)+E(f257(x2731,x2733),f257(x2732,x2733))
% 179.72/179.60 [274]~E(x2741,x2742)+E(f257(x2743,x2741),f257(x2743,x2742))
% 179.72/179.60 [275]~E(x2751,x2752)+E(f130(x2751),f130(x2752))
% 179.72/179.60 [276]~E(x2761,x2762)+E(f114(x2761,x2763),f114(x2762,x2763))
% 179.72/179.60 [277]~E(x2771,x2772)+E(f114(x2773,x2771),f114(x2773,x2772))
% 179.72/179.60 [278]~E(x2781,x2782)+E(f294(x2781,x2783,x2784),f294(x2782,x2783,x2784))
% 179.72/179.60 [279]~E(x2791,x2792)+E(f294(x2793,x2791,x2794),f294(x2793,x2792,x2794))
% 179.72/179.60 [280]~E(x2801,x2802)+E(f294(x2803,x2804,x2801),f294(x2803,x2804,x2802))
% 179.72/179.60 [281]~E(x2811,x2812)+E(f191(x2811),f191(x2812))
% 179.72/179.60 [282]~E(x2821,x2822)+E(f214(x2821),f214(x2822))
% 179.72/179.60 [283]~E(x2831,x2832)+E(f115(x2831),f115(x2832))
% 179.72/179.60 [284]~E(x2841,x2842)+E(f303(x2841,x2843,x2844),f303(x2842,x2843,x2844))
% 179.72/179.60 [285]~E(x2851,x2852)+E(f303(x2853,x2851,x2854),f303(x2853,x2852,x2854))
% 179.72/179.60 [286]~E(x2861,x2862)+E(f303(x2863,x2864,x2861),f303(x2863,x2864,x2862))
% 179.72/179.60 [287]~E(x2871,x2872)+E(f16(x2871,x2873),f16(x2872,x2873))
% 179.72/179.60 [288]~E(x2881,x2882)+E(f16(x2883,x2881),f16(x2883,x2882))
% 179.72/179.60 [289]~E(x2891,x2892)+E(f141(x2891,x2893,x2894),f141(x2892,x2893,x2894))
% 179.72/179.60 [290]~E(x2901,x2902)+E(f141(x2903,x2901,x2904),f141(x2903,x2902,x2904))
% 179.72/179.60 [291]~E(x2911,x2912)+E(f141(x2913,x2914,x2911),f141(x2913,x2914,x2912))
% 179.72/179.60 [292]~E(x2921,x2922)+E(f183(x2921,x2923),f183(x2922,x2923))
% 179.72/179.60 [293]~E(x2931,x2932)+E(f183(x2933,x2931),f183(x2933,x2932))
% 179.72/179.60 [294]~E(x2941,x2942)+E(f161(x2941),f161(x2942))
% 179.72/179.60 [295]~E(x2951,x2952)+E(f175(x2951,x2953),f175(x2952,x2953))
% 179.72/179.60 [296]~E(x2961,x2962)+E(f175(x2963,x2961),f175(x2963,x2962))
% 179.72/179.60 [297]~E(x2971,x2972)+E(f177(x2971,x2973,x2974),f177(x2972,x2973,x2974))
% 179.72/179.60 [298]~E(x2981,x2982)+E(f177(x2983,x2981,x2984),f177(x2983,x2982,x2984))
% 179.72/179.60 [299]~E(x2991,x2992)+E(f177(x2993,x2994,x2991),f177(x2993,x2994,x2992))
% 179.72/179.60 [300]~E(x3001,x3002)+E(f148(x3001,x3003,x3004),f148(x3002,x3003,x3004))
% 179.72/179.60 [301]~E(x3011,x3012)+E(f148(x3013,x3011,x3014),f148(x3013,x3012,x3014))
% 179.72/179.60 [302]~E(x3021,x3022)+E(f148(x3023,x3024,x3021),f148(x3023,x3024,x3022))
% 179.72/179.60 [303]~E(x3031,x3032)+E(f90(x3031),f90(x3032))
% 179.72/179.60 [304]~E(x3041,x3042)+E(f137(x3041,x3043),f137(x3042,x3043))
% 179.72/179.60 [305]~E(x3051,x3052)+E(f137(x3053,x3051),f137(x3053,x3052))
% 179.72/179.60 [306]~E(x3061,x3062)+E(f523(x3061,x3063,x3064),f523(x3062,x3063,x3064))
% 179.72/179.60 [307]~E(x3071,x3072)+E(f523(x3073,x3071,x3074),f523(x3073,x3072,x3074))
% 179.72/179.60 [308]~E(x3081,x3082)+E(f523(x3083,x3084,x3081),f523(x3083,x3084,x3082))
% 179.72/179.60 [309]~E(x3091,x3092)+E(f633(x3091,x3093,x3094,x3095),f633(x3092,x3093,x3094,x3095))
% 179.72/179.60 [310]~E(x3101,x3102)+E(f633(x3103,x3101,x3104,x3105),f633(x3103,x3102,x3104,x3105))
% 179.72/179.60 [311]~E(x3111,x3112)+E(f633(x3113,x3114,x3111,x3115),f633(x3113,x3114,x3112,x3115))
% 179.72/179.60 [312]~E(x3121,x3122)+E(f633(x3123,x3124,x3125,x3121),f633(x3123,x3124,x3125,x3122))
% 179.72/179.60 [313]~E(x3131,x3132)+E(f162(x3131),f162(x3132))
% 179.72/179.60 [314]~E(x3141,x3142)+E(f247(x3141,x3143,x3144),f247(x3142,x3143,x3144))
% 179.72/179.60 [315]~E(x3151,x3152)+E(f247(x3153,x3151,x3154),f247(x3153,x3152,x3154))
% 179.72/179.60 [316]~E(x3161,x3162)+E(f247(x3163,x3164,x3161),f247(x3163,x3164,x3162))
% 179.72/179.60 [317]~E(x3171,x3172)+E(f80(x3171,x3173),f80(x3172,x3173))
% 179.72/179.60 [318]~E(x3181,x3182)+E(f80(x3183,x3181),f80(x3183,x3182))
% 179.72/179.60 [319]~E(x3191,x3192)+E(f393(x3191,x3193,x3194,x3195),f393(x3192,x3193,x3194,x3195))
% 179.72/179.60 [320]~E(x3201,x3202)+E(f393(x3203,x3201,x3204,x3205),f393(x3203,x3202,x3204,x3205))
% 179.72/179.60 [321]~E(x3211,x3212)+E(f393(x3213,x3214,x3211,x3215),f393(x3213,x3214,x3212,x3215))
% 179.72/179.60 [322]~E(x3221,x3222)+E(f393(x3223,x3224,x3225,x3221),f393(x3223,x3224,x3225,x3222))
% 179.72/179.60 [323]~E(x3231,x3232)+E(f518(x3231,x3233,x3234,x3235),f518(x3232,x3233,x3234,x3235))
% 179.72/179.60 [324]~E(x3241,x3242)+E(f518(x3243,x3241,x3244,x3245),f518(x3243,x3242,x3244,x3245))
% 179.72/179.60 [325]~E(x3251,x3252)+E(f518(x3253,x3254,x3251,x3255),f518(x3253,x3254,x3252,x3255))
% 179.72/179.60 [326]~E(x3261,x3262)+E(f518(x3263,x3264,x3265,x3261),f518(x3263,x3264,x3265,x3262))
% 179.72/179.60 [327]~E(x3271,x3272)+E(f282(x3271,x3273),f282(x3272,x3273))
% 179.72/179.60 [328]~E(x3281,x3282)+E(f282(x3283,x3281),f282(x3283,x3282))
% 179.72/179.60 [329]~E(x3291,x3292)+E(f295(x3291),f295(x3292))
% 179.72/179.60 [330]~E(x3301,x3302)+E(f805(x3301,x3303,x3304),f805(x3302,x3303,x3304))
% 179.72/179.60 [331]~E(x3311,x3312)+E(f805(x3313,x3311,x3314),f805(x3313,x3312,x3314))
% 179.72/179.60 [332]~E(x3321,x3322)+E(f805(x3323,x3324,x3321),f805(x3323,x3324,x3322))
% 179.72/179.60 [333]~E(x3331,x3332)+E(f25(x3331,x3333),f25(x3332,x3333))
% 179.72/179.60 [334]~E(x3341,x3342)+E(f25(x3343,x3341),f25(x3343,x3342))
% 179.72/179.60 [335]~E(x3351,x3352)+E(f797(x3351,x3353,x3354,x3355),f797(x3352,x3353,x3354,x3355))
% 179.72/179.60 [336]~E(x3361,x3362)+E(f797(x3363,x3361,x3364,x3365),f797(x3363,x3362,x3364,x3365))
% 179.72/179.60 [337]~E(x3371,x3372)+E(f797(x3373,x3374,x3371,x3375),f797(x3373,x3374,x3372,x3375))
% 179.72/179.60 [338]~E(x3381,x3382)+E(f797(x3383,x3384,x3385,x3381),f797(x3383,x3384,x3385,x3382))
% 179.72/179.60 [339]~E(x3391,x3392)+E(f277(x3391,x3393,x3394),f277(x3392,x3393,x3394))
% 179.72/179.60 [340]~E(x3401,x3402)+E(f277(x3403,x3401,x3404),f277(x3403,x3402,x3404))
% 179.72/179.60 [341]~E(x3411,x3412)+E(f277(x3413,x3414,x3411),f277(x3413,x3414,x3412))
% 179.72/179.60 [342]~E(x3421,x3422)+E(f253(x3421,x3423,x3424),f253(x3422,x3423,x3424))
% 179.72/179.60 [343]~E(x3431,x3432)+E(f253(x3433,x3431,x3434),f253(x3433,x3432,x3434))
% 179.72/179.60 [344]~E(x3441,x3442)+E(f253(x3443,x3444,x3441),f253(x3443,x3444,x3442))
% 179.72/179.60 [345]~E(x3451,x3452)+E(f314(x3451,x3453),f314(x3452,x3453))
% 179.72/179.60 [346]~E(x3461,x3462)+E(f314(x3463,x3461),f314(x3463,x3462))
% 179.72/179.60 [347]~E(x3471,x3472)+E(f256(x3471,x3473),f256(x3472,x3473))
% 179.72/179.60 [348]~E(x3481,x3482)+E(f256(x3483,x3481),f256(x3483,x3482))
% 179.72/179.60 [349]~E(x3491,x3492)+E(f316(x3491,x3493),f316(x3492,x3493))
% 179.72/179.60 [350]~E(x3501,x3502)+E(f316(x3503,x3501),f316(x3503,x3502))
% 179.72/179.60 [351]~E(x3511,x3512)+E(f345(x3511,x3513,x3514,x3515,x3516,x3517,x3518),f345(x3512,x3513,x3514,x3515,x3516,x3517,x3518))
% 179.72/179.60 [352]~E(x3521,x3522)+E(f345(x3523,x3521,x3524,x3525,x3526,x3527,x3528),f345(x3523,x3522,x3524,x3525,x3526,x3527,x3528))
% 179.72/179.60 [353]~E(x3531,x3532)+E(f345(x3533,x3534,x3531,x3535,x3536,x3537,x3538),f345(x3533,x3534,x3532,x3535,x3536,x3537,x3538))
% 179.72/179.60 [354]~E(x3541,x3542)+E(f345(x3543,x3544,x3545,x3541,x3546,x3547,x3548),f345(x3543,x3544,x3545,x3542,x3546,x3547,x3548))
% 179.72/179.60 [355]~E(x3551,x3552)+E(f345(x3553,x3554,x3555,x3556,x3551,x3557,x3558),f345(x3553,x3554,x3555,x3556,x3552,x3557,x3558))
% 179.72/179.60 [356]~E(x3561,x3562)+E(f345(x3563,x3564,x3565,x3566,x3567,x3561,x3568),f345(x3563,x3564,x3565,x3566,x3567,x3562,x3568))
% 179.72/179.60 [357]~E(x3571,x3572)+E(f345(x3573,x3574,x3575,x3576,x3577,x3578,x3571),f345(x3573,x3574,x3575,x3576,x3577,x3578,x3572))
% 179.72/179.60 [358]~E(x3581,x3582)+E(f13(x3581,x3583,x3584),f13(x3582,x3583,x3584))
% 179.72/179.60 [359]~E(x3591,x3592)+E(f13(x3593,x3591,x3594),f13(x3593,x3592,x3594))
% 179.72/179.60 [360]~E(x3601,x3602)+E(f13(x3603,x3604,x3601),f13(x3603,x3604,x3602))
% 179.72/179.60 [361]~E(x3611,x3612)+E(f637(x3611,x3613,x3614,x3615,x3616),f637(x3612,x3613,x3614,x3615,x3616))
% 179.72/179.60 [362]~E(x3621,x3622)+E(f637(x3623,x3621,x3624,x3625,x3626),f637(x3623,x3622,x3624,x3625,x3626))
% 179.72/179.60 [363]~E(x3631,x3632)+E(f637(x3633,x3634,x3631,x3635,x3636),f637(x3633,x3634,x3632,x3635,x3636))
% 179.72/179.60 [364]~E(x3641,x3642)+E(f637(x3643,x3644,x3645,x3641,x3646),f637(x3643,x3644,x3645,x3642,x3646))
% 179.72/179.60 [365]~E(x3651,x3652)+E(f637(x3653,x3654,x3655,x3656,x3651),f637(x3653,x3654,x3655,x3656,x3652))
% 179.72/179.60 [366]~E(x3661,x3662)+E(f159(x3661),f159(x3662))
% 179.72/179.60 [367]~E(x3671,x3672)+E(f292(x3671),f292(x3672))
% 179.72/179.60 [368]~E(x3681,x3682)+E(f149(x3681,x3683,x3684,x3685),f149(x3682,x3683,x3684,x3685))
% 179.72/179.60 [369]~E(x3691,x3692)+E(f149(x3693,x3691,x3694,x3695),f149(x3693,x3692,x3694,x3695))
% 179.72/179.60 [370]~E(x3701,x3702)+E(f149(x3703,x3704,x3701,x3705),f149(x3703,x3704,x3702,x3705))
% 179.72/179.60 [371]~E(x3711,x3712)+E(f149(x3713,x3714,x3715,x3711),f149(x3713,x3714,x3715,x3712))
% 179.72/179.60 [372]~E(x3721,x3722)+E(f14(x3721,x3723),f14(x3722,x3723))
% 179.72/179.60 [373]~E(x3731,x3732)+E(f14(x3733,x3731),f14(x3733,x3732))
% 179.72/179.60 [374]~E(x3741,x3742)+E(f762(x3741,x3743,x3744,x3745),f762(x3742,x3743,x3744,x3745))
% 179.72/179.60 [375]~E(x3751,x3752)+E(f762(x3753,x3751,x3754,x3755),f762(x3753,x3752,x3754,x3755))
% 179.72/179.60 [376]~E(x3761,x3762)+E(f762(x3763,x3764,x3761,x3765),f762(x3763,x3764,x3762,x3765))
% 179.72/179.60 [377]~E(x3771,x3772)+E(f762(x3773,x3774,x3775,x3771),f762(x3773,x3774,x3775,x3772))
% 179.72/179.60 [378]~E(x3781,x3782)+E(f109(x3781),f109(x3782))
% 179.72/179.60 [379]~E(x3791,x3792)+E(f445(x3791,x3793,x3794,x3795,x3796),f445(x3792,x3793,x3794,x3795,x3796))
% 179.72/179.60 [380]~E(x3801,x3802)+E(f445(x3803,x3801,x3804,x3805,x3806),f445(x3803,x3802,x3804,x3805,x3806))
% 179.72/179.60 [381]~E(x3811,x3812)+E(f445(x3813,x3814,x3811,x3815,x3816),f445(x3813,x3814,x3812,x3815,x3816))
% 179.72/179.60 [382]~E(x3821,x3822)+E(f445(x3823,x3824,x3825,x3821,x3826),f445(x3823,x3824,x3825,x3822,x3826))
% 179.72/179.60 [383]~E(x3831,x3832)+E(f445(x3833,x3834,x3835,x3836,x3831),f445(x3833,x3834,x3835,x3836,x3832))
% 179.72/179.60 [384]~E(x3841,x3842)+E(f702(x3841,x3843,x3844),f702(x3842,x3843,x3844))
% 179.72/179.60 [385]~E(x3851,x3852)+E(f702(x3853,x3851,x3854),f702(x3853,x3852,x3854))
% 179.72/179.60 [386]~E(x3861,x3862)+E(f702(x3863,x3864,x3861),f702(x3863,x3864,x3862))
% 179.72/179.60 [387]~E(x3871,x3872)+E(f163(x3871,x3873,x3874),f163(x3872,x3873,x3874))
% 179.72/179.60 [388]~E(x3881,x3882)+E(f163(x3883,x3881,x3884),f163(x3883,x3882,x3884))
% 179.72/179.60 [389]~E(x3891,x3892)+E(f163(x3893,x3894,x3891),f163(x3893,x3894,x3892))
% 179.72/179.60 [390]~E(x3901,x3902)+E(f200(x3901),f200(x3902))
% 179.72/179.60 [391]~E(x3911,x3912)+E(f556(x3911,x3913,x3914),f556(x3912,x3913,x3914))
% 179.72/179.60 [392]~E(x3921,x3922)+E(f556(x3923,x3921,x3924),f556(x3923,x3922,x3924))
% 179.72/179.60 [393]~E(x3931,x3932)+E(f556(x3933,x3934,x3931),f556(x3933,x3934,x3932))
% 179.72/179.60 [394]~E(x3941,x3942)+E(f53(x3941),f53(x3942))
% 179.72/179.60 [395]~E(x3951,x3952)+E(f132(x3951,x3953),f132(x3952,x3953))
% 179.72/179.60 [396]~E(x3961,x3962)+E(f132(x3963,x3961),f132(x3963,x3962))
% 179.72/179.60 [397]~E(x3971,x3972)+E(f84(x3971,x3973),f84(x3972,x3973))
% 179.72/179.60 [398]~E(x3981,x3982)+E(f84(x3983,x3981),f84(x3983,x3982))
% 179.72/179.60 [399]~E(x3991,x3992)+E(f485(x3991,x3993,x3994,x3995),f485(x3992,x3993,x3994,x3995))
% 179.72/179.60 [400]~E(x4001,x4002)+E(f485(x4003,x4001,x4004,x4005),f485(x4003,x4002,x4004,x4005))
% 179.72/179.60 [401]~E(x4011,x4012)+E(f485(x4013,x4014,x4011,x4015),f485(x4013,x4014,x4012,x4015))
% 179.72/179.60 [402]~E(x4021,x4022)+E(f485(x4023,x4024,x4025,x4021),f485(x4023,x4024,x4025,x4022))
% 179.72/179.60 [403]~E(x4031,x4032)+E(f88(x4031,x4033),f88(x4032,x4033))
% 179.72/179.60 [404]~E(x4041,x4042)+E(f88(x4043,x4041),f88(x4043,x4042))
% 179.72/179.60 [405]~E(x4051,x4052)+E(f172(x4051,x4053),f172(x4052,x4053))
% 179.72/179.60 [406]~E(x4061,x4062)+E(f172(x4063,x4061),f172(x4063,x4062))
% 179.72/179.60 [407]~E(x4071,x4072)+E(f146(x4071,x4073),f146(x4072,x4073))
% 179.72/179.60 [408]~E(x4081,x4082)+E(f146(x4083,x4081),f146(x4083,x4082))
% 179.72/179.60 [409]~E(x4091,x4092)+E(f158(x4091),f158(x4092))
% 179.72/179.60 [410]~E(x4101,x4102)+E(f171(x4101,x4103,x4104),f171(x4102,x4103,x4104))
% 179.72/179.60 [411]~E(x4111,x4112)+E(f171(x4113,x4111,x4114),f171(x4113,x4112,x4114))
% 179.72/179.60 [412]~E(x4121,x4122)+E(f171(x4123,x4124,x4121),f171(x4123,x4124,x4122))
% 179.72/179.60 [413]~E(x4131,x4132)+E(f751(x4131,x4133,x4134,x4135),f751(x4132,x4133,x4134,x4135))
% 179.72/179.60 [414]~E(x4141,x4142)+E(f751(x4143,x4141,x4144,x4145),f751(x4143,x4142,x4144,x4145))
% 179.72/179.60 [415]~E(x4151,x4152)+E(f751(x4153,x4154,x4151,x4155),f751(x4153,x4154,x4152,x4155))
% 179.72/179.60 [416]~E(x4161,x4162)+E(f751(x4163,x4164,x4165,x4161),f751(x4163,x4164,x4165,x4162))
% 179.72/179.60 [417]~E(x4171,x4172)+E(f155(x4171,x4173),f155(x4172,x4173))
% 179.72/179.60 [418]~E(x4181,x4182)+E(f155(x4183,x4181),f155(x4183,x4182))
% 179.72/179.60 [419]~E(x4191,x4192)+E(f70(x4191,x4193),f70(x4192,x4193))
% 179.72/179.60 [420]~E(x4201,x4202)+E(f70(x4203,x4201),f70(x4203,x4202))
% 179.72/179.60 [421]~E(x4211,x4212)+E(f224(x4211,x4213,x4214,x4215),f224(x4212,x4213,x4214,x4215))
% 179.72/179.60 [422]~E(x4221,x4222)+E(f224(x4223,x4221,x4224,x4225),f224(x4223,x4222,x4224,x4225))
% 179.72/179.60 [423]~E(x4231,x4232)+E(f224(x4233,x4234,x4231,x4235),f224(x4233,x4234,x4232,x4235))
% 179.72/179.60 [424]~E(x4241,x4242)+E(f224(x4243,x4244,x4245,x4241),f224(x4243,x4244,x4245,x4242))
% 179.72/179.60 [425]~E(x4251,x4252)+E(f537(x4251,x4253),f537(x4252,x4253))
% 179.72/179.60 [426]~E(x4261,x4262)+E(f537(x4263,x4261),f537(x4263,x4262))
% 179.72/179.60 [427]~E(x4271,x4272)+E(f444(x4271,x4273,x4274,x4275),f444(x4272,x4273,x4274,x4275))
% 179.72/179.60 [428]~E(x4281,x4282)+E(f444(x4283,x4281,x4284,x4285),f444(x4283,x4282,x4284,x4285))
% 179.72/179.60 [429]~E(x4291,x4292)+E(f444(x4293,x4294,x4291,x4295),f444(x4293,x4294,x4292,x4295))
% 179.72/179.60 [430]~E(x4301,x4302)+E(f444(x4303,x4304,x4305,x4301),f444(x4303,x4304,x4305,x4302))
% 179.72/179.60 [431]~E(x4311,x4312)+E(f12(x4311,x4313,x4314),f12(x4312,x4313,x4314))
% 179.72/179.60 [432]~E(x4321,x4322)+E(f12(x4323,x4321,x4324),f12(x4323,x4322,x4324))
% 179.72/179.60 [433]~E(x4331,x4332)+E(f12(x4333,x4334,x4331),f12(x4333,x4334,x4332))
% 179.72/179.60 [434]~E(x4341,x4342)+E(f669(x4341,x4343,x4344,x4345),f669(x4342,x4343,x4344,x4345))
% 179.72/179.60 [435]~E(x4351,x4352)+E(f669(x4353,x4351,x4354,x4355),f669(x4353,x4352,x4354,x4355))
% 179.72/179.60 [436]~E(x4361,x4362)+E(f669(x4363,x4364,x4361,x4365),f669(x4363,x4364,x4362,x4365))
% 179.72/179.60 [437]~E(x4371,x4372)+E(f669(x4373,x4374,x4375,x4371),f669(x4373,x4374,x4375,x4372))
% 179.72/179.60 [438]~E(x4381,x4382)+E(f60(x4381,x4383,x4384),f60(x4382,x4383,x4384))
% 179.72/179.60 [439]~E(x4391,x4392)+E(f60(x4393,x4391,x4394),f60(x4393,x4392,x4394))
% 179.72/179.60 [440]~E(x4401,x4402)+E(f60(x4403,x4404,x4401),f60(x4403,x4404,x4402))
% 179.72/179.60 [441]~E(x4411,x4412)+E(f801(x4411,x4413,x4414),f801(x4412,x4413,x4414))
% 179.72/179.60 [442]~E(x4421,x4422)+E(f801(x4423,x4421,x4424),f801(x4423,x4422,x4424))
% 179.72/179.60 [443]~E(x4431,x4432)+E(f801(x4433,x4434,x4431),f801(x4433,x4434,x4432))
% 179.72/179.60 [444]~E(x4441,x4442)+E(f703(x4441,x4443,x4444),f703(x4442,x4443,x4444))
% 179.72/179.60 [445]~E(x4451,x4452)+E(f703(x4453,x4451,x4454),f703(x4453,x4452,x4454))
% 179.72/179.60 [446]~E(x4461,x4462)+E(f703(x4463,x4464,x4461),f703(x4463,x4464,x4462))
% 179.72/179.60 [447]~E(x4471,x4472)+E(f91(x4471,x4473,x4474,x4475),f91(x4472,x4473,x4474,x4475))
% 179.72/179.60 [448]~E(x4481,x4482)+E(f91(x4483,x4481,x4484,x4485),f91(x4483,x4482,x4484,x4485))
% 179.72/179.60 [449]~E(x4491,x4492)+E(f91(x4493,x4494,x4491,x4495),f91(x4493,x4494,x4492,x4495))
% 179.72/179.60 [450]~E(x4501,x4502)+E(f91(x4503,x4504,x4505,x4501),f91(x4503,x4504,x4505,x4502))
% 179.72/179.60 [451]~E(x4511,x4512)+E(f123(x4511,x4513,x4514),f123(x4512,x4513,x4514))
% 179.72/179.60 [452]~E(x4521,x4522)+E(f123(x4523,x4521,x4524),f123(x4523,x4522,x4524))
% 179.72/179.60 [453]~E(x4531,x4532)+E(f123(x4533,x4534,x4531),f123(x4533,x4534,x4532))
% 179.72/179.60 [454]~E(x4541,x4542)+E(f228(x4541,x4543,x4544,x4545),f228(x4542,x4543,x4544,x4545))
% 179.72/179.60 [455]~E(x4551,x4552)+E(f228(x4553,x4551,x4554,x4555),f228(x4553,x4552,x4554,x4555))
% 179.72/179.60 [456]~E(x4561,x4562)+E(f228(x4563,x4564,x4561,x4565),f228(x4563,x4564,x4562,x4565))
% 179.72/179.60 [457]~E(x4571,x4572)+E(f228(x4573,x4574,x4575,x4571),f228(x4573,x4574,x4575,x4572))
% 179.72/179.60 [458]~E(x4581,x4582)+E(f748(x4581,x4583,x4584,x4585,x4586),f748(x4582,x4583,x4584,x4585,x4586))
% 179.72/179.60 [459]~E(x4591,x4592)+E(f748(x4593,x4591,x4594,x4595,x4596),f748(x4593,x4592,x4594,x4595,x4596))
% 179.72/179.60 [460]~E(x4601,x4602)+E(f748(x4603,x4604,x4601,x4605,x4606),f748(x4603,x4604,x4602,x4605,x4606))
% 179.72/179.60 [461]~E(x4611,x4612)+E(f748(x4613,x4614,x4615,x4611,x4616),f748(x4613,x4614,x4615,x4612,x4616))
% 179.72/179.60 [462]~E(x4621,x4622)+E(f748(x4623,x4624,x4625,x4626,x4621),f748(x4623,x4624,x4625,x4626,x4622))
% 179.72/179.60 [463]~E(x4631,x4632)+E(f428(x4631,x4633,x4634),f428(x4632,x4633,x4634))
% 179.72/179.60 [464]~E(x4641,x4642)+E(f428(x4643,x4641,x4644),f428(x4643,x4642,x4644))
% 179.72/179.60 [465]~E(x4651,x4652)+E(f428(x4653,x4654,x4651),f428(x4653,x4654,x4652))
% 179.72/179.60 [466]~E(x4661,x4662)+E(f254(x4661,x4663),f254(x4662,x4663))
% 179.72/179.60 [467]~E(x4671,x4672)+E(f254(x4673,x4671),f254(x4673,x4672))
% 179.72/179.60 [468]~E(x4681,x4682)+E(f740(x4681,x4683,x4684,x4685,x4686),f740(x4682,x4683,x4684,x4685,x4686))
% 179.72/179.60 [469]~E(x4691,x4692)+E(f740(x4693,x4691,x4694,x4695,x4696),f740(x4693,x4692,x4694,x4695,x4696))
% 179.72/179.60 [470]~E(x4701,x4702)+E(f740(x4703,x4704,x4701,x4705,x4706),f740(x4703,x4704,x4702,x4705,x4706))
% 179.72/179.60 [471]~E(x4711,x4712)+E(f740(x4713,x4714,x4715,x4711,x4716),f740(x4713,x4714,x4715,x4712,x4716))
% 179.72/179.60 [472]~E(x4721,x4722)+E(f740(x4723,x4724,x4725,x4726,x4721),f740(x4723,x4724,x4725,x4726,x4722))
% 179.72/179.60 [473]~E(x4731,x4732)+E(f134(x4731),f134(x4732))
% 179.72/179.60 [474]~E(x4741,x4742)+E(f586(x4741,x4743,x4744,x4745),f586(x4742,x4743,x4744,x4745))
% 179.72/179.60 [475]~E(x4751,x4752)+E(f586(x4753,x4751,x4754,x4755),f586(x4753,x4752,x4754,x4755))
% 179.72/179.60 [476]~E(x4761,x4762)+E(f586(x4763,x4764,x4761,x4765),f586(x4763,x4764,x4762,x4765))
% 179.72/179.60 [477]~E(x4771,x4772)+E(f586(x4773,x4774,x4775,x4771),f586(x4773,x4774,x4775,x4772))
% 179.72/179.60 [478]~E(x4781,x4782)+E(f300(x4781),f300(x4782))
% 179.72/179.60 [479]~E(x4791,x4792)+E(f494(x4791,x4793,x4794,x4795,x4796,x4797),f494(x4792,x4793,x4794,x4795,x4796,x4797))
% 179.72/179.60 [480]~E(x4801,x4802)+E(f494(x4803,x4801,x4804,x4805,x4806,x4807),f494(x4803,x4802,x4804,x4805,x4806,x4807))
% 179.72/179.60 [481]~E(x4811,x4812)+E(f494(x4813,x4814,x4811,x4815,x4816,x4817),f494(x4813,x4814,x4812,x4815,x4816,x4817))
% 179.72/179.60 [482]~E(x4821,x4822)+E(f494(x4823,x4824,x4825,x4821,x4826,x4827),f494(x4823,x4824,x4825,x4822,x4826,x4827))
% 179.72/179.60 [483]~E(x4831,x4832)+E(f494(x4833,x4834,x4835,x4836,x4831,x4837),f494(x4833,x4834,x4835,x4836,x4832,x4837))
% 179.72/179.60 [484]~E(x4841,x4842)+E(f494(x4843,x4844,x4845,x4846,x4847,x4841),f494(x4843,x4844,x4845,x4846,x4847,x4842))
% 179.72/179.60 [485]~E(x4851,x4852)+E(f43(x4851,x4853),f43(x4852,x4853))
% 179.72/179.60 [486]~E(x4861,x4862)+E(f43(x4863,x4861),f43(x4863,x4862))
% 179.72/179.60 [487]~E(x4871,x4872)+E(f298(x4871),f298(x4872))
% 179.72/179.60 [488]~E(x4881,x4882)+E(f517(x4881,x4883,x4884,x4885),f517(x4882,x4883,x4884,x4885))
% 179.72/179.60 [489]~E(x4891,x4892)+E(f517(x4893,x4891,x4894,x4895),f517(x4893,x4892,x4894,x4895))
% 179.72/179.60 [490]~E(x4901,x4902)+E(f517(x4903,x4904,x4901,x4905),f517(x4903,x4904,x4902,x4905))
% 179.72/179.60 [491]~E(x4911,x4912)+E(f517(x4913,x4914,x4915,x4911),f517(x4913,x4914,x4915,x4912))
% 179.72/179.60 [492]~E(x4921,x4922)+E(f182(x4921,x4923,x4924,x4925),f182(x4922,x4923,x4924,x4925))
% 179.72/179.60 [493]~E(x4931,x4932)+E(f182(x4933,x4931,x4934,x4935),f182(x4933,x4932,x4934,x4935))
% 179.72/179.60 [494]~E(x4941,x4942)+E(f182(x4943,x4944,x4941,x4945),f182(x4943,x4944,x4942,x4945))
% 179.72/179.60 [495]~E(x4951,x4952)+E(f182(x4953,x4954,x4955,x4951),f182(x4953,x4954,x4955,x4952))
% 179.72/179.60 [496]~E(x4961,x4962)+E(f831(x4961,x4963,x4964,x4965,x4966,x4967,x4968),f831(x4962,x4963,x4964,x4965,x4966,x4967,x4968))
% 179.72/179.60 [497]~E(x4971,x4972)+E(f831(x4973,x4971,x4974,x4975,x4976,x4977,x4978),f831(x4973,x4972,x4974,x4975,x4976,x4977,x4978))
% 179.72/179.60 [498]~E(x4981,x4982)+E(f831(x4983,x4984,x4981,x4985,x4986,x4987,x4988),f831(x4983,x4984,x4982,x4985,x4986,x4987,x4988))
% 179.72/179.60 [499]~E(x4991,x4992)+E(f831(x4993,x4994,x4995,x4991,x4996,x4997,x4998),f831(x4993,x4994,x4995,x4992,x4996,x4997,x4998))
% 179.72/179.60 [500]~E(x5001,x5002)+E(f831(x5003,x5004,x5005,x5006,x5001,x5007,x5008),f831(x5003,x5004,x5005,x5006,x5002,x5007,x5008))
% 179.72/179.60 [501]~E(x5011,x5012)+E(f831(x5013,x5014,x5015,x5016,x5017,x5011,x5018),f831(x5013,x5014,x5015,x5016,x5017,x5012,x5018))
% 179.72/179.60 [502]~E(x5021,x5022)+E(f831(x5023,x5024,x5025,x5026,x5027,x5028,x5021),f831(x5023,x5024,x5025,x5026,x5027,x5028,x5022))
% 179.72/179.60 [503]~E(x5031,x5032)+E(f624(x5031,x5033,x5034,x5035),f624(x5032,x5033,x5034,x5035))
% 179.72/179.60 [504]~E(x5041,x5042)+E(f624(x5043,x5041,x5044,x5045),f624(x5043,x5042,x5044,x5045))
% 179.72/179.60 [505]~E(x5051,x5052)+E(f624(x5053,x5054,x5051,x5055),f624(x5053,x5054,x5052,x5055))
% 179.72/179.60 [506]~E(x5061,x5062)+E(f624(x5063,x5064,x5065,x5061),f624(x5063,x5064,x5065,x5062))
% 179.72/179.60 [507]~E(x5071,x5072)+E(f86(x5071),f86(x5072))
% 179.72/179.60 [508]~E(x5081,x5082)+E(f752(x5081,x5083,x5084,x5085),f752(x5082,x5083,x5084,x5085))
% 179.72/179.60 [509]~E(x5091,x5092)+E(f752(x5093,x5091,x5094,x5095),f752(x5093,x5092,x5094,x5095))
% 179.72/179.60 [510]~E(x5101,x5102)+E(f752(x5103,x5104,x5101,x5105),f752(x5103,x5104,x5102,x5105))
% 179.72/179.60 [511]~E(x5111,x5112)+E(f752(x5113,x5114,x5115,x5111),f752(x5113,x5114,x5115,x5112))
% 179.72/179.60 [512]~E(x5121,x5122)+E(f185(x5121,x5123,x5124,x5125),f185(x5122,x5123,x5124,x5125))
% 179.72/179.60 [513]~E(x5131,x5132)+E(f185(x5133,x5131,x5134,x5135),f185(x5133,x5132,x5134,x5135))
% 179.72/179.60 [514]~E(x5141,x5142)+E(f185(x5143,x5144,x5141,x5145),f185(x5143,x5144,x5142,x5145))
% 179.72/179.60 [515]~E(x5151,x5152)+E(f185(x5153,x5154,x5155,x5151),f185(x5153,x5154,x5155,x5152))
% 179.72/179.60 [516]~E(x5161,x5162)+E(f63(x5161,x5163,x5164),f63(x5162,x5163,x5164))
% 179.72/179.60 [517]~E(x5171,x5172)+E(f63(x5173,x5171,x5174),f63(x5173,x5172,x5174))
% 179.72/179.60 [518]~E(x5181,x5182)+E(f63(x5183,x5184,x5181),f63(x5183,x5184,x5182))
% 179.72/179.60 [519]~E(x5191,x5192)+E(f725(x5191,x5193,x5194,x5195,x5196),f725(x5192,x5193,x5194,x5195,x5196))
% 179.72/179.60 [520]~E(x5201,x5202)+E(f725(x5203,x5201,x5204,x5205,x5206),f725(x5203,x5202,x5204,x5205,x5206))
% 179.72/179.60 [521]~E(x5211,x5212)+E(f725(x5213,x5214,x5211,x5215,x5216),f725(x5213,x5214,x5212,x5215,x5216))
% 179.72/179.60 [522]~E(x5221,x5222)+E(f725(x5223,x5224,x5225,x5221,x5226),f725(x5223,x5224,x5225,x5222,x5226))
% 179.72/179.60 [523]~E(x5231,x5232)+E(f725(x5233,x5234,x5235,x5236,x5231),f725(x5233,x5234,x5235,x5236,x5232))
% 179.72/179.60 [524]~E(x5241,x5242)+E(f402(x5241,x5243),f402(x5242,x5243))
% 179.72/179.60 [525]~E(x5251,x5252)+E(f402(x5253,x5251),f402(x5253,x5252))
% 179.72/179.60 [526]~E(x5261,x5262)+E(f730(x5261,x5263),f730(x5262,x5263))
% 179.72/179.60 [527]~E(x5271,x5272)+E(f730(x5273,x5271),f730(x5273,x5272))
% 179.72/179.60 [528]~E(x5281,x5282)+E(f245(x5281),f245(x5282))
% 179.72/179.60 [529]~E(x5291,x5292)+E(f47(x5291,x5293),f47(x5292,x5293))
% 179.72/179.60 [530]~E(x5301,x5302)+E(f47(x5303,x5301),f47(x5303,x5302))
% 179.72/179.60 [531]~E(x5311,x5312)+E(f654(x5311,x5313),f654(x5312,x5313))
% 179.72/179.60 [532]~E(x5321,x5322)+E(f654(x5323,x5321),f654(x5323,x5322))
% 179.72/179.60 [533]~E(x5331,x5332)+E(f432(x5331,x5333,x5334),f432(x5332,x5333,x5334))
% 179.72/179.60 [534]~E(x5341,x5342)+E(f432(x5343,x5341,x5344),f432(x5343,x5342,x5344))
% 179.72/179.60 [535]~E(x5351,x5352)+E(f432(x5353,x5354,x5351),f432(x5353,x5354,x5352))
% 179.72/179.60 [536]~E(x5361,x5362)+E(f31(x5361,x5363,x5364,x5365,x5366,x5367,x5368,x5369,x53610,x53611),f31(x5362,x5363,x5364,x5365,x5366,x5367,x5368,x5369,x53610,x53611))
% 179.72/179.60 [537]~E(x5371,x5372)+E(f31(x5373,x5371,x5374,x5375,x5376,x5377,x5378,x5379,x53710,x53711),f31(x5373,x5372,x5374,x5375,x5376,x5377,x5378,x5379,x53710,x53711))
% 179.72/179.60 [538]~E(x5381,x5382)+E(f31(x5383,x5384,x5381,x5385,x5386,x5387,x5388,x5389,x53810,x53811),f31(x5383,x5384,x5382,x5385,x5386,x5387,x5388,x5389,x53810,x53811))
% 179.72/179.60 [539]~E(x5391,x5392)+E(f31(x5393,x5394,x5395,x5391,x5396,x5397,x5398,x5399,x53910,x53911),f31(x5393,x5394,x5395,x5392,x5396,x5397,x5398,x5399,x53910,x53911))
% 179.72/179.60 [540]~E(x5401,x5402)+E(f31(x5403,x5404,x5405,x5406,x5401,x5407,x5408,x5409,x54010,x54011),f31(x5403,x5404,x5405,x5406,x5402,x5407,x5408,x5409,x54010,x54011))
% 179.72/179.60 [541]~E(x5411,x5412)+E(f31(x5413,x5414,x5415,x5416,x5417,x5411,x5418,x5419,x54110,x54111),f31(x5413,x5414,x5415,x5416,x5417,x5412,x5418,x5419,x54110,x54111))
% 179.72/179.60 [542]~E(x5421,x5422)+E(f31(x5423,x5424,x5425,x5426,x5427,x5428,x5421,x5429,x54210,x54211),f31(x5423,x5424,x5425,x5426,x5427,x5428,x5422,x5429,x54210,x54211))
% 179.72/179.60 [543]~E(x5431,x5432)+E(f31(x5433,x5434,x5435,x5436,x5437,x5438,x5439,x5431,x54310,x54311),f31(x5433,x5434,x5435,x5436,x5437,x5438,x5439,x5432,x54310,x54311))
% 179.72/179.60 [544]~E(x5441,x5442)+E(f31(x5443,x5444,x5445,x5446,x5447,x5448,x5449,x54410,x5441,x54411),f31(x5443,x5444,x5445,x5446,x5447,x5448,x5449,x54410,x5442,x54411))
% 179.72/179.60 [545]~E(x5451,x5452)+E(f31(x5453,x5454,x5455,x5456,x5457,x5458,x5459,x54510,x54511,x5451),f31(x5453,x5454,x5455,x5456,x5457,x5458,x5459,x54510,x54511,x5452))
% 179.72/179.60 [546]~E(x5461,x5462)+E(f204(x5461),f204(x5462))
% 179.72/179.60 [547]~E(x5471,x5472)+E(f790(x5471,x5473,x5474),f790(x5472,x5473,x5474))
% 179.72/179.60 [548]~E(x5481,x5482)+E(f790(x5483,x5481,x5484),f790(x5483,x5482,x5484))
% 179.72/179.60 [549]~E(x5491,x5492)+E(f790(x5493,x5494,x5491),f790(x5493,x5494,x5492))
% 179.72/179.60 [550]~E(x5501,x5502)+E(f802(x5501,x5503,x5504),f802(x5502,x5503,x5504))
% 179.72/179.60 [551]~E(x5511,x5512)+E(f802(x5513,x5511,x5514),f802(x5513,x5512,x5514))
% 179.72/179.60 [552]~E(x5521,x5522)+E(f802(x5523,x5524,x5521),f802(x5523,x5524,x5522))
% 179.72/179.60 [553]~E(x5531,x5532)+E(f784(x5531,x5533,x5534,x5535),f784(x5532,x5533,x5534,x5535))
% 179.72/179.60 [554]~E(x5541,x5542)+E(f784(x5543,x5541,x5544,x5545),f784(x5543,x5542,x5544,x5545))
% 179.72/179.60 [555]~E(x5551,x5552)+E(f784(x5553,x5554,x5551,x5555),f784(x5553,x5554,x5552,x5555))
% 179.72/179.60 [556]~E(x5561,x5562)+E(f784(x5563,x5564,x5565,x5561),f784(x5563,x5564,x5565,x5562))
% 179.72/179.60 [557]~E(x5571,x5572)+E(f618(x5571,x5573,x5574,x5575,x5576),f618(x5572,x5573,x5574,x5575,x5576))
% 179.72/179.60 [558]~E(x5581,x5582)+E(f618(x5583,x5581,x5584,x5585,x5586),f618(x5583,x5582,x5584,x5585,x5586))
% 179.72/179.60 [559]~E(x5591,x5592)+E(f618(x5593,x5594,x5591,x5595,x5596),f618(x5593,x5594,x5592,x5595,x5596))
% 179.72/179.60 [560]~E(x5601,x5602)+E(f618(x5603,x5604,x5605,x5601,x5606),f618(x5603,x5604,x5605,x5602,x5606))
% 179.72/179.60 [561]~E(x5611,x5612)+E(f618(x5613,x5614,x5615,x5616,x5611),f618(x5613,x5614,x5615,x5616,x5612))
% 179.72/179.60 [562]~E(x5621,x5622)+E(f418(x5621,x5623,x5624,x5625),f418(x5622,x5623,x5624,x5625))
% 179.72/179.60 [563]~E(x5631,x5632)+E(f418(x5633,x5631,x5634,x5635),f418(x5633,x5632,x5634,x5635))
% 179.72/179.60 [564]~E(x5641,x5642)+E(f418(x5643,x5644,x5641,x5645),f418(x5643,x5644,x5642,x5645))
% 179.72/179.60 [565]~E(x5651,x5652)+E(f418(x5653,x5654,x5655,x5651),f418(x5653,x5654,x5655,x5652))
% 179.72/179.60 [566]~E(x5661,x5662)+E(f232(x5661,x5663,x5664,x5665),f232(x5662,x5663,x5664,x5665))
% 179.72/179.60 [567]~E(x5671,x5672)+E(f232(x5673,x5671,x5674,x5675),f232(x5673,x5672,x5674,x5675))
% 179.72/179.60 [568]~E(x5681,x5682)+E(f232(x5683,x5684,x5681,x5685),f232(x5683,x5684,x5682,x5685))
% 179.72/179.60 [569]~E(x5691,x5692)+E(f232(x5693,x5694,x5695,x5691),f232(x5693,x5694,x5695,x5692))
% 179.72/179.60 [570]~E(x5701,x5702)+E(f385(x5701,x5703),f385(x5702,x5703))
% 179.72/179.60 [571]~E(x5711,x5712)+E(f385(x5713,x5711),f385(x5713,x5712))
% 179.72/179.60 [572]~E(x5721,x5722)+E(f437(x5721,x5723,x5724),f437(x5722,x5723,x5724))
% 179.72/179.60 [573]~E(x5731,x5732)+E(f437(x5733,x5731,x5734),f437(x5733,x5732,x5734))
% 179.72/179.60 [574]~E(x5741,x5742)+E(f437(x5743,x5744,x5741),f437(x5743,x5744,x5742))
% 179.72/179.60 [575]~E(x5751,x5752)+E(f353(x5751,x5753,x5754),f353(x5752,x5753,x5754))
% 179.72/179.60 [576]~E(x5761,x5762)+E(f353(x5763,x5761,x5764),f353(x5763,x5762,x5764))
% 179.72/179.60 [577]~E(x5771,x5772)+E(f353(x5773,x5774,x5771),f353(x5773,x5774,x5772))
% 179.72/179.60 [578]~E(x5781,x5782)+E(f791(x5781,x5783,x5784),f791(x5782,x5783,x5784))
% 179.72/179.60 [579]~E(x5791,x5792)+E(f791(x5793,x5791,x5794),f791(x5793,x5792,x5794))
% 179.72/179.60 [580]~E(x5801,x5802)+E(f791(x5803,x5804,x5801),f791(x5803,x5804,x5802))
% 179.72/179.60 [581]~E(x5811,x5812)+E(f729(x5811,x5813),f729(x5812,x5813))
% 179.72/179.60 [582]~E(x5821,x5822)+E(f729(x5823,x5821),f729(x5823,x5822))
% 179.72/179.60 [583]~E(x5831,x5832)+E(f639(x5831,x5833,x5834,x5835),f639(x5832,x5833,x5834,x5835))
% 179.72/179.60 [584]~E(x5841,x5842)+E(f639(x5843,x5841,x5844,x5845),f639(x5843,x5842,x5844,x5845))
% 179.72/179.60 [585]~E(x5851,x5852)+E(f639(x5853,x5854,x5851,x5855),f639(x5853,x5854,x5852,x5855))
% 179.72/179.60 [586]~E(x5861,x5862)+E(f639(x5863,x5864,x5865,x5861),f639(x5863,x5864,x5865,x5862))
% 179.72/179.60 [587]~E(x5871,x5872)+E(f116(x5871,x5873,x5874),f116(x5872,x5873,x5874))
% 179.72/179.60 [588]~E(x5881,x5882)+E(f116(x5883,x5881,x5884),f116(x5883,x5882,x5884))
% 179.72/179.60 [589]~E(x5891,x5892)+E(f116(x5893,x5894,x5891),f116(x5893,x5894,x5892))
% 179.72/179.60 [590]~E(x5901,x5902)+E(f229(x5901,x5903),f229(x5902,x5903))
% 179.72/179.60 [591]~E(x5911,x5912)+E(f229(x5913,x5911),f229(x5913,x5912))
% 179.72/179.60 [592]~E(x5921,x5922)+E(f682(x5921,x5923),f682(x5922,x5923))
% 179.72/179.60 [593]~E(x5931,x5932)+E(f682(x5933,x5931),f682(x5933,x5932))
% 179.72/179.60 [594]~E(x5941,x5942)+E(f557(x5941,x5943,x5944,x5945,x5946),f557(x5942,x5943,x5944,x5945,x5946))
% 179.72/179.60 [595]~E(x5951,x5952)+E(f557(x5953,x5951,x5954,x5955,x5956),f557(x5953,x5952,x5954,x5955,x5956))
% 179.72/179.60 [596]~E(x5961,x5962)+E(f557(x5963,x5964,x5961,x5965,x5966),f557(x5963,x5964,x5962,x5965,x5966))
% 179.72/179.60 [597]~E(x5971,x5972)+E(f557(x5973,x5974,x5975,x5971,x5976),f557(x5973,x5974,x5975,x5972,x5976))
% 179.72/179.60 [598]~E(x5981,x5982)+E(f557(x5983,x5984,x5985,x5986,x5981),f557(x5983,x5984,x5985,x5986,x5982))
% 179.72/179.60 [599]~E(x5991,x5992)+E(f534(x5991,x5993,x5994,x5995,x5996),f534(x5992,x5993,x5994,x5995,x5996))
% 179.72/179.60 [600]~E(x6001,x6002)+E(f534(x6003,x6001,x6004,x6005,x6006),f534(x6003,x6002,x6004,x6005,x6006))
% 179.72/179.60 [601]~E(x6011,x6012)+E(f534(x6013,x6014,x6011,x6015,x6016),f534(x6013,x6014,x6012,x6015,x6016))
% 179.72/179.60 [602]~E(x6021,x6022)+E(f534(x6023,x6024,x6025,x6021,x6026),f534(x6023,x6024,x6025,x6022,x6026))
% 179.72/179.60 [603]~E(x6031,x6032)+E(f534(x6033,x6034,x6035,x6036,x6031),f534(x6033,x6034,x6035,x6036,x6032))
% 179.72/179.60 [604]~E(x6041,x6042)+E(f194(x6041,x6043),f194(x6042,x6043))
% 179.72/179.60 [605]~E(x6051,x6052)+E(f194(x6053,x6051),f194(x6053,x6052))
% 179.72/179.60 [606]~E(x6061,x6062)+E(f398(x6061,x6063,x6064),f398(x6062,x6063,x6064))
% 179.72/179.60 [607]~E(x6071,x6072)+E(f398(x6073,x6071,x6074),f398(x6073,x6072,x6074))
% 179.72/179.60 [608]~E(x6081,x6082)+E(f398(x6083,x6084,x6081),f398(x6083,x6084,x6082))
% 179.72/179.60 [609]~E(x6091,x6092)+E(f85(x6091),f85(x6092))
% 179.72/179.60 [610]~E(x6101,x6102)+E(f511(x6101,x6103),f511(x6102,x6103))
% 179.72/179.60 [611]~E(x6111,x6112)+E(f511(x6113,x6111),f511(x6113,x6112))
% 179.72/179.60 [612]~E(x6121,x6122)+E(f589(x6121,x6123,x6124,x6125),f589(x6122,x6123,x6124,x6125))
% 179.72/179.60 [613]~E(x6131,x6132)+E(f589(x6133,x6131,x6134,x6135),f589(x6133,x6132,x6134,x6135))
% 179.72/179.60 [614]~E(x6141,x6142)+E(f589(x6143,x6144,x6141,x6145),f589(x6143,x6144,x6142,x6145))
% 179.72/179.60 [615]~E(x6151,x6152)+E(f589(x6153,x6154,x6155,x6151),f589(x6153,x6154,x6155,x6152))
% 179.72/179.60 [616]~E(x6161,x6162)+E(f373(x6161,x6163,x6164,x6165,x6166,x6167),f373(x6162,x6163,x6164,x6165,x6166,x6167))
% 179.72/179.60 [617]~E(x6171,x6172)+E(f373(x6173,x6171,x6174,x6175,x6176,x6177),f373(x6173,x6172,x6174,x6175,x6176,x6177))
% 179.72/179.60 [618]~E(x6181,x6182)+E(f373(x6183,x6184,x6181,x6185,x6186,x6187),f373(x6183,x6184,x6182,x6185,x6186,x6187))
% 179.72/179.60 [619]~E(x6191,x6192)+E(f373(x6193,x6194,x6195,x6191,x6196,x6197),f373(x6193,x6194,x6195,x6192,x6196,x6197))
% 179.72/179.60 [620]~E(x6201,x6202)+E(f373(x6203,x6204,x6205,x6206,x6201,x6207),f373(x6203,x6204,x6205,x6206,x6202,x6207))
% 179.72/179.60 [621]~E(x6211,x6212)+E(f373(x6213,x6214,x6215,x6216,x6217,x6211),f373(x6213,x6214,x6215,x6216,x6217,x6212))
% 179.72/179.60 [622]~E(x6221,x6222)+E(f789(x6221,x6223,x6224),f789(x6222,x6223,x6224))
% 179.72/179.60 [623]~E(x6231,x6232)+E(f789(x6233,x6231,x6234),f789(x6233,x6232,x6234))
% 179.72/179.60 [624]~E(x6241,x6242)+E(f789(x6243,x6244,x6241),f789(x6243,x6244,x6242))
% 179.72/179.60 [625]~E(x6251,x6252)+E(f698(x6251,x6253,x6254,x6255),f698(x6252,x6253,x6254,x6255))
% 179.72/179.60 [626]~E(x6261,x6262)+E(f698(x6263,x6261,x6264,x6265),f698(x6263,x6262,x6264,x6265))
% 179.72/179.60 [627]~E(x6271,x6272)+E(f698(x6273,x6274,x6271,x6275),f698(x6273,x6274,x6272,x6275))
% 179.72/179.60 [628]~E(x6281,x6282)+E(f698(x6283,x6284,x6285,x6281),f698(x6283,x6284,x6285,x6282))
% 179.72/179.60 [629]~E(x6291,x6292)+E(f833(x6291,x6293,x6294,x6295),f833(x6292,x6293,x6294,x6295))
% 179.72/179.60 [630]~E(x6301,x6302)+E(f833(x6303,x6301,x6304,x6305),f833(x6303,x6302,x6304,x6305))
% 179.72/179.60 [631]~E(x6311,x6312)+E(f833(x6313,x6314,x6311,x6315),f833(x6313,x6314,x6312,x6315))
% 179.72/179.60 [632]~E(x6321,x6322)+E(f833(x6323,x6324,x6325,x6321),f833(x6323,x6324,x6325,x6322))
% 179.72/179.60 [633]~E(x6331,x6332)+E(f217(x6331,x6333),f217(x6332,x6333))
% 179.72/179.60 [634]~E(x6341,x6342)+E(f217(x6343,x6341),f217(x6343,x6342))
% 179.72/179.60 [635]~E(x6351,x6352)+E(f543(x6351,x6353),f543(x6352,x6353))
% 179.72/179.60 [636]~E(x6361,x6362)+E(f543(x6363,x6361),f543(x6363,x6362))
% 179.72/179.60 [637]~E(x6371,x6372)+E(f447(x6371,x6373,x6374,x6375,x6376),f447(x6372,x6373,x6374,x6375,x6376))
% 179.72/179.60 [638]~E(x6381,x6382)+E(f447(x6383,x6381,x6384,x6385,x6386),f447(x6383,x6382,x6384,x6385,x6386))
% 179.72/179.60 [639]~E(x6391,x6392)+E(f447(x6393,x6394,x6391,x6395,x6396),f447(x6393,x6394,x6392,x6395,x6396))
% 179.72/179.60 [640]~E(x6401,x6402)+E(f447(x6403,x6404,x6405,x6401,x6406),f447(x6403,x6404,x6405,x6402,x6406))
% 179.72/179.60 [641]~E(x6411,x6412)+E(f447(x6413,x6414,x6415,x6416,x6411),f447(x6413,x6414,x6415,x6416,x6412))
% 179.72/179.60 [642]~E(x6421,x6422)+E(f55(x6421),f55(x6422))
% 179.72/179.60 [643]~E(x6431,x6432)+E(f599(x6431,x6433,x6434),f599(x6432,x6433,x6434))
% 179.72/179.60 [644]~E(x6441,x6442)+E(f599(x6443,x6441,x6444),f599(x6443,x6442,x6444))
% 179.72/179.60 [645]~E(x6451,x6452)+E(f599(x6453,x6454,x6451),f599(x6453,x6454,x6452))
% 179.72/179.60 [646]~E(x6461,x6462)+E(f140(x6461,x6463),f140(x6462,x6463))
% 179.72/179.60 [647]~E(x6471,x6472)+E(f140(x6473,x6471),f140(x6473,x6472))
% 179.72/179.60 [648]~E(x6481,x6482)+E(f509(x6481,x6483,x6484,x6485,x6486,x6487,x6488),f509(x6482,x6483,x6484,x6485,x6486,x6487,x6488))
% 179.72/179.60 [649]~E(x6491,x6492)+E(f509(x6493,x6491,x6494,x6495,x6496,x6497,x6498),f509(x6493,x6492,x6494,x6495,x6496,x6497,x6498))
% 179.72/179.60 [650]~E(x6501,x6502)+E(f509(x6503,x6504,x6501,x6505,x6506,x6507,x6508),f509(x6503,x6504,x6502,x6505,x6506,x6507,x6508))
% 179.72/179.60 [651]~E(x6511,x6512)+E(f509(x6513,x6514,x6515,x6511,x6516,x6517,x6518),f509(x6513,x6514,x6515,x6512,x6516,x6517,x6518))
% 179.72/179.60 [652]~E(x6521,x6522)+E(f509(x6523,x6524,x6525,x6526,x6521,x6527,x6528),f509(x6523,x6524,x6525,x6526,x6522,x6527,x6528))
% 179.72/179.60 [653]~E(x6531,x6532)+E(f509(x6533,x6534,x6535,x6536,x6537,x6531,x6538),f509(x6533,x6534,x6535,x6536,x6537,x6532,x6538))
% 179.72/179.60 [654]~E(x6541,x6542)+E(f509(x6543,x6544,x6545,x6546,x6547,x6548,x6541),f509(x6543,x6544,x6545,x6546,x6547,x6548,x6542))
% 179.72/179.60 [655]~E(x6551,x6552)+E(f815(x6551,x6553,x6554),f815(x6552,x6553,x6554))
% 179.72/179.60 [656]~E(x6561,x6562)+E(f815(x6563,x6561,x6564),f815(x6563,x6562,x6564))
% 179.72/179.60 [657]~E(x6571,x6572)+E(f815(x6573,x6574,x6571),f815(x6573,x6574,x6572))
% 179.72/179.60 [658]~E(x6581,x6582)+E(f259(x6581,x6583,x6584,x6585,x6586),f259(x6582,x6583,x6584,x6585,x6586))
% 179.72/179.60 [659]~E(x6591,x6592)+E(f259(x6593,x6591,x6594,x6595,x6596),f259(x6593,x6592,x6594,x6595,x6596))
% 179.72/179.60 [660]~E(x6601,x6602)+E(f259(x6603,x6604,x6601,x6605,x6606),f259(x6603,x6604,x6602,x6605,x6606))
% 179.72/179.60 [661]~E(x6611,x6612)+E(f259(x6613,x6614,x6615,x6611,x6616),f259(x6613,x6614,x6615,x6612,x6616))
% 179.72/179.60 [662]~E(x6621,x6622)+E(f259(x6623,x6624,x6625,x6626,x6621),f259(x6623,x6624,x6625,x6626,x6622))
% 179.72/179.60 [663]~E(x6631,x6632)+E(f57(x6631,x6633,x6634,x6635),f57(x6632,x6633,x6634,x6635))
% 179.72/179.60 [664]~E(x6641,x6642)+E(f57(x6643,x6641,x6644,x6645),f57(x6643,x6642,x6644,x6645))
% 179.72/179.60 [665]~E(x6651,x6652)+E(f57(x6653,x6654,x6651,x6655),f57(x6653,x6654,x6652,x6655))
% 179.72/179.60 [666]~E(x6661,x6662)+E(f57(x6663,x6664,x6665,x6661),f57(x6663,x6664,x6665,x6662))
% 179.72/179.60 [667]~E(x6671,x6672)+E(f186(x6671),f186(x6672))
% 179.72/179.60 [668]~E(x6681,x6682)+E(f374(x6681,x6683,x6684,x6685,x6686,x6687),f374(x6682,x6683,x6684,x6685,x6686,x6687))
% 179.72/179.60 [669]~E(x6691,x6692)+E(f374(x6693,x6691,x6694,x6695,x6696,x6697),f374(x6693,x6692,x6694,x6695,x6696,x6697))
% 179.72/179.60 [670]~E(x6701,x6702)+E(f374(x6703,x6704,x6701,x6705,x6706,x6707),f374(x6703,x6704,x6702,x6705,x6706,x6707))
% 179.72/179.60 [671]~E(x6711,x6712)+E(f374(x6713,x6714,x6715,x6711,x6716,x6717),f374(x6713,x6714,x6715,x6712,x6716,x6717))
% 179.72/179.60 [672]~E(x6721,x6722)+E(f374(x6723,x6724,x6725,x6726,x6721,x6727),f374(x6723,x6724,x6725,x6726,x6722,x6727))
% 179.72/179.60 [673]~E(x6731,x6732)+E(f374(x6733,x6734,x6735,x6736,x6737,x6731),f374(x6733,x6734,x6735,x6736,x6737,x6732))
% 179.72/179.60 [674]~E(x6741,x6742)+E(f220(x6741,x6743),f220(x6742,x6743))
% 179.72/179.60 [675]~E(x6751,x6752)+E(f220(x6753,x6751),f220(x6753,x6752))
% 179.72/179.60 [676]~E(x6761,x6762)+E(f423(x6761,x6763),f423(x6762,x6763))
% 179.72/179.60 [677]~E(x6771,x6772)+E(f423(x6773,x6771),f423(x6773,x6772))
% 179.72/179.60 [678]~E(x6781,x6782)+E(f530(x6781,x6783),f530(x6782,x6783))
% 179.72/179.60 [679]~E(x6791,x6792)+E(f530(x6793,x6791),f530(x6793,x6792))
% 179.72/179.60 [680]~E(x6801,x6802)+E(f64(x6801,x6803,x6804,x6805,x6806),f64(x6802,x6803,x6804,x6805,x6806))
% 179.72/179.60 [681]~E(x6811,x6812)+E(f64(x6813,x6811,x6814,x6815,x6816),f64(x6813,x6812,x6814,x6815,x6816))
% 179.72/179.60 [682]~E(x6821,x6822)+E(f64(x6823,x6824,x6821,x6825,x6826),f64(x6823,x6824,x6822,x6825,x6826))
% 179.72/179.60 [683]~E(x6831,x6832)+E(f64(x6833,x6834,x6835,x6831,x6836),f64(x6833,x6834,x6835,x6832,x6836))
% 179.72/179.60 [684]~E(x6841,x6842)+E(f64(x6843,x6844,x6845,x6846,x6841),f64(x6843,x6844,x6845,x6846,x6842))
% 179.72/179.60 [685]~E(x6851,x6852)+E(f758(x6851,x6853,x6854),f758(x6852,x6853,x6854))
% 179.72/179.60 [686]~E(x6861,x6862)+E(f758(x6863,x6861,x6864),f758(x6863,x6862,x6864))
% 179.72/179.60 [687]~E(x6871,x6872)+E(f758(x6873,x6874,x6871),f758(x6873,x6874,x6872))
% 179.72/179.60 [688]~E(x6881,x6882)+E(f305(x6881,x6883,x6884),f305(x6882,x6883,x6884))
% 179.72/179.60 [689]~E(x6891,x6892)+E(f305(x6893,x6891,x6894),f305(x6893,x6892,x6894))
% 179.72/179.60 [690]~E(x6901,x6902)+E(f305(x6903,x6904,x6901),f305(x6903,x6904,x6902))
% 179.72/179.60 [691]~E(x6911,x6912)+E(f160(x6911,x6913,x6914),f160(x6912,x6913,x6914))
% 179.72/179.60 [692]~E(x6921,x6922)+E(f160(x6923,x6921,x6924),f160(x6923,x6922,x6924))
% 179.72/179.60 [693]~E(x6931,x6932)+E(f160(x6933,x6934,x6931),f160(x6933,x6934,x6932))
% 179.72/179.60 [694]~E(x6941,x6942)+E(f239(x6941,x6943),f239(x6942,x6943))
% 179.72/179.60 [695]~E(x6951,x6952)+E(f239(x6953,x6951),f239(x6953,x6952))
% 179.72/179.60 [696]~E(x6961,x6962)+E(f296(x6961,x6963,x6964),f296(x6962,x6963,x6964))
% 179.72/179.60 [697]~E(x6971,x6972)+E(f296(x6973,x6971,x6974),f296(x6973,x6972,x6974))
% 179.72/179.60 [698]~E(x6981,x6982)+E(f296(x6983,x6984,x6981),f296(x6983,x6984,x6982))
% 179.72/179.60 [699]~E(x6991,x6992)+E(f203(x6991),f203(x6992))
% 179.72/179.60 [700]~E(x7001,x7002)+E(f549(x7001,x7003,x7004),f549(x7002,x7003,x7004))
% 179.72/179.60 [701]~E(x7011,x7012)+E(f549(x7013,x7011,x7014),f549(x7013,x7012,x7014))
% 179.72/179.60 [702]~E(x7021,x7022)+E(f549(x7023,x7024,x7021),f549(x7023,x7024,x7022))
% 179.72/179.60 [703]~E(x7031,x7032)+E(f792(x7031,x7033,x7034),f792(x7032,x7033,x7034))
% 179.72/179.60 [704]~E(x7041,x7042)+E(f792(x7043,x7041,x7044),f792(x7043,x7042,x7044))
% 179.72/179.60 [705]~E(x7051,x7052)+E(f792(x7053,x7054,x7051),f792(x7053,x7054,x7052))
% 179.72/179.60 [706]~E(x7061,x7062)+E(f719(x7061,x7063,x7064,x7065,x7066),f719(x7062,x7063,x7064,x7065,x7066))
% 179.72/179.60 [707]~E(x7071,x7072)+E(f719(x7073,x7071,x7074,x7075,x7076),f719(x7073,x7072,x7074,x7075,x7076))
% 179.72/179.60 [708]~E(x7081,x7082)+E(f719(x7083,x7084,x7081,x7085,x7086),f719(x7083,x7084,x7082,x7085,x7086))
% 179.72/179.60 [709]~E(x7091,x7092)+E(f719(x7093,x7094,x7095,x7091,x7096),f719(x7093,x7094,x7095,x7092,x7096))
% 179.72/179.60 [710]~E(x7101,x7102)+E(f719(x7103,x7104,x7105,x7106,x7101),f719(x7103,x7104,x7105,x7106,x7102))
% 179.72/179.60 [711]~E(x7111,x7112)+E(f251(x7111,x7113),f251(x7112,x7113))
% 179.72/179.60 [712]~E(x7121,x7122)+E(f251(x7123,x7121),f251(x7123,x7122))
% 179.72/179.60 [713]~E(x7131,x7132)+E(f498(x7131,x7133,x7134,x7135),f498(x7132,x7133,x7134,x7135))
% 179.72/179.60 [714]~E(x7141,x7142)+E(f498(x7143,x7141,x7144,x7145),f498(x7143,x7142,x7144,x7145))
% 179.72/179.60 [715]~E(x7151,x7152)+E(f498(x7153,x7154,x7151,x7155),f498(x7153,x7154,x7152,x7155))
% 179.72/179.60 [716]~E(x7161,x7162)+E(f498(x7163,x7164,x7165,x7161),f498(x7163,x7164,x7165,x7162))
% 179.72/179.60 [717]~E(x7171,x7172)+E(f651(x7171,x7173,x7174,x7175),f651(x7172,x7173,x7174,x7175))
% 179.72/179.60 [718]~E(x7181,x7182)+E(f651(x7183,x7181,x7184,x7185),f651(x7183,x7182,x7184,x7185))
% 179.72/179.60 [719]~E(x7191,x7192)+E(f651(x7193,x7194,x7191,x7195),f651(x7193,x7194,x7192,x7195))
% 179.72/179.60 [720]~E(x7201,x7202)+E(f651(x7203,x7204,x7205,x7201),f651(x7203,x7204,x7205,x7202))
% 179.72/179.60 [721]~E(x7211,x7212)+E(f378(x7211,x7213,x7214,x7215),f378(x7212,x7213,x7214,x7215))
% 179.72/179.60 [722]~E(x7221,x7222)+E(f378(x7223,x7221,x7224,x7225),f378(x7223,x7222,x7224,x7225))
% 179.72/179.60 [723]~E(x7231,x7232)+E(f378(x7233,x7234,x7231,x7235),f378(x7233,x7234,x7232,x7235))
% 179.72/179.60 [724]~E(x7241,x7242)+E(f378(x7243,x7244,x7245,x7241),f378(x7243,x7244,x7245,x7242))
% 179.72/179.60 [725]~E(x7251,x7252)+E(f660(x7251,x7253,x7254,x7255),f660(x7252,x7253,x7254,x7255))
% 179.72/179.60 [726]~E(x7261,x7262)+E(f660(x7263,x7261,x7264,x7265),f660(x7263,x7262,x7264,x7265))
% 179.72/179.60 [727]~E(x7271,x7272)+E(f660(x7273,x7274,x7271,x7275),f660(x7273,x7274,x7272,x7275))
% 179.72/179.60 [728]~E(x7281,x7282)+E(f660(x7283,x7284,x7285,x7281),f660(x7283,x7284,x7285,x7282))
% 179.72/179.60 [729]~E(x7291,x7292)+E(f809(x7291,x7293,x7294,x7295),f809(x7292,x7293,x7294,x7295))
% 179.72/179.60 [730]~E(x7301,x7302)+E(f809(x7303,x7301,x7304,x7305),f809(x7303,x7302,x7304,x7305))
% 179.72/179.60 [731]~E(x7311,x7312)+E(f809(x7313,x7314,x7311,x7315),f809(x7313,x7314,x7312,x7315))
% 179.72/179.60 [732]~E(x7321,x7322)+E(f809(x7323,x7324,x7325,x7321),f809(x7323,x7324,x7325,x7322))
% 179.72/179.60 [733]~E(x7331,x7332)+E(f279(x7331,x7333),f279(x7332,x7333))
% 179.72/179.60 [734]~E(x7341,x7342)+E(f279(x7343,x7341),f279(x7343,x7342))
% 179.72/179.60 [735]~E(x7351,x7352)+E(f737(x7351,x7353,x7354,x7355,x7356),f737(x7352,x7353,x7354,x7355,x7356))
% 179.72/179.60 [736]~E(x7361,x7362)+E(f737(x7363,x7361,x7364,x7365,x7366),f737(x7363,x7362,x7364,x7365,x7366))
% 179.72/179.60 [737]~E(x7371,x7372)+E(f737(x7373,x7374,x7371,x7375,x7376),f737(x7373,x7374,x7372,x7375,x7376))
% 179.72/179.60 [738]~E(x7381,x7382)+E(f737(x7383,x7384,x7385,x7381,x7386),f737(x7383,x7384,x7385,x7382,x7386))
% 179.72/179.60 [739]~E(x7391,x7392)+E(f737(x7393,x7394,x7395,x7396,x7391),f737(x7393,x7394,x7395,x7396,x7392))
% 179.72/179.60 [740]~E(x7401,x7402)+E(f72(x7401,x7403),f72(x7402,x7403))
% 179.72/179.60 [741]~E(x7411,x7412)+E(f72(x7413,x7411),f72(x7413,x7412))
% 179.72/179.60 [742]~E(x7421,x7422)+E(f566(x7421,x7423,x7424),f566(x7422,x7423,x7424))
% 179.72/179.60 [743]~E(x7431,x7432)+E(f566(x7433,x7431,x7434),f566(x7433,x7432,x7434))
% 179.72/179.60 [744]~E(x7441,x7442)+E(f566(x7443,x7444,x7441),f566(x7443,x7444,x7442))
% 179.72/179.60 [745]~E(x7451,x7452)+E(f119(x7451,x7453,x7454,x7455),f119(x7452,x7453,x7454,x7455))
% 179.72/179.60 [746]~E(x7461,x7462)+E(f119(x7463,x7461,x7464,x7465),f119(x7463,x7462,x7464,x7465))
% 179.72/179.60 [747]~E(x7471,x7472)+E(f119(x7473,x7474,x7471,x7475),f119(x7473,x7474,x7472,x7475))
% 179.72/179.60 [748]~E(x7481,x7482)+E(f119(x7483,x7484,x7485,x7481),f119(x7483,x7484,x7485,x7482))
% 179.72/179.60 [749]~E(x7491,x7492)+E(f372(x7491,x7493,x7494,x7495,x7496,x7497),f372(x7492,x7493,x7494,x7495,x7496,x7497))
% 179.72/179.60 [750]~E(x7501,x7502)+E(f372(x7503,x7501,x7504,x7505,x7506,x7507),f372(x7503,x7502,x7504,x7505,x7506,x7507))
% 179.72/179.60 [751]~E(x7511,x7512)+E(f372(x7513,x7514,x7511,x7515,x7516,x7517),f372(x7513,x7514,x7512,x7515,x7516,x7517))
% 179.72/179.60 [752]~E(x7521,x7522)+E(f372(x7523,x7524,x7525,x7521,x7526,x7527),f372(x7523,x7524,x7525,x7522,x7526,x7527))
% 179.72/179.60 [753]~E(x7531,x7532)+E(f372(x7533,x7534,x7535,x7536,x7531,x7537),f372(x7533,x7534,x7535,x7536,x7532,x7537))
% 179.72/179.60 [754]~E(x7541,x7542)+E(f372(x7543,x7544,x7545,x7546,x7547,x7541),f372(x7543,x7544,x7545,x7546,x7547,x7542))
% 179.72/179.60 [755]~E(x7551,x7552)+E(f779(x7551,x7553,x7554),f779(x7552,x7553,x7554))
% 179.72/179.60 [756]~E(x7561,x7562)+E(f779(x7563,x7561,x7564),f779(x7563,x7562,x7564))
% 179.72/179.60 [757]~E(x7571,x7572)+E(f779(x7573,x7574,x7571),f779(x7573,x7574,x7572))
% 179.72/179.60 [758]~E(x7581,x7582)+E(f598(x7581,x7583,x7584),f598(x7582,x7583,x7584))
% 179.72/179.60 [759]~E(x7591,x7592)+E(f598(x7593,x7591,x7594),f598(x7593,x7592,x7594))
% 179.72/179.60 [760]~E(x7601,x7602)+E(f598(x7603,x7604,x7601),f598(x7603,x7604,x7602))
% 179.72/179.60 [761]~E(x7611,x7612)+E(f731(x7611,x7613,x7614),f731(x7612,x7613,x7614))
% 179.72/179.60 [762]~E(x7621,x7622)+E(f731(x7623,x7621,x7624),f731(x7623,x7622,x7624))
% 179.72/179.60 [763]~E(x7631,x7632)+E(f731(x7633,x7634,x7631),f731(x7633,x7634,x7632))
% 179.72/179.60 [764]~E(x7641,x7642)+E(f358(x7641,x7643,x7644,x7645,x7646),f358(x7642,x7643,x7644,x7645,x7646))
% 179.72/179.60 [765]~E(x7651,x7652)+E(f358(x7653,x7651,x7654,x7655,x7656),f358(x7653,x7652,x7654,x7655,x7656))
% 179.72/179.60 [766]~E(x7661,x7662)+E(f358(x7663,x7664,x7661,x7665,x7666),f358(x7663,x7664,x7662,x7665,x7666))
% 179.72/179.60 [767]~E(x7671,x7672)+E(f358(x7673,x7674,x7675,x7671,x7676),f358(x7673,x7674,x7675,x7672,x7676))
% 179.72/179.60 [768]~E(x7681,x7682)+E(f358(x7683,x7684,x7685,x7686,x7681),f358(x7683,x7684,x7685,x7686,x7682))
% 179.72/179.60 [769]~E(x7691,x7692)+E(f96(x7691),f96(x7692))
% 179.72/179.60 [770]~E(x7701,x7702)+E(f225(x7701,x7703,x7704),f225(x7702,x7703,x7704))
% 179.72/179.60 [771]~E(x7711,x7712)+E(f225(x7713,x7711,x7714),f225(x7713,x7712,x7714))
% 179.72/179.60 [772]~E(x7721,x7722)+E(f225(x7723,x7724,x7721),f225(x7723,x7724,x7722))
% 179.72/179.60 [773]~E(x7731,x7732)+E(f349(x7731,x7733,x7734),f349(x7732,x7733,x7734))
% 179.72/179.60 [774]~E(x7741,x7742)+E(f349(x7743,x7741,x7744),f349(x7743,x7742,x7744))
% 179.72/179.60 [775]~E(x7751,x7752)+E(f349(x7753,x7754,x7751),f349(x7753,x7754,x7752))
% 179.72/179.60 [776]~E(x7761,x7762)+E(f133(x7761,x7763,x7764),f133(x7762,x7763,x7764))
% 179.72/179.60 [777]~E(x7771,x7772)+E(f133(x7773,x7771,x7774),f133(x7773,x7772,x7774))
% 179.72/179.60 [778]~E(x7781,x7782)+E(f133(x7783,x7784,x7781),f133(x7783,x7784,x7782))
% 179.72/179.60 [779]~E(x7791,x7792)+E(f469(x7791,x7793,x7794),f469(x7792,x7793,x7794))
% 179.72/179.60 [780]~E(x7801,x7802)+E(f469(x7803,x7801,x7804),f469(x7803,x7802,x7804))
% 179.72/179.60 [781]~E(x7811,x7812)+E(f469(x7813,x7814,x7811),f469(x7813,x7814,x7812))
% 179.72/179.60 [782]~E(x7821,x7822)+E(f401(x7821,x7823),f401(x7822,x7823))
% 179.72/179.60 [783]~E(x7831,x7832)+E(f401(x7833,x7831),f401(x7833,x7832))
% 179.72/179.60 [784]~E(x7841,x7842)+E(f460(x7841,x7843,x7844,x7845),f460(x7842,x7843,x7844,x7845))
% 179.72/179.60 [785]~E(x7851,x7852)+E(f460(x7853,x7851,x7854,x7855),f460(x7853,x7852,x7854,x7855))
% 179.72/179.60 [786]~E(x7861,x7862)+E(f460(x7863,x7864,x7861,x7865),f460(x7863,x7864,x7862,x7865))
% 179.72/179.60 [787]~E(x7871,x7872)+E(f460(x7873,x7874,x7875,x7871),f460(x7873,x7874,x7875,x7872))
% 179.72/179.60 [788]~E(x7881,x7882)+E(f647(x7881,x7883),f647(x7882,x7883))
% 179.72/179.60 [789]~E(x7891,x7892)+E(f647(x7893,x7891),f647(x7893,x7892))
% 179.72/179.60 [790]~E(x7901,x7902)+E(f625(x7901,x7903,x7904),f625(x7902,x7903,x7904))
% 179.72/179.60 [791]~E(x7911,x7912)+E(f625(x7913,x7911,x7914),f625(x7913,x7912,x7914))
% 179.72/179.60 [792]~E(x7921,x7922)+E(f625(x7923,x7924,x7921),f625(x7923,x7924,x7922))
% 179.72/179.60 [793]~E(x7931,x7932)+E(f379(x7931,x7933),f379(x7932,x7933))
% 179.72/179.60 [794]~E(x7941,x7942)+E(f379(x7943,x7941),f379(x7943,x7942))
% 179.72/179.60 [795]~E(x7951,x7952)+E(f240(x7951,x7953),f240(x7952,x7953))
% 179.72/179.60 [796]~E(x7961,x7962)+E(f240(x7963,x7961),f240(x7963,x7962))
% 179.72/179.60 [797]~E(x7971,x7972)+E(f399(x7971,x7973,x7974),f399(x7972,x7973,x7974))
% 179.72/179.60 [798]~E(x7981,x7982)+E(f399(x7983,x7981,x7984),f399(x7983,x7982,x7984))
% 179.72/179.60 [799]~E(x7991,x7992)+E(f399(x7993,x7994,x7991),f399(x7993,x7994,x7992))
% 179.72/179.60 [800]~E(x8001,x8002)+E(f452(x8001,x8003,x8004,x8005,x8006),f452(x8002,x8003,x8004,x8005,x8006))
% 179.72/179.60 [801]~E(x8011,x8012)+E(f452(x8013,x8011,x8014,x8015,x8016),f452(x8013,x8012,x8014,x8015,x8016))
% 179.72/179.60 [802]~E(x8021,x8022)+E(f452(x8023,x8024,x8021,x8025,x8026),f452(x8023,x8024,x8022,x8025,x8026))
% 179.72/179.60 [803]~E(x8031,x8032)+E(f452(x8033,x8034,x8035,x8031,x8036),f452(x8033,x8034,x8035,x8032,x8036))
% 179.72/179.60 [804]~E(x8041,x8042)+E(f452(x8043,x8044,x8045,x8046,x8041),f452(x8043,x8044,x8045,x8046,x8042))
% 179.72/179.60 [805]~E(x8051,x8052)+E(f653(x8051,x8053),f653(x8052,x8053))
% 179.72/179.60 [806]~E(x8061,x8062)+E(f653(x8063,x8061),f653(x8063,x8062))
% 179.72/179.60 [807]~E(x8071,x8072)+E(f522(x8071,x8073,x8074),f522(x8072,x8073,x8074))
% 179.72/179.60 [808]~E(x8081,x8082)+E(f522(x8083,x8081,x8084),f522(x8083,x8082,x8084))
% 179.72/179.60 [809]~E(x8091,x8092)+E(f522(x8093,x8094,x8091),f522(x8093,x8094,x8092))
% 179.72/179.60 [810]~E(x8101,x8102)+E(f269(x8101,x8103),f269(x8102,x8103))
% 179.72/179.60 [811]~E(x8111,x8112)+E(f269(x8113,x8111),f269(x8113,x8112))
% 179.72/179.60 [812]~E(x8121,x8122)+E(f317(x8121,x8123,x8124),f317(x8122,x8123,x8124))
% 179.72/179.60 [813]~E(x8131,x8132)+E(f317(x8133,x8131,x8134),f317(x8133,x8132,x8134))
% 179.72/179.60 [814]~E(x8141,x8142)+E(f317(x8143,x8144,x8141),f317(x8143,x8144,x8142))
% 179.72/179.60 [815]~E(x8151,x8152)+E(f331(x8151,x8153,x8154),f331(x8152,x8153,x8154))
% 179.72/179.60 [816]~E(x8161,x8162)+E(f331(x8163,x8161,x8164),f331(x8163,x8162,x8164))
% 179.72/179.60 [817]~E(x8171,x8172)+E(f331(x8173,x8174,x8171),f331(x8173,x8174,x8172))
% 179.72/179.60 [818]~E(x8181,x8182)+E(f310(x8181,x8183,x8184,x8185),f310(x8182,x8183,x8184,x8185))
% 179.72/179.60 [819]~E(x8191,x8192)+E(f310(x8193,x8191,x8194,x8195),f310(x8193,x8192,x8194,x8195))
% 179.72/179.60 [820]~E(x8201,x8202)+E(f310(x8203,x8204,x8201,x8205),f310(x8203,x8204,x8202,x8205))
% 179.72/179.60 [821]~E(x8211,x8212)+E(f310(x8213,x8214,x8215,x8211),f310(x8213,x8214,x8215,x8212))
% 179.72/179.60 [822]~E(x8221,x8222)+E(f478(x8221,x8223,x8224,x8225,x8226),f478(x8222,x8223,x8224,x8225,x8226))
% 179.72/179.60 [823]~E(x8231,x8232)+E(f478(x8233,x8231,x8234,x8235,x8236),f478(x8233,x8232,x8234,x8235,x8236))
% 179.72/179.60 [824]~E(x8241,x8242)+E(f478(x8243,x8244,x8241,x8245,x8246),f478(x8243,x8244,x8242,x8245,x8246))
% 179.72/179.60 [825]~E(x8251,x8252)+E(f478(x8253,x8254,x8255,x8251,x8256),f478(x8253,x8254,x8255,x8252,x8256))
% 179.72/179.60 [826]~E(x8261,x8262)+E(f478(x8263,x8264,x8265,x8266,x8261),f478(x8263,x8264,x8265,x8266,x8262))
% 179.72/179.60 [827]~E(x8271,x8272)+E(f726(x8271,x8273,x8274,x8275,x8276),f726(x8272,x8273,x8274,x8275,x8276))
% 179.72/179.60 [828]~E(x8281,x8282)+E(f726(x8283,x8281,x8284,x8285,x8286),f726(x8283,x8282,x8284,x8285,x8286))
% 179.72/179.60 [829]~E(x8291,x8292)+E(f726(x8293,x8294,x8291,x8295,x8296),f726(x8293,x8294,x8292,x8295,x8296))
% 179.72/179.60 [830]~E(x8301,x8302)+E(f726(x8303,x8304,x8305,x8301,x8306),f726(x8303,x8304,x8305,x8302,x8306))
% 179.72/179.60 [831]~E(x8311,x8312)+E(f726(x8313,x8314,x8315,x8316,x8311),f726(x8313,x8314,x8315,x8316,x8312))
% 179.72/179.60 [832]~E(x8321,x8322)+E(f17(x8321,x8323,x8324,x8325),f17(x8322,x8323,x8324,x8325))
% 179.72/179.60 [833]~E(x8331,x8332)+E(f17(x8333,x8331,x8334,x8335),f17(x8333,x8332,x8334,x8335))
% 179.72/179.60 [834]~E(x8341,x8342)+E(f17(x8343,x8344,x8341,x8345),f17(x8343,x8344,x8342,x8345))
% 179.72/179.60 [835]~E(x8351,x8352)+E(f17(x8353,x8354,x8355,x8351),f17(x8353,x8354,x8355,x8352))
% 179.72/179.60 [836]~E(x8361,x8362)+E(f190(x8361,x8363,x8364,x8365),f190(x8362,x8363,x8364,x8365))
% 179.72/179.60 [837]~E(x8371,x8372)+E(f190(x8373,x8371,x8374,x8375),f190(x8373,x8372,x8374,x8375))
% 179.72/179.60 [838]~E(x8381,x8382)+E(f190(x8383,x8384,x8381,x8385),f190(x8383,x8384,x8382,x8385))
% 179.72/179.60 [839]~E(x8391,x8392)+E(f190(x8393,x8394,x8395,x8391),f190(x8393,x8394,x8395,x8392))
% 179.72/179.60 [840]~E(x8401,x8402)+E(f514(x8401,x8403,x8404),f514(x8402,x8403,x8404))
% 179.72/179.60 [841]~E(x8411,x8412)+E(f514(x8413,x8411,x8414),f514(x8413,x8412,x8414))
% 179.72/179.60 [842]~E(x8421,x8422)+E(f514(x8423,x8424,x8421),f514(x8423,x8424,x8422))
% 179.72/179.60 [843]~E(x8431,x8432)+E(f38(x8431,x8433),f38(x8432,x8433))
% 179.72/179.60 [844]~E(x8441,x8442)+E(f38(x8443,x8441),f38(x8443,x8442))
% 179.72/179.60 [845]~E(x8451,x8452)+E(f506(x8451,x8453,x8454),f506(x8452,x8453,x8454))
% 179.72/179.60 [846]~E(x8461,x8462)+E(f506(x8463,x8461,x8464),f506(x8463,x8462,x8464))
% 179.72/179.60 [847]~E(x8471,x8472)+E(f506(x8473,x8474,x8471),f506(x8473,x8474,x8472))
% 179.72/179.60 [848]~E(x8481,x8482)+E(f848(x8481,x8483,x8484),f848(x8482,x8483,x8484))
% 179.72/179.60 [849]~E(x8491,x8492)+E(f848(x8493,x8491,x8494),f848(x8493,x8492,x8494))
% 179.72/179.60 [850]~E(x8501,x8502)+E(f848(x8503,x8504,x8501),f848(x8503,x8504,x8502))
% 179.72/179.60 [851]~E(x8511,x8512)+E(f717(x8511,x8513,x8514),f717(x8512,x8513,x8514))
% 179.72/179.60 [852]~E(x8521,x8522)+E(f717(x8523,x8521,x8524),f717(x8523,x8522,x8524))
% 179.72/179.60 [853]~E(x8531,x8532)+E(f717(x8533,x8534,x8531),f717(x8533,x8534,x8532))
% 179.72/179.60 [854]~E(x8541,x8542)+E(f351(x8541,x8543,x8544,x8545),f351(x8542,x8543,x8544,x8545))
% 179.72/179.60 [855]~E(x8551,x8552)+E(f351(x8553,x8551,x8554,x8555),f351(x8553,x8552,x8554,x8555))
% 179.72/179.60 [856]~E(x8561,x8562)+E(f351(x8563,x8564,x8561,x8565),f351(x8563,x8564,x8562,x8565))
% 179.72/179.60 [857]~E(x8571,x8572)+E(f351(x8573,x8574,x8575,x8571),f351(x8573,x8574,x8575,x8572))
% 179.72/179.60 [858]~E(x8581,x8582)+E(f475(x8581,x8583,x8584,x8585,x8586),f475(x8582,x8583,x8584,x8585,x8586))
% 179.72/179.60 [859]~E(x8591,x8592)+E(f475(x8593,x8591,x8594,x8595,x8596),f475(x8593,x8592,x8594,x8595,x8596))
% 179.72/179.60 [860]~E(x8601,x8602)+E(f475(x8603,x8604,x8601,x8605,x8606),f475(x8603,x8604,x8602,x8605,x8606))
% 179.72/179.60 [861]~E(x8611,x8612)+E(f475(x8613,x8614,x8615,x8611,x8616),f475(x8613,x8614,x8615,x8612,x8616))
% 179.72/179.60 [862]~E(x8621,x8622)+E(f475(x8623,x8624,x8625,x8626,x8621),f475(x8623,x8624,x8625,x8626,x8622))
% 179.72/179.60 [863]~E(x8631,x8632)+E(f26(x8631,x8633,x8634),f26(x8632,x8633,x8634))
% 179.72/179.60 [864]~E(x8641,x8642)+E(f26(x8643,x8641,x8644),f26(x8643,x8642,x8644))
% 179.72/179.60 [865]~E(x8651,x8652)+E(f26(x8653,x8654,x8651),f26(x8653,x8654,x8652))
% 179.72/179.60 [866]~E(x8661,x8662)+E(f167(x8661,x8663,x8664),f167(x8662,x8663,x8664))
% 179.72/179.60 [867]~E(x8671,x8672)+E(f167(x8673,x8671,x8674),f167(x8673,x8672,x8674))
% 179.72/179.60 [868]~E(x8681,x8682)+E(f167(x8683,x8684,x8681),f167(x8683,x8684,x8682))
% 179.72/179.60 [869]~E(x8691,x8692)+E(f747(x8691,x8693,x8694,x8695,x8696),f747(x8692,x8693,x8694,x8695,x8696))
% 179.72/179.60 [870]~E(x8701,x8702)+E(f747(x8703,x8701,x8704,x8705,x8706),f747(x8703,x8702,x8704,x8705,x8706))
% 179.72/179.60 [871]~E(x8711,x8712)+E(f747(x8713,x8714,x8711,x8715,x8716),f747(x8713,x8714,x8712,x8715,x8716))
% 179.72/179.60 [872]~E(x8721,x8722)+E(f747(x8723,x8724,x8725,x8721,x8726),f747(x8723,x8724,x8725,x8722,x8726))
% 179.72/179.60 [873]~E(x8731,x8732)+E(f747(x8733,x8734,x8735,x8736,x8731),f747(x8733,x8734,x8735,x8736,x8732))
% 179.72/179.60 [874]~E(x8741,x8742)+E(f732(x8741,x8743,x8744),f732(x8742,x8743,x8744))
% 179.72/179.60 [875]~E(x8751,x8752)+E(f732(x8753,x8751,x8754),f732(x8753,x8752,x8754))
% 179.72/179.60 [876]~E(x8761,x8762)+E(f732(x8763,x8764,x8761),f732(x8763,x8764,x8762))
% 179.72/179.60 [877]~E(x8771,x8772)+E(f216(x8771,x8773),f216(x8772,x8773))
% 179.72/179.60 [878]~E(x8781,x8782)+E(f216(x8783,x8781),f216(x8783,x8782))
% 179.72/179.60 [879]~E(x8791,x8792)+E(f489(x8791,x8793,x8794),f489(x8792,x8793,x8794))
% 179.72/179.60 [880]~E(x8801,x8802)+E(f489(x8803,x8801,x8804),f489(x8803,x8802,x8804))
% 179.72/179.60 [881]~E(x8811,x8812)+E(f489(x8813,x8814,x8811),f489(x8813,x8814,x8812))
% 179.72/179.60 [882]~E(x8821,x8822)+E(f626(x8821,x8823,x8824,x8825),f626(x8822,x8823,x8824,x8825))
% 179.72/179.60 [883]~E(x8831,x8832)+E(f626(x8833,x8831,x8834,x8835),f626(x8833,x8832,x8834,x8835))
% 179.72/179.60 [884]~E(x8841,x8842)+E(f626(x8843,x8844,x8841,x8845),f626(x8843,x8844,x8842,x8845))
% 179.72/179.60 [885]~E(x8851,x8852)+E(f626(x8853,x8854,x8855,x8851),f626(x8853,x8854,x8855,x8852))
% 179.72/179.60 [886]~E(x8861,x8862)+E(f666(x8861,x8863,x8864),f666(x8862,x8863,x8864))
% 179.72/179.60 [887]~E(x8871,x8872)+E(f666(x8873,x8871,x8874),f666(x8873,x8872,x8874))
% 179.72/179.60 [888]~E(x8881,x8882)+E(f666(x8883,x8884,x8881),f666(x8883,x8884,x8882))
% 179.72/179.60 [889]~E(x8891,x8892)+E(f468(x8891,x8893,x8894),f468(x8892,x8893,x8894))
% 179.72/179.60 [890]~E(x8901,x8902)+E(f468(x8903,x8901,x8904),f468(x8903,x8902,x8904))
% 179.72/179.60 [891]~E(x8911,x8912)+E(f468(x8913,x8914,x8911),f468(x8913,x8914,x8912))
% 179.72/179.60 [892]~E(x8921,x8922)+E(f658(x8921,x8923,x8924,x8925,x8926),f658(x8922,x8923,x8924,x8925,x8926))
% 179.72/179.60 [893]~E(x8931,x8932)+E(f658(x8933,x8931,x8934,x8935,x8936),f658(x8933,x8932,x8934,x8935,x8936))
% 179.72/179.60 [894]~E(x8941,x8942)+E(f658(x8943,x8944,x8941,x8945,x8946),f658(x8943,x8944,x8942,x8945,x8946))
% 179.72/179.60 [895]~E(x8951,x8952)+E(f658(x8953,x8954,x8955,x8951,x8956),f658(x8953,x8954,x8955,x8952,x8956))
% 179.72/179.60 [896]~E(x8961,x8962)+E(f658(x8963,x8964,x8965,x8966,x8961),f658(x8963,x8964,x8965,x8966,x8962))
% 179.72/179.60 [897]~E(x8971,x8972)+E(f609(x8971,x8973,x8974),f609(x8972,x8973,x8974))
% 179.72/179.60 [898]~E(x8981,x8982)+E(f609(x8983,x8981,x8984),f609(x8983,x8982,x8984))
% 179.72/179.60 [899]~E(x8991,x8992)+E(f609(x8993,x8994,x8991),f609(x8993,x8994,x8992))
% 179.72/179.60 [900]~E(x9001,x9002)+E(f851(x9001,x9003),f851(x9002,x9003))
% 179.72/179.60 [901]~E(x9011,x9012)+E(f851(x9013,x9011),f851(x9013,x9012))
% 179.72/179.60 [902]~E(x9021,x9022)+E(f142(x9021,x9023,x9024,x9025,x9026),f142(x9022,x9023,x9024,x9025,x9026))
% 179.72/179.60 [903]~E(x9031,x9032)+E(f142(x9033,x9031,x9034,x9035,x9036),f142(x9033,x9032,x9034,x9035,x9036))
% 179.72/179.60 [904]~E(x9041,x9042)+E(f142(x9043,x9044,x9041,x9045,x9046),f142(x9043,x9044,x9042,x9045,x9046))
% 179.72/179.60 [905]~E(x9051,x9052)+E(f142(x9053,x9054,x9055,x9051,x9056),f142(x9053,x9054,x9055,x9052,x9056))
% 179.72/179.60 [906]~E(x9061,x9062)+E(f142(x9063,x9064,x9065,x9066,x9061),f142(x9063,x9064,x9065,x9066,x9062))
% 179.72/179.60 [907]~E(x9071,x9072)+E(f192(x9071,x9073),f192(x9072,x9073))
% 179.72/179.60 [908]~E(x9081,x9082)+E(f192(x9083,x9081),f192(x9083,x9082))
% 179.72/179.60 [909]~E(x9091,x9092)+E(f255(x9091,x9093),f255(x9092,x9093))
% 179.72/179.60 [910]~E(x9101,x9102)+E(f255(x9103,x9101),f255(x9103,x9102))
% 179.72/179.60 [911]~E(x9111,x9112)+E(f118(x9111,x9113),f118(x9112,x9113))
% 179.72/179.60 [912]~E(x9121,x9122)+E(f118(x9123,x9121),f118(x9123,x9122))
% 179.72/179.60 [913]~E(x9131,x9132)+E(f212(x9131,x9133,x9134,x9135),f212(x9132,x9133,x9134,x9135))
% 179.72/179.60 [914]~E(x9141,x9142)+E(f212(x9143,x9141,x9144,x9145),f212(x9143,x9142,x9144,x9145))
% 179.72/179.60 [915]~E(x9151,x9152)+E(f212(x9153,x9154,x9151,x9155),f212(x9153,x9154,x9152,x9155))
% 179.72/179.60 [916]~E(x9161,x9162)+E(f212(x9163,x9164,x9165,x9161),f212(x9163,x9164,x9165,x9162))
% 179.72/179.60 [917]~E(x9171,x9172)+E(f417(x9171,x9173,x9174,x9175),f417(x9172,x9173,x9174,x9175))
% 179.72/179.60 [918]~E(x9181,x9182)+E(f417(x9183,x9181,x9184,x9185),f417(x9183,x9182,x9184,x9185))
% 179.72/179.60 [919]~E(x9191,x9192)+E(f417(x9193,x9194,x9191,x9195),f417(x9193,x9194,x9192,x9195))
% 179.72/179.60 [920]~E(x9201,x9202)+E(f417(x9203,x9204,x9205,x9201),f417(x9203,x9204,x9205,x9202))
% 179.72/179.60 [921]~E(x9211,x9212)+E(f515(x9211,x9213,x9214),f515(x9212,x9213,x9214))
% 179.72/179.60 [922]~E(x9221,x9222)+E(f515(x9223,x9221,x9224),f515(x9223,x9222,x9224))
% 179.72/179.60 [923]~E(x9231,x9232)+E(f515(x9233,x9234,x9231),f515(x9233,x9234,x9232))
% 179.72/179.60 [924]~E(x9241,x9242)+E(f136(x9241,x9243),f136(x9242,x9243))
% 179.72/179.60 [925]~E(x9251,x9252)+E(f136(x9253,x9251),f136(x9253,x9252))
% 179.72/179.60 [926]~E(x9261,x9262)+E(f264(x9261,x9263,x9264,x9265),f264(x9262,x9263,x9264,x9265))
% 179.72/179.60 [927]~E(x9271,x9272)+E(f264(x9273,x9271,x9274,x9275),f264(x9273,x9272,x9274,x9275))
% 179.72/179.60 [928]~E(x9281,x9282)+E(f264(x9283,x9284,x9281,x9285),f264(x9283,x9284,x9282,x9285))
% 179.72/179.60 [929]~E(x9291,x9292)+E(f264(x9293,x9294,x9295,x9291),f264(x9293,x9294,x9295,x9292))
% 179.72/179.60 [930]~E(x9301,x9302)+E(f764(x9301,x9303,x9304,x9305),f764(x9302,x9303,x9304,x9305))
% 179.72/179.60 [931]~E(x9311,x9312)+E(f764(x9313,x9311,x9314,x9315),f764(x9313,x9312,x9314,x9315))
% 179.72/179.60 [932]~E(x9321,x9322)+E(f764(x9323,x9324,x9321,x9325),f764(x9323,x9324,x9322,x9325))
% 179.72/179.60 [933]~E(x9331,x9332)+E(f764(x9333,x9334,x9335,x9331),f764(x9333,x9334,x9335,x9332))
% 179.72/179.60 [934]~E(x9341,x9342)+E(f505(x9341,x9343),f505(x9342,x9343))
% 179.72/179.60 [935]~E(x9351,x9352)+E(f505(x9353,x9351),f505(x9353,x9352))
% 179.72/179.60 [936]~E(x9361,x9362)+E(f306(x9361,x9363,x9364),f306(x9362,x9363,x9364))
% 179.72/179.60 [937]~E(x9371,x9372)+E(f306(x9373,x9371,x9374),f306(x9373,x9372,x9374))
% 179.72/179.60 [938]~E(x9381,x9382)+E(f306(x9383,x9384,x9381),f306(x9383,x9384,x9382))
% 179.72/179.60 [939]~E(x9391,x9392)+E(f394(x9391,x9393,x9394,x9395),f394(x9392,x9393,x9394,x9395))
% 179.72/179.60 [940]~E(x9401,x9402)+E(f394(x9403,x9401,x9404,x9405),f394(x9403,x9402,x9404,x9405))
% 179.72/179.60 [941]~E(x9411,x9412)+E(f394(x9413,x9414,x9411,x9415),f394(x9413,x9414,x9412,x9415))
% 179.72/179.60 [942]~E(x9421,x9422)+E(f394(x9423,x9424,x9425,x9421),f394(x9423,x9424,x9425,x9422))
% 179.72/179.60 [943]~E(x9431,x9432)+E(f796(x9431,x9433),f796(x9432,x9433))
% 179.72/179.60 [944]~E(x9441,x9442)+E(f796(x9443,x9441),f796(x9443,x9442))
% 179.72/179.60 [945]~E(x9451,x9452)+E(f718(x9451,x9453,x9454),f718(x9452,x9453,x9454))
% 179.72/179.60 [946]~E(x9461,x9462)+E(f718(x9463,x9461,x9464),f718(x9463,x9462,x9464))
% 179.72/179.60 [947]~E(x9471,x9472)+E(f718(x9473,x9474,x9471),f718(x9473,x9474,x9472))
% 179.72/179.60 [948]~E(x9481,x9482)+E(f467(x9481,x9483,x9484),f467(x9482,x9483,x9484))
% 179.72/179.60 [949]~E(x9491,x9492)+E(f467(x9493,x9491,x9494),f467(x9493,x9492,x9494))
% 179.72/179.60 [950]~E(x9501,x9502)+E(f467(x9503,x9504,x9501),f467(x9503,x9504,x9502))
% 179.72/179.60 [951]~E(x9511,x9512)+E(f488(x9511),f488(x9512))
% 179.72/179.60 [952]~E(x9521,x9522)+E(f560(x9521,x9523),f560(x9522,x9523))
% 179.72/179.60 [953]~E(x9531,x9532)+E(f560(x9533,x9531),f560(x9533,x9532))
% 179.72/179.60 [954]~E(x9541,x9542)+E(f65(x9541,x9543,x9544),f65(x9542,x9543,x9544))
% 179.72/179.60 [955]~E(x9551,x9552)+E(f65(x9553,x9551,x9554),f65(x9553,x9552,x9554))
% 179.72/179.60 [956]~E(x9561,x9562)+E(f65(x9563,x9564,x9561),f65(x9563,x9564,x9562))
% 179.72/179.60 [957]~E(x9571,x9572)+E(f749(x9571,x9573,x9574,x9575,x9576),f749(x9572,x9573,x9574,x9575,x9576))
% 179.72/179.60 [958]~E(x9581,x9582)+E(f749(x9583,x9581,x9584,x9585,x9586),f749(x9583,x9582,x9584,x9585,x9586))
% 179.72/179.60 [959]~E(x9591,x9592)+E(f749(x9593,x9594,x9591,x9595,x9596),f749(x9593,x9594,x9592,x9595,x9596))
% 179.72/179.60 [960]~E(x9601,x9602)+E(f749(x9603,x9604,x9605,x9601,x9606),f749(x9603,x9604,x9605,x9602,x9606))
% 179.72/179.60 [961]~E(x9611,x9612)+E(f749(x9613,x9614,x9615,x9616,x9611),f749(x9613,x9614,x9615,x9616,x9612))
% 179.72/179.60 [962]~E(x9621,x9622)+E(f364(x9621),f364(x9622))
% 179.72/179.60 [963]~E(x9631,x9632)+E(f519(x9631,x9633,x9634,x9635),f519(x9632,x9633,x9634,x9635))
% 179.72/179.60 [964]~E(x9641,x9642)+E(f519(x9643,x9641,x9644,x9645),f519(x9643,x9642,x9644,x9645))
% 179.72/179.60 [965]~E(x9651,x9652)+E(f519(x9653,x9654,x9651,x9655),f519(x9653,x9654,x9652,x9655))
% 179.72/179.60 [966]~E(x9661,x9662)+E(f519(x9663,x9664,x9665,x9661),f519(x9663,x9664,x9665,x9662))
% 179.72/179.60 [967]~E(x9671,x9672)+E(f665(x9671,x9673,x9674,x9675),f665(x9672,x9673,x9674,x9675))
% 179.72/179.60 [968]~E(x9681,x9682)+E(f665(x9683,x9681,x9684,x9685),f665(x9683,x9682,x9684,x9685))
% 179.72/179.60 [969]~E(x9691,x9692)+E(f665(x9693,x9694,x9691,x9695),f665(x9693,x9694,x9692,x9695))
% 179.72/179.60 [970]~E(x9701,x9702)+E(f665(x9703,x9704,x9705,x9701),f665(x9703,x9704,x9705,x9702))
% 179.72/179.60 [971]~E(x9711,x9712)+E(f623(x9711,x9713,x9714),f623(x9712,x9713,x9714))
% 179.72/179.60 [972]~E(x9721,x9722)+E(f623(x9723,x9721,x9724),f623(x9723,x9722,x9724))
% 179.72/179.60 [973]~E(x9731,x9732)+E(f623(x9733,x9734,x9731),f623(x9733,x9734,x9732))
% 179.72/179.60 [974]~E(x9741,x9742)+E(f384(x9741,x9743),f384(x9742,x9743))
% 179.72/179.60 [975]~E(x9751,x9752)+E(f384(x9753,x9751),f384(x9753,x9752))
% 179.72/179.60 [976]~E(x9761,x9762)+E(f793(x9761,x9763,x9764),f793(x9762,x9763,x9764))
% 179.72/179.60 [977]~E(x9771,x9772)+E(f793(x9773,x9771,x9774),f793(x9773,x9772,x9774))
% 179.72/179.60 [978]~E(x9781,x9782)+E(f793(x9783,x9784,x9781),f793(x9783,x9784,x9782))
% 179.72/179.60 [979]~E(x9791,x9792)+E(f284(x9791,x9793,x9794),f284(x9792,x9793,x9794))
% 179.72/179.60 [980]~E(x9801,x9802)+E(f284(x9803,x9801,x9804),f284(x9803,x9802,x9804))
% 179.72/179.60 [981]~E(x9811,x9812)+E(f284(x9813,x9814,x9811),f284(x9813,x9814,x9812))
% 179.72/179.60 [982]~E(x9821,x9822)+E(f438(x9821,x9823,x9824),f438(x9822,x9823,x9824))
% 179.72/179.60 [983]~E(x9831,x9832)+E(f438(x9833,x9831,x9834),f438(x9833,x9832,x9834))
% 179.72/179.60 [984]~E(x9841,x9842)+E(f438(x9843,x9844,x9841),f438(x9843,x9844,x9842))
% 179.72/179.60 [985]~E(x9851,x9852)+E(f308(x9851),f308(x9852))
% 179.72/179.60 [986]~E(x9861,x9862)+E(f117(x9861,x9863,x9864),f117(x9862,x9863,x9864))
% 179.72/179.60 [987]~E(x9871,x9872)+E(f117(x9873,x9871,x9874),f117(x9873,x9872,x9874))
% 179.72/179.60 [988]~E(x9881,x9882)+E(f117(x9883,x9884,x9881),f117(x9883,x9884,x9882))
% 179.72/179.60 [989]~E(x9891,x9892)+E(f837(x9891,x9893,x9894,x9895,x9896,x9897),f837(x9892,x9893,x9894,x9895,x9896,x9897))
% 179.72/179.60 [990]~E(x9901,x9902)+E(f837(x9903,x9901,x9904,x9905,x9906,x9907),f837(x9903,x9902,x9904,x9905,x9906,x9907))
% 179.72/179.60 [991]~E(x9911,x9912)+E(f837(x9913,x9914,x9911,x9915,x9916,x9917),f837(x9913,x9914,x9912,x9915,x9916,x9917))
% 179.72/179.60 [992]~E(x9921,x9922)+E(f837(x9923,x9924,x9925,x9921,x9926,x9927),f837(x9923,x9924,x9925,x9922,x9926,x9927))
% 179.72/179.60 [993]~E(x9931,x9932)+E(f837(x9933,x9934,x9935,x9936,x9931,x9937),f837(x9933,x9934,x9935,x9936,x9932,x9937))
% 179.72/179.60 [994]~E(x9941,x9942)+E(f837(x9943,x9944,x9945,x9946,x9947,x9941),f837(x9943,x9944,x9945,x9946,x9947,x9942))
% 179.72/179.60 [995]~E(x9951,x9952)+E(f561(x9951,x9953,x9954),f561(x9952,x9953,x9954))
% 179.72/179.60 [996]~E(x9961,x9962)+E(f561(x9963,x9961,x9964),f561(x9963,x9962,x9964))
% 179.72/179.60 [997]~E(x9971,x9972)+E(f561(x9973,x9974,x9971),f561(x9973,x9974,x9972))
% 179.72/179.60 [998]~E(x9981,x9982)+E(f617(x9981,x9983,x9984,x9985),f617(x9982,x9983,x9984,x9985))
% 179.72/179.60 [999]~E(x9991,x9992)+E(f617(x9993,x9991,x9994,x9995),f617(x9993,x9992,x9994,x9995))
% 179.72/179.60 [1000]~E(x10001,x10002)+E(f617(x10003,x10004,x10001,x10005),f617(x10003,x10004,x10002,x10005))
% 179.72/179.60 [1001]~E(x10011,x10012)+E(f617(x10013,x10014,x10015,x10011),f617(x10013,x10014,x10015,x10012))
% 179.72/179.60 [1002]~E(x10021,x10022)+E(f52(x10021,x10023,x10024),f52(x10022,x10023,x10024))
% 179.72/179.60 [1003]~E(x10031,x10032)+E(f52(x10033,x10031,x10034),f52(x10033,x10032,x10034))
% 179.72/179.60 [1004]~E(x10041,x10042)+E(f52(x10043,x10044,x10041),f52(x10043,x10044,x10042))
% 179.72/179.60 [1005]~E(x10051,x10052)+E(f425(x10051),f425(x10052))
% 179.72/179.60 [1006]~E(x10061,x10062)+E(f727(x10061,x10063,x10064),f727(x10062,x10063,x10064))
% 179.72/179.60 [1007]~E(x10071,x10072)+E(f727(x10073,x10071,x10074),f727(x10073,x10072,x10074))
% 179.72/179.60 [1008]~E(x10081,x10082)+E(f727(x10083,x10084,x10081),f727(x10083,x10084,x10082))
% 179.72/179.60 [1009]~E(x10091,x10092)+E(f824(x10091,x10093,x10094),f824(x10092,x10093,x10094))
% 179.72/179.60 [1010]~E(x10101,x10102)+E(f824(x10103,x10101,x10104),f824(x10103,x10102,x10104))
% 179.72/179.60 [1011]~E(x10111,x10112)+E(f824(x10113,x10114,x10111),f824(x10113,x10114,x10112))
% 179.72/179.60 [1012]~E(x10121,x10122)+E(f487(x10121,x10123,x10124),f487(x10122,x10123,x10124))
% 179.72/179.60 [1013]~E(x10131,x10132)+E(f487(x10133,x10131,x10134),f487(x10133,x10132,x10134))
% 179.72/179.60 [1014]~E(x10141,x10142)+E(f487(x10143,x10144,x10141),f487(x10143,x10144,x10142))
% 179.72/179.60 [1015]~E(x10151,x10152)+E(f446(x10151,x10153,x10154,x10155,x10156),f446(x10152,x10153,x10154,x10155,x10156))
% 179.72/179.60 [1016]~E(x10161,x10162)+E(f446(x10163,x10161,x10164,x10165,x10166),f446(x10163,x10162,x10164,x10165,x10166))
% 179.72/179.60 [1017]~E(x10171,x10172)+E(f446(x10173,x10174,x10171,x10175,x10176),f446(x10173,x10174,x10172,x10175,x10176))
% 179.72/179.60 [1018]~E(x10181,x10182)+E(f446(x10183,x10184,x10185,x10181,x10186),f446(x10183,x10184,x10185,x10182,x10186))
% 179.72/179.60 [1019]~E(x10191,x10192)+E(f446(x10193,x10194,x10195,x10196,x10191),f446(x10193,x10194,x10195,x10196,x10192))
% 179.72/179.60 [1020]~E(x10201,x10202)+E(f700(x10201,x10203,x10204),f700(x10202,x10203,x10204))
% 179.72/179.60 [1021]~E(x10211,x10212)+E(f700(x10213,x10211,x10214),f700(x10213,x10212,x10214))
% 179.72/179.60 [1022]~E(x10221,x10222)+E(f700(x10223,x10224,x10221),f700(x10223,x10224,x10222))
% 179.72/179.60 [1023]~E(x10231,x10232)+E(f156(x10231,x10233,x10234,x10235),f156(x10232,x10233,x10234,x10235))
% 179.72/179.60 [1024]~E(x10241,x10242)+E(f156(x10243,x10241,x10244,x10245),f156(x10243,x10242,x10244,x10245))
% 179.72/179.60 [1025]~E(x10251,x10252)+E(f156(x10253,x10254,x10251,x10255),f156(x10253,x10254,x10252,x10255))
% 179.72/179.60 [1026]~E(x10261,x10262)+E(f156(x10263,x10264,x10265,x10261),f156(x10263,x10264,x10265,x10262))
% 179.72/179.60 [1027]~E(x10271,x10272)+E(f448(x10271,x10273,x10274,x10275,x10276),f448(x10272,x10273,x10274,x10275,x10276))
% 179.72/179.60 [1028]~E(x10281,x10282)+E(f448(x10283,x10281,x10284,x10285,x10286),f448(x10283,x10282,x10284,x10285,x10286))
% 179.72/179.60 [1029]~E(x10291,x10292)+E(f448(x10293,x10294,x10291,x10295,x10296),f448(x10293,x10294,x10292,x10295,x10296))
% 179.72/179.60 [1030]~E(x10301,x10302)+E(f448(x10303,x10304,x10305,x10301,x10306),f448(x10303,x10304,x10305,x10302,x10306))
% 179.72/179.60 [1031]~E(x10311,x10312)+E(f448(x10313,x10314,x10315,x10316,x10311),f448(x10313,x10314,x10315,x10316,x10312))
% 179.72/179.60 [1032]~E(x10321,x10322)+E(f768(x10321,x10323),f768(x10322,x10323))
% 179.72/179.60 [1033]~E(x10331,x10332)+E(f768(x10333,x10331),f768(x10333,x10332))
% 179.72/179.60 [1034]~E(x10341,x10342)+E(f547(x10341,x10343,x10344),f547(x10342,x10343,x10344))
% 179.72/179.60 [1035]~E(x10351,x10352)+E(f547(x10353,x10351,x10354),f547(x10353,x10352,x10354))
% 179.72/179.60 [1036]~E(x10361,x10362)+E(f547(x10363,x10364,x10361),f547(x10363,x10364,x10362))
% 179.72/179.60 [1037]~E(x10371,x10372)+E(f686(x10371,x10373),f686(x10372,x10373))
% 179.72/179.60 [1038]~E(x10381,x10382)+E(f686(x10383,x10381),f686(x10383,x10382))
% 179.72/179.60 [1039]~E(x10391,x10392)+E(f568(x10391,x10393,x10394,x10395,x10396),f568(x10392,x10393,x10394,x10395,x10396))
% 179.72/179.60 [1040]~E(x10401,x10402)+E(f568(x10403,x10401,x10404,x10405,x10406),f568(x10403,x10402,x10404,x10405,x10406))
% 179.72/179.60 [1041]~E(x10411,x10412)+E(f568(x10413,x10414,x10411,x10415,x10416),f568(x10413,x10414,x10412,x10415,x10416))
% 179.72/179.60 [1042]~E(x10421,x10422)+E(f568(x10423,x10424,x10425,x10421,x10426),f568(x10423,x10424,x10425,x10422,x10426))
% 179.72/179.60 [1043]~E(x10431,x10432)+E(f568(x10433,x10434,x10435,x10436,x10431),f568(x10433,x10434,x10435,x10436,x10432))
% 179.72/179.60 [1044]~E(x10441,x10442)+E(f297(x10441,x10443,x10444),f297(x10442,x10443,x10444))
% 179.72/179.60 [1045]~E(x10451,x10452)+E(f297(x10453,x10451,x10454),f297(x10453,x10452,x10454))
% 179.72/179.60 [1046]~E(x10461,x10462)+E(f297(x10463,x10464,x10461),f297(x10463,x10464,x10462))
% 179.72/179.60 [1047]~E(x10471,x10472)+E(f780(x10471,x10473,x10474),f780(x10472,x10473,x10474))
% 179.72/179.60 [1048]~E(x10481,x10482)+E(f780(x10483,x10481,x10484),f780(x10483,x10482,x10484))
% 179.72/179.60 [1049]~E(x10491,x10492)+E(f780(x10493,x10494,x10491),f780(x10493,x10494,x10492))
% 179.72/179.60 [1050]~E(x10501,x10502)+E(f771(x10501,x10503,x10504),f771(x10502,x10503,x10504))
% 179.72/179.60 [1051]~E(x10511,x10512)+E(f771(x10513,x10511,x10514),f771(x10513,x10512,x10514))
% 179.72/179.60 [1052]~E(x10521,x10522)+E(f771(x10523,x10524,x10521),f771(x10523,x10524,x10522))
% 179.72/179.60 [1053]~E(x10531,x10532)+E(f403(x10531,x10533),f403(x10532,x10533))
% 179.72/179.60 [1054]~E(x10541,x10542)+E(f403(x10543,x10541),f403(x10543,x10542))
% 179.72/179.60 [1055]~E(x10551,x10552)+E(f490(x10551,x10553,x10554),f490(x10552,x10553,x10554))
% 179.72/179.60 [1056]~E(x10561,x10562)+E(f490(x10563,x10561,x10564),f490(x10563,x10562,x10564))
% 179.72/179.60 [1057]~E(x10571,x10572)+E(f490(x10573,x10574,x10571),f490(x10573,x10574,x10572))
% 179.72/179.60 [1058]~E(x10581,x10582)+E(f436(x10581,x10583,x10584,x10585,x10586),f436(x10582,x10583,x10584,x10585,x10586))
% 179.72/179.60 [1059]~E(x10591,x10592)+E(f436(x10593,x10591,x10594,x10595,x10596),f436(x10593,x10592,x10594,x10595,x10596))
% 179.72/179.60 [1060]~E(x10601,x10602)+E(f436(x10603,x10604,x10601,x10605,x10606),f436(x10603,x10604,x10602,x10605,x10606))
% 179.72/179.60 [1061]~E(x10611,x10612)+E(f436(x10613,x10614,x10615,x10611,x10616),f436(x10613,x10614,x10615,x10612,x10616))
% 179.72/179.60 [1062]~E(x10621,x10622)+E(f436(x10623,x10624,x10625,x10626,x10621),f436(x10623,x10624,x10625,x10626,x10622))
% 179.72/179.60 [1063]~E(x10631,x10632)+E(f638(x10631,x10633,x10634),f638(x10632,x10633,x10634))
% 179.72/179.60 [1064]~E(x10641,x10642)+E(f638(x10643,x10641,x10644),f638(x10643,x10642,x10644))
% 179.72/179.60 [1065]~E(x10651,x10652)+E(f638(x10653,x10654,x10651),f638(x10653,x10654,x10652))
% 179.72/179.60 [1066]~E(x10661,x10662)+E(f716(x10661,x10663,x10664,x10665,x10666),f716(x10662,x10663,x10664,x10665,x10666))
% 179.72/179.60 [1067]~E(x10671,x10672)+E(f716(x10673,x10671,x10674,x10675,x10676),f716(x10673,x10672,x10674,x10675,x10676))
% 179.72/179.60 [1068]~E(x10681,x10682)+E(f716(x10683,x10684,x10681,x10685,x10686),f716(x10683,x10684,x10682,x10685,x10686))
% 179.72/179.60 [1069]~E(x10691,x10692)+E(f716(x10693,x10694,x10695,x10691,x10696),f716(x10693,x10694,x10695,x10692,x10696))
% 179.72/179.60 [1070]~E(x10701,x10702)+E(f716(x10703,x10704,x10705,x10706,x10701),f716(x10703,x10704,x10705,x10706,x10702))
% 179.72/179.60 [1071]~E(x10711,x10712)+E(f573(x10711,x10713,x10714,x10715,x10716),f573(x10712,x10713,x10714,x10715,x10716))
% 179.72/179.60 [1072]~E(x10721,x10722)+E(f573(x10723,x10721,x10724,x10725,x10726),f573(x10723,x10722,x10724,x10725,x10726))
% 179.72/179.60 [1073]~E(x10731,x10732)+E(f573(x10733,x10734,x10731,x10735,x10736),f573(x10733,x10734,x10732,x10735,x10736))
% 179.72/179.60 [1074]~E(x10741,x10742)+E(f573(x10743,x10744,x10745,x10741,x10746),f573(x10743,x10744,x10745,x10742,x10746))
% 179.72/179.60 [1075]~E(x10751,x10752)+E(f573(x10753,x10754,x10755,x10756,x10751),f573(x10753,x10754,x10755,x10756,x10752))
% 179.72/179.60 [1076]~E(x10761,x10762)+E(f178(x10761,x10763,x10764),f178(x10762,x10763,x10764))
% 179.72/179.60 [1077]~E(x10771,x10772)+E(f178(x10773,x10771,x10774),f178(x10773,x10772,x10774))
% 179.72/179.60 [1078]~E(x10781,x10782)+E(f178(x10783,x10784,x10781),f178(x10783,x10784,x10782))
% 179.72/179.60 [1079]~E(x10791,x10792)+E(f548(x10791,x10793,x10794),f548(x10792,x10793,x10794))
% 179.72/179.60 [1080]~E(x10801,x10802)+E(f548(x10803,x10801,x10804),f548(x10803,x10802,x10804))
% 179.72/179.60 [1081]~E(x10811,x10812)+E(f548(x10813,x10814,x10811),f548(x10813,x10814,x10812))
% 179.72/179.60 [1082]~E(x10821,x10822)+E(f605(x10821,x10823,x10824,x10825,x10826,x10827,x10828),f605(x10822,x10823,x10824,x10825,x10826,x10827,x10828))
% 179.72/179.60 [1083]~E(x10831,x10832)+E(f605(x10833,x10831,x10834,x10835,x10836,x10837,x10838),f605(x10833,x10832,x10834,x10835,x10836,x10837,x10838))
% 179.72/179.60 [1084]~E(x10841,x10842)+E(f605(x10843,x10844,x10841,x10845,x10846,x10847,x10848),f605(x10843,x10844,x10842,x10845,x10846,x10847,x10848))
% 179.72/179.60 [1085]~E(x10851,x10852)+E(f605(x10853,x10854,x10855,x10851,x10856,x10857,x10858),f605(x10853,x10854,x10855,x10852,x10856,x10857,x10858))
% 179.72/179.60 [1086]~E(x10861,x10862)+E(f605(x10863,x10864,x10865,x10866,x10861,x10867,x10868),f605(x10863,x10864,x10865,x10866,x10862,x10867,x10868))
% 179.72/179.60 [1087]~E(x10871,x10872)+E(f605(x10873,x10874,x10875,x10876,x10877,x10871,x10878),f605(x10873,x10874,x10875,x10876,x10877,x10872,x10878))
% 179.72/179.60 [1088]~E(x10881,x10882)+E(f605(x10883,x10884,x10885,x10886,x10887,x10888,x10881),f605(x10883,x10884,x10885,x10886,x10887,x10888,x10882))
% 179.72/179.60 [1089]~E(x10891,x10892)+E(f597(x10891,x10893,x10894,x10895,x10896,x10897,x10898),f597(x10892,x10893,x10894,x10895,x10896,x10897,x10898))
% 179.72/179.60 [1090]~E(x10901,x10902)+E(f597(x10903,x10901,x10904,x10905,x10906,x10907,x10908),f597(x10903,x10902,x10904,x10905,x10906,x10907,x10908))
% 179.72/179.60 [1091]~E(x10911,x10912)+E(f597(x10913,x10914,x10911,x10915,x10916,x10917,x10918),f597(x10913,x10914,x10912,x10915,x10916,x10917,x10918))
% 179.72/179.60 [1092]~E(x10921,x10922)+E(f597(x10923,x10924,x10925,x10921,x10926,x10927,x10928),f597(x10923,x10924,x10925,x10922,x10926,x10927,x10928))
% 179.72/179.60 [1093]~E(x10931,x10932)+E(f597(x10933,x10934,x10935,x10936,x10931,x10937,x10938),f597(x10933,x10934,x10935,x10936,x10932,x10937,x10938))
% 179.72/179.60 [1094]~E(x10941,x10942)+E(f597(x10943,x10944,x10945,x10946,x10947,x10941,x10948),f597(x10943,x10944,x10945,x10946,x10947,x10942,x10948))
% 179.72/179.60 [1095]~E(x10951,x10952)+E(f597(x10953,x10954,x10955,x10956,x10957,x10958,x10951),f597(x10953,x10954,x10955,x10956,x10957,x10958,x10952))
% 179.72/179.60 [1096]~E(x10961,x10962)+E(f678(x10961,x10963,x10964,x10965,x10966,x10967,x10968,x10969),f678(x10962,x10963,x10964,x10965,x10966,x10967,x10968,x10969))
% 179.72/179.60 [1097]~E(x10971,x10972)+E(f678(x10973,x10971,x10974,x10975,x10976,x10977,x10978,x10979),f678(x10973,x10972,x10974,x10975,x10976,x10977,x10978,x10979))
% 179.72/179.60 [1098]~E(x10981,x10982)+E(f678(x10983,x10984,x10981,x10985,x10986,x10987,x10988,x10989),f678(x10983,x10984,x10982,x10985,x10986,x10987,x10988,x10989))
% 179.72/179.60 [1099]~E(x10991,x10992)+E(f678(x10993,x10994,x10995,x10991,x10996,x10997,x10998,x10999),f678(x10993,x10994,x10995,x10992,x10996,x10997,x10998,x10999))
% 179.72/179.60 [1100]~E(x11001,x11002)+E(f678(x11003,x11004,x11005,x11006,x11001,x11007,x11008,x11009),f678(x11003,x11004,x11005,x11006,x11002,x11007,x11008,x11009))
% 179.72/179.60 [1101]~E(x11011,x11012)+E(f678(x11013,x11014,x11015,x11016,x11017,x11011,x11018,x11019),f678(x11013,x11014,x11015,x11016,x11017,x11012,x11018,x11019))
% 179.72/179.60 [1102]~E(x11021,x11022)+E(f678(x11023,x11024,x11025,x11026,x11027,x11028,x11021,x11029),f678(x11023,x11024,x11025,x11026,x11027,x11028,x11022,x11029))
% 179.72/179.60 [1103]~E(x11031,x11032)+E(f678(x11033,x11034,x11035,x11036,x11037,x11038,x11039,x11031),f678(x11033,x11034,x11035,x11036,x11037,x11038,x11039,x11032))
% 179.72/179.60 [1104]~E(x11041,x11042)+E(f843(x11041,x11043,x11044,x11045,x11046),f843(x11042,x11043,x11044,x11045,x11046))
% 179.72/179.60 [1105]~E(x11051,x11052)+E(f843(x11053,x11051,x11054,x11055,x11056),f843(x11053,x11052,x11054,x11055,x11056))
% 179.72/179.60 [1106]~E(x11061,x11062)+E(f843(x11063,x11064,x11061,x11065,x11066),f843(x11063,x11064,x11062,x11065,x11066))
% 179.72/179.60 [1107]~E(x11071,x11072)+E(f843(x11073,x11074,x11075,x11071,x11076),f843(x11073,x11074,x11075,x11072,x11076))
% 179.72/179.60 [1108]~E(x11081,x11082)+E(f843(x11083,x11084,x11085,x11086,x11081),f843(x11083,x11084,x11085,x11086,x11082))
% 179.72/179.60 [1109]~E(x11091,x11092)+E(f798(x11091,x11093,x11094,x11095),f798(x11092,x11093,x11094,x11095))
% 179.72/179.60 [1110]~E(x11101,x11102)+E(f798(x11103,x11101,x11104,x11105),f798(x11103,x11102,x11104,x11105))
% 179.72/179.60 [1111]~E(x11111,x11112)+E(f798(x11113,x11114,x11111,x11115),f798(x11113,x11114,x11112,x11115))
% 179.72/179.60 [1112]~E(x11121,x11122)+E(f798(x11123,x11124,x11125,x11121),f798(x11123,x11124,x11125,x11122))
% 179.72/179.60 [1113]~E(x11131,x11132)+E(f249(x11131,x11133,x11134),f249(x11132,x11133,x11134))
% 179.72/179.60 [1114]~E(x11141,x11142)+E(f249(x11143,x11141,x11144),f249(x11143,x11142,x11144))
% 179.72/179.60 [1115]~E(x11151,x11152)+E(f249(x11153,x11154,x11151),f249(x11153,x11154,x11152))
% 179.72/179.60 [1116]~E(x11161,x11162)+E(f841(x11161,x11163,x11164,x11165,x11166),f841(x11162,x11163,x11164,x11165,x11166))
% 179.72/179.60 [1117]~E(x11171,x11172)+E(f841(x11173,x11171,x11174,x11175,x11176),f841(x11173,x11172,x11174,x11175,x11176))
% 179.72/179.60 [1118]~E(x11181,x11182)+E(f841(x11183,x11184,x11181,x11185,x11186),f841(x11183,x11184,x11182,x11185,x11186))
% 179.72/179.60 [1119]~E(x11191,x11192)+E(f841(x11193,x11194,x11195,x11191,x11196),f841(x11193,x11194,x11195,x11192,x11196))
% 179.72/179.60 [1120]~E(x11201,x11202)+E(f841(x11203,x11204,x11205,x11206,x11201),f841(x11203,x11204,x11205,x11206,x11202))
% 179.72/179.60 [1121]~E(x11211,x11212)+E(f138(x11211,x11213),f138(x11212,x11213))
% 179.72/179.60 [1122]~E(x11221,x11222)+E(f138(x11223,x11221),f138(x11223,x11222))
% 179.72/179.60 [1123]~E(x11231,x11232)+E(f634(x11231,x11233,x11234,x11235,x11236),f634(x11232,x11233,x11234,x11235,x11236))
% 179.72/179.60 [1124]~E(x11241,x11242)+E(f634(x11243,x11241,x11244,x11245,x11246),f634(x11243,x11242,x11244,x11245,x11246))
% 179.72/179.60 [1125]~E(x11251,x11252)+E(f634(x11253,x11254,x11251,x11255,x11256),f634(x11253,x11254,x11252,x11255,x11256))
% 179.72/179.60 [1126]~E(x11261,x11262)+E(f634(x11263,x11264,x11265,x11261,x11266),f634(x11263,x11264,x11265,x11262,x11266))
% 179.72/179.60 [1127]~E(x11271,x11272)+E(f634(x11273,x11274,x11275,x11276,x11271),f634(x11273,x11274,x11275,x11276,x11272))
% 179.72/179.60 [1128]~E(x11281,x11282)+E(f29(x11281,x11283),f29(x11282,x11283))
% 179.72/179.60 [1129]~E(x11291,x11292)+E(f29(x11293,x11291),f29(x11293,x11292))
% 179.72/179.60 [1130]~E(x11301,x11302)+E(f429(x11301,x11303,x11304,x11305),f429(x11302,x11303,x11304,x11305))
% 179.72/179.60 [1131]~E(x11311,x11312)+E(f429(x11313,x11311,x11314,x11315),f429(x11313,x11312,x11314,x11315))
% 179.72/179.60 [1132]~E(x11321,x11322)+E(f429(x11323,x11324,x11321,x11325),f429(x11323,x11324,x11322,x11325))
% 179.72/179.60 [1133]~E(x11331,x11332)+E(f429(x11333,x11334,x11335,x11331),f429(x11333,x11334,x11335,x11332))
% 179.72/179.60 [1134]~E(x11341,x11342)+E(f794(x11341,x11343,x11344,x11345),f794(x11342,x11343,x11344,x11345))
% 179.72/179.60 [1135]~E(x11351,x11352)+E(f794(x11353,x11351,x11354,x11355),f794(x11353,x11352,x11354,x11355))
% 179.72/179.60 [1136]~E(x11361,x11362)+E(f794(x11363,x11364,x11361,x11365),f794(x11363,x11364,x11362,x11365))
% 179.72/179.60 [1137]~E(x11371,x11372)+E(f794(x11373,x11374,x11375,x11371),f794(x11373,x11374,x11375,x11372))
% 179.72/179.60 [1138]~E(x11381,x11382)+E(f838(x11381,x11383),f838(x11382,x11383))
% 179.72/179.60 [1139]~E(x11391,x11392)+E(f838(x11393,x11391),f838(x11393,x11392))
% 179.72/179.60 [1140]~E(x11401,x11402)+E(f550(x11401,x11403,x11404),f550(x11402,x11403,x11404))
% 179.72/179.60 [1141]~E(x11411,x11412)+E(f550(x11413,x11411,x11414),f550(x11413,x11412,x11414))
% 179.72/179.60 [1142]~E(x11421,x11422)+E(f550(x11423,x11424,x11421),f550(x11423,x11424,x11422))
% 179.72/179.60 [1143]~E(x11431,x11432)+E(f781(x11431,x11433,x11434),f781(x11432,x11433,x11434))
% 179.72/179.60 [1144]~E(x11441,x11442)+E(f781(x11443,x11441,x11444),f781(x11443,x11442,x11444))
% 179.72/179.60 [1145]~E(x11451,x11452)+E(f781(x11453,x11454,x11451),f781(x11453,x11454,x11452))
% 179.72/179.60 [1146]~E(x11461,x11462)+E(f416(x11461,x11463,x11464,x11465),f416(x11462,x11463,x11464,x11465))
% 179.72/179.60 [1147]~E(x11471,x11472)+E(f416(x11473,x11471,x11474,x11475),f416(x11473,x11472,x11474,x11475))
% 179.72/179.60 [1148]~E(x11481,x11482)+E(f416(x11483,x11484,x11481,x11485),f416(x11483,x11484,x11482,x11485))
% 179.72/179.60 [1149]~E(x11491,x11492)+E(f416(x11493,x11494,x11495,x11491),f416(x11493,x11494,x11495,x11492))
% 179.72/179.60 [1150]~E(x11501,x11502)+E(f458(x11501,x11503,x11504,x11505),f458(x11502,x11503,x11504,x11505))
% 179.72/179.60 [1151]~E(x11511,x11512)+E(f458(x11513,x11511,x11514,x11515),f458(x11513,x11512,x11514,x11515))
% 179.72/179.60 [1152]~E(x11521,x11522)+E(f458(x11523,x11524,x11521,x11525),f458(x11523,x11524,x11522,x11525))
% 179.72/179.60 [1153]~E(x11531,x11532)+E(f458(x11533,x11534,x11535,x11531),f458(x11533,x11534,x11535,x11532))
% 179.72/179.60 [1154]~E(x11541,x11542)+E(f463(x11541,x11543),f463(x11542,x11543))
% 179.72/179.60 [1155]~E(x11551,x11552)+E(f463(x11553,x11551),f463(x11553,x11552))
% 179.72/179.60 [1156]~E(x11561,x11562)+E(f839(x11561,x11563,x11564,x11565,x11566,x11567),f839(x11562,x11563,x11564,x11565,x11566,x11567))
% 179.72/179.60 [1157]~E(x11571,x11572)+E(f839(x11573,x11571,x11574,x11575,x11576,x11577),f839(x11573,x11572,x11574,x11575,x11576,x11577))
% 179.72/179.60 [1158]~E(x11581,x11582)+E(f839(x11583,x11584,x11581,x11585,x11586,x11587),f839(x11583,x11584,x11582,x11585,x11586,x11587))
% 179.72/179.60 [1159]~E(x11591,x11592)+E(f839(x11593,x11594,x11595,x11591,x11596,x11597),f839(x11593,x11594,x11595,x11592,x11596,x11597))
% 179.72/179.60 [1160]~E(x11601,x11602)+E(f839(x11603,x11604,x11605,x11606,x11601,x11607),f839(x11603,x11604,x11605,x11606,x11602,x11607))
% 179.72/179.60 [1161]~E(x11611,x11612)+E(f839(x11613,x11614,x11615,x11616,x11617,x11611),f839(x11613,x11614,x11615,x11616,x11617,x11612))
% 179.72/179.60 [1162]~E(x11621,x11622)+E(f476(x11621,x11623,x11624,x11625,x11626),f476(x11622,x11623,x11624,x11625,x11626))
% 179.72/179.60 [1163]~E(x11631,x11632)+E(f476(x11633,x11631,x11634,x11635,x11636),f476(x11633,x11632,x11634,x11635,x11636))
% 179.72/179.60 [1164]~E(x11641,x11642)+E(f476(x11643,x11644,x11641,x11645,x11646),f476(x11643,x11644,x11642,x11645,x11646))
% 179.72/179.60 [1165]~E(x11651,x11652)+E(f476(x11653,x11654,x11655,x11651,x11656),f476(x11653,x11654,x11655,x11652,x11656))
% 179.72/179.60 [1166]~E(x11661,x11662)+E(f476(x11663,x11664,x11665,x11666,x11661),f476(x11663,x11664,x11665,x11666,x11662))
% 179.72/179.60 [1167]~E(x11671,x11672)+E(f739(x11671,x11673,x11674,x11675,x11676),f739(x11672,x11673,x11674,x11675,x11676))
% 179.72/179.60 [1168]~E(x11681,x11682)+E(f739(x11683,x11681,x11684,x11685,x11686),f739(x11683,x11682,x11684,x11685,x11686))
% 179.72/179.60 [1169]~E(x11691,x11692)+E(f739(x11693,x11694,x11691,x11695,x11696),f739(x11693,x11694,x11692,x11695,x11696))
% 179.72/179.60 [1170]~E(x11701,x11702)+E(f739(x11703,x11704,x11705,x11701,x11706),f739(x11703,x11704,x11705,x11702,x11706))
% 179.72/179.60 [1171]~E(x11711,x11712)+E(f739(x11713,x11714,x11715,x11716,x11711),f739(x11713,x11714,x11715,x11716,x11712))
% 179.72/179.60 [1172]~E(x11721,x11722)+E(f420(x11721),f420(x11722))
% 179.72/179.60 [1173]~E(x11731,x11732)+E(f679(x11731,x11733,x11734,x11735),f679(x11732,x11733,x11734,x11735))
% 179.72/179.60 [1174]~E(x11741,x11742)+E(f679(x11743,x11741,x11744,x11745),f679(x11743,x11742,x11744,x11745))
% 179.72/179.60 [1175]~E(x11751,x11752)+E(f679(x11753,x11754,x11751,x11755),f679(x11753,x11754,x11752,x11755))
% 179.72/179.60 [1176]~E(x11761,x11762)+E(f679(x11763,x11764,x11765,x11761),f679(x11763,x11764,x11765,x11762))
% 179.72/179.60 [1177]~E(x11771,x11772)+E(f388(x11771,x11773,x11774,x11775),f388(x11772,x11773,x11774,x11775))
% 179.72/179.60 [1178]~E(x11781,x11782)+E(f388(x11783,x11781,x11784,x11785),f388(x11783,x11782,x11784,x11785))
% 179.72/179.60 [1179]~E(x11791,x11792)+E(f388(x11793,x11794,x11791,x11795),f388(x11793,x11794,x11792,x11795))
% 179.72/179.60 [1180]~E(x11801,x11802)+E(f388(x11803,x11804,x11805,x11801),f388(x11803,x11804,x11805,x11802))
% 179.72/179.60 [1181]~E(x11811,x11812)+E(f268(x11811),f268(x11812))
% 179.72/179.60 [1182]~E(x11821,x11822)+E(f75(x11821,x11823,x11824,x11825),f75(x11822,x11823,x11824,x11825))
% 179.72/179.60 [1183]~E(x11831,x11832)+E(f75(x11833,x11831,x11834,x11835),f75(x11833,x11832,x11834,x11835))
% 179.72/179.60 [1184]~E(x11841,x11842)+E(f75(x11843,x11844,x11841,x11845),f75(x11843,x11844,x11842,x11845))
% 179.72/179.60 [1185]~E(x11851,x11852)+E(f75(x11853,x11854,x11855,x11851),f75(x11853,x11854,x11855,x11852))
% 179.72/179.60 [1186]~E(x11861,x11862)+E(f587(x11861,x11863,x11864),f587(x11862,x11863,x11864))
% 179.72/179.60 [1187]~E(x11871,x11872)+E(f587(x11873,x11871,x11874),f587(x11873,x11872,x11874))
% 179.72/179.60 [1188]~E(x11881,x11882)+E(f587(x11883,x11884,x11881),f587(x11883,x11884,x11882))
% 179.72/179.60 [1189]~E(x11891,x11892)+E(f397(x11891,x11893,x11894),f397(x11892,x11893,x11894))
% 179.72/179.60 [1190]~E(x11901,x11902)+E(f397(x11903,x11901,x11904),f397(x11903,x11902,x11904))
% 179.72/179.60 [1191]~E(x11911,x11912)+E(f397(x11913,x11914,x11911),f397(x11913,x11914,x11912))
% 179.72/179.60 [1192]~E(x11921,x11922)+E(f266(x11921,x11923,x11924,x11925,x11926),f266(x11922,x11923,x11924,x11925,x11926))
% 179.72/179.60 [1193]~E(x11931,x11932)+E(f266(x11933,x11931,x11934,x11935,x11936),f266(x11933,x11932,x11934,x11935,x11936))
% 179.72/179.60 [1194]~E(x11941,x11942)+E(f266(x11943,x11944,x11941,x11945,x11946),f266(x11943,x11944,x11942,x11945,x11946))
% 179.72/179.60 [1195]~E(x11951,x11952)+E(f266(x11953,x11954,x11955,x11951,x11956),f266(x11953,x11954,x11955,x11952,x11956))
% 179.72/179.60 [1196]~E(x11961,x11962)+E(f266(x11963,x11964,x11965,x11966,x11961),f266(x11963,x11964,x11965,x11966,x11962))
% 179.72/179.60 [1197]~E(x11971,x11972)+E(f529(x11971),f529(x11972))
% 179.72/179.60 [1198]~E(x11981,x11982)+E(f741(x11981,x11983,x11984,x11985,x11986),f741(x11982,x11983,x11984,x11985,x11986))
% 179.72/179.60 [1199]~E(x11991,x11992)+E(f741(x11993,x11991,x11994,x11995,x11996),f741(x11993,x11992,x11994,x11995,x11996))
% 179.72/179.60 [1200]~E(x12001,x12002)+E(f741(x12003,x12004,x12001,x12005,x12006),f741(x12003,x12004,x12002,x12005,x12006))
% 179.72/179.60 [1201]~E(x12011,x12012)+E(f741(x12013,x12014,x12015,x12011,x12016),f741(x12013,x12014,x12015,x12012,x12016))
% 179.72/179.60 [1202]~E(x12021,x12022)+E(f741(x12023,x12024,x12025,x12026,x12021),f741(x12023,x12024,x12025,x12026,x12022))
% 179.72/179.60 [1203]~E(x12031,x12032)+E(f208(x12031,x12033,x12034,x12035),f208(x12032,x12033,x12034,x12035))
% 179.72/179.60 [1204]~E(x12041,x12042)+E(f208(x12043,x12041,x12044,x12045),f208(x12043,x12042,x12044,x12045))
% 179.72/179.60 [1205]~E(x12051,x12052)+E(f208(x12053,x12054,x12051,x12055),f208(x12053,x12054,x12052,x12055))
% 179.72/179.60 [1206]~E(x12061,x12062)+E(f208(x12063,x12064,x12065,x12061),f208(x12063,x12064,x12065,x12062))
% 179.72/179.60 [1207]~E(x12071,x12072)+E(f315(x12071,x12073,x12074,x12075),f315(x12072,x12073,x12074,x12075))
% 179.72/179.60 [1208]~E(x12081,x12082)+E(f315(x12083,x12081,x12084,x12085),f315(x12083,x12082,x12084,x12085))
% 179.72/179.60 [1209]~E(x12091,x12092)+E(f315(x12093,x12094,x12091,x12095),f315(x12093,x12094,x12092,x12095))
% 179.72/179.60 [1210]~E(x12101,x12102)+E(f315(x12103,x12104,x12105,x12101),f315(x12103,x12104,x12105,x12102))
% 179.72/179.60 [1211]~E(x12111,x12112)+E(f453(x12111,x12113,x12114),f453(x12112,x12113,x12114))
% 179.72/179.60 [1212]~E(x12121,x12122)+E(f453(x12123,x12121,x12124),f453(x12123,x12122,x12124))
% 179.72/179.60 [1213]~E(x12131,x12132)+E(f453(x12133,x12134,x12131),f453(x12133,x12134,x12132))
% 179.72/179.60 [1214]~E(x12141,x12142)+E(f202(x12141,x12143),f202(x12142,x12143))
% 179.72/179.60 [1215]~E(x12151,x12152)+E(f202(x12153,x12151),f202(x12153,x12152))
% 179.72/179.60 [1216]~E(x12161,x12162)+E(f74(x12161,x12163,x12164,x12165,x12166),f74(x12162,x12163,x12164,x12165,x12166))
% 179.72/179.60 [1217]~E(x12171,x12172)+E(f74(x12173,x12171,x12174,x12175,x12176),f74(x12173,x12172,x12174,x12175,x12176))
% 179.72/179.60 [1218]~E(x12181,x12182)+E(f74(x12183,x12184,x12181,x12185,x12186),f74(x12183,x12184,x12182,x12185,x12186))
% 179.72/179.60 [1219]~E(x12191,x12192)+E(f74(x12193,x12194,x12195,x12191,x12196),f74(x12193,x12194,x12195,x12192,x12196))
% 179.72/179.60 [1220]~E(x12201,x12202)+E(f74(x12203,x12204,x12205,x12206,x12201),f74(x12203,x12204,x12205,x12206,x12202))
% 179.72/179.60 [1221]~E(x12211,x12212)+E(f122(x12211),f122(x12212))
% 179.72/179.60 [1222]~E(x12221,x12222)+E(f481(x12221,x12223,x12224),f481(x12222,x12223,x12224))
% 179.72/179.60 [1223]~E(x12231,x12232)+E(f481(x12233,x12231,x12234),f481(x12233,x12232,x12234))
% 179.72/179.60 [1224]~E(x12241,x12242)+E(f481(x12243,x12244,x12241),f481(x12243,x12244,x12242))
% 179.72/179.60 [1225]~E(x12251,x12252)+E(f335(x12251,x12253,x12254),f335(x12252,x12253,x12254))
% 179.72/179.60 [1226]~E(x12261,x12262)+E(f335(x12263,x12261,x12264),f335(x12263,x12262,x12264))
% 179.72/179.60 [1227]~E(x12271,x12272)+E(f335(x12273,x12274,x12271),f335(x12273,x12274,x12272))
% 179.72/179.60 [1228]~E(x12281,x12282)+E(f210(x12281),f210(x12282))
% 179.72/179.60 [1229]~E(x12291,x12292)+E(f724(x12291,x12293,x12294),f724(x12292,x12293,x12294))
% 179.72/179.60 [1230]~E(x12301,x12302)+E(f724(x12303,x12301,x12304),f724(x12303,x12302,x12304))
% 179.72/179.60 [1231]~E(x12311,x12312)+E(f724(x12313,x12314,x12311),f724(x12313,x12314,x12312))
% 179.72/179.60 [1232]~E(x12321,x12322)+E(f198(x12321,x12323,x12324,x12325),f198(x12322,x12323,x12324,x12325))
% 179.72/179.60 [1233]~E(x12331,x12332)+E(f198(x12333,x12331,x12334,x12335),f198(x12333,x12332,x12334,x12335))
% 179.72/179.60 [1234]~E(x12341,x12342)+E(f198(x12343,x12344,x12341,x12345),f198(x12343,x12344,x12342,x12345))
% 179.72/179.60 [1235]~E(x12351,x12352)+E(f198(x12353,x12354,x12355,x12351),f198(x12353,x12354,x12355,x12352))
% 179.72/179.60 [1236]~E(x12361,x12362)+E(f620(x12361,x12363,x12364,x12365,x12366,x12367),f620(x12362,x12363,x12364,x12365,x12366,x12367))
% 179.72/179.60 [1237]~E(x12371,x12372)+E(f620(x12373,x12371,x12374,x12375,x12376,x12377),f620(x12373,x12372,x12374,x12375,x12376,x12377))
% 179.72/179.60 [1238]~E(x12381,x12382)+E(f620(x12383,x12384,x12381,x12385,x12386,x12387),f620(x12383,x12384,x12382,x12385,x12386,x12387))
% 179.72/179.60 [1239]~E(x12391,x12392)+E(f620(x12393,x12394,x12395,x12391,x12396,x12397),f620(x12393,x12394,x12395,x12392,x12396,x12397))
% 179.72/179.60 [1240]~E(x12401,x12402)+E(f620(x12403,x12404,x12405,x12406,x12401,x12407),f620(x12403,x12404,x12405,x12406,x12402,x12407))
% 179.72/179.60 [1241]~E(x12411,x12412)+E(f620(x12413,x12414,x12415,x12416,x12417,x12411),f620(x12413,x12414,x12415,x12416,x12417,x12412))
% 179.72/179.60 [1242]~E(x12421,x12422)+E(f664(x12421,x12423,x12424,x12425,x12426),f664(x12422,x12423,x12424,x12425,x12426))
% 179.72/179.60 [1243]~E(x12431,x12432)+E(f664(x12433,x12431,x12434,x12435,x12436),f664(x12433,x12432,x12434,x12435,x12436))
% 179.72/179.60 [1244]~E(x12441,x12442)+E(f664(x12443,x12444,x12441,x12445,x12446),f664(x12443,x12444,x12442,x12445,x12446))
% 179.72/179.60 [1245]~E(x12451,x12452)+E(f664(x12453,x12454,x12455,x12451,x12456),f664(x12453,x12454,x12455,x12452,x12456))
% 179.72/179.60 [1246]~E(x12461,x12462)+E(f664(x12463,x12464,x12465,x12466,x12461),f664(x12463,x12464,x12465,x12466,x12462))
% 179.72/179.60 [1247]~E(x12471,x12472)+E(f51(x12471,x12473),f51(x12472,x12473))
% 179.72/179.60 [1248]~E(x12481,x12482)+E(f51(x12483,x12481),f51(x12483,x12482))
% 179.72/179.60 [1249]~E(x12491,x12492)+E(f30(x12491,x12493),f30(x12492,x12493))
% 179.72/179.60 [1250]~E(x12501,x12502)+E(f30(x12503,x12501),f30(x12503,x12502))
% 179.72/179.60 [1251]~E(x12511,x12512)+E(f765(x12511,x12513,x12514,x12515),f765(x12512,x12513,x12514,x12515))
% 179.72/179.60 [1252]~E(x12521,x12522)+E(f765(x12523,x12521,x12524,x12525),f765(x12523,x12522,x12524,x12525))
% 179.72/179.60 [1253]~E(x12531,x12532)+E(f765(x12533,x12534,x12531,x12535),f765(x12533,x12534,x12532,x12535))
% 179.72/179.60 [1254]~E(x12541,x12542)+E(f765(x12543,x12544,x12545,x12541),f765(x12543,x12544,x12545,x12542))
% 179.72/179.60 [1255]~E(x12551,x12552)+E(f344(x12551,x12553),f344(x12552,x12553))
% 179.72/179.60 [1256]~E(x12561,x12562)+E(f344(x12563,x12561),f344(x12563,x12562))
% 179.72/179.60 [1257]~E(x12571,x12572)+E(f604(x12571,x12573),f604(x12572,x12573))
% 179.72/179.60 [1258]~E(x12581,x12582)+E(f604(x12583,x12581),f604(x12583,x12582))
% 179.72/179.60 [1259]~E(x12591,x12592)+E(f332(x12591,x12593,x12594),f332(x12592,x12593,x12594))
% 179.72/179.60 [1260]~E(x12601,x12602)+E(f332(x12603,x12601,x12604),f332(x12603,x12602,x12604))
% 179.72/179.60 [1261]~E(x12611,x12612)+E(f332(x12613,x12614,x12611),f332(x12613,x12614,x12612))
% 179.72/179.60 [1262]~E(x12621,x12622)+E(f56(x12621),f56(x12622))
% 179.72/179.60 [1263]~E(x12631,x12632)+E(f772(x12631,x12633,x12634,x12635),f772(x12632,x12633,x12634,x12635))
% 179.72/179.60 [1264]~E(x12641,x12642)+E(f772(x12643,x12641,x12644,x12645),f772(x12643,x12642,x12644,x12645))
% 179.72/179.60 [1265]~E(x12651,x12652)+E(f772(x12653,x12654,x12651,x12655),f772(x12653,x12654,x12652,x12655))
% 179.72/179.60 [1266]~E(x12661,x12662)+E(f772(x12663,x12664,x12665,x12661),f772(x12663,x12664,x12665,x12662))
% 179.72/179.60 [1267]~E(x12671,x12672)+E(f563(x12671,x12673,x12674),f563(x12672,x12673,x12674))
% 179.72/179.60 [1268]~E(x12681,x12682)+E(f563(x12683,x12681,x12684),f563(x12683,x12682,x12684))
% 179.72/179.60 [1269]~E(x12691,x12692)+E(f563(x12693,x12694,x12691),f563(x12693,x12694,x12692))
% 179.72/179.60 [1270]~E(x12701,x12702)+E(f126(x12701,x12703,x12704,x12705,x12706),f126(x12702,x12703,x12704,x12705,x12706))
% 179.72/179.60 [1271]~E(x12711,x12712)+E(f126(x12713,x12711,x12714,x12715,x12716),f126(x12713,x12712,x12714,x12715,x12716))
% 179.72/179.60 [1272]~E(x12721,x12722)+E(f126(x12723,x12724,x12721,x12725,x12726),f126(x12723,x12724,x12722,x12725,x12726))
% 179.72/179.60 [1273]~E(x12731,x12732)+E(f126(x12733,x12734,x12735,x12731,x12736),f126(x12733,x12734,x12735,x12732,x12736))
% 179.72/179.60 [1274]~E(x12741,x12742)+E(f126(x12743,x12744,x12745,x12746,x12741),f126(x12743,x12744,x12745,x12746,x12742))
% 179.72/179.60 [1275]~E(x12751,x12752)+E(f371(x12751,x12753,x12754,x12755,x12756,x12757),f371(x12752,x12753,x12754,x12755,x12756,x12757))
% 179.72/179.60 [1276]~E(x12761,x12762)+E(f371(x12763,x12761,x12764,x12765,x12766,x12767),f371(x12763,x12762,x12764,x12765,x12766,x12767))
% 179.72/179.60 [1277]~E(x12771,x12772)+E(f371(x12773,x12774,x12771,x12775,x12776,x12777),f371(x12773,x12774,x12772,x12775,x12776,x12777))
% 179.72/179.60 [1278]~E(x12781,x12782)+E(f371(x12783,x12784,x12785,x12781,x12786,x12787),f371(x12783,x12784,x12785,x12782,x12786,x12787))
% 179.72/179.60 [1279]~E(x12791,x12792)+E(f371(x12793,x12794,x12795,x12796,x12791,x12797),f371(x12793,x12794,x12795,x12796,x12792,x12797))
% 179.72/179.60 [1280]~E(x12801,x12802)+E(f371(x12803,x12804,x12805,x12806,x12807,x12801),f371(x12803,x12804,x12805,x12806,x12807,x12802))
% 179.72/179.60 [1281]~E(x12811,x12812)+E(f800(x12811,x12813,x12814,x12815,x12816,x12817),f800(x12812,x12813,x12814,x12815,x12816,x12817))
% 179.72/179.60 [1282]~E(x12821,x12822)+E(f800(x12823,x12821,x12824,x12825,x12826,x12827),f800(x12823,x12822,x12824,x12825,x12826,x12827))
% 179.72/179.60 [1283]~E(x12831,x12832)+E(f800(x12833,x12834,x12831,x12835,x12836,x12837),f800(x12833,x12834,x12832,x12835,x12836,x12837))
% 179.72/179.60 [1284]~E(x12841,x12842)+E(f800(x12843,x12844,x12845,x12841,x12846,x12847),f800(x12843,x12844,x12845,x12842,x12846,x12847))
% 179.72/179.60 [1285]~E(x12851,x12852)+E(f800(x12853,x12854,x12855,x12856,x12851,x12857),f800(x12853,x12854,x12855,x12856,x12852,x12857))
% 179.72/179.60 [1286]~E(x12861,x12862)+E(f800(x12863,x12864,x12865,x12866,x12867,x12861),f800(x12863,x12864,x12865,x12866,x12867,x12862))
% 179.72/179.60 [1287]~E(x12871,x12872)+E(f341(x12871,x12873),f341(x12872,x12873))
% 179.72/179.60 [1288]~E(x12881,x12882)+E(f341(x12883,x12881),f341(x12883,x12882))
% 179.72/179.60 [1289]~E(x12891,x12892)+E(f400(x12891,x12893,x12894),f400(x12892,x12893,x12894))
% 179.72/179.60 [1290]~E(x12901,x12902)+E(f400(x12903,x12901,x12904),f400(x12903,x12902,x12904))
% 179.72/179.60 [1291]~E(x12911,x12912)+E(f400(x12913,x12914,x12911),f400(x12913,x12914,x12912))
% 179.72/179.60 [1292]~E(x12921,x12922)+E(f845(x12921,x12923,x12924,x12925,x12926,x12927,x12928),f845(x12922,x12923,x12924,x12925,x12926,x12927,x12928))
% 179.72/179.60 [1293]~E(x12931,x12932)+E(f845(x12933,x12931,x12934,x12935,x12936,x12937,x12938),f845(x12933,x12932,x12934,x12935,x12936,x12937,x12938))
% 179.72/179.60 [1294]~E(x12941,x12942)+E(f845(x12943,x12944,x12941,x12945,x12946,x12947,x12948),f845(x12943,x12944,x12942,x12945,x12946,x12947,x12948))
% 179.72/179.60 [1295]~E(x12951,x12952)+E(f845(x12953,x12954,x12955,x12951,x12956,x12957,x12958),f845(x12953,x12954,x12955,x12952,x12956,x12957,x12958))
% 179.72/179.60 [1296]~E(x12961,x12962)+E(f845(x12963,x12964,x12965,x12966,x12961,x12967,x12968),f845(x12963,x12964,x12965,x12966,x12962,x12967,x12968))
% 179.72/179.60 [1297]~E(x12971,x12972)+E(f845(x12973,x12974,x12975,x12976,x12977,x12971,x12978),f845(x12973,x12974,x12975,x12976,x12977,x12972,x12978))
% 179.72/179.60 [1298]~E(x12981,x12982)+E(f845(x12983,x12984,x12985,x12986,x12987,x12988,x12981),f845(x12983,x12984,x12985,x12986,x12987,x12988,x12982))
% 179.72/179.60 [1299]~E(x12991,x12992)+E(f120(x12991),f120(x12992))
% 179.72/179.60 [1300]~E(x13001,x13002)+E(f681(x13001,x13003),f681(x13002,x13003))
% 179.72/179.60 [1301]~E(x13011,x13012)+E(f681(x13013,x13011),f681(x13013,x13012))
% 179.72/179.60 [1302]~E(x13021,x13022)+E(f555(x13021,x13023,x13024),f555(x13022,x13023,x13024))
% 179.72/179.60 [1303]~E(x13031,x13032)+E(f555(x13033,x13031,x13034),f555(x13033,x13032,x13034))
% 179.72/179.60 [1304]~E(x13041,x13042)+E(f555(x13043,x13044,x13041),f555(x13043,x13044,x13042))
% 179.72/179.60 [1305]~E(x13051,x13052)+E(f493(x13051,x13053,x13054,x13055),f493(x13052,x13053,x13054,x13055))
% 179.72/179.60 [1306]~E(x13061,x13062)+E(f493(x13063,x13061,x13064,x13065),f493(x13063,x13062,x13064,x13065))
% 179.72/179.60 [1307]~E(x13071,x13072)+E(f493(x13073,x13074,x13071,x13075),f493(x13073,x13074,x13072,x13075))
% 179.72/179.60 [1308]~E(x13081,x13082)+E(f493(x13083,x13084,x13085,x13081),f493(x13083,x13084,x13085,x13082))
% 179.72/179.60 [1309]~E(x13091,x13092)+E(f288(x13091,x13093,x13094,x13095,x13096),f288(x13092,x13093,x13094,x13095,x13096))
% 179.72/179.60 [1310]~E(x13101,x13102)+E(f288(x13103,x13101,x13104,x13105,x13106),f288(x13103,x13102,x13104,x13105,x13106))
% 179.72/179.60 [1311]~E(x13111,x13112)+E(f288(x13113,x13114,x13111,x13115,x13116),f288(x13113,x13114,x13112,x13115,x13116))
% 179.72/179.60 [1312]~E(x13121,x13122)+E(f288(x13123,x13124,x13125,x13121,x13126),f288(x13123,x13124,x13125,x13122,x13126))
% 179.72/179.60 [1313]~E(x13131,x13132)+E(f288(x13133,x13134,x13135,x13136,x13131),f288(x13133,x13134,x13135,x13136,x13132))
% 179.72/179.60 [1314]~E(x13141,x13142)+E(f499(x13141,x13143,x13144),f499(x13142,x13143,x13144))
% 179.72/179.60 [1315]~E(x13151,x13152)+E(f499(x13153,x13151,x13154),f499(x13153,x13152,x13154))
% 179.72/179.60 [1316]~E(x13161,x13162)+E(f499(x13163,x13164,x13161),f499(x13163,x13164,x13162))
% 179.72/179.60 [1317]~E(x13171,x13172)+E(f424(x13171),f424(x13172))
% 179.72/179.60 [1318]~E(x13181,x13182)+E(f380(x13181),f380(x13182))
% 179.72/179.60 [1319]~E(x13191,x13192)+E(f808(x13191,x13193,x13194,x13195,x13196,x13197,x13198,x13199,x131910),f808(x13192,x13193,x13194,x13195,x13196,x13197,x13198,x13199,x131910))
% 179.72/179.60 [1320]~E(x13201,x13202)+E(f808(x13203,x13201,x13204,x13205,x13206,x13207,x13208,x13209,x132010),f808(x13203,x13202,x13204,x13205,x13206,x13207,x13208,x13209,x132010))
% 179.72/179.60 [1321]~E(x13211,x13212)+E(f808(x13213,x13214,x13211,x13215,x13216,x13217,x13218,x13219,x132110),f808(x13213,x13214,x13212,x13215,x13216,x13217,x13218,x13219,x132110))
% 179.72/179.60 [1322]~E(x13221,x13222)+E(f808(x13223,x13224,x13225,x13221,x13226,x13227,x13228,x13229,x132210),f808(x13223,x13224,x13225,x13222,x13226,x13227,x13228,x13229,x132210))
% 179.72/179.60 [1323]~E(x13231,x13232)+E(f808(x13233,x13234,x13235,x13236,x13231,x13237,x13238,x13239,x132310),f808(x13233,x13234,x13235,x13236,x13232,x13237,x13238,x13239,x132310))
% 179.72/179.60 [1324]~E(x13241,x13242)+E(f808(x13243,x13244,x13245,x13246,x13247,x13241,x13248,x13249,x132410),f808(x13243,x13244,x13245,x13246,x13247,x13242,x13248,x13249,x132410))
% 179.72/179.60 [1325]~E(x13251,x13252)+E(f808(x13253,x13254,x13255,x13256,x13257,x13258,x13251,x13259,x132510),f808(x13253,x13254,x13255,x13256,x13257,x13258,x13252,x13259,x132510))
% 179.72/179.60 [1326]~E(x13261,x13262)+E(f808(x13263,x13264,x13265,x13266,x13267,x13268,x13269,x13261,x132610),f808(x13263,x13264,x13265,x13266,x13267,x13268,x13269,x13262,x132610))
% 179.72/179.60 [1327]~E(x13271,x13272)+E(f808(x13273,x13274,x13275,x13276,x13277,x13278,x13279,x132710,x13271),f808(x13273,x13274,x13275,x13276,x13277,x13278,x13279,x132710,x13272))
% 179.72/179.60 [1328]~E(x13281,x13282)+E(f592(x13281,x13283,x13284,x13285),f592(x13282,x13283,x13284,x13285))
% 179.72/179.60 [1329]~E(x13291,x13292)+E(f592(x13293,x13291,x13294,x13295),f592(x13293,x13292,x13294,x13295))
% 179.72/179.60 [1330]~E(x13301,x13302)+E(f592(x13303,x13304,x13301,x13305),f592(x13303,x13304,x13302,x13305))
% 179.72/179.60 [1331]~E(x13311,x13312)+E(f592(x13313,x13314,x13315,x13311),f592(x13313,x13314,x13315,x13312))
% 179.72/179.60 [1332]~E(x13321,x13322)+E(f252(x13321,x13323,x13324),f252(x13322,x13323,x13324))
% 179.72/179.60 [1333]~E(x13331,x13332)+E(f252(x13333,x13331,x13334),f252(x13333,x13332,x13334))
% 179.72/179.60 [1334]~E(x13341,x13342)+E(f252(x13343,x13344,x13341),f252(x13343,x13344,x13342))
% 179.72/179.60 [1335]~E(x13351,x13352)+E(f770(x13351,x13353,x13354),f770(x13352,x13353,x13354))
% 179.72/179.60 [1336]~E(x13361,x13362)+E(f770(x13363,x13361,x13364),f770(x13363,x13362,x13364))
% 179.72/179.60 [1337]~E(x13371,x13372)+E(f770(x13373,x13374,x13371),f770(x13373,x13374,x13372))
% 179.72/179.60 [1338]~E(x13381,x13382)+E(f769(x13381,x13383),f769(x13382,x13383))
% 179.72/179.60 [1339]~E(x13391,x13392)+E(f769(x13393,x13391),f769(x13393,x13392))
% 179.72/179.60 [1340]~E(x13401,x13402)+E(f821(x13401,x13403,x13404),f821(x13402,x13403,x13404))
% 179.72/179.60 [1341]~E(x13411,x13412)+E(f821(x13413,x13411,x13414),f821(x13413,x13412,x13414))
% 179.72/179.60 [1342]~E(x13421,x13422)+E(f821(x13423,x13424,x13421),f821(x13423,x13424,x13422))
% 179.72/179.60 [1343]~E(x13431,x13432)+E(f387(x13431,x13433,x13434,x13435),f387(x13432,x13433,x13434,x13435))
% 179.72/179.60 [1344]~E(x13441,x13442)+E(f387(x13443,x13441,x13444,x13445),f387(x13443,x13442,x13444,x13445))
% 179.72/179.60 [1345]~E(x13451,x13452)+E(f387(x13453,x13454,x13451,x13455),f387(x13453,x13454,x13452,x13455))
% 179.72/179.60 [1346]~E(x13461,x13462)+E(f387(x13463,x13464,x13465,x13461),f387(x13463,x13464,x13465,x13462))
% 179.72/179.60 [1347]~E(x13471,x13472)+E(f357(x13471,x13473,x13474,x13475),f357(x13472,x13473,x13474,x13475))
% 179.72/179.60 [1348]~E(x13481,x13482)+E(f357(x13483,x13481,x13484,x13485),f357(x13483,x13482,x13484,x13485))
% 179.72/179.60 [1349]~E(x13491,x13492)+E(f357(x13493,x13494,x13491,x13495),f357(x13493,x13494,x13492,x13495))
% 179.72/179.60 [1350]~E(x13501,x13502)+E(f357(x13503,x13504,x13505,x13501),f357(x13503,x13504,x13505,x13502))
% 179.72/179.60 [1351]~E(x13511,x13512)+E(f746(x13511,x13513,x13514,x13515,x13516),f746(x13512,x13513,x13514,x13515,x13516))
% 179.72/179.60 [1352]~E(x13521,x13522)+E(f746(x13523,x13521,x13524,x13525,x13526),f746(x13523,x13522,x13524,x13525,x13526))
% 179.72/179.60 [1353]~E(x13531,x13532)+E(f746(x13533,x13534,x13531,x13535,x13536),f746(x13533,x13534,x13532,x13535,x13536))
% 179.72/179.60 [1354]~E(x13541,x13542)+E(f746(x13543,x13544,x13545,x13541,x13546),f746(x13543,x13544,x13545,x13542,x13546))
% 179.72/179.60 [1355]~E(x13551,x13552)+E(f746(x13553,x13554,x13555,x13556,x13551),f746(x13553,x13554,x13555,x13556,x13552))
% 179.72/179.60 [1356]~E(x13561,x13562)+E(f835(x13561,x13563,x13564),f835(x13562,x13563,x13564))
% 179.72/179.60 [1357]~E(x13571,x13572)+E(f835(x13573,x13571,x13574),f835(x13573,x13572,x13574))
% 179.72/179.60 [1358]~E(x13581,x13582)+E(f835(x13583,x13584,x13581),f835(x13583,x13584,x13582))
% 179.72/179.60 [1359]~E(x13591,x13592)+E(f408(x13591,x13593,x13594,x13595),f408(x13592,x13593,x13594,x13595))
% 179.72/179.60 [1360]~E(x13601,x13602)+E(f408(x13603,x13601,x13604,x13605),f408(x13603,x13602,x13604,x13605))
% 179.72/179.60 [1361]~E(x13611,x13612)+E(f408(x13613,x13614,x13611,x13615),f408(x13613,x13614,x13612,x13615))
% 179.72/179.60 [1362]~E(x13621,x13622)+E(f408(x13623,x13624,x13625,x13621),f408(x13623,x13624,x13625,x13622))
% 179.72/179.60 [1363]~E(x13631,x13632)+E(f849(x13631,x13633,x13634),f849(x13632,x13633,x13634))
% 179.72/179.60 [1364]~E(x13641,x13642)+E(f849(x13643,x13641,x13644),f849(x13643,x13642,x13644))
% 179.72/179.60 [1365]~E(x13651,x13652)+E(f849(x13653,x13654,x13651),f849(x13653,x13654,x13652))
% 179.72/179.60 [1366]~E(x13661,x13662)+E(f289(x13661,x13663,x13664),f289(x13662,x13663,x13664))
% 179.72/179.60 [1367]~E(x13671,x13672)+E(f289(x13673,x13671,x13674),f289(x13673,x13672,x13674))
% 179.72/179.60 [1368]~E(x13681,x13682)+E(f289(x13683,x13684,x13681),f289(x13683,x13684,x13682))
% 179.72/179.60 [1369]~E(x13691,x13692)+E(f712(x13691,x13693,x13694,x13695,x13696,x13697,x13698),f712(x13692,x13693,x13694,x13695,x13696,x13697,x13698))
% 179.72/179.60 [1370]~E(x13701,x13702)+E(f712(x13703,x13701,x13704,x13705,x13706,x13707,x13708),f712(x13703,x13702,x13704,x13705,x13706,x13707,x13708))
% 179.72/179.60 [1371]~E(x13711,x13712)+E(f712(x13713,x13714,x13711,x13715,x13716,x13717,x13718),f712(x13713,x13714,x13712,x13715,x13716,x13717,x13718))
% 179.72/179.60 [1372]~E(x13721,x13722)+E(f712(x13723,x13724,x13725,x13721,x13726,x13727,x13728),f712(x13723,x13724,x13725,x13722,x13726,x13727,x13728))
% 179.72/179.60 [1373]~E(x13731,x13732)+E(f712(x13733,x13734,x13735,x13736,x13731,x13737,x13738),f712(x13733,x13734,x13735,x13736,x13732,x13737,x13738))
% 179.72/179.60 [1374]~E(x13741,x13742)+E(f712(x13743,x13744,x13745,x13746,x13747,x13741,x13748),f712(x13743,x13744,x13745,x13746,x13747,x13742,x13748))
% 179.72/179.60 [1375]~E(x13751,x13752)+E(f712(x13753,x13754,x13755,x13756,x13757,x13758,x13751),f712(x13753,x13754,x13755,x13756,x13757,x13758,x13752))
% 179.72/179.60 [1376]~E(x13761,x13762)+E(f652(x13761,x13763),f652(x13762,x13763))
% 179.72/179.60 [1377]~E(x13771,x13772)+E(f652(x13773,x13771),f652(x13773,x13772))
% 179.72/179.60 [1378]~E(x13781,x13782)+E(f574(x13781,x13783,x13784,x13785,x13786),f574(x13782,x13783,x13784,x13785,x13786))
% 179.72/179.60 [1379]~E(x13791,x13792)+E(f574(x13793,x13791,x13794,x13795,x13796),f574(x13793,x13792,x13794,x13795,x13796))
% 179.72/179.60 [1380]~E(x13801,x13802)+E(f574(x13803,x13804,x13801,x13805,x13806),f574(x13803,x13804,x13802,x13805,x13806))
% 179.72/179.60 [1381]~E(x13811,x13812)+E(f574(x13813,x13814,x13815,x13811,x13816),f574(x13813,x13814,x13815,x13812,x13816))
% 179.72/179.60 [1382]~E(x13821,x13822)+E(f574(x13823,x13824,x13825,x13826,x13821),f574(x13823,x13824,x13825,x13826,x13822))
% 179.72/179.60 [1383]~E(x13831,x13832)+E(f576(x13831,x13833,x13834,x13835,x13836),f576(x13832,x13833,x13834,x13835,x13836))
% 179.72/179.60 [1384]~E(x13841,x13842)+E(f576(x13843,x13841,x13844,x13845,x13846),f576(x13843,x13842,x13844,x13845,x13846))
% 179.72/179.60 [1385]~E(x13851,x13852)+E(f576(x13853,x13854,x13851,x13855,x13856),f576(x13853,x13854,x13852,x13855,x13856))
% 179.72/179.60 [1386]~E(x13861,x13862)+E(f576(x13863,x13864,x13865,x13861,x13866),f576(x13863,x13864,x13865,x13862,x13866))
% 179.72/179.60 [1387]~E(x13871,x13872)+E(f576(x13873,x13874,x13875,x13876,x13871),f576(x13873,x13874,x13875,x13876,x13872))
% 179.72/179.60 [1388]~E(x13881,x13882)+E(f486(x13881,x13883),f486(x13882,x13883))
% 179.72/179.60 [1389]~E(x13891,x13892)+E(f486(x13893,x13891),f486(x13893,x13892))
% 179.72/179.60 [1390]~E(x13901,x13902)+E(f720(x13901,x13903,x13904),f720(x13902,x13903,x13904))
% 179.72/179.60 [1391]~E(x13911,x13912)+E(f720(x13913,x13911,x13914),f720(x13913,x13912,x13914))
% 179.72/179.60 [1392]~E(x13921,x13922)+E(f720(x13923,x13924,x13921),f720(x13923,x13924,x13922))
% 179.72/179.60 [1393]~E(x13931,x13932)+E(f440(x13931,x13933),f440(x13932,x13933))
% 179.72/179.60 [1394]~E(x13941,x13942)+E(f440(x13943,x13941),f440(x13943,x13942))
% 179.72/179.60 [1395]~E(x13951,x13952)+E(f222(x13951,x13953),f222(x13952,x13953))
% 179.72/179.60 [1396]~E(x13961,x13962)+E(f222(x13963,x13961),f222(x13963,x13962))
% 179.72/179.60 [1397]~E(x13971,x13972)+E(f421(x13971),f421(x13972))
% 179.72/179.60 [1398]~E(x13981,x13982)+E(f139(x13981,x13983),f139(x13982,x13983))
% 179.72/179.60 [1399]~E(x13991,x13992)+E(f139(x13993,x13991),f139(x13993,x13992))
% 179.72/179.60 [1400]~E(x14001,x14002)+E(f359(x14001,x14003,x14004,x14005,x14006),f359(x14002,x14003,x14004,x14005,x14006))
% 179.72/179.60 [1401]~E(x14011,x14012)+E(f359(x14013,x14011,x14014,x14015,x14016),f359(x14013,x14012,x14014,x14015,x14016))
% 179.72/179.60 [1402]~E(x14021,x14022)+E(f359(x14023,x14024,x14021,x14025,x14026),f359(x14023,x14024,x14022,x14025,x14026))
% 179.72/179.60 [1403]~E(x14031,x14032)+E(f359(x14033,x14034,x14035,x14031,x14036),f359(x14033,x14034,x14035,x14032,x14036))
% 179.72/179.60 [1404]~E(x14041,x14042)+E(f359(x14043,x14044,x14045,x14046,x14041),f359(x14043,x14044,x14045,x14046,x14042))
% 179.72/179.60 [1405]~E(x14051,x14052)+E(f773(x14051,x14053,x14054,x14055),f773(x14052,x14053,x14054,x14055))
% 179.72/179.60 [1406]~E(x14061,x14062)+E(f773(x14063,x14061,x14064,x14065),f773(x14063,x14062,x14064,x14065))
% 179.72/179.60 [1407]~E(x14071,x14072)+E(f773(x14073,x14074,x14071,x14075),f773(x14073,x14074,x14072,x14075))
% 179.72/179.60 [1408]~E(x14081,x14082)+E(f773(x14083,x14084,x14085,x14081),f773(x14083,x14084,x14085,x14082))
% 179.72/179.60 [1409]~E(x14091,x14092)+E(f627(x14091,x14093,x14094),f627(x14092,x14093,x14094))
% 179.72/179.60 [1410]~E(x14101,x14102)+E(f627(x14103,x14101,x14104),f627(x14103,x14102,x14104))
% 179.72/179.60 [1411]~E(x14111,x14112)+E(f627(x14113,x14114,x14111),f627(x14113,x14114,x14112))
% 179.72/179.60 [1412]~E(x14121,x14122)+E(f649(x14121,x14123),f649(x14122,x14123))
% 179.72/179.60 [1413]~E(x14131,x14132)+E(f649(x14133,x14131),f649(x14133,x14132))
% 179.72/179.60 [1414]~E(x14141,x14142)+E(f439(x14141,x14143,x14144,x14145,x14146),f439(x14142,x14143,x14144,x14145,x14146))
% 179.72/179.60 [1415]~E(x14151,x14152)+E(f439(x14153,x14151,x14154,x14155,x14156),f439(x14153,x14152,x14154,x14155,x14156))
% 179.72/179.60 [1416]~E(x14161,x14162)+E(f439(x14163,x14164,x14161,x14165,x14166),f439(x14163,x14164,x14162,x14165,x14166))
% 179.72/179.60 [1417]~E(x14171,x14172)+E(f439(x14173,x14174,x14175,x14171,x14176),f439(x14173,x14174,x14175,x14172,x14176))
% 179.72/179.60 [1418]~E(x14181,x14182)+E(f439(x14183,x14184,x14185,x14186,x14181),f439(x14183,x14184,x14185,x14186,x14182))
% 179.72/179.60 [1419]~E(x14191,x14192)+E(f504(x14191,x14193,x14194,x14195),f504(x14192,x14193,x14194,x14195))
% 179.72/179.60 [1420]~E(x14201,x14202)+E(f504(x14203,x14201,x14204,x14205),f504(x14203,x14202,x14204,x14205))
% 179.72/179.60 [1421]~E(x14211,x14212)+E(f504(x14213,x14214,x14211,x14215),f504(x14213,x14214,x14212,x14215))
% 179.72/179.60 [1422]~E(x14221,x14222)+E(f504(x14223,x14224,x14225,x14221),f504(x14223,x14224,x14225,x14222))
% 179.72/179.60 [1423]~E(x14231,x14232)+E(f273(x14231,x14233,x14234),f273(x14232,x14233,x14234))
% 179.72/179.60 [1424]~E(x14241,x14242)+E(f273(x14243,x14241,x14244),f273(x14243,x14242,x14244))
% 179.72/179.60 [1425]~E(x14251,x14252)+E(f273(x14253,x14254,x14251),f273(x14253,x14254,x14252))
% 179.72/179.60 [1426]~E(x14261,x14262)+E(f231(x14261,x14263,x14264),f231(x14262,x14263,x14264))
% 179.72/179.60 [1427]~E(x14271,x14272)+E(f231(x14273,x14271,x14274),f231(x14273,x14272,x14274))
% 179.72/179.60 [1428]~E(x14281,x14282)+E(f231(x14283,x14284,x14281),f231(x14283,x14284,x14282))
% 179.72/179.60 [1429]~E(x14291,x14292)+E(f337(x14291,x14293),f337(x14292,x14293))
% 179.72/179.60 [1430]~E(x14301,x14302)+E(f337(x14303,x14301),f337(x14303,x14302))
% 179.72/179.60 [1431]~E(x14311,x14312)+E(f594(x14311,x14313,x14314),f594(x14312,x14313,x14314))
% 179.72/179.60 [1432]~E(x14321,x14322)+E(f594(x14323,x14321,x14324),f594(x14323,x14322,x14324))
% 179.72/179.60 [1433]~E(x14331,x14332)+E(f594(x14333,x14334,x14331),f594(x14333,x14334,x14332))
% 179.72/179.60 [1434]~E(x14341,x14342)+E(f631(x14341,x14343,x14344,x14345),f631(x14342,x14343,x14344,x14345))
% 179.72/179.60 [1435]~E(x14351,x14352)+E(f631(x14353,x14351,x14354,x14355),f631(x14353,x14352,x14354,x14355))
% 179.72/179.60 [1436]~E(x14361,x14362)+E(f631(x14363,x14364,x14361,x14365),f631(x14363,x14364,x14362,x14365))
% 179.72/179.60 [1437]~E(x14371,x14372)+E(f631(x14373,x14374,x14375,x14371),f631(x14373,x14374,x14375,x14372))
% 179.72/179.60 [1438]~E(x14381,x14382)+E(f466(x14381,x14383,x14384,x14385),f466(x14382,x14383,x14384,x14385))
% 179.72/179.60 [1439]~E(x14391,x14392)+E(f466(x14393,x14391,x14394,x14395),f466(x14393,x14392,x14394,x14395))
% 179.72/179.60 [1440]~E(x14401,x14402)+E(f466(x14403,x14404,x14401,x14405),f466(x14403,x14404,x14402,x14405))
% 179.72/179.60 [1441]~E(x14411,x14412)+E(f466(x14413,x14414,x14415,x14411),f466(x14413,x14414,x14415,x14412))
% 179.72/179.60 [1442]~E(x14421,x14422)+E(f709(x14421,x14423,x14424,x14425,x14426),f709(x14422,x14423,x14424,x14425,x14426))
% 179.72/179.60 [1443]~E(x14431,x14432)+E(f709(x14433,x14431,x14434,x14435,x14436),f709(x14433,x14432,x14434,x14435,x14436))
% 179.72/179.60 [1444]~E(x14441,x14442)+E(f709(x14443,x14444,x14441,x14445,x14446),f709(x14443,x14444,x14442,x14445,x14446))
% 179.72/179.60 [1445]~E(x14451,x14452)+E(f709(x14453,x14454,x14455,x14451,x14456),f709(x14453,x14454,x14455,x14452,x14456))
% 179.72/179.60 [1446]~E(x14461,x14462)+E(f709(x14463,x14464,x14465,x14466,x14461),f709(x14463,x14464,x14465,x14466,x14462))
% 179.72/179.60 [1447]~E(x14471,x14472)+E(f635(x14471,x14473,x14474,x14475,x14476),f635(x14472,x14473,x14474,x14475,x14476))
% 179.72/179.60 [1448]~E(x14481,x14482)+E(f635(x14483,x14481,x14484,x14485,x14486),f635(x14483,x14482,x14484,x14485,x14486))
% 179.72/179.60 [1449]~E(x14491,x14492)+E(f635(x14493,x14494,x14491,x14495,x14496),f635(x14493,x14494,x14492,x14495,x14496))
% 179.72/179.60 [1450]~E(x14501,x14502)+E(f635(x14503,x14504,x14505,x14501,x14506),f635(x14503,x14504,x14505,x14502,x14506))
% 179.72/179.60 [1451]~E(x14511,x14512)+E(f635(x14513,x14514,x14515,x14516,x14511),f635(x14513,x14514,x14515,x14516,x14512))
% 179.72/179.60 [1452]~E(x14521,x14522)+E(f370(x14521,x14523,x14524,x14525,x14526,x14527),f370(x14522,x14523,x14524,x14525,x14526,x14527))
% 179.72/179.60 [1453]~E(x14531,x14532)+E(f370(x14533,x14531,x14534,x14535,x14536,x14537),f370(x14533,x14532,x14534,x14535,x14536,x14537))
% 179.72/179.60 [1454]~E(x14541,x14542)+E(f370(x14543,x14544,x14541,x14545,x14546,x14547),f370(x14543,x14544,x14542,x14545,x14546,x14547))
% 179.72/179.60 [1455]~E(x14551,x14552)+E(f370(x14553,x14554,x14555,x14551,x14556,x14557),f370(x14553,x14554,x14555,x14552,x14556,x14557))
% 179.72/179.60 [1456]~E(x14561,x14562)+E(f370(x14563,x14564,x14565,x14566,x14561,x14567),f370(x14563,x14564,x14565,x14566,x14562,x14567))
% 179.72/179.60 [1457]~E(x14571,x14572)+E(f370(x14573,x14574,x14575,x14576,x14577,x14571),f370(x14573,x14574,x14575,x14576,x14577,x14572))
% 179.72/179.60 [1458]~E(x14581,x14582)+E(f580(x14581,x14583),f580(x14582,x14583))
% 179.72/179.60 [1459]~E(x14591,x14592)+E(f580(x14593,x14591),f580(x14593,x14592))
% 179.72/179.60 [1460]~E(x14601,x14602)+E(f184(x14601,x14603,x14604),f184(x14602,x14603,x14604))
% 179.72/179.60 [1461]~E(x14611,x14612)+E(f184(x14613,x14611,x14614),f184(x14613,x14612,x14614))
% 179.72/179.60 [1462]~E(x14621,x14622)+E(f184(x14623,x14624,x14621),f184(x14623,x14624,x14622))
% 179.72/179.60 [1463]~E(x14631,x14632)+E(f356(x14631,x14633,x14634,x14635),f356(x14632,x14633,x14634,x14635))
% 179.72/179.60 [1464]~E(x14641,x14642)+E(f356(x14643,x14641,x14644,x14645),f356(x14643,x14642,x14644,x14645))
% 179.72/179.60 [1465]~E(x14651,x14652)+E(f356(x14653,x14654,x14651,x14655),f356(x14653,x14654,x14652,x14655))
% 179.72/179.60 [1466]~E(x14661,x14662)+E(f356(x14663,x14664,x14665,x14661),f356(x14663,x14664,x14665,x14662))
% 179.72/179.60 [1467]~E(x14671,x14672)+E(f590(x14671,x14673,x14674,x14675),f590(x14672,x14673,x14674,x14675))
% 179.72/179.60 [1468]~E(x14681,x14682)+E(f590(x14683,x14681,x14684,x14685),f590(x14683,x14682,x14684,x14685))
% 179.72/179.60 [1469]~E(x14691,x14692)+E(f590(x14693,x14694,x14691,x14695),f590(x14693,x14694,x14692,x14695))
% 179.72/179.60 [1470]~E(x14701,x14702)+E(f590(x14703,x14704,x14705,x14701),f590(x14703,x14704,x14705,x14702))
% 179.72/179.60 [1471]~E(x14711,x14712)+E(f143(x14711,x14713,x14714,x14715),f143(x14712,x14713,x14714,x14715))
% 179.72/179.60 [1472]~E(x14721,x14722)+E(f143(x14723,x14721,x14724,x14725),f143(x14723,x14722,x14724,x14725))
% 179.72/179.60 [1473]~E(x14731,x14732)+E(f143(x14733,x14734,x14731,x14735),f143(x14733,x14734,x14732,x14735))
% 179.72/179.60 [1474]~E(x14741,x14742)+E(f143(x14743,x14744,x14745,x14741),f143(x14743,x14744,x14745,x14742))
% 179.72/179.60 [1475]~E(x14751,x14752)+E(f276(x14751),f276(x14752))
% 179.72/179.60 [1476]~E(x14761,x14762)+E(f546(x14761,x14763),f546(x14762,x14763))
% 179.72/179.60 [1477]~E(x14771,x14772)+E(f546(x14773,x14771),f546(x14773,x14772))
% 179.72/179.60 [1478]~E(x14781,x14782)+E(f688(x14781,x14783,x14784),f688(x14782,x14783,x14784))
% 179.72/179.60 [1479]~E(x14791,x14792)+E(f688(x14793,x14791,x14794),f688(x14793,x14792,x14794))
% 179.72/179.60 [1480]~E(x14801,x14802)+E(f688(x14803,x14804,x14801),f688(x14803,x14804,x14802))
% 179.72/179.60 [1481]~E(x14811,x14812)+E(f362(x14811),f362(x14812))
% 179.72/179.60 [1482]~E(x14821,x14822)+E(f170(x14821,x14823,x14824),f170(x14822,x14823,x14824))
% 179.72/179.60 [1483]~E(x14831,x14832)+E(f170(x14833,x14831,x14834),f170(x14833,x14832,x14834))
% 179.72/179.60 [1484]~E(x14841,x14842)+E(f170(x14843,x14844,x14841),f170(x14843,x14844,x14842))
% 179.72/179.60 [1485]~E(x14851,x14852)+E(f285(x14851,x14853,x14854),f285(x14852,x14853,x14854))
% 179.72/179.60 [1486]~E(x14861,x14862)+E(f285(x14863,x14861,x14864),f285(x14863,x14862,x14864))
% 179.72/179.60 [1487]~E(x14871,x14872)+E(f285(x14873,x14874,x14871),f285(x14873,x14874,x14872))
% 179.72/179.60 [1488]~E(x14881,x14882)+E(f205(x14881,x14883),f205(x14882,x14883))
% 179.72/179.60 [1489]~E(x14891,x14892)+E(f205(x14893,x14891),f205(x14893,x14892))
% 179.72/179.60 [1490]~E(x14901,x14902)+E(f411(x14901,x14903,x14904,x14905),f411(x14902,x14903,x14904,x14905))
% 179.72/179.60 [1491]~E(x14911,x14912)+E(f411(x14913,x14911,x14914,x14915),f411(x14913,x14912,x14914,x14915))
% 179.72/179.60 [1492]~E(x14921,x14922)+E(f411(x14923,x14924,x14921,x14925),f411(x14923,x14924,x14922,x14925))
% 179.72/179.60 [1493]~E(x14931,x14932)+E(f411(x14933,x14934,x14935,x14931),f411(x14933,x14934,x14935,x14932))
% 179.72/179.60 [1494]~E(x14941,x14942)+E(f606(x14941,x14943),f606(x14942,x14943))
% 179.72/179.60 [1495]~E(x14951,x14952)+E(f606(x14953,x14951),f606(x14953,x14952))
% 179.72/179.60 [1496]~E(x14961,x14962)+E(f750(x14961,x14963,x14964,x14965,x14966),f750(x14962,x14963,x14964,x14965,x14966))
% 179.72/179.60 [1497]~E(x14971,x14972)+E(f750(x14973,x14971,x14974,x14975,x14976),f750(x14973,x14972,x14974,x14975,x14976))
% 179.72/179.60 [1498]~E(x14981,x14982)+E(f750(x14983,x14984,x14981,x14985,x14986),f750(x14983,x14984,x14982,x14985,x14986))
% 179.72/179.60 [1499]~E(x14991,x14992)+E(f750(x14993,x14994,x14995,x14991,x14996),f750(x14993,x14994,x14995,x14992,x14996))
% 179.72/179.60 [1500]~E(x15001,x15002)+E(f750(x15003,x15004,x15005,x15006,x15001),f750(x15003,x15004,x15005,x15006,x15002))
% 179.72/179.60 [1501]~E(x15011,x15012)+E(f588(x15011,x15013,x15014),f588(x15012,x15013,x15014))
% 179.72/179.60 [1502]~E(x15021,x15022)+E(f588(x15023,x15021,x15024),f588(x15023,x15022,x15024))
% 179.72/179.60 [1503]~E(x15031,x15032)+E(f588(x15033,x15034,x15031),f588(x15033,x15034,x15032))
% 179.72/179.60 [1504]~E(x15041,x15042)+E(f92(x15041,x15043,x15044),f92(x15042,x15043,x15044))
% 179.72/179.60 [1505]~E(x15051,x15052)+E(f92(x15053,x15051,x15054),f92(x15053,x15052,x15054))
% 179.72/179.60 [1506]~E(x15061,x15062)+E(f92(x15063,x15064,x15061),f92(x15063,x15064,x15062))
% 179.72/179.60 [1507]~E(x15071,x15072)+E(f271(x15071,x15073),f271(x15072,x15073))
% 179.72/179.60 [1508]~E(x15081,x15082)+E(f271(x15083,x15081),f271(x15083,x15082))
% 179.72/179.60 [1509]~E(x15091,x15092)+E(f584(x15091,x15093,x15094,x15095),f584(x15092,x15093,x15094,x15095))
% 179.72/179.60 [1510]~E(x15101,x15102)+E(f584(x15103,x15101,x15104,x15105),f584(x15103,x15102,x15104,x15105))
% 179.72/179.60 [1511]~E(x15111,x15112)+E(f584(x15113,x15114,x15111,x15115),f584(x15113,x15114,x15112,x15115))
% 179.72/179.60 [1512]~E(x15121,x15122)+E(f584(x15123,x15124,x15125,x15121),f584(x15123,x15124,x15125,x15122))
% 179.72/179.60 [1513]~E(x15131,x15132)+E(f692(x15131,x15133,x15134,x15135),f692(x15132,x15133,x15134,x15135))
% 179.72/179.60 [1514]~E(x15141,x15142)+E(f692(x15143,x15141,x15144,x15145),f692(x15143,x15142,x15144,x15145))
% 179.72/179.60 [1515]~E(x15151,x15152)+E(f692(x15153,x15154,x15151,x15155),f692(x15153,x15154,x15152,x15155))
% 179.72/179.60 [1516]~E(x15161,x15162)+E(f692(x15163,x15164,x15165,x15161),f692(x15163,x15164,x15165,x15162))
% 179.72/179.60 [1517]~E(x15171,x15172)+E(f690(x15171,x15173,x15174),f690(x15172,x15173,x15174))
% 179.72/179.60 [1518]~E(x15181,x15182)+E(f690(x15183,x15181,x15184),f690(x15183,x15182,x15184))
% 179.72/179.60 [1519]~E(x15191,x15192)+E(f690(x15193,x15194,x15191),f690(x15193,x15194,x15192))
% 179.72/179.60 [1520]~E(x15201,x15202)+E(f41(x15201),f41(x15202))
% 179.72/179.60 [1521]~E(x15211,x15212)+E(f814(x15211,x15213,x15214),f814(x15212,x15213,x15214))
% 179.72/179.60 [1522]~E(x15221,x15222)+E(f814(x15223,x15221,x15224),f814(x15223,x15222,x15224))
% 179.72/179.60 [1523]~E(x15231,x15232)+E(f814(x15233,x15234,x15231),f814(x15233,x15234,x15232))
% 179.72/179.60 [1524]~E(x15241,x15242)+E(f795(x15241,x15243,x15244),f795(x15242,x15243,x15244))
% 179.72/179.60 [1525]~E(x15251,x15252)+E(f795(x15253,x15251,x15254),f795(x15253,x15252,x15254))
% 179.72/179.60 [1526]~E(x15261,x15262)+E(f795(x15263,x15264,x15261),f795(x15263,x15264,x15262))
% 179.72/179.60 [1527]~E(x15271,x15272)+E(f753(x15271,x15273,x15274,x15275,x15276),f753(x15272,x15273,x15274,x15275,x15276))
% 179.72/179.60 [1528]~E(x15281,x15282)+E(f753(x15283,x15281,x15284,x15285,x15286),f753(x15283,x15282,x15284,x15285,x15286))
% 179.72/179.60 [1529]~E(x15291,x15292)+E(f753(x15293,x15294,x15291,x15295,x15296),f753(x15293,x15294,x15292,x15295,x15296))
% 179.72/179.60 [1530]~E(x15301,x15302)+E(f753(x15303,x15304,x15305,x15301,x15306),f753(x15303,x15304,x15305,x15302,x15306))
% 179.72/179.60 [1531]~E(x15311,x15312)+E(f753(x15313,x15314,x15315,x15316,x15311),f753(x15313,x15314,x15315,x15316,x15312))
% 179.72/179.60 [1532]~E(x15321,x15322)+E(f414(x15321,x15323,x15324,x15325),f414(x15322,x15323,x15324,x15325))
% 179.72/179.60 [1533]~E(x15331,x15332)+E(f414(x15333,x15331,x15334,x15335),f414(x15333,x15332,x15334,x15335))
% 179.72/179.60 [1534]~E(x15341,x15342)+E(f414(x15343,x15344,x15341,x15345),f414(x15343,x15344,x15342,x15345))
% 179.72/179.60 [1535]~E(x15351,x15352)+E(f414(x15353,x15354,x15355,x15351),f414(x15353,x15354,x15355,x15352))
% 179.72/179.60 [1536]~E(x15361,x15362)+E(f745(x15361,x15363,x15364,x15365,x15366),f745(x15362,x15363,x15364,x15365,x15366))
% 179.72/179.60 [1537]~E(x15371,x15372)+E(f745(x15373,x15371,x15374,x15375,x15376),f745(x15373,x15372,x15374,x15375,x15376))
% 179.72/179.60 [1538]~E(x15381,x15382)+E(f745(x15383,x15384,x15381,x15385,x15386),f745(x15383,x15384,x15382,x15385,x15386))
% 179.72/179.60 [1539]~E(x15391,x15392)+E(f745(x15393,x15394,x15395,x15391,x15396),f745(x15393,x15394,x15395,x15392,x15396))
% 179.72/179.60 [1540]~E(x15401,x15402)+E(f745(x15403,x15404,x15405,x15406,x15401),f745(x15403,x15404,x15405,x15406,x15402))
% 179.72/179.60 [1541]~E(x15411,x15412)+E(f844(x15411,x15413,x15414,x15415,x15416,x15417,x15418),f844(x15412,x15413,x15414,x15415,x15416,x15417,x15418))
% 179.72/179.60 [1542]~E(x15421,x15422)+E(f844(x15423,x15421,x15424,x15425,x15426,x15427,x15428),f844(x15423,x15422,x15424,x15425,x15426,x15427,x15428))
% 179.72/179.60 [1543]~E(x15431,x15432)+E(f844(x15433,x15434,x15431,x15435,x15436,x15437,x15438),f844(x15433,x15434,x15432,x15435,x15436,x15437,x15438))
% 179.72/179.60 [1544]~E(x15441,x15442)+E(f844(x15443,x15444,x15445,x15441,x15446,x15447,x15448),f844(x15443,x15444,x15445,x15442,x15446,x15447,x15448))
% 179.72/179.60 [1545]~E(x15451,x15452)+E(f844(x15453,x15454,x15455,x15456,x15451,x15457,x15458),f844(x15453,x15454,x15455,x15456,x15452,x15457,x15458))
% 179.72/179.60 [1546]~E(x15461,x15462)+E(f844(x15463,x15464,x15465,x15466,x15467,x15461,x15468),f844(x15463,x15464,x15465,x15466,x15467,x15462,x15468))
% 179.72/179.60 [1547]~E(x15471,x15472)+E(f844(x15473,x15474,x15475,x15476,x15477,x15478,x15471),f844(x15473,x15474,x15475,x15476,x15477,x15478,x15472))
% 179.72/179.60 [1548]~E(x15481,x15482)+E(f583(x15481,x15483,x15484,x15485),f583(x15482,x15483,x15484,x15485))
% 179.72/179.60 [1549]~E(x15491,x15492)+E(f583(x15493,x15491,x15494,x15495),f583(x15493,x15492,x15494,x15495))
% 179.72/179.60 [1550]~E(x15501,x15502)+E(f583(x15503,x15504,x15501,x15505),f583(x15503,x15504,x15502,x15505))
% 179.72/179.60 [1551]~E(x15511,x15512)+E(f583(x15513,x15514,x15515,x15511),f583(x15513,x15514,x15515,x15512))
% 179.72/179.60 [1552]~E(x15521,x15522)+E(f846(x15521,x15523),f846(x15522,x15523))
% 179.72/179.60 [1553]~E(x15531,x15532)+E(f846(x15533,x15531),f846(x15533,x15532))
% 179.72/179.60 [1554]~E(x15541,x15542)+E(f338(x15541,x15543),f338(x15542,x15543))
% 179.72/179.60 [1555]~E(x15551,x15552)+E(f338(x15553,x15551),f338(x15553,x15552))
% 179.72/179.60 [1556]~E(x15561,x15562)+E(f761(x15561,x15563,x15564,x15565,x15566,x15567,x15568),f761(x15562,x15563,x15564,x15565,x15566,x15567,x15568))
% 179.72/179.60 [1557]~E(x15571,x15572)+E(f761(x15573,x15571,x15574,x15575,x15576,x15577,x15578),f761(x15573,x15572,x15574,x15575,x15576,x15577,x15578))
% 179.72/179.60 [1558]~E(x15581,x15582)+E(f761(x15583,x15584,x15581,x15585,x15586,x15587,x15588),f761(x15583,x15584,x15582,x15585,x15586,x15587,x15588))
% 179.72/179.60 [1559]~E(x15591,x15592)+E(f761(x15593,x15594,x15595,x15591,x15596,x15597,x15598),f761(x15593,x15594,x15595,x15592,x15596,x15597,x15598))
% 179.72/179.60 [1560]~E(x15601,x15602)+E(f761(x15603,x15604,x15605,x15606,x15601,x15607,x15608),f761(x15603,x15604,x15605,x15606,x15602,x15607,x15608))
% 179.72/179.60 [1561]~E(x15611,x15612)+E(f761(x15613,x15614,x15615,x15616,x15617,x15611,x15618),f761(x15613,x15614,x15615,x15616,x15617,x15612,x15618))
% 179.72/179.60 [1562]~E(x15621,x15622)+E(f761(x15623,x15624,x15625,x15626,x15627,x15628,x15621),f761(x15623,x15624,x15625,x15626,x15627,x15628,x15622))
% 179.72/179.60 [1563]~E(x15631,x15632)+E(f525(x15631,x15633,x15634),f525(x15632,x15633,x15634))
% 179.72/179.60 [1564]~E(x15641,x15642)+E(f525(x15643,x15641,x15644),f525(x15643,x15642,x15644))
% 179.72/179.60 [1565]~E(x15651,x15652)+E(f525(x15653,x15654,x15651),f525(x15653,x15654,x15652))
% 179.72/179.60 [1566]~E(x15661,x15662)+E(f782(x15661,x15663),f782(x15662,x15663))
% 179.72/179.60 [1567]~E(x15671,x15672)+E(f782(x15673,x15671),f782(x15673,x15672))
% 179.72/179.60 [1568]~E(x15681,x15682)+E(f427(x15681,x15683,x15684),f427(x15682,x15683,x15684))
% 179.72/179.60 [1569]~E(x15691,x15692)+E(f427(x15693,x15691,x15694),f427(x15693,x15692,x15694))
% 179.72/179.60 [1570]~E(x15701,x15702)+E(f427(x15703,x15704,x15701),f427(x15703,x15704,x15702))
% 179.72/179.60 [1571]~E(x15711,x15712)+E(f535(x15711,x15713,x15714),f535(x15712,x15713,x15714))
% 179.72/179.60 [1572]~E(x15721,x15722)+E(f535(x15723,x15721,x15724),f535(x15723,x15722,x15724))
% 179.72/179.60 [1573]~E(x15731,x15732)+E(f535(x15733,x15734,x15731),f535(x15733,x15734,x15732))
% 179.72/179.60 [1574]~E(x15741,x15742)+E(f128(x15741),f128(x15742))
% 179.72/179.60 [1575]~E(x15751,x15752)+E(f459(x15751,x15753,x15754,x15755),f459(x15752,x15753,x15754,x15755))
% 179.72/179.60 [1576]~E(x15761,x15762)+E(f459(x15763,x15761,x15764,x15765),f459(x15763,x15762,x15764,x15765))
% 179.72/179.60 [1577]~E(x15771,x15772)+E(f459(x15773,x15774,x15771,x15775),f459(x15773,x15774,x15772,x15775))
% 179.72/179.60 [1578]~E(x15781,x15782)+E(f459(x15783,x15784,x15785,x15781),f459(x15783,x15784,x15785,x15782))
% 179.72/179.60 [1579]~E(x15791,x15792)+E(f480(x15791,x15793,x15794),f480(x15792,x15793,x15794))
% 179.72/179.60 [1580]~E(x15801,x15802)+E(f480(x15803,x15801,x15804),f480(x15803,x15802,x15804))
% 179.72/179.60 [1581]~E(x15811,x15812)+E(f480(x15813,x15814,x15811),f480(x15813,x15814,x15812))
% 179.72/179.60 [1582]~E(x15821,x15822)+E(f676(x15821,x15823,x15824,x15825),f676(x15822,x15823,x15824,x15825))
% 179.72/179.60 [1583]~E(x15831,x15832)+E(f676(x15833,x15831,x15834,x15835),f676(x15833,x15832,x15834,x15835))
% 179.72/179.60 [1584]~E(x15841,x15842)+E(f676(x15843,x15844,x15841,x15845),f676(x15843,x15844,x15842,x15845))
% 179.72/179.60 [1585]~E(x15851,x15852)+E(f676(x15853,x15854,x15855,x15851),f676(x15853,x15854,x15855,x15852))
% 179.72/179.60 [1586]~E(x15861,x15862)+E(f206(x15861),f206(x15862))
% 179.72/179.60 [1587]~E(x15871,x15872)+E(f500(x15871,x15873,x15874,x15875,x15876),f500(x15872,x15873,x15874,x15875,x15876))
% 179.72/179.60 [1588]~E(x15881,x15882)+E(f500(x15883,x15881,x15884,x15885,x15886),f500(x15883,x15882,x15884,x15885,x15886))
% 179.72/179.60 [1589]~E(x15891,x15892)+E(f500(x15893,x15894,x15891,x15895,x15896),f500(x15893,x15894,x15892,x15895,x15896))
% 179.72/179.60 [1590]~E(x15901,x15902)+E(f500(x15903,x15904,x15905,x15901,x15906),f500(x15903,x15904,x15905,x15902,x15906))
% 179.72/179.60 [1591]~E(x15911,x15912)+E(f500(x15913,x15914,x15915,x15916,x15911),f500(x15913,x15914,x15915,x15916,x15912))
% 179.72/179.60 [1592]~E(x15921,x15922)+E(f569(x15921,x15923,x15924,x15925),f569(x15922,x15923,x15924,x15925))
% 179.72/179.60 [1593]~E(x15931,x15932)+E(f569(x15933,x15931,x15934,x15935),f569(x15933,x15932,x15934,x15935))
% 179.72/179.60 [1594]~E(x15941,x15942)+E(f569(x15943,x15944,x15941,x15945),f569(x15943,x15944,x15942,x15945))
% 179.72/179.60 [1595]~E(x15951,x15952)+E(f569(x15953,x15954,x15955,x15951),f569(x15953,x15954,x15955,x15952))
% 179.72/179.60 [1596]~E(x15961,x15962)+E(f95(x15961,x15963,x15964,x15965),f95(x15962,x15963,x15964,x15965))
% 179.72/179.60 [1597]~E(x15971,x15972)+E(f95(x15973,x15971,x15974,x15975),f95(x15973,x15972,x15974,x15975))
% 179.72/179.60 [1598]~E(x15981,x15982)+E(f95(x15983,x15984,x15981,x15985),f95(x15983,x15984,x15982,x15985))
% 179.72/179.60 [1599]~E(x15991,x15992)+E(f95(x15993,x15994,x15995,x15991),f95(x15993,x15994,x15995,x15992))
% 179.72/179.60 [1600]~E(x16001,x16002)+E(f521(x16001,x16003,x16004),f521(x16002,x16003,x16004))
% 179.72/179.60 [1601]~E(x16011,x16012)+E(f521(x16013,x16011,x16014),f521(x16013,x16012,x16014))
% 179.72/179.60 [1602]~E(x16021,x16022)+E(f521(x16023,x16024,x16021),f521(x16023,x16024,x16022))
% 179.72/179.60 [1603]~E(x16031,x16032)+E(f827(x16031,x16033,x16034,x16035),f827(x16032,x16033,x16034,x16035))
% 179.72/179.60 [1604]~E(x16041,x16042)+E(f827(x16043,x16041,x16044,x16045),f827(x16043,x16042,x16044,x16045))
% 179.72/179.60 [1605]~E(x16051,x16052)+E(f827(x16053,x16054,x16051,x16055),f827(x16053,x16054,x16052,x16055))
% 179.72/179.60 [1606]~E(x16061,x16062)+E(f827(x16063,x16064,x16065,x16061),f827(x16063,x16064,x16065,x16062))
% 179.72/179.60 [1607]~E(x16071,x16072)+E(f640(x16071,x16073,x16074,x16075,x16076),f640(x16072,x16073,x16074,x16075,x16076))
% 179.72/179.60 [1608]~E(x16081,x16082)+E(f640(x16083,x16081,x16084,x16085,x16086),f640(x16083,x16082,x16084,x16085,x16086))
% 179.72/179.60 [1609]~E(x16091,x16092)+E(f640(x16093,x16094,x16091,x16095,x16096),f640(x16093,x16094,x16092,x16095,x16096))
% 179.72/179.60 [1610]~E(x16101,x16102)+E(f640(x16103,x16104,x16105,x16101,x16106),f640(x16103,x16104,x16105,x16102,x16106))
% 179.72/179.60 [1611]~E(x16111,x16112)+E(f640(x16113,x16114,x16115,x16116,x16111),f640(x16113,x16114,x16115,x16116,x16112))
% 179.72/179.60 [1612]~E(x16121,x16122)+E(f482(x16121,x16123,x16124,x16125,x16126),f482(x16122,x16123,x16124,x16125,x16126))
% 179.72/179.60 [1613]~E(x16131,x16132)+E(f482(x16133,x16131,x16134,x16135,x16136),f482(x16133,x16132,x16134,x16135,x16136))
% 179.72/179.60 [1614]~E(x16141,x16142)+E(f482(x16143,x16144,x16141,x16145,x16146),f482(x16143,x16144,x16142,x16145,x16146))
% 179.72/179.60 [1615]~E(x16151,x16152)+E(f482(x16153,x16154,x16155,x16151,x16156),f482(x16153,x16154,x16155,x16152,x16156))
% 179.72/179.60 [1616]~E(x16161,x16162)+E(f482(x16163,x16164,x16165,x16166,x16161),f482(x16163,x16164,x16165,x16166,x16162))
% 179.72/179.60 [1617]~E(x16171,x16172)+E(f413(x16171,x16173,x16174,x16175),f413(x16172,x16173,x16174,x16175))
% 179.72/179.60 [1618]~E(x16181,x16182)+E(f413(x16183,x16181,x16184,x16185),f413(x16183,x16182,x16184,x16185))
% 179.72/179.60 [1619]~E(x16191,x16192)+E(f413(x16193,x16194,x16191,x16195),f413(x16193,x16194,x16192,x16195))
% 179.72/179.60 [1620]~E(x16201,x16202)+E(f413(x16203,x16204,x16205,x16201),f413(x16203,x16204,x16205,x16202))
% 179.72/179.60 [1621]~E(x16211,x16212)+E(f457(x16211,x16213,x16214),f457(x16212,x16213,x16214))
% 179.72/179.60 [1622]~E(x16221,x16222)+E(f457(x16223,x16221,x16224),f457(x16223,x16222,x16224))
% 179.72/179.60 [1623]~E(x16231,x16232)+E(f457(x16233,x16234,x16231),f457(x16233,x16234,x16232))
% 179.72/179.60 [1624]~E(x16241,x16242)+E(f799(x16241,x16243,x16244,x16245),f799(x16242,x16243,x16244,x16245))
% 179.72/179.60 [1625]~E(x16251,x16252)+E(f799(x16253,x16251,x16254,x16255),f799(x16253,x16252,x16254,x16255))
% 179.72/179.60 [1626]~E(x16261,x16262)+E(f799(x16263,x16264,x16261,x16265),f799(x16263,x16264,x16262,x16265))
% 179.72/179.60 [1627]~E(x16271,x16272)+E(f799(x16273,x16274,x16275,x16271),f799(x16273,x16274,x16275,x16272))
% 179.72/179.60 [1628]~E(x16281,x16282)+E(f735(x16281,x16283),f735(x16282,x16283))
% 179.72/179.60 [1629]~E(x16291,x16292)+E(f735(x16293,x16291),f735(x16293,x16292))
% 179.72/179.60 [1630]~E(x16301,x16302)+E(f474(x16301,x16303,x16304,x16305,x16306),f474(x16302,x16303,x16304,x16305,x16306))
% 179.72/179.60 [1631]~E(x16311,x16312)+E(f474(x16313,x16311,x16314,x16315,x16316),f474(x16313,x16312,x16314,x16315,x16316))
% 179.72/179.60 [1632]~E(x16321,x16322)+E(f474(x16323,x16324,x16321,x16325,x16326),f474(x16323,x16324,x16322,x16325,x16326))
% 179.72/179.60 [1633]~E(x16331,x16332)+E(f474(x16333,x16334,x16335,x16331,x16336),f474(x16333,x16334,x16335,x16332,x16336))
% 179.72/179.60 [1634]~E(x16341,x16342)+E(f474(x16343,x16344,x16345,x16346,x16341),f474(x16343,x16344,x16345,x16346,x16342))
% 179.72/179.60 [1635]~E(x16351,x16352)+E(f582(x16351,x16353,x16354),f582(x16352,x16353,x16354))
% 179.72/179.60 [1636]~E(x16361,x16362)+E(f582(x16363,x16361,x16364),f582(x16363,x16362,x16364))
% 179.72/179.60 [1637]~E(x16371,x16372)+E(f582(x16373,x16374,x16371),f582(x16373,x16374,x16372))
% 179.72/179.60 [1638]~E(x16381,x16382)+E(f728(x16381,x16383,x16384),f728(x16382,x16383,x16384))
% 179.72/179.60 [1639]~E(x16391,x16392)+E(f728(x16393,x16391,x16394),f728(x16393,x16392,x16394))
% 179.72/179.60 [1640]~E(x16401,x16402)+E(f728(x16403,x16404,x16401),f728(x16403,x16404,x16402))
% 179.72/179.60 [1641]~E(x16411,x16412)+E(f812(x16411,x16413),f812(x16412,x16413))
% 179.72/179.60 [1642]~E(x16421,x16422)+E(f812(x16423,x16421),f812(x16423,x16422))
% 179.72/179.60 [1643]~E(x16431,x16432)+E(f376(x16431,x16433),f376(x16432,x16433))
% 179.72/179.60 [1644]~E(x16441,x16442)+E(f376(x16443,x16441),f376(x16443,x16442))
% 179.72/179.60 [1645]~E(x16451,x16452)+E(f450(x16451,x16453,x16454,x16455,x16456),f450(x16452,x16453,x16454,x16455,x16456))
% 179.72/179.60 [1646]~E(x16461,x16462)+E(f450(x16463,x16461,x16464,x16465,x16466),f450(x16463,x16462,x16464,x16465,x16466))
% 179.72/179.60 [1647]~E(x16471,x16472)+E(f450(x16473,x16474,x16471,x16475,x16476),f450(x16473,x16474,x16472,x16475,x16476))
% 179.72/179.60 [1648]~E(x16481,x16482)+E(f450(x16483,x16484,x16485,x16481,x16486),f450(x16483,x16484,x16485,x16482,x16486))
% 179.72/179.60 [1649]~E(x16491,x16492)+E(f450(x16493,x16494,x16495,x16496,x16491),f450(x16493,x16494,x16495,x16496,x16492))
% 179.72/179.60 [1650]~E(x16501,x16502)+E(f404(x16501,x16503,x16504,x16505),f404(x16502,x16503,x16504,x16505))
% 179.72/179.60 [1651]~E(x16511,x16512)+E(f404(x16513,x16511,x16514,x16515),f404(x16513,x16512,x16514,x16515))
% 179.72/179.60 [1652]~E(x16521,x16522)+E(f404(x16523,x16524,x16521,x16525),f404(x16523,x16524,x16522,x16525))
% 179.72/179.60 [1653]~E(x16531,x16532)+E(f404(x16533,x16534,x16535,x16531),f404(x16533,x16534,x16535,x16532))
% 179.72/179.60 [1654]~E(x16541,x16542)+E(f479(x16541,x16543,x16544),f479(x16542,x16543,x16544))
% 179.72/179.60 [1655]~E(x16551,x16552)+E(f479(x16553,x16551,x16554),f479(x16553,x16552,x16554))
% 179.72/179.60 [1656]~E(x16561,x16562)+E(f479(x16563,x16564,x16561),f479(x16563,x16564,x16562))
% 179.72/179.60 [1657]~E(x16571,x16572)+E(f562(x16571,x16573,x16574),f562(x16572,x16573,x16574))
% 179.72/179.60 [1658]~E(x16581,x16582)+E(f562(x16583,x16581,x16584),f562(x16583,x16582,x16584))
% 179.72/179.60 [1659]~E(x16591,x16592)+E(f562(x16593,x16594,x16591),f562(x16593,x16594,x16592))
% 179.72/179.60 [1660]~E(x16601,x16602)+E(f713(x16601,x16603,x16604),f713(x16602,x16603,x16604))
% 179.72/179.60 [1661]~E(x16611,x16612)+E(f713(x16613,x16611,x16614),f713(x16613,x16612,x16614))
% 179.72/179.60 [1662]~E(x16621,x16622)+E(f713(x16623,x16624,x16621),f713(x16623,x16624,x16622))
% 179.72/179.60 [1663]~E(x16631,x16632)+E(f828(x16631,x16633,x16634,x16635),f828(x16632,x16633,x16634,x16635))
% 179.72/179.60 [1664]~E(x16641,x16642)+E(f828(x16643,x16641,x16644,x16645),f828(x16643,x16642,x16644,x16645))
% 179.72/179.60 [1665]~E(x16651,x16652)+E(f828(x16653,x16654,x16651,x16655),f828(x16653,x16654,x16652,x16655))
% 179.72/179.60 [1666]~E(x16661,x16662)+E(f828(x16663,x16664,x16665,x16661),f828(x16663,x16664,x16665,x16662))
% 179.72/179.60 [1667]~E(x16671,x16672)+E(f834(x16671,x16673,x16674,x16675,x16676),f834(x16672,x16673,x16674,x16675,x16676))
% 179.72/179.60 [1668]~E(x16681,x16682)+E(f834(x16683,x16681,x16684,x16685,x16686),f834(x16683,x16682,x16684,x16685,x16686))
% 179.72/179.60 [1669]~E(x16691,x16692)+E(f834(x16693,x16694,x16691,x16695,x16696),f834(x16693,x16694,x16692,x16695,x16696))
% 179.72/179.60 [1670]~E(x16701,x16702)+E(f834(x16703,x16704,x16705,x16701,x16706),f834(x16703,x16704,x16705,x16702,x16706))
% 179.72/179.60 [1671]~E(x16711,x16712)+E(f834(x16713,x16714,x16715,x16716,x16711),f834(x16713,x16714,x16715,x16716,x16712))
% 179.72/179.60 [1672]~E(x16721,x16722)+E(f406(x16721,x16723,x16724,x16725),f406(x16722,x16723,x16724,x16725))
% 179.72/179.60 [1673]~E(x16731,x16732)+E(f406(x16733,x16731,x16734,x16735),f406(x16733,x16732,x16734,x16735))
% 179.72/179.60 [1674]~E(x16741,x16742)+E(f406(x16743,x16744,x16741,x16745),f406(x16743,x16744,x16742,x16745))
% 179.72/179.60 [1675]~E(x16751,x16752)+E(f406(x16753,x16754,x16755,x16751),f406(x16753,x16754,x16755,x16752))
% 179.72/179.60 [1676]~E(x16761,x16762)+E(f558(x16761,x16763,x16764,x16765),f558(x16762,x16763,x16764,x16765))
% 179.72/179.60 [1677]~E(x16771,x16772)+E(f558(x16773,x16771,x16774,x16775),f558(x16773,x16772,x16774,x16775))
% 179.72/179.60 [1678]~E(x16781,x16782)+E(f558(x16783,x16784,x16781,x16785),f558(x16783,x16784,x16782,x16785))
% 179.72/179.60 [1679]~E(x16791,x16792)+E(f558(x16793,x16794,x16795,x16791),f558(x16793,x16794,x16795,x16792))
% 179.72/179.60 [1680]~E(x16801,x16802)+E(f541(x16801,x16803,x16804),f541(x16802,x16803,x16804))
% 179.72/179.60 [1681]~E(x16811,x16812)+E(f541(x16813,x16811,x16814),f541(x16813,x16812,x16814))
% 179.72/179.60 [1682]~E(x16821,x16822)+E(f541(x16823,x16824,x16821),f541(x16823,x16824,x16822))
% 179.72/179.60 [1683]~E(x16831,x16832)+E(f552(x16831,x16833,x16834,x16835,x16836),f552(x16832,x16833,x16834,x16835,x16836))
% 179.72/179.60 [1684]~E(x16841,x16842)+E(f552(x16843,x16841,x16844,x16845,x16846),f552(x16843,x16842,x16844,x16845,x16846))
% 179.72/179.60 [1685]~E(x16851,x16852)+E(f552(x16853,x16854,x16851,x16855,x16856),f552(x16853,x16854,x16852,x16855,x16856))
% 179.72/179.60 [1686]~E(x16861,x16862)+E(f552(x16863,x16864,x16865,x16861,x16866),f552(x16863,x16864,x16865,x16862,x16866))
% 179.72/179.60 [1687]~E(x16871,x16872)+E(f552(x16873,x16874,x16875,x16876,x16871),f552(x16873,x16874,x16875,x16876,x16872))
% 179.72/179.60 [1688]~E(x16881,x16882)+E(f545(x16881,x16883,x16884),f545(x16882,x16883,x16884))
% 179.72/179.60 [1689]~E(x16891,x16892)+E(f545(x16893,x16891,x16894),f545(x16893,x16892,x16894))
% 179.72/179.60 [1690]~E(x16901,x16902)+E(f545(x16903,x16904,x16901),f545(x16903,x16904,x16902))
% 179.72/179.60 [1691]~E(x16911,x16912)+E(f426(x16911,x16913,x16914),f426(x16912,x16913,x16914))
% 179.72/179.60 [1692]~E(x16921,x16922)+E(f426(x16923,x16921,x16924),f426(x16923,x16922,x16924))
% 179.72/179.60 [1693]~E(x16931,x16932)+E(f426(x16933,x16934,x16931),f426(x16933,x16934,x16932))
% 179.72/179.60 [1694]~E(x16941,x16942)+E(f830(x16941,x16943,x16944,x16945,x16946,x16947),f830(x16942,x16943,x16944,x16945,x16946,x16947))
% 179.72/179.60 [1695]~E(x16951,x16952)+E(f830(x16953,x16951,x16954,x16955,x16956,x16957),f830(x16953,x16952,x16954,x16955,x16956,x16957))
% 179.72/179.60 [1696]~E(x16961,x16962)+E(f830(x16963,x16964,x16961,x16965,x16966,x16967),f830(x16963,x16964,x16962,x16965,x16966,x16967))
% 179.72/179.60 [1697]~E(x16971,x16972)+E(f830(x16973,x16974,x16975,x16971,x16976,x16977),f830(x16973,x16974,x16975,x16972,x16976,x16977))
% 179.72/179.60 [1698]~E(x16981,x16982)+E(f830(x16983,x16984,x16985,x16986,x16981,x16987),f830(x16983,x16984,x16985,x16986,x16982,x16987))
% 179.72/179.60 [1699]~E(x16991,x16992)+E(f830(x16993,x16994,x16995,x16996,x16997,x16991),f830(x16993,x16994,x16995,x16996,x16997,x16992))
% 179.72/179.60 [1700]~E(x17001,x17002)+E(f641(x17001,x17003,x17004,x17005,x17006,x17007,x17008),f641(x17002,x17003,x17004,x17005,x17006,x17007,x17008))
% 179.72/179.60 [1701]~E(x17011,x17012)+E(f641(x17013,x17011,x17014,x17015,x17016,x17017,x17018),f641(x17013,x17012,x17014,x17015,x17016,x17017,x17018))
% 179.72/179.60 [1702]~E(x17021,x17022)+E(f641(x17023,x17024,x17021,x17025,x17026,x17027,x17028),f641(x17023,x17024,x17022,x17025,x17026,x17027,x17028))
% 179.72/179.60 [1703]~E(x17031,x17032)+E(f641(x17033,x17034,x17035,x17031,x17036,x17037,x17038),f641(x17033,x17034,x17035,x17032,x17036,x17037,x17038))
% 179.72/179.60 [1704]~E(x17041,x17042)+E(f641(x17043,x17044,x17045,x17046,x17041,x17047,x17048),f641(x17043,x17044,x17045,x17046,x17042,x17047,x17048))
% 179.72/179.60 [1705]~E(x17051,x17052)+E(f641(x17053,x17054,x17055,x17056,x17057,x17051,x17058),f641(x17053,x17054,x17055,x17056,x17057,x17052,x17058))
% 179.72/179.60 [1706]~E(x17061,x17062)+E(f641(x17063,x17064,x17065,x17066,x17067,x17068,x17061),f641(x17063,x17064,x17065,x17066,x17067,x17068,x17062))
% 179.72/179.60 [1707]~E(x17071,x17072)+E(f705(x17071,x17073,x17074,x17075,x17076),f705(x17072,x17073,x17074,x17075,x17076))
% 179.72/179.60 [1708]~E(x17081,x17082)+E(f705(x17083,x17081,x17084,x17085,x17086),f705(x17083,x17082,x17084,x17085,x17086))
% 179.72/179.60 [1709]~E(x17091,x17092)+E(f705(x17093,x17094,x17091,x17095,x17096),f705(x17093,x17094,x17092,x17095,x17096))
% 179.72/179.60 [1710]~E(x17101,x17102)+E(f705(x17103,x17104,x17105,x17101,x17106),f705(x17103,x17104,x17105,x17102,x17106))
% 179.72/179.60 [1711]~E(x17111,x17112)+E(f705(x17113,x17114,x17115,x17116,x17111),f705(x17113,x17114,x17115,x17116,x17112))
% 179.72/179.60 [1712]~E(x17121,x17122)+E(f157(x17121,x17123,x17124,x17125),f157(x17122,x17123,x17124,x17125))
% 179.72/179.60 [1713]~E(x17131,x17132)+E(f157(x17133,x17131,x17134,x17135),f157(x17133,x17132,x17134,x17135))
% 179.72/179.60 [1714]~E(x17141,x17142)+E(f157(x17143,x17144,x17141,x17145),f157(x17143,x17144,x17142,x17145))
% 179.72/179.60 [1715]~E(x17151,x17152)+E(f157(x17153,x17154,x17155,x17151),f157(x17153,x17154,x17155,x17152))
% 179.72/179.60 [1716]~E(x17161,x17162)+E(f829(x17161,x17163,x17164,x17165),f829(x17162,x17163,x17164,x17165))
% 179.72/179.60 [1717]~E(x17171,x17172)+E(f829(x17173,x17171,x17174,x17175),f829(x17173,x17172,x17174,x17175))
% 179.72/179.60 [1718]~E(x17181,x17182)+E(f829(x17183,x17184,x17181,x17185),f829(x17183,x17184,x17182,x17185))
% 179.72/179.60 [1719]~E(x17191,x17192)+E(f829(x17193,x17194,x17195,x17191),f829(x17193,x17194,x17195,x17192))
% 179.72/179.60 [1720]~E(x17201,x17202)+E(f361(x17201,x17203,x17204,x17205,x17206),f361(x17202,x17203,x17204,x17205,x17206))
% 179.72/179.60 [1721]~E(x17211,x17212)+E(f361(x17213,x17211,x17214,x17215,x17216),f361(x17213,x17212,x17214,x17215,x17216))
% 179.72/179.60 [1722]~E(x17221,x17222)+E(f361(x17223,x17224,x17221,x17225,x17226),f361(x17223,x17224,x17222,x17225,x17226))
% 179.72/179.60 [1723]~E(x17231,x17232)+E(f361(x17233,x17234,x17235,x17231,x17236),f361(x17233,x17234,x17235,x17232,x17236))
% 179.72/179.60 [1724]~E(x17241,x17242)+E(f361(x17243,x17244,x17245,x17246,x17241),f361(x17243,x17244,x17245,x17246,x17242))
% 179.72/179.60 [1725]~E(x17251,x17252)+E(f657(x17251,x17253,x17254,x17255,x17256),f657(x17252,x17253,x17254,x17255,x17256))
% 179.72/179.60 [1726]~E(x17261,x17262)+E(f657(x17263,x17261,x17264,x17265,x17266),f657(x17263,x17262,x17264,x17265,x17266))
% 179.72/179.60 [1727]~E(x17271,x17272)+E(f657(x17273,x17274,x17271,x17275,x17276),f657(x17273,x17274,x17272,x17275,x17276))
% 179.72/179.60 [1728]~E(x17281,x17282)+E(f657(x17283,x17284,x17285,x17281,x17286),f657(x17283,x17284,x17285,x17282,x17286))
% 179.72/179.60 [1729]~E(x17291,x17292)+E(f657(x17293,x17294,x17295,x17296,x17291),f657(x17293,x17294,x17295,x17296,x17292))
% 179.72/179.60 [1730]~E(x17301,x17302)+E(f813(x17301,x17303,x17304),f813(x17302,x17303,x17304))
% 179.72/179.60 [1731]~E(x17311,x17312)+E(f813(x17313,x17311,x17314),f813(x17313,x17312,x17314))
% 179.72/179.60 [1732]~E(x17321,x17322)+E(f813(x17323,x17324,x17321),f813(x17323,x17324,x17322))
% 179.72/179.60 [1733]~E(x17331,x17332)+E(f663(x17331,x17333),f663(x17332,x17333))
% 179.72/179.60 [1734]~E(x17341,x17342)+E(f663(x17343,x17341),f663(x17343,x17342))
% 179.72/179.60 [1735]~E(x17351,x17352)+E(f778(x17351,x17353,x17354,x17355),f778(x17352,x17353,x17354,x17355))
% 179.72/179.60 [1736]~E(x17361,x17362)+E(f778(x17363,x17361,x17364,x17365),f778(x17363,x17362,x17364,x17365))
% 179.72/179.60 [1737]~E(x17371,x17372)+E(f778(x17373,x17374,x17371,x17375),f778(x17373,x17374,x17372,x17375))
% 179.72/179.60 [1738]~E(x17381,x17382)+E(f778(x17383,x17384,x17385,x17381),f778(x17383,x17384,x17385,x17382))
% 179.72/179.60 [1739]~E(x17391,x17392)+E(f415(x17391,x17393,x17394,x17395),f415(x17392,x17393,x17394,x17395))
% 179.72/179.60 [1740]~E(x17401,x17402)+E(f415(x17403,x17401,x17404,x17405),f415(x17403,x17402,x17404,x17405))
% 179.72/179.60 [1741]~E(x17411,x17412)+E(f415(x17413,x17414,x17411,x17415),f415(x17413,x17414,x17412,x17415))
% 179.72/179.60 [1742]~E(x17421,x17422)+E(f415(x17423,x17424,x17425,x17421),f415(x17423,x17424,x17425,x17422))
% 179.72/179.60 [1743]~E(x17431,x17432)+E(f391(x17431,x17433,x17434,x17435),f391(x17432,x17433,x17434,x17435))
% 179.72/179.60 [1744]~E(x17441,x17442)+E(f391(x17443,x17441,x17444,x17445),f391(x17443,x17442,x17444,x17445))
% 179.72/179.60 [1745]~E(x17451,x17452)+E(f391(x17453,x17454,x17451,x17455),f391(x17453,x17454,x17452,x17455))
% 179.72/179.60 [1746]~E(x17461,x17462)+E(f391(x17463,x17464,x17465,x17461),f391(x17463,x17464,x17465,x17462))
% 179.72/179.60 [1747]~E(x17471,x17472)+E(f207(x17471,x17473,x17474,x17475),f207(x17472,x17473,x17474,x17475))
% 179.72/179.60 [1748]~E(x17481,x17482)+E(f207(x17483,x17481,x17484,x17485),f207(x17483,x17482,x17484,x17485))
% 179.72/179.60 [1749]~E(x17491,x17492)+E(f207(x17493,x17494,x17491,x17495),f207(x17493,x17494,x17492,x17495))
% 179.72/179.60 [1750]~E(x17501,x17502)+E(f207(x17503,x17504,x17505,x17501),f207(x17503,x17504,x17505,x17502))
% 179.72/179.60 [1751]~E(x17511,x17512)+E(f554(x17511,x17513,x17514),f554(x17512,x17513,x17514))
% 179.72/179.60 [1752]~E(x17521,x17522)+E(f554(x17523,x17521,x17524),f554(x17523,x17522,x17524))
% 179.72/179.60 [1753]~E(x17531,x17532)+E(f554(x17533,x17534,x17531),f554(x17533,x17534,x17532))
% 179.72/179.60 [1754]~E(x17541,x17542)+E(f250(x17541,x17543,x17544),f250(x17542,x17543,x17544))
% 179.72/179.60 [1755]~E(x17551,x17552)+E(f250(x17553,x17551,x17554),f250(x17553,x17552,x17554))
% 179.72/179.60 [1756]~E(x17561,x17562)+E(f250(x17563,x17564,x17561),f250(x17563,x17564,x17562))
% 179.72/179.60 [1757]~E(x17571,x17572)+E(f567(x17571,x17573,x17574),f567(x17572,x17573,x17574))
% 179.72/179.60 [1758]~E(x17581,x17582)+E(f567(x17583,x17581,x17584),f567(x17583,x17582,x17584))
% 179.72/179.60 [1759]~E(x17591,x17592)+E(f567(x17593,x17594,x17591),f567(x17593,x17594,x17592))
% 179.72/179.60 [1760]~E(x17601,x17602)+E(f612(x17601,x17603,x17604),f612(x17602,x17603,x17604))
% 179.72/179.60 [1761]~E(x17611,x17612)+E(f612(x17613,x17611,x17614),f612(x17613,x17612,x17614))
% 179.72/179.60 [1762]~E(x17621,x17622)+E(f612(x17623,x17624,x17621),f612(x17623,x17624,x17622))
% 179.72/179.60 [1763]~E(x17631,x17632)+E(f496(x17631,x17633,x17634),f496(x17632,x17633,x17634))
% 179.72/179.60 [1764]~E(x17641,x17642)+E(f496(x17643,x17641,x17644),f496(x17643,x17642,x17644))
% 179.72/179.60 [1765]~E(x17651,x17652)+E(f496(x17653,x17654,x17651),f496(x17653,x17654,x17652))
% 179.72/179.60 [1766]~E(x17661,x17662)+E(f342(x17661,x17663),f342(x17662,x17663))
% 179.72/179.60 [1767]~E(x17671,x17672)+E(f342(x17673,x17671),f342(x17673,x17672))
% 179.72/179.60 [1768]~E(x17681,x17682)+E(f777(x17681,x17683,x17684,x17685,x17686,x17687),f777(x17682,x17683,x17684,x17685,x17686,x17687))
% 179.72/179.60 [1769]~E(x17691,x17692)+E(f777(x17693,x17691,x17694,x17695,x17696,x17697),f777(x17693,x17692,x17694,x17695,x17696,x17697))
% 179.72/179.60 [1770]~E(x17701,x17702)+E(f777(x17703,x17704,x17701,x17705,x17706,x17707),f777(x17703,x17704,x17702,x17705,x17706,x17707))
% 179.72/179.60 [1771]~E(x17711,x17712)+E(f777(x17713,x17714,x17715,x17711,x17716,x17717),f777(x17713,x17714,x17715,x17712,x17716,x17717))
% 179.72/179.60 [1772]~E(x17721,x17722)+E(f777(x17723,x17724,x17725,x17726,x17721,x17727),f777(x17723,x17724,x17725,x17726,x17722,x17727))
% 179.72/179.60 [1773]~E(x17731,x17732)+E(f777(x17733,x17734,x17735,x17736,x17737,x17731),f777(x17733,x17734,x17735,x17736,x17737,x17732))
% 179.72/179.60 [1774]~E(x17741,x17742)+E(f699(x17741,x17743,x17744,x17745,x17746),f699(x17742,x17743,x17744,x17745,x17746))
% 179.72/179.60 [1775]~E(x17751,x17752)+E(f699(x17753,x17751,x17754,x17755,x17756),f699(x17753,x17752,x17754,x17755,x17756))
% 179.72/179.60 [1776]~E(x17761,x17762)+E(f699(x17763,x17764,x17761,x17765,x17766),f699(x17763,x17764,x17762,x17765,x17766))
% 179.72/179.60 [1777]~E(x17771,x17772)+E(f699(x17773,x17774,x17775,x17771,x17776),f699(x17773,x17774,x17775,x17772,x17776))
% 179.72/179.60 [1778]~E(x17781,x17782)+E(f699(x17783,x17784,x17785,x17786,x17781),f699(x17783,x17784,x17785,x17786,x17782))
% 179.72/179.60 [1779]~E(x17791,x17792)+E(f512(x17791,x17793,x17794),f512(x17792,x17793,x17794))
% 179.72/179.60 [1780]~E(x17801,x17802)+E(f512(x17803,x17801,x17804),f512(x17803,x17802,x17804))
% 179.72/179.60 [1781]~E(x17811,x17812)+E(f512(x17813,x17814,x17811),f512(x17813,x17814,x17812))
% 179.72/179.60 [1782]~E(x17821,x17822)+E(f632(x17821,x17823,x17824,x17825),f632(x17822,x17823,x17824,x17825))
% 179.72/179.60 [1783]~E(x17831,x17832)+E(f632(x17833,x17831,x17834,x17835),f632(x17833,x17832,x17834,x17835))
% 179.72/179.60 [1784]~E(x17841,x17842)+E(f632(x17843,x17844,x17841,x17845),f632(x17843,x17844,x17842,x17845))
% 179.72/179.60 [1785]~E(x17851,x17852)+E(f632(x17853,x17854,x17855,x17851),f632(x17853,x17854,x17855,x17852))
% 179.72/179.60 [1786]~E(x17861,x17862)+E(f516(x17861,x17863,x17864,x17865),f516(x17862,x17863,x17864,x17865))
% 179.72/179.60 [1787]~E(x17871,x17872)+E(f516(x17873,x17871,x17874,x17875),f516(x17873,x17872,x17874,x17875))
% 179.72/179.60 [1788]~E(x17881,x17882)+E(f516(x17883,x17884,x17881,x17885),f516(x17883,x17884,x17882,x17885))
% 179.72/179.60 [1789]~E(x17891,x17892)+E(f516(x17893,x17894,x17895,x17891),f516(x17893,x17894,x17895,x17892))
% 179.72/179.60 [1790]~E(x17901,x17902)+E(f551(x17901,x17903,x17904),f551(x17902,x17903,x17904))
% 179.72/179.60 [1791]~E(x17911,x17912)+E(f551(x17913,x17911,x17914),f551(x17913,x17912,x17914))
% 179.72/179.60 [1792]~E(x17921,x17922)+E(f551(x17923,x17924,x17921),f551(x17923,x17924,x17922))
% 179.72/179.60 [1793]~E(x17931,x17932)+E(f738(x17931,x17933,x17934,x17935,x17936),f738(x17932,x17933,x17934,x17935,x17936))
% 179.72/179.60 [1794]~E(x17941,x17942)+E(f738(x17943,x17941,x17944,x17945,x17946),f738(x17943,x17942,x17944,x17945,x17946))
% 179.72/179.60 [1795]~E(x17951,x17952)+E(f738(x17953,x17954,x17951,x17955,x17956),f738(x17953,x17954,x17952,x17955,x17956))
% 179.72/179.60 [1796]~E(x17961,x17962)+E(f738(x17963,x17964,x17965,x17961,x17966),f738(x17963,x17964,x17965,x17962,x17966))
% 179.72/179.60 [1797]~E(x17971,x17972)+E(f738(x17973,x17974,x17975,x17976,x17971),f738(x17973,x17974,x17975,x17976,x17972))
% 179.72/179.60 [1798]~E(x17981,x17982)+E(f471(x17981,x17983,x17984,x17985),f471(x17982,x17983,x17984,x17985))
% 179.72/179.60 [1799]~E(x17991,x17992)+E(f471(x17993,x17991,x17994,x17995),f471(x17993,x17992,x17994,x17995))
% 179.72/179.60 [1800]~E(x18001,x18002)+E(f471(x18003,x18004,x18001,x18005),f471(x18003,x18004,x18002,x18005))
% 179.72/179.60 [1801]~E(x18011,x18012)+E(f471(x18013,x18014,x18015,x18011),f471(x18013,x18014,x18015,x18012))
% 179.72/179.60 [1802]~E(x18021,x18022)+E(f495(x18021,x18023,x18024),f495(x18022,x18023,x18024))
% 179.72/179.60 [1803]~E(x18031,x18032)+E(f495(x18033,x18031,x18034),f495(x18033,x18032,x18034))
% 179.72/179.60 [1804]~E(x18041,x18042)+E(f495(x18043,x18044,x18041),f495(x18043,x18044,x18042))
% 179.72/179.60 [1805]~E(x18051,x18052)+E(f656(x18051,x18053,x18054,x18055,x18056),f656(x18052,x18053,x18054,x18055,x18056))
% 179.72/179.60 [1806]~E(x18061,x18062)+E(f656(x18063,x18061,x18064,x18065,x18066),f656(x18063,x18062,x18064,x18065,x18066))
% 179.72/179.60 [1807]~E(x18071,x18072)+E(f656(x18073,x18074,x18071,x18075,x18076),f656(x18073,x18074,x18072,x18075,x18076))
% 179.72/179.60 [1808]~E(x18081,x18082)+E(f656(x18083,x18084,x18085,x18081,x18086),f656(x18083,x18084,x18085,x18082,x18086))
% 179.72/179.60 [1809]~E(x18091,x18092)+E(f656(x18093,x18094,x18095,x18096,x18091),f656(x18093,x18094,x18095,x18096,x18092))
% 179.72/179.60 [1810]~E(x18101,x18102)+E(f610(x18101,x18103),f610(x18102,x18103))
% 179.72/179.60 [1811]~E(x18111,x18112)+E(f610(x18113,x18111),f610(x18113,x18112))
% 179.72/179.60 [1812]~E(x18121,x18122)+E(f513(x18121,x18123,x18124),f513(x18122,x18123,x18124))
% 179.72/179.60 [1813]~E(x18131,x18132)+E(f513(x18133,x18131,x18134),f513(x18133,x18132,x18134))
% 179.72/179.60 [1814]~E(x18141,x18142)+E(f513(x18143,x18144,x18141),f513(x18143,x18144,x18142))
% 179.72/179.60 [1815]~E(x18151,x18152)+E(f274(x18151,x18153),f274(x18152,x18153))
% 179.72/179.60 [1816]~E(x18161,x18162)+E(f274(x18163,x18161),f274(x18163,x18162))
% 179.72/179.60 [1817]~E(x18171,x18172)+E(f615(x18171,x18173,x18174),f615(x18172,x18173,x18174))
% 179.72/179.60 [1818]~E(x18181,x18182)+E(f615(x18183,x18181,x18184),f615(x18183,x18182,x18184))
% 179.72/179.60 [1819]~E(x18191,x18192)+E(f615(x18193,x18194,x18191),f615(x18193,x18194,x18192))
% 179.72/179.60 [1820]~E(x18201,x18202)+E(f611(x18201,x18203),f611(x18202,x18203))
% 179.72/179.60 [1821]~E(x18211,x18212)+E(f611(x18213,x18211),f611(x18213,x18212))
% 179.72/179.60 [1822]~E(x18221,x18222)+E(f307(x18221,x18223,x18224),f307(x18222,x18223,x18224))
% 179.72/179.60 [1823]~E(x18231,x18232)+E(f307(x18233,x18231,x18234),f307(x18233,x18232,x18234))
% 179.72/179.60 [1824]~E(x18241,x18242)+E(f307(x18243,x18244,x18241),f307(x18243,x18244,x18242))
% 179.72/179.60 [1825]~E(x18251,x18252)+E(f559(x18251,x18253),f559(x18252,x18253))
% 179.72/179.60 [1826]~E(x18261,x18262)+E(f559(x18263,x18261),f559(x18263,x18262))
% 179.72/179.60 [1827]~E(x18271,x18272)+E(f847(x18271,x18273,x18274),f847(x18272,x18273,x18274))
% 179.72/179.60 [1828]~E(x18281,x18282)+E(f847(x18283,x18281,x18284),f847(x18283,x18282,x18284))
% 179.72/179.60 [1829]~E(x18291,x18292)+E(f847(x18293,x18294,x18291),f847(x18293,x18294,x18292))
% 179.72/179.60 [1830]~E(x18301,x18302)+E(f209(x18301,x18303,x18304,x18305,x18306,x18307,x18308),f209(x18302,x18303,x18304,x18305,x18306,x18307,x18308))
% 179.72/179.60 [1831]~E(x18311,x18312)+E(f209(x18313,x18311,x18314,x18315,x18316,x18317,x18318),f209(x18313,x18312,x18314,x18315,x18316,x18317,x18318))
% 179.72/179.60 [1832]~E(x18321,x18322)+E(f209(x18323,x18324,x18321,x18325,x18326,x18327,x18328),f209(x18323,x18324,x18322,x18325,x18326,x18327,x18328))
% 179.72/179.60 [1833]~E(x18331,x18332)+E(f209(x18333,x18334,x18335,x18331,x18336,x18337,x18338),f209(x18333,x18334,x18335,x18332,x18336,x18337,x18338))
% 179.72/179.60 [1834]~E(x18341,x18342)+E(f209(x18343,x18344,x18345,x18346,x18341,x18347,x18348),f209(x18343,x18344,x18345,x18346,x18342,x18347,x18348))
% 179.72/179.60 [1835]~E(x18351,x18352)+E(f209(x18353,x18354,x18355,x18356,x18357,x18351,x18358),f209(x18353,x18354,x18355,x18356,x18357,x18352,x18358))
% 179.72/179.60 [1836]~E(x18361,x18362)+E(f209(x18363,x18364,x18365,x18366,x18367,x18368,x18361),f209(x18363,x18364,x18365,x18366,x18367,x18368,x18362))
% 179.72/179.60 [1837]~E(x18371,x18372)+E(f329(x18371),f329(x18372))
% 179.72/179.60 [1838]~E(x18381,x18382)+E(f593(x18381,x18383,x18384,x18385,x18386),f593(x18382,x18383,x18384,x18385,x18386))
% 179.72/179.60 [1839]~E(x18391,x18392)+E(f593(x18393,x18391,x18394,x18395,x18396),f593(x18393,x18392,x18394,x18395,x18396))
% 179.72/179.60 [1840]~E(x18401,x18402)+E(f593(x18403,x18404,x18401,x18405,x18406),f593(x18403,x18404,x18402,x18405,x18406))
% 179.72/179.60 [1841]~E(x18411,x18412)+E(f593(x18413,x18414,x18415,x18411,x18416),f593(x18413,x18414,x18415,x18412,x18416))
% 179.72/179.60 [1842]~E(x18421,x18422)+E(f593(x18423,x18424,x18425,x18426,x18421),f593(x18423,x18424,x18425,x18426,x18422))
% 179.72/179.60 [1843]~E(x18431,x18432)+E(f825(x18431,x18433),f825(x18432,x18433))
% 179.72/179.60 [1844]~E(x18441,x18442)+E(f825(x18443,x18441),f825(x18443,x18442))
% 179.72/179.60 [1845]~E(x18451,x18452)+E(f275(x18451,x18453,x18454,x18455),f275(x18452,x18453,x18454,x18455))
% 179.72/179.60 [1846]~E(x18461,x18462)+E(f275(x18463,x18461,x18464,x18465),f275(x18463,x18462,x18464,x18465))
% 179.72/179.60 [1847]~E(x18471,x18472)+E(f275(x18473,x18474,x18471,x18475),f275(x18473,x18474,x18472,x18475))
% 179.72/179.60 [1848]~E(x18481,x18482)+E(f275(x18483,x18484,x18485,x18481),f275(x18483,x18484,x18485,x18482))
% 179.72/179.60 [1849]~E(x18491,x18492)+E(f646(x18491,x18493),f646(x18492,x18493))
% 179.72/179.60 [1850]~E(x18501,x18502)+E(f646(x18503,x18501),f646(x18503,x18502))
% 179.72/179.60 [1851]~E(x18511,x18512)+E(f642(x18511,x18513,x18514),f642(x18512,x18513,x18514))
% 179.72/179.60 [1852]~E(x18521,x18522)+E(f642(x18523,x18521,x18524),f642(x18523,x18522,x18524))
% 179.72/179.60 [1853]~E(x18531,x18532)+E(f642(x18533,x18534,x18531),f642(x18533,x18534,x18532))
% 179.72/179.60 [1854]~E(x18541,x18542)+E(f788(x18541),f788(x18542))
% 179.72/179.60 [1855]~E(x18551,x18552)+E(f483(x18551,x18553,x18554),f483(x18552,x18553,x18554))
% 179.72/179.60 [1856]~E(x18561,x18562)+E(f483(x18563,x18561,x18564),f483(x18563,x18562,x18564))
% 179.72/179.60 [1857]~E(x18571,x18572)+E(f483(x18573,x18574,x18571),f483(x18573,x18574,x18572))
% 179.72/179.60 [1858]~E(x18581,x18582)+E(f125(x18581,x18583),f125(x18582,x18583))
% 179.72/179.60 [1859]~E(x18591,x18592)+E(f125(x18593,x18591),f125(x18593,x18592))
% 179.72/179.60 [1860]~E(x18601,x18602)+E(f528(x18601),f528(x18602))
% 179.72/179.60 [1861]~E(x18611,x18612)+E(f365(x18611,x18613),f365(x18612,x18613))
% 179.72/179.60 [1862]~E(x18621,x18622)+E(f365(x18623,x18621),f365(x18623,x18622))
% 179.72/179.60 [1863]~E(x18631,x18632)+E(f608(x18631,x18633,x18634,x18635,x18636,x18637,x18638,x18639),f608(x18632,x18633,x18634,x18635,x18636,x18637,x18638,x18639))
% 179.72/179.60 [1864]~E(x18641,x18642)+E(f608(x18643,x18641,x18644,x18645,x18646,x18647,x18648,x18649),f608(x18643,x18642,x18644,x18645,x18646,x18647,x18648,x18649))
% 179.72/179.60 [1865]~E(x18651,x18652)+E(f608(x18653,x18654,x18651,x18655,x18656,x18657,x18658,x18659),f608(x18653,x18654,x18652,x18655,x18656,x18657,x18658,x18659))
% 179.72/179.60 [1866]~E(x18661,x18662)+E(f608(x18663,x18664,x18665,x18661,x18666,x18667,x18668,x18669),f608(x18663,x18664,x18665,x18662,x18666,x18667,x18668,x18669))
% 179.72/179.60 [1867]~E(x18671,x18672)+E(f608(x18673,x18674,x18675,x18676,x18671,x18677,x18678,x18679),f608(x18673,x18674,x18675,x18676,x18672,x18677,x18678,x18679))
% 179.72/179.60 [1868]~E(x18681,x18682)+E(f608(x18683,x18684,x18685,x18686,x18687,x18681,x18688,x18689),f608(x18683,x18684,x18685,x18686,x18687,x18682,x18688,x18689))
% 179.72/179.60 [1869]~E(x18691,x18692)+E(f608(x18693,x18694,x18695,x18696,x18697,x18698,x18691,x18699),f608(x18693,x18694,x18695,x18696,x18697,x18698,x18692,x18699))
% 179.72/179.60 [1870]~E(x18701,x18702)+E(f608(x18703,x18704,x18705,x18706,x18707,x18708,x18709,x18701),f608(x18703,x18704,x18705,x18706,x18707,x18708,x18709,x18702))
% 179.72/179.60 [1871]~E(x18711,x18712)+E(f832(x18711,x18713,x18714,x18715),f832(x18712,x18713,x18714,x18715))
% 179.72/179.60 [1872]~E(x18721,x18722)+E(f832(x18723,x18721,x18724,x18725),f832(x18723,x18722,x18724,x18725))
% 179.72/179.60 [1873]~E(x18731,x18732)+E(f832(x18733,x18734,x18731,x18735),f832(x18733,x18734,x18732,x18735))
% 179.72/179.60 [1874]~E(x18741,x18742)+E(f832(x18743,x18744,x18745,x18741),f832(x18743,x18744,x18745,x18742))
% 179.72/179.60 [1875]~E(x18751,x18752)+E(f715(x18751,x18753,x18754,x18755),f715(x18752,x18753,x18754,x18755))
% 179.72/179.60 [1876]~E(x18761,x18762)+E(f715(x18763,x18761,x18764,x18765),f715(x18763,x18762,x18764,x18765))
% 179.72/179.60 [1877]~E(x18771,x18772)+E(f715(x18773,x18774,x18771,x18775),f715(x18773,x18774,x18772,x18775))
% 179.72/179.60 [1878]~E(x18781,x18782)+E(f715(x18783,x18784,x18785,x18781),f715(x18783,x18784,x18785,x18782))
% 179.72/179.60 [1879]~E(x18791,x18792)+E(f743(x18791,x18793,x18794,x18795),f743(x18792,x18793,x18794,x18795))
% 179.72/179.60 [1880]~E(x18801,x18802)+E(f743(x18803,x18801,x18804,x18805),f743(x18803,x18802,x18804,x18805))
% 179.72/179.60 [1881]~E(x18811,x18812)+E(f743(x18813,x18814,x18811,x18815),f743(x18813,x18814,x18812,x18815))
% 179.72/179.60 [1882]~E(x18821,x18822)+E(f743(x18823,x18824,x18825,x18821),f743(x18823,x18824,x18825,x18822))
% 179.72/179.60 [1883]~E(x18831,x18832)+E(f622(x18831,x18833,x18834),f622(x18832,x18833,x18834))
% 179.72/179.60 [1884]~E(x18841,x18842)+E(f622(x18843,x18841,x18844),f622(x18843,x18842,x18844))
% 179.72/179.60 [1885]~E(x18851,x18852)+E(f622(x18853,x18854,x18851),f622(x18853,x18854,x18852))
% 179.72/179.60 [1886]~E(x18861,x18862)+E(f810(x18861,x18863),f810(x18862,x18863))
% 179.72/179.60 [1887]~E(x18871,x18872)+E(f810(x18873,x18871),f810(x18873,x18872))
% 179.72/179.60 [1888]~E(x18881,x18882)+E(f396(x18881,x18883,x18884,x18885),f396(x18882,x18883,x18884,x18885))
% 179.72/179.60 [1889]~E(x18891,x18892)+E(f396(x18893,x18891,x18894,x18895),f396(x18893,x18892,x18894,x18895))
% 179.72/179.60 [1890]~E(x18901,x18902)+E(f396(x18903,x18904,x18901,x18905),f396(x18903,x18904,x18902,x18905))
% 179.72/179.60 [1891]~E(x18911,x18912)+E(f396(x18913,x18914,x18915,x18911),f396(x18913,x18914,x18915,x18912))
% 179.72/179.60 [1892]~E(x18921,x18922)+E(f722(x18921,x18923,x18924,x18925,x18926,x18927,x18928,x18929),f722(x18922,x18923,x18924,x18925,x18926,x18927,x18928,x18929))
% 179.72/179.60 [1893]~E(x18931,x18932)+E(f722(x18933,x18931,x18934,x18935,x18936,x18937,x18938,x18939),f722(x18933,x18932,x18934,x18935,x18936,x18937,x18938,x18939))
% 179.72/179.60 [1894]~E(x18941,x18942)+E(f722(x18943,x18944,x18941,x18945,x18946,x18947,x18948,x18949),f722(x18943,x18944,x18942,x18945,x18946,x18947,x18948,x18949))
% 179.72/179.60 [1895]~E(x18951,x18952)+E(f722(x18953,x18954,x18955,x18951,x18956,x18957,x18958,x18959),f722(x18953,x18954,x18955,x18952,x18956,x18957,x18958,x18959))
% 179.72/179.60 [1896]~E(x18961,x18962)+E(f722(x18963,x18964,x18965,x18966,x18961,x18967,x18968,x18969),f722(x18963,x18964,x18965,x18966,x18962,x18967,x18968,x18969))
% 179.72/179.60 [1897]~E(x18971,x18972)+E(f722(x18973,x18974,x18975,x18976,x18977,x18971,x18978,x18979),f722(x18973,x18974,x18975,x18976,x18977,x18972,x18978,x18979))
% 179.72/179.60 [1898]~E(x18981,x18982)+E(f722(x18983,x18984,x18985,x18986,x18987,x18988,x18981,x18989),f722(x18983,x18984,x18985,x18986,x18987,x18988,x18982,x18989))
% 179.72/179.60 [1899]~E(x18991,x18992)+E(f722(x18993,x18994,x18995,x18996,x18997,x18998,x18999,x18991),f722(x18993,x18994,x18995,x18996,x18997,x18998,x18999,x18992))
% 179.72/179.60 [1900]~E(x19001,x19002)+E(f283(x19001,x19003),f283(x19002,x19003))
% 179.72/179.60 [1901]~E(x19011,x19012)+E(f283(x19013,x19011),f283(x19013,x19012))
% 179.72/179.60 [1902]~E(x19021,x19022)+E(f687(x19021,x19023),f687(x19022,x19023))
% 179.72/179.60 [1903]~E(x19031,x19032)+E(f687(x19033,x19031),f687(x19033,x19032))
% 179.72/179.60 [1904]~E(x19041,x19042)+E(f630(x19041,x19043,x19044,x19045),f630(x19042,x19043,x19044,x19045))
% 179.72/179.60 [1905]~E(x19051,x19052)+E(f630(x19053,x19051,x19054,x19055),f630(x19053,x19052,x19054,x19055))
% 179.72/179.60 [1906]~E(x19061,x19062)+E(f630(x19063,x19064,x19061,x19065),f630(x19063,x19064,x19062,x19065))
% 179.72/179.60 [1907]~E(x19071,x19072)+E(f630(x19073,x19074,x19075,x19071),f630(x19073,x19074,x19075,x19072))
% 179.72/179.60 [1908]~E(x19081,x19082)+E(f533(x19081,x19083,x19084,x19085,x19086),f533(x19082,x19083,x19084,x19085,x19086))
% 179.72/179.60 [1909]~E(x19091,x19092)+E(f533(x19093,x19091,x19094,x19095,x19096),f533(x19093,x19092,x19094,x19095,x19096))
% 179.72/179.60 [1910]~E(x19101,x19102)+E(f533(x19103,x19104,x19101,x19105,x19106),f533(x19103,x19104,x19102,x19105,x19106))
% 179.72/179.60 [1911]~E(x19111,x19112)+E(f533(x19113,x19114,x19115,x19111,x19116),f533(x19113,x19114,x19115,x19112,x19116))
% 179.72/179.60 [1912]~E(x19121,x19122)+E(f533(x19123,x19124,x19125,x19126,x19121),f533(x19123,x19124,x19125,x19126,x19122))
% 179.72/179.60 [1913]~E(x19131,x19132)+E(f233(x19131,x19133,x19134,x19135,x19136),f233(x19132,x19133,x19134,x19135,x19136))
% 179.72/179.60 [1914]~E(x19141,x19142)+E(f233(x19143,x19141,x19144,x19145,x19146),f233(x19143,x19142,x19144,x19145,x19146))
% 179.72/179.60 [1915]~E(x19151,x19152)+E(f233(x19153,x19154,x19151,x19155,x19156),f233(x19153,x19154,x19152,x19155,x19156))
% 179.72/179.60 [1916]~E(x19161,x19162)+E(f233(x19163,x19164,x19165,x19161,x19166),f233(x19163,x19164,x19165,x19162,x19166))
% 179.72/179.60 [1917]~E(x19171,x19172)+E(f233(x19173,x19174,x19175,x19176,x19171),f233(x19173,x19174,x19175,x19176,x19172))
% 179.72/179.60 [1918]~E(x19181,x19182)+E(f355(x19181,x19183,x19184),f355(x19182,x19183,x19184))
% 179.72/179.60 [1919]~E(x19191,x19192)+E(f355(x19193,x19191,x19194),f355(x19193,x19192,x19194))
% 179.72/179.60 [1920]~E(x19201,x19202)+E(f355(x19203,x19204,x19201),f355(x19203,x19204,x19202))
% 179.72/179.60 [1921]~E(x19211,x19212)+E(f383(x19211,x19213),f383(x19212,x19213))
% 179.72/179.60 [1922]~E(x19221,x19222)+E(f383(x19223,x19221),f383(x19223,x19222))
% 179.72/179.60 [1923]~E(x19231,x19232)+E(f670(x19231,x19233,x19234,x19235),f670(x19232,x19233,x19234,x19235))
% 179.72/179.60 [1924]~E(x19241,x19242)+E(f670(x19243,x19241,x19244,x19245),f670(x19243,x19242,x19244,x19245))
% 179.72/179.60 [1925]~E(x19251,x19252)+E(f670(x19253,x19254,x19251,x19255),f670(x19253,x19254,x19252,x19255))
% 179.72/179.60 [1926]~E(x19261,x19262)+E(f670(x19263,x19264,x19265,x19261),f670(x19263,x19264,x19265,x19262))
% 179.72/179.60 [1927]~E(x19271,x19272)+E(f227(x19271,x19273,x19274),f227(x19272,x19273,x19274))
% 179.72/179.60 [1928]~E(x19281,x19282)+E(f227(x19283,x19281,x19284),f227(x19283,x19282,x19284))
% 179.72/179.60 [1929]~E(x19291,x19292)+E(f227(x19293,x19294,x19291),f227(x19293,x19294,x19292))
% 179.72/179.60 [1930]~E(x19301,x19302)+E(f706(x19301,x19303,x19304,x19305,x19306),f706(x19302,x19303,x19304,x19305,x19306))
% 179.72/179.60 [1931]~E(x19311,x19312)+E(f706(x19313,x19311,x19314,x19315,x19316),f706(x19313,x19312,x19314,x19315,x19316))
% 179.72/179.60 [1932]~E(x19321,x19322)+E(f706(x19323,x19324,x19321,x19325,x19326),f706(x19323,x19324,x19322,x19325,x19326))
% 179.72/179.60 [1933]~E(x19331,x19332)+E(f706(x19333,x19334,x19335,x19331,x19336),f706(x19333,x19334,x19335,x19332,x19336))
% 179.72/179.60 [1934]~E(x19341,x19342)+E(f706(x19343,x19344,x19345,x19346,x19341),f706(x19343,x19344,x19345,x19346,x19342))
% 179.72/179.60 [1935]~E(x19351,x19352)+E(f422(x19351,x19353),f422(x19352,x19353))
% 179.72/179.60 [1936]~E(x19361,x19362)+E(f422(x19363,x19361),f422(x19363,x19362))
% 179.72/179.60 [1937]~E(x19371,x19372)+E(f290(x19371,x19373,x19374,x19375),f290(x19372,x19373,x19374,x19375))
% 179.72/179.60 [1938]~E(x19381,x19382)+E(f290(x19383,x19381,x19384,x19385),f290(x19383,x19382,x19384,x19385))
% 179.72/179.60 [1939]~E(x19391,x19392)+E(f290(x19393,x19394,x19391,x19395),f290(x19393,x19394,x19392,x19395))
% 179.72/179.60 [1940]~E(x19401,x19402)+E(f290(x19403,x19404,x19405,x19401),f290(x19403,x19404,x19405,x19402))
% 179.72/179.60 [1941]~E(x19411,x19412)+E(f501(x19411,x19413,x19414,x19415,x19416,x19417,x19418),f501(x19412,x19413,x19414,x19415,x19416,x19417,x19418))
% 179.72/179.60 [1942]~E(x19421,x19422)+E(f501(x19423,x19421,x19424,x19425,x19426,x19427,x19428),f501(x19423,x19422,x19424,x19425,x19426,x19427,x19428))
% 179.72/179.60 [1943]~E(x19431,x19432)+E(f501(x19433,x19434,x19431,x19435,x19436,x19437,x19438),f501(x19433,x19434,x19432,x19435,x19436,x19437,x19438))
% 179.72/179.60 [1944]~E(x19441,x19442)+E(f501(x19443,x19444,x19445,x19441,x19446,x19447,x19448),f501(x19443,x19444,x19445,x19442,x19446,x19447,x19448))
% 179.72/179.60 [1945]~E(x19451,x19452)+E(f501(x19453,x19454,x19455,x19456,x19451,x19457,x19458),f501(x19453,x19454,x19455,x19456,x19452,x19457,x19458))
% 179.72/179.60 [1946]~E(x19461,x19462)+E(f501(x19463,x19464,x19465,x19466,x19467,x19461,x19468),f501(x19463,x19464,x19465,x19466,x19467,x19462,x19468))
% 179.72/179.60 [1947]~E(x19471,x19472)+E(f501(x19473,x19474,x19475,x19476,x19477,x19478,x19471),f501(x19473,x19474,x19475,x19476,x19477,x19478,x19472))
% 179.72/179.60 [1948]~E(x19481,x19482)+E(f714(x19481,x19483,x19484,x19485),f714(x19482,x19483,x19484,x19485))
% 179.72/179.60 [1949]~E(x19491,x19492)+E(f714(x19493,x19491,x19494,x19495),f714(x19493,x19492,x19494,x19495))
% 179.72/179.60 [1950]~E(x19501,x19502)+E(f714(x19503,x19504,x19501,x19505),f714(x19503,x19504,x19502,x19505))
% 179.72/179.60 [1951]~E(x19511,x19512)+E(f714(x19513,x19514,x19515,x19511),f714(x19513,x19514,x19515,x19512))
% 179.72/179.60 [1952]~E(x19521,x19522)+E(f291(x19521,x19523,x19524,x19525,x19526),f291(x19522,x19523,x19524,x19525,x19526))
% 179.72/179.60 [1953]~E(x19531,x19532)+E(f291(x19533,x19531,x19534,x19535,x19536),f291(x19533,x19532,x19534,x19535,x19536))
% 179.72/179.60 [1954]~E(x19541,x19542)+E(f291(x19543,x19544,x19541,x19545,x19546),f291(x19543,x19544,x19542,x19545,x19546))
% 179.72/179.60 [1955]~E(x19551,x19552)+E(f291(x19553,x19554,x19555,x19551,x19556),f291(x19553,x19554,x19555,x19552,x19556))
% 179.72/179.60 [1956]~E(x19561,x19562)+E(f291(x19563,x19564,x19565,x19566,x19561),f291(x19563,x19564,x19565,x19566,x19562))
% 179.72/179.60 [1957]~E(x19571,x19572)+E(f570(x19571,x19573,x19574,x19575,x19576),f570(x19572,x19573,x19574,x19575,x19576))
% 179.72/179.60 [1958]~E(x19581,x19582)+E(f570(x19583,x19581,x19584,x19585,x19586),f570(x19583,x19582,x19584,x19585,x19586))
% 179.72/179.60 [1959]~E(x19591,x19592)+E(f570(x19593,x19594,x19591,x19595,x19596),f570(x19593,x19594,x19592,x19595,x19596))
% 179.72/179.60 [1960]~E(x19601,x19602)+E(f570(x19603,x19604,x19605,x19601,x19606),f570(x19603,x19604,x19605,x19602,x19606))
% 179.72/179.60 [1961]~E(x19611,x19612)+E(f570(x19613,x19614,x19615,x19616,x19611),f570(x19613,x19614,x19615,x19616,x19612))
% 179.72/179.60 [1962]~E(x19621,x19622)+E(f520(x19621,x19623,x19624),f520(x19622,x19623,x19624))
% 179.72/179.60 [1963]~E(x19631,x19632)+E(f520(x19633,x19631,x19634),f520(x19633,x19632,x19634))
% 179.72/179.60 [1964]~E(x19641,x19642)+E(f520(x19643,x19644,x19641),f520(x19643,x19644,x19642))
% 179.72/179.60 [1965]~E(x19651,x19652)+E(f336(x19651,x19653,x19654),f336(x19652,x19653,x19654))
% 179.72/179.60 [1966]~E(x19661,x19662)+E(f336(x19663,x19661,x19664),f336(x19663,x19662,x19664))
% 179.72/179.60 [1967]~E(x19671,x19672)+E(f336(x19673,x19674,x19671),f336(x19673,x19674,x19672))
% 179.72/179.60 [1968]~E(x19681,x19682)+E(f419(x19681),f419(x19682))
% 179.72/179.60 [1969]~E(x19691,x19692)+E(f756(x19691,x19693,x19694),f756(x19692,x19693,x19694))
% 179.72/179.60 [1970]~E(x19701,x19702)+E(f756(x19703,x19701,x19704),f756(x19703,x19702,x19704))
% 179.72/179.60 [1971]~E(x19711,x19712)+E(f756(x19713,x19714,x19711),f756(x19713,x19714,x19712))
% 179.72/179.60 [1972]~E(x19721,x19722)+E(f565(x19721,x19723,x19724,x19725,x19726),f565(x19722,x19723,x19724,x19725,x19726))
% 179.72/179.60 [1973]~E(x19731,x19732)+E(f565(x19733,x19731,x19734,x19735,x19736),f565(x19733,x19732,x19734,x19735,x19736))
% 179.72/179.60 [1974]~E(x19741,x19742)+E(f565(x19743,x19744,x19741,x19745,x19746),f565(x19743,x19744,x19742,x19745,x19746))
% 179.72/179.60 [1975]~E(x19751,x19752)+E(f565(x19753,x19754,x19755,x19751,x19756),f565(x19753,x19754,x19755,x19752,x19756))
% 179.72/179.60 [1976]~E(x19761,x19762)+E(f565(x19763,x19764,x19765,x19766,x19761),f565(x19763,x19764,x19765,x19766,x19762))
% 179.72/179.60 [1977]~E(x19771,x19772)+E(f595(x19771,x19773,x19774),f595(x19772,x19773,x19774))
% 179.72/179.60 [1978]~E(x19781,x19782)+E(f595(x19783,x19781,x19784),f595(x19783,x19782,x19784))
% 179.72/179.60 [1979]~E(x19791,x19792)+E(f595(x19793,x19794,x19791),f595(x19793,x19794,x19792))
% 179.72/179.60 [1980]~E(x19801,x19802)+E(f451(x19801,x19803,x19804,x19805),f451(x19802,x19803,x19804,x19805))
% 179.72/179.60 [1981]~E(x19811,x19812)+E(f451(x19813,x19811,x19814,x19815),f451(x19813,x19812,x19814,x19815))
% 179.72/179.60 [1982]~E(x19821,x19822)+E(f451(x19823,x19824,x19821,x19825),f451(x19823,x19824,x19822,x19825))
% 179.72/179.60 [1983]~E(x19831,x19832)+E(f451(x19833,x19834,x19835,x19831),f451(x19833,x19834,x19835,x19832))
% 179.72/179.60 [1984]~E(x19841,x19842)+E(f470(x19841,x19843,x19844),f470(x19842,x19843,x19844))
% 179.72/179.60 [1985]~E(x19851,x19852)+E(f470(x19853,x19851,x19854),f470(x19853,x19852,x19854))
% 179.72/179.60 [1986]~E(x19861,x19862)+E(f470(x19863,x19864,x19861),f470(x19863,x19864,x19862))
% 179.72/179.60 [1987]~E(x19871,x19872)+E(f826(x19871,x19873),f826(x19872,x19873))
% 179.72/179.60 [1988]~E(x19881,x19882)+E(f826(x19883,x19881),f826(x19883,x19882))
% 179.72/179.60 [1989]~E(x19891,x19892)+E(f674(x19891,x19893),f674(x19892,x19893))
% 179.72/179.60 [1990]~E(x19901,x19902)+E(f674(x19903,x19901),f674(x19903,x19902))
% 179.72/179.60 [1991]~E(x19911,x19912)+E(f783(x19911,x19913,x19914),f783(x19912,x19913,x19914))
% 179.72/179.60 [1992]~E(x19921,x19922)+E(f783(x19923,x19921,x19924),f783(x19923,x19922,x19924))
% 179.72/179.60 [1993]~E(x19931,x19932)+E(f783(x19933,x19934,x19931),f783(x19933,x19934,x19932))
% 179.72/179.60 [1994]~E(x19941,x19942)+E(f600(x19941,x19943,x19944),f600(x19942,x19943,x19944))
% 179.72/179.60 [1995]~E(x19951,x19952)+E(f600(x19953,x19951,x19954),f600(x19953,x19952,x19954))
% 179.72/179.60 [1996]~E(x19961,x19962)+E(f600(x19963,x19964,x19961),f600(x19963,x19964,x19962))
% 179.72/179.60 [1997]~E(x19971,x19972)+E(f455(x19971,x19973),f455(x19972,x19973))
% 179.72/179.60 [1998]~E(x19981,x19982)+E(f455(x19983,x19981),f455(x19983,x19982))
% 179.72/179.60 [1999]~E(x19991,x19992)+E(f409(x19991,x19993,x19994,x19995),f409(x19992,x19993,x19994,x19995))
% 179.72/179.60 [2000]~E(x20001,x20002)+E(f409(x20003,x20001,x20004,x20005),f409(x20003,x20002,x20004,x20005))
% 179.72/179.60 [2001]~E(x20011,x20012)+E(f409(x20013,x20014,x20011,x20015),f409(x20013,x20014,x20012,x20015))
% 179.72/179.60 [2002]~E(x20021,x20022)+E(f409(x20023,x20024,x20025,x20021),f409(x20023,x20024,x20025,x20022))
% 179.72/179.60 [2003]~E(x20031,x20032)+E(f811(x20031),f811(x20032))
% 179.72/179.60 [2004]~E(x20041,x20042)+E(f539(x20041,x20043,x20044),f539(x20042,x20043,x20044))
% 179.72/179.60 [2005]~E(x20051,x20052)+E(f539(x20053,x20051,x20054),f539(x20053,x20052,x20054))
% 179.72/179.60 [2006]~E(x20061,x20062)+E(f539(x20063,x20064,x20061),f539(x20063,x20064,x20062))
% 179.72/179.60 [2007]~E(x20071,x20072)+E(f431(x20071,x20073,x20074),f431(x20072,x20073,x20074))
% 179.72/179.60 [2008]~E(x20081,x20082)+E(f431(x20083,x20081,x20084),f431(x20083,x20082,x20084))
% 179.72/179.60 [2009]~E(x20091,x20092)+E(f431(x20093,x20094,x20091),f431(x20093,x20094,x20092))
% 179.72/179.60 [2010]~E(x20101,x20102)+E(f540(x20101,x20103,x20104),f540(x20102,x20103,x20104))
% 179.72/179.60 [2011]~E(x20111,x20112)+E(f540(x20113,x20111,x20114),f540(x20113,x20112,x20114))
% 179.72/179.60 [2012]~E(x20121,x20122)+E(f540(x20123,x20124,x20121),f540(x20123,x20124,x20122))
% 179.72/179.60 [2013]~E(x20131,x20132)+E(f270(x20131,x20133),f270(x20132,x20133))
% 179.72/179.60 [2014]~E(x20141,x20142)+E(f270(x20143,x20141),f270(x20143,x20142))
% 179.72/179.60 [2015]~E(x20151,x20152)+E(f272(x20151,x20153,x20154,x20155),f272(x20152,x20153,x20154,x20155))
% 179.72/179.60 [2016]~E(x20161,x20162)+E(f272(x20163,x20161,x20164,x20165),f272(x20163,x20162,x20164,x20165))
% 179.72/179.60 [2017]~E(x20171,x20172)+E(f272(x20173,x20174,x20171,x20175),f272(x20173,x20174,x20172,x20175))
% 179.72/179.60 [2018]~E(x20181,x20182)+E(f272(x20183,x20184,x20185,x20181),f272(x20183,x20184,x20185,x20182))
% 179.72/179.60 [2019]~E(x20191,x20192)+E(f733(x20191,x20193),f733(x20192,x20193))
% 179.72/179.60 [2020]~E(x20201,x20202)+E(f733(x20203,x20201),f733(x20203,x20202))
% 179.72/179.60 [2021]~E(x20211,x20212)+E(f392(x20211,x20213,x20214,x20215),f392(x20212,x20213,x20214,x20215))
% 179.72/179.60 [2022]~E(x20221,x20222)+E(f392(x20223,x20221,x20224,x20225),f392(x20223,x20222,x20224,x20225))
% 179.72/179.60 [2023]~E(x20231,x20232)+E(f392(x20233,x20234,x20231,x20235),f392(x20233,x20234,x20232,x20235))
% 179.72/179.60 [2024]~E(x20241,x20242)+E(f392(x20243,x20244,x20245,x20241),f392(x20243,x20244,x20245,x20242))
% 179.72/179.60 [2025]~E(x20251,x20252)+E(f776(x20251,x20253,x20254,x20255,x20256,x20257),f776(x20252,x20253,x20254,x20255,x20256,x20257))
% 179.72/179.60 [2026]~E(x20261,x20262)+E(f776(x20263,x20261,x20264,x20265,x20266,x20267),f776(x20263,x20262,x20264,x20265,x20266,x20267))
% 179.72/179.60 [2027]~E(x20271,x20272)+E(f776(x20273,x20274,x20271,x20275,x20276,x20277),f776(x20273,x20274,x20272,x20275,x20276,x20277))
% 179.72/179.60 [2028]~E(x20281,x20282)+E(f776(x20283,x20284,x20285,x20281,x20286,x20287),f776(x20283,x20284,x20285,x20282,x20286,x20287))
% 179.72/179.60 [2029]~E(x20291,x20292)+E(f776(x20293,x20294,x20295,x20296,x20291,x20297),f776(x20293,x20294,x20295,x20296,x20292,x20297))
% 179.72/179.60 [2030]~E(x20301,x20302)+E(f776(x20303,x20304,x20305,x20306,x20307,x20301),f776(x20303,x20304,x20305,x20306,x20307,x20302))
% 179.72/179.60 [2031]~E(x20311,x20312)+E(f710(x20311,x20313,x20314,x20315,x20316,x20317,x20318),f710(x20312,x20313,x20314,x20315,x20316,x20317,x20318))
% 179.72/179.60 [2032]~E(x20321,x20322)+E(f710(x20323,x20321,x20324,x20325,x20326,x20327,x20328),f710(x20323,x20322,x20324,x20325,x20326,x20327,x20328))
% 179.72/179.60 [2033]~E(x20331,x20332)+E(f710(x20333,x20334,x20331,x20335,x20336,x20337,x20338),f710(x20333,x20334,x20332,x20335,x20336,x20337,x20338))
% 179.72/179.60 [2034]~E(x20341,x20342)+E(f710(x20343,x20344,x20345,x20341,x20346,x20347,x20348),f710(x20343,x20344,x20345,x20342,x20346,x20347,x20348))
% 179.72/179.60 [2035]~E(x20351,x20352)+E(f710(x20353,x20354,x20355,x20356,x20351,x20357,x20358),f710(x20353,x20354,x20355,x20356,x20352,x20357,x20358))
% 179.72/179.60 [2036]~E(x20361,x20362)+E(f710(x20363,x20364,x20365,x20366,x20367,x20361,x20368),f710(x20363,x20364,x20365,x20366,x20367,x20362,x20368))
% 179.72/179.60 [2037]~E(x20371,x20372)+E(f710(x20373,x20374,x20375,x20376,x20377,x20378,x20371),f710(x20373,x20374,x20375,x20376,x20377,x20378,x20372))
% 179.72/179.60 [2038]~E(x20381,x20382)+E(f820(x20381,x20383),f820(x20382,x20383))
% 179.72/179.60 [2039]~E(x20391,x20392)+E(f820(x20393,x20391),f820(x20393,x20392))
% 179.72/179.60 [2040]~E(x20401,x20402)+E(f742(x20401,x20403,x20404,x20405),f742(x20402,x20403,x20404,x20405))
% 179.72/179.60 [2041]~E(x20411,x20412)+E(f742(x20413,x20411,x20414,x20415),f742(x20413,x20412,x20414,x20415))
% 179.72/179.60 [2042]~E(x20421,x20422)+E(f742(x20423,x20424,x20421,x20425),f742(x20423,x20424,x20422,x20425))
% 179.72/179.60 [2043]~E(x20431,x20432)+E(f742(x20433,x20434,x20435,x20431),f742(x20433,x20434,x20435,x20432))
% 179.72/179.60 [2044]~E(x20441,x20442)+E(f602(x20441,x20443,x20444),f602(x20442,x20443,x20444))
% 179.72/179.60 [2045]~E(x20451,x20452)+E(f602(x20453,x20451,x20454),f602(x20453,x20452,x20454))
% 179.72/179.60 [2046]~E(x20461,x20462)+E(f602(x20463,x20464,x20461),f602(x20463,x20464,x20462))
% 179.72/179.60 [2047]~E(x20471,x20472)+E(f645(x20471,x20473,x20474,x20475,x20476),f645(x20472,x20473,x20474,x20475,x20476))
% 179.72/179.60 [2048]~E(x20481,x20482)+E(f645(x20483,x20481,x20484,x20485,x20486),f645(x20483,x20482,x20484,x20485,x20486))
% 179.72/179.60 [2049]~E(x20491,x20492)+E(f645(x20493,x20494,x20491,x20495,x20496),f645(x20493,x20494,x20492,x20495,x20496))
% 179.72/179.60 [2050]~E(x20501,x20502)+E(f645(x20503,x20504,x20505,x20501,x20506),f645(x20503,x20504,x20505,x20502,x20506))
% 179.72/179.60 [2051]~E(x20511,x20512)+E(f645(x20513,x20514,x20515,x20516,x20511),f645(x20513,x20514,x20515,x20516,x20512))
% 179.72/179.60 [2052]~E(x20521,x20522)+E(f127(x20521,x20523,x20524,x20525),f127(x20522,x20523,x20524,x20525))
% 179.72/179.60 [2053]~E(x20531,x20532)+E(f127(x20533,x20531,x20534,x20535),f127(x20533,x20532,x20534,x20535))
% 179.72/179.60 [2054]~E(x20541,x20542)+E(f127(x20543,x20544,x20541,x20545),f127(x20543,x20544,x20542,x20545))
% 179.72/179.60 [2055]~E(x20551,x20552)+E(f127(x20553,x20554,x20555,x20551),f127(x20553,x20554,x20555,x20552))
% 179.72/179.60 [2056]~E(x20561,x20562)+E(f819(x20561,x20563),f819(x20562,x20563))
% 179.72/179.60 [2057]~E(x20571,x20572)+E(f819(x20573,x20571),f819(x20573,x20572))
% 179.72/179.60 [2058]~E(x20581,x20582)+E(f360(x20581,x20583,x20584,x20585,x20586),f360(x20582,x20583,x20584,x20585,x20586))
% 179.72/179.60 [2059]~E(x20591,x20592)+E(f360(x20593,x20591,x20594,x20595,x20596),f360(x20593,x20592,x20594,x20595,x20596))
% 179.72/179.60 [2060]~E(x20601,x20602)+E(f360(x20603,x20604,x20601,x20605,x20606),f360(x20603,x20604,x20602,x20605,x20606))
% 179.72/179.60 [2061]~E(x20611,x20612)+E(f360(x20613,x20614,x20615,x20611,x20616),f360(x20613,x20614,x20615,x20612,x20616))
% 179.72/179.60 [2062]~E(x20621,x20622)+E(f360(x20623,x20624,x20625,x20626,x20621),f360(x20623,x20624,x20625,x20626,x20622))
% 179.72/179.60 [2063]~E(x20631,x20632)+E(f443(x20631,x20633,x20634,x20635),f443(x20632,x20633,x20634,x20635))
% 179.72/179.60 [2064]~E(x20641,x20642)+E(f443(x20643,x20641,x20644,x20645),f443(x20643,x20642,x20644,x20645))
% 179.72/179.60 [2065]~E(x20651,x20652)+E(f443(x20653,x20654,x20651,x20655),f443(x20653,x20654,x20652,x20655))
% 179.72/179.60 [2066]~E(x20661,x20662)+E(f443(x20663,x20664,x20665,x20661),f443(x20663,x20664,x20665,x20662))
% 179.72/179.60 [2067]~E(x20671,x20672)+E(f410(x20671,x20673,x20674,x20675),f410(x20672,x20673,x20674,x20675))
% 179.72/179.60 [2068]~E(x20681,x20682)+E(f410(x20683,x20681,x20684,x20685),f410(x20683,x20682,x20684,x20685))
% 179.72/179.60 [2069]~E(x20691,x20692)+E(f410(x20693,x20694,x20691,x20695),f410(x20693,x20694,x20692,x20695))
% 179.72/179.60 [2070]~E(x20701,x20702)+E(f410(x20703,x20704,x20705,x20701),f410(x20703,x20704,x20705,x20702))
% 179.72/179.60 [2071]~E(x20711,x20712)+E(f836(x20711,x20713),f836(x20712,x20713))
% 179.72/179.60 [2072]~E(x20721,x20722)+E(f836(x20723,x20721),f836(x20723,x20722))
% 179.72/179.60 [2073]~E(x20731,x20732)+E(f577(x20731,x20733,x20734,x20735,x20736),f577(x20732,x20733,x20734,x20735,x20736))
% 179.72/179.60 [2074]~E(x20741,x20742)+E(f577(x20743,x20741,x20744,x20745,x20746),f577(x20743,x20742,x20744,x20745,x20746))
% 179.72/179.60 [2075]~E(x20751,x20752)+E(f577(x20753,x20754,x20751,x20755,x20756),f577(x20753,x20754,x20752,x20755,x20756))
% 179.72/179.60 [2076]~E(x20761,x20762)+E(f577(x20763,x20764,x20765,x20761,x20766),f577(x20763,x20764,x20765,x20762,x20766))
% 179.72/179.60 [2077]~E(x20771,x20772)+E(f577(x20773,x20774,x20775,x20776,x20771),f577(x20773,x20774,x20775,x20776,x20772))
% 179.72/179.60 [2078]~E(x20781,x20782)+E(f449(x20781,x20783,x20784,x20785,x20786),f449(x20782,x20783,x20784,x20785,x20786))
% 179.72/179.60 [2079]~E(x20791,x20792)+E(f449(x20793,x20791,x20794,x20795,x20796),f449(x20793,x20792,x20794,x20795,x20796))
% 179.72/179.60 [2080]~E(x20801,x20802)+E(f449(x20803,x20804,x20801,x20805,x20806),f449(x20803,x20804,x20802,x20805,x20806))
% 179.72/179.60 [2081]~E(x20811,x20812)+E(f449(x20813,x20814,x20815,x20811,x20816),f449(x20813,x20814,x20815,x20812,x20816))
% 179.72/179.60 [2082]~E(x20821,x20822)+E(f449(x20823,x20824,x20825,x20826,x20821),f449(x20823,x20824,x20825,x20826,x20822))
% 179.72/179.60 [2083]~E(x20831,x20832)+E(f389(x20831,x20833,x20834,x20835),f389(x20832,x20833,x20834,x20835))
% 179.72/179.60 [2084]~E(x20841,x20842)+E(f389(x20843,x20841,x20844,x20845),f389(x20843,x20842,x20844,x20845))
% 179.72/179.60 [2085]~E(x20851,x20852)+E(f389(x20853,x20854,x20851,x20855),f389(x20853,x20854,x20852,x20855))
% 179.72/179.60 [2086]~E(x20861,x20862)+E(f389(x20863,x20864,x20865,x20861),f389(x20863,x20864,x20865,x20862))
% 179.72/179.60 [2087]~E(x20871,x20872)+E(f526(x20871,x20873,x20874,x20875,x20876),f526(x20872,x20873,x20874,x20875,x20876))
% 179.72/179.60 [2088]~E(x20881,x20882)+E(f526(x20883,x20881,x20884,x20885,x20886),f526(x20883,x20882,x20884,x20885,x20886))
% 179.72/179.60 [2089]~E(x20891,x20892)+E(f526(x20893,x20894,x20891,x20895,x20896),f526(x20893,x20894,x20892,x20895,x20896))
% 179.72/179.60 [2090]~E(x20901,x20902)+E(f526(x20903,x20904,x20905,x20901,x20906),f526(x20903,x20904,x20905,x20902,x20906))
% 179.72/179.60 [2091]~E(x20911,x20912)+E(f526(x20913,x20914,x20915,x20916,x20911),f526(x20913,x20914,x20915,x20916,x20912))
% 179.72/179.60 [2092]~E(x20921,x20922)+E(f536(x20921,x20923,x20924),f536(x20922,x20923,x20924))
% 179.72/179.60 [2093]~E(x20931,x20932)+E(f536(x20933,x20931,x20934),f536(x20933,x20932,x20934))
% 179.72/179.60 [2094]~E(x20941,x20942)+E(f536(x20943,x20944,x20941),f536(x20943,x20944,x20942))
% 179.72/179.60 [2095]~E(x20951,x20952)+E(f497(x20951,x20953,x20954),f497(x20952,x20953,x20954))
% 179.72/179.60 [2096]~E(x20961,x20962)+E(f497(x20963,x20961,x20964),f497(x20963,x20962,x20964))
% 179.72/179.60 [2097]~E(x20971,x20972)+E(f497(x20973,x20974,x20971),f497(x20973,x20974,x20972))
% 179.72/179.60 [2098]~E(x20981,x20982)+E(f347(x20981,x20983,x20984),f347(x20982,x20983,x20984))
% 179.72/179.60 [2099]~E(x20991,x20992)+E(f347(x20993,x20991,x20994),f347(x20993,x20992,x20994))
% 179.72/179.60 [2100]~E(x21001,x21002)+E(f347(x21003,x21004,x21001),f347(x21003,x21004,x21002))
% 179.72/179.60 [2101]~E(x21011,x21012)+E(f575(x21011,x21013,x21014,x21015),f575(x21012,x21013,x21014,x21015))
% 179.72/179.60 [2102]~E(x21021,x21022)+E(f575(x21023,x21021,x21024,x21025),f575(x21023,x21022,x21024,x21025))
% 179.72/179.60 [2103]~E(x21031,x21032)+E(f575(x21033,x21034,x21031,x21035),f575(x21033,x21034,x21032,x21035))
% 179.72/179.60 [2104]~E(x21041,x21042)+E(f575(x21043,x21044,x21045,x21041),f575(x21043,x21044,x21045,x21042))
% 179.72/179.60 [2105]~E(x21051,x21052)+E(f412(x21051,x21053,x21054,x21055),f412(x21052,x21053,x21054,x21055))
% 179.72/179.60 [2106]~E(x21061,x21062)+E(f412(x21063,x21061,x21064,x21065),f412(x21063,x21062,x21064,x21065))
% 179.72/179.60 [2107]~E(x21071,x21072)+E(f412(x21073,x21074,x21071,x21075),f412(x21073,x21074,x21072,x21075))
% 179.72/179.60 [2108]~E(x21081,x21082)+E(f412(x21083,x21084,x21085,x21081),f412(x21083,x21084,x21085,x21082))
% 179.72/179.60 [2109]~E(x21091,x21092)+E(f853(x21091,x21093,x21094,x21095,x21096,x21097,x21098),f853(x21092,x21093,x21094,x21095,x21096,x21097,x21098))
% 179.72/179.60 [2110]~E(x21101,x21102)+E(f853(x21103,x21101,x21104,x21105,x21106,x21107,x21108),f853(x21103,x21102,x21104,x21105,x21106,x21107,x21108))
% 179.72/179.60 [2111]~E(x21111,x21112)+E(f853(x21113,x21114,x21111,x21115,x21116,x21117,x21118),f853(x21113,x21114,x21112,x21115,x21116,x21117,x21118))
% 179.72/179.60 [2112]~E(x21121,x21122)+E(f853(x21123,x21124,x21125,x21121,x21126,x21127,x21128),f853(x21123,x21124,x21125,x21122,x21126,x21127,x21128))
% 179.72/179.60 [2113]~E(x21131,x21132)+E(f853(x21133,x21134,x21135,x21136,x21131,x21137,x21138),f853(x21133,x21134,x21135,x21136,x21132,x21137,x21138))
% 179.72/179.60 [2114]~E(x21141,x21142)+E(f853(x21143,x21144,x21145,x21146,x21147,x21141,x21148),f853(x21143,x21144,x21145,x21146,x21147,x21142,x21148))
% 179.72/179.60 [2115]~E(x21151,x21152)+E(f853(x21153,x21154,x21155,x21156,x21157,x21158,x21151),f853(x21153,x21154,x21155,x21156,x21157,x21158,x21152))
% 179.72/179.60 [2116]~E(x21161,x21162)+E(f757(x21161,x21163,x21164),f757(x21162,x21163,x21164))
% 179.72/179.60 [2117]~E(x21171,x21172)+E(f757(x21173,x21171,x21174),f757(x21173,x21172,x21174))
% 179.72/179.60 [2118]~E(x21181,x21182)+E(f757(x21183,x21184,x21181),f757(x21183,x21184,x21182))
% 179.72/179.60 [2119]~E(x21191,x21192)+E(f621(x21191,x21193,x21194),f621(x21192,x21193,x21194))
% 179.72/179.60 [2120]~E(x21201,x21202)+E(f621(x21203,x21201,x21204),f621(x21203,x21202,x21204))
% 179.72/179.60 [2121]~E(x21211,x21212)+E(f621(x21213,x21214,x21211),f621(x21213,x21214,x21212))
% 179.72/179.60 [2122]~E(x21221,x21222)+E(f405(x21221,x21223,x21224,x21225),f405(x21222,x21223,x21224,x21225))
% 179.72/179.60 [2123]~E(x21231,x21232)+E(f405(x21233,x21231,x21234,x21235),f405(x21233,x21232,x21234,x21235))
% 179.72/179.60 [2124]~E(x21241,x21242)+E(f405(x21243,x21244,x21241,x21245),f405(x21243,x21244,x21242,x21245))
% 179.72/179.60 [2125]~E(x21251,x21252)+E(f405(x21253,x21254,x21255,x21251),f405(x21253,x21254,x21255,x21252))
% 179.72/179.60 [2126]~E(x21261,x21262)+E(f462(x21261,x21263),f462(x21262,x21263))
% 179.72/179.60 [2127]~E(x21271,x21272)+E(f462(x21273,x21271),f462(x21273,x21272))
% 179.72/179.60 [2128]~E(x21281,x21282)+E(f636(x21281,x21283,x21284,x21285,x21286),f636(x21282,x21283,x21284,x21285,x21286))
% 179.72/179.60 [2129]~E(x21291,x21292)+E(f636(x21293,x21291,x21294,x21295,x21296),f636(x21293,x21292,x21294,x21295,x21296))
% 179.72/179.60 [2130]~E(x21301,x21302)+E(f636(x21303,x21304,x21301,x21305,x21306),f636(x21303,x21304,x21302,x21305,x21306))
% 179.72/179.60 [2131]~E(x21311,x21312)+E(f636(x21313,x21314,x21315,x21311,x21316),f636(x21313,x21314,x21315,x21312,x21316))
% 179.72/179.60 [2132]~E(x21321,x21322)+E(f636(x21323,x21324,x21325,x21326,x21321),f636(x21323,x21324,x21325,x21326,x21322))
% 179.72/179.60 [2133]~E(x21331,x21332)+E(f693(x21331,x21333,x21334,x21335,x21336),f693(x21332,x21333,x21334,x21335,x21336))
% 179.72/179.60 [2134]~E(x21341,x21342)+E(f693(x21343,x21341,x21344,x21345,x21346),f693(x21343,x21342,x21344,x21345,x21346))
% 179.72/179.60 [2135]~E(x21351,x21352)+E(f693(x21353,x21354,x21351,x21355,x21356),f693(x21353,x21354,x21352,x21355,x21356))
% 179.72/179.60 [2136]~E(x21361,x21362)+E(f693(x21363,x21364,x21365,x21361,x21366),f693(x21363,x21364,x21365,x21362,x21366))
% 179.72/179.60 [2137]~E(x21371,x21372)+E(f693(x21373,x21374,x21375,x21376,x21371),f693(x21373,x21374,x21375,x21376,x21372))
% 179.72/179.60 [2138]~E(x21381,x21382)+E(f363(x21381),f363(x21382))
% 179.72/179.60 [2139]~E(x21391,x21392)+E(f691(x21391,x21393,x21394),f691(x21392,x21393,x21394))
% 179.72/179.60 [2140]~E(x21401,x21402)+E(f691(x21403,x21401,x21404),f691(x21403,x21402,x21404))
% 179.72/179.60 [2141]~E(x21411,x21412)+E(f691(x21413,x21414,x21411),f691(x21413,x21414,x21412))
% 179.72/179.60 [2142]~E(x21421,x21422)+E(f346(x21421,x21423,x21424),f346(x21422,x21423,x21424))
% 179.72/179.60 [2143]~E(x21431,x21432)+E(f346(x21433,x21431,x21434),f346(x21433,x21432,x21434))
% 179.72/179.60 [2144]~E(x21441,x21442)+E(f346(x21443,x21444,x21441),f346(x21443,x21444,x21442))
% 179.72/179.60 [2145]~E(x21451,x21452)+E(f465(x21451,x21453,x21454,x21455,x21456,x21457,x21458),f465(x21452,x21453,x21454,x21455,x21456,x21457,x21458))
% 179.72/179.60 [2146]~E(x21461,x21462)+E(f465(x21463,x21461,x21464,x21465,x21466,x21467,x21468),f465(x21463,x21462,x21464,x21465,x21466,x21467,x21468))
% 179.72/179.60 [2147]~E(x21471,x21472)+E(f465(x21473,x21474,x21471,x21475,x21476,x21477,x21478),f465(x21473,x21474,x21472,x21475,x21476,x21477,x21478))
% 179.72/179.60 [2148]~E(x21481,x21482)+E(f465(x21483,x21484,x21485,x21481,x21486,x21487,x21488),f465(x21483,x21484,x21485,x21482,x21486,x21487,x21488))
% 179.72/179.60 [2149]~E(x21491,x21492)+E(f465(x21493,x21494,x21495,x21496,x21491,x21497,x21498),f465(x21493,x21494,x21495,x21496,x21492,x21497,x21498))
% 179.72/179.60 [2150]~E(x21501,x21502)+E(f465(x21503,x21504,x21505,x21506,x21507,x21501,x21508),f465(x21503,x21504,x21505,x21506,x21507,x21502,x21508))
% 179.72/179.60 [2151]~E(x21511,x21512)+E(f465(x21513,x21514,x21515,x21516,x21517,x21518,x21511),f465(x21513,x21514,x21515,x21516,x21517,x21518,x21512))
% 179.72/179.60 [2152]~E(x21521,x21522)+E(f672(x21521,x21523),f672(x21522,x21523))
% 179.72/179.60 [2153]~E(x21531,x21532)+E(f672(x21533,x21531),f672(x21533,x21532))
% 179.72/179.60 [2154]~E(x21541,x21542)+E(f348(x21541,x21543,x21544),f348(x21542,x21543,x21544))
% 179.72/179.60 [2155]~E(x21551,x21552)+E(f348(x21553,x21551,x21554),f348(x21553,x21552,x21554))
% 179.72/179.60 [2156]~E(x21561,x21562)+E(f348(x21563,x21564,x21561),f348(x21563,x21564,x21562))
% 179.72/179.60 [2157]~E(x21571,x21572)+E(f578(x21571,x21573,x21574,x21575,x21576),f578(x21572,x21573,x21574,x21575,x21576))
% 179.72/179.60 [2158]~E(x21581,x21582)+E(f578(x21583,x21581,x21584,x21585,x21586),f578(x21583,x21582,x21584,x21585,x21586))
% 179.72/179.60 [2159]~E(x21591,x21592)+E(f578(x21593,x21594,x21591,x21595,x21596),f578(x21593,x21594,x21592,x21595,x21596))
% 179.72/179.60 [2160]~E(x21601,x21602)+E(f578(x21603,x21604,x21605,x21601,x21606),f578(x21603,x21604,x21605,x21602,x21606))
% 179.72/179.60 [2161]~E(x21611,x21612)+E(f578(x21613,x21614,x21615,x21616,x21611),f578(x21613,x21614,x21615,x21616,x21612))
% 179.72/179.60 [2162]~E(x21621,x21622)+E(f755(x21621,x21623,x21624),f755(x21622,x21623,x21624))
% 179.72/179.60 [2163]~E(x21631,x21632)+E(f755(x21633,x21631,x21634),f755(x21633,x21632,x21634))
% 179.72/179.60 [2164]~E(x21641,x21642)+E(f755(x21643,x21644,x21641),f755(x21643,x21644,x21642))
% 179.72/179.60 [2165]~E(x21651,x21652)+E(f596(x21651,x21653,x21654),f596(x21652,x21653,x21654))
% 179.72/179.60 [2166]~E(x21661,x21662)+E(f596(x21663,x21661,x21664),f596(x21663,x21662,x21664))
% 179.72/179.60 [2167]~E(x21671,x21672)+E(f596(x21673,x21674,x21671),f596(x21673,x21674,x21672))
% 179.72/179.60 [2168]~E(x21681,x21682)+E(f327(x21681,x21683,x21684,x21685),f327(x21682,x21683,x21684,x21685))
% 179.72/179.60 [2169]~E(x21691,x21692)+E(f327(x21693,x21691,x21694,x21695),f327(x21693,x21692,x21694,x21695))
% 179.72/179.60 [2170]~E(x21701,x21702)+E(f327(x21703,x21704,x21701,x21705),f327(x21703,x21704,x21702,x21705))
% 179.72/179.60 [2171]~E(x21711,x21712)+E(f327(x21713,x21714,x21715,x21711),f327(x21713,x21714,x21715,x21712))
% 179.72/179.60 [2172]~E(x21721,x21722)+E(f822(x21721,x21723,x21724),f822(x21722,x21723,x21724))
% 179.72/179.60 [2173]~E(x21731,x21732)+E(f822(x21733,x21731,x21734),f822(x21733,x21732,x21734))
% 179.72/179.60 [2174]~E(x21741,x21742)+E(f822(x21743,x21744,x21741),f822(x21743,x21744,x21742))
% 179.72/179.60 [2175]~E(x21751,x21752)+E(f697(x21751,x21753,x21754,x21755,x21756,x21757),f697(x21752,x21753,x21754,x21755,x21756,x21757))
% 179.72/179.60 [2176]~E(x21761,x21762)+E(f697(x21763,x21761,x21764,x21765,x21766,x21767),f697(x21763,x21762,x21764,x21765,x21766,x21767))
% 179.72/179.60 [2177]~E(x21771,x21772)+E(f697(x21773,x21774,x21771,x21775,x21776,x21777),f697(x21773,x21774,x21772,x21775,x21776,x21777))
% 179.72/179.60 [2178]~E(x21781,x21782)+E(f697(x21783,x21784,x21785,x21781,x21786,x21787),f697(x21783,x21784,x21785,x21782,x21786,x21787))
% 179.72/179.60 [2179]~E(x21791,x21792)+E(f697(x21793,x21794,x21795,x21796,x21791,x21797),f697(x21793,x21794,x21795,x21796,x21792,x21797))
% 179.72/179.60 [2180]~E(x21801,x21802)+E(f697(x21803,x21804,x21805,x21806,x21807,x21801),f697(x21803,x21804,x21805,x21806,x21807,x21802))
% 179.72/179.60 [2181]~E(x21811,x21812)+E(f527(x21811,x21813,x21814,x21815,x21816),f527(x21812,x21813,x21814,x21815,x21816))
% 179.72/179.60 [2182]~E(x21821,x21822)+E(f527(x21823,x21821,x21824,x21825,x21826),f527(x21823,x21822,x21824,x21825,x21826))
% 179.72/179.60 [2183]~E(x21831,x21832)+E(f527(x21833,x21834,x21831,x21835,x21836),f527(x21833,x21834,x21832,x21835,x21836))
% 179.72/179.60 [2184]~E(x21841,x21842)+E(f527(x21843,x21844,x21845,x21841,x21846),f527(x21843,x21844,x21845,x21842,x21846))
% 179.72/179.60 [2185]~E(x21851,x21852)+E(f527(x21853,x21854,x21855,x21856,x21851),f527(x21853,x21854,x21855,x21856,x21852))
% 179.72/179.60 [2186]~E(x21861,x21862)+E(f655(x21861,x21863,x21864,x21865,x21866),f655(x21862,x21863,x21864,x21865,x21866))
% 179.72/179.60 [2187]~E(x21871,x21872)+E(f655(x21873,x21871,x21874,x21875,x21876),f655(x21873,x21872,x21874,x21875,x21876))
% 179.72/179.60 [2188]~E(x21881,x21882)+E(f655(x21883,x21884,x21881,x21885,x21886),f655(x21883,x21884,x21882,x21885,x21886))
% 179.72/179.60 [2189]~E(x21891,x21892)+E(f655(x21893,x21894,x21895,x21891,x21896),f655(x21893,x21894,x21895,x21892,x21896))
% 179.72/179.60 [2190]~E(x21901,x21902)+E(f655(x21903,x21904,x21905,x21906,x21901),f655(x21903,x21904,x21905,x21906,x21902))
% 179.72/179.60 [2191]~E(x21911,x21912)+E(f817(x21911,x21913,x21914,x21915,x21916,x21917),f817(x21912,x21913,x21914,x21915,x21916,x21917))
% 179.72/179.60 [2192]~E(x21921,x21922)+E(f817(x21923,x21921,x21924,x21925,x21926,x21927),f817(x21923,x21922,x21924,x21925,x21926,x21927))
% 179.72/179.60 [2193]~E(x21931,x21932)+E(f817(x21933,x21934,x21931,x21935,x21936,x21937),f817(x21933,x21934,x21932,x21935,x21936,x21937))
% 179.72/179.60 [2194]~E(x21941,x21942)+E(f817(x21943,x21944,x21945,x21941,x21946,x21947),f817(x21943,x21944,x21945,x21942,x21946,x21947))
% 179.72/179.60 [2195]~E(x21951,x21952)+E(f817(x21953,x21954,x21955,x21956,x21951,x21957),f817(x21953,x21954,x21955,x21956,x21952,x21957))
% 179.72/179.60 [2196]~E(x21961,x21962)+E(f817(x21963,x21964,x21965,x21966,x21967,x21961),f817(x21963,x21964,x21965,x21966,x21967,x21962))
% 179.72/179.60 [2197]~E(x21971,x21972)+E(f581(x21971,x21973,x21974,x21975),f581(x21972,x21973,x21974,x21975))
% 179.72/179.60 [2198]~E(x21981,x21982)+E(f581(x21983,x21981,x21984,x21985),f581(x21983,x21982,x21984,x21985))
% 179.72/179.60 [2199]~E(x21991,x21992)+E(f581(x21993,x21994,x21991,x21995),f581(x21993,x21994,x21992,x21995))
% 179.72/179.60 [2200]~E(x22001,x22002)+E(f581(x22003,x22004,x22005,x22001),f581(x22003,x22004,x22005,x22002))
% 179.72/179.60 [2201]~E(x22011,x22012)+E(f195(x22011,x22013,x22014,x22015),f195(x22012,x22013,x22014,x22015))
% 179.72/179.60 [2202]~E(x22021,x22022)+E(f195(x22023,x22021,x22024,x22025),f195(x22023,x22022,x22024,x22025))
% 179.72/179.60 [2203]~E(x22031,x22032)+E(f195(x22033,x22034,x22031,x22035),f195(x22033,x22034,x22032,x22035))
% 179.72/179.60 [2204]~E(x22041,x22042)+E(f195(x22043,x22044,x22045,x22041),f195(x22043,x22044,x22045,x22042))
% 179.72/179.60 [2205]~E(x22051,x22052)+E(f211(x22051,x22053,x22054,x22055),f211(x22052,x22053,x22054,x22055))
% 179.72/179.60 [2206]~E(x22061,x22062)+E(f211(x22063,x22061,x22064,x22065),f211(x22063,x22062,x22064,x22065))
% 179.72/179.60 [2207]~E(x22071,x22072)+E(f211(x22073,x22074,x22071,x22075),f211(x22073,x22074,x22072,x22075))
% 179.72/179.60 [2208]~E(x22081,x22082)+E(f211(x22083,x22084,x22085,x22081),f211(x22083,x22084,x22085,x22082))
% 179.72/179.60 [2209]~E(x22091,x22092)+E(f508(x22091,x22093,x22094,x22095,x22096,x22097,x22098),f508(x22092,x22093,x22094,x22095,x22096,x22097,x22098))
% 179.72/179.60 [2210]~E(x22101,x22102)+E(f508(x22103,x22101,x22104,x22105,x22106,x22107,x22108),f508(x22103,x22102,x22104,x22105,x22106,x22107,x22108))
% 179.72/179.60 [2211]~E(x22111,x22112)+E(f508(x22113,x22114,x22111,x22115,x22116,x22117,x22118),f508(x22113,x22114,x22112,x22115,x22116,x22117,x22118))
% 179.72/179.60 [2212]~E(x22121,x22122)+E(f508(x22123,x22124,x22125,x22121,x22126,x22127,x22128),f508(x22123,x22124,x22125,x22122,x22126,x22127,x22128))
% 179.72/179.60 [2213]~E(x22131,x22132)+E(f508(x22133,x22134,x22135,x22136,x22131,x22137,x22138),f508(x22133,x22134,x22135,x22136,x22132,x22137,x22138))
% 179.72/179.60 [2214]~E(x22141,x22142)+E(f508(x22143,x22144,x22145,x22146,x22147,x22141,x22148),f508(x22143,x22144,x22145,x22146,x22147,x22142,x22148))
% 179.72/179.60 [2215]~E(x22151,x22152)+E(f508(x22153,x22154,x22155,x22156,x22157,x22158,x22151),f508(x22153,x22154,x22155,x22156,x22157,x22158,x22152))
% 179.72/179.60 [2216]~E(x22161,x22162)+E(f484(x22161,x22163,x22164),f484(x22162,x22163,x22164))
% 179.72/179.60 [2217]~E(x22171,x22172)+E(f484(x22173,x22171,x22174),f484(x22173,x22172,x22174))
% 179.72/179.60 [2218]~E(x22181,x22182)+E(f484(x22183,x22184,x22181),f484(x22183,x22184,x22182))
% 179.72/179.60 [2219]~E(x22191,x22192)+E(f607(x22191,x22193,x22194,x22195,x22196,x22197,x22198,x22199),f607(x22192,x22193,x22194,x22195,x22196,x22197,x22198,x22199))
% 179.72/179.60 [2220]~E(x22201,x22202)+E(f607(x22203,x22201,x22204,x22205,x22206,x22207,x22208,x22209),f607(x22203,x22202,x22204,x22205,x22206,x22207,x22208,x22209))
% 179.72/179.60 [2221]~E(x22211,x22212)+E(f607(x22213,x22214,x22211,x22215,x22216,x22217,x22218,x22219),f607(x22213,x22214,x22212,x22215,x22216,x22217,x22218,x22219))
% 179.72/179.60 [2222]~E(x22221,x22222)+E(f607(x22223,x22224,x22225,x22221,x22226,x22227,x22228,x22229),f607(x22223,x22224,x22225,x22222,x22226,x22227,x22228,x22229))
% 179.72/179.60 [2223]~E(x22231,x22232)+E(f607(x22233,x22234,x22235,x22236,x22231,x22237,x22238,x22239),f607(x22233,x22234,x22235,x22236,x22232,x22237,x22238,x22239))
% 179.72/179.60 [2224]~E(x22241,x22242)+E(f607(x22243,x22244,x22245,x22246,x22247,x22241,x22248,x22249),f607(x22243,x22244,x22245,x22246,x22247,x22242,x22248,x22249))
% 179.72/179.60 [2225]~E(x22251,x22252)+E(f607(x22253,x22254,x22255,x22256,x22257,x22258,x22251,x22259),f607(x22253,x22254,x22255,x22256,x22257,x22258,x22252,x22259))
% 179.72/179.60 [2226]~E(x22261,x22262)+E(f607(x22263,x22264,x22265,x22266,x22267,x22268,x22269,x22261),f607(x22263,x22264,x22265,x22266,x22267,x22268,x22269,x22262))
% 179.72/179.60 [2227]~E(x22271,x22272)+E(f613(x22271,x22273,x22274),f613(x22272,x22273,x22274))
% 179.72/179.60 [2228]~E(x22281,x22282)+E(f613(x22283,x22281,x22284),f613(x22283,x22282,x22284))
% 179.72/179.60 [2229]~E(x22291,x22292)+E(f613(x22293,x22294,x22291),f613(x22293,x22294,x22292))
% 179.72/179.60 [2230]~E(x22301,x22302)+E(f531(x22301,x22303,x22304),f531(x22302,x22303,x22304))
% 179.72/179.60 [2231]~E(x22311,x22312)+E(f531(x22313,x22311,x22314),f531(x22313,x22312,x22314))
% 179.72/179.60 [2232]~E(x22321,x22322)+E(f531(x22323,x22324,x22321),f531(x22323,x22324,x22322))
% 179.72/179.60 [2233]~E(x22331,x22332)+E(f628(x22331,x22333,x22334),f628(x22332,x22333,x22334))
% 179.72/179.60 [2234]~E(x22341,x22342)+E(f628(x22343,x22341,x22344),f628(x22343,x22342,x22344))
% 179.72/179.60 [2235]~E(x22351,x22352)+E(f628(x22353,x22354,x22351),f628(x22353,x22354,x22352))
% 179.72/179.60 [2236]~E(x22361,x22362)+E(f689(x22361,x22363,x22364),f689(x22362,x22363,x22364))
% 179.72/179.60 [2237]~E(x22371,x22372)+E(f689(x22373,x22371,x22374),f689(x22373,x22372,x22374))
% 179.72/179.60 [2238]~E(x22381,x22382)+E(f689(x22383,x22384,x22381),f689(x22383,x22384,x22382))
% 179.72/179.60 [2239]~E(x22391,x22392)+E(f340(x22391,x22393),f340(x22392,x22393))
% 179.72/179.60 [2240]~E(x22401,x22402)+E(f340(x22403,x22401),f340(x22403,x22402))
% 179.72/179.60 [2241]~E(x22411,x22412)+E(f286(x22411,x22413,x22414),f286(x22412,x22413,x22414))
% 179.72/179.60 [2242]~E(x22421,x22422)+E(f286(x22423,x22421,x22424),f286(x22423,x22422,x22424))
% 179.72/179.60 [2243]~E(x22431,x22432)+E(f286(x22433,x22434,x22431),f286(x22433,x22434,x22432))
% 179.72/179.60 [2244]~E(x22441,x22442)+E(f168(x22441,x22443,x22444),f168(x22442,x22443,x22444))
% 179.72/179.60 [2245]~E(x22451,x22452)+E(f168(x22453,x22451,x22454),f168(x22453,x22452,x22454))
% 179.72/179.60 [2246]~E(x22461,x22462)+E(f168(x22463,x22464,x22461),f168(x22463,x22464,x22462))
% 179.72/179.60 [2247]~E(x22471,x22472)+E(f744(x22471,x22473,x22474,x22475,x22476),f744(x22472,x22473,x22474,x22475,x22476))
% 179.72/179.60 [2248]~E(x22481,x22482)+E(f744(x22483,x22481,x22484,x22485,x22486),f744(x22483,x22482,x22484,x22485,x22486))
% 179.72/179.60 [2249]~E(x22491,x22492)+E(f744(x22493,x22494,x22491,x22495,x22496),f744(x22493,x22494,x22492,x22495,x22496))
% 179.72/179.60 [2250]~E(x22501,x22502)+E(f744(x22503,x22504,x22505,x22501,x22506),f744(x22503,x22504,x22505,x22502,x22506))
% 179.72/179.60 [2251]~E(x22511,x22512)+E(f744(x22513,x22514,x22515,x22516,x22511),f744(x22513,x22514,x22515,x22516,x22512))
% 179.72/179.60 [2252]~E(x22521,x22522)+E(f579(x22521,x22523),f579(x22522,x22523))
% 179.72/179.60 [2253]~E(x22531,x22532)+E(f579(x22533,x22531),f579(x22533,x22532))
% 179.72/179.60 [2254]~E(x22541,x22542)+E(f842(x22541,x22543,x22544,x22545,x22546),f842(x22542,x22543,x22544,x22545,x22546))
% 179.72/179.60 [2255]~E(x22551,x22552)+E(f842(x22553,x22551,x22554,x22555,x22556),f842(x22553,x22552,x22554,x22555,x22556))
% 179.72/179.60 [2256]~E(x22561,x22562)+E(f842(x22563,x22564,x22561,x22565,x22566),f842(x22563,x22564,x22562,x22565,x22566))
% 179.72/179.60 [2257]~E(x22571,x22572)+E(f842(x22573,x22574,x22575,x22571,x22576),f842(x22573,x22574,x22575,x22572,x22576))
% 179.72/179.60 [2258]~E(x22581,x22582)+E(f842(x22583,x22584,x22585,x22586,x22581),f842(x22583,x22584,x22585,x22586,x22582))
% 179.72/179.60 [2259]~E(x22591,x22592)+E(f369(x22591,x22593,x22594,x22595,x22596),f369(x22592,x22593,x22594,x22595,x22596))
% 179.72/179.60 [2260]~E(x22601,x22602)+E(f369(x22603,x22601,x22604,x22605,x22606),f369(x22603,x22602,x22604,x22605,x22606))
% 179.72/179.60 [2261]~E(x22611,x22612)+E(f369(x22613,x22614,x22611,x22615,x22616),f369(x22613,x22614,x22612,x22615,x22616))
% 179.72/179.60 [2262]~E(x22621,x22622)+E(f369(x22623,x22624,x22625,x22621,x22626),f369(x22623,x22624,x22625,x22622,x22626))
% 179.72/179.60 [2263]~E(x22631,x22632)+E(f369(x22633,x22634,x22635,x22636,x22631),f369(x22633,x22634,x22635,x22636,x22632))
% 179.72/179.60 [2264]~E(x22641,x22642)+E(f477(x22641,x22643,x22644,x22645,x22646,x22647,x22648,x22649),f477(x22642,x22643,x22644,x22645,x22646,x22647,x22648,x22649))
% 179.72/179.60 [2265]~E(x22651,x22652)+E(f477(x22653,x22651,x22654,x22655,x22656,x22657,x22658,x22659),f477(x22653,x22652,x22654,x22655,x22656,x22657,x22658,x22659))
% 179.72/179.60 [2266]~E(x22661,x22662)+E(f477(x22663,x22664,x22661,x22665,x22666,x22667,x22668,x22669),f477(x22663,x22664,x22662,x22665,x22666,x22667,x22668,x22669))
% 179.72/179.60 [2267]~E(x22671,x22672)+E(f477(x22673,x22674,x22675,x22671,x22676,x22677,x22678,x22679),f477(x22673,x22674,x22675,x22672,x22676,x22677,x22678,x22679))
% 179.72/179.60 [2268]~E(x22681,x22682)+E(f477(x22683,x22684,x22685,x22686,x22681,x22687,x22688,x22689),f477(x22683,x22684,x22685,x22686,x22682,x22687,x22688,x22689))
% 179.72/179.60 [2269]~E(x22691,x22692)+E(f477(x22693,x22694,x22695,x22696,x22697,x22691,x22698,x22699),f477(x22693,x22694,x22695,x22696,x22697,x22692,x22698,x22699))
% 179.72/179.60 [2270]~E(x22701,x22702)+E(f477(x22703,x22704,x22705,x22706,x22707,x22708,x22701,x22709),f477(x22703,x22704,x22705,x22706,x22707,x22708,x22702,x22709))
% 179.72/179.60 [2271]~E(x22711,x22712)+E(f477(x22713,x22714,x22715,x22716,x22717,x22718,x22719,x22711),f477(x22713,x22714,x22715,x22716,x22717,x22718,x22719,x22712))
% 179.72/179.60 [2272]~E(x22721,x22722)+E(f661(x22721,x22723,x22724),f661(x22722,x22723,x22724))
% 179.72/179.60 [2273]~E(x22731,x22732)+E(f661(x22733,x22731,x22734),f661(x22733,x22732,x22734))
% 179.72/179.60 [2274]~E(x22741,x22742)+E(f661(x22743,x22744,x22741),f661(x22743,x22744,x22742))
% 179.72/179.60 [2275]~E(x22751,x22752)+E(f619(x22751,x22753,x22754,x22755,x22756,x22757),f619(x22752,x22753,x22754,x22755,x22756,x22757))
% 179.72/179.60 [2276]~E(x22761,x22762)+E(f619(x22763,x22761,x22764,x22765,x22766,x22767),f619(x22763,x22762,x22764,x22765,x22766,x22767))
% 179.72/179.60 [2277]~E(x22771,x22772)+E(f619(x22773,x22774,x22771,x22775,x22776,x22777),f619(x22773,x22774,x22772,x22775,x22776,x22777))
% 179.72/179.60 [2278]~E(x22781,x22782)+E(f619(x22783,x22784,x22785,x22781,x22786,x22787),f619(x22783,x22784,x22785,x22782,x22786,x22787))
% 179.72/179.60 [2279]~E(x22791,x22792)+E(f619(x22793,x22794,x22795,x22796,x22791,x22797),f619(x22793,x22794,x22795,x22796,x22792,x22797))
% 179.72/179.60 [2280]~E(x22801,x22802)+E(f619(x22803,x22804,x22805,x22806,x22807,x22801),f619(x22803,x22804,x22805,x22806,x22807,x22802))
% 179.72/179.60 [2281]~E(x22811,x22812)+E(f723(x22811,x22813,x22814,x22815,x22816,x22817,x22818,x22819),f723(x22812,x22813,x22814,x22815,x22816,x22817,x22818,x22819))
% 179.72/179.60 [2282]~E(x22821,x22822)+E(f723(x22823,x22821,x22824,x22825,x22826,x22827,x22828,x22829),f723(x22823,x22822,x22824,x22825,x22826,x22827,x22828,x22829))
% 179.72/179.60 [2283]~E(x22831,x22832)+E(f723(x22833,x22834,x22831,x22835,x22836,x22837,x22838,x22839),f723(x22833,x22834,x22832,x22835,x22836,x22837,x22838,x22839))
% 179.72/179.60 [2284]~E(x22841,x22842)+E(f723(x22843,x22844,x22845,x22841,x22846,x22847,x22848,x22849),f723(x22843,x22844,x22845,x22842,x22846,x22847,x22848,x22849))
% 179.72/179.60 [2285]~E(x22851,x22852)+E(f723(x22853,x22854,x22855,x22856,x22851,x22857,x22858,x22859),f723(x22853,x22854,x22855,x22856,x22852,x22857,x22858,x22859))
% 179.72/179.60 [2286]~E(x22861,x22862)+E(f723(x22863,x22864,x22865,x22866,x22867,x22861,x22868,x22869),f723(x22863,x22864,x22865,x22866,x22867,x22862,x22868,x22869))
% 179.72/179.60 [2287]~E(x22871,x22872)+E(f723(x22873,x22874,x22875,x22876,x22877,x22878,x22871,x22879),f723(x22873,x22874,x22875,x22876,x22877,x22878,x22872,x22879))
% 179.72/179.60 [2288]~E(x22881,x22882)+E(f723(x22883,x22884,x22885,x22886,x22887,x22888,x22889,x22881),f723(x22883,x22884,x22885,x22886,x22887,x22888,x22889,x22882))
% 179.72/179.60 [2289]~E(x22891,x22892)+E(f464(x22891,x22893,x22894,x22895),f464(x22892,x22893,x22894,x22895))
% 179.72/179.60 [2290]~E(x22901,x22902)+E(f464(x22903,x22901,x22904,x22905),f464(x22903,x22902,x22904,x22905))
% 179.72/179.60 [2291]~E(x22911,x22912)+E(f464(x22913,x22914,x22911,x22915),f464(x22913,x22914,x22912,x22915))
% 179.72/179.60 [2292]~E(x22921,x22922)+E(f464(x22923,x22924,x22925,x22921),f464(x22923,x22924,x22925,x22922))
% 179.72/179.60 [2293]~E(x22931,x22932)+E(f350(x22931,x22933,x22934),f350(x22932,x22933,x22934))
% 179.72/179.60 [2294]~E(x22941,x22942)+E(f350(x22943,x22941,x22944),f350(x22943,x22942,x22944))
% 179.72/179.60 [2295]~E(x22951,x22952)+E(f350(x22953,x22954,x22951),f350(x22953,x22954,x22952))
% 179.72/179.60 [2296]~E(x22961,x22962)+E(f395(x22961,x22963,x22964,x22965),f395(x22962,x22963,x22964,x22965))
% 179.72/179.60 [2297]~E(x22971,x22972)+E(f395(x22973,x22971,x22974,x22975),f395(x22973,x22972,x22974,x22975))
% 179.72/179.60 [2298]~E(x22981,x22982)+E(f395(x22983,x22984,x22981,x22985),f395(x22983,x22984,x22982,x22985))
% 179.72/179.60 [2299]~E(x22991,x22992)+E(f395(x22993,x22994,x22995,x22991),f395(x22993,x22994,x22995,x22992))
% 179.72/179.60 [2300]~E(x23001,x23002)+E(f774(x23001,x23003,x23004,x23005,x23006,x23007),f774(x23002,x23003,x23004,x23005,x23006,x23007))
% 179.72/179.60 [2301]~E(x23011,x23012)+E(f774(x23013,x23011,x23014,x23015,x23016,x23017),f774(x23013,x23012,x23014,x23015,x23016,x23017))
% 179.72/179.60 [2302]~E(x23021,x23022)+E(f774(x23023,x23024,x23021,x23025,x23026,x23027),f774(x23023,x23024,x23022,x23025,x23026,x23027))
% 179.72/179.60 [2303]~E(x23031,x23032)+E(f774(x23033,x23034,x23035,x23031,x23036,x23037),f774(x23033,x23034,x23035,x23032,x23036,x23037))
% 179.72/179.60 [2304]~E(x23041,x23042)+E(f774(x23043,x23044,x23045,x23046,x23041,x23047),f774(x23043,x23044,x23045,x23046,x23042,x23047))
% 179.72/179.60 [2305]~E(x23051,x23052)+E(f774(x23053,x23054,x23055,x23056,x23057,x23051),f774(x23053,x23054,x23055,x23056,x23057,x23052))
% 179.72/179.60 [2306]~E(x23061,x23062)+E(f787(x23061,x23063),f787(x23062,x23063))
% 179.72/179.60 [2307]~E(x23071,x23072)+E(f787(x23073,x23071),f787(x23073,x23072))
% 179.72/179.60 [2308]~E(x23081,x23082)+E(f538(x23081,x23083,x23084),f538(x23082,x23083,x23084))
% 179.72/179.60 [2309]~E(x23091,x23092)+E(f538(x23093,x23091,x23094),f538(x23093,x23092,x23094))
% 179.72/179.60 [2310]~E(x23101,x23102)+E(f538(x23103,x23104,x23101),f538(x23103,x23104,x23102))
% 179.72/179.60 [2311]~E(x23111,x23112)+E(f643(x23111,x23113,x23114),f643(x23112,x23113,x23114))
% 179.72/179.60 [2312]~E(x23121,x23122)+E(f643(x23123,x23121,x23124),f643(x23123,x23122,x23124))
% 179.72/179.60 [2313]~E(x23131,x23132)+E(f643(x23133,x23134,x23131),f643(x23133,x23134,x23132))
% 179.72/179.60 [2314]~E(x23141,x23142)+E(f775(x23141,x23143,x23144,x23145,x23146,x23147),f775(x23142,x23143,x23144,x23145,x23146,x23147))
% 179.72/179.60 [2315]~E(x23151,x23152)+E(f775(x23153,x23151,x23154,x23155,x23156,x23157),f775(x23153,x23152,x23154,x23155,x23156,x23157))
% 179.72/179.60 [2316]~E(x23161,x23162)+E(f775(x23163,x23164,x23161,x23165,x23166,x23167),f775(x23163,x23164,x23162,x23165,x23166,x23167))
% 179.72/179.60 [2317]~E(x23171,x23172)+E(f775(x23173,x23174,x23175,x23171,x23176,x23177),f775(x23173,x23174,x23175,x23172,x23176,x23177))
% 179.72/179.60 [2318]~E(x23181,x23182)+E(f775(x23183,x23184,x23185,x23186,x23181,x23187),f775(x23183,x23184,x23185,x23186,x23182,x23187))
% 179.72/179.60 [2319]~E(x23191,x23192)+E(f775(x23193,x23194,x23195,x23196,x23197,x23191),f775(x23193,x23194,x23195,x23196,x23197,x23192))
% 179.72/179.60 [2320]~E(x23201,x23202)+E(f767(x23201,x23203,x23204),f767(x23202,x23203,x23204))
% 179.72/179.60 [2321]~E(x23211,x23212)+E(f767(x23213,x23211,x23214),f767(x23213,x23212,x23214))
% 179.72/179.60 [2322]~E(x23221,x23222)+E(f767(x23223,x23224,x23221),f767(x23223,x23224,x23222))
% 179.72/179.60 [2323]~E(x23231,x23232)+E(f507(x23231,x23233,x23234),f507(x23232,x23233,x23234))
% 179.72/179.60 [2324]~E(x23241,x23242)+E(f507(x23243,x23241,x23244),f507(x23243,x23242,x23244))
% 179.72/179.60 [2325]~E(x23251,x23252)+E(f507(x23253,x23254,x23251),f507(x23253,x23254,x23252))
% 179.72/179.60 [2326]~E(x23261,x23262)+E(f614(x23261,x23263,x23264,x23265),f614(x23262,x23263,x23264,x23265))
% 179.72/179.60 [2327]~E(x23271,x23272)+E(f614(x23273,x23271,x23274,x23275),f614(x23273,x23272,x23274,x23275))
% 179.72/179.60 [2328]~E(x23281,x23282)+E(f614(x23283,x23284,x23281,x23285),f614(x23283,x23284,x23282,x23285))
% 179.72/179.60 [2329]~E(x23291,x23292)+E(f614(x23293,x23294,x23295,x23291),f614(x23293,x23294,x23295,x23292))
% 179.72/179.60 [2330]~E(x23301,x23302)+E(f629(x23301,x23303,x23304,x23305),f629(x23302,x23303,x23304,x23305))
% 179.72/179.60 [2331]~E(x23311,x23312)+E(f629(x23313,x23311,x23314,x23315),f629(x23313,x23312,x23314,x23315))
% 179.72/179.60 [2332]~E(x23321,x23322)+E(f629(x23323,x23324,x23321,x23325),f629(x23323,x23324,x23322,x23325))
% 179.72/179.60 [2333]~E(x23331,x23332)+E(f629(x23333,x23334,x23335,x23331),f629(x23333,x23334,x23335,x23332))
% 179.72/179.60 [2334]~E(x23341,x23342)+E(f684(x23341,x23343,x23344,x23345,x23346,x23347),f684(x23342,x23343,x23344,x23345,x23346,x23347))
% 179.72/179.60 [2335]~E(x23351,x23352)+E(f684(x23353,x23351,x23354,x23355,x23356,x23357),f684(x23353,x23352,x23354,x23355,x23356,x23357))
% 179.72/179.60 [2336]~E(x23361,x23362)+E(f684(x23363,x23364,x23361,x23365,x23366,x23367),f684(x23363,x23364,x23362,x23365,x23366,x23367))
% 179.72/179.60 [2337]~E(x23371,x23372)+E(f684(x23373,x23374,x23375,x23371,x23376,x23377),f684(x23373,x23374,x23375,x23372,x23376,x23377))
% 179.72/179.60 [2338]~E(x23381,x23382)+E(f684(x23383,x23384,x23385,x23386,x23381,x23387),f684(x23383,x23384,x23385,x23386,x23382,x23387))
% 179.72/179.60 [2339]~E(x23391,x23392)+E(f684(x23393,x23394,x23395,x23396,x23397,x23391),f684(x23393,x23394,x23395,x23396,x23397,x23392))
% 179.72/179.60 [2340]~E(x23401,x23402)+E(f708(x23401,x23403,x23404,x23405,x23406),f708(x23402,x23403,x23404,x23405,x23406))
% 179.72/179.60 [2341]~E(x23411,x23412)+E(f708(x23413,x23411,x23414,x23415,x23416),f708(x23413,x23412,x23414,x23415,x23416))
% 179.72/179.60 [2342]~E(x23421,x23422)+E(f708(x23423,x23424,x23421,x23425,x23426),f708(x23423,x23424,x23422,x23425,x23426))
% 179.72/179.60 [2343]~E(x23431,x23432)+E(f708(x23433,x23434,x23435,x23431,x23436),f708(x23433,x23434,x23435,x23432,x23436))
% 179.72/179.60 [2344]~E(x23441,x23442)+E(f708(x23443,x23444,x23445,x23446,x23441),f708(x23443,x23444,x23445,x23446,x23442))
% 179.72/179.60 [2345]~E(x23451,x23452)+E(f368(x23451,x23453,x23454),f368(x23452,x23453,x23454))
% 179.72/179.60 [2346]~E(x23461,x23462)+E(f368(x23463,x23461,x23464),f368(x23463,x23462,x23464))
% 179.72/179.60 [2347]~E(x23471,x23472)+E(f368(x23473,x23474,x23471),f368(x23473,x23474,x23472))
% 179.72/179.60 [2348]~E(x23481,x23482)+E(f671(x23481,x23483),f671(x23482,x23483))
% 179.72/179.60 [2349]~E(x23491,x23492)+E(f671(x23493,x23491),f671(x23493,x23492))
% 179.72/179.60 [2350]~E(x23501,x23502)+E(f852(x23501,x23503,x23504),f852(x23502,x23503,x23504))
% 179.72/179.60 [2351]~E(x23511,x23512)+E(f852(x23513,x23511,x23514),f852(x23513,x23512,x23514))
% 179.72/179.60 [2352]~E(x23521,x23522)+E(f852(x23523,x23524,x23521),f852(x23523,x23524,x23522))
% 179.72/179.60 [2353]~E(x23531,x23532)+E(f390(x23531,x23533,x23534,x23535),f390(x23532,x23533,x23534,x23535))
% 179.72/179.60 [2354]~E(x23541,x23542)+E(f390(x23543,x23541,x23544,x23545),f390(x23543,x23542,x23544,x23545))
% 179.72/179.60 [2355]~E(x23551,x23552)+E(f390(x23553,x23554,x23551,x23555),f390(x23553,x23554,x23552,x23555))
% 179.72/179.60 [2356]~E(x23561,x23562)+E(f390(x23563,x23564,x23565,x23561),f390(x23563,x23564,x23565,x23562))
% 179.72/179.60 [2357]~E(x23571,x23572)+E(f339(x23571,x23573),f339(x23572,x23573))
% 179.72/179.60 [2358]~E(x23581,x23582)+E(f339(x23583,x23581),f339(x23583,x23582))
% 179.72/179.60 [2359]~E(x23591,x23592)+E(f433(x23591,x23593,x23594,x23595,x23596),f433(x23592,x23593,x23594,x23595,x23596))
% 179.72/179.60 [2360]~E(x23601,x23602)+E(f433(x23603,x23601,x23604,x23605,x23606),f433(x23603,x23602,x23604,x23605,x23606))
% 179.72/179.60 [2361]~E(x23611,x23612)+E(f433(x23613,x23614,x23611,x23615,x23616),f433(x23613,x23614,x23612,x23615,x23616))
% 179.72/179.60 [2362]~E(x23621,x23622)+E(f433(x23623,x23624,x23625,x23621,x23626),f433(x23623,x23624,x23625,x23622,x23626))
% 179.72/179.60 [2363]~E(x23631,x23632)+E(f433(x23633,x23634,x23635,x23636,x23631),f433(x23633,x23634,x23635,x23636,x23632))
% 179.72/179.60 [2364]~E(x23641,x23642)+E(f21(x23641,x23643),f21(x23642,x23643))
% 179.72/179.60 [2365]~E(x23651,x23652)+E(f21(x23653,x23651),f21(x23653,x23652))
% 179.72/179.60 [2366]~E(x23661,x23662)+E(f377(x23661,x23663),f377(x23662,x23663))
% 179.72/179.60 [2367]~E(x23671,x23672)+E(f377(x23673,x23671),f377(x23673,x23672))
% 179.72/179.60 [2368]~E(x23681,x23682)+E(f93(x23681,x23683,x23684),f93(x23682,x23683,x23684))
% 179.72/179.60 [2369]~E(x23691,x23692)+E(f93(x23693,x23691,x23694),f93(x23693,x23692,x23694))
% 179.72/179.60 [2370]~E(x23701,x23702)+E(f93(x23703,x23704,x23701),f93(x23703,x23704,x23702))
% 179.72/179.60 [2371]~E(x23711,x23712)+E(f94(x23711,x23713,x23714,x23715),f94(x23712,x23713,x23714,x23715))
% 179.72/179.60 [2372]~E(x23721,x23722)+E(f94(x23723,x23721,x23724,x23725),f94(x23723,x23722,x23724,x23725))
% 179.72/179.60 [2373]~E(x23731,x23732)+E(f94(x23733,x23734,x23731,x23735),f94(x23733,x23734,x23732,x23735))
% 179.72/179.60 [2374]~E(x23741,x23742)+E(f94(x23743,x23744,x23745,x23741),f94(x23743,x23744,x23745,x23742))
% 179.72/179.60 [2375]~E(x23751,x23752)+E(f304(x23751,x23753),f304(x23752,x23753))
% 179.72/179.60 [2376]~E(x23761,x23762)+E(f304(x23763,x23761),f304(x23763,x23762))
% 179.72/179.60 [2377]~E(x23771,x23772)+E(f806(x23771,x23773,x23774,x23775,x23776),f806(x23772,x23773,x23774,x23775,x23776))
% 179.72/179.60 [2378]~E(x23781,x23782)+E(f806(x23783,x23781,x23784,x23785,x23786),f806(x23783,x23782,x23784,x23785,x23786))
% 179.72/179.60 [2379]~E(x23791,x23792)+E(f806(x23793,x23794,x23791,x23795,x23796),f806(x23793,x23794,x23792,x23795,x23796))
% 179.72/179.60 [2380]~E(x23801,x23802)+E(f806(x23803,x23804,x23805,x23801,x23806),f806(x23803,x23804,x23805,x23802,x23806))
% 179.72/179.60 [2381]~E(x23811,x23812)+E(f806(x23813,x23814,x23815,x23816,x23811),f806(x23813,x23814,x23815,x23816,x23812))
% 179.72/179.60 [2382]~E(x23821,x23822)+E(f816(x23821,x23823),f816(x23822,x23823))
% 179.72/179.60 [2383]~E(x23831,x23832)+E(f816(x23833,x23831),f816(x23833,x23832))
% 179.72/179.60 [2384]~E(x23841,x23842)+E(f524(x23841),f524(x23842))
% 179.72/179.60 [2385]~E(x23851,x23852)+E(f461(x23851,x23853,x23854,x23855),f461(x23852,x23853,x23854,x23855))
% 179.72/179.60 [2386]~E(x23861,x23862)+E(f461(x23863,x23861,x23864,x23865),f461(x23863,x23862,x23864,x23865))
% 179.72/179.60 [2387]~E(x23871,x23872)+E(f461(x23873,x23874,x23871,x23875),f461(x23873,x23874,x23872,x23875))
% 179.72/179.60 [2388]~E(x23881,x23882)+E(f461(x23883,x23884,x23885,x23881),f461(x23883,x23884,x23885,x23882))
% 179.72/179.60 [2389]~E(x23891,x23892)+E(f763(x23891,x23893,x23894,x23895),f763(x23892,x23893,x23894,x23895))
% 179.72/179.60 [2390]~E(x23901,x23902)+E(f763(x23903,x23901,x23904,x23905),f763(x23903,x23902,x23904,x23905))
% 179.72/179.60 [2391]~E(x23911,x23912)+E(f763(x23913,x23914,x23911,x23915),f763(x23913,x23914,x23912,x23915))
% 179.72/179.60 [2392]~E(x23921,x23922)+E(f763(x23923,x23924,x23925,x23921),f763(x23923,x23924,x23925,x23922))
% 179.72/179.60 [2393]~E(x23931,x23932)+E(f564(x23931,x23933,x23934,x23935,x23936),f564(x23932,x23933,x23934,x23935,x23936))
% 179.72/179.60 [2394]~E(x23941,x23942)+E(f564(x23943,x23941,x23944,x23945,x23946),f564(x23943,x23942,x23944,x23945,x23946))
% 179.72/179.60 [2395]~E(x23951,x23952)+E(f564(x23953,x23954,x23951,x23955,x23956),f564(x23953,x23954,x23952,x23955,x23956))
% 179.72/179.60 [2396]~E(x23961,x23962)+E(f564(x23963,x23964,x23965,x23961,x23966),f564(x23963,x23964,x23965,x23962,x23966))
% 179.72/179.60 [2397]~E(x23971,x23972)+E(f564(x23973,x23974,x23975,x23976,x23971),f564(x23973,x23974,x23975,x23976,x23972))
% 179.72/179.60 [2398]~E(x23981,x23982)+E(f197(x23981,x23983,x23984,x23985),f197(x23982,x23983,x23984,x23985))
% 179.72/179.60 [2399]~E(x23991,x23992)+E(f197(x23993,x23991,x23994,x23995),f197(x23993,x23992,x23994,x23995))
% 179.72/179.60 [2400]~E(x24001,x24002)+E(f197(x24003,x24004,x24001,x24005),f197(x24003,x24004,x24002,x24005))
% 179.72/179.60 [2401]~E(x24011,x24012)+E(f197(x24013,x24014,x24015,x24011),f197(x24013,x24014,x24015,x24012))
% 179.72/179.60 [2402]~E(x24021,x24022)+E(f616(x24021,x24023,x24024,x24025,x24026,x24027),f616(x24022,x24023,x24024,x24025,x24026,x24027))
% 179.72/179.60 [2403]~E(x24031,x24032)+E(f616(x24033,x24031,x24034,x24035,x24036,x24037),f616(x24033,x24032,x24034,x24035,x24036,x24037))
% 179.72/179.60 [2404]~E(x24041,x24042)+E(f616(x24043,x24044,x24041,x24045,x24046,x24047),f616(x24043,x24044,x24042,x24045,x24046,x24047))
% 179.72/179.60 [2405]~E(x24051,x24052)+E(f616(x24053,x24054,x24055,x24051,x24056,x24057),f616(x24053,x24054,x24055,x24052,x24056,x24057))
% 179.72/179.60 [2406]~E(x24061,x24062)+E(f616(x24063,x24064,x24065,x24066,x24061,x24067),f616(x24063,x24064,x24065,x24066,x24062,x24067))
% 179.72/179.60 [2407]~E(x24071,x24072)+E(f616(x24073,x24074,x24075,x24076,x24077,x24071),f616(x24073,x24074,x24075,x24076,x24077,x24072))
% 179.72/179.60 [2408]~E(x24081,x24082)+E(f328(x24081),f328(x24082))
% 179.72/179.60 [2409]~E(x24091,x24092)+E(f807(x24091,x24093,x24094,x24095),f807(x24092,x24093,x24094,x24095))
% 179.72/179.60 [2410]~E(x24101,x24102)+E(f807(x24103,x24101,x24104,x24105),f807(x24103,x24102,x24104,x24105))
% 179.72/179.60 [2411]~E(x24111,x24112)+E(f807(x24113,x24114,x24111,x24115),f807(x24113,x24114,x24112,x24115))
% 179.72/179.60 [2412]~E(x24121,x24122)+E(f807(x24123,x24124,x24125,x24121),f807(x24123,x24124,x24125,x24122))
% 179.72/179.60 [2413]~E(x24131,x24132)+E(f491(x24131,x24133,x24134),f491(x24132,x24133,x24134))
% 179.72/179.60 [2414]~E(x24141,x24142)+E(f491(x24143,x24141,x24144),f491(x24143,x24142,x24144))
% 179.72/179.60 [2415]~E(x24151,x24152)+E(f491(x24153,x24154,x24151),f491(x24153,x24154,x24152))
% 179.72/179.60 [2416]~E(x24161,x24162)+E(f544(x24161,x24163),f544(x24162,x24163))
% 179.72/179.60 [2417]~E(x24171,x24172)+E(f544(x24173,x24171),f544(x24173,x24172))
% 179.72/179.60 [2418]~E(x24181,x24182)+E(f407(x24181,x24183),f407(x24182,x24183))
% 179.72/179.60 [2419]~E(x24191,x24192)+E(f407(x24193,x24191),f407(x24193,x24192))
% 179.72/179.60 [2420]~E(x24201,x24202)+E(f553(x24201,x24203,x24204),f553(x24202,x24203,x24204))
% 179.72/179.60 [2421]~E(x24211,x24212)+E(f553(x24213,x24211,x24214),f553(x24213,x24212,x24214))
% 179.72/179.60 [2422]~E(x24221,x24222)+E(f553(x24223,x24224,x24221),f553(x24223,x24224,x24222))
% 179.72/179.60 [2423]~E(x24231,x24232)+E(f704(x24231,x24233,x24234),f704(x24232,x24233,x24234))
% 179.72/179.60 [2424]~E(x24241,x24242)+E(f704(x24243,x24241,x24244),f704(x24243,x24242,x24244))
% 179.72/179.60 [2425]~E(x24251,x24252)+E(f704(x24253,x24254,x24251),f704(x24253,x24254,x24252))
% 179.72/179.60 [2426]~E(x24261,x24262)+E(f736(x24261,x24263,x24264),f736(x24262,x24263,x24264))
% 179.72/179.60 [2427]~E(x24271,x24272)+E(f736(x24273,x24271,x24274),f736(x24273,x24272,x24274))
% 179.72/179.60 [2428]~E(x24281,x24282)+E(f736(x24283,x24284,x24281),f736(x24283,x24284,x24282))
% 179.72/179.60 [2429]~E(x24291,x24292)+E(f473(x24291,x24293,x24294,x24295,x24296),f473(x24292,x24293,x24294,x24295,x24296))
% 179.72/179.60 [2430]~E(x24301,x24302)+E(f473(x24303,x24301,x24304,x24305,x24306),f473(x24303,x24302,x24304,x24305,x24306))
% 179.72/179.60 [2431]~E(x24311,x24312)+E(f473(x24313,x24314,x24311,x24315,x24316),f473(x24313,x24314,x24312,x24315,x24316))
% 179.72/179.60 [2432]~E(x24321,x24322)+E(f473(x24323,x24324,x24325,x24321,x24326),f473(x24323,x24324,x24325,x24322,x24326))
% 179.72/179.60 [2433]~E(x24331,x24332)+E(f473(x24333,x24334,x24335,x24336,x24331),f473(x24333,x24334,x24335,x24336,x24332))
% 179.72/179.60 [2434]~E(x24341,x24342)+E(f343(x24341,x24343),f343(x24342,x24343))
% 179.72/179.60 [2435]~E(x24351,x24352)+E(f343(x24353,x24351),f343(x24353,x24352))
% 179.72/179.60 [2436]~E(x24361,x24362)+E(f707(x24361,x24363,x24364,x24365,x24366),f707(x24362,x24363,x24364,x24365,x24366))
% 179.72/179.60 [2437]~E(x24371,x24372)+E(f707(x24373,x24371,x24374,x24375,x24376),f707(x24373,x24372,x24374,x24375,x24376))
% 179.72/179.60 [2438]~E(x24381,x24382)+E(f707(x24383,x24384,x24381,x24385,x24386),f707(x24383,x24384,x24382,x24385,x24386))
% 179.72/179.60 [2439]~E(x24391,x24392)+E(f707(x24393,x24394,x24395,x24391,x24396),f707(x24393,x24394,x24395,x24392,x24396))
% 179.72/179.60 [2440]~E(x24401,x24402)+E(f707(x24403,x24404,x24405,x24406,x24401),f707(x24403,x24404,x24405,x24406,x24402))
% 179.72/179.60 [2441]~E(x24411,x24412)+E(f818(x24411,x24413),f818(x24412,x24413))
% 179.72/179.60 [2442]~E(x24421,x24422)+E(f818(x24423,x24421),f818(x24423,x24422))
% 179.72/179.60 [2443]~E(x24431,x24432)+E(f701(x24431,x24433,x24434),f701(x24432,x24433,x24434))
% 179.72/179.60 [2444]~E(x24441,x24442)+E(f701(x24443,x24441,x24444),f701(x24443,x24442,x24444))
% 179.72/179.60 [2445]~E(x24451,x24452)+E(f701(x24453,x24454,x24451),f701(x24453,x24454,x24452))
% 179.72/179.60 [2446]~E(x24461,x24462)+E(f662(x24461,x24463,x24464,x24465),f662(x24462,x24463,x24464,x24465))
% 179.72/179.60 [2447]~E(x24471,x24472)+E(f662(x24473,x24471,x24474,x24475),f662(x24473,x24472,x24474,x24475))
% 179.72/179.60 [2448]~E(x24481,x24482)+E(f662(x24483,x24484,x24481,x24485),f662(x24483,x24484,x24482,x24485))
% 179.72/179.60 [2449]~E(x24491,x24492)+E(f662(x24493,x24494,x24495,x24491),f662(x24493,x24494,x24495,x24492))
% 179.72/179.60 [2450]~E(x24501,x24502)+E(f759(x24501,x24503,x24504,x24505),f759(x24502,x24503,x24504,x24505))
% 179.72/179.60 [2451]~E(x24511,x24512)+E(f759(x24513,x24511,x24514,x24515),f759(x24513,x24512,x24514,x24515))
% 179.72/179.60 [2452]~E(x24521,x24522)+E(f759(x24523,x24524,x24521,x24525),f759(x24523,x24524,x24522,x24525))
% 179.72/179.60 [2453]~E(x24531,x24532)+E(f759(x24533,x24534,x24535,x24531),f759(x24533,x24534,x24535,x24532))
% 179.72/179.60 [2454]~E(x24541,x24542)+E(f601(x24541,x24543),f601(x24542,x24543))
% 179.72/179.60 [2455]~E(x24551,x24552)+E(f601(x24553,x24551),f601(x24553,x24552))
% 179.72/179.60 [2456]~E(x24561,x24562)+E(f667(x24561,x24563,x24564,x24565,x24566),f667(x24562,x24563,x24564,x24565,x24566))
% 179.72/179.60 [2457]~E(x24571,x24572)+E(f667(x24573,x24571,x24574,x24575,x24576),f667(x24573,x24572,x24574,x24575,x24576))
% 179.72/179.60 [2458]~E(x24581,x24582)+E(f667(x24583,x24584,x24581,x24585,x24586),f667(x24583,x24584,x24582,x24585,x24586))
% 179.72/179.60 [2459]~E(x24591,x24592)+E(f667(x24593,x24594,x24595,x24591,x24596),f667(x24593,x24594,x24595,x24592,x24596))
% 179.72/179.60 [2460]~E(x24601,x24602)+E(f667(x24603,x24604,x24605,x24606,x24601),f667(x24603,x24604,x24605,x24606,x24602))
% 179.72/179.60 [2461]~E(x24611,x24612)+E(f591(x24611,x24613,x24614,x24615),f591(x24612,x24613,x24614,x24615))
% 179.72/179.60 [2462]~E(x24621,x24622)+E(f591(x24623,x24621,x24624,x24625),f591(x24623,x24622,x24624,x24625))
% 179.72/179.60 [2463]~E(x24631,x24632)+E(f591(x24633,x24634,x24631,x24635),f591(x24633,x24634,x24632,x24635))
% 179.72/179.60 [2464]~E(x24641,x24642)+E(f591(x24643,x24644,x24645,x24641),f591(x24643,x24644,x24645,x24642))
% 179.72/179.60 [2465]~E(x24651,x24652)+E(f668(x24651,x24653,x24654,x24655),f668(x24652,x24653,x24654,x24655))
% 179.72/179.60 [2466]~E(x24661,x24662)+E(f668(x24663,x24661,x24664,x24665),f668(x24663,x24662,x24664,x24665))
% 179.72/179.60 [2467]~E(x24671,x24672)+E(f668(x24673,x24674,x24671,x24675),f668(x24673,x24674,x24672,x24675))
% 179.72/179.60 [2468]~E(x24681,x24682)+E(f668(x24683,x24684,x24685,x24681),f668(x24683,x24684,x24685,x24682))
% 179.72/179.60 [2469]~E(x24691,x24692)+E(f174(x24691),f174(x24692))
% 179.72/179.60 [2470]~E(x24701,x24702)+E(f386(x24701,x24703),f386(x24702,x24703))
% 179.72/179.60 [2471]~E(x24711,x24712)+E(f386(x24713,x24711),f386(x24713,x24712))
% 179.72/179.60 [2472]~E(x24721,x24722)+E(f287(x24721,x24723,x24724,x24725),f287(x24722,x24723,x24724,x24725))
% 179.72/179.60 [2473]~E(x24731,x24732)+E(f287(x24733,x24731,x24734,x24735),f287(x24733,x24732,x24734,x24735))
% 179.72/179.60 [2474]~E(x24741,x24742)+E(f287(x24743,x24744,x24741,x24745),f287(x24743,x24744,x24742,x24745))
% 179.72/179.60 [2475]~E(x24751,x24752)+E(f287(x24753,x24754,x24755,x24751),f287(x24753,x24754,x24755,x24752))
% 179.72/179.60 [2476]~E(x24761,x24762)+E(f721(x24761,x24763),f721(x24762,x24763))
% 179.72/179.60 [2477]~E(x24771,x24772)+E(f721(x24773,x24771),f721(x24773,x24772))
% 179.72/179.60 [2478]~E(x24781,x24782)+E(f683(x24781,x24783,x24784,x24785),f683(x24782,x24783,x24784,x24785))
% 179.72/179.60 [2479]~E(x24791,x24792)+E(f683(x24793,x24791,x24794,x24795),f683(x24793,x24792,x24794,x24795))
% 179.72/179.60 [2480]~E(x24801,x24802)+E(f683(x24803,x24804,x24801,x24805),f683(x24803,x24804,x24802,x24805))
% 179.72/179.60 [2481]~E(x24811,x24812)+E(f683(x24813,x24814,x24815,x24811),f683(x24813,x24814,x24815,x24812))
% 179.72/179.60 [2482]~E(x24821,x24822)+E(f375(x24821,x24823,x24824,x24825,x24826),f375(x24822,x24823,x24824,x24825,x24826))
% 179.72/179.60 [2483]~E(x24831,x24832)+E(f375(x24833,x24831,x24834,x24835,x24836),f375(x24833,x24832,x24834,x24835,x24836))
% 179.72/179.60 [2484]~E(x24841,x24842)+E(f375(x24843,x24844,x24841,x24845,x24846),f375(x24843,x24844,x24842,x24845,x24846))
% 179.72/179.60 [2485]~E(x24851,x24852)+E(f375(x24853,x24854,x24855,x24851,x24856),f375(x24853,x24854,x24855,x24852,x24856))
% 179.72/179.60 [2486]~E(x24861,x24862)+E(f375(x24863,x24864,x24865,x24866,x24861),f375(x24863,x24864,x24865,x24866,x24862))
% 179.72/179.60 [2487]~E(x24871,x24872)+E(f659(x24871,x24873,x24874),f659(x24872,x24873,x24874))
% 179.72/179.60 [2488]~E(x24881,x24882)+E(f659(x24883,x24881,x24884),f659(x24883,x24882,x24884))
% 179.72/179.60 [2489]~E(x24891,x24892)+E(f659(x24893,x24894,x24891),f659(x24893,x24894,x24892))
% 179.72/179.60 [2490]~E(x24901,x24902)+E(f124(x24901),f124(x24902))
% 179.72/179.60 [2491]~E(x24911,x24912)+E(f766(x24911,x24913,x24914),f766(x24912,x24913,x24914))
% 179.72/179.60 [2492]~E(x24921,x24922)+E(f766(x24923,x24921,x24924),f766(x24923,x24922,x24924))
% 179.72/179.60 [2493]~E(x24931,x24932)+E(f766(x24933,x24934,x24931),f766(x24933,x24934,x24932))
% 179.72/179.60 [2494]~E(x24941,x24942)+E(f456(x24941,x24943,x24944,x24945),f456(x24942,x24943,x24944,x24945))
% 179.72/179.60 [2495]~E(x24951,x24952)+E(f456(x24953,x24951,x24954,x24955),f456(x24953,x24952,x24954,x24955))
% 179.72/179.60 [2496]~E(x24961,x24962)+E(f456(x24963,x24964,x24961,x24965),f456(x24963,x24964,x24962,x24965))
% 179.72/179.60 [2497]~E(x24971,x24972)+E(f456(x24973,x24974,x24975,x24971),f456(x24973,x24974,x24975,x24972))
% 179.72/179.60 [2498]~E(x24981,x24982)+E(f734(x24981,x24983,x24984),f734(x24982,x24983,x24984))
% 179.72/179.60 [2499]~E(x24991,x24992)+E(f734(x24993,x24991,x24994),f734(x24993,x24992,x24994))
% 179.72/179.60 [2500]~E(x25001,x25002)+E(f734(x25003,x25004,x25001),f734(x25003,x25004,x25002))
% 179.72/179.60 [2501]~E(x25011,x25012)+E(f333(x25011,x25013,x25014),f333(x25012,x25013,x25014))
% 179.72/179.60 [2502]~E(x25021,x25022)+E(f333(x25023,x25021,x25024),f333(x25023,x25022,x25024))
% 179.72/179.60 [2503]~E(x25031,x25032)+E(f333(x25033,x25034,x25031),f333(x25033,x25034,x25032))
% 179.72/179.60 [2504]~E(x25041,x25042)+E(f603(x25041,x25043,x25044),f603(x25042,x25043,x25044))
% 179.72/179.60 [2505]~E(x25051,x25052)+E(f603(x25053,x25051,x25054),f603(x25053,x25052,x25054))
% 179.72/179.60 [2506]~E(x25061,x25062)+E(f603(x25063,x25064,x25061),f603(x25063,x25064,x25062))
% 179.72/179.60 [2507]~E(x25071,x25072)+E(f223(x25071,x25073,x25074),f223(x25072,x25073,x25074))
% 179.72/179.60 [2508]~E(x25081,x25082)+E(f223(x25083,x25081,x25084),f223(x25083,x25082,x25084))
% 179.72/179.60 [2509]~E(x25091,x25092)+E(f223(x25093,x25094,x25091),f223(x25093,x25094,x25092))
% 179.72/179.60 [2510]~E(x25101,x25102)+E(f696(x25101,x25103,x25104,x25105,x25106,x25107),f696(x25102,x25103,x25104,x25105,x25106,x25107))
% 179.72/179.60 [2511]~E(x25111,x25112)+E(f696(x25113,x25111,x25114,x25115,x25116,x25117),f696(x25113,x25112,x25114,x25115,x25116,x25117))
% 179.72/179.60 [2512]~E(x25121,x25122)+E(f696(x25123,x25124,x25121,x25125,x25126,x25127),f696(x25123,x25124,x25122,x25125,x25126,x25127))
% 179.72/179.60 [2513]~E(x25131,x25132)+E(f696(x25133,x25134,x25135,x25131,x25136,x25137),f696(x25133,x25134,x25135,x25132,x25136,x25137))
% 179.72/179.60 [2514]~E(x25141,x25142)+E(f696(x25143,x25144,x25145,x25146,x25141,x25147),f696(x25143,x25144,x25145,x25146,x25142,x25147))
% 179.72/179.60 [2515]~E(x25151,x25152)+E(f696(x25153,x25154,x25155,x25156,x25157,x25151),f696(x25153,x25154,x25155,x25156,x25157,x25152))
% 179.72/179.60 [2516]~E(x25161,x25162)+E(f585(x25161,x25163,x25164,x25165),f585(x25162,x25163,x25164,x25165))
% 179.72/179.60 [2517]~E(x25171,x25172)+E(f585(x25173,x25171,x25174,x25175),f585(x25173,x25172,x25174,x25175))
% 179.72/179.60 [2518]~E(x25181,x25182)+E(f585(x25183,x25184,x25181,x25185),f585(x25183,x25184,x25182,x25185))
% 179.72/179.60 [2519]~E(x25191,x25192)+E(f585(x25193,x25194,x25195,x25191),f585(x25193,x25194,x25195,x25192))
% 179.72/179.60 [2520]~E(x25201,x25202)+E(f366(x25201,x25203),f366(x25202,x25203))
% 179.72/179.60 [2521]~E(x25211,x25212)+E(f366(x25213,x25211),f366(x25213,x25212))
% 179.72/179.60 [2522]~E(x25221,x25222)+E(f760(x25221,x25223,x25224,x25225,x25226,x25227,x25228),f760(x25222,x25223,x25224,x25225,x25226,x25227,x25228))
% 179.72/179.60 [2523]~E(x25231,x25232)+E(f760(x25233,x25231,x25234,x25235,x25236,x25237,x25238),f760(x25233,x25232,x25234,x25235,x25236,x25237,x25238))
% 179.72/179.60 [2524]~E(x25241,x25242)+E(f760(x25243,x25244,x25241,x25245,x25246,x25247,x25248),f760(x25243,x25244,x25242,x25245,x25246,x25247,x25248))
% 179.72/179.60 [2525]~E(x25251,x25252)+E(f760(x25253,x25254,x25255,x25251,x25256,x25257,x25258),f760(x25253,x25254,x25255,x25252,x25256,x25257,x25258))
% 179.72/179.60 [2526]~E(x25261,x25262)+E(f760(x25263,x25264,x25265,x25266,x25261,x25267,x25268),f760(x25263,x25264,x25265,x25266,x25262,x25267,x25268))
% 179.72/179.60 [2527]~E(x25271,x25272)+E(f760(x25273,x25274,x25275,x25276,x25277,x25271,x25278),f760(x25273,x25274,x25275,x25276,x25277,x25272,x25278))
% 179.72/179.60 [2528]~E(x25281,x25282)+E(f760(x25283,x25284,x25285,x25286,x25287,x25288,x25281),f760(x25283,x25284,x25285,x25286,x25287,x25288,x25282))
% 179.72/179.60 [2529]~E(x25291,x25292)+E(f785(x25291),f785(x25292))
% 179.72/179.60 [2530]~E(x25301,x25302)+E(f330(x25301),f330(x25302))
% 179.72/179.60 [2531]~E(x25311,x25312)+E(f382(x25311),f382(x25312))
% 179.72/179.60 [2532]~E(x25321,x25322)+E(f786(x25321,x25323),f786(x25322,x25323))
% 179.72/179.60 [2533]~E(x25331,x25332)+E(f786(x25333,x25331),f786(x25333,x25332))
% 179.72/179.60 [2534]~E(x25341,x25342)+E(f673(x25341,x25343),f673(x25342,x25343))
% 179.72/179.60 [2535]~E(x25351,x25352)+E(f673(x25353,x25351),f673(x25353,x25352))
% 179.72/179.60 [2536]~E(x25361,x25362)+E(f442(x25361,x25363),f442(x25362,x25363))
% 179.72/179.60 [2537]~E(x25371,x25372)+E(f442(x25373,x25371),f442(x25373,x25372))
% 179.72/179.60 [2538]~E(x25381,x25382)+E(f454(x25381,x25383,x25384),f454(x25382,x25383,x25384))
% 179.72/179.60 [2539]~E(x25391,x25392)+E(f454(x25393,x25391,x25394),f454(x25393,x25392,x25394))
% 179.72/179.60 [2540]~E(x25401,x25402)+E(f454(x25403,x25404,x25401),f454(x25403,x25404,x25402))
% 179.72/179.60 [2541]~E(x25411,x25412)+E(f265(x25411,x25413,x25414,x25415,x25416),f265(x25412,x25413,x25414,x25415,x25416))
% 179.72/179.60 [2542]~E(x25421,x25422)+E(f265(x25423,x25421,x25424,x25425,x25426),f265(x25423,x25422,x25424,x25425,x25426))
% 179.72/179.60 [2543]~E(x25431,x25432)+E(f265(x25433,x25434,x25431,x25435,x25436),f265(x25433,x25434,x25432,x25435,x25436))
% 179.72/179.60 [2544]~E(x25441,x25442)+E(f265(x25443,x25444,x25445,x25441,x25446),f265(x25443,x25444,x25445,x25442,x25446))
% 179.72/179.60 [2545]~E(x25451,x25452)+E(f265(x25453,x25454,x25455,x25456,x25451),f265(x25453,x25454,x25455,x25456,x25452))
% 179.72/179.60 [2546]~E(x25461,x25462)+E(f367(x25461,x25463),f367(x25462,x25463))
% 179.72/179.60 [2547]~E(x25471,x25472)+E(f367(x25473,x25471),f367(x25473,x25472))
% 179.72/179.60 [2548]~E(x25481,x25482)+E(f644(x25481,x25483,x25484,x25485,x25486,x25487,x25488,x25489),f644(x25482,x25483,x25484,x25485,x25486,x25487,x25488,x25489))
% 179.72/179.60 [2549]~E(x25491,x25492)+E(f644(x25493,x25491,x25494,x25495,x25496,x25497,x25498,x25499),f644(x25493,x25492,x25494,x25495,x25496,x25497,x25498,x25499))
% 179.72/179.60 [2550]~E(x25501,x25502)+E(f644(x25503,x25504,x25501,x25505,x25506,x25507,x25508,x25509),f644(x25503,x25504,x25502,x25505,x25506,x25507,x25508,x25509))
% 179.72/179.60 [2551]~E(x25511,x25512)+E(f644(x25513,x25514,x25515,x25511,x25516,x25517,x25518,x25519),f644(x25513,x25514,x25515,x25512,x25516,x25517,x25518,x25519))
% 179.72/179.60 [2552]~E(x25521,x25522)+E(f644(x25523,x25524,x25525,x25526,x25521,x25527,x25528,x25529),f644(x25523,x25524,x25525,x25526,x25522,x25527,x25528,x25529))
% 179.72/179.60 [2553]~E(x25531,x25532)+E(f644(x25533,x25534,x25535,x25536,x25537,x25531,x25538,x25539),f644(x25533,x25534,x25535,x25536,x25537,x25532,x25538,x25539))
% 179.72/179.60 [2554]~E(x25541,x25542)+E(f644(x25543,x25544,x25545,x25546,x25547,x25548,x25541,x25549),f644(x25543,x25544,x25545,x25546,x25547,x25548,x25542,x25549))
% 179.72/179.60 [2555]~E(x25551,x25552)+E(f644(x25553,x25554,x25555,x25556,x25557,x25558,x25559,x25551),f644(x25553,x25554,x25555,x25556,x25557,x25558,x25559,x25552))
% 179.72/179.60 [2556]~E(x25561,x25562)+E(f441(x25561,x25563),f441(x25562,x25563))
% 179.72/179.60 [2557]~E(x25571,x25572)+E(f441(x25573,x25571),f441(x25573,x25572))
% 179.72/179.60 [2558]~E(x25581,x25582)+E(f334(x25581,x25583,x25584),f334(x25582,x25583,x25584))
% 179.72/179.60 [2559]~E(x25591,x25592)+E(f334(x25593,x25591,x25594),f334(x25593,x25592,x25594))
% 179.72/179.60 [2560]~E(x25601,x25602)+E(f334(x25603,x25604,x25601),f334(x25603,x25604,x25602))
% 179.72/179.60 [2561]~E(x25611,x25612)+E(f430(x25611,x25613),f430(x25612,x25613))
% 179.72/179.60 [2562]~E(x25621,x25622)+E(f430(x25623,x25621),f430(x25623,x25622))
% 179.72/179.60 [2563]~E(x25631,x25632)+E(f532(x25631,x25633,x25634,x25635,x25636),f532(x25632,x25633,x25634,x25635,x25636))
% 179.72/179.60 [2564]~E(x25641,x25642)+E(f532(x25643,x25641,x25644,x25645,x25646),f532(x25643,x25642,x25644,x25645,x25646))
% 179.72/179.60 [2565]~E(x25651,x25652)+E(f532(x25653,x25654,x25651,x25655,x25656),f532(x25653,x25654,x25652,x25655,x25656))
% 179.72/179.60 [2566]~E(x25661,x25662)+E(f532(x25663,x25664,x25665,x25661,x25666),f532(x25663,x25664,x25665,x25662,x25666))
% 179.72/179.60 [2567]~E(x25671,x25672)+E(f532(x25673,x25674,x25675,x25676,x25671),f532(x25673,x25674,x25675,x25676,x25672))
% 179.72/179.60 [2568]~E(x25681,x25682)+E(f648(x25681,x25683),f648(x25682,x25683))
% 179.72/179.60 [2569]~E(x25691,x25692)+E(f648(x25693,x25691),f648(x25693,x25692))
% 179.72/179.60 [2570]~E(x25701,x25702)+E(f677(x25701,x25703,x25704,x25705),f677(x25702,x25703,x25704,x25705))
% 179.72/179.60 [2571]~E(x25711,x25712)+E(f677(x25713,x25711,x25714,x25715),f677(x25713,x25712,x25714,x25715))
% 179.72/179.60 [2572]~E(x25721,x25722)+E(f677(x25723,x25724,x25721,x25725),f677(x25723,x25724,x25722,x25725))
% 179.72/179.60 [2573]~E(x25731,x25732)+E(f677(x25733,x25734,x25735,x25731),f677(x25733,x25734,x25735,x25732))
% 179.72/179.60 [2574]~E(x25741,x25742)+E(f492(x25741,x25743,x25744),f492(x25742,x25743,x25744))
% 179.72/179.60 [2575]~E(x25751,x25752)+E(f492(x25753,x25751,x25754),f492(x25753,x25752,x25754))
% 179.72/179.60 [2576]~E(x25761,x25762)+E(f492(x25763,x25764,x25761),f492(x25763,x25764,x25762))
% 179.72/179.60 [2577]~E(x25771,x25772)+E(f823(x25771,x25773,x25774),f823(x25772,x25773,x25774))
% 179.72/179.60 [2578]~E(x25781,x25782)+E(f823(x25783,x25781,x25784),f823(x25783,x25782,x25784))
% 179.72/179.60 [2579]~E(x25791,x25792)+E(f823(x25793,x25794,x25791),f823(x25793,x25794,x25792))
% 179.72/179.60 [2580]~E(x25801,x25802)+E(f571(x25801,x25803,x25804,x25805),f571(x25802,x25803,x25804,x25805))
% 179.72/179.60 [2581]~E(x25811,x25812)+E(f571(x25813,x25811,x25814,x25815),f571(x25813,x25812,x25814,x25815))
% 179.72/179.60 [2582]~E(x25821,x25822)+E(f571(x25823,x25824,x25821,x25825),f571(x25823,x25824,x25822,x25825))
% 179.72/179.60 [2583]~E(x25831,x25832)+E(f571(x25833,x25834,x25835,x25831),f571(x25833,x25834,x25835,x25832))
% 179.72/179.60 [2584]~E(x25841,x25842)+E(f381(x25841),f381(x25842))
% 179.72/179.60 [2585]~E(x25851,x25852)+E(f685(x25851,x25853),f685(x25852,x25853))
% 179.72/179.60 [2586]~E(x25861,x25862)+E(f685(x25863,x25861),f685(x25863,x25862))
% 179.72/179.60 [2587]~E(x25871,x25872)+E(f675(x25871,x25873,x25874,x25875),f675(x25872,x25873,x25874,x25875))
% 179.72/179.60 [2588]~E(x25881,x25882)+E(f675(x25883,x25881,x25884,x25885),f675(x25883,x25882,x25884,x25885))
% 179.72/179.60 [2589]~E(x25891,x25892)+E(f675(x25893,x25894,x25891,x25895),f675(x25893,x25894,x25892,x25895))
% 179.72/179.60 [2590]~E(x25901,x25902)+E(f675(x25903,x25904,x25905,x25901),f675(x25903,x25904,x25905,x25902))
% 179.72/179.60 [2591]~E(x25911,x25912)+E(f650(x25911,x25913,x25914),f650(x25912,x25913,x25914))
% 179.72/179.60 [2592]~E(x25921,x25922)+E(f650(x25923,x25921,x25924),f650(x25923,x25922,x25924))
% 179.72/179.60 [2593]~E(x25931,x25932)+E(f650(x25933,x25934,x25931),f650(x25933,x25934,x25932))
% 179.72/179.60 [2594]~E(x25941,x25942)+E(f754(x25941,x25943,x25944),f754(x25942,x25943,x25944))
% 179.72/179.60 [2595]~E(x25951,x25952)+E(f754(x25953,x25951,x25954),f754(x25953,x25952,x25954))
% 179.72/179.60 [2596]~E(x25961,x25962)+E(f754(x25963,x25964,x25961),f754(x25963,x25964,x25962))
% 179.72/179.60 [2597]~E(x25971,x25972)+E(f850(x25971,x25973,x25974),f850(x25972,x25973,x25974))
% 179.72/179.60 [2598]~E(x25981,x25982)+E(f850(x25983,x25981,x25984),f850(x25983,x25982,x25984))
% 179.72/179.60 [2599]~E(x25991,x25992)+E(f850(x25993,x25994,x25991),f850(x25993,x25994,x25992))
% 179.72/179.60 [2600]~E(x26001,x26002)+E(f680(x26001),f680(x26002))
% 179.72/179.60 [2601]~E(x26011,x26012)+E(f542(x26011,x26013,x26014,x26015),f542(x26012,x26013,x26014,x26015))
% 179.86/179.60 [2602]~E(x26021,x26022)+E(f542(x26023,x26021,x26024,x26025),f542(x26023,x26022,x26024,x26025))
% 179.86/179.60 [2603]~E(x26031,x26032)+E(f542(x26033,x26034,x26031,x26035),f542(x26033,x26034,x26032,x26035))
% 179.86/179.60 [2604]~E(x26041,x26042)+E(f542(x26043,x26044,x26045,x26041),f542(x26043,x26044,x26045,x26042))
% 179.86/179.60 [2605]~P1(x26051)+P1(x26052)+~E(x26051,x26052)
% 179.86/179.60 [2606]~P101(x26061)+P101(x26062)+~E(x26061,x26062)
% 179.86/179.60 [2607]P26(x26072,x26073,x26074)+~E(x26071,x26072)+~P26(x26071,x26073,x26074)
% 179.86/179.60 [2608]P26(x26083,x26082,x26084)+~E(x26081,x26082)+~P26(x26083,x26081,x26084)
% 179.86/179.60 [2609]P26(x26093,x26094,x26092)+~E(x26091,x26092)+~P26(x26093,x26094,x26091)
% 179.86/179.60 [2610]~P2(x26101)+P2(x26102)+~E(x26101,x26102)
% 179.86/179.60 [2611]P38(x26112,x26113)+~E(x26111,x26112)+~P38(x26111,x26113)
% 179.86/179.60 [2612]P38(x26123,x26122)+~E(x26121,x26122)+~P38(x26123,x26121)
% 179.86/179.60 [2613]P56(x26132,x26133)+~E(x26131,x26132)+~P56(x26131,x26133)
% 179.86/179.60 [2614]P56(x26143,x26142)+~E(x26141,x26142)+~P56(x26143,x26141)
% 179.86/179.60 [2615]~P3(x26151)+P3(x26152)+~E(x26151,x26152)
% 179.86/179.60 [2616]~P97(x26161)+P97(x26162)+~E(x26161,x26162)
% 179.86/179.60 [2617]P142(x26172,x26173,x26174)+~E(x26171,x26172)+~P142(x26171,x26173,x26174)
% 179.86/179.60 [2618]P142(x26183,x26182,x26184)+~E(x26181,x26182)+~P142(x26183,x26181,x26184)
% 179.86/179.60 [2619]P142(x26193,x26194,x26192)+~E(x26191,x26192)+~P142(x26193,x26194,x26191)
% 179.86/179.60 [2620]~P135(x26201)+P135(x26202)+~E(x26201,x26202)
% 179.86/179.60 [2621]~P4(x26211)+P4(x26212)+~E(x26211,x26212)
% 179.86/179.60 [2622]~P72(x26221)+P72(x26222)+~E(x26221,x26222)
% 179.86/179.60 [2623]P27(x26232,x26233,x26234,x26235)+~E(x26231,x26232)+~P27(x26231,x26233,x26234,x26235)
% 179.86/179.60 [2624]P27(x26243,x26242,x26244,x26245)+~E(x26241,x26242)+~P27(x26243,x26241,x26244,x26245)
% 179.86/179.60 [2625]P27(x26253,x26254,x26252,x26255)+~E(x26251,x26252)+~P27(x26253,x26254,x26251,x26255)
% 179.86/179.60 [2626]P27(x26263,x26264,x26265,x26262)+~E(x26261,x26262)+~P27(x26263,x26264,x26265,x26261)
% 179.86/179.60 [2627]~P103(x26271)+P103(x26272)+~E(x26271,x26272)
% 179.86/179.60 [2628]~P102(x26281)+P102(x26282)+~E(x26281,x26282)
% 179.86/179.60 [2629]~P80(x26291)+P80(x26292)+~E(x26291,x26292)
% 179.86/179.60 [2630]~P74(x26301)+P74(x26302)+~E(x26301,x26302)
% 179.86/179.60 [2631]~P82(x26311)+P82(x26312)+~E(x26311,x26312)
% 179.86/179.60 [2632]~P98(x26321)+P98(x26322)+~E(x26321,x26322)
% 179.86/179.60 [2633]~P64(x26331)+P64(x26332)+~E(x26331,x26332)
% 179.86/179.60 [2634]~P65(x26341)+P65(x26342)+~E(x26341,x26342)
% 179.86/179.60 [2635]~P75(x26351)+P75(x26352)+~E(x26351,x26352)
% 179.86/179.60 [2636]~P119(x26361)+P119(x26362)+~E(x26361,x26362)
% 179.86/179.60 [2637]~P116(x26371)+P116(x26372)+~E(x26371,x26372)
% 179.86/179.60 [2638]~P104(x26381)+P104(x26382)+~E(x26381,x26382)
% 179.86/179.60 [2639]~P125(x26391)+P125(x26392)+~E(x26391,x26392)
% 179.86/179.60 [2640]~P105(x26401)+P105(x26402)+~E(x26401,x26402)
% 179.86/179.60 [2641]~P57(x26411)+P57(x26412)+~E(x26411,x26412)
% 179.86/179.60 [2642]P28(x26422,x26423,x26424,x26425,x26426)+~E(x26421,x26422)+~P28(x26421,x26423,x26424,x26425,x26426)
% 179.86/179.60 [2643]P28(x26433,x26432,x26434,x26435,x26436)+~E(x26431,x26432)+~P28(x26433,x26431,x26434,x26435,x26436)
% 179.86/179.60 [2644]P28(x26443,x26444,x26442,x26445,x26446)+~E(x26441,x26442)+~P28(x26443,x26444,x26441,x26445,x26446)
% 179.86/179.60 [2645]P28(x26453,x26454,x26455,x26452,x26456)+~E(x26451,x26452)+~P28(x26453,x26454,x26455,x26451,x26456)
% 179.86/179.60 [2646]P28(x26463,x26464,x26465,x26466,x26462)+~E(x26461,x26462)+~P28(x26463,x26464,x26465,x26466,x26461)
% 179.86/179.60 [2647]~P91(x26471)+P91(x26472)+~E(x26471,x26472)
% 179.86/179.60 [2648]~P140(x26481)+P140(x26482)+~E(x26481,x26482)
% 179.86/179.60 [2649]P8(x26492,x26493)+~E(x26491,x26492)+~P8(x26491,x26493)
% 179.86/179.60 [2650]P8(x26503,x26502)+~E(x26501,x26502)+~P8(x26503,x26501)
% 179.86/179.60 [2651]~P106(x26511)+P106(x26512)+~E(x26511,x26512)
% 179.86/179.60 [2652]~P95(x26521)+P95(x26522)+~E(x26521,x26522)
% 179.86/179.60 [2653]~P96(x26531)+P96(x26532)+~E(x26531,x26532)
% 179.86/179.60 [2654]P50(x26542,x26543,x26544,x26545)+~E(x26541,x26542)+~P50(x26541,x26543,x26544,x26545)
% 179.86/179.60 [2655]P50(x26553,x26552,x26554,x26555)+~E(x26551,x26552)+~P50(x26553,x26551,x26554,x26555)
% 179.86/179.60 [2656]P50(x26563,x26564,x26562,x26565)+~E(x26561,x26562)+~P50(x26563,x26564,x26561,x26565)
% 179.86/179.60 [2657]P50(x26573,x26574,x26575,x26572)+~E(x26571,x26572)+~P50(x26573,x26574,x26575,x26571)
% 179.86/179.60 [2658]P143(x26582,x26583,x26584)+~E(x26581,x26582)+~P143(x26581,x26583,x26584)
% 179.86/179.60 [2659]P143(x26593,x26592,x26594)+~E(x26591,x26592)+~P143(x26593,x26591,x26594)
% 179.86/179.60 [2660]P143(x26603,x26604,x26602)+~E(x26601,x26602)+~P143(x26603,x26604,x26601)
% 179.86/179.60 [2661]~P63(x26611)+P63(x26612)+~E(x26611,x26612)
% 179.86/179.60 [2662]~P5(x26621)+P5(x26622)+~E(x26621,x26622)
% 179.86/179.60 [2663]P36(x26632,x26633,x26634)+~E(x26631,x26632)+~P36(x26631,x26633,x26634)
% 179.86/179.60 [2664]P36(x26643,x26642,x26644)+~E(x26641,x26642)+~P36(x26643,x26641,x26644)
% 179.86/179.60 [2665]P36(x26653,x26654,x26652)+~E(x26651,x26652)+~P36(x26653,x26654,x26651)
% 179.86/179.60 [2666]~P79(x26661)+P79(x26662)+~E(x26661,x26662)
% 179.86/179.60 [2667]P16(x26672,x26673)+~E(x26671,x26672)+~P16(x26671,x26673)
% 179.86/179.60 [2668]P16(x26683,x26682)+~E(x26681,x26682)+~P16(x26683,x26681)
% 179.86/179.60 [2669]~P87(x26691)+P87(x26692)+~E(x26691,x26692)
% 179.86/179.60 [2670]~P59(x26701)+P59(x26702)+~E(x26701,x26702)
% 179.86/179.60 [2671]~P60(x26711)+P60(x26712)+~E(x26711,x26712)
% 179.86/179.60 [2672]~P66(x26721)+P66(x26722)+~E(x26721,x26722)
% 179.86/179.60 [2673]~P7(x26731)+P7(x26732)+~E(x26731,x26732)
% 179.86/179.60 [2674]~P39(x26741)+P39(x26742)+~E(x26741,x26742)
% 179.86/179.60 [2675]~P107(x26751)+P107(x26752)+~E(x26751,x26752)
% 179.86/179.60 [2676]~P108(x26761)+P108(x26762)+~E(x26761,x26762)
% 179.86/179.60 [2677]P55(x26772,x26773,x26774,x26775)+~E(x26771,x26772)+~P55(x26771,x26773,x26774,x26775)
% 179.86/179.60 [2678]P55(x26783,x26782,x26784,x26785)+~E(x26781,x26782)+~P55(x26783,x26781,x26784,x26785)
% 179.86/179.60 [2679]P55(x26793,x26794,x26792,x26795)+~E(x26791,x26792)+~P55(x26793,x26794,x26791,x26795)
% 179.86/179.60 [2680]P55(x26803,x26804,x26805,x26802)+~E(x26801,x26802)+~P55(x26803,x26804,x26805,x26801)
% 179.86/179.60 [2681]~P61(x26811)+P61(x26812)+~E(x26811,x26812)
% 179.86/179.60 [2682]~P6(x26821)+P6(x26822)+~E(x26821,x26822)
% 179.86/179.60 [2683]~P68(x26831)+P68(x26832)+~E(x26831,x26832)
% 179.86/179.60 [2684]P30(x26842,x26843)+~E(x26841,x26842)+~P30(x26841,x26843)
% 179.86/179.60 [2685]P30(x26853,x26852)+~E(x26851,x26852)+~P30(x26853,x26851)
% 179.86/179.60 [2686]P9(x26862,x26863,x26864)+~E(x26861,x26862)+~P9(x26861,x26863,x26864)
% 179.86/179.60 [2687]P9(x26873,x26872,x26874)+~E(x26871,x26872)+~P9(x26873,x26871,x26874)
% 179.86/179.60 [2688]P9(x26883,x26884,x26882)+~E(x26881,x26882)+~P9(x26883,x26884,x26881)
% 179.86/179.60 [2689]~P76(x26891)+P76(x26892)+~E(x26891,x26892)
% 179.86/179.60 [2690]P14(x26902,x26903,x26904,x26905)+~E(x26901,x26902)+~P14(x26901,x26903,x26904,x26905)
% 179.86/179.60 [2691]P14(x26913,x26912,x26914,x26915)+~E(x26911,x26912)+~P14(x26913,x26911,x26914,x26915)
% 179.86/179.60 [2692]P14(x26923,x26924,x26922,x26925)+~E(x26921,x26922)+~P14(x26923,x26924,x26921,x26925)
% 179.86/179.60 [2693]P14(x26933,x26934,x26935,x26932)+~E(x26931,x26932)+~P14(x26933,x26934,x26935,x26931)
% 179.86/179.60 [2694]~P114(x26941)+P114(x26942)+~E(x26941,x26942)
% 179.86/179.60 [2695]~P77(x26951)+P77(x26952)+~E(x26951,x26952)
% 179.86/179.60 [2696]P21(x26962,x26963,x26964,x26965)+~E(x26961,x26962)+~P21(x26961,x26963,x26964,x26965)
% 179.86/179.60 [2697]P21(x26973,x26972,x26974,x26975)+~E(x26971,x26972)+~P21(x26973,x26971,x26974,x26975)
% 179.86/179.60 [2698]P21(x26983,x26984,x26982,x26985)+~E(x26981,x26982)+~P21(x26983,x26984,x26981,x26985)
% 179.86/179.60 [2699]P21(x26993,x26994,x26995,x26992)+~E(x26991,x26992)+~P21(x26993,x26994,x26995,x26991)
% 179.86/179.60 [2700]~P78(x27001)+P78(x27002)+~E(x27001,x27002)
% 179.86/179.60 [2701]P34(x27012,x27013,x27014)+~E(x27011,x27012)+~P34(x27011,x27013,x27014)
% 179.86/179.60 [2702]P34(x27023,x27022,x27024)+~E(x27021,x27022)+~P34(x27023,x27021,x27024)
% 179.86/179.60 [2703]P34(x27033,x27034,x27032)+~E(x27031,x27032)+~P34(x27033,x27034,x27031)
% 179.86/179.60 [2704]~P134(x27041)+P134(x27042)+~E(x27041,x27042)
% 179.86/179.60 [2705]~P83(x27051)+P83(x27052)+~E(x27051,x27052)
% 179.86/179.60 [2706]~P133(x27061)+P133(x27062)+~E(x27061,x27062)
% 179.86/179.60 [2707]~P109(x27071)+P109(x27072)+~E(x27071,x27072)
% 179.86/179.60 [2708]~P112(x27081)+P112(x27082)+~E(x27081,x27082)
% 179.86/179.60 [2709]~P120(x27091)+P120(x27092)+~E(x27091,x27092)
% 179.86/179.60 [2710]~P90(x27101)+P90(x27102)+~E(x27101,x27102)
% 179.86/179.60 [2711]P35(x27112,x27113,x27114,x27115,x27116)+~E(x27111,x27112)+~P35(x27111,x27113,x27114,x27115,x27116)
% 179.86/179.60 [2712]P35(x27123,x27122,x27124,x27125,x27126)+~E(x27121,x27122)+~P35(x27123,x27121,x27124,x27125,x27126)
% 179.86/179.60 [2713]P35(x27133,x27134,x27132,x27135,x27136)+~E(x27131,x27132)+~P35(x27133,x27134,x27131,x27135,x27136)
% 179.86/179.60 [2714]P35(x27143,x27144,x27145,x27142,x27146)+~E(x27141,x27142)+~P35(x27143,x27144,x27145,x27141,x27146)
% 179.86/179.60 [2715]P35(x27153,x27154,x27155,x27156,x27152)+~E(x27151,x27152)+~P35(x27153,x27154,x27155,x27156,x27151)
% 179.86/179.60 [2716]~P124(x27161)+P124(x27162)+~E(x27161,x27162)
% 179.86/179.60 [2717]~P67(x27171)+P67(x27172)+~E(x27171,x27172)
% 179.86/179.60 [2718]~P99(x27181)+P99(x27182)+~E(x27181,x27182)
% 179.86/179.60 [2719]P40(x27192,x27193,x27194)+~E(x27191,x27192)+~P40(x27191,x27193,x27194)
% 179.86/179.60 [2720]P40(x27203,x27202,x27204)+~E(x27201,x27202)+~P40(x27203,x27201,x27204)
% 179.86/179.60 [2721]P40(x27213,x27214,x27212)+~E(x27211,x27212)+~P40(x27213,x27214,x27211)
% 179.86/179.60 [2722]~P69(x27221)+P69(x27222)+~E(x27221,x27222)
% 179.86/179.60 [2723]P17(x27232,x27233,x27234)+~E(x27231,x27232)+~P17(x27231,x27233,x27234)
% 179.86/179.60 [2724]P17(x27243,x27242,x27244)+~E(x27241,x27242)+~P17(x27243,x27241,x27244)
% 179.86/179.60 [2725]P17(x27253,x27254,x27252)+~E(x27251,x27252)+~P17(x27253,x27254,x27251)
% 179.86/179.60 [2726]P13(x27262,x27263,x27264)+~E(x27261,x27262)+~P13(x27261,x27263,x27264)
% 179.86/179.60 [2727]P13(x27273,x27272,x27274)+~E(x27271,x27272)+~P13(x27273,x27271,x27274)
% 179.86/179.60 [2728]P13(x27283,x27284,x27282)+~E(x27281,x27282)+~P13(x27283,x27284,x27281)
% 179.86/179.60 [2729]~P70(x27291)+P70(x27292)+~E(x27291,x27292)
% 179.86/179.60 [2730]~P122(x27301)+P122(x27302)+~E(x27301,x27302)
% 179.86/179.60 [2731]P29(x27312,x27313)+~E(x27311,x27312)+~P29(x27311,x27313)
% 179.86/179.60 [2732]P29(x27323,x27322)+~E(x27321,x27322)+~P29(x27323,x27321)
% 179.86/179.60 [2733]~P37(x27331)+P37(x27332)+~E(x27331,x27332)
% 179.86/179.60 [2734]~P84(x27341)+P84(x27342)+~E(x27341,x27342)
% 179.86/179.60 [2735]P25(x27352,x27353,x27354,x27355,x27356,x27357)+~E(x27351,x27352)+~P25(x27351,x27353,x27354,x27355,x27356,x27357)
% 179.86/179.60 [2736]P25(x27363,x27362,x27364,x27365,x27366,x27367)+~E(x27361,x27362)+~P25(x27363,x27361,x27364,x27365,x27366,x27367)
% 179.86/179.60 [2737]P25(x27373,x27374,x27372,x27375,x27376,x27377)+~E(x27371,x27372)+~P25(x27373,x27374,x27371,x27375,x27376,x27377)
% 179.86/179.60 [2738]P25(x27383,x27384,x27385,x27382,x27386,x27387)+~E(x27381,x27382)+~P25(x27383,x27384,x27385,x27381,x27386,x27387)
% 179.86/179.60 [2739]P25(x27393,x27394,x27395,x27396,x27392,x27397)+~E(x27391,x27392)+~P25(x27393,x27394,x27395,x27396,x27391,x27397)
% 179.86/179.60 [2740]P25(x27403,x27404,x27405,x27406,x27407,x27402)+~E(x27401,x27402)+~P25(x27403,x27404,x27405,x27406,x27407,x27401)
% 179.86/179.60 [2741]~P81(x27411)+P81(x27412)+~E(x27411,x27412)
% 179.86/179.60 [2742]~P62(x27421)+P62(x27422)+~E(x27421,x27422)
% 179.86/179.60 [2743]~P92(x27431)+P92(x27432)+~E(x27431,x27432)
% 179.86/179.60 [2744]P18(x27442,x27443,x27444)+~E(x27441,x27442)+~P18(x27441,x27443,x27444)
% 179.86/179.60 [2745]P18(x27453,x27452,x27454)+~E(x27451,x27452)+~P18(x27453,x27451,x27454)
% 179.86/179.60 [2746]P18(x27463,x27464,x27462)+~E(x27461,x27462)+~P18(x27463,x27464,x27461)
% 179.86/179.60 [2747]~P139(x27471)+P139(x27472)+~E(x27471,x27472)
% 179.86/179.60 [2748]P51(x27482,x27483,x27484)+~E(x27481,x27482)+~P51(x27481,x27483,x27484)
% 179.86/179.60 [2749]P51(x27493,x27492,x27494)+~E(x27491,x27492)+~P51(x27493,x27491,x27494)
% 179.86/179.60 [2750]P51(x27503,x27504,x27502)+~E(x27501,x27502)+~P51(x27503,x27504,x27501)
% 179.86/179.60 [2751]~P113(x27511)+P113(x27512)+~E(x27511,x27512)
% 179.86/179.60 [2752]P23(x27522,x27523,x27524,x27525,x27526)+~E(x27521,x27522)+~P23(x27521,x27523,x27524,x27525,x27526)
% 179.86/179.60 [2753]P23(x27533,x27532,x27534,x27535,x27536)+~E(x27531,x27532)+~P23(x27533,x27531,x27534,x27535,x27536)
% 179.86/179.60 [2754]P23(x27543,x27544,x27542,x27545,x27546)+~E(x27541,x27542)+~P23(x27543,x27544,x27541,x27545,x27546)
% 179.86/179.60 [2755]P23(x27553,x27554,x27555,x27552,x27556)+~E(x27551,x27552)+~P23(x27553,x27554,x27555,x27551,x27556)
% 179.86/179.60 [2756]P23(x27563,x27564,x27565,x27566,x27562)+~E(x27561,x27562)+~P23(x27563,x27564,x27565,x27566,x27561)
% 179.86/179.60 [2757]P19(x27572,x27573,x27574)+~E(x27571,x27572)+~P19(x27571,x27573,x27574)
% 179.86/179.60 [2758]P19(x27583,x27582,x27584)+~E(x27581,x27582)+~P19(x27583,x27581,x27584)
% 179.86/179.60 [2759]P19(x27593,x27594,x27592)+~E(x27591,x27592)+~P19(x27593,x27594,x27591)
% 179.86/179.60 [2760]~P136(x27601)+P136(x27602)+~E(x27601,x27602)
% 179.86/179.60 [2761]P44(x27612,x27613)+~E(x27611,x27612)+~P44(x27611,x27613)
% 179.86/179.60 [2762]P44(x27623,x27622)+~E(x27621,x27622)+~P44(x27623,x27621)
% 179.86/179.60 [2763]~P132(x27631)+P132(x27632)+~E(x27631,x27632)
% 179.86/179.60 [2764]~P130(x27641)+P130(x27642)+~E(x27641,x27642)
% 179.86/179.60 [2765]~P73(x27651)+P73(x27652)+~E(x27651,x27652)
% 179.86/179.60 [2766]P32(x27662,x27663,x27664)+~E(x27661,x27662)+~P32(x27661,x27663,x27664)
% 179.86/179.60 [2767]P32(x27673,x27672,x27674)+~E(x27671,x27672)+~P32(x27673,x27671,x27674)
% 179.86/179.60 [2768]P32(x27683,x27684,x27682)+~E(x27681,x27682)+~P32(x27683,x27684,x27681)
% 179.86/179.60 [2769]~P123(x27691)+P123(x27692)+~E(x27691,x27692)
% 179.86/179.60 [2770]~P88(x27701)+P88(x27702)+~E(x27701,x27702)
% 179.86/179.60 [2771]P54(x27712,x27713)+~E(x27711,x27712)+~P54(x27711,x27713)
% 179.86/179.60 [2772]P54(x27723,x27722)+~E(x27721,x27722)+~P54(x27723,x27721)
% 179.86/179.60 [2773]P20(x27732,x27733,x27734)+~E(x27731,x27732)+~P20(x27731,x27733,x27734)
% 179.86/179.60 [2774]P20(x27743,x27742,x27744)+~E(x27741,x27742)+~P20(x27743,x27741,x27744)
% 179.86/179.60 [2775]P20(x27753,x27754,x27752)+~E(x27751,x27752)+~P20(x27753,x27754,x27751)
% 179.86/179.60 [2776]P53(x27762,x27763,x27764,x27765,x27766)+~E(x27761,x27762)+~P53(x27761,x27763,x27764,x27765,x27766)
% 179.86/179.60 [2777]P53(x27773,x27772,x27774,x27775,x27776)+~E(x27771,x27772)+~P53(x27773,x27771,x27774,x27775,x27776)
% 179.86/179.60 [2778]P53(x27783,x27784,x27782,x27785,x27786)+~E(x27781,x27782)+~P53(x27783,x27784,x27781,x27785,x27786)
% 179.86/179.60 [2779]P53(x27793,x27794,x27795,x27792,x27796)+~E(x27791,x27792)+~P53(x27793,x27794,x27795,x27791,x27796)
% 179.86/179.60 [2780]P53(x27803,x27804,x27805,x27806,x27802)+~E(x27801,x27802)+~P53(x27803,x27804,x27805,x27806,x27801)
% 179.86/179.60 [2781]P33(x27812,x27813,x27814,x27815)+~E(x27811,x27812)+~P33(x27811,x27813,x27814,x27815)
% 179.86/179.60 [2782]P33(x27823,x27822,x27824,x27825)+~E(x27821,x27822)+~P33(x27823,x27821,x27824,x27825)
% 179.86/179.60 [2783]P33(x27833,x27834,x27832,x27835)+~E(x27831,x27832)+~P33(x27833,x27834,x27831,x27835)
% 179.86/179.60 [2784]P33(x27843,x27844,x27845,x27842)+~E(x27841,x27842)+~P33(x27843,x27844,x27845,x27841)
% 179.86/179.60 [2785]P12(x27852,x27853,x27854)+~E(x27851,x27852)+~P12(x27851,x27853,x27854)
% 179.86/179.60 [2786]P12(x27863,x27862,x27864)+~E(x27861,x27862)+~P12(x27863,x27861,x27864)
% 179.86/179.60 [2787]P12(x27873,x27874,x27872)+~E(x27871,x27872)+~P12(x27873,x27874,x27871)
% 179.86/179.60 [2788]~P85(x27881)+P85(x27882)+~E(x27881,x27882)
% 179.86/179.60 [2789]~P58(x27891)+P58(x27892)+~E(x27891,x27892)
% 179.86/179.60 [2790]~P118(x27901)+P118(x27902)+~E(x27901,x27902)
% 179.86/179.60 [2791]P43(x27912,x27913,x27914,x27915,x27916,x27917)+~E(x27911,x27912)+~P43(x27911,x27913,x27914,x27915,x27916,x27917)
% 179.86/179.60 [2792]P43(x27923,x27922,x27924,x27925,x27926,x27927)+~E(x27921,x27922)+~P43(x27923,x27921,x27924,x27925,x27926,x27927)
% 179.86/179.60 [2793]P43(x27933,x27934,x27932,x27935,x27936,x27937)+~E(x27931,x27932)+~P43(x27933,x27934,x27931,x27935,x27936,x27937)
% 179.86/179.60 [2794]P43(x27943,x27944,x27945,x27942,x27946,x27947)+~E(x27941,x27942)+~P43(x27943,x27944,x27945,x27941,x27946,x27947)
% 179.86/179.60 [2795]P43(x27953,x27954,x27955,x27956,x27952,x27957)+~E(x27951,x27952)+~P43(x27953,x27954,x27955,x27956,x27951,x27957)
% 179.86/179.60 [2796]P43(x27963,x27964,x27965,x27966,x27967,x27962)+~E(x27961,x27962)+~P43(x27963,x27964,x27965,x27966,x27967,x27961)
% 179.86/179.60 [2797]~P131(x27971)+P131(x27972)+~E(x27971,x27972)
% 179.86/179.60 [2798]P24(x27982,x27983,x27984,x27985,x27986,x27987)+~E(x27981,x27982)+~P24(x27981,x27983,x27984,x27985,x27986,x27987)
% 179.86/179.60 [2799]P24(x27993,x27992,x27994,x27995,x27996,x27997)+~E(x27991,x27992)+~P24(x27993,x27991,x27994,x27995,x27996,x27997)
% 179.86/179.60 [2800]P24(x28003,x28004,x28002,x28005,x28006,x28007)+~E(x28001,x28002)+~P24(x28003,x28004,x28001,x28005,x28006,x28007)
% 179.86/179.60 [2801]P24(x28013,x28014,x28015,x28012,x28016,x28017)+~E(x28011,x28012)+~P24(x28013,x28014,x28015,x28011,x28016,x28017)
% 179.86/179.60 [2802]P24(x28023,x28024,x28025,x28026,x28022,x28027)+~E(x28021,x28022)+~P24(x28023,x28024,x28025,x28026,x28021,x28027)
% 179.86/179.60 [2803]P24(x28033,x28034,x28035,x28036,x28037,x28032)+~E(x28031,x28032)+~P24(x28033,x28034,x28035,x28036,x28037,x28031)
% 179.86/179.60 [2804]P52(x28042,x28043,x28044)+~E(x28041,x28042)+~P52(x28041,x28043,x28044)
% 179.86/179.60 [2805]P52(x28053,x28052,x28054)+~E(x28051,x28052)+~P52(x28053,x28051,x28054)
% 179.86/179.60 [2806]P52(x28063,x28064,x28062)+~E(x28061,x28062)+~P52(x28063,x28064,x28061)
% 179.86/179.60 [2807]~P137(x28071)+P137(x28072)+~E(x28071,x28072)
% 179.86/179.60 [2808]~P110(x28081)+P110(x28082)+~E(x28081,x28082)
% 179.86/179.60 [2809]~P117(x28091)+P117(x28092)+~E(x28091,x28092)
% 179.86/179.60 [2810]~P93(x28101)+P93(x28102)+~E(x28101,x28102)
% 179.86/179.60 [2811]~P138(x28111)+P138(x28112)+~E(x28111,x28112)
% 179.86/179.60 [2812]P47(x28122,x28123,x28124)+~E(x28121,x28122)+~P47(x28121,x28123,x28124)
% 179.86/179.60 [2813]P47(x28133,x28132,x28134)+~E(x28131,x28132)+~P47(x28133,x28131,x28134)
% 179.86/179.60 [2814]P47(x28143,x28144,x28142)+~E(x28141,x28142)+~P47(x28143,x28144,x28141)
% 179.86/179.60 [2815]P15(x28152,x28153,x28154,x28155,x28156,x28157)+~E(x28151,x28152)+~P15(x28151,x28153,x28154,x28155,x28156,x28157)
% 179.86/179.60 [2816]P15(x28163,x28162,x28164,x28165,x28166,x28167)+~E(x28161,x28162)+~P15(x28163,x28161,x28164,x28165,x28166,x28167)
% 179.86/179.60 [2817]P15(x28173,x28174,x28172,x28175,x28176,x28177)+~E(x28171,x28172)+~P15(x28173,x28174,x28171,x28175,x28176,x28177)
% 179.86/179.60 [2818]P15(x28183,x28184,x28185,x28182,x28186,x28187)+~E(x28181,x28182)+~P15(x28183,x28184,x28185,x28181,x28186,x28187)
% 179.86/179.60 [2819]P15(x28193,x28194,x28195,x28196,x28192,x28197)+~E(x28191,x28192)+~P15(x28193,x28194,x28195,x28196,x28191,x28197)
% 179.86/179.60 [2820]P15(x28203,x28204,x28205,x28206,x28207,x28202)+~E(x28201,x28202)+~P15(x28203,x28204,x28205,x28206,x28207,x28201)
% 179.86/179.60 [2821]P31(x28212,x28213,x28214)+~E(x28211,x28212)+~P31(x28211,x28213,x28214)
% 179.86/179.60 [2822]P31(x28223,x28222,x28224)+~E(x28221,x28222)+~P31(x28223,x28221,x28224)
% 179.86/179.60 [2823]P31(x28233,x28234,x28232)+~E(x28231,x28232)+~P31(x28233,x28234,x28231)
% 179.86/179.60 [2824]~P121(x28241)+P121(x28242)+~E(x28241,x28242)
% 179.86/179.60 [2825]~P89(x28251)+P89(x28252)+~E(x28251,x28252)
% 179.86/179.60 [2826]P42(x28262,x28263)+~E(x28261,x28262)+~P42(x28261,x28263)
% 179.86/179.60 [2827]P42(x28273,x28272)+~E(x28271,x28272)+~P42(x28273,x28271)
% 179.86/179.60 [2828]P22(x28282,x28283,x28284,x28285)+~E(x28281,x28282)+~P22(x28281,x28283,x28284,x28285)
% 179.86/179.60 [2829]P22(x28293,x28292,x28294,x28295)+~E(x28291,x28292)+~P22(x28293,x28291,x28294,x28295)
% 179.86/179.60 [2830]P22(x28303,x28304,x28302,x28305)+~E(x28301,x28302)+~P22(x28303,x28304,x28301,x28305)
% 179.86/179.60 [2831]P22(x28313,x28314,x28315,x28312)+~E(x28311,x28312)+~P22(x28313,x28314,x28315,x28311)
% 179.86/179.60 [2832]~P129(x28321)+P129(x28322)+~E(x28321,x28322)
% 179.86/179.60 [2833]~P94(x28331)+P94(x28332)+~E(x28331,x28332)
% 179.86/179.60 [2834]~P100(x28341)+P100(x28342)+~E(x28341,x28342)
% 179.86/179.60 [2835]~P45(x28351)+P45(x28352)+~E(x28351,x28352)
% 179.86/179.60 [2836]~P86(x28361)+P86(x28362)+~E(x28361,x28362)
% 179.86/179.60 [2837]P10(x28372,x28373,x28374)+~E(x28371,x28372)+~P10(x28371,x28373,x28374)
% 179.86/179.60 [2838]P10(x28383,x28382,x28384)+~E(x28381,x28382)+~P10(x28383,x28381,x28384)
% 179.86/179.60 [2839]P10(x28393,x28394,x28392)+~E(x28391,x28392)+~P10(x28393,x28394,x28391)
% 179.86/179.60 [2840]P11(x28402,x28403,x28404,x28405,x28406)+~E(x28401,x28402)+~P11(x28401,x28403,x28404,x28405,x28406)
% 179.86/179.60 [2841]P11(x28413,x28412,x28414,x28415,x28416)+~E(x28411,x28412)+~P11(x28413,x28411,x28414,x28415,x28416)
% 179.86/179.60 [2842]P11(x28423,x28424,x28422,x28425,x28426)+~E(x28421,x28422)+~P11(x28423,x28424,x28421,x28425,x28426)
% 179.86/179.60 [2843]P11(x28433,x28434,x28435,x28432,x28436)+~E(x28431,x28432)+~P11(x28433,x28434,x28435,x28431,x28436)
% 179.86/179.60 [2844]P11(x28443,x28444,x28445,x28446,x28442)+~E(x28441,x28442)+~P11(x28443,x28444,x28445,x28446,x28441)
% 179.86/179.60 [2845]~P141(x28451)+P141(x28452)+~E(x28451,x28452)
% 179.86/179.60 [2846]P46(x28462,x28463)+~E(x28461,x28462)+~P46(x28461,x28463)
% 179.86/179.60 [2847]P46(x28473,x28472)+~E(x28471,x28472)+~P46(x28473,x28471)
% 179.86/179.60 [2848]~P126(x28481)+P126(x28482)+~E(x28481,x28482)
% 179.86/179.60 [2849]~P71(x28491)+P71(x28492)+~E(x28491,x28492)
% 179.86/179.60 [2850]P48(x28502,x28503,x28504)+~E(x28501,x28502)+~P48(x28501,x28503,x28504)
% 179.86/179.60 [2851]P48(x28513,x28512,x28514)+~E(x28511,x28512)+~P48(x28513,x28511,x28514)
% 179.86/179.60 [2852]P48(x28523,x28524,x28522)+~E(x28521,x28522)+~P48(x28523,x28524,x28521)
% 179.86/179.60 [2853]~P111(x28531)+P111(x28532)+~E(x28531,x28532)
% 179.86/179.60 [2854]~P115(x28541)+P115(x28542)+~E(x28541,x28542)
% 179.86/179.60 [2855]~P127(x28551)+P127(x28552)+~E(x28551,x28552)
% 179.86/179.60 [2856]P41(x28562,x28563,x28564,x28565)+~E(x28561,x28562)+~P41(x28561,x28563,x28564,x28565)
% 179.86/179.60 [2857]P41(x28573,x28572,x28574,x28575)+~E(x28571,x28572)+~P41(x28573,x28571,x28574,x28575)
% 179.86/179.60 [2858]P41(x28583,x28584,x28582,x28585)+~E(x28581,x28582)+~P41(x28583,x28584,x28581,x28585)
% 179.86/179.60 [2859]P41(x28593,x28594,x28595,x28592)+~E(x28591,x28592)+~P41(x28593,x28594,x28595,x28591)
% 179.86/179.60 [2860]~P128(x28601)+P128(x28602)+~E(x28601,x28602)
% 179.86/179.60 [2861]P49(x28612,x28613)+~E(x28611,x28612)+~P49(x28611,x28613)
% 179.86/179.60 [2862]P49(x28623,x28622)+~E(x28621,x28622)+~P49(x28623,x28621)
% 179.86/179.60
% 179.86/179.60 %-------------------------------------------
% 179.86/179.66 cnf(10153,plain,
% 179.86/179.66 (E(f31(x101531,x101532,x101533,x101534,x101535,x101536,x101537,x101538,x101539,a24),x101532)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(10156,plain,
% 179.86/179.66 (~E(f323(a112,x101561),x101561)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(10159,plain,
% 179.86/179.66 (E(f31(x101591,x101592,x101593,x101594,x101595,x101596,x101597,x101598,x101599,a24),x101592)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(10166,plain,
% 179.86/179.66 (~E(f323(a112,x101661),x101661)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(10173,plain,
% 179.86/179.66 (E(f31(x101731,x101732,x101733,x101734,x101735,x101736,x101737,x101738,x101739,a24),x101732)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(10180,plain,
% 179.86/179.66 (~E(f323(a112,x101801),x101801)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(10185,plain,
% 179.86/179.66 (~P101(f323(f60(x101851,x101852,f188(f867(x101851,a855))),x101853))),
% 179.86/179.66 inference(rename_variables,[],[4549])).
% 179.86/179.66 cnf(10188,plain,
% 179.86/179.66 (~P101(f323(f60(x101881,x101882,f188(f867(x101881,a855))),x101883))),
% 179.86/179.66 inference(rename_variables,[],[4549])).
% 179.86/179.66 cnf(10191,plain,
% 179.86/179.66 (~E(f323(a112,x101911),x101911)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(10194,plain,
% 179.86/179.66 (~E(f323(a112,x101941),x101941)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(10197,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x101971),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(10200,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x102001),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(10217,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x102171)),x102171))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(10220,plain,
% 179.86/179.66 (~E(f323(f323(f144(x102201),x102202),x102203),x102203)),
% 179.86/179.66 inference(rename_variables,[],[4489])).
% 179.86/179.66 cnf(10226,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x102261),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(10228,plain,
% 179.86/179.66 (E(f42(a860,f31(x102281,f323(f323(f79(a860),x102282),x102283),x102284,x102285,x102286,x102287,x102288,x102289,x1022810,a24),x102282),f2(a860))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,4462,10156,10166,10180,10191,3104,3163,3130,3113,4489,3254,4529,10197,10200,4526,4484,4534,4532,3245,4516,4549,10185,4553,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049])).
% 179.86/179.66 cnf(10229,plain,
% 179.86/179.66 (E(f31(x102291,x102292,x102293,x102294,x102295,x102296,x102297,x102298,x102299,a24),x102292)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(10232,plain,
% 179.86/179.66 (E(f31(x102321,x102322,x102323,x102324,x102325,x102326,x102327,x102328,x102329,a24),x102322)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(10239,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),f323(f323(f78(a860),x102391),x102392)),x102392))),
% 179.86/179.66 inference(rename_variables,[],[4551])).
% 179.86/179.66 cnf(10242,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),f323(f323(f78(a860),x102421),x102422)),x102422))),
% 179.86/179.66 inference(rename_variables,[],[4551])).
% 179.86/179.66 cnf(10249,plain,
% 179.86/179.66 (~E(x102491,f323(a112,x102491))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,4462,10156,10166,10180,10191,3104,3163,3130,3113,4489,3339,3254,4529,10197,10200,4526,4484,4534,4107,4532,3245,4516,4549,10185,4553,4551,10239,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155])).
% 179.86/179.66 cnf(10263,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x102631),x102631))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(10266,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f42(a860,x102661,x102662)),x102661))),
% 179.86/179.66 inference(rename_variables,[],[3730])).
% 179.86/179.66 cnf(10287,plain,
% 179.86/179.66 (E(f323(f35(a860),f323(f244(a860),x102871)),x102871)),
% 179.86/179.66 inference(rename_variables,[],[3161])).
% 179.86/179.66 cnf(10295,plain,
% 179.86/179.66 (~E(f323(a112,x102951),x102951)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(10298,plain,
% 179.86/179.66 (~E(f323(a112,x102981),x102981)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(10301,plain,
% 179.86/179.66 (~E(f323(a112,x103011),x103011)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(10303,plain,
% 179.86/179.66 (P101(f323(a193,a97))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,4462,10156,10166,10180,10191,10194,10295,10298,3104,3163,3130,3113,3198,4489,3161,4558,3181,3339,3254,4529,10197,10200,3864,3273,4526,4484,4525,10263,3365,3794,3730,4534,10217,4107,4532,4515,3245,4516,4520,4549,10185,4553,4551,10239,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296])).
% 179.86/179.66 cnf(10306,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x103061),f323(a112,x103061)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(10315,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x103151),x103151))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10322,plain,
% 179.86/179.66 (E(f31(x103221,x103222,x103223,x103224,x103225,x103226,x103227,x103228,x103229,a24),x103222)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(10325,plain,
% 179.86/179.66 (E(f31(x103251,x103252,x103253,x103254,x103255,x103256,x103257,x103258,x103259,a24),x103252)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(10344,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x103441),x103441))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(10353,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x103531),x103531))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(10358,plain,
% 179.86/179.66 (~E(f323(f323(f323(f70(x103581,f864(x103582)),x103583),x103584),f323(f230(x103582),x103585)),f323(f16(f864(x103582),x103581),f200(x103582)))),
% 179.86/179.66 inference(rename_variables,[],[4546])).
% 179.86/179.66 cnf(10385,plain,
% 179.86/179.66 (~E(f323(f323(f144(x103851),x103852),x103853),x103853)),
% 179.86/179.66 inference(rename_variables,[],[4489])).
% 179.86/179.66 cnf(10388,plain,
% 179.86/179.66 (~E(f323(a112,x103881),f2(a860))),
% 179.86/179.66 inference(rename_variables,[],[4474])).
% 179.86/179.66 cnf(10399,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x103991),x103991))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(10404,plain,
% 179.86/179.66 (~E(f323(a112,x104041),x104041)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(10411,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x104111),x104111))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10424,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x104241),f323(a112,x104241)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(10445,plain,
% 179.86/179.66 (~P101(f323(f60(x104451,x104452,f188(f867(x104451,a855))),x104453))),
% 179.86/179.66 inference(rename_variables,[],[4549])).
% 179.86/179.66 cnf(10464,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x104641),x104641))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(10479,plain,
% 179.86/179.66 (~E(f323(a112,x104791),f2(a860))),
% 179.86/179.66 inference(rename_variables,[],[4474])).
% 179.86/179.66 cnf(10488,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x104881),x104881))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(10493,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x104931),f323(a112,x104931)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(10496,plain,
% 179.86/179.66 (~P101(f323(f60(x104961,x104962,f188(f867(x104961,a855))),x104963))),
% 179.86/179.66 inference(rename_variables,[],[4549])).
% 179.86/179.66 cnf(10499,plain,
% 179.86/179.66 (~P101(f323(f60(x104991,x104992,f188(f867(x104991,a855))),x104993))),
% 179.86/179.66 inference(rename_variables,[],[4549])).
% 179.86/179.66 cnf(10504,plain,
% 179.86/179.66 (~P101(f323(f60(x105041,x105042,f188(f867(x105041,a855))),x105043))),
% 179.86/179.66 inference(rename_variables,[],[4549])).
% 179.86/179.66 cnf(10515,plain,
% 179.86/179.66 (~E(f323(a112,x105151),x105151)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(10533,plain,
% 179.86/179.66 (P101(f323(f323(f238(a99),f323(a3,x105331)),f323(a3,f323(a112,x105331))))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,10232,10322,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,4474,10388,3104,3163,3130,3113,3745,3198,4546,4489,10220,3161,4063,4558,3181,3636,3339,10306,10424,10493,3725,3254,4529,10197,10200,10226,4541,3712,3864,3298,3300,3273,4526,4484,4016,3270,10315,10411,3271,10344,3272,4525,10263,10353,10464,3365,3794,3730,10266,4534,10217,4107,4532,4515,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,4553,3754,4551,10239,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052])).
% 179.86/179.66 cnf(10540,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x105401),x105401))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10543,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x105431),f323(f323(f79(a860),x105431),x105431)))),
% 179.86/179.66 inference(rename_variables,[],[3538])).
% 179.86/179.66 cnf(10545,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x105451),f323(f323(f79(a860),f323(a112,x105451)),f323(a112,x105451))))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,10232,10322,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,4474,10388,3104,3163,3130,3113,3745,3198,4546,4489,10220,3161,4063,4558,3181,3636,3339,10306,10424,10493,3725,3254,4529,10197,10200,10226,4541,3712,3864,3298,3300,3273,4526,4484,4016,3270,10315,10411,3271,10344,3272,4525,10263,10353,10464,3365,3794,3730,10266,4534,10217,4107,4532,4515,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,3538,10543,4553,3754,4551,10239,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074])).
% 179.86/179.66 cnf(10546,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x105461),f323(f323(f79(a860),x105461),x105461)))),
% 179.86/179.66 inference(rename_variables,[],[3538])).
% 179.86/179.66 cnf(10549,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x105491),f323(a112,f323(f323(f78(a860),x105492),x105491))))),
% 179.86/179.66 inference(rename_variables,[],[3723])).
% 179.86/179.66 cnf(10554,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x105541),f323(a112,x105541)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(10557,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x105571),f323(a112,x105571)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(10560,plain,
% 179.86/179.66 (P101(f323(f323(f325(x105601),x105602),f246(f867(x105601,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3429])).
% 179.86/179.66 cnf(10577,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x105771)),x105771))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(10580,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x105801)),x105801))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(10583,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),f323(f323(f78(a860),x105831),x105832)),x105832))),
% 179.86/179.66 inference(rename_variables,[],[4551])).
% 179.86/179.66 cnf(10586,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),f323(f323(f78(a860),x105861),x105862)),x105862))),
% 179.86/179.66 inference(rename_variables,[],[4551])).
% 179.86/179.66 cnf(10589,plain,
% 179.86/179.66 (P101(f323(f246(f867(x105891,a855)),x105892))),
% 179.86/179.66 inference(rename_variables,[],[3332])).
% 179.86/179.66 cnf(10592,plain,
% 179.86/179.66 (E(f323(f35(a860),f323(f244(a860),x105921)),x105921)),
% 179.86/179.66 inference(rename_variables,[],[3161])).
% 179.86/179.66 cnf(10595,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x105951),f323(a112,x105951)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(10602,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x106021),x106021))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10607,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x106071),x106071))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(10616,plain,
% 179.86/179.66 (E(f31(x106161,x106162,x106163,x106164,x106165,x106166,x106167,x106168,x106169,a24),x106162)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(10619,plain,
% 179.86/179.66 (P101(f323(f246(f867(x106191,a855)),x106192))),
% 179.86/179.66 inference(rename_variables,[],[3332])).
% 179.86/179.66 cnf(10622,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f2(a860)),x106221))),
% 179.86/179.66 inference(rename_variables,[],[3292])).
% 179.86/179.66 cnf(10625,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x106251,a855)),f188(f867(x106251,a855))),x106252))),
% 179.86/179.66 inference(rename_variables,[],[3721])).
% 179.86/179.66 cnf(10628,plain,
% 179.86/179.66 (P101(f323(f246(f867(x106281,a855)),x106282))),
% 179.86/179.66 inference(rename_variables,[],[3332])).
% 179.86/179.66 cnf(10630,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(f323(f79(a860),f323(a112,x106301)),f323(a112,x106301))),x106301))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,10232,10322,10325,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,4474,10388,3104,3163,3130,3113,3745,3198,4546,4489,10220,3161,10287,4063,4558,3181,3636,3575,3339,10306,10424,10493,10554,10557,3725,3254,4529,10197,10200,10226,4541,3712,3482,3864,3298,3300,3273,4526,4484,4016,3270,10315,10411,10540,3271,10344,10399,3272,4525,10263,10353,10464,3429,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,3292,4107,4532,4515,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,4556,3721,3538,10543,10546,4553,3754,4551,10239,10242,10583,3723,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279])).
% 179.86/179.66 cnf(10631,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x106311),f323(f323(f79(a860),x106311),x106311)))),
% 179.86/179.66 inference(rename_variables,[],[3538])).
% 179.86/179.66 cnf(10636,plain,
% 179.86/179.66 (E(f31(x106361,x106362,x106363,x106364,x106365,x106366,x106367,x106368,x106369,a24),x106362)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(10640,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,f323(a112,f323(f323(f78(a860),x106401),x106402)))),f323(a112,x106402)))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,10232,10322,10325,10616,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,4474,10388,3104,3163,3130,3113,3745,3198,4546,4489,10220,3161,10287,4063,4558,3181,3636,3575,3339,10306,10424,10493,10554,10557,10595,3725,3254,4529,10197,10200,10226,4541,3712,3482,3864,3298,3300,3273,4526,4484,4016,3270,10315,10411,10540,3271,10344,10399,3272,4525,10263,10353,10464,3429,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,3292,4107,4532,4515,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,4556,3721,3538,10543,10546,4553,3754,4551,10239,10242,10583,3723,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321])).
% 179.86/179.66 cnf(10673,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x106731),x106731))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10684,plain,
% 179.86/179.66 (~P101(f323(f323(f188(f867(x106841,f867(x106842,a855))),x106843),x106844))),
% 179.86/179.66 inference(rename_variables,[],[4554])).
% 179.86/179.66 cnf(10693,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x106931),f323(a112,x106931)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(10695,plain,
% 179.86/179.66 (P101(f323(f323(f238(a1),f323(f323(f22(a1),x106951),f76(a1))),x106951))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,10232,10322,10325,10616,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,4474,10388,3104,3163,3130,3113,3745,3198,4546,4489,10220,3161,10287,4063,3916,4558,3181,3636,3575,3339,10306,10424,10493,10554,10557,10595,3725,3254,4529,10197,10200,10226,4541,3712,3482,3864,3298,3300,3273,4526,4484,4016,3270,10315,10411,10540,10602,10673,3271,10344,10399,10607,3272,4525,10263,10353,10464,3429,4537,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,3292,4107,4532,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,4556,3721,3538,10543,10546,4553,4554,3754,4551,10239,10242,10583,3723,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580])).
% 179.86/179.66 cnf(10696,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x106961),x106961))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(10701,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x107011),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(10714,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x107141),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(10717,plain,
% 179.86/179.66 (~P101(f323(f323(f238(f867(x107171,a855)),x107172),f188(f867(x107171,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4547])).
% 179.86/179.66 cnf(10720,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x107201),x107201))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10723,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x107231),x107231))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10738,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x107381),x107381))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(10747,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x107471),x107472),f188(f867(x107471,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(10756,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x107561),x107561))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10759,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x107591,a855)),f323(f302(x107592,x107591,x107593),f323(f303(x107592,x107591,x107593),x107594))),x107594))),
% 179.86/179.66 inference(rename_variables,[],[4166])).
% 179.86/179.66 cnf(10766,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x107661,a855)),f323(f166(x107661),f323(f129(x107661,x107662),x107663))),f323(f166(x107661),x107663)))),
% 179.86/179.66 inference(rename_variables,[],[3926])).
% 179.86/179.66 cnf(10769,plain,
% 179.86/179.66 (E(f323(f302(x107691,x107691,f5(x107691)),x107692),x107692)),
% 179.86/179.66 inference(rename_variables,[],[3328])).
% 179.86/179.66 cnf(10774,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f2(a860)),x107741))),
% 179.86/179.66 inference(rename_variables,[],[3292])).
% 179.86/179.66 cnf(10777,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x107771),x107771))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10780,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x107801),x107801))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(10783,plain,
% 179.86/179.66 (~P101(f323(f323(f188(f867(x107831,f867(x107832,a855))),x107833),x107834))),
% 179.86/179.66 inference(rename_variables,[],[4554])).
% 179.86/179.66 cnf(10790,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x107901),x107901))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(10801,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x108011),f323(f323(f79(a860),x108011),x108011)))),
% 179.86/179.66 inference(rename_variables,[],[3538])).
% 179.86/179.66 cnf(10807,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x108071),f323(a112,f323(f323(f78(a860),x108072),x108071))))),
% 179.86/179.66 inference(rename_variables,[],[3723])).
% 179.86/179.66 cnf(10814,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x108141),x108141))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10817,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x108171),x108171))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(10820,plain,
% 179.86/179.66 (~E(f323(a112,x108201),x108201)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(10825,plain,
% 179.86/179.66 (P101(f323(f323(f325(x108251),x108252),f246(f867(x108251,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3429])).
% 179.86/179.66 cnf(10830,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x108301),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(10832,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x108321,a855)),x108322),f37(f867(x108321,a855),f323(f300(x108321),x108322))))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,10232,10322,10325,10616,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,4474,10388,3104,3163,3130,3113,3745,3328,3198,4546,4489,10220,3161,10287,4063,3916,4558,3181,3473,3636,3575,3339,10306,10424,10493,10554,10557,10595,10693,3725,3254,4529,10197,10200,10226,10701,10714,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3637,4016,4547,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,4537,10747,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,3292,10622,4107,4532,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,4556,3721,3538,10543,10546,10631,10801,4553,4554,10684,4166,3754,4551,10239,10242,10583,3723,10549,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443])).
% 179.86/179.66 cnf(10845,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f2(a860)),x108451))),
% 179.86/179.66 inference(rename_variables,[],[3292])).
% 179.86/179.66 cnf(10852,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x108521),x108521))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10861,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x108611),x108612),f188(f867(x108611,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(10863,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x108631,a855)),f38(f867(x108631,a855),f323(f300(x108631),x108632))),x108632))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,10232,10322,10325,10616,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,4474,10388,3104,3163,3130,3113,3745,3328,3198,4546,4489,10220,3161,10287,4063,3916,4558,3181,3473,3636,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,3725,3254,4529,10197,10200,10226,10701,10714,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3637,4016,4547,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,4537,10747,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,4556,3721,3538,10543,10546,10631,10801,4553,4554,10684,4166,3754,4551,10239,10242,10583,3723,10549,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717])).
% 179.86/179.66 cnf(10869,plain,
% 179.86/179.66 (P101(f323(f323(f325(x108691),x108692),f246(f867(x108691,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3429])).
% 179.86/179.66 cnf(10872,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x108721),f861(x108721))),f323(f323(f258(f861(x108721),f861(x108721)),x108722),f113(x108721))),f138(x108721,x108723)))),
% 179.86/179.66 inference(rename_variables,[],[4558])).
% 179.86/179.66 cnf(10878,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(x108781,x108781)),x108782),f255(x108781,f188(f867(x108781,a855)))))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,10232,10322,10325,10616,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,4474,10388,3104,3163,3130,3113,3745,3328,3198,4546,4489,10220,3161,10287,4063,3916,4558,3181,3473,3636,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,3725,3254,4529,10197,10200,10226,10701,10714,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3637,4016,4547,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,4537,10747,10861,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,4556,3721,3538,10543,10546,10631,10801,4553,4554,10684,4166,3754,4551,10239,10242,10583,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861])).
% 179.86/179.66 cnf(10879,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x108791),x108792),f188(f867(x108791,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(10882,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x108821),x108822),f188(f867(x108821,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(10885,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x108851,a855)),x108852),f323(f323(f301(x108851),x108853),x108852)))),
% 179.86/179.66 inference(rename_variables,[],[3719])).
% 179.86/179.66 cnf(10888,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x108881),x108881))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(10891,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x108911,a855)),x108912),f323(f323(f301(x108911),x108913),x108912)))),
% 179.86/179.66 inference(rename_variables,[],[3719])).
% 179.86/179.66 cnf(10894,plain,
% 179.86/179.66 (E(f323(f302(x108941,x108941,f5(x108941)),x108942),x108942)),
% 179.86/179.66 inference(rename_variables,[],[3328])).
% 179.86/179.66 cnf(10896,plain,
% 179.86/179.66 (P35(x108961,x108962,x108963,f31(x108964,f113(x108961),x108965,x108966,x108967,x108968,x108969,x1089610,x1089611,a24),f113(x108962))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,4474,10388,3104,3163,3130,3113,3745,3328,10769,3198,4546,4489,10220,3161,10287,4063,3916,4558,3181,3473,3636,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,3725,3254,4529,10197,10200,10226,10701,10714,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3637,4016,4547,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,4537,10747,10861,10879,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,4556,3719,10885,3721,3538,10543,10546,10631,10801,4553,4554,10684,4166,3754,4551,10239,10242,10583,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001])).
% 179.86/179.66 cnf(10897,plain,
% 179.86/179.66 (E(f31(x108971,x108972,x108973,x108974,x108975,x108976,x108977,x108978,x108979,a24),x108972)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(10900,plain,
% 179.86/179.66 (E(f31(x109001,x109002,x109003,x109004,x109005,x109006,x109007,x109008,x109009,a24),x109002)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(10913,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x109131,a855)),x109132),f323(f323(f301(x109131),x109133),x109132)))),
% 179.86/179.66 inference(rename_variables,[],[3719])).
% 179.86/179.66 cnf(10926,plain,
% 179.86/179.66 (~E(f323(a112,x109261),f2(a860))),
% 179.86/179.66 inference(rename_variables,[],[4474])).
% 179.86/179.66 cnf(10929,plain,
% 179.86/179.66 (~P101(f323(f60(x109291,x109292,f188(f867(x109291,a855))),x109293))),
% 179.86/179.66 inference(rename_variables,[],[4549])).
% 179.86/179.66 cnf(10942,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x109421),f323(a112,x109421)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(10952,plain,
% 179.86/179.66 (~E(f323(f302(x109521,f867(x109521,a855),x109522),x109523),f323(f300(x109521),x109523))),
% 179.86/179.66 inference(rename_variables,[],[4535])).
% 179.86/179.66 cnf(10955,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x109551),x109552),f188(f867(x109551,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(10958,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(x109581,x109581)),f323(f323(f258(x109581,x109581),x109582),x109582)),f299(x109581,x109583)))),
% 179.86/179.66 inference(rename_variables,[],[3916])).
% 179.86/179.66 cnf(10961,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x109611,a855)),x109612),f246(f867(x109611,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3654])).
% 179.86/179.66 cnf(10964,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x109641,a855)),f323(f166(x109641),f164(x109641,x109642,x109643))),f323(f166(x109641),x109643)))),
% 179.86/179.66 inference(rename_variables,[],[3979])).
% 179.86/179.66 cnf(10980,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x109801,a855)),f188(f867(x109801,a855))),x109802))),
% 179.86/179.66 inference(rename_variables,[],[3721])).
% 179.86/179.66 cnf(10991,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x109911),f861(x109911))),f323(f323(f258(f861(x109911),f861(x109911)),x109912),f113(x109911))),f140(x109911,x109913)))),
% 179.86/179.66 inference(rename_variables,[],[4559])).
% 179.86/179.66 cnf(11002,plain,
% 179.86/179.66 (~E(f323(a112,x110021),x110021)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11005,plain,
% 179.86/179.66 (~E(f323(a112,x110051),x110051)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11007,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(f861(x110071),f861(x110071))),f323(f323(f258(f861(x110071),f861(x110071)),f113(x110071)),f113(x110071))),f323(f323(f280(f861(x110071),f861(x110071),f861(x110071)),f151(x110071,x110072)),f299(f861(x110071),f151(x110071,x110072)))))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,4474,10388,10479,3732,3104,3163,3130,3113,3745,3328,10769,3198,4546,3914,4489,10220,4535,3161,10287,4063,3916,10958,4558,10872,4559,3181,3473,3636,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,3725,3254,4529,10197,10200,10226,10701,10714,10830,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3979,3637,4016,3654,4547,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,10869,4537,10747,10861,10879,10882,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,10504,4556,3881,3719,10885,10891,3721,10625,3538,10543,10546,10631,10801,4553,4554,10684,4166,3754,4551,10239,10242,10583,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547])).
% 179.86/179.66 cnf(11010,plain,
% 179.86/179.66 (~E(f323(a112,x110101),f2(a860))),
% 179.86/179.66 inference(rename_variables,[],[4474])).
% 179.86/179.66 cnf(11015,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x110151,a855)),x110152),x110152))),
% 179.86/179.66 inference(rename_variables,[],[3571])).
% 179.86/179.66 cnf(11022,plain,
% 179.86/179.66 (~E(f323(a112,x110221),x110221)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11025,plain,
% 179.86/179.66 (~E(f323(a112,x110251),x110251)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11027,plain,
% 179.86/179.66 (~P28(x110271,f867(x110271,a855),x110272,x110273,f323(f300(x110271),x110273))),
% 179.86/179.66 inference(scs_inference,[],[4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,4474,10388,10479,10926,3732,3104,3163,3130,3113,3745,3328,10769,3198,4546,3914,4489,10220,4535,10952,3161,10287,4063,3916,10958,4558,10872,4559,3181,3473,3636,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,3725,3254,4529,10197,10200,10226,10701,10714,10830,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3979,3637,4016,3654,4547,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,10869,4537,10747,10861,10879,10882,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,10504,4556,3881,3719,10885,10891,3571,3721,10625,3538,10543,10546,10631,10801,4553,4554,10684,4166,3754,4551,10239,10242,10583,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600])).
% 179.86/179.66 cnf(11030,plain,
% 179.86/179.66 (P27(x110301,x110301,f5(x110301),x110302)),
% 179.86/179.66 inference(rename_variables,[],[3512])).
% 179.86/179.66 cnf(11035,plain,
% 179.86/179.66 (~E(f323(f302(x110351,f867(x110351,a855),x110352),x110353),f323(f300(x110351),x110353))),
% 179.86/179.66 inference(rename_variables,[],[4535])).
% 179.86/179.66 cnf(11040,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x110401,a855)),x110402),f246(f867(x110401,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3654])).
% 179.86/179.66 cnf(11056,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x110561),x110562),f188(f867(x110561,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11059,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x110591)),x110591))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(11064,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x110641),x110642),f188(f867(x110641,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11077,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x110771)),x110771))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(11080,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x110801),x110802),f188(f867(x110801,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11090,plain,
% 179.86/179.66 (E(f323(f129(x110901,f246(f867(x110902,a855))),f705(x110903,x110904,f323(f323(f144(x110901),x110904),x110903),f246(f867(x110902,a855)),x110901)),x110903)),
% 179.86/179.66 inference(scs_inference,[],[3512,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,4474,10388,10479,10926,3732,3104,3163,3130,3113,3745,3328,10769,3198,4546,3914,4489,10220,4535,10952,3376,3161,10287,4063,3916,10958,4558,10872,4559,3181,3473,3636,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,10942,3725,3254,4529,10197,10200,10226,10701,10714,10830,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3979,3637,4016,3654,10961,4547,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,10869,4537,10747,10861,10879,10882,10955,11056,11064,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,11059,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,10504,4556,3881,3719,10885,10891,3571,3721,10625,3538,10543,10546,10631,10801,4553,4554,10684,4166,3754,4551,10239,10242,10583,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858])).
% 179.86/179.66 cnf(11092,plain,
% 179.86/179.66 (E(f323(x110921,f834(f323(x110921,x110922),f323(f230(x110923),x110922),x110921,x110924,x110923)),f323(x110921,x110922))),
% 179.86/179.66 inference(scs_inference,[],[3512,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,4474,10388,10479,10926,3732,3104,3163,3130,3113,3745,3328,10769,3198,3375,4546,3914,4489,10220,4535,10952,3376,3161,10287,4063,3916,10958,4558,10872,4559,3181,3473,3636,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,10942,3725,3254,4529,10197,10200,10226,10701,10714,10830,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3979,3637,4016,3654,10961,4547,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,10869,4537,10747,10861,10879,10882,10955,11056,11064,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,11059,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,10504,4556,3881,3719,10885,10891,3571,3721,10625,3538,10543,10546,10631,10801,4553,4554,10684,4166,3754,4551,10239,10242,10583,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860])).
% 179.86/179.66 cnf(11101,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(x111011,x111011)),f323(f323(f258(x111011,x111011),x111012),x111012)),f299(x111011,x111013)))),
% 179.86/179.66 inference(rename_variables,[],[3916])).
% 179.86/179.66 cnf(11106,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x111061),f861(x111061))),f323(f323(f258(f861(x111061),f861(x111061)),x111062),f113(x111061))),f138(x111061,x111063)))),
% 179.86/179.66 inference(rename_variables,[],[4558])).
% 179.86/179.66 cnf(11109,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x111091),f861(x111091))),f323(f323(f258(f861(x111091),f861(x111091)),x111092),f113(x111091))),f140(x111091,x111093)))),
% 179.86/179.66 inference(rename_variables,[],[4559])).
% 179.86/179.66 cnf(11112,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x111121),f861(x111121))),f323(f323(f258(f861(x111121),f861(x111121)),x111122),f113(x111121))),f150(x111121,x111123)))),
% 179.86/179.66 inference(rename_variables,[],[4560])).
% 179.86/179.66 cnf(11117,plain,
% 179.86/179.66 (~P101(f323(f323(f238(f867(x111171,a855)),x111172),f188(f867(x111171,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4547])).
% 179.86/179.66 cnf(11120,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x111201),x111202),f188(f867(x111201,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11127,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x111271,a855)),x111272),f246(f867(x111271,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3654])).
% 179.86/179.66 cnf(11138,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x111381),x111382),f188(f867(x111381,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11141,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(x111411,x111411)),f323(f323(f258(x111411,x111411),x111412),x111413)),f146(x111411,f113(f867(x111411,a860)))))),
% 179.86/179.66 inference(rename_variables,[],[4556])).
% 179.86/179.66 cnf(11144,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x111441,a855)),x111442),x111442))),
% 179.86/179.66 inference(rename_variables,[],[3571])).
% 179.86/179.66 cnf(11147,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x111471),x111472),f188(f867(x111471,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11149,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x111491,a855)),f323(f277(x111492,x111491,f188(f867(f866(x111492,x111491),a855))),x111493)),x111494))),
% 179.86/179.66 inference(scs_inference,[],[3512,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,4474,10388,10479,10926,3732,3104,3163,3130,3113,3745,3328,10769,3198,3375,4546,3914,4489,10220,4535,10952,3376,3161,10287,4063,3916,10958,4558,10872,11106,4559,10991,4560,3181,3473,3636,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,10942,3725,3254,4529,10197,10200,10226,10701,10714,10830,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3979,3637,4016,3654,10961,11040,4547,10717,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,10869,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,11059,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,10504,4556,3881,3719,10885,10891,3571,11015,3721,10625,10980,3538,10543,10546,10631,10801,4553,4554,10684,4166,3754,4551,10239,10242,10583,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225])).
% 179.86/179.66 cnf(11150,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x111501,a855)),f188(f867(x111501,a855))),x111502))),
% 179.86/179.66 inference(rename_variables,[],[3721])).
% 179.86/179.66 cnf(11153,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(x111531,x111531)),f323(f323(f258(x111531,x111531),x111532),x111532)),f299(x111531,x111533)))),
% 179.86/179.66 inference(rename_variables,[],[3916])).
% 179.86/179.66 cnf(11155,plain,
% 179.86/179.66 (~P35(x111551,x111552,x111553,f323(f323(f147(x111554,x111551),x111555),f323(a112,f113(x111554))),f113(x111552))),
% 179.86/179.66 inference(scs_inference,[],[3512,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,4474,10388,10479,10926,3732,3104,3163,3130,3113,3745,3328,10769,3198,3375,4546,3914,4489,10220,4535,10952,3376,3161,10287,4063,3916,10958,11101,4558,10872,11106,4559,10991,4560,3181,3473,3636,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,10942,3725,3254,4529,10197,10200,10226,10701,10714,10830,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3979,3637,4016,3654,10961,11040,4547,10717,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,10869,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,11059,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,10504,4556,3881,3719,10885,10891,3571,11015,3721,10625,10980,3538,10543,10546,10631,10801,4553,4554,10684,4166,3754,4551,10239,10242,10583,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232])).
% 179.86/179.66 cnf(11159,plain,
% 179.86/179.66 (P35(x111591,x111592,x111593,f323(f323(f147(x111594,x111591),x111595),f31(x111596,f113(x111594),x111597,x111598,x111599,x1115910,x1115911,x1115912,x1115913,a24)),f113(x111592))),
% 179.86/179.66 inference(scs_inference,[],[3512,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,4474,10388,10479,10926,3732,3104,3163,3130,3113,3745,3328,10769,3198,3375,4546,3914,4489,10220,4535,10952,3376,3161,10287,4063,3916,10958,11101,4558,10872,11106,4559,10991,4560,3181,3473,3636,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,10942,3725,3254,4529,10197,10200,10226,10701,10714,10830,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3979,3637,4016,3654,10961,11040,4547,10717,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,10869,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,11059,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,10504,4556,3881,3719,10885,10891,3571,11015,3721,10625,10980,3538,10543,10546,10631,10801,4553,4554,10684,4166,3754,4551,10239,10242,10583,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253])).
% 179.86/179.66 cnf(11164,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x111641),f861(x111641))),f323(f323(f258(f861(x111641),f861(x111641)),x111642),f113(x111641))),f150(x111641,x111643)))),
% 179.86/179.66 inference(rename_variables,[],[4560])).
% 179.86/179.66 cnf(11167,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x111671),f861(x111671))),f323(f323(f258(f861(x111671),f861(x111671)),f113(x111671)),x111672)),f138(x111671,x111673)))),
% 179.86/179.66 inference(rename_variables,[],[4561])).
% 179.86/179.66 cnf(11175,plain,
% 179.86/179.66 (P101(f323(f323(f325(x111751),x111752),f246(f867(x111751,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3429])).
% 179.86/179.66 cnf(11180,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x111801,a855)),f188(f867(x111801,a855))),x111802))),
% 179.86/179.66 inference(rename_variables,[],[3721])).
% 179.86/179.66 cnf(11183,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x111831),x111832),f188(f867(x111831,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11186,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x111861,a855)),x111862),f246(f867(x111861,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3654])).
% 179.86/179.66 cnf(11190,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x111901,a855)),f323(f277(x111902,x111901,x111903),f188(f867(x111902,a855)))),x111904))),
% 179.86/179.66 inference(scs_inference,[],[3512,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,4474,10388,10479,10926,3732,3104,3163,3130,3113,3745,3328,10769,3198,3375,4546,3914,4489,10220,4535,10952,3376,3161,10287,4063,3916,10958,11101,4558,10872,11106,4559,10991,4560,11112,4561,4562,3181,3473,3636,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,10942,3725,3254,4529,10197,10200,10226,10701,10714,10830,4541,3712,3482,3864,3298,3300,3273,4526,4484,4027,3926,10766,3979,3637,4016,3654,10961,11040,11127,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,3271,10344,10399,10607,10696,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,10869,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,3332,10589,10619,3365,3794,3730,10266,4534,10217,10577,10580,11059,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,10504,4556,3881,3719,10885,10891,3571,11015,3721,10625,10980,11150,11180,3538,10543,10546,10631,10801,4553,4554,10684,4166,4068,3754,4551,10239,10242,10583,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486])).
% 179.86/179.66 cnf(11191,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x111911,a855)),f188(f867(x111911,a855))),x111912))),
% 179.86/179.66 inference(rename_variables,[],[3721])).
% 179.86/179.66 cnf(11204,plain,
% 179.86/179.66 (P101(f323(f246(f867(x112041,a855)),x112042))),
% 179.86/179.66 inference(rename_variables,[],[3332])).
% 179.86/179.66 cnf(11212,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x112121),f861(x112121))),f323(f323(f258(f861(x112121),f861(x112121)),x112122),f113(x112121))),f138(x112121,x112123)))),
% 179.86/179.66 inference(rename_variables,[],[4558])).
% 179.86/179.66 cnf(11215,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x112151),f861(x112151))),f323(f323(f258(f861(x112151),f861(x112151)),x112152),f113(x112151))),f140(x112151,x112153)))),
% 179.86/179.66 inference(rename_variables,[],[4559])).
% 179.86/179.66 cnf(11218,plain,
% 179.86/179.66 (~E(f323(f323(f144(x112181),x112182),x112183),x112183)),
% 179.86/179.66 inference(rename_variables,[],[4489])).
% 179.86/179.66 cnf(11221,plain,
% 179.86/179.66 (~E(f323(a112,x112211),x112211)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11224,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x112241),x112242),f188(f867(x112241,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11229,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(f861(x112291),f861(x112291))),f323(f323(f258(f861(x112291),f861(x112291)),x112292),x112292)),f151(x112291,f299(x112291,x112293))))),
% 179.86/179.66 inference(rename_variables,[],[4057])).
% 179.86/179.66 cnf(11234,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x112341),f861(x112341))),f323(f323(f258(f861(x112341),f861(x112341)),x112342),f113(x112341))),f138(x112341,x112343)))),
% 179.86/179.66 inference(rename_variables,[],[4558])).
% 179.86/179.66 cnf(11244,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x112441),x112442),f188(f867(x112441,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11247,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x112471),x112472),f188(f867(x112471,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11250,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x112501),x112502),f188(f867(x112501,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11253,plain,
% 179.86/179.66 (P101(f323(f323(f325(x112531),x112532),f246(f867(x112531,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3429])).
% 179.86/179.66 cnf(11256,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x112561),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(11261,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(x112611,x112611)),f323(f323(f258(x112611,x112611),x112612),x112613)),f146(x112611,f113(f867(x112611,a860)))))),
% 179.86/179.66 inference(rename_variables,[],[4556])).
% 179.86/179.66 cnf(11264,plain,
% 179.86/179.66 (~E(f323(f302(x112641,f867(x112641,a855),x112642),x112643),f323(f300(x112641),x112643))),
% 179.86/179.66 inference(rename_variables,[],[4535])).
% 179.86/179.66 cnf(11267,plain,
% 179.86/179.66 (~E(f323(f302(x112671,f867(x112671,a855),x112672),x112673),f323(f300(x112671),x112673))),
% 179.86/179.66 inference(rename_variables,[],[4535])).
% 179.86/179.66 cnf(11272,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x112721),f861(x112721))),f323(f323(f258(f861(x112721),f861(x112721)),x112722),f113(x112721))),f138(x112721,x112723)))),
% 179.86/179.66 inference(rename_variables,[],[4558])).
% 179.86/179.66 cnf(11275,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x112751),f861(x112751))),f323(f323(f258(f861(x112751),f861(x112751)),x112752),f113(x112751))),f140(x112751,x112753)))),
% 179.86/179.66 inference(rename_variables,[],[4559])).
% 179.86/179.66 cnf(11278,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x112781),f861(x112781))),f323(f323(f258(f861(x112781),f861(x112781)),x112782),f113(x112781))),f138(x112781,x112783)))),
% 179.86/179.66 inference(rename_variables,[],[4558])).
% 179.86/179.66 cnf(11281,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x112811),x112812),f188(f867(x112811,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11288,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x112881),x112882),f188(f867(x112881,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11291,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x112911),x112912),f188(f867(x112911,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11294,plain,
% 179.86/179.66 (P101(f323(f323(f325(x112941),f323(x112942,x112943)),f323(f302(x112944,x112941,x112942),f246(f867(x112944,a855)))))),
% 179.86/179.66 inference(rename_variables,[],[3881])).
% 179.86/179.66 cnf(11297,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(x112971,x112971)),f323(f323(f258(x112971,x112971),x112972),x112973)),f146(x112971,f113(f867(x112971,a860)))))),
% 179.86/179.66 inference(rename_variables,[],[4556])).
% 179.86/179.66 cnf(11303,plain,
% 179.86/179.66 (E(f31(x113031,x113032,x113033,x113034,x113035,x113036,x113037,x113038,x113039,a24),x113032)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11306,plain,
% 179.86/179.66 (E(f31(x113061,x113062,x113063,x113064,x113065,x113066,x113067,x113068,x113069,a24),x113062)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11309,plain,
% 179.86/179.66 (~E(f323(a112,x113091),x113091)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11316,plain,
% 179.86/179.66 (~E(f323(a112,x113161),x113161)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11321,plain,
% 179.86/179.66 (E(f31(x113211,x113212,x113213,x113214,x113215,x113216,x113217,x113218,x113219,a24),x113212)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11324,plain,
% 179.86/179.66 (E(f31(x113241,x113242,x113243,x113244,x113245,x113246,x113247,x113248,x113249,a24),x113242)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11330,plain,
% 179.86/179.66 (~E(f323(a112,x113301),x113301)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11337,plain,
% 179.86/179.66 (~E(f323(f323(f78(a1),x113371),x113371),a97)),
% 179.86/179.66 inference(rename_variables,[],[4487])).
% 179.86/179.66 cnf(11346,plain,
% 179.86/179.66 (E(f323(f323(f22(a860),f2(a860)),x113461),f2(a860))),
% 179.86/179.66 inference(rename_variables,[],[3182])).
% 179.86/179.66 cnf(11349,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x113491),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(11356,plain,
% 179.86/179.66 (E(f323(f323(f78(a1),f323(f323(f79(a1),x113561),f323(f323(f36(a1),x113562),x113561))),f42(a1,x113562,x113561)),x113562)),
% 179.86/179.66 inference(rename_variables,[],[3827])).
% 179.86/179.66 cnf(11368,plain,
% 179.86/179.66 (E(f31(x113681,x113682,x113683,x113684,x113685,x113686,x113687,x113688,x113689,a24),x113682)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11375,plain,
% 179.86/179.66 (E(f31(x113751,x113752,x113753,x113754,x113755,x113756,x113757,x113758,x113759,a24),x113752)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11378,plain,
% 179.86/179.66 (E(f31(x113781,x113782,x113783,x113784,x113785,x113786,x113787,x113788,x113789,a24),x113782)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11381,plain,
% 179.86/179.66 (E(f31(x113811,x113812,x113813,x113814,x113815,x113816,x113817,x113818,x113819,a24),x113812)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11384,plain,
% 179.86/179.66 (E(f31(x113841,x113842,x113843,x113844,x113845,x113846,x113847,x113848,x113849,a24),x113842)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11387,plain,
% 179.86/179.66 (~E(f323(a112,x113871),x113871)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11390,plain,
% 179.86/179.66 (~E(f323(a112,x113901),x113901)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11394,plain,
% 179.86/179.66 (E(f31(x113941,x113942,x113943,x113944,x113945,x113946,x113947,x113948,x113949,a24),x113942)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11417,plain,
% 179.86/179.66 (~P101(f323(f60(x114171,x114172,f188(f867(x114171,a855))),x114173))),
% 179.86/179.66 inference(rename_variables,[],[4549])).
% 179.86/179.66 cnf(11420,plain,
% 179.86/179.66 (~P101(f323(f323(f188(f867(x114201,f867(x114202,a855))),x114203),x114204))),
% 179.86/179.66 inference(rename_variables,[],[4554])).
% 179.86/179.66 cnf(11423,plain,
% 179.86/179.66 (P101(f323(f323(f325(x114231),x114232),f246(f867(x114231,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3429])).
% 179.86/179.66 cnf(11431,plain,
% 179.86/179.66 (E(f31(x114311,x114312,x114313,x114314,x114315,x114316,x114317,x114318,x114319,a24),x114312)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11436,plain,
% 179.86/179.66 (~E(f323(a112,x114361),x114361)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11439,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x114391),x114391))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11446,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x114461),x114461))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(11447,plain,
% 179.86/179.66 (E(f31(x114471,x114472,x114473,x114474,x114475,x114476,x114477,x114478,x114479,a24),x114472)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11452,plain,
% 179.86/179.66 (~P101(f323(f323(f188(f867(x114521,f867(x114522,a855))),x114523),x114524))),
% 179.86/179.66 inference(rename_variables,[],[4554])).
% 179.86/179.66 cnf(11463,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),f323(f323(f78(a860),x114631),x114632)),x114632))),
% 179.86/179.66 inference(rename_variables,[],[4551])).
% 179.86/179.66 cnf(11466,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a1),f323(f100(a1),x114661)),f2(a1)))),
% 179.86/179.66 inference(rename_variables,[],[4541])).
% 179.86/179.66 cnf(11477,plain,
% 179.86/179.66 (E(f31(x114771,x114772,x114773,x114774,x114775,x114776,x114777,x114778,x114779,a24),x114772)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11480,plain,
% 179.86/179.66 (E(f31(x114801,x114802,x114803,x114804,x114805,x114806,x114807,x114808,x114809,a24),x114802)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11484,plain,
% 179.86/179.66 (~E(f323(f323(f101(a860),f323(a112,x114841)),x114841),f323(a112,x114841))),
% 179.86/179.66 inference(scs_inference,[],[3512,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,4474,10388,10479,10926,2870,2874,2882,2885,2887,2895,2896,2904,2908,2909,2916,2919,2936,2937,2941,2972,2975,3011,3020,3025,3046,3062,4460,3732,3104,3827,11356,3163,3130,3113,3745,3328,10769,3198,3375,4546,3914,4489,10220,10385,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3084,3182,11346,4063,3916,10958,11101,11153,4558,10872,11106,11212,11234,11272,11278,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,3636,4487,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,10942,3725,3254,4529,10197,10200,10226,10701,10714,10830,11256,11349,4541,3712,3482,3864,3298,3300,3273,4526,4484,3466,4542,4057,11229,3597,4027,3926,10766,3979,3637,4016,3654,10961,11040,11127,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,3271,10344,10399,10607,10696,10817,3272,4525,10263,10353,10464,10488,10738,10780,3429,10560,10825,10869,11175,11253,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,3332,10589,10619,10628,3365,3794,3730,10266,4534,10217,10577,10580,11059,11077,3292,10622,10774,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,4549,10185,10188,10445,10496,10499,10504,10929,4556,11141,11261,3881,3719,10885,10891,3571,11015,3721,10625,10980,11150,11180,3538,10543,10546,10631,10801,4553,4543,4554,10684,10783,11420,4166,4068,3754,4551,10239,10242,10583,10586,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342])).
% 179.86/179.66 cnf(11491,plain,
% 179.86/179.66 (E(f31(x114911,x114912,x114913,x114914,x114915,x114916,x114917,x114918,x114919,a24),x114912)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11496,plain,
% 179.86/179.66 (E(f31(x114961,x114962,x114963,x114964,x114965,x114966,x114967,x114968,x114969,a24),x114962)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11499,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a1),f323(f100(a1),x114991)),f2(a1)))),
% 179.86/179.66 inference(rename_variables,[],[4541])).
% 179.86/179.66 cnf(11502,plain,
% 179.86/179.66 (E(f31(x115021,x115022,x115023,x115024,x115025,x115026,x115027,x115028,x115029,a24),x115022)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11505,plain,
% 179.86/179.66 (~E(f323(a112,x115051),x115051)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11508,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x115081),x115081))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11515,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x115151),x115151))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11536,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a1),f323(f100(a1),x115361)),f2(a1)))),
% 179.86/179.66 inference(rename_variables,[],[4541])).
% 179.86/179.66 cnf(11551,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x115511)),x115511))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(11552,plain,
% 179.86/179.66 (~E(f323(a112,x115521),x115521)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11562,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),f323(f323(f78(a860),x115621),x115622)),x115621))),
% 179.86/179.66 inference(rename_variables,[],[4552])).
% 179.86/179.66 cnf(11565,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a1),f323(f100(a1),x115651)),f2(a1)))),
% 179.86/179.66 inference(rename_variables,[],[4541])).
% 179.86/179.66 cnf(11568,plain,
% 179.86/179.66 (~E(f323(a112,x115681),x115681)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11581,plain,
% 179.86/179.66 (P101(f323(f323(f325(x115811),x115812),f323(f323(f301(x115811),x115812),x115813)))),
% 179.86/179.66 inference(rename_variables,[],[3587])).
% 179.86/179.66 cnf(11582,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a1),f2(a1)),f323(f77(a1),f323(f100(a1),f323(a112,x115821)))))),
% 179.86/179.66 inference(rename_variables,[],[4553])).
% 179.86/179.66 cnf(11585,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),f323(f323(f22(a860),x115851),x115852)),f323(a112,x115851)))),
% 179.86/179.66 inference(rename_variables,[],[3725])).
% 179.86/179.66 cnf(11588,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f42(a860,x115881,x115882)),x115881))),
% 179.86/179.66 inference(rename_variables,[],[3730])).
% 179.86/179.66 cnf(11594,plain,
% 179.86/179.66 (E(f31(x115941,x115942,x115943,x115944,x115945,x115946,x115947,x115948,x115949,a24),x115942)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11597,plain,
% 179.86/179.66 (E(f31(x115971,x115972,x115973,x115974,x115975,x115976,x115977,x115978,x115979,a24),x115972)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11600,plain,
% 179.86/179.66 (E(f31(x116001,x116002,x116003,x116004,x116005,x116006,x116007,x116008,x116009,a24),x116002)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11603,plain,
% 179.86/179.66 (E(f31(x116031,x116032,x116033,x116034,x116035,x116036,x116037,x116038,x116039,a24),x116032)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11606,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x116061)),x116061))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(11607,plain,
% 179.86/179.66 (E(f31(x116071,x116072,x116073,x116074,x116075,x116076,x116077,x116078,x116079,a24),x116072)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11616,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x116161),x116161))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11617,plain,
% 179.86/179.66 (E(f31(x116171,x116172,x116173,x116174,x116175,x116176,x116177,x116178,x116179,a24),x116172)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11620,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f42(a860,x116201,x116202)),x116201))),
% 179.86/179.66 inference(rename_variables,[],[3730])).
% 179.86/179.66 cnf(11621,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f2(a860)),x116211))),
% 179.86/179.66 inference(rename_variables,[],[3292])).
% 179.86/179.66 cnf(11638,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x116381),x116381))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11641,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x116411),x116411))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11644,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x116441),x116441))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11647,plain,
% 179.86/179.66 (P101(f323(f323(f325(x116471),f323(x116472,x116473)),f323(f302(x116474,x116471,x116472),f246(f867(x116474,a855)))))),
% 179.86/179.66 inference(rename_variables,[],[3881])).
% 179.86/179.66 cnf(11648,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x116481)),x116481))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(11651,plain,
% 179.86/179.66 (P101(f323(f323(f325(x116511),f323(x116512,x116513)),f323(f302(x116514,x116511,x116512),f246(f867(x116514,a855)))))),
% 179.86/179.66 inference(rename_variables,[],[3881])).
% 179.86/179.66 cnf(11652,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),f323(f323(f78(a860),x116521),x116522)),x116522))),
% 179.86/179.66 inference(rename_variables,[],[4551])).
% 179.86/179.66 cnf(11657,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),f323(f323(f78(a860),x116571),x116572)),x116571))),
% 179.86/179.66 inference(rename_variables,[],[4552])).
% 179.86/179.66 cnf(11660,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x116601),x116601))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11663,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x116631),x116631))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(11669,plain,
% 179.86/179.66 (~P36(x116691,x116692,f113(x116691))),
% 179.86/179.66 inference(rename_variables,[],[4498])).
% 179.86/179.66 cnf(11672,plain,
% 179.86/179.66 (P101(f323(f323(f325(x116721),x116722),f246(f867(x116721,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3429])).
% 179.86/179.66 cnf(11673,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x116731)),x116731))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(11676,plain,
% 179.86/179.66 (~P101(f323(f60(x116761,x116762,f188(f867(x116761,a855))),x116763))),
% 179.86/179.66 inference(rename_variables,[],[4549])).
% 179.86/179.66 cnf(11689,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x116891),x116892),f188(f867(x116891,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11692,plain,
% 179.86/179.66 (E(f323(f323(f16(x116921,x116922),x116923),x116924),x116923)),
% 179.86/179.66 inference(rename_variables,[],[3261])).
% 179.86/179.66 cnf(11695,plain,
% 179.86/179.66 (E(f323(f323(f16(x116951,x116952),x116953),x116954),x116953)),
% 179.86/179.66 inference(rename_variables,[],[3261])).
% 179.86/179.66 cnf(11707,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),f2(a860)),f323(a112,x117071)))),
% 179.86/179.66 inference(rename_variables,[],[3351])).
% 179.86/179.66 cnf(11710,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x117101),x117101))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(11711,plain,
% 179.86/179.66 (E(f31(x117111,x117112,x117113,x117114,x117115,x117116,x117117,x117118,x117119,a24),x117112)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11714,plain,
% 179.86/179.66 (P101(f323(f323(f325(x117141),f323(x117142,x117143)),f323(f302(x117144,x117141,x117142),f246(f867(x117144,a855)))))),
% 179.86/179.66 inference(rename_variables,[],[3881])).
% 179.86/179.66 cnf(11717,plain,
% 179.86/179.66 (P101(f323(f59(x117171),f323(f166(x117171),x117172)))),
% 179.86/179.66 inference(rename_variables,[],[3311])).
% 179.86/179.66 cnf(11720,plain,
% 179.86/179.66 (P101(f323(f59(x117201),f323(f166(x117201),x117202)))),
% 179.86/179.66 inference(rename_variables,[],[3311])).
% 179.86/179.66 cnf(11723,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),f323(f77(a1),f323(f100(a1),x117231))),f323(f100(a1),x117232)))),
% 179.86/179.66 inference(rename_variables,[],[3755])).
% 179.86/179.66 cnf(11726,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x117261),x117262),f188(f867(x117261,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(11742,plain,
% 179.86/179.66 (~P101(f323(f323(f325(a860),x117421),f323(f244(a860),f2(a860))))),
% 179.86/179.66 inference(scs_inference,[],[3512,4497,4498,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2891,2895,2896,2904,2908,2909,2916,2919,2936,2937,2941,2972,2975,3011,3020,3023,3025,3026,3046,3062,4460,3842,3312,3732,3104,3827,11356,3163,3130,3125,3113,3114,3745,3328,10769,3198,3375,4546,3914,4489,10220,10385,3261,11692,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3434,3084,3182,11346,4063,3916,10958,11101,11153,4558,10872,11106,11212,11234,11272,11278,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,3636,4347,4348,4487,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,10942,3725,11585,3254,3351,4529,10197,10200,10226,10701,10714,10830,11256,11349,4541,11466,11499,11536,3712,3482,3864,3298,3300,3273,4526,4484,3466,4542,4057,11229,3597,3311,11717,4027,3926,10766,3979,3637,4016,3654,10961,11040,11127,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,3271,10344,10399,10607,10696,10817,11439,3272,3347,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,3429,10560,10825,10869,11175,11253,11423,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,3332,10589,10619,10628,3371,3365,3794,3730,10266,11588,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,3292,10622,10774,10845,3755,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,3587,4549,10185,10188,10445,10496,10499,10504,10929,11417,4556,11141,11261,3993,3881,11294,11647,11651,3719,10885,10891,3571,11015,3721,10625,10980,11150,11180,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,4166,4068,3754,3698,4551,10239,10242,10583,10586,11463,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106])).
% 179.86/179.66 cnf(11745,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x117451),x117451))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11746,plain,
% 179.86/179.66 (E(f31(x117461,x117462,x117463,x117464,x117465,x117466,x117467,x117468,x117469,a24),x117462)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(11749,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x117491),x117491))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11758,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x117581),x117581))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11761,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x117611),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(11766,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x117661),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(11773,plain,
% 179.86/179.66 (P101(f323(f246(f867(x117731,a855)),x117732))),
% 179.86/179.66 inference(rename_variables,[],[3332])).
% 179.86/179.66 cnf(11778,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f2(a860)),x117781))),
% 179.86/179.66 inference(rename_variables,[],[3292])).
% 179.86/179.66 cnf(11779,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x117791)),x117791))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(11782,plain,
% 179.86/179.66 (~P101(f323(f60(x117821,x117822,f188(f867(x117821,a855))),x117823))),
% 179.86/179.66 inference(rename_variables,[],[4549])).
% 179.86/179.66 cnf(11788,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x117881),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(11789,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x117891),f323(a112,x117891)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(11805,plain,
% 179.86/179.66 (P101(f323(f323(f238(a1),f323(f77(a1),f76(a1))),f2(a1)))),
% 179.86/179.66 inference(scs_inference,[],[3512,4497,4498,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2891,2895,2896,2903,2904,2908,2909,2916,2919,2928,2936,2937,2941,2972,2975,3011,3020,3023,3025,3026,3034,3046,3062,4460,3842,3312,3732,3104,3827,11356,3163,3130,3125,3113,3114,3745,3328,10769,3198,3375,4546,3914,4489,10220,10385,3261,11692,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3434,3084,3182,11346,4063,3916,10958,11101,11153,4558,10872,11106,11212,11234,11272,11278,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,3636,4347,4348,4487,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,10942,3725,11585,3254,3351,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,4541,11466,11499,11536,11565,3712,3482,3864,3298,3300,3273,4526,4484,3466,4542,4057,11229,3597,3311,11717,4027,3926,10766,3979,3637,4016,3654,10961,11040,11127,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,3272,3347,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,3429,10560,10825,10869,11175,11253,11423,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,3332,10589,10619,10628,11204,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,3292,10622,10774,10845,11621,3755,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,3587,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,3993,3881,11294,11647,11651,3719,10885,10891,3571,11015,3721,10625,10980,11150,11180,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,4166,4068,3754,3698,4551,10239,10242,10583,10586,11463,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405])).
% 179.86/179.66 cnf(11808,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x118081)),x118081))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(11811,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x118111)),x118111))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(11814,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x118141)),x118141))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(11817,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x118171)),x118171))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(11820,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x118201),x118201))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11823,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x118231),x118231))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11826,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x118261),x118261))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11829,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x118291),x118291))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11846,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x118461),x118461))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(11849,plain,
% 179.86/179.66 (P27(a860,a860,a112,x118491)),
% 179.86/179.66 inference(rename_variables,[],[3481])).
% 179.86/179.66 cnf(11851,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x118511),f323(f73(a1),x118511)))),
% 179.86/179.66 inference(scs_inference,[],[3512,4497,4498,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,3481,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2891,2895,2896,2903,2904,2908,2909,2916,2919,2928,2936,2937,2941,2972,2975,3011,3020,3023,3025,3026,3034,3046,3062,4460,3842,3312,3732,3104,3827,11356,3163,3130,3125,3113,3114,3745,3328,10769,3198,3375,4546,3914,4489,10220,10385,3261,11692,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3434,3084,3182,11346,4063,3916,10958,11101,11153,4558,10872,11106,11212,11234,11272,11278,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,3636,4347,4348,4487,3575,3790,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,3725,11585,3254,3351,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,4541,11466,11499,11536,11565,3712,3482,3864,3298,3300,3273,4526,4484,3466,4542,4057,11229,3597,3311,11717,4027,3926,10766,3979,3637,4016,3654,10961,11040,11127,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,3272,3347,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,3429,10560,10825,10869,11175,11253,11423,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,3332,10589,10619,10628,11204,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,3292,10622,10774,10845,11621,3755,4107,4532,3802,4515,4518,3245,3249,4517,4516,4520,3587,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,3993,3881,11294,11647,11651,3719,10885,10891,3571,11015,3721,10625,10980,11150,11180,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,4166,4068,3754,3698,4551,10239,10242,10583,10586,11463,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500])).
% 179.86/179.66 cnf(11852,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x118521),x118521))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11863,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x118631),x118631))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11866,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(f866(f861(x118661),f861(x118661)),a855)),f151(x118661,x118662)),f299(f861(x118661),f150(x118661,x118662))))),
% 179.86/179.66 inference(rename_variables,[],[3984])).
% 179.86/179.66 cnf(11873,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x118731),f323(a112,x118731)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(11876,plain,
% 179.86/179.66 (P101(f323(f323(f325(f867(x118761,a855)),x118762),f323(f300(x118761),x118762)))),
% 179.86/179.66 inference(rename_variables,[],[3637])).
% 179.86/179.66 cnf(11877,plain,
% 179.86/179.66 (~E(f323(a112,x118771),x118771)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11882,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x118821),x118821))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11887,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x118871),x118871))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11898,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x118981,a855)),x118982),f323(f323(f301(x118981),x118983),x118982)))),
% 179.86/179.66 inference(rename_variables,[],[3719])).
% 179.86/179.66 cnf(11901,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x119011),x119011))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(11902,plain,
% 179.86/179.66 (~E(f323(a112,x119021),x119021)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11913,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x119131),x119131))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11914,plain,
% 179.86/179.66 (~E(f323(a112,x119141),x119141)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11917,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x119171),x119171))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(11920,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x119201),x119201))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(11923,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x119231),x119231))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(11926,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x119261),x119261))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(11929,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x119291),x119291))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11932,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x119321),x119321))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11935,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x119351),x119351))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11936,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x119361),f323(a112,x119361)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(11943,plain,
% 179.86/179.66 (~E(f323(a112,x119431),x119431)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11948,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x119481),x119481))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(11949,plain,
% 179.86/179.66 (~E(f323(a112,x119491),x119491)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(11952,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x119521),x119521))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11969,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x119691),x119691))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(11974,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f2(a860)),x119741))),
% 179.86/179.66 inference(rename_variables,[],[3292])).
% 179.86/179.66 cnf(11991,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x119911),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(11994,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x119941),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(11997,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x119971),x119972),f188(f867(x119971,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12000,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x120001),x120002),f188(f867(x120001,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12003,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x120031),x120031))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12006,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x120061),x120061))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12009,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x120091),x120091))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12012,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x120121),x120121))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12015,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x120151),f323(a112,x120151)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(12022,plain,
% 179.86/179.66 (P101(f323(f323(f325(f867(x120221,a855)),x120222),f323(f300(x120221),x120222)))),
% 179.86/179.66 inference(rename_variables,[],[3637])).
% 179.86/179.66 cnf(12027,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x120271,a855)),x120272),f323(f323(f301(x120271),x120273),x120272)))),
% 179.86/179.66 inference(rename_variables,[],[3719])).
% 179.86/179.66 cnf(12034,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x120341),x120342),f188(f867(x120341,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12043,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x120431,a855)),x120432),f246(f867(x120431,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3654])).
% 179.86/179.66 cnf(12044,plain,
% 179.86/179.66 (~E(f323(a112,x120441),x120441)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(12047,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x120471,a855)),f188(f867(x120471,a855))),x120472))),
% 179.86/179.66 inference(rename_variables,[],[3721])).
% 179.86/179.66 cnf(12050,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x120501,a855)),f323(f166(x120501),f323(f129(x120501,x120502),x120503))),f323(f166(x120501),x120503)))),
% 179.86/179.66 inference(rename_variables,[],[3926])).
% 179.86/179.66 cnf(12056,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x120561),f323(a112,x120561)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(12064,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(x120641,x120641)),x120642),f146(x120641,f113(f867(x120641,a860)))))),
% 179.86/179.66 inference(scs_inference,[],[4565,3512,4497,4498,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,3481,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2895,2896,2903,2904,2908,2909,2916,2919,2928,2936,2937,2941,2972,2975,3011,3020,3023,3025,3026,3034,3046,3062,4460,3842,3312,3213,3732,3976,3104,3827,11356,3163,3130,3125,3113,3114,3745,3328,10769,3198,3375,4546,3914,4489,10220,10385,3261,11692,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3434,3084,3182,11346,4063,3916,10958,11101,11153,4558,10872,11106,11212,11234,11272,11278,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,3636,4347,4348,4487,3575,3790,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,3725,11585,3254,3351,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,4541,11466,11499,11536,11565,3712,3482,3864,3298,3300,3273,4526,4484,3466,4542,4057,11229,3597,3311,11717,4027,3984,3926,10766,3979,3637,11876,4016,3654,10961,11040,11127,11186,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,3272,3347,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,3429,10560,10825,10869,11175,11253,11423,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,3332,10589,10619,10628,11204,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,3292,10622,10774,10845,11621,11778,3755,4107,4532,3766,3802,4515,4518,3245,3249,4517,4516,4520,3773,3587,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,3993,3881,11294,11647,11651,3719,10885,10891,10913,11898,3571,11015,3721,10625,10980,11150,11180,11191,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,4166,4068,3754,3698,4551,10239,10242,10583,10586,11463,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194])).
% 179.86/179.66 cnf(12065,plain,
% 179.86/179.66 (E(f31(x120651,x120652,x120653,x120654,x120655,x120656,x120657,x120658,x120659,a24),x120652)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12076,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a860),f323(a112,x120761)),x120761))),
% 179.86/179.66 inference(rename_variables,[],[4534])).
% 179.86/179.66 cnf(12077,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x120771),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(12080,plain,
% 179.86/179.66 (P101(f323(f59(x120801),f188(f867(x120801,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3347])).
% 179.86/179.66 cnf(12081,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x120811),x120812),f188(f867(x120811,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12086,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x120861),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(12087,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x120871),x120871))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12092,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x120921,a855)),f323(f166(x120921),f164(x120921,x120922,x120923))),f323(f166(x120921),x120923)))),
% 179.86/179.66 inference(rename_variables,[],[3979])).
% 179.86/179.66 cnf(12095,plain,
% 179.86/179.66 (P27(x120951,x120951,f5(x120951),x120952)),
% 179.86/179.66 inference(rename_variables,[],[3512])).
% 179.86/179.66 cnf(12100,plain,
% 179.86/179.66 (P101(f323(f323(f325(f867(x121001,a855)),x121002),f323(f300(x121001),x121002)))),
% 179.86/179.66 inference(rename_variables,[],[3637])).
% 179.86/179.66 cnf(12107,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x121071),x121071))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12110,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x121101),x121102),f188(f867(x121101,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12113,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x121131,a855)),x121132),f323(f323(f301(x121131),x121133),x121132)))),
% 179.86/179.66 inference(rename_variables,[],[3719])).
% 179.86/179.66 cnf(12114,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x121141,a855)),x121142),f246(f867(x121141,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3654])).
% 179.86/179.66 cnf(12121,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x121211),x121211))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12124,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x121241),x121241))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12127,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x121271),x121271))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12130,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x121301),x121301))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12133,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x121331),f323(a112,x121331)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(12136,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x121361),f323(a112,x121361)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(12139,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x121391,a855)),x121392),x121392))),
% 179.86/179.66 inference(rename_variables,[],[3571])).
% 179.86/179.66 cnf(12141,plain,
% 179.86/179.66 (~P101(f323(f323(f237(a1),f323(f323(f22(a1),a81),a97)),f2(a1)))),
% 179.86/179.66 inference(scs_inference,[],[4565,3512,11030,4497,4498,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,3481,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2916,2919,2928,2936,2937,2941,2972,2975,3011,3020,3023,3025,3026,3034,3046,3062,4460,3842,3312,3213,3732,3976,3104,3827,11356,3163,3130,3125,3113,3114,3745,3328,10769,3198,3375,4546,3914,4489,10220,10385,3261,11692,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3434,3084,3182,11346,4063,3916,10958,11101,11153,4558,10872,11106,11212,11234,11272,11278,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,3636,4347,4348,4487,3575,3790,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,3725,11585,3254,3351,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,4541,11466,11499,11536,11565,3712,3482,3864,3298,3300,3273,4526,4484,3466,4542,4057,11229,3597,3311,11717,11720,4027,3984,3926,10766,3979,10964,3637,11876,12022,4016,3654,10961,11040,11127,11186,12043,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,3272,3347,12080,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,3429,10560,10825,10869,11175,11253,11423,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,3332,10589,10619,10628,11204,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,3292,10622,10774,10845,11621,11778,3755,4107,4532,3766,3802,4515,4518,3245,3249,4517,4516,4520,3773,3587,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,3993,3881,11294,11647,11651,3719,10885,10891,10913,11898,12027,3571,11015,11144,3721,10625,10980,11150,11180,11191,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,4166,4068,3754,3698,4551,10239,10242,10583,10586,11463,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580])).
% 179.86/179.66 cnf(12146,plain,
% 179.86/179.66 (P101(f323(f323(f325(f867(x121461,a855)),x121462),f323(f300(x121461),x121462)))),
% 179.86/179.66 inference(rename_variables,[],[3637])).
% 179.86/179.66 cnf(12152,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a1),f323(f323(f78(a1),a81),a81)),f2(a1)))),
% 179.86/179.66 inference(scs_inference,[],[4565,3512,11030,4497,4498,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,3481,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2916,2919,2928,2936,2937,2941,2972,2975,3011,3020,3023,3025,3026,3034,3046,3062,4460,3842,3312,3213,3732,3976,3104,3827,11356,3163,3130,3125,3113,3114,3745,3328,10769,3198,3375,4546,3914,4489,10220,10385,3261,11692,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3434,3084,3182,11346,4063,3916,10958,11101,11153,4558,10872,11106,11212,11234,11272,11278,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,3636,4347,4348,4487,3575,3790,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,3725,11585,3254,3351,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,4541,11466,11499,11536,11565,3712,3482,3864,3298,3300,3273,4526,4484,3466,4542,4057,11229,3597,3311,11717,11720,4027,3984,3926,10766,3979,10964,3637,11876,12022,12100,4016,3654,10961,11040,11127,11186,12043,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,3272,3347,12080,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,3429,10560,10825,10869,11175,11253,11423,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,3332,10589,10619,10628,11204,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,3292,10622,10774,10845,11621,11778,3755,4107,4532,3766,3802,4515,4518,3245,3249,4517,4516,4520,3773,3587,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,3993,3881,11294,11647,11651,3719,10885,10891,10913,11898,12027,3571,11015,11144,3721,10625,10980,11150,11180,11191,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,4166,4068,3754,3698,4551,10239,10242,10583,10586,11463,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,97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% 179.86/179.66 cnf(12155,plain,
% 179.86/179.66 (~E(f323(a112,x121551),x121551)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(12156,plain,
% 179.86/179.66 (E(f323(f302(x121561,x121561,f5(x121561)),x121562),x121562)),
% 179.86/179.66 inference(rename_variables,[],[3328])).
% 179.86/179.66 cnf(12159,plain,
% 179.86/179.66 (P33(x121591,x121592,f113(x121591),f113(x121591))),
% 179.86/179.66 inference(rename_variables,[],[3521])).
% 179.86/179.66 cnf(12162,plain,
% 179.86/179.66 (~E(f323(a112,x121621),x121621)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(12165,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x121651,a855)),f323(f166(x121651),f164(x121651,x121652,x121653))),f323(f166(x121651),x121653)))),
% 179.86/179.66 inference(rename_variables,[],[3979])).
% 179.86/179.66 cnf(12166,plain,
% 179.86/179.66 (P101(f323(f59(x121661),f323(f166(x121661),x121662)))),
% 179.86/179.66 inference(rename_variables,[],[3311])).
% 179.86/179.66 cnf(12177,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x121771),x121771))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12180,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x121801),x121801))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12185,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f2(a860)),x121851))),
% 179.86/179.66 inference(rename_variables,[],[3292])).
% 179.86/179.66 cnf(12192,plain,
% 179.86/179.66 (P16(a860,f323(f162(a860),f323(f323(f147(f861(x121921),a860),f189(f861(x121921))),f173(x121921,x121922))))),
% 179.86/179.66 inference(rename_variables,[],[3837])).
% 179.86/179.66 cnf(12195,plain,
% 179.86/179.66 (P27(x121951,x121951,f5(x121951),x121952)),
% 179.86/179.66 inference(rename_variables,[],[3512])).
% 179.86/179.66 cnf(12198,plain,
% 179.86/179.66 (P27(x121981,x121981,f5(x121981),x121982)),
% 179.86/179.66 inference(rename_variables,[],[3512])).
% 179.86/179.66 cnf(12201,plain,
% 179.86/179.66 (P101(f323(f323(f325(f861(x122011)),f113(x122011)),f154(x122011,x122012)))),
% 179.86/179.66 inference(rename_variables,[],[3473])).
% 179.86/179.66 cnf(12204,plain,
% 179.86/179.66 (~P101(f323(f323(f188(f867(x122041,f867(x122042,a855))),x122043),x122044))),
% 179.86/179.66 inference(rename_variables,[],[4554])).
% 179.86/179.66 cnf(12209,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x122091),x122091))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12210,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f2(a860)),x122101))),
% 179.86/179.66 inference(rename_variables,[],[3292])).
% 179.86/179.66 cnf(12213,plain,
% 179.86/179.66 (~P101(f323(f323(f188(f867(x122131,f867(x122132,a855))),x122133),x122134))),
% 179.86/179.66 inference(rename_variables,[],[4554])).
% 179.86/179.66 cnf(12216,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(f866(f861(x122161),f861(x122161)),a855)),f151(x122161,x122162)),f299(f861(x122161),f150(x122161,x122162))))),
% 179.86/179.66 inference(rename_variables,[],[3984])).
% 179.86/179.66 cnf(12222,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x122221,a855)),f323(f166(x122221),f164(x122221,x122222,x122223))),f323(f166(x122221),x122223)))),
% 179.86/179.66 inference(rename_variables,[],[3979])).
% 179.86/179.66 cnf(12223,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x122231,a855)),f323(f166(x122231),f323(f129(x122231,x122232),x122233))),f323(f166(x122231),x122233)))),
% 179.86/179.66 inference(rename_variables,[],[3926])).
% 179.86/179.66 cnf(12226,plain,
% 179.86/179.66 (~P101(f323(f323(f238(f867(x122261,a855)),x122262),f188(f867(x122261,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4547])).
% 179.86/179.66 cnf(12229,plain,
% 179.86/179.66 (P27(x122291,f864(x122291),f230(x122291),x122292)),
% 179.86/179.66 inference(rename_variables,[],[3522])).
% 179.86/179.66 cnf(12234,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x122341,a855)),f323(f302(x122342,x122341,x122343),f323(f303(x122342,x122341,x122343),x122344))),x122344))),
% 179.86/179.66 inference(rename_variables,[],[4166])).
% 179.86/179.66 cnf(12237,plain,
% 179.86/179.66 (P101(f323(f59(f864(x122371)),f323(f302(x122372,f864(x122371),f323(f179(x122372,x122371),x122373)),f246(f867(x122372,a855)))))),
% 179.86/179.66 inference(rename_variables,[],[3993])).
% 179.86/179.66 cnf(12242,plain,
% 179.86/179.66 (P101(f323(f323(f325(f861(x122421)),f113(x122421)),f154(x122421,x122422)))),
% 179.86/179.66 inference(rename_variables,[],[3473])).
% 179.86/179.66 cnf(12245,plain,
% 179.86/179.66 (~P101(f323(f323(f325(f866(f861(x122451),f861(x122451))),f323(f323(f258(f861(x122451),f861(x122451)),x122452),f113(x122451))),f138(x122451,x122453)))),
% 179.86/179.66 inference(rename_variables,[],[4558])).
% 179.86/179.66 cnf(12248,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x122481),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(12250,plain,
% 179.86/179.66 (~P101(f323(f59(x122501),f246(f867(x122501,a855))))),
% 179.86/179.66 inference(scs_inference,[],[4565,3512,11030,12095,12195,3521,3522,3239,4497,4498,3139,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,3481,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2916,2919,2928,2936,2937,2941,2947,2972,2975,3011,3020,3023,3025,3026,3034,3046,3062,4460,3842,3312,3213,3732,3976,3104,3827,11356,3163,3130,3125,3113,3114,3745,3145,3328,10769,10894,3198,3375,4546,3914,4489,10220,10385,3261,11692,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3434,3084,3182,11346,4063,3916,10958,11101,11153,4558,10872,11106,11212,11234,11272,11278,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,12201,12242,3636,4347,4348,4487,3575,3790,3837,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,3725,11585,3254,3351,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,4541,11466,11499,11536,11565,3712,3482,3864,3298,3300,3273,4526,4484,3466,4542,4057,11229,3597,3311,11717,11720,4027,3984,11866,12216,3926,10766,12050,3979,10964,12092,12165,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,3272,3347,12080,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,3429,10560,10825,10869,11175,11253,11423,11672,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,3332,10589,10619,10628,11204,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,3292,10622,10774,10845,11621,11778,11974,12185,3755,4107,4532,3766,3802,4515,4518,3245,3249,4517,4516,4520,3773,3587,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,3993,3881,11294,11647,11651,3719,10885,10891,10913,11898,12027,3571,11015,11144,12139,3721,10625,10980,11150,11180,11191,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,11452,12204,4166,10759,4068,3754,3698,4551,10239,10242,10583,10586,11463,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,92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% 179.86/179.66 cnf(12251,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x122511,a855)),x122512),x122512))),
% 179.86/179.66 inference(rename_variables,[],[3571])).
% 179.86/179.66 cnf(12254,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x122541),x122542),f188(f867(x122541,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12257,plain,
% 179.86/179.66 (~P101(f323(f323(f188(f867(x122571,f867(x122572,a855))),x122573),x122574))),
% 179.86/179.66 inference(rename_variables,[],[4554])).
% 179.86/179.66 cnf(12260,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x122601,a855)),f323(f302(x122602,x122601,x122603),f323(f303(x122602,x122601,x122603),x122604))),x122604))),
% 179.86/179.66 inference(rename_variables,[],[4166])).
% 179.86/179.66 cnf(12261,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x122611,a855)),x122612),x122612))),
% 179.86/179.66 inference(rename_variables,[],[3571])).
% 179.86/179.66 cnf(12266,plain,
% 179.86/179.66 (E(f31(x122661,x122662,x122663,x122664,x122665,x122666,x122667,x122668,x122669,a24),x122662)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12269,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x122691,a855)),f323(f166(x122691),f164(x122691,x122692,x122693))),f323(f166(x122691),x122693)))),
% 179.86/179.66 inference(rename_variables,[],[3979])).
% 179.86/179.66 cnf(12270,plain,
% 179.86/179.66 (P101(f323(f59(x122701),f323(f166(x122701),x122702)))),
% 179.86/179.66 inference(rename_variables,[],[3311])).
% 179.86/179.66 cnf(12273,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x122731),x122731))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12276,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x122761),x122761))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12279,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x122791),x122791))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12290,plain,
% 179.86/179.66 (P27(x122901,x122901,f5(x122901),x122902)),
% 179.86/179.66 inference(rename_variables,[],[3512])).
% 179.86/179.66 cnf(12298,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x122981),x122982),f188(f867(x122981,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12301,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(x123011,x123011)),f323(f323(f258(x123011,x123011),x123012),x123012)),f299(x123011,x123013)))),
% 179.86/179.66 inference(rename_variables,[],[3916])).
% 179.86/179.66 cnf(12304,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x123041),x123042),f188(f867(x123041,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12307,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(x123071,x123071)),f323(f323(f258(x123071,x123071),x123072),x123072)),f299(x123071,x123073)))),
% 179.86/179.66 inference(rename_variables,[],[3916])).
% 179.86/179.66 cnf(12317,plain,
% 179.86/179.66 (~E(f323(f323(f144(x123171),x123172),x123173),x123173)),
% 179.86/179.66 inference(rename_variables,[],[4489])).
% 179.86/179.66 cnf(12319,plain,
% 179.86/179.66 (~P28(a860,a860,x123191,f246(f867(a860,a855)),f294(a860,x123192,x123193))),
% 179.86/179.66 inference(scs_inference,[],[4565,3512,11030,12095,12195,12198,3521,3522,3239,4497,4498,3139,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,3481,11849,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2914,2916,2919,2928,2936,2937,2941,2947,2972,2975,3011,3020,3023,3025,3026,3034,3046,3062,4460,3842,3312,3213,3732,3976,3104,4476,3827,11356,3163,3130,3592,3125,3113,3114,3745,3145,3328,10769,10894,3197,3198,3375,4546,3914,4489,10220,10385,11218,3261,11692,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3434,3084,3182,11346,4063,3916,10958,11101,11153,12301,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,12201,12242,3636,4347,4348,4487,11337,3575,3790,3837,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,3725,11585,3254,3351,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,4541,11466,11499,11536,11565,3712,3482,3864,3298,3300,3273,4526,4484,3466,4542,4057,11229,3597,3311,11717,11720,12166,4027,3984,11866,12216,3926,10766,12050,3979,10964,12092,12165,12222,12269,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,3272,3347,12080,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,3429,10560,10825,10869,11175,11253,11423,11672,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,3332,10589,10619,10628,11204,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,3292,10622,10774,10845,11621,11778,11974,12185,3755,4107,4532,3766,3802,4515,4518,3245,3249,4517,4516,4520,3773,3587,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,3881,11294,11647,11651,3719,10885,10891,10913,11898,12027,3571,11015,11144,12139,12251,3721,10625,10980,11150,11180,11191,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,11452,12204,12213,4166,10759,12234,4068,3754,3698,4551,10239,10242,10583,10586,11463,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580,7581,7613,7615,7616,7617,7622,7644,7653,7663,7668,7674,7676,7682,7694,7695,7697,7720,7726,7747,7814,7815,7816,7864,7872,7873,7898,7899,7916,7917,7974,7975,8004,8031,8041,8043,8052,8064,8094,8100,8107,8120,8139,8144,8166,8210,8240,8254,8273,8276,8306,8332,8391,8392,8395,8396,8460,8494,8495,8496,8497,8524,8556,8585,8593])).
% 179.86/179.66 cnf(12324,plain,
% 179.86/179.66 (P101(f323(f323(f325(x123241),x123242),f246(f867(x123241,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3429])).
% 179.86/179.66 cnf(12325,plain,
% 179.86/179.66 (~E(f323(a112,x123251),x123251)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(12328,plain,
% 179.86/179.66 (P101(f323(f323(f325(f861(x123281)),f113(x123281)),f154(x123281,x123282)))),
% 179.86/179.66 inference(rename_variables,[],[3473])).
% 179.86/179.66 cnf(12329,plain,
% 179.86/179.66 (~E(f323(f323(f144(x123291),x123292),x123293),f113(x123291))),
% 179.86/179.66 inference(rename_variables,[],[4496])).
% 179.86/179.66 cnf(12332,plain,
% 179.86/179.66 (P27(x123321,x123321,f5(x123321),x123322)),
% 179.86/179.66 inference(rename_variables,[],[3512])).
% 179.86/179.66 cnf(12335,plain,
% 179.86/179.66 (P101(f323(f323(f325(x123351),f323(x123352,x123353)),f323(f302(x123354,x123351,x123352),f246(f867(x123354,a855)))))),
% 179.86/179.66 inference(rename_variables,[],[3881])).
% 179.86/179.66 cnf(12336,plain,
% 179.86/179.66 (P27(x123361,x123361,f5(x123361),x123362)),
% 179.86/179.66 inference(rename_variables,[],[3512])).
% 179.86/179.66 cnf(12339,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x123391,a855)),f188(f867(x123391,a855))),x123392))),
% 179.86/179.66 inference(rename_variables,[],[3721])).
% 179.86/179.66 cnf(12340,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x123401,a855)),x123402),x123402))),
% 179.86/179.66 inference(rename_variables,[],[3571])).
% 179.86/179.66 cnf(12343,plain,
% 179.86/179.66 (P101(f323(f323(f325(x123431),f323(x123432,x123433)),f323(f302(x123434,x123431,x123432),f246(f867(x123434,a855)))))),
% 179.86/179.66 inference(rename_variables,[],[3881])).
% 179.86/179.66 cnf(12344,plain,
% 179.86/179.66 (P27(x123441,x123441,f5(x123441),x123442)),
% 179.86/179.66 inference(rename_variables,[],[3512])).
% 179.86/179.66 cnf(12347,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(f861(x123471),f861(x123471))),f323(f323(f258(f861(x123471),f861(x123471)),f113(x123471)),f113(x123471))),f151(x123471,x123472)))),
% 179.86/179.66 inference(rename_variables,[],[4063])).
% 179.86/179.66 cnf(12350,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x123501),x123501))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12351,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x123511),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(12357,plain,
% 179.86/179.66 (E(f323(f323(f121(x123571),x123572),f113(x123571)),x123572)),
% 179.86/179.66 inference(rename_variables,[],[3199])).
% 179.86/179.66 cnf(12358,plain,
% 179.86/179.66 (~E(f323(f323(f144(x123581),x123582),x123583),x123583)),
% 179.86/179.66 inference(rename_variables,[],[4489])).
% 179.86/179.66 cnf(12361,plain,
% 179.86/179.66 (E(f323(f323(f121(x123611),x123612),f113(x123611)),x123612)),
% 179.86/179.66 inference(rename_variables,[],[3199])).
% 179.86/179.66 cnf(12362,plain,
% 179.86/179.66 (~E(f323(f323(f144(x123621),x123622),x123623),x123623)),
% 179.86/179.66 inference(rename_variables,[],[4489])).
% 179.86/179.66 cnf(12365,plain,
% 179.86/179.66 (E(f323(f323(f121(x123651),x123652),f113(x123651)),x123652)),
% 179.86/179.66 inference(rename_variables,[],[3199])).
% 179.86/179.66 cnf(12372,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x123721,a855)),f323(f166(x123721),f323(f129(x123721,x123722),x123723))),f323(f166(x123721),x123723)))),
% 179.86/179.66 inference(rename_variables,[],[3926])).
% 179.86/179.66 cnf(12373,plain,
% 179.86/179.66 (E(f323(f302(x123731,x123731,f5(x123731)),x123732),x123732)),
% 179.86/179.66 inference(rename_variables,[],[3328])).
% 179.86/179.66 cnf(12378,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x123781,a855)),x123782),f246(f867(x123781,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3654])).
% 179.86/179.66 cnf(12382,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x123821),x123821))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12383,plain,
% 179.86/179.66 (~E(f323(a112,x123831),x123831)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(12386,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x123861,a855)),f188(f867(x123861,a855))),x123862))),
% 179.86/179.66 inference(rename_variables,[],[3721])).
% 179.86/179.66 cnf(12389,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x123891),x123891))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12392,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x123921,a855)),x123922),x123922))),
% 179.86/179.66 inference(rename_variables,[],[3571])).
% 179.86/179.66 cnf(12397,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x123971,a855)),x123972),f323(f323(f301(x123971),x123973),x123972)))),
% 179.86/179.66 inference(rename_variables,[],[3719])).
% 179.86/179.66 cnf(12400,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x124001,a855)),x124002),x124002))),
% 179.86/179.66 inference(rename_variables,[],[3571])).
% 179.86/179.66 cnf(12401,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x124011),x124012),f188(f867(x124011,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12404,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x124041),x124042),f188(f867(x124041,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12412,plain,
% 179.86/179.66 (~P101(f323(f323(f237(f867(f866(x124121,x124121),a855)),f323(f302(f866(x124121,x124121),f866(x124121,x124121),f5(f866(x124121,x124121))),f246(f867(f866(x124121,x124121),a855)))),f323(f302(f866(x124121,x124121),f866(x124121,x124121),f5(f866(x124121,x124121))),f188(f867(f866(x124121,x124121),a855)))))),
% 179.86/179.66 inference(scs_inference,[],[4565,3512,11030,12095,12195,12198,12290,12332,12336,12344,3521,3522,3239,4497,4498,3139,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,3327,3481,11849,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2914,2916,2919,2928,2936,2937,2941,2947,2972,2975,3011,3020,3023,3025,3026,3034,3046,3062,4460,3842,3312,3199,12357,12361,3213,3732,3976,3104,4476,3827,11356,3163,3130,3592,3125,3113,3114,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,3914,4489,10220,10385,11218,12317,12358,4496,12329,3261,11692,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3434,3084,3182,11346,4063,12347,3916,10958,11101,11153,12301,12307,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,4487,11337,3575,3790,3837,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,3725,11585,3254,3351,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,4541,11466,11499,11536,11565,3712,3482,3864,3298,3300,3273,4526,4484,3663,3466,4542,4057,11229,3597,3311,11717,11720,12166,4027,3984,11866,12216,3926,10766,12050,12223,3979,10964,12092,12165,12222,12269,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,3272,3347,12080,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,3429,10560,10825,10869,11175,11253,11423,11672,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,3332,10589,10619,10628,11204,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,3292,10622,10774,10845,11621,11778,11974,12185,3755,4107,4532,3766,3802,4515,4518,3245,3249,4517,4516,4520,3773,3587,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,3881,11294,11647,11651,11714,12335,3719,10885,10891,10913,11898,12027,12113,3571,11015,11144,12139,12251,12261,12340,12392,3721,10625,10980,11150,11180,11191,12047,12339,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,11452,12204,12213,4166,10759,12234,4068,3754,3698,4551,10239,10242,10583,10586,11463,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490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% 179.86/179.66 cnf(12413,plain,
% 179.86/179.66 (P27(x124131,x124131,f5(x124131),x124132)),
% 179.86/179.66 inference(rename_variables,[],[3512])).
% 179.86/179.66 cnf(12416,plain,
% 179.86/179.66 (E(f323(f189(f861(x124161)),f163(x124161,x124162,x124163)),x124162)),
% 179.86/179.66 inference(rename_variables,[],[3338])).
% 179.86/179.66 cnf(12419,plain,
% 179.86/179.66 (P28(x124191,x124191,f32(x124191),x124192,x124192)),
% 179.86/179.66 inference(rename_variables,[],[3941])).
% 179.86/179.66 cnf(12422,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x124221),x124221))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12423,plain,
% 179.86/179.66 (P101(f323(f246(f867(x124231,a855)),x124232))),
% 179.86/179.66 inference(rename_variables,[],[3332])).
% 179.86/179.66 cnf(12426,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x124261),x124262),f188(f867(x124261,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12429,plain,
% 179.86/179.66 (P101(f323(f323(f325(x124291),f323(x124292,x124293)),f323(f302(x124294,x124291,x124292),f246(f867(x124294,a855)))))),
% 179.86/179.66 inference(rename_variables,[],[3881])).
% 179.86/179.66 cnf(12430,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(x124301,x124301)),f323(f323(f258(x124301,x124301),x124302),x124302)),f299(x124301,x124303)))),
% 179.86/179.66 inference(rename_variables,[],[3916])).
% 179.86/179.66 cnf(12433,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(x124331,x124331)),f323(f323(f258(x124331,x124331),x124332),x124332)),f299(x124331,x124333)))),
% 179.86/179.66 inference(rename_variables,[],[3916])).
% 179.86/179.66 cnf(12436,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x124361),x124361))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12437,plain,
% 179.86/179.66 (P101(f323(f246(f867(x124371,a855)),x124372))),
% 179.86/179.66 inference(rename_variables,[],[3332])).
% 179.86/179.66 cnf(12440,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x124401,a855)),x124402),f246(f867(x124401,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3654])).
% 179.86/179.66 cnf(12441,plain,
% 179.86/179.66 (P28(x124411,x124411,f32(x124411),x124412,x124412)),
% 179.86/179.66 inference(rename_variables,[],[3941])).
% 179.86/179.66 cnf(12444,plain,
% 179.86/179.66 (P101(f323(f59(x124441),f323(f166(x124441),x124442)))),
% 179.86/179.66 inference(rename_variables,[],[3311])).
% 179.86/179.66 cnf(12449,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(f861(x124491),f861(x124491))),f323(f323(f258(f861(x124491),f861(x124491)),f113(x124491)),f113(x124491))),f323(f323(f280(f861(x124491),f861(x124491),f861(x124491)),f151(x124491,x124492)),f151(x124491,x124492))))),
% 179.86/179.66 inference(scs_inference,[],[4565,3941,12419,3512,11030,12095,12195,12198,12290,12332,12336,12344,3521,3522,3239,4497,4498,3139,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,3327,3481,11849,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2914,2916,2919,2928,2936,2937,2941,2947,2972,2975,3011,3020,3023,3025,3026,3034,3046,3062,4460,3842,3312,3199,12357,12361,12365,3213,3732,3338,3976,3104,4476,3827,11356,3163,3130,3592,3125,3113,3114,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,3914,4489,10220,10385,11218,12317,12358,4496,12329,3261,11692,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3434,3084,3182,11346,4063,12347,3916,10958,11101,11153,12301,12307,12430,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,4487,11337,3575,3790,3837,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,3725,11585,3254,3351,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,4541,11466,11499,11536,11565,3712,3482,3864,3298,3300,3273,4526,4484,3663,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,4027,3984,11866,12216,3926,10766,12050,12223,3979,10964,12092,12165,12222,12269,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,3272,3347,12080,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,3429,10560,10825,10869,11175,11253,11423,11672,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,3332,10589,10619,10628,11204,11773,12423,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,3292,10622,10774,10845,11621,11778,11974,12185,3755,4107,4532,3766,3802,4515,4518,3245,3249,4517,4516,4520,3773,3587,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,3881,11294,11647,11651,11714,12335,12343,3719,10885,10891,10913,11898,12027,12113,3571,11015,11144,12139,12251,12261,12340,12392,3721,10625,10980,11150,11180,11191,12047,12339,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,11452,12204,12213,4166,10759,12234,4068,3754,3698,4551,10239,10242,10583,10586,11463,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580,7581,7613,7615,7616,7617,7622,7644,7653,7663,7668,7674,7676,7682,7694,7695,7697,7720,7726,7747,7814,7815,7816,7864,7872,7873,7898,7899,7916,7917,7974,7975,8004,8031,8041,8043,8052,8064,8094,8100,8107,8120,8139,8144,8166,8210,8240,8254,8273,8276,8306,8332,8391,8392,8395,8396,8460,8494,8495,8496,8497,8524,8556,8585,8593,8594,8636,8657,8703,8718,8765,8768,8783,8790,8826,8874,8875,8891,8892,9021,9027,9031,9052,9062,9085,9087,9090,9094,9096,9097,9108,9109,9129,9136,9149,9158,9195,9213,9265,9266,9273,9312,9335,9340,9375])).
% 179.86/179.66 cnf(12454,plain,
% 179.86/179.66 (~P101(f323(f323(f188(f867(x124541,f867(x124542,a855))),x124543),x124544))),
% 179.86/179.66 inference(rename_variables,[],[4554])).
% 179.86/179.66 cnf(12457,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x124571,a855)),x124572),f246(f867(x124571,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3654])).
% 179.86/179.66 cnf(12460,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(x124601,x124601)),f323(f323(f258(x124601,x124601),x124602),x124602)),f299(x124601,x124603)))),
% 179.86/179.66 inference(rename_variables,[],[3916])).
% 179.86/179.66 cnf(12463,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),f323(f323(f78(a860),x124631),x124632)),x124632))),
% 179.86/179.66 inference(rename_variables,[],[4551])).
% 179.86/179.66 cnf(12464,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x124641),f323(a112,x124641)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(12467,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x124671,a855)),f323(f166(x124671),f323(f129(x124671,x124672),x124673))),f323(f166(x124671),x124673)))),
% 179.86/179.66 inference(rename_variables,[],[3926])).
% 179.86/179.66 cnf(12470,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x124701,a855)),x124702),f246(f867(x124701,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3654])).
% 179.86/179.66 cnf(12473,plain,
% 179.86/179.66 (E(f31(x124731,x124732,x124733,x124734,x124735,x124736,x124737,x124738,x124739,a24),x124732)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12484,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x124841),x124842),f188(f867(x124841,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12485,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(f861(x124851),f861(x124851))),f323(f323(f258(f861(x124851),f861(x124851)),f113(x124851)),f113(x124851))),f151(x124851,x124852)))),
% 179.86/179.66 inference(rename_variables,[],[4063])).
% 179.86/179.66 cnf(12490,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x124901),x124902),f188(f867(x124901,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12493,plain,
% 179.86/179.66 (P32(x124931,x124932,f113(x124931))),
% 179.86/179.66 inference(rename_variables,[],[3204])).
% 179.86/179.66 cnf(12496,plain,
% 179.86/179.66 (E(f323(f189(f861(x124961)),f163(x124961,x124962,x124963)),x124962)),
% 179.86/179.66 inference(rename_variables,[],[3338])).
% 179.86/179.66 cnf(12499,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x124991),x124992),f188(f867(x124991,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12505,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x125051),x125051))),
% 179.86/179.66 inference(rename_variables,[],[4525])).
% 179.86/179.66 cnf(12507,plain,
% 179.86/179.66 (P101(f323(f323(f325(f866(f861(x125071),f861(x125071))),f323(f323(f258(f861(x125071),f861(x125071)),f163(x125071,f323(f189(f861(x125071)),x125072),x125073)),x125072)),f151(x125071,f246(f867(f866(x125071,x125071),a855)))))),
% 179.86/179.66 inference(scs_inference,[],[4565,3941,12419,3512,11030,12095,12195,12198,12290,12332,12336,12344,3521,3522,3239,3204,4497,4498,3139,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,3327,3481,11849,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2914,2916,2919,2928,2936,2937,2941,2947,2972,2975,3011,3020,3023,3025,3026,3034,3046,3062,4460,3610,3842,3312,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,4476,3827,11356,3163,3130,3592,3125,3113,3114,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,3914,4489,10220,10385,11218,12317,12358,4496,12329,3261,11692,4535,10952,11035,11264,11267,3376,3160,3161,10287,10592,3434,3084,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,4487,11337,3575,3790,3837,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,3725,11585,3254,3351,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,4541,11466,11499,11536,11565,3712,3482,3864,3298,3300,3273,4526,4484,3663,4200,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,4027,3984,11866,12216,3926,10766,12050,12223,12372,3979,10964,12092,12165,12222,12269,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,3272,3347,12080,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,3429,10560,10825,10869,11175,11253,11423,11672,12324,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,3332,10589,10619,10628,11204,11773,12423,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,3292,10622,10774,10845,11621,11778,11974,12185,3755,4107,4532,3766,3802,4515,4518,3245,3249,4517,4516,4520,3773,3587,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,3881,11294,11647,11651,11714,12335,12343,3719,10885,10891,10913,11898,12027,12113,3571,11015,11144,12139,12251,12261,12340,12392,4061,3721,10625,10980,11150,11180,11191,12047,12339,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,11452,12204,12213,12257,4166,10759,12234,4068,3754,3698,4551,10239,10242,10583,10586,11463,11652,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580,7581,7613,7615,7616,7617,7622,7644,7653,7663,7668,7674,7676,7682,7694,7695,7697,7720,7726,7747,7814,7815,7816,7864,7872,7873,7898,7899,7916,7917,7974,7975,8004,8031,8041,8043,8052,8064,8094,8100,8107,8120,8139,8144,8166,8210,8240,8254,8273,8276,8306,8332,8391,8392,8395,8396,8460,8494,8495,8496,8497,8524,8556,8585,8593,8594,8636,8657,8703,8718,8765,8768,8783,8790,8826,8874,8875,8891,8892,9021,9027,9031,9052,9062,9085,9087,9090,9094,9096,9097,9108,9109,9129,9136,9149,9158,9195,9213,9265,9266,9273,9312,9335,9340,9375,9383,9386,9389,9390,9403,9420,9429,9443,9452,9453,9455,9457,9485,9609,9655,9656,9698,9743,9858,9915])).
% 179.86/179.66 cnf(12508,plain,
% 179.86/179.66 (P101(f323(f323(f325(x125081),x125082),f246(f867(x125081,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3429])).
% 179.86/179.66 cnf(12512,plain,
% 179.86/179.66 (P101(f323(f323(f237(f867(x125121,a855)),x125122),x125122))),
% 179.86/179.66 inference(rename_variables,[],[3571])).
% 179.86/179.66 cnf(12515,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x125151),x125152),f188(f867(x125151,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12518,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),f2(a1)),f323(f323(f248(a1),f323(f73(a1),x125181)),x125182)))),
% 179.86/179.66 inference(rename_variables,[],[3754])).
% 179.86/179.66 cnf(12521,plain,
% 179.86/179.66 (E(f31(x125211,x125212,x125213,x125214,x125215,x125216,x125217,x125218,x125219,a24),x125212)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12523,plain,
% 179.86/179.66 (E(f31(x125231,x125232,x125233,x125234,x125235,x125236,x125237,x125238,x125239,a24),x125232)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12525,plain,
% 179.86/179.66 (P26(x125251,x125252,f188(f867(f859(x125251),a855)))),
% 179.86/179.66 inference(rename_variables,[],[3326])).
% 179.86/179.66 cnf(12531,plain,
% 179.86/179.66 (P38(x125311,f146(x125311,x125312))),
% 179.86/179.66 inference(rename_variables,[],[3139])).
% 179.86/179.66 cnf(12540,plain,
% 179.86/179.66 (P27(x125401,x125401,f5(x125401),x125402)),
% 179.86/179.66 inference(rename_variables,[],[3512])).
% 179.86/179.66 cnf(12542,plain,
% 179.86/179.66 (P27(x125421,x125421,f5(x125421),x125422)),
% 179.86/179.66 inference(rename_variables,[],[3512])).
% 179.86/179.66 cnf(12548,plain,
% 179.86/179.66 (E(f31(x125481,x125482,x125483,x125484,x125485,x125486,x125487,x125488,x125489,a24),x125482)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12550,plain,
% 179.86/179.66 (E(f31(x125501,x125502,x125503,x125504,x125505,x125506,x125507,x125508,x125509,a24),x125502)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12552,plain,
% 179.86/179.66 (P28(x125521,x125521,f32(x125521),x125522,x125522)),
% 179.86/179.66 inference(rename_variables,[],[3941])).
% 179.86/179.66 cnf(12554,plain,
% 179.86/179.66 (P28(x125541,x125541,f32(x125541),x125542,x125542)),
% 179.86/179.66 inference(rename_variables,[],[3941])).
% 179.86/179.66 cnf(12556,plain,
% 179.86/179.66 (P28(x125561,x125561,f32(x125561),x125562,x125562)),
% 179.86/179.66 inference(rename_variables,[],[3941])).
% 179.86/179.66 cnf(12562,plain,
% 179.86/179.66 (E(f31(x125621,x125622,x125623,x125624,x125625,x125626,x125627,x125628,x125629,a24),x125622)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12575,plain,
% 179.86/179.66 (E(f31(x125751,x125752,x125753,x125754,x125755,x125756,x125757,x125758,x125759,a24),x125752)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12577,plain,
% 179.86/179.66 (E(f31(x125771,x125772,x125773,x125774,x125775,x125776,x125777,x125778,x125779,a24),x125772)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12579,plain,
% 179.86/179.66 (E(f31(x125791,x125792,x125793,x125794,x125795,x125796,x125797,x125798,x125799,a24),x125792)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12581,plain,
% 179.86/179.66 (E(f31(x125811,x125812,x125813,x125814,x125815,x125816,x125817,x125818,x125819,a24),x125812)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12583,plain,
% 179.86/179.66 (E(f31(x125831,x125832,x125833,x125834,x125835,x125836,x125837,x125838,x125839,a24),x125832)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12585,plain,
% 179.86/179.66 (E(f31(x125851,x125852,x125853,x125854,x125855,x125856,x125857,x125858,x125859,a24),x125852)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12590,plain,
% 179.86/179.66 (E(f188(f867(f866(x125901,x125901),a855)),f255(x125901,f188(f867(x125901,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3342])).
% 179.86/179.66 cnf(12598,plain,
% 179.86/179.66 (P40(x125981,x125982,f255(x125981,x125982))),
% 179.86/179.66 inference(rename_variables,[],[3238])).
% 179.86/179.66 cnf(12600,plain,
% 179.86/179.66 (P40(x126001,x126002,f255(x126001,x126002))),
% 179.86/179.66 inference(rename_variables,[],[3238])).
% 179.86/179.66 cnf(12604,plain,
% 179.86/179.66 (P17(x126041,f867(x126041,a855),f301(x126041))),
% 179.86/179.66 inference(rename_variables,[],[3242])).
% 179.86/179.66 cnf(12608,plain,
% 179.86/179.66 (P51(x126081,x126081,f255(x126081,x126082))),
% 179.86/179.66 inference(rename_variables,[],[3239])).
% 179.86/179.66 cnf(12620,plain,
% 179.86/179.66 (P33(x126201,x126202,f113(x126201),f113(x126201))),
% 179.86/179.66 inference(rename_variables,[],[3521])).
% 179.86/179.66 cnf(12621,plain,
% 179.86/179.66 (E(f31(x126211,x126212,x126213,x126214,x126215,x126216,x126217,x126218,x126219,a24),x126212)),
% 179.86/179.66 inference(rename_variables,[],[4448])).
% 179.86/179.66 cnf(12623,plain,
% 179.86/179.66 (P33(x126231,x126232,f113(x126231),f113(x126231))),
% 179.86/179.66 inference(rename_variables,[],[3521])).
% 179.86/179.66 cnf(12627,plain,
% 179.86/179.66 (P43(x126271,x126272,x126273,x126274,f188(f867(x126271,a855)),x126274)),
% 179.86/179.66 inference(rename_variables,[],[4230])).
% 179.86/179.66 cnf(12630,plain,
% 179.86/179.66 (P43(x126301,x126302,x126303,x126304,f188(f867(x126301,a855)),x126304)),
% 179.86/179.66 inference(rename_variables,[],[4230])).
% 179.86/179.66 cnf(12634,plain,
% 179.86/179.66 (P52(x126341,f188(f867(x126341,a855)),x126342)),
% 179.86/179.66 inference(rename_variables,[],[3290])).
% 179.86/179.66 cnf(12643,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),f2(a860)),f323(a112,x126431)))),
% 179.86/179.66 inference(rename_variables,[],[3351])).
% 179.86/179.66 cnf(12644,plain,
% 179.86/179.66 (~E(f323(a112,x126441),x126441)),
% 179.86/179.66 inference(rename_variables,[],[4462])).
% 179.86/179.66 cnf(12650,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x126501),f323(a112,x126501)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(12655,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x126551),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(12657,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),a81),f2(a1)))),
% 179.86/179.66 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,3327,3290,12634,3481,11849,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2914,2916,2919,2928,2936,2937,2941,2947,2972,2975,3011,3020,3023,3025,3026,3034,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,4476,3827,11356,3326,12525,3163,3130,3592,3125,3230,3949,3652,3113,3114,3087,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,4496,12329,3261,11692,4535,10952,11035,11264,11267,3376,3598,3342,12590,3160,3161,10287,10592,3434,3152,3084,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,4487,11337,3575,3790,3837,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,3725,11585,3254,3351,11707,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,4541,11466,11499,11536,11565,3712,3482,3864,3298,3300,3273,4526,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,4027,3984,11866,12216,3926,10766,12050,12223,12372,3979,10964,12092,12165,12222,12269,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,3272,3347,12080,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,3429,10560,10825,10869,11175,11253,11423,11672,12324,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,3332,10589,10619,10628,11204,11773,12423,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,3292,10622,10774,10845,11621,11778,11974,12185,3755,4107,4532,3766,3802,4515,4518,3245,3249,4517,4516,4520,3773,3587,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,3881,11294,11647,11651,11714,12335,12343,3719,10885,10891,10913,11898,12027,12113,3571,11015,11144,12139,12251,12261,12340,12392,12400,4061,3721,10625,10980,11150,11180,11191,12047,12339,3538,10543,10546,10631,10801,4553,11582,4543,4554,10684,10783,11420,11452,12204,12213,12257,4166,10759,12234,4068,3754,3698,4551,10239,10242,10583,10586,11463,11652,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580,7581,7613,7615,7616,7617,7622,7644,7653,7663,7668,7674,7676,7682,7694,7695,7697,7720,7726,7747,7814,7815,7816,7864,7872,7873,7898,7899,7916,7917,7974,7975,8004,8031,8041,8043,8052,8064,8094,8100,8107,8120,8139,8144,8166,8210,8240,8254,8273,8276,8306,8332,8391,8392,8395,8396,8460,8494,8495,8496,8497,8524,8556,8585,8593,8594,8636,8657,8703,8718,8765,8768,8783,8790,8826,8874,8875,8891,8892,9021,9027,9031,9052,9062,9085,9087,9090,9094,9096,9097,9108,9109,9129,9136,9149,9158,9195,9213,9265,9266,9273,9312,9335,9340,9375,9383,9386,9389,9390,9403,9420,9429,9443,9452,9453,9455,9457,9485,9609,9655,9656,9698,9743,9858,9915,10052,10065,10070,3,2606,2607,2608,2609,2611,2612,2613,2617,2618,2619,2623,2624,2625,2626,2635,2637,2642,2643,2644,2645,2646,2650,2651,2656,2657,2658,2659,2660,2663,2664,2665,2668,2670,2671,2673,2674,2681,2682,2685,2686,2687,2688,2690,2692,2711,2712,2714,2715,2719,2720,2721,2723,2725,2748,2749,2750,2766,2767,2768,2778,2779,2781,2783,2784,2791,2794,2795,2796,2804,2805,2826,2827,2846,2847,5204,5263,5361,5447,5448,5449])).
% 179.86/179.66 cnf(12664,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a1),f323(f100(a1),x126641)),f323(f77(a1),f323(f100(a1),x126642))))),
% 179.86/179.66 inference(rename_variables,[],[4548])).
% 179.86/179.66 cnf(12674,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x126741),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(12677,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x126771),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(12680,plain,
% 179.86/179.66 (P101(f323(f59(a860),f296(a860,x126801,x126802)))),
% 179.86/179.66 inference(rename_variables,[],[3484])).
% 179.86/179.66 cnf(12683,plain,
% 179.86/179.66 (P101(f323(f59(a860),f296(a860,x126831,x126832)))),
% 179.86/179.66 inference(rename_variables,[],[3484])).
% 179.86/179.66 cnf(12686,plain,
% 179.86/179.66 (P101(f323(f59(a860),f296(a860,x126861,x126862)))),
% 179.86/179.66 inference(rename_variables,[],[3484])).
% 179.86/179.66 cnf(12689,plain,
% 179.86/179.66 (P101(f323(f59(a860),f296(a860,x126891,x126892)))),
% 179.86/179.66 inference(rename_variables,[],[3484])).
% 179.86/179.66 cnf(12696,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),f323(f77(a1),f323(f100(a1),x126961))),f323(f100(a1),x126962)))),
% 179.86/179.66 inference(rename_variables,[],[3755])).
% 179.86/179.66 cnf(12698,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),f2(a1)),f323(f103(a1),f2(a1))))),
% 179.86/179.66 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,3327,3290,12634,3481,11849,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2914,2916,2919,2928,2936,2937,2941,2947,2972,2975,3011,3013,3020,3023,3025,3026,3034,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,4476,3827,11356,3326,12525,3163,3130,3592,3125,3230,3949,3652,3113,3114,3087,3093,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,4496,12329,3261,11692,4535,10952,11035,11264,11267,3376,3598,3342,12590,3160,3161,10287,10592,3434,3152,3084,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,4487,11337,3575,3790,3837,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,3725,11585,3254,3351,11707,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,12655,12674,4541,11466,11499,11536,11565,3712,3482,3484,12680,12683,12686,3864,3298,3300,3273,4526,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,4027,3984,11866,12216,3926,10766,12050,12223,12372,3979,10964,12092,12165,12222,12269,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,3272,3347,12080,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,3429,10560,10825,10869,11175,11253,11423,11672,12324,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,3332,10589,10619,10628,11204,11773,12423,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,3292,10622,10774,10845,11621,11778,11974,12185,3755,11723,4107,4532,3766,3802,4515,4518,4519,3245,3249,4517,4516,4520,3773,3587,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,3881,11294,11647,11651,11714,12335,12343,3719,10885,10891,10913,11898,12027,12113,3571,11015,11144,12139,12251,12261,12340,12392,12400,4061,3721,10625,10980,11150,11180,11191,12047,12339,3538,10543,10546,10631,10801,3540,4553,11582,4543,4548,12664,4554,10684,10783,11420,11452,12204,12213,12257,4166,10759,12234,4068,3754,3698,3699,4551,10239,10242,10583,10586,11463,11652,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,647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% 179.86/179.66 cnf(12701,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x127011),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(12702,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x127021),x127021))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12709,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x127091),f323(a112,x127091)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(12711,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),f2(a1)),a81))),
% 179.86/179.66 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,3327,3290,12634,3481,11849,4474,10388,10479,10926,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2914,2916,2919,2928,2936,2937,2941,2947,2972,2975,3011,3013,3020,3023,3025,3026,3034,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,4476,3827,11356,3326,12525,3163,3130,3592,3125,3230,3949,3652,3113,3114,3087,3093,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,4496,12329,3261,11692,4535,10952,11035,11264,11267,3376,3598,3342,12590,3160,3161,10287,10592,3434,3152,3084,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,4487,11337,3575,3613,3790,3837,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,12650,3725,11585,3254,3351,11707,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,12655,12674,12677,4541,11466,11499,11536,11565,3712,3482,3484,12680,12683,12686,3864,3298,3300,3273,4526,3159,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,4027,3984,11866,12216,3926,10766,12050,12223,12372,3979,10964,12092,12165,12222,12269,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,12436,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,3272,3347,12080,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,3429,10560,10825,10869,11175,11253,11423,11672,12324,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,3332,10589,10619,10628,11204,11773,12423,3371,3365,3794,3730,10266,11588,11620,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,3292,10622,10774,10845,11621,11778,11974,12185,3755,11723,4107,3488,4532,3766,3802,4515,4518,4519,3245,3249,4517,4516,4520,3773,3587,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,3881,11294,11647,11651,11714,12335,12343,3719,10885,10891,10913,11898,12027,12113,3571,11015,11144,12139,12251,12261,12340,12392,12400,4061,3721,10625,10980,11150,11180,11191,12047,12339,3538,10543,10546,10631,10801,3540,4553,11582,4543,4548,12664,4554,10684,10783,11420,11452,12204,12213,12257,4166,10759,12234,4068,3754,3698,3699,4551,10239,10242,10583,10586,11463,11652,4552,11562,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,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% 179.86/179.66 cnf(12714,plain,
% 179.86/179.66 (P101(f323(f323(f325(x127141),f323(x127142,x127143)),f323(f302(x127144,x127141,x127142),f246(f867(x127144,a855)))))),
% 179.86/179.66 inference(rename_variables,[],[3881])).
% 179.86/179.66 cnf(12715,plain,
% 179.86/179.66 (~E(f323(a112,x127151),f2(a860))),
% 179.86/179.66 inference(rename_variables,[],[4474])).
% 179.86/179.66 cnf(12720,plain,
% 179.86/179.66 (P101(f323(f323(f237(a1),x127201),x127201))),
% 179.86/179.66 inference(rename_variables,[],[3271])).
% 179.86/179.66 cnf(12723,plain,
% 179.86/179.66 (P101(f323(f59(a860),f296(a860,x127231,x127232)))),
% 179.86/179.66 inference(rename_variables,[],[3484])).
% 179.86/179.66 cnf(12726,plain,
% 179.86/179.66 (P101(f323(f59(a860),f296(a860,x127261,x127262)))),
% 179.86/179.66 inference(rename_variables,[],[3484])).
% 179.86/179.66 cnf(12729,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x127291),x127291))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12730,plain,
% 179.86/179.66 (~E(f323(a112,x127301),f2(a860))),
% 179.86/179.66 inference(rename_variables,[],[4474])).
% 179.86/179.66 cnf(12747,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f42(a860,x127471,x127472)),x127471))),
% 179.86/179.66 inference(rename_variables,[],[3730])).
% 179.86/179.66 cnf(12752,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x127521),f323(a112,x127521)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(12755,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x127551),f323(a112,x127551)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(12756,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a860),x127561),f2(a860)))),
% 179.86/179.66 inference(rename_variables,[],[4529])).
% 179.86/179.66 cnf(12765,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a1),f323(f100(a1),x127651)),f2(a1)))),
% 179.86/179.66 inference(rename_variables,[],[4541])).
% 179.86/179.66 cnf(12766,plain,
% 179.86/179.66 (P101(f323(f246(f867(x127661,a855)),x127662))),
% 179.86/179.66 inference(rename_variables,[],[3332])).
% 179.86/179.66 cnf(12769,plain,
% 179.86/179.66 (~P101(f323(f323(f238(a1),f323(f100(a1),x127691)),f2(a1)))),
% 179.86/179.66 inference(rename_variables,[],[4541])).
% 179.86/179.66 cnf(12770,plain,
% 179.86/179.66 (P101(f323(f246(f867(x127701,a855)),x127702))),
% 179.86/179.66 inference(rename_variables,[],[3332])).
% 179.86/179.66 cnf(12773,plain,
% 179.86/179.66 (P101(f323(f246(f867(x127731,a855)),x127732))),
% 179.86/179.66 inference(rename_variables,[],[3332])).
% 179.86/179.66 cnf(12784,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x127841),x127842),f188(f867(x127841,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12785,plain,
% 179.86/179.66 (P101(f323(f59(x127851),f188(f867(x127851,a855))))),
% 179.86/179.66 inference(rename_variables,[],[3347])).
% 179.86/179.66 cnf(12794,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),f2(a860)),x127941))),
% 179.86/179.66 inference(rename_variables,[],[3292])).
% 179.86/179.66 cnf(12797,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x127971),x127972),f188(f867(x127971,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12800,plain,
% 179.86/179.66 (~P101(f323(f323(f325(x128001),x128002),f188(f867(x128001,a855))))),
% 179.86/179.66 inference(rename_variables,[],[4537])).
% 179.86/179.66 cnf(12803,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x128031),x128031))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12811,plain,
% 179.86/179.66 (P101(f323(f323(f238(a860),x128111),f323(a112,x128111)))),
% 179.86/179.66 inference(rename_variables,[],[3339])).
% 179.86/179.66 cnf(12814,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x128141),x128141))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12819,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x128191),x128191))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.66 cnf(12822,plain,
% 179.86/179.66 (P101(f323(f323(f237(a860),x128221),x128221))),
% 179.86/179.66 inference(rename_variables,[],[3270])).
% 179.86/179.67 cnf(12825,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),x128251),x128251))),
% 179.86/179.67 inference(rename_variables,[],[3270])).
% 179.86/179.67 cnf(12828,plain,
% 179.86/179.67 (E(f323(f323(f22(f867(x128281,a855)),f188(f867(x128281,a855))),x128282),f188(f867(x128281,a855)))),
% 179.86/179.67 inference(rename_variables,[],[3543])).
% 179.86/179.67 cnf(12829,plain,
% 179.86/179.67 (P101(f323(f59(x128291),f188(f867(x128291,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3347])).
% 179.86/179.67 cnf(12832,plain,
% 179.86/179.67 (E(f323(f323(f22(f867(x128321,a855)),f188(f867(x128321,a855))),x128322),f188(f867(x128321,a855)))),
% 179.86/179.67 inference(rename_variables,[],[3543])).
% 179.86/179.67 cnf(12833,plain,
% 179.86/179.67 (P101(f323(f59(x128331),f188(f867(x128331,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3347])).
% 179.86/179.67 cnf(12836,plain,
% 179.86/179.67 (E(f323(f323(f22(f867(x128361,a855)),f188(f867(x128361,a855))),x128362),f188(f867(x128361,a855)))),
% 179.86/179.67 inference(rename_variables,[],[3543])).
% 179.86/179.67 cnf(12837,plain,
% 179.86/179.67 (P101(f323(f59(x128371),f188(f867(x128371,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3347])).
% 179.86/179.67 cnf(12840,plain,
% 179.86/179.67 (E(f323(f323(f22(f867(x128401,a855)),f188(f867(x128401,a855))),x128402),f188(f867(x128401,a855)))),
% 179.86/179.67 inference(rename_variables,[],[3543])).
% 179.86/179.67 cnf(12841,plain,
% 179.86/179.67 (P101(f323(f59(x128411),f188(f867(x128411,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3347])).
% 179.86/179.67 cnf(12845,plain,
% 179.86/179.67 (E(f323(f254(x128451,x128451),f255(x128451,x128452)),x128452)),
% 179.86/179.67 inference(rename_variables,[],[3228])).
% 179.86/179.67 cnf(12850,plain,
% 179.86/179.67 (E(f323(f323(f22(f867(x128501,a855)),f188(f867(x128501,a855))),x128502),f188(f867(x128501,a855)))),
% 179.86/179.67 inference(rename_variables,[],[3543])).
% 179.86/179.67 cnf(12851,plain,
% 179.86/179.67 (P101(f323(f59(x128511),f188(f867(x128511,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3347])).
% 179.86/179.67 cnf(12855,plain,
% 179.86/179.67 (P101(f323(f59(x128551),f188(f867(x128551,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3347])).
% 179.86/179.67 cnf(12858,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),x128581),x128581))),
% 179.86/179.67 inference(rename_variables,[],[3270])).
% 179.86/179.67 cnf(12862,plain,
% 179.86/179.67 (P101(f323(f323(f237(a1),x128621),x128621))),
% 179.86/179.67 inference(rename_variables,[],[3271])).
% 179.86/179.67 cnf(12871,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),x128711),x128711))),
% 179.86/179.67 inference(rename_variables,[],[3270])).
% 179.86/179.67 cnf(12882,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),x128821),x128821))),
% 179.86/179.67 inference(rename_variables,[],[3270])).
% 179.86/179.67 cnf(12885,plain,
% 179.86/179.67 (P101(f323(f323(f237(a1),x128851),x128851))),
% 179.86/179.67 inference(rename_variables,[],[3271])).
% 179.86/179.67 cnf(12892,plain,
% 179.86/179.67 (~P101(f323(f323(f325(x128921),x128922),f188(f867(x128921,a855))))),
% 179.86/179.67 inference(rename_variables,[],[4537])).
% 179.86/179.67 cnf(12903,plain,
% 179.86/179.67 (P101(f323(f323(f325(x129031),x129032),f246(f867(x129031,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3429])).
% 179.86/179.67 cnf(12904,plain,
% 179.86/179.67 (E(f323(f232(f864(x129041),x129042,f200(x129041),f323(f16(f864(x129041),x129042),f200(x129041))),f323(x129043,x129044)),f200(x129041))),
% 179.86/179.67 inference(rename_variables,[],[3855])).
% 179.86/179.67 cnf(12910,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x129101,a855)),x129102),f246(f867(x129101,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3654])).
% 179.86/179.67 cnf(12913,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x129131,a855)),x129132),x129132))),
% 179.86/179.67 inference(rename_variables,[],[3571])).
% 179.86/179.67 cnf(12919,plain,
% 179.86/179.67 (~P101(f323(f323(f238(a860),x129191),f2(a860)))),
% 179.86/179.67 inference(rename_variables,[],[4529])).
% 179.86/179.67 cnf(12920,plain,
% 179.86/179.67 (P101(f323(f323(f237(a1),x129201),x129201))),
% 179.86/179.67 inference(rename_variables,[],[3271])).
% 179.86/179.67 cnf(12924,plain,
% 179.86/179.67 (~P101(f323(f323(f238(a860),x129241),f2(a860)))),
% 179.86/179.67 inference(rename_variables,[],[4529])).
% 179.86/179.67 cnf(12925,plain,
% 179.86/179.67 (P101(f323(f323(f237(a1),x129251),x129251))),
% 179.86/179.67 inference(rename_variables,[],[3271])).
% 179.86/179.67 cnf(12930,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),x129301),x129301))),
% 179.86/179.67 inference(rename_variables,[],[3270])).
% 179.86/179.67 cnf(12931,plain,
% 179.86/179.67 (P101(f323(f59(a860),f294(a860,x129311,x129312)))),
% 179.86/179.67 inference(rename_variables,[],[3482])).
% 179.86/179.67 cnf(12938,plain,
% 179.86/179.67 (E(f323(f323(f16(x129381,x129382),x129383),x129384),x129383)),
% 179.86/179.67 inference(rename_variables,[],[3261])).
% 179.86/179.67 cnf(12941,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x129411,a855)),f323(f166(x129411),f164(x129411,x129412,x129413))),f323(f166(x129411),x129413)))),
% 179.86/179.67 inference(rename_variables,[],[3979])).
% 179.86/179.67 cnf(12945,plain,
% 179.86/179.67 (~P101(f323(f323(f238(a860),x129451),f2(a860)))),
% 179.86/179.67 inference(rename_variables,[],[4529])).
% 179.86/179.67 cnf(12946,plain,
% 179.86/179.67 (P101(f323(f323(f237(a1),x129461),x129461))),
% 179.86/179.67 inference(rename_variables,[],[3271])).
% 179.86/179.67 cnf(12950,plain,
% 179.86/179.67 (~P101(f323(f323(f238(a860),x129501),f2(a860)))),
% 179.86/179.67 inference(rename_variables,[],[4529])).
% 179.86/179.67 cnf(12951,plain,
% 179.86/179.67 (P101(f323(f323(f237(a1),x129511),x129511))),
% 179.86/179.67 inference(rename_variables,[],[3271])).
% 179.86/179.67 cnf(12955,plain,
% 179.86/179.67 (~P101(f323(f323(f237(f867(a860,a855)),f294(a860,f323(a112,x129551),f323(a112,x129551))),f294(a860,x129552,x129551)))),
% 179.86/179.67 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,3327,3290,12634,3481,11849,4474,10388,10479,10926,11010,12715,2869,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2911,2914,2916,2919,2928,2936,2937,2941,2947,2953,2972,2975,2986,2988,2991,2992,3001,3011,3013,3020,3023,3024,3025,3026,3034,3035,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3228,3855,12904,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,4476,3827,11356,3326,12525,3163,3130,3592,3125,3230,3949,3652,3113,3114,3087,3093,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,4496,12329,3261,11692,11695,4535,10952,11035,11264,11267,3376,3598,3342,12590,3160,3161,10287,10592,3434,3152,3084,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,4487,11337,3575,3613,3790,3543,12828,12832,12836,12840,12850,3837,12192,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,12650,12709,12752,12755,12811,3725,11585,3254,3351,11707,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,12655,12674,12677,12701,12756,12919,12924,12945,4541,11466,11499,11536,11565,12765,12769,3712,3482,12931,3484,12680,12683,12686,12689,12723,3864,3298,3300,3273,4526,3159,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,12444,4027,3984,11866,12216,3926,10766,12050,12223,12372,3979,10964,12092,12165,12222,12269,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,12436,12702,12729,12803,12814,12819,12822,12825,12858,12871,12882,12930,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,11969,12720,12862,12885,12920,12925,12946,3272,3347,12080,12785,12829,12833,12837,12841,12851,12855,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,12505,3429,10560,10825,10869,11175,11253,11423,11672,12324,12508,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,12515,12784,12797,12800,3332,10589,10619,10628,11204,11773,12423,12437,12766,12770,12773,3371,3365,3794,3730,10266,11588,11620,12747,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,3292,10622,10774,10845,11621,11778,11974,12185,12210,3755,11723,12696,4107,3488,4532,3766,3802,4515,4518,4519,3245,3249,4517,4516,4520,3773,3587,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,12237,3881,11294,11647,11651,11714,12335,12343,12429,3719,10885,10891,10913,11898,12027,12113,3571,11015,11144,12139,12251,12261,12340,12392,12400,12512,4061,3721,10625,10980,11150,11180,11191,12047,12339,3538,10543,10546,10631,10801,3540,4553,11582,4543,4548,12664,4554,10684,10783,11420,11452,12204,12213,12257,4166,10759,12234,4068,3754,12518,3698,3699,4551,10239,10242,10583,10586,11463,11652,12463,4552,11562,11657,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5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% 179.86/179.67 cnf(12956,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),x129561),x129561))),
% 179.86/179.67 inference(rename_variables,[],[3270])).
% 179.86/179.67 cnf(12958,plain,
% 179.86/179.67 (~P101(f323(f323(f238(f867(a860,a855)),f294(a860,f323(a112,x129581),f323(a112,x129581))),f294(a860,x129582,x129581)))),
% 179.86/179.67 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,3327,3290,12634,3481,11849,4474,10388,10479,10926,11010,12715,2869,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2911,2914,2916,2919,2928,2936,2937,2941,2947,2953,2972,2975,2986,2988,2991,2992,3001,3011,3013,3020,3023,3024,3025,3026,3034,3035,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3228,3855,12904,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,4476,3827,11356,3326,12525,3163,3130,3592,3125,3230,3949,3652,3113,3114,3087,3093,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,4496,12329,3261,11692,11695,4535,10952,11035,11264,11267,3376,3598,3342,12590,3160,3161,10287,10592,3434,3152,3084,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,4487,11337,3575,3613,3790,3543,12828,12832,12836,12840,12850,3837,12192,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,12650,12709,12752,12755,12811,3725,11585,3254,3351,11707,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,12655,12674,12677,12701,12756,12919,12924,12945,4541,11466,11499,11536,11565,12765,12769,3712,3482,12931,3484,12680,12683,12686,12689,12723,3864,3298,3300,3273,4526,3159,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,12444,4027,3984,11866,12216,3926,10766,12050,12223,12372,3979,10964,12092,12165,12222,12269,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,4547,10717,11117,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,12436,12702,12729,12803,12814,12819,12822,12825,12858,12871,12882,12930,12956,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,11969,12720,12862,12885,12920,12925,12946,3272,3347,12080,12785,12829,12833,12837,12841,12851,12855,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,12505,3429,10560,10825,10869,11175,11253,11423,11672,12324,12508,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,12515,12784,12797,12800,3332,10589,10619,10628,11204,11773,12423,12437,12766,12770,12773,3371,3365,3794,3730,10266,11588,11620,12747,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,3292,10622,10774,10845,11621,11778,11974,12185,12210,3755,11723,12696,4107,3488,4532,3766,3802,4515,4518,4519,3245,3249,4517,4516,4520,3773,3587,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,12237,3881,11294,11647,11651,11714,12335,12343,12429,3719,10885,10891,10913,11898,12027,12113,3571,11015,11144,12139,12251,12261,12340,12392,12400,12512,4061,3721,10625,10980,11150,11180,11191,12047,12339,3538,10543,10546,10631,10801,3540,4553,11582,4543,4548,12664,4554,10684,10783,11420,11452,12204,12213,12257,4166,10759,12234,4068,3754,12518,3698,3699,4551,10239,10242,10583,10586,11463,11652,12463,4552,11562,11657,3723,10549,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580,7581,7613,7615,7616,7617,7622,7644,7653,7663,7668,7674,7676,7682,7694,7695,7697,7720,7726,7747,7814,7815,7816,7864,7872,7873,7898,7899,7916,7917,7974,7975,8004,8031,8041,8043,8052,8064,8094,8100,8107,8120,8139,8144,8166,8210,8240,8254,8273,8276,8306,8332,8391,8392,8395,8396,8460,8494,8495,8496,8497,8524,8556,8585,8593,8594,8636,8657,8703,8718,8765,8768,8783,8790,8826,8874,8875,8891,8892,9021,9027,9031,9052,9062,9085,9087,9090,9094,9096,9097,9108,9109,9129,9136,9149,9158,9195,9213,9265,9266,9273,9312,9335,9340,9375,9383,9386,9389,9390,9403,9420,9429,9443,9452,9453,9455,9457,9485,9609,9655,9656,9698,9743,9858,9915,10052,10065,10070,3,2606,2607,2608,2609,2611,2612,2613,2617,2618,2619,2623,2624,2625,2626,2635,2637,2642,2643,2644,2645,2646,2650,2651,2656,2657,2658,2659,2660,2663,2664,2665,2668,2670,2671,2673,2674,2681,2682,2685,2686,2687,2688,2690,2692,2711,2712,2714,2715,2719,2720,2721,2723,2725,2748,2749,2750,2766,2767,2768,2778,2779,2781,2783,2784,2791,2794,2795,2796,2804,2805,2826,2827,2846,2847,5204,5263,5361,5447,5448,5449,5525,5622,5653,5687,5703,5705,5711,5772,5773,5774,5775,5781,5814,5941,5975,5984,6007,6044,6079,6084,6224,6229,6264,6265,6285,6288,6290,6297,6298,6299,6300,6301,6302,6303,6304,6383,6450,6451,6537,6570,6571,6611,6612,6749,6764,6837,6838,6844,6864,6895,6897,6944,6967,6968,6986,6987,7022,7066,7067,7164,7225,7226,7227,7228,7242,7275,7328,7329,7338,7345,7346,7358,7390,7391,7392,7393,7535,7536,7538,7540,7546,7547,7755,7761,7762,7772,7811,7812,7893,7933,7987,8009,8010,8080,8181,8250,8251,8255,8291,8354,8355,8419,8437,8438])).
% 179.86/179.67 cnf(12959,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),x129591),x129591))),
% 179.86/179.67 inference(rename_variables,[],[3270])).
% 179.86/179.67 cnf(12962,plain,
% 179.86/179.67 (~P101(f323(f323(f237(a860),f323(a112,x129621)),x129621))),
% 179.86/179.67 inference(rename_variables,[],[4534])).
% 179.86/179.67 cnf(12968,plain,
% 179.86/179.67 (P101(f323(f323(f325(x129681),f323(x129682,x129683)),f323(f302(x129684,x129681,x129682),f246(f867(x129684,a855)))))),
% 179.86/179.67 inference(rename_variables,[],[3881])).
% 179.86/179.67 cnf(12969,plain,
% 179.86/179.67 (P27(x129691,x129691,f5(x129691),x129692)),
% 179.86/179.67 inference(rename_variables,[],[3512])).
% 179.86/179.67 cnf(12974,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x129741,a855)),x129742),f246(f867(x129741,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3654])).
% 179.86/179.67 cnf(12975,plain,
% 179.86/179.67 (P27(x129751,x129751,f5(x129751),x129752)),
% 179.86/179.67 inference(rename_variables,[],[3512])).
% 179.86/179.67 cnf(12979,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x129791,a855)),x129792),f246(f867(x129791,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3654])).
% 179.86/179.67 cnf(12980,plain,
% 179.86/179.67 (P27(x129801,x129801,f5(x129801),x129802)),
% 179.86/179.67 inference(rename_variables,[],[3512])).
% 179.86/179.67 cnf(12984,plain,
% 179.86/179.67 (P27(x129841,x129841,f5(x129841),x129842)),
% 179.86/179.67 inference(rename_variables,[],[3512])).
% 179.86/179.67 cnf(12987,plain,
% 179.86/179.67 (~P101(f323(f323(f238(f867(x129871,a855)),x129872),f188(f867(x129871,a855))))),
% 179.86/179.67 inference(rename_variables,[],[4547])).
% 179.86/179.67 cnf(12990,plain,
% 179.86/179.67 (P27(x129901,x129901,f5(x129901),x129902)),
% 179.86/179.67 inference(rename_variables,[],[3512])).
% 179.86/179.67 cnf(12993,plain,
% 179.86/179.67 (P27(x129931,x129931,f5(x129931),x129932)),
% 179.86/179.67 inference(rename_variables,[],[3512])).
% 179.86/179.67 cnf(12999,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x129991,a855)),x129992),f246(f867(x129991,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3654])).
% 179.86/179.67 cnf(13004,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x130041,a855)),f188(f867(x130041,a855))),x130042))),
% 179.86/179.67 inference(rename_variables,[],[3721])).
% 179.86/179.67 cnf(13008,plain,
% 179.86/179.67 (E(f323(f254(x130081,x130081),f255(x130081,x130082)),x130082)),
% 179.86/179.67 inference(rename_variables,[],[3228])).
% 179.86/179.67 cnf(13012,plain,
% 179.86/179.67 (~P101(f323(f323(f325(x130121),x130122),f188(f867(x130121,a855))))),
% 179.86/179.67 inference(rename_variables,[],[4537])).
% 179.86/179.67 cnf(13016,plain,
% 179.86/179.67 (P101(f323(f323(f325(x130161),f323(x130162,x130163)),f323(f302(x130164,x130161,x130162),f246(f867(x130164,a855)))))),
% 179.86/179.67 inference(rename_variables,[],[3881])).
% 179.86/179.67 cnf(13017,plain,
% 179.86/179.67 (P27(x130171,x130171,f5(x130171),x130172)),
% 179.86/179.67 inference(rename_variables,[],[3512])).
% 179.86/179.67 cnf(13020,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x130201,a855)),x130202),f246(f867(x130201,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3654])).
% 179.86/179.67 cnf(13024,plain,
% 179.86/179.67 (P101(f323(f323(f325(x130241),x130242),f246(f867(x130241,a855))))),
% 179.86/179.67 inference(rename_variables,[],[3429])).
% 179.86/179.67 cnf(13028,plain,
% 179.86/179.67 (E(f323(f323(f16(x130281,x130282),x130283),x130284),x130283)),
% 179.86/179.67 inference(rename_variables,[],[3261])).
% 179.86/179.67 cnf(13031,plain,
% 179.86/179.67 (~P101(f323(f323(f325(x130311),x130312),f188(f867(x130311,a855))))),
% 179.86/179.67 inference(rename_variables,[],[4537])).
% 179.86/179.67 cnf(13034,plain,
% 179.86/179.67 (~P101(f323(f323(f325(x130341),x130342),f188(f867(x130341,a855))))),
% 179.86/179.67 inference(rename_variables,[],[4537])).
% 179.86/179.67 cnf(13038,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),x130381),x130381))),
% 179.86/179.67 inference(rename_variables,[],[3270])).
% 179.86/179.67 cnf(13042,plain,
% 179.86/179.67 (E(f323(f323(f16(x130421,x130422),x130423),x130424),x130423)),
% 179.86/179.67 inference(rename_variables,[],[3261])).
% 179.86/179.67 cnf(13045,plain,
% 179.86/179.67 (P101(f323(f323(f238(a860),x130451),f323(a112,x130451)))),
% 179.86/179.67 inference(rename_variables,[],[3339])).
% 179.86/179.67 cnf(13046,plain,
% 179.86/179.67 (~E(f323(a112,x130461),x130461)),
% 179.86/179.67 inference(rename_variables,[],[4462])).
% 179.86/179.67 cnf(13049,plain,
% 179.86/179.67 (P101(f323(f323(f238(a860),x130491),f323(a112,f323(f323(f78(a860),x130492),x130491))))),
% 179.86/179.67 inference(rename_variables,[],[3723])).
% 179.86/179.67 cnf(13050,plain,
% 179.86/179.67 (P101(f323(f323(f238(a860),x130501),f323(a112,x130501)))),
% 179.86/179.67 inference(rename_variables,[],[3339])).
% 179.86/179.67 cnf(13052,plain,
% 179.86/179.67 (~E(f323(f323(f79(a860),f323(a112,f2(a860))),f30(x130521,x130522)),f323(f323(f79(a860),f323(a112,f2(a860))),f29(x130523,x130524)))),
% 179.86/179.67 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,12556,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,12542,12969,12975,12980,12984,12990,12993,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,12644,13046,3327,3290,12634,3481,11849,4474,10388,10479,10926,11010,12715,2869,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2911,2914,2916,2919,2928,2933,2936,2937,2941,2947,2953,2972,2975,2986,2988,2991,2992,3001,3011,3013,3020,3023,3024,3025,3026,3034,3035,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3228,12845,3855,12904,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,3105,4476,3827,11356,3326,12525,3163,3130,3592,3125,3230,3949,3652,3113,3114,3087,3093,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,12362,4496,12329,3261,11692,11695,12938,13028,4535,10952,11035,11264,11267,3258,3376,3598,3342,12590,3160,3161,10287,10592,4523,3434,3152,3084,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,11164,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,4487,11337,3575,3613,3790,3543,12828,12832,12836,12840,12850,3837,12192,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,12650,12709,12752,12755,12811,13045,3725,11585,3254,3351,11707,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,12655,12674,12677,12701,12756,12919,12924,12945,4541,11466,11499,11536,11565,12765,12769,3712,3482,12931,3484,12680,12683,12686,12689,12723,3864,3298,3300,3273,4526,3159,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,12444,4027,3984,11866,12216,3926,10766,12050,12223,12372,3979,10964,12092,12165,12222,12269,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,12910,12974,12979,12999,4547,10717,11117,12226,12987,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,12436,12702,12729,12803,12814,12819,12822,12825,12858,12871,12882,12930,12956,12959,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,11969,12720,12862,12885,12920,12925,12946,3272,3347,12080,12785,12829,12833,12837,12841,12851,12855,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,12505,3429,10560,10825,10869,11175,11253,11423,11672,12324,12508,12903,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,12515,12784,12797,12800,12892,13012,13031,3332,10589,10619,10628,11204,11773,12423,12437,12766,12770,12773,3371,3365,3794,3730,10266,11588,11620,12747,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,12962,3292,10622,10774,10845,11621,11778,11974,12185,12210,3755,11723,12696,4107,3488,4532,3766,3802,4515,4518,4519,3245,3249,4517,4516,4520,3773,3587,11581,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,12237,3881,11294,11647,11651,11714,12335,12343,12429,12714,12968,13016,3719,10885,10891,10913,11898,12027,12113,12397,3571,11015,11144,12139,12251,12261,12340,12392,12400,12512,4061,3721,10625,10980,11150,11180,11191,12047,12339,12386,3538,10543,10546,10631,10801,3540,4553,11582,4543,4548,12664,4554,10684,10783,11420,11452,12204,12213,12257,12454,4166,10759,12234,12260,4068,3754,12518,3698,3699,4551,10239,10242,10583,10586,11463,11652,12463,4552,11562,11657,3723,10549,10807,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580,7581,7613,7615,7616,7617,7622,7644,7653,7663,7668,7674,7676,7682,7694,7695,7697,7720,7726,7747,7814,7815,7816,7864,7872,7873,7898,7899,7916,7917,7974,7975,8004,8031,8041,8043,8052,8064,8094,8100,8107,8120,8139,8144,8166,8210,8240,8254,8273,8276,8306,8332,8391,8392,8395,8396,8460,8494,8495,8496,8497,8524,8556,8585,8593,8594,8636,8657,8703,8718,8765,8768,8783,8790,8826,8874,8875,8891,8892,9021,9027,9031,9052,9062,9085,9087,9090,9094,9096,9097,9108,9109,9129,9136,9149,9158,9195,9213,9265,9266,9273,9312,9335,9340,9375,9383,9386,9389,9390,9403,9420,9429,9443,9452,9453,9455,9457,9485,9609,9655,9656,9698,9743,9858,9915,10052,10065,10070,3,2606,2607,2608,2609,2611,2612,2613,2617,2618,2619,2623,2624,2625,2626,2635,2637,2642,2643,2644,2645,2646,2650,2651,2656,2657,2658,2659,2660,2663,2664,2665,2668,2670,2671,2673,2674,2681,2682,2685,2686,2687,2688,2690,2692,2711,2712,2714,2715,2719,2720,2721,2723,2725,2748,2749,2750,2766,2767,2768,2778,2779,2781,2783,2784,2791,2794,2795,2796,2804,2805,2826,2827,2846,2847,5204,5263,5361,5447,5448,5449,5525,5622,5653,5687,5703,5705,5711,5772,5773,5774,5775,5781,5814,5941,5975,5984,6007,6044,6079,6084,6224,6229,6264,6265,6285,6288,6290,6297,6298,6299,6300,6301,6302,6303,6304,6383,6450,6451,6537,6570,6571,6611,6612,6749,6764,6837,6838,6844,6864,6895,6897,6944,6967,6968,6986,6987,7022,7066,7067,7164,7225,7226,7227,7228,7242,7275,7328,7329,7338,7345,7346,7358,7390,7391,7392,7393,7535,7536,7538,7540,7546,7547,7755,7761,7762,7772,7811,7812,7893,7933,7987,8009,8010,8080,8181,8250,8251,8255,8291,8354,8355,8419,8437,8438,8439,8440,8589,8844,8845,8917,8931,8984,8985,9105,9140,9167,9196,9237,9427,9550,9692,9884,9940,9942,10075,6002,6366,6367,6453])).
% 179.86/179.67 cnf(13054,plain,
% 179.86/179.67 (~E(f323(a112,x130541),x130541)),
% 179.86/179.67 inference(rename_variables,[],[4462])).
% 179.86/179.67 cnf(13059,plain,
% 179.86/179.67 (P101(f323(f323(f237(a1),f2(a1)),f323(f100(a1),x130591)))),
% 179.86/179.67 inference(rename_variables,[],[3371])).
% 179.86/179.67 cnf(13062,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),f2(a860)),x130621))),
% 179.86/179.67 inference(rename_variables,[],[3292])).
% 179.86/179.67 cnf(13066,plain,
% 179.86/179.67 (~E(f323(a112,x130661),f2(a860))),
% 179.86/179.67 inference(rename_variables,[],[4474])).
% 179.86/179.67 cnf(13069,plain,
% 179.86/179.67 (P101(f323(f323(f237(a1),x130691),x130691))),
% 179.86/179.67 inference(rename_variables,[],[3271])).
% 179.86/179.67 cnf(13079,plain,
% 179.86/179.67 (~P101(f323(f323(f325(x130791),x130792),f188(f867(x130791,a855))))),
% 179.86/179.67 inference(rename_variables,[],[4537])).
% 179.86/179.67 cnf(13082,plain,
% 179.86/179.67 (P101(f323(f59(a860),f296(a860,x130821,x130822)))),
% 179.86/179.67 inference(rename_variables,[],[3484])).
% 179.86/179.67 cnf(13083,plain,
% 179.86/179.67 (E(f323(f323(f236(a860),f323(a112,x130831)),f323(a112,x130832)),f323(a112,f323(f323(f236(a860),x130831),x130832)))),
% 179.86/179.67 inference(rename_variables,[],[3447])).
% 179.86/179.67 cnf(13086,plain,
% 179.86/179.67 (P101(f323(f59(a860),f296(a860,x130861,x130862)))),
% 179.86/179.67 inference(rename_variables,[],[3484])).
% 179.86/179.67 cnf(13087,plain,
% 179.86/179.67 (E(f323(f323(f235(a860),f323(a112,x130871)),f323(a112,x130872)),f323(a112,f323(f323(f235(a860),x130871),x130872)))),
% 179.86/179.67 inference(rename_variables,[],[3446])).
% 179.86/179.67 cnf(13090,plain,
% 179.86/179.67 (P101(f323(f59(a860),f296(a860,x130901,x130902)))),
% 179.86/179.67 inference(rename_variables,[],[3484])).
% 179.86/179.67 cnf(13094,plain,
% 179.86/179.67 (P101(f323(f59(a860),f296(a860,x130941,x130942)))),
% 179.86/179.67 inference(rename_variables,[],[3484])).
% 179.86/179.67 cnf(13098,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x130981,a855)),f323(f166(x130981),f323(f129(x130981,x130982),x130983))),f323(f166(x130981),x130983)))),
% 179.86/179.67 inference(rename_variables,[],[3926])).
% 179.86/179.67 cnf(13099,plain,
% 179.86/179.67 (E(f323(f323(f16(x130991,x130992),x130993),x130994),x130993)),
% 179.86/179.67 inference(rename_variables,[],[3261])).
% 179.86/179.67 cnf(13102,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x131021,a855)),f323(f166(x131021),f323(f323(f169(x131021),x131022),x131023))),f323(f166(x131021),x131023)))),
% 179.86/179.67 inference(rename_variables,[],[3973])).
% 179.86/179.67 cnf(13103,plain,
% 179.86/179.67 (E(f323(f323(f16(x131031,x131032),x131033),x131034),x131033)),
% 179.86/179.67 inference(rename_variables,[],[3261])).
% 179.86/179.67 cnf(13107,plain,
% 179.86/179.67 (E(f323(f323(f16(x131071,x131072),x131073),x131074),x131073)),
% 179.86/179.67 inference(rename_variables,[],[3261])).
% 179.86/179.67 cnf(13120,plain,
% 179.86/179.67 (P101(f323(f323(f237(a1),f2(a1)),f323(f100(a1),x131201)))),
% 179.86/179.67 inference(rename_variables,[],[3371])).
% 179.86/179.67 cnf(13125,plain,
% 179.86/179.67 (P27(x131251,x131251,f5(x131251),x131252)),
% 179.86/179.67 inference(rename_variables,[],[3512])).
% 179.86/179.67 cnf(13128,plain,
% 179.86/179.67 (~P101(f323(f323(f325(x131281),x131282),f188(f867(x131281,a855))))),
% 179.86/179.67 inference(rename_variables,[],[4537])).
% 179.86/179.67 cnf(13131,plain,
% 179.86/179.67 (~P101(f323(f323(f325(x131311),x131312),f188(f867(x131311,a855))))),
% 179.86/179.67 inference(rename_variables,[],[4537])).
% 179.86/179.67 cnf(13132,plain,
% 179.86/179.67 (E(f323(f254(x131321,x131321),f255(x131321,x131322)),x131322)),
% 179.86/179.67 inference(rename_variables,[],[3228])).
% 179.86/179.67 cnf(13133,plain,
% 179.86/179.67 (P27(x131331,x131331,f5(x131331),x131332)),
% 179.86/179.67 inference(rename_variables,[],[3512])).
% 179.86/179.67 cnf(13137,plain,
% 179.86/179.67 (E(f323(f254(x131371,x131371),f255(x131371,x131372)),x131372)),
% 179.86/179.67 inference(rename_variables,[],[3228])).
% 179.86/179.67 cnf(13151,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),f2(a860)),x131511))),
% 179.86/179.67 inference(rename_variables,[],[3292])).
% 179.86/179.67 cnf(13152,plain,
% 179.86/179.67 (P101(f323(f323(f238(a860),f2(a860)),f323(a112,x131521)))),
% 179.86/179.67 inference(rename_variables,[],[3351])).
% 179.86/179.67 cnf(13153,plain,
% 179.86/179.67 (E(f323(f254(x131531,x131531),f255(x131531,x131532)),x131532)),
% 179.86/179.67 inference(rename_variables,[],[3228])).
% 179.86/179.67 cnf(13221,plain,
% 179.86/179.67 (~P101(f323(f323(f238(a1),f2(a1)),f2(a1)))),
% 179.86/179.67 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,12556,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,12542,12969,12975,12980,12984,12990,12993,13017,13125,13133,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,12644,13046,3327,3290,12634,3481,11849,4474,10388,10479,10926,11010,12715,12730,13066,2869,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2911,2914,2916,2919,2928,2933,2936,2937,2941,2947,2951,2953,2972,2973,2975,2976,2986,2988,2989,2991,2992,3001,3011,3013,3020,3023,3024,3025,3026,3034,3035,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3228,12845,13008,13132,13137,13153,3855,12904,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,3105,4476,3827,11356,3326,12525,3163,3130,3592,3125,3230,3949,3652,3113,3114,3087,3093,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,12362,4496,12329,3261,11692,11695,12938,13028,13042,13099,13103,13107,4535,10952,11035,11264,11267,3258,3376,3598,3368,3342,12590,3160,3161,10287,10592,4523,3434,3152,3084,3266,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,11164,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,3457,4487,11337,3575,3613,3790,3543,12828,12832,12836,12840,12850,3837,12192,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,12650,12709,12752,12755,12811,13045,13050,3725,11585,3254,3351,11707,12643,13152,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,12655,12674,12677,12701,12756,12919,12924,12945,12950,4541,11466,11499,11536,11565,12765,12769,3712,3482,12931,3484,12680,12683,12686,12689,12723,12726,13082,13086,13090,3485,3864,3446,13087,3447,13083,3298,3300,3273,4526,3159,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,12444,4027,3984,11866,12216,3926,10766,12050,12223,12372,12467,13098,3973,13102,3979,10964,12092,12165,12222,12269,12941,3980,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,12910,12974,12979,12999,13020,4547,10717,11117,12226,12987,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,12436,12702,12729,12803,12814,12819,12822,12825,12858,12871,12882,12930,12956,12959,13038,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,11969,12720,12862,12885,12920,12925,12946,12951,13069,3272,3347,12080,12785,12829,12833,12837,12841,12851,12855,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,12505,3429,10560,10825,10869,11175,11253,11423,11672,12324,12508,12903,13024,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,12515,12784,12797,12800,12892,13012,13031,13034,13079,13128,13131,3332,10589,10619,10628,11204,11773,12423,12437,12766,12770,12773,3371,13059,13120,3365,3794,3730,10266,11588,11620,12747,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,12962,3292,10622,10774,10845,11621,11778,11974,12185,12210,12794,13062,13151,3755,11723,12696,4107,3488,4532,3766,3802,4515,4518,4519,3245,3249,4517,4516,4520,4283,3773,3587,11581,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,12237,3881,11294,11647,11651,11714,12335,12343,12429,12714,12968,13016,3719,10885,10891,10913,11898,12027,12113,12397,3571,11015,11144,12139,12251,12261,12340,12392,12400,12512,12913,4061,3721,10625,10980,11150,11180,11191,12047,12339,12386,13004,3538,10543,10546,10631,10801,3540,4553,11582,4543,4548,12664,4554,10684,10783,11420,11452,12204,12213,12257,12454,4166,10759,12234,12260,4068,3754,12518,3698,3699,4551,10239,10242,10583,10586,11463,11652,12463,4552,11562,11657,3723,10549,10807,13049,4000,4573,4599,4647,4649,4681,4698,4705,4706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% 179.86/179.67 cnf(13223,plain,
% 179.86/179.67 (P101(f323(f323(f238(a1),f2(a1)),f323(f73(a1),f76(a1))))),
% 179.86/179.67 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,12556,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,12542,12969,12975,12980,12984,12990,12993,13017,13125,13133,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,12644,13046,3327,3290,12634,3481,11849,4474,10388,10479,10926,11010,12715,12730,13066,2869,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2911,2914,2916,2919,2928,2933,2936,2937,2941,2947,2951,2953,2972,2973,2975,2976,2986,2988,2989,2991,2992,3001,3011,3013,3020,3023,3024,3025,3026,3034,3035,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3228,12845,13008,13132,13137,13153,3855,12904,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,3105,4476,3827,11356,3326,12525,3163,3130,3592,3125,3230,3949,3652,3113,3114,3087,3093,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,12362,4496,12329,3261,11692,11695,12938,13028,13042,13099,13103,13107,4535,10952,11035,11264,11267,3258,3376,3598,3368,3342,12590,3160,3161,10287,10592,4523,3434,3152,3084,3266,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,11164,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,3457,4487,11337,3575,3613,3790,3543,12828,12832,12836,12840,12850,3837,12192,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,12650,12709,12752,12755,12811,13045,13050,3725,11585,3254,3351,11707,12643,13152,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,12655,12674,12677,12701,12756,12919,12924,12945,12950,4541,11466,11499,11536,11565,12765,12769,3712,3482,12931,3484,12680,12683,12686,12689,12723,12726,13082,13086,13090,3485,3864,3446,13087,3447,13083,3298,3300,3273,4526,3159,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,12444,4027,3984,11866,12216,3926,10766,12050,12223,12372,12467,13098,3973,13102,3979,10964,12092,12165,12222,12269,12941,3980,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,12910,12974,12979,12999,13020,4547,10717,11117,12226,12987,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,12436,12702,12729,12803,12814,12819,12822,12825,12858,12871,12882,12930,12956,12959,13038,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,11969,12720,12862,12885,12920,12925,12946,12951,13069,3272,3347,12080,12785,12829,12833,12837,12841,12851,12855,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,12505,3429,10560,10825,10869,11175,11253,11423,11672,12324,12508,12903,13024,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,12515,12784,12797,12800,12892,13012,13031,13034,13079,13128,13131,3332,10589,10619,10628,11204,11773,12423,12437,12766,12770,12773,3371,13059,13120,3365,3794,3730,10266,11588,11620,12747,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,12962,3292,10622,10774,10845,11621,11778,11974,12185,12210,12794,13062,13151,3755,11723,12696,4107,3488,4532,3766,3802,4515,4518,4519,3245,3249,4517,4516,4520,4283,3773,3587,11581,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,12237,3881,11294,11647,11651,11714,12335,12343,12429,12714,12968,13016,3719,10885,10891,10913,11898,12027,12113,12397,3571,11015,11144,12139,12251,12261,12340,12392,12400,12512,12913,4061,3721,10625,10980,11150,11180,11191,12047,12339,12386,13004,3538,10543,10546,10631,10801,3540,4553,11582,4543,4548,12664,4554,10684,10783,11420,11452,12204,12213,12257,12454,4166,10759,12234,12260,4068,3754,12518,3698,3699,4551,10239,10242,10583,10586,11463,11652,12463,4552,11562,11657,3723,10549,10807,13049,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580,7581,7613,7615,7616,7617,7622,7644,7653,7663,7668,7674,7676,7682,7694,7695,7697,7720,7726,7747,7814,7815,7816,7864,7872,7873,7898,7899,7916,7917,7974,7975,8004,8031,8041,8043,8052,8064,8094,8100,8107,8120,8139,8144,8166,8210,8240,8254,8273,8276,8306,8332,8391,8392,8395,8396,8460,8494,8495,8496,8497,8524,8556,8585,8593,8594,8636,8657,8703,8718,8765,8768,8783,8790,8826,8874,8875,8891,8892,9021,9027,9031,9052,9062,9085,9087,9090,9094,9096,9097,9108,9109,9129,9136,9149,9158,9195,9213,9265,9266,9273,9312,9335,9340,9375,9383,9386,9389,9390,9403,9420,9429,9443,9452,9453,9455,9457,9485,9609,9655,9656,9698,9743,9858,9915,10052,10065,10070,3,2606,2607,2608,2609,2611,2612,2613,2617,2618,2619,2623,2624,2625,2626,2635,2637,2642,2643,2644,2645,2646,2650,2651,2656,2657,2658,2659,2660,2663,2664,2665,2668,2670,2671,2673,2674,2681,2682,2685,2686,2687,2688,2690,2692,2711,2712,2714,2715,2719,2720,2721,2723,2725,2748,2749,2750,2766,2767,2768,2778,2779,2781,2783,2784,2791,2794,2795,2796,2804,2805,2826,2827,2846,2847,5204,5263,5361,5447,5448,5449,5525,5622,5653,5687,5703,5705,5711,5772,5773,5774,5775,5781,5814,5941,5975,5984,6007,6044,6079,6084,6224,6229,6264,6265,6285,6288,6290,6297,6298,6299,6300,6301,6302,6303,6304,6383,6450,6451,6537,6570,6571,6611,6612,6749,6764,6837,6838,6844,6864,6895,6897,6944,6967,6968,6986,6987,7022,7066,7067,7164,7225,7226,7227,7228,7242,7275,7328,7329,7338,7345,7346,7358,7390,7391,7392,7393,7535,7536,7538,7540,7546,7547,7755,7761,7762,7772,7811,7812,7893,7933,7987,8009,8010,8080,8181,8250,8251,8255,8291,8354,8355,8419,8437,8438,8439,8440,8589,8844,8845,8917,8931,8984,8985,9105,9140,9167,9196,9237,9427,9550,9692,9884,9940,9942,10075,6002,6366,6367,6453,6473,6474,6886,7102,8237,8509,8545,8759,8942,8943,9012,9013,9284,9285,9286,9287,9487,9763,9777,10061,10115,10116,6435,8345,8346,8810,8827,9764,10114,4641,4642,4643,4699,4707,4844,4860,4861,4888,4889,4920,4975,5035,5163,5199,5202,5207,5208,5234,5308,5329,5463,5530,5531,5532,5649,5650])).
% 179.86/179.67 cnf(13237,plain,
% 179.86/179.67 (~P101(f323(f323(f238(a860),f323(a112,f323(f323(f78(a860),x132371),x132372))),f323(a112,x132371)))),
% 179.86/179.67 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,12556,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,12542,12969,12975,12980,12984,12990,12993,13017,13125,13133,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,12644,13046,3327,3290,12634,3481,11849,4474,10388,10479,10926,11010,12715,12730,13066,2869,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2911,2914,2916,2919,2928,2933,2936,2937,2941,2947,2951,2953,2972,2973,2975,2976,2986,2988,2989,2991,2992,3001,3011,3013,3020,3023,3024,3025,3026,3034,3035,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3228,12845,13008,13132,13137,13153,3855,12904,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,3105,4476,3827,11356,3326,12525,3163,3130,3592,3125,3230,3949,3652,3113,3114,3087,3093,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,12362,4496,12329,3261,11692,11695,12938,13028,13042,13099,13103,13107,4535,10952,11035,11264,11267,3258,3376,3598,3368,3342,12590,3160,3161,10287,10592,4523,3434,3152,3084,3266,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,11164,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,3457,4487,11337,3575,3613,3790,3543,12828,12832,12836,12840,12850,3837,12192,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,12650,12709,12752,12755,12811,13045,13050,3725,11585,3254,3351,11707,12643,13152,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,12655,12674,12677,12701,12756,12919,12924,12945,12950,4541,11466,11499,11536,11565,12765,12769,3712,3482,12931,3484,12680,12683,12686,12689,12723,12726,13082,13086,13090,3485,3864,3446,13087,3447,13083,3298,3300,3273,4526,3159,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,12444,4027,3984,11866,12216,3926,10766,12050,12223,12372,12467,13098,3973,13102,3979,10964,12092,12165,12222,12269,12941,3980,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,12910,12974,12979,12999,13020,4547,10717,11117,12226,12987,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,12436,12702,12729,12803,12814,12819,12822,12825,12858,12871,12882,12930,12956,12959,13038,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,11969,12720,12862,12885,12920,12925,12946,12951,13069,3272,3347,12080,12785,12829,12833,12837,12841,12851,12855,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,12505,3429,10560,10825,10869,11175,11253,11423,11672,12324,12508,12903,13024,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,12515,12784,12797,12800,12892,13012,13031,13034,13079,13128,13131,3332,10589,10619,10628,11204,11773,12423,12437,12766,12770,12773,3371,13059,13120,3365,3794,3730,10266,11588,11620,12747,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,12962,3292,10622,10774,10845,11621,11778,11974,12185,12210,12794,13062,13151,3755,11723,12696,4107,3488,4532,3766,3802,4515,4518,4519,3245,3249,4517,4516,4520,4283,3773,3587,11581,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,12237,3881,11294,11647,11651,11714,12335,12343,12429,12714,12968,13016,3719,10885,10891,10913,11898,12027,12113,12397,3571,11015,11144,12139,12251,12261,12340,12392,12400,12512,12913,4061,3721,10625,10980,11150,11180,11191,12047,12339,12386,13004,3538,10543,10546,10631,10801,3540,4553,11582,4543,4548,12664,4554,10684,10783,11420,11452,12204,12213,12257,12454,4166,10759,12234,12260,4068,3754,12518,3698,3699,4551,10239,10242,10583,10586,11463,11652,12463,4552,11562,11657,3723,10549,10807,13049,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580,7581,7613,7615,7616,7617,7622,7644,7653,7663,7668,7674,7676,7682,7694,7695,7697,7720,7726,7747,7814,7815,7816,7864,7872,7873,7898,7899,7916,7917,7974,7975,8004,8031,8041,8043,8052,8064,8094,8100,8107,8120,8139,8144,8166,8210,8240,8254,8273,8276,8306,8332,8391,8392,8395,8396,8460,8494,8495,8496,8497,8524,8556,8585,8593,8594,8636,8657,8703,8718,8765,8768,8783,8790,8826,8874,8875,8891,8892,9021,9027,9031,9052,9062,9085,9087,9090,9094,9096,9097,9108,9109,9129,9136,9149,9158,9195,9213,9265,9266,9273,9312,9335,9340,9375,9383,9386,9389,9390,9403,9420,9429,9443,9452,9453,9455,9457,9485,9609,9655,9656,9698,9743,9858,9915,10052,10065,10070,3,2606,2607,2608,2609,2611,2612,2613,2617,2618,2619,2623,2624,2625,2626,2635,2637,2642,2643,2644,2645,2646,2650,2651,2656,2657,2658,2659,2660,2663,2664,2665,2668,2670,2671,2673,2674,2681,2682,2685,2686,2687,2688,2690,2692,2711,2712,2714,2715,2719,2720,2721,2723,2725,2748,2749,2750,2766,2767,2768,2778,2779,2781,2783,2784,2791,2794,2795,2796,2804,2805,2826,2827,2846,2847,5204,5263,5361,5447,5448,5449,5525,5622,5653,5687,5703,5705,5711,5772,5773,5774,5775,5781,5814,5941,5975,5984,6007,6044,6079,6084,6224,6229,6264,6265,6285,6288,6290,6297,6298,6299,6300,6301,6302,6303,6304,6383,6450,6451,6537,6570,6571,6611,6612,6749,6764,6837,6838,6844,6864,6895,6897,6944,6967,6968,6986,6987,7022,7066,7067,7164,7225,7226,7227,7228,7242,7275,7328,7329,7338,7345,7346,7358,7390,7391,7392,7393,7535,7536,7538,7540,7546,7547,7755,7761,7762,7772,7811,7812,7893,7933,7987,8009,8010,8080,8181,8250,8251,8255,8291,8354,8355,8419,8437,8438,8439,8440,8589,8844,8845,8917,8931,8984,8985,9105,9140,9167,9196,9237,9427,9550,9692,9884,9940,9942,10075,6002,6366,6367,6453,6473,6474,6886,7102,8237,8509,8545,8759,8942,8943,9012,9013,9284,9285,9286,9287,9487,9763,9777,10061,10115,10116,6435,8345,8346,8810,8827,9764,10114,4641,4642,4643,4699,4707,4844,4860,4861,4888,4889,4920,4975,5035,5163,5199,5202,5207,5208,5234,5308,5329,5463,5530,5531,5532,5649,5650,5676,5680,5738,5740,5749,5755,5827])).
% 179.86/179.67 cnf(13245,plain,
% 179.86/179.67 (~P101(f323(f59(x132451),f37(f867(x132451,a855),f246(f867(f867(x132451,a855),a855)))))),
% 179.86/179.67 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,12556,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,12542,12969,12975,12980,12984,12990,12993,13017,13125,13133,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,12644,13046,3327,3290,12634,3481,11849,4474,10388,10479,10926,11010,12715,12730,13066,2869,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2911,2914,2916,2919,2928,2933,2936,2937,2941,2947,2951,2953,2972,2973,2975,2976,2986,2988,2989,2991,2992,3001,3011,3013,3020,3023,3024,3025,3026,3034,3035,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3228,12845,13008,13132,13137,13153,3855,12904,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,3105,4476,3827,11356,3326,12525,3163,3130,3592,3125,3230,3949,3652,3113,3114,3087,3093,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,12362,4496,12329,3261,11692,11695,12938,13028,13042,13099,13103,13107,4535,10952,11035,11264,11267,3258,3376,3598,3368,3342,12590,3160,3161,10287,10592,4523,3434,3152,3084,3266,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,11164,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,3457,4487,11337,3575,3613,3790,3543,12828,12832,12836,12840,12850,3837,12192,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,12650,12709,12752,12755,12811,13045,13050,3725,11585,3254,3351,11707,12643,13152,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,12655,12674,12677,12701,12756,12919,12924,12945,12950,4541,11466,11499,11536,11565,12765,12769,3712,3482,12931,3484,12680,12683,12686,12689,12723,12726,13082,13086,13090,3485,3864,3446,13087,3447,13083,3298,3300,3273,4526,3159,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,12444,4027,3984,11866,12216,3926,10766,12050,12223,12372,12467,13098,3973,13102,3979,10964,12092,12165,12222,12269,12941,3980,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,12910,12974,12979,12999,13020,4547,10717,11117,12226,12987,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,12436,12702,12729,12803,12814,12819,12822,12825,12858,12871,12882,12930,12956,12959,13038,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,11969,12720,12862,12885,12920,12925,12946,12951,13069,3272,3347,12080,12785,12829,12833,12837,12841,12851,12855,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,12505,3429,10560,10825,10869,11175,11253,11423,11672,12324,12508,12903,13024,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,12515,12784,12797,12800,12892,13012,13031,13034,13079,13128,13131,3332,10589,10619,10628,11204,11773,12423,12437,12766,12770,12773,3371,13059,13120,3365,3794,3730,10266,11588,11620,12747,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,12962,3292,10622,10774,10845,11621,11778,11974,12185,12210,12794,13062,13151,3755,11723,12696,4107,3488,4532,3766,3802,4515,4518,4519,3245,3249,4517,4516,4520,4283,3773,3587,11581,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,12237,3881,11294,11647,11651,11714,12335,12343,12429,12714,12968,13016,3719,10885,10891,10913,11898,12027,12113,12397,3571,11015,11144,12139,12251,12261,12340,12392,12400,12512,12913,4061,3721,10625,10980,11150,11180,11191,12047,12339,12386,13004,3538,10543,10546,10631,10801,3540,4553,11582,4543,4548,12664,4554,10684,10783,11420,11452,12204,12213,12257,12454,4166,10759,12234,12260,4068,3754,12518,3698,3699,4551,10239,10242,10583,10586,11463,11652,12463,4552,11562,11657,3723,10549,10807,13049,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580,7581,7613,7615,7616,7617,7622,7644,7653,7663,7668,7674,7676,7682,7694,7695,7697,7720,7726,7747,7814,7815,7816,7864,7872,7873,7898,7899,7916,7917,7974,7975,8004,8031,8041,8043,8052,8064,8094,8100,8107,8120,8139,8144,8166,8210,8240,8254,8273,8276,8306,8332,8391,8392,8395,8396,8460,8494,8495,8496,8497,8524,8556,8585,8593,8594,8636,8657,8703,8718,8765,8768,8783,8790,8826,8874,8875,8891,8892,9021,9027,9031,9052,9062,9085,9087,9090,9094,9096,9097,9108,9109,9129,9136,9149,9158,9195,9213,9265,9266,9273,9312,9335,9340,9375,9383,9386,9389,9390,9403,9420,9429,9443,9452,9453,9455,9457,9485,9609,9655,9656,9698,9743,9858,9915,10052,10065,10070,3,2606,2607,2608,2609,2611,2612,2613,2617,2618,2619,2623,2624,2625,2626,2635,2637,2642,2643,2644,2645,2646,2650,2651,2656,2657,2658,2659,2660,2663,2664,2665,2668,2670,2671,2673,2674,2681,2682,2685,2686,2687,2688,2690,2692,2711,2712,2714,2715,2719,2720,2721,2723,2725,2748,2749,2750,2766,2767,2768,2778,2779,2781,2783,2784,2791,2794,2795,2796,2804,2805,2826,2827,2846,2847,5204,5263,5361,5447,5448,5449,5525,5622,5653,5687,5703,5705,5711,5772,5773,5774,5775,5781,5814,5941,5975,5984,6007,6044,6079,6084,6224,6229,6264,6265,6285,6288,6290,6297,6298,6299,6300,6301,6302,6303,6304,6383,6450,6451,6537,6570,6571,6611,6612,6749,6764,6837,6838,6844,6864,6895,6897,6944,6967,6968,6986,6987,7022,7066,7067,7164,7225,7226,7227,7228,7242,7275,7328,7329,7338,7345,7346,7358,7390,7391,7392,7393,7535,7536,7538,7540,7546,7547,7755,7761,7762,7772,7811,7812,7893,7933,7987,8009,8010,8080,8181,8250,8251,8255,8291,8354,8355,8419,8437,8438,8439,8440,8589,8844,8845,8917,8931,8984,8985,9105,9140,9167,9196,9237,9427,9550,9692,9884,9940,9942,10075,6002,6366,6367,6453,6473,6474,6886,7102,8237,8509,8545,8759,8942,8943,9012,9013,9284,9285,9286,9287,9487,9763,9777,10061,10115,10116,6435,8345,8346,8810,8827,9764,10114,4641,4642,4643,4699,4707,4844,4860,4861,4888,4889,4920,4975,5035,5163,5199,5202,5207,5208,5234,5308,5329,5463,5530,5531,5532,5649,5650,5676,5680,5738,5740,5749,5755,5827,5903,6025,6051,6211])).
% 179.86/179.67 cnf(13257,plain,
% 179.86/179.67 (~P101(f323(f323(f238(a860),f2(a860)),f31(x132571,f2(a860),x132572,x132573,x132574,x132575,x132576,x132577,x132578,a24)))),
% 179.86/179.67 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,12556,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,12542,12969,12975,12980,12984,12990,12993,13017,13125,13133,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,12644,13046,3327,3290,12634,3481,11849,4474,10388,10479,10926,11010,12715,12730,13066,2869,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2911,2914,2916,2919,2928,2933,2936,2937,2941,2947,2951,2953,2972,2973,2975,2976,2986,2988,2989,2991,2992,3001,3011,3013,3020,3023,3024,3025,3026,3034,3035,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3228,12845,13008,13132,13137,13153,3855,12904,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,3105,4476,3827,11356,3326,12525,3163,3130,3592,3125,3230,3949,3652,3113,3114,3087,3093,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,12362,4496,12329,3261,11692,11695,12938,13028,13042,13099,13103,13107,4535,10952,11035,11264,11267,3258,3376,3598,3368,3342,12590,3160,3161,10287,10592,4523,3434,3152,3084,3266,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,4560,11112,11164,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,3457,4487,11337,3575,3613,3790,3543,12828,12832,12836,12840,12850,3837,12192,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,12650,12709,12752,12755,12811,13045,13050,3725,11585,3254,3351,11707,12643,13152,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,12655,12674,12677,12701,12756,12919,12924,12945,12950,4541,11466,11499,11536,11565,12765,12769,3712,3482,12931,3484,12680,12683,12686,12689,12723,12726,13082,13086,13090,3485,3864,3446,13087,3447,13083,3298,3300,3273,4526,3159,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,12444,4027,3984,11866,12216,3926,10766,12050,12223,12372,12467,13098,3973,13102,3979,10964,12092,12165,12222,12269,12941,3980,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,12910,12974,12979,12999,13020,4547,10717,11117,12226,12987,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,12436,12702,12729,12803,12814,12819,12822,12825,12858,12871,12882,12930,12956,12959,13038,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,11969,12720,12862,12885,12920,12925,12946,12951,13069,3272,3347,12080,12785,12829,12833,12837,12841,12851,12855,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,12505,3429,10560,10825,10869,11175,11253,11423,11672,12324,12508,12903,13024,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,12515,12784,12797,12800,12892,13012,13031,13034,13079,13128,13131,3332,10589,10619,10628,11204,11773,12423,12437,12766,12770,12773,3371,13059,13120,3365,3794,3730,10266,11588,11620,12747,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,12962,3292,10622,10774,10845,11621,11778,11974,12185,12210,12794,13062,13151,3755,11723,12696,4107,3488,4532,3766,3802,4515,4518,4519,3245,3249,4517,4516,4520,4283,3773,3587,11581,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,12237,3881,11294,11647,11651,11714,12335,12343,12429,12714,12968,13016,3719,10885,10891,10913,11898,12027,12113,12397,3571,11015,11144,12139,12251,12261,12340,12392,12400,12512,12913,4061,3721,10625,10980,11150,11180,11191,12047,12339,12386,13004,3538,10543,10546,10631,10801,3540,4553,11582,4543,4548,12664,4554,10684,10783,11420,11452,12204,12213,12257,12454,4166,10759,12234,12260,4068,3754,12518,3698,3699,4551,10239,10242,10583,10586,11463,11652,12463,4552,11562,11657,3723,10549,10807,13049,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580,7581,7613,7615,7616,7617,7622,7644,7653,7663,7668,7674,7676,7682,7694,7695,7697,7720,7726,7747,7814,7815,7816,7864,7872,7873,7898,7899,7916,7917,7974,7975,8004,8031,8041,8043,8052,8064,8094,8100,8107,8120,8139,8144,8166,8210,8240,8254,8273,8276,8306,8332,8391,8392,8395,8396,8460,8494,8495,8496,8497,8524,8556,8585,8593,8594,8636,8657,8703,8718,8765,8768,8783,8790,8826,8874,8875,8891,8892,9021,9027,9031,9052,9062,9085,9087,9090,9094,9096,9097,9108,9109,9129,9136,9149,9158,9195,9213,9265,9266,9273,9312,9335,9340,9375,9383,9386,9389,9390,9403,9420,9429,9443,9452,9453,9455,9457,9485,9609,9655,9656,9698,9743,9858,9915,10052,10065,10070,3,2606,2607,2608,2609,2611,2612,2613,2617,2618,2619,2623,2624,2625,2626,2635,2637,2642,2643,2644,2645,2646,2650,2651,2656,2657,2658,2659,2660,2663,2664,2665,2668,2670,2671,2673,2674,2681,2682,2685,2686,2687,2688,2690,2692,2711,2712,2714,2715,2719,2720,2721,2723,2725,2748,2749,2750,2766,2767,2768,2778,2779,2781,2783,2784,2791,2794,2795,2796,2804,2805,2826,2827,2846,2847,5204,5263,5361,5447,5448,5449,5525,5622,5653,5687,5703,5705,5711,5772,5773,5774,5775,5781,5814,5941,5975,5984,6007,6044,6079,6084,6224,6229,6264,6265,6285,6288,6290,6297,6298,6299,6300,6301,6302,6303,6304,6383,6450,6451,6537,6570,6571,6611,6612,6749,6764,6837,6838,6844,6864,6895,6897,6944,6967,6968,6986,6987,7022,7066,7067,7164,7225,7226,7227,7228,7242,7275,7328,7329,7338,7345,7346,7358,7390,7391,7392,7393,7535,7536,7538,7540,7546,7547,7755,7761,7762,7772,7811,7812,7893,7933,7987,8009,8010,8080,8181,8250,8251,8255,8291,8354,8355,8419,8437,8438,8439,8440,8589,8844,8845,8917,8931,8984,8985,9105,9140,9167,9196,9237,9427,9550,9692,9884,9940,9942,10075,6002,6366,6367,6453,6473,6474,6886,7102,8237,8509,8545,8759,8942,8943,9012,9013,9284,9285,9286,9287,9487,9763,9777,10061,10115,10116,6435,8345,8346,8810,8827,9764,10114,4641,4642,4643,4699,4707,4844,4860,4861,4888,4889,4920,4975,5035,5163,5199,5202,5207,5208,5234,5308,5329,5463,5530,5531,5532,5649,5650,5676,5680,5738,5740,5749,5755,5827,5903,6025,6051,6211,6329,6483,6684,6685,6898,6939])).
% 179.86/179.67 cnf(13297,plain,
% 179.86/179.67 (~P101(f323(f323(f237(a860),f323(a112,f323(f135(a860,a860,f78(a860),f2(a860)),f163(a860,f323(a112,f2(a860)),f323(a112,f2(a860)))))),f323(a112,f2(a860))))),
% 179.86/179.67 inference(scs_inference,[],[4565,3941,12419,12441,12552,12554,12556,3512,11030,12095,12195,12198,12290,12332,12336,12344,12413,12540,12542,12969,12975,12980,12984,12990,12993,13017,13125,13133,3521,12159,12620,12623,3522,12229,3238,12598,12600,3239,12608,3204,12493,4497,4498,11669,4230,12627,12630,3242,12604,3083,3139,12531,4478,4448,10153,10159,10173,10229,10232,10322,10325,10616,10636,10897,10900,11303,11306,11321,11324,11368,11375,11378,11381,11384,11394,11431,11447,11477,11480,11491,11496,11502,11594,11597,11600,11603,11607,11617,11711,11746,12065,12266,12473,12521,12523,12548,12550,12562,12575,12577,12579,12581,12583,12585,12621,3573,4462,10156,10166,10180,10191,10194,10295,10298,10301,10404,10515,10820,11002,11005,11022,11025,11221,11309,11316,11330,11387,11390,11436,11505,11552,11568,11877,11902,11914,11943,11949,12044,12155,12162,12325,12383,12644,13046,13054,3327,3290,12634,3481,11849,4474,10388,10479,10926,11010,12715,12730,13066,2869,2870,2874,2875,2881,2882,2885,2886,2887,2888,2890,2891,2894,2895,2896,2903,2904,2908,2909,2910,2911,2914,2916,2919,2928,2933,2936,2937,2941,2947,2951,2953,2972,2973,2975,2976,2986,2988,2989,2991,2992,3001,3011,3013,3020,3023,3024,3025,3026,3034,3035,3046,4459,3062,3138,4460,3610,3842,3252,3312,3225,3228,12845,13008,13132,13137,13153,3855,12904,3199,12357,12361,12365,3213,3732,3338,12416,12496,3976,3104,3105,4476,3827,11356,3326,12525,3163,3640,3130,3592,3125,3230,3949,3652,3113,3114,3087,3093,3745,3145,3328,10769,10894,12156,12373,3197,3198,3375,4546,10358,3914,4489,10220,10385,11218,12317,12358,12362,4496,12329,3261,11692,11695,12938,13028,13042,13099,13103,13107,4535,10952,11035,11264,11267,3258,3376,3598,3368,3342,12590,3160,3161,10287,10592,4523,3434,3152,3084,3266,3182,11346,4063,12347,12485,3916,10958,11101,11153,12301,12307,12430,12433,12460,4558,10872,11106,11212,11234,11272,11278,12245,4559,10991,11109,11215,11275,4560,11112,11164,4561,11167,4562,3181,3473,12201,12242,12328,3636,4347,4348,3457,4487,11337,3575,3613,3790,3543,12828,12832,12836,12840,12850,3837,12192,3460,3714,3339,10306,10424,10493,10554,10557,10595,10693,10942,11789,11873,11936,12015,12056,12133,12136,12464,12650,12709,12752,12755,12811,13045,13050,3725,11585,3254,3351,11707,12643,13152,3537,4529,10197,10200,10226,10701,10714,10830,11256,11349,11761,11766,11788,11991,11994,12077,12086,12248,12351,12655,12674,12677,12701,12756,12919,12924,12945,12950,4541,11466,11499,11536,11565,12765,12769,3712,3482,12931,3484,12680,12683,12686,12689,12723,12726,13082,13086,13090,13094,3485,3864,3446,13087,3447,13083,3298,3300,3273,4526,3159,4484,3663,4200,3985,3466,4542,4057,11229,3597,3311,11717,11720,12166,12270,12444,4027,3984,11866,12216,3926,10766,12050,12223,12372,12467,13098,3973,13102,3979,10964,12092,12165,12222,12269,12941,3980,3637,11876,12022,12100,12146,4016,3654,10961,11040,11127,11186,12043,12114,12378,12440,12457,12470,12910,12974,12979,12999,13020,4547,10717,11117,12226,12987,3270,10315,10411,10540,10602,10673,10720,10723,10756,10777,10814,10852,10888,11446,11663,11710,11846,11901,11917,11920,11923,11926,12107,12121,12124,12127,12130,12209,12273,12389,12436,12702,12729,12803,12814,12819,12822,12825,12858,12871,12882,12930,12956,12959,13038,3271,10344,10399,10607,10696,10817,11439,11508,11745,11749,11758,11852,11863,11882,11887,11929,11952,11969,12720,12862,12885,12920,12925,12946,12951,13069,3272,3347,12080,12785,12829,12833,12837,12841,12851,12855,4525,10263,10353,10464,10488,10738,10780,10790,11515,11616,11638,11641,11644,11660,11820,11823,11826,11829,11913,11932,11935,11948,12003,12006,12009,12012,12087,12177,12180,12276,12279,12350,12382,12422,12505,3429,10560,10825,10869,11175,11253,11423,11672,12324,12508,12903,13024,4537,10747,10861,10879,10882,10955,11056,11064,11080,11120,11138,11147,11183,11224,11244,11247,11250,11281,11288,11291,11689,11726,11997,12000,12034,12081,12110,12254,12298,12304,12401,12404,12426,12484,12490,12499,12515,12784,12797,12800,12892,13012,13031,13034,13079,13128,13131,3332,10589,10619,10628,11204,11773,12423,12437,12766,12770,12773,3371,13059,13120,3365,3794,3730,10266,11588,11620,12747,4534,10217,10577,10580,11059,11077,11551,11606,11648,11673,11779,11808,11811,11814,11817,12076,12962,3292,10622,10774,10845,11621,11778,11974,12185,12210,12794,13062,13151,3755,11723,12696,4107,3488,4532,3766,3802,4515,4518,4519,3245,3249,4517,4516,4520,4283,3773,3587,11581,4206,4549,10185,10188,10445,10496,10499,10504,10929,11417,11676,11782,4556,11141,11261,11297,3993,12237,3881,11294,11647,11651,11714,12335,12343,12429,12714,12968,13016,3719,10885,10891,10913,11898,12027,12113,12397,3571,11015,11144,12139,12251,12261,12340,12392,12400,12512,12913,4061,3721,10625,10980,11150,11180,11191,12047,12339,12386,13004,3538,10543,10546,10631,10801,3540,4553,11582,4543,4548,12664,4554,10684,10783,11420,11452,12204,12213,12257,12454,4166,10759,12234,12260,4068,3754,12518,3698,3699,4551,10239,10242,10583,10586,11463,11652,12463,4552,11562,11657,3723,10549,10807,13049,4000,4573,4599,4647,4649,4681,4698,4705,4706,4742,4747,4777,4783,4866,4890,4891,4906,4928,4953,4954,4976,4977,4990,4994,5017,5023,5039,5042,5043,5044,5049,5050,5072,5097,5098,5108,5113,5119,5155,5156,5164,5174,5178,5180,5190,5192,5198,5201,5215,5222,5225,5226,5227,5231,5266,5279,5287,5289,5290,5294,5295,5296,5304,5307,5311,5312,5313,5320,5324,5325,5326,5334,5338,5339,5340,5345,5358,5367,5379,5381,5389,5390,5394,5398,5423,5429,5439,5440,5455,5467,5489,5495,5512,5513,5516,5535,5543,5544,5549,5550,5560,5562,5574,5578,5587,5588,5590,5605,5610,5620,5621,5633,5640,5654,5658,5661,5667,5668,5669,5672,5677,5713,5714,5717,5719,5722,5723,5724,5726,5728,5730,5735,5742,5757,5771,5776,5777,5790,5791,5796,5800,5802,5807,5848,5860,5869,5873,5882,5886,5887,5895,5908,5914,5932,5935,5944,5969,5983,6008,6028,6029,6032,6046,6048,6050,6052,6065,6066,6069,6071,6074,6075,6087,6093,6094,6095,6097,6099,6136,6137,6144,6150,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6222,6225,6233,6240,6241,6242,6247,6269,6270,6271,6273,6279,6284,6318,6319,6321,6322,6323,6325,6326,6327,6328,6336,6368,6369,6370,6379,6399,6400,6420,6422,6433,6434,6440,6470,6472,6486,6490,6524,6526,6527,6580,6604,6646,6666,6675,6676,6677,6678,6696,6697,6703,6716,6719,6721,6723,6724,6725,6727,6741,6752,6754,6755,6768,6772,6823,6834,6836,6856,6857,6891,6903,6934,6966,7020,7048,7103,7124,7133,7136,7191,7199,7257,7259,7274,7284,7285,7286,7302,7308,7310,7359,7369,7372,7388,7438,7440,7443,7486,7487,7505,7572,7591,7614,7637,7652,7666,7677,7686,7687,7714,7717,7719,7728,7764,7775,7800,7861,7896,7928,7967,7983,7985,8001,8002,8073,8125,8143,8167,8173,8188,8213,8214,8252,8253,8270,8313,8315,8317,8324,8338,8342,8358,8380,8388,8390,8401,8406,8410,8430,8444,8445,8462,8463,8468,8469,8470,8471,8472,8490,8491,8492,8501,8514,8517,8529,8534,8536,8538,8539,8547,8553,8561,8564,8581,8582,8591,8592,8600,8620,8633,8637,8658,8680,8681,8684,8685,8691,8700,8701,8724,8736,8746,8747,8748,8749,8751,8774,8775,8786,8829,8835,8840,8842,8853,8858,8860,8862,8863,8868,8878,8950,8981,8982,8983,8998,9016,9024,9025,9054,9055,9098,9122,9159,9172,9173,9174,9183,9209,9225,9228,9232,9252,9253,9281,9343,9379,9380,9381,9404,9405,9424,9444,9450,9463,9486,9508,9517,9518,9519,9520,9535,9537,9542,9574,9575,9581,9582,9626,9627,9660,9669,9679,9681,9682,9691,9705,9708,9736,9769,9771,9775,9831,9872,9873,9875,9885,9886,9906,9911,9952,10002,10073,10074,10127,10141,2,8,9,4586,4587,4605,4636,4637,4639,4665,4673,4674,4685,4734,4736,4768,4782,4811,4907,4908,4922,4941,4997,4998,5001,5002,5004,5006,5007,5016,5019,5020,5028,5040,5041,5047,5067,5068,5085,5090,5091,5092,5093,5096,5104,5107,5114,5170,5176,5177,5184,5212,5223,5229,5245,5264,5265,5272,5273,5274,5283,5293,5300,5302,5303,5309,5316,5317,5330,5331,5332,5333,5335,5336,5341,5342,5343,5344,5375,5376,5377,5385,5386,5387,5388,5431,5436,5438,5474,5476,5477,5479,5480,5482,5483,5485,5494,5499,5501,5502,5503,5504,5505,5506,5514,5524,5527,5538,5554,5555,5558,5568,5570,5571,5572,5597,5607,5623,5624,5634,5635,5637,5639,5644,5679,5684,5686,5744,5778,5779,5783,5789,5792,5793,5794,5795,5801,5812,5813,5815,5816,5824,5845,5874,5890,5893,5894,5896,5905,5922,5926,5929,5930,5931,5946,5956,5957,5985,5986,5990,6010,6013,6017,6036,6041,6042,6067,6070,6078,6086,6092,6096,6103,6104,6105,6106,6139,6155,6208,6243,6245,6266,6267,6272,6276,6277,6280,6286,6295,6310,6330,6331,6334,6337,6346,6361,6382,6387,6389,6404,6405,6408,6409,6411,6413,6414,6415,6417,6419,6421,6426,6427,6429,6430,6436,6438,6480,6485,6500,6502,6503,6504,6538,6543,6545,6550,6551,6559,6563,6575,6599,6600,6602,6603,6614,6620,6637,6640,6659,6691,6692,6693,6698,6712,6731,6733,6735,6737,6742,6748,6750,6765,6770,6773,6809,6810,6811,6825,6826,6828,6829,6847,6849,6863,6889,6911,6922,6924,6926,6928,6929,6930,6963,6964,6969,6970,6977,6978,6980,6982,7001,7010,7011,7023,7033,7072,7082,7086,7093,7104,7110,7112,7118,7126,7127,7140,7157,7175,7177,7194,7243,7244,7245,7247,7249,7253,7258,7281,7323,7355,7370,7387,7419,7422,7447,7471,7488,7491,7492,7502,7521,7523,7525,7527,7528,7529,7554,7580,7581,7613,7615,7616,7617,7622,7644,7653,7663,7668,7674,7676,7682,7694,7695,7697,7720,7726,7747,7814,7815,7816,7864,7872,7873,7898,7899,7916,7917,7974,7975,8004,8031,8041,8043,8052,8064,8094,8100,8107,8120,8139,8144,8166,8210,8240,8254,8273,8276,8306,8332,8391,8392,8395,8396,8460,8494,8495,8496,8497,8524,8556,8585,8593,8594,8636,8657,8703,8718,8765,8768,8783,8790,8826,8874,8875,8891,8892,9021,9027,9031,9052,9062,9085,9087,9090,9094,9096,9097,9108,9109,9129,9136,9149,9158,9195,9213,9265,9266,9273,9312,9335,9340,9375,9383,9386,9389,9390,9403,9420,9429,9443,9452,9453,9455,9457,9485,9609,9655,9656,9698,9743,9858,9915,10052,10065,10070,3,2606,2607,2608,2609,2611,2612,2613,2617,2618,2619,2623,2624,2625,2626,2635,2637,2642,2643,2644,2645,2646,2650,2651,2656,2657,2658,2659,2660,2663,2664,2665,2668,2670,2671,2673,2674,2681,2682,2685,2686,2687,2688,2690,2692,2711,2712,2714,2715,2719,2720,2721,2723,2725,2748,2749,2750,2766,2767,2768,2778,2779,2781,2783,2784,2791,2794,2795,2796,2804,2805,2826,2827,2846,2847,5204,5263,5361,5447,5448,5449,5525,5622,5653,5687,5703,5705,5711,5772,5773,5774,5775,5781,5814,5941,5975,5984,6007,6044,6079,6084,6224,6229,6264,6265,6285,6288,6290,6297,6298,6299,6300,6301,6302,6303,6304,6383,6450,6451,6537,6570,6571,6611,6612,6749,6764,6837,6838,6844,6864,6895,6897,6944,6967,6968,6986,6987,7022,7066,7067,7164,7225,7226,7227,7228,7242,7275,7328,7329,7338,7345,7346,7358,7390,7391,7392,7393,7535,7536,7538,7540,7546,7547,7755,7761,7762,7772,7811,7812,7893,7933,7987,8009,8010,8080,8181,8250,8251,8255,8291,8354,8355,8419,8437,8438,8439,8440,8589,8844,8845,8917,8931,8984,8985,9105,9140,9167,9196,9237,9427,9550,9692,9884,9940,9942,10075,6002,6366,6367,6453,6473,6474,6886,7102,8237,8509,8545,8759,8942,8943,9012,9013,9284,9285,9286,9287,9487,9763,9777,10061,10115,10116,6435,8345,8346,8810,8827,9764,10114,4641,4642,4643,4699,4707,4844,4860,4861,4888,4889,4920,4975,5035,5163,5199,5202,5207,5208,5234,5308,5329,5463,5530,5531,5532,5649,5650,5676,5680,5738,5740,5749,5755,5827,5903,6025,6051,6211,6329,6483,6684,6685,6898,6939,6953,7108,7330,7733,7735,7829,7984,7990,8683,8766,8914,9249,4874,4921,5056,5060,5642,5877])).
% 179.86/179.67 cnf(13404,plain,
% 179.86/179.67 (~P101(f323(f323(f325(f866(x134041,x134041)),x134042),f255(x134041,f188(f867(x134041,a855)))))),
% 179.86/179.67 inference(rename_variables,[],[10878])).
% 179.86/179.67 cnf(13414,plain,
% 179.86/179.67 (P101(f323(f323(f237(a1),x134141),x134141))),
% 179.86/179.67 inference(rename_variables,[],[3271])).
% 179.86/179.67 cnf(13417,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),f2(a860)),x134171))),
% 179.86/179.67 inference(rename_variables,[],[3292])).
% 179.86/179.67 cnf(13437,plain,
% 179.86/179.67 (~P101(f323(f323(f325(a860),x134371),f323(f244(a860),f2(a860))))),
% 179.86/179.67 inference(rename_variables,[],[11742])).
% 179.86/179.67 cnf(13440,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),x134401),f323(f323(f78(a860),x134401),x134402)))),
% 179.86/179.67 inference(rename_variables,[],[3540])).
% 179.86/179.67 cnf(13443,plain,
% 179.86/179.67 (~P101(f323(f323(f188(f867(x134431,f867(x134432,a855))),x134433),x134434))),
% 179.86/179.67 inference(rename_variables,[],[4554])).
% 179.86/179.67 cnf(13452,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x134521,a855)),f323(f166(x134521),f164(x134521,x134522,x134523))),f323(f166(x134521),x134523)))),
% 179.86/179.67 inference(rename_variables,[],[3979])).
% 179.86/179.67 cnf(13455,plain,
% 179.86/179.67 (~P101(f323(f323(f325(f866(x134551,x134551)),x134552),f255(x134551,f188(f867(x134551,a855)))))),
% 179.86/179.67 inference(rename_variables,[],[10878])).
% 179.86/179.67 cnf(13460,plain,
% 179.86/179.67 (~P101(f323(f323(f325(x134601),x134602),f188(f867(x134601,a855))))),
% 179.86/179.67 inference(rename_variables,[],[4537])).
% 179.86/179.67 cnf(13470,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x134701,a855)),x134702),x134702))),
% 179.86/179.67 inference(rename_variables,[],[3571])).
% 179.86/179.67 cnf(13473,plain,
% 179.86/179.67 (~P101(f323(f323(f237(a860),f323(f323(f79(a860),f323(a112,x134731)),f323(a112,x134731))),x134731))),
% 179.86/179.67 inference(rename_variables,[],[10630])).
% 179.86/179.67 cnf(13487,plain,
% 179.86/179.67 (~E(f323(f323(f101(a860),f323(a112,x134871)),x134871),f323(a112,x134871))),
% 179.86/179.67 inference(rename_variables,[],[11484])).
% 179.86/179.67 cnf(13516,plain,
% 179.86/179.67 (~P101(f323(f323(f325(x135161),x135162),f188(f867(x135161,a855))))),
% 179.86/179.67 inference(rename_variables,[],[4537])).
% 179.86/179.67 cnf(13524,plain,
% 179.86/179.67 (~P101(f323(f323(f237(a860),f323(f323(f79(a860),f323(a112,x135241)),f323(a112,x135241))),x135241))),
% 179.86/179.67 inference(rename_variables,[],[10630])).
% 179.86/179.67 cnf(13527,plain,
% 179.86/179.67 (~P101(f323(f323(f325(a860),x135271),f323(f244(a860),f2(a860))))),
% 179.86/179.67 inference(rename_variables,[],[11742])).
% 179.86/179.67 cnf(13536,plain,
% 179.86/179.67 (~P101(f323(f323(f325(a860),x135361),f323(f244(a860),f2(a860))))),
% 179.86/179.67 inference(rename_variables,[],[11742])).
% 179.86/179.67 cnf(13546,plain,
% 179.86/179.67 (P101(f323(f323(f237(a860),x135461),f323(f323(f78(a860),x135461),x135462)))),
% 179.86/179.67 inference(rename_variables,[],[3540])).
% 179.86/179.67 cnf(13549,plain,
% 179.86/179.67 (E(f323(f254(x135491,x135491),f255(x135491,x135492)),x135492)),
% 179.86/179.67 inference(rename_variables,[],[3228])).
% 179.86/179.67 cnf(13552,plain,
% 179.86/179.67 (~E(f323(f323(f144(x135521),x135522),x135523),x135523)),
% 179.86/179.67 inference(rename_variables,[],[4489])).
% 179.86/179.67 cnf(13559,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x135591,a855)),f323(f166(x135591),f164(x135591,x135592,x135593))),f323(f166(x135591),x135593)))),
% 179.86/179.67 inference(rename_variables,[],[3979])).
% 179.86/179.67 cnf(13567,plain,
% 179.86/179.67 (~E(f323(f323(f144(x135671),x135672),x135673),x135673)),
% 179.86/179.67 inference(rename_variables,[],[4489])).
% 179.86/179.67 cnf(13581,plain,
% 179.86/179.67 (~P101(f323(f323(f188(f867(x135811,f867(x135812,a855))),x135813),x135814))),
% 179.86/179.67 inference(rename_variables,[],[4554])).
% 179.86/179.67 cnf(13591,plain,
% 179.86/179.67 (P101(f323(f323(f238(a1),f323(f323(f22(a1),x135911),f76(a1))),x135911))),
% 179.86/179.67 inference(rename_variables,[],[10695])).
% 179.86/179.67 cnf(13611,plain,
% 179.86/179.67 (~E(f323(f323(f144(x136111),x136112),x136113),x136113)),
% 179.86/179.67 inference(rename_variables,[],[4489])).
% 179.86/179.67 cnf(13614,plain,
% 179.86/179.67 (~P101(f323(f323(f325(f866(x136141,x136141)),x136142),f255(x136141,f188(f867(x136141,a855)))))),
% 179.86/179.67 inference(rename_variables,[],[10878])).
% 179.86/179.67 cnf(13619,plain,
% 179.86/179.67 (~P101(f323(f323(f325(a860),x136191),f323(f244(a860),f2(a860))))),
% 179.86/179.67 inference(rename_variables,[],[11742])).
% 179.86/179.67 cnf(13627,plain,
% 179.86/179.67 (E(f323(f254(x136271,x136271),f255(x136271,x136272)),x136272)),
% 179.86/179.67 inference(rename_variables,[],[3228])).
% 179.86/179.67 cnf(13644,plain,
% 179.86/179.67 (~P101(f323(f323(f188(f867(x136441,f867(x136442,a855))),x136443),x136444))),
% 179.86/179.67 inference(rename_variables,[],[4554])).
% 179.86/179.67 cnf(13670,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x136701,a855)),x136702),x136702))),
% 179.86/179.67 inference(rename_variables,[],[3571])).
% 179.86/179.67 cnf(13676,plain,
% 179.86/179.67 (~P101(f323(f323(f325(f866(x136761,x136761)),x136762),f255(x136761,f188(f867(x136761,a855)))))),
% 179.86/179.67 inference(rename_variables,[],[10878])).
% 179.86/179.67 cnf(13696,plain,
% 179.86/179.67 (~P101(f323(f323(f325(a860),x136961),f323(f244(a860),f2(a860))))),
% 179.86/179.67 inference(rename_variables,[],[11742])).
% 179.86/179.67 cnf(13706,plain,
% 179.86/179.67 (~P101(f323(f323(f325(f866(x137061,x137061)),x137062),f255(x137061,f188(f867(x137061,a855)))))),
% 179.86/179.67 inference(rename_variables,[],[10878])).
% 179.86/179.67 cnf(13732,plain,
% 179.86/179.67 (~P101(f323(f323(f237(a860),f323(a112,x137321)),x137321))),
% 179.86/179.67 inference(rename_variables,[],[4534])).
% 179.86/179.67 cnf(13760,plain,
% 179.86/179.67 (~E(f323(f323(f101(a860),f323(a112,x137601)),x137601),f323(a112,x137601))),
% 179.86/179.67 inference(rename_variables,[],[11484])).
% 179.86/179.67 cnf(13763,plain,
% 179.86/179.67 (~E(f323(f323(f144(x137631),x137632),x137633),x137633)),
% 179.86/179.67 inference(rename_variables,[],[4489])).
% 179.86/179.67 cnf(13778,plain,
% 179.86/179.67 (P101(f323(f323(f237(f867(x137781,a855)),f323(f166(x137781),f164(x137781,x137782,x137783))),f323(f166(x137781),x137783)))),
% 179.86/179.67 inference(rename_variables,[],[3979])).
% 179.86/179.67 cnf(13847,plain,
% 179.86/179.67 ($false),
% 179.86/179.67 inference(scs_inference,[],[3712,3300,4027,4063,3864,4553,4541,4526,4558,3916,3347,4517,3365,3725,3881,4537,13460,13516,3979,13452,13559,13778,3754,3375,4476,4489,13552,13567,13611,13763,4487,3254,3351,4057,3270,3271,13414,3730,3292,13417,3587,3571,13470,13670,3538,3540,13440,13546,3723,3228,13549,13627,3223,3212,4559,4562,4525,4534,13732,4543,4548,4554,13443,13581,13644,4551,4552,3481,11484,13487,13760,10249,13052,10303,12657,11805,12449,13223,10545,11851,12698,10533,12711,11007,10832,10695,13591,3639,12507,10863,11190,11149,11092,10228,3329,11090,12955,12958,13237,10640,13221,12152,12141,13257,12250,11742,13437,13527,13536,13619,13696,13297,10878,13404,13455,13614,13676,13706,12064,10630,13473,13524,12412,13245,11155,11159,10896,12319,11027,2917,3828,5279,5587,6322,10074,6051,7990,4747,6099,6273,7637,5108,5513,6066,6225,8490,7591,9016,6684,7285,4890,5983,6325,6399,8358,9831,6472,7764,9,5621,8950,5463,9463,6192,9542,6326,6755,8858,5044,8406,4705,5562,6217,6526,8472,4866,6211,5423,6069,6856,7308,9886,7259,7984,8736,8747,6095,8786,9024,5860,6966,8878,6074,5049,5295,8471,9520,8774,8463,6279,8592,6270,5777,8835,8073,6323,4891,5017,8188,5222,5791,5873,6420,7438,5516,5308,4647,7020,5338,4783,5531,6754,7861,8252,8529,8002,8253,8390,5097,9517,9159,5164,5908,7985,8125,9381,9875,6075,5802,5749,5155,6527,6604,9225,9660,9172,6097,6422,9535,7686,8492,5381,5903,6470,8724,8701,6319,7440,8749,5234,4953,5156,5201,6369,9705,8,8469,5231,5226,5304,5398,7302,8315,9519,5755,7330,5728,8536,5439,6240,8470,6137,6284,9872,4698,8684,6898,5667,8637,9343,8581,8582,5512,5668,6029,6247,6823,7687,4977,5190,6434,5042,5588,7652,8491,9424,5290,5738,9444,5827,9775,9873,7359,6440,6685,5543,8620,4681]),
% 179.86/179.67 ['proof']).
% 179.97/179.68 % SZS output end Proof
% 179.97/179.68 % Total time :164.460000s
%------------------------------------------------------------------------------